AN INVESTIGATION OF THE INSURANCE SECTOR’S CONTRIBUTION TO ECONOMIC GROWTH

AN INVESTIGATION OF THE INSURANCE SECTOR’S CONTRIBUTION

TO ECONOMIC GROWTH

By

Haizhi Tong

A DISSERTATION

Presented to the Faculty of

The Graduate College at the University of Nebraska

In Partial Fulfillment of Requirements

For the Degree of Doctor of Philosophy

Major: Economics

Under the Supervision of Professor Hendrik van den Berg

Lincoln, Nebraska

August, 2008

3315878

3315878 2008

AN INVESTIGATION OF THE INSURANCE SECTOR’S CONTRIBUTION

TO ECONOMIC GROWTH

Haizhi Tong, PhD.

University of Nebraska, 2008

Adviser: Hendrik van den Berg

The importance of the insurance industry in an economy has been well recognized.

Yet there is no extensive study on this area. In this dissertation, the economic role of the

Insurance sector has been studied through 1) setting up theoretical models to illustrate

how insurance growth may contribute to economic growth and 2) conducting a series of

empirical studies to find whether there is empirical evidence to support the models

developed. Although the insurance sector plays several important roles in economic

growth, I only focus on two roles here in the dissertation. First, property and liability

insurance serve as risk sharing institutions in an economy. Second, life insurance sector

can provide more long run capital into an economy.

I develop two theoretical models to illustrate the above two roles separately. In

the property and liability insurance model, an economy, which is composed of risk-averse

agents, without an insurance sector is set up first. It shows that individual utility

maximization can not achieve social optimization. After an insurance sector is introduced

into the economy, social optimization can be achieved through individual utility

maximization. In the life insurance model, contractual savings institutions, which include

life insurance companies, can shift short term savings to long term savings. At the end of

this part, a discussion is presented to link insurance sector with the technological progress.

Four countries data have been studied to see whether there is empirical evidence

for the above models developed. Three empirical methods are employed and compared:

OLS, simultaneous equations and fixed effect model. All four countries data show

evidence that property and liability insurance promote economic growth. However, two

countries data show that life insurance promote economic growth while the other two

countries data have just the opposite conclusion. Some possible reasons for this evidence

are presented.

Acknowledgements

I would like to express my sincere appreciation to several of the people who have

contributed to my graduate study and dissertation:

First, to my advisor, Dr. Hendrik van den Berg, for having the patience to let me

work at my own pace when the rest of my life tried to take over. Dr. van den Berg

supported me with great ideas, provided guidance and feedback on my progress, and

encouraged me to continue when I needed it most.

To my committee members, Dr. Craig MacPhee, Dr. Mary McGarvey, and Dr.

Lilyan Fulginiti, for their great teachings and advices through my PhD study years,

valuable suggestions and comments on this dissertation and always being ready in

helping me. They have been so patient and considerate to me during these years.

To my friends, Doug and Carol Tanner, for their friendly assistance on

proofreading the draft of this dissertation.

To my Parent, Zemin Tong and Chunyu Yang, for their love and encouragement

through my life.

To my son, Luke Zhang, for his love and understanding especially when I was too

busy to spend time with him while I was working on this dissertation.

Most of All, to my beloved husband, Lingfeng Zhang, for his ongoing love and

constant support. Words are not sufficient to express the thanks I owe to him.

I thank you all from the bottom of my heart. I could not have done this alone

without you.

TABLE OF CONTENTS

CHAPTERS.................................................................................................................................... I LIST OF TABLES ....................................................................................................................IVV CHAPTERS CHAPTER 1 INTRODUCTION...............................................................................................................1

I. RISK AND INSURANCE ..............................................................................................................................1

i) Risk and Insurable Risk......................................................................................................................1

ii) Insurance and How It Works.............................................................................................................3

iii) Cost of Insurance .............................................................................................................................5

II. THE IMPORTANCE AND THE FUNCTION OF INSURANCE IN AN ECONOMY ................................................7

III. TYPES OF INSURANCE............................................................................................................................9

IV. AIMS OF THIS DISSERTATION ..............................................................................................................11

CHAPTER 2 THEORETICAL FRAMEWORK ...................................................................................14

I. PROPERTY/CASUALTY/LIABILITY INSURANCE AND ECONOMIC GROWTH..............................................14

i) The Risk Sharing Role of Property/Casualty and Liability Insurance in an Economy.....................14

ii) Literature Review on the Economic Role of a Financial Sector......................................................15

iii) Theoretical Model Linking Insurance to Economic growth ...........................................................24

II. THE LONG TERM CAPITAL ACCUMULATION ROLE OF INSURANCE IN AN ECONOMY ............................33

i) Individual Savings Behaviors without Contractual Savings Institutions..........................................36

ii) Individual Savings Behaviors with Contractual Savings Institutions..............................................39

iii) Compositions of Savings with and without Contractual Savings Institutions ...............................42

III. DISCUSSION: TECHNOLOGICAL PROGRESS, INSURANCE AND ECONOMIC GROWTH .............................44

i) Factors that Affect Technological Progress .....................................................................................44

ii) Insurance and Technological Progress...........................................................................................49

II

CHAPTER 3 EMPIRICAL STUDY OF INSURANCE GROWTH AND ECONOMIC GROWTH53

I. LITERATURE REVIEW .............................................................................................................................53

II. DATA AND METHODOLOGY ..................................................................................................................56

i) Data..................................................................................................................................................56

ii) Methodology....................................................................................................................................58

III. DEFINITION OF VARIABLES ..................................................................................................................64

CHAPTER 4 EMPIRICAL RESULT FROM FOUR COUNTRIES ...................................................67

I. ANALYSIS OF THE US DATA ...................................................................................................................67

i) Unit Root Test Results ......................................................................................................................67

ii) OLS Regression..............................................................................................................................69

iii) Simultaneous Equations .................................................................................................................71

II. ANALYSIS OF KOREAN DATA................................................................................................................80

i) Unit Root Test...................................................................................................................................80

ii) Simple OLS Regression ...................................................................................................................81


III. ANALYSIS OF SWEDISH DATA .............................................................................................................90

i) Unit Root Test...................................................................................................................................90

ii) Simple OLS Regression ...................................................................................................................91


IV. ANALYSIS OF THE GERMAN DATA.......................................................................................................99

i) Unit Root Test Results ......................................................................................................................99

ii) Simple OLS Regression .................................................................................................................100

iii) Simultaneous Equations ...............................................................................................................103

V. FIXED EFFECT MODEL ........................................................................................................................109

VI. SUMMARY AND COMPARISON OF THE RESULTS ACROSS THE FOUR COUNTRIES ...............................114

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH .......118

I. SUMMARY OF THEORETICAL MODELS...................................................................................................119

III

II. SUMMARY OF EMPIRICAL FINDINGS ...................................................................................................121

III. LIMITATION OF THE RESEARCH..........................................................................................................123

IV. SUGGESTION FOR FUTURE RESEARCH ...............................................................................................125

APPENDIX A ............................................................................................................................................127

APPENDIX B.............................................................................................................................................129

APPENDIX C ............................................................................................................................................132

APPENDIX D ............................................................................................................................................133

BIBLIOGRAPHY .....................................................................................................................................134

IV

LIST OF TABLES TABLE 2.2.1 ASSUMED LIFE EXPECTANCY PROBABILITY DISTRIBUTION................................................38

TABLE 2.2.2 INFLOW AND OUTFLOW OF FUNDS (PENSION) ......................................................................40

TABLE 2.2.3 INFLOW AND OUTFLOW OF FUNDS (LIFE INSURANCE).........................................................43

TABLE 4.1.1 UNIT ROOT TEST RESULTS (US DATA) .................................................................................68

TABLE 4.1.2 ESTIMATION RESULTS FROM OLS (US DATA) - POPULATION GROWTH IS USED AS A

PROXY OF LABOR GROWTH ...............................................................................................................69

TABLE 4.1.3 ESTIMATION RESULTS FROM OLS (US DATA) - LABOR FORCE GROWTH IS USED AS A


TABLE 4.1.4 ESTIMATION RESULTS FROM SIMULTANEOUS EQUATIONS—EQUATION 1 (US DATA) –

POPULATION GROWTH IS USED AS A PROXY OF LABOR GROWTH...................................................72






LABOR FORTH GROWTH IS USED AS A PROXY OF LABOR GROWTH ................................................76





TABLE 4.2.1 UNIT ROOT TEST RESULTS (KOREAN DATA) .......................................................................80

TABLE 4.2.2 ESTIMATION RESULTS FROM OLS (KOREAN DATA) - POPULATION GROWTH IS USED AS A


TABLE 4.2.3 ESTIMATION RESULTS FROM OLS (KOREAN DATA) - LABOR FORCE GROWTH IS USED AS

A PROXY OF LABOR GROWTH ............................................................................................................83

V

TABLE 4.2.4 ESTIMATION RESULTS FROM SIMULTANEOUS EQUATIONS—EQUATION 1 (KOREAN DATA)

- LABOR FORCE GROWTH IS USED AS A PROXY OF LABOR GROWTH ..............................................84

TABLE 4.3.5 ESTIMATION RESULTS FROM SIMULTANEOUS EQUATIONS—EQUATION 2 (KOREAN DATA)

- LABOR FORCE GROWTH IS USED AS A PROXY OF LABOR GROWTH ..............................................85

TABLE 4.2.6 ESTIMATION RESULTS FROM THE SIMULTANEOUS EQUATIONS—EQUATION 3 (KOREAN

DATA) - LABOR FORCE GROWTH IS USED AS A PROXY OF LABOR GROWTH ..................................86


DATA) - POPULATION GROWTH IS USED AS A PROXY OF LABOR GROWTH .....................................88





TABLE 4.3.1 UNIT ROOT TEST RESULTS (SWEDISH DATA).......................................................................90

TABLE 4.3.2 ESTIMATION RESULTS FROM OLS (SWEDISH DATA) - POPULATION GROWTH IS USED AS A


TABLE 4.3.3 ESTIMATION RESULTS FROM OLS (SWEDISH DATA) - LABOR FORCE GROWTH IS USED AS

A PROXY OF LABOR GROWTH ............................................................................................................92

TABLE 4.3.4 ESTIMATION RESULTS FROM SME—EQUATION 1 (SWEDISH DATA) - LABOR FORCE

GROWTH IS USED AS A PROXY OF LABOR GROWTH .........................................................................93





TABLE 4.3.7 ESTIMATION RESULTS FROM SME—EQUATION 1(SWEDISH DATA) - POPULATION


TABLE 4.3.8 ESTIMATION RESULTS FROM SME—EQUATION 2 (SWEDISH DATA) - POPULATION


VI

TABLE 4.3.9 ESTIMATION RESULTS FROM SME—EQUATION 3 (SWEDISH DATA) - POPULATION


TABLE 4.4.1 UNIT ROOT TEST RESULTS (GERMAN DATA) .......................................................................99

TABLE 4.4.2 ESTIMATION RESULT FROM OLS (GERMAN DATA) – POPULATION GROWTH IS USED AS A

PROXY OF LABOR GROWTH .............................................................................................................101

TABLE 4.4.3 ESTIMATION RESULTS FROM OLS (GERMAN DATA) – LABOR FORTH GROWTH IS USED AS

A PROXY OF LABOR GROWTH ..........................................................................................................102

TABLE 4.4.4 ESTIMATION RESULTS FROM SME—EQUATION 1 (GERMAN DATA) - LABOR FORCE

GROWTH IS USED AS A PROXY OF LABOR GROWTH .......................................................................103


GROWTH IS USED AS THE PROXY OF LABOR GROWTH ...................................................................104



TABLE 4.4.7 ESTIMATION RESULTS FROM SME—EQUATION 1 (GERMAN DATA) - POPULATION






TABLE 4.5.1 ESTIMATION RESULTS FROM FEM (INCLUDES GERMAN DATA BEFORE THE MERGE) -

POPULATION GROWTH IS USED AS A PROXY OF LABOR GROWTH.................................................110

TABLE 4.5.2 ESTIMATION RESULTS FROM FEM (INCLUDES GERMAN DATA BEFORE THE MERGE) -

LABOR FORCE GROWTH IS USED AS THE PROXY OF LABOR GROWTH ..........................................110

TABLE 4.5.3 ESTIMATION RESULTS FROM FEM (INCLUDES ALL GERMAN DATA) - POPULATION


TABLE 4.5.4 ESTIMATION RESULTS FROM FEM (INCLUDES ALL GERMAN DATA) - LABOR FORCE


TABLE 4.6.1 EFFECT OF INSURANCE GROWTH ON ECONOMIC GROWTH ..............................................114

VII

TABLE 4.6.2 EFFECT OF ECONOMIC GROWTH ON INSURANCE GROWTH ..............................................115

TABLE AP-1 PROFITS FROM SHORT TERM PROJECTS ............................................................................130

TABLE AP-2 PROFITS FROM LONG TERM PROJECTS .............................................................................130

1

Chapter 1 Introduction

I. Risk and Insurance

One major feature in the modern society is increasing risks in economic life.

When we talk about risk in the economic life here, we are referring to the risk which

may lead to the occurrence of loss. Although classic economics acknowledges the

difference of risk bearing across different individuals, there is lack of modeling on

different economic results due to the existence of risks. The role of insurance sector

in an economy is not studied broadly by economists. In this dissertation, I am trying

to build some models to illustrate how insurance can affect an individual’s economic

behavior and therefore affect the whole economy. Before we do that, we will first

start with the types of risks and the function of insurance in reducing some types of

risks.

i) Risk and Insurable Risk

1. Objective Risk vs. Subjective Risk

Objective risk is measurable risk which can be derived from facts and data.

On the other hand, subjective risk is based on a person’s perspective on a specific

uncertain outcome. Because subjective risk is related to a person’s opinion, it can not

be measured. An example of the objective risk is the variation of car accidents in a

particular year in a city. Suppose we know the expected number of car accidents in

the long run. But from year to year, the actual number of car accidents can be quite

different. The variation from the expected number of car accidents is an example of

objective risk.

2

On the other hand, we can think about people with similar situations such as

same age, same gender and same marriage status driving a same car in the same city

may perceive differently on their involvement of a car accident. This is an example of

subjective risk.

Only objective risk is insurable. However, not all objective risk is insurable.

To be insurable, the risk should also be a pure risk.

2. Pure Risk vs. Speculative Risk

There are only two outcomes for pure risk—loss or no loss. An example of

pure risk is that a person who drives a car facing two possible results, a car accident

which will result in loss and no car accident which incurs no loss.

Speculative risk is associated with three outcomes—loss, no loss and gain. For

example, a person holding some stock is facing three outcomes—an increase of the

price of the stock, a decrease of the price of the stock and no change in the price of

the stock after a period of time. Although speculative risk is greatly dealt with in risk

management, it is not in the scope of insurance. Insurable risk is pure risk. This

means insurance protects against the risk of loss but not as a tool to gain profit.

3. Financial Risk vs. Non Financial Risk

Financial risk is measurable in money. The physical loss from the fire of a

particular residence can be measured by the amount of dollars.

Non financial risk is not compensated by money. For example, loss of

precious photographs from a fire is more related with the fond memory of the owner,

which we can not measure by money.

Insurance deals with financial risk rather than non financial risk.

3

4. Diversifiable Risk vs. Non-Diversifiable Risk

Diversifiable risk is the risk that can be “spread out” in a large group. It is also

called unsystematic risk or particular risk. The risk exposures in the group are not

correlated with each other theoretically. When more risk exposures are included into

the group, there is less variation from the expected number of loss occurrence. Some

examples are car accidents, fire, disability, premature death etc.

Non diversifiable risk is also called systematic risk or fundamental risk. It is

the risk that will affect the large number of units in the group at the same time.

Examples of non-diversifiable risk are earthquakes, hurricanes, economic inflation,

and unemployment.

Insurance commonly deals with diversifiable risk whereas government usually

deals with non-diversifiable risk.

From what we summarized above, we can see that usually the character of

insurable risk is objective, pure, financial and diversifiable risk.

ii) Insurance and How It Works

According to the American Risk and Insurance Association, “Insurance is the

pooling of fortuitous losses by transfer of such risks to insurers, who agree to

indemnify an insured for such losses, to provide other pecuniary benefits on their

occurrence, or to render services connected with the risk.” 1

For insurable risk, insurance works by pooling of losses based on the law of

large numbers.

1 Bulletin of the commission on Insurance Terminology of the American Risk and Insurance Association, October 1965

4

Pooling is the spreading of losses incurred by a few over the entire group, so

that in the process, average loss is substituted for actual loss2. By pooling a large

number of similar exposure units with same perils group together so that the entire

group can share the risk with relative accurate predictions.

The accurate prediction is based on the law of large numbers. The law of large

numbers states that as the number of exposure units increases, the more closely the

actual loss will approach the expected loss experience3.

We can use an example to put all those concepts together to see how insurance

works. Suppose for a particular city, each year there is 1000 houses that will catch on

fire out of, say, 1 million houses. Also, for simplicity, the fire will incur the whole

loss of the house and each house has the same value like $100,000. Therefore, each

individual will face either no loss when there is no fire or a total loss of $100,000

when there is a fire. The probability of fire is 0.001. The expected loss for that

individual is $100. However, this number is not a number this individual will face if

there is no insurance. The individual either has a huge loss with very small

probability or no loss with a very big probability.

When we pool all those individuals who own a house in the city, we get a very

large group. We can see that if there are exactly 1000 houses burnt down in a

particular year, the average loss of each individual in the group is $100, which is the

same as the expected loss faced by an individual. In real life, the real number of

houses burnt down will be different from 1000 very obviously. Yet we can expect

that the real number of houses burnt down from year to year is close to 1000. And the 2 Principles of Risk Management and Insurance, George E. Rejda, 2000, pg. 20. 3 Principles of Risk Management and Insurance, George E. Rejda, 2000, pg. 4.

5

average loss of each individual will be pretty close to $100, which is the expected

value that each individual will face. For the group, the average loss for each

individual is very close to the expected loss for each individual due to the law of large

numbers. Also, what we can see here is that by pooling the exposure units together,

the loss is very predictable.

The existence of insurance makes individual exchange their risk of loss for a

certain amount of money which is called premium. By doing so, individuals will

change their risky economic situation to a safe economic situation. Therefore, an

economy with or without an insurance sector can affect the economic behavior of the

agents in the economy.

iii) Cost of Insurance

Of course, in the real world situation, insurance companies also need to face

the dishonesty and carelessness of individuals. Insurance companies need to deal with

moral hazard, morale hazard, and adverse selection. Let us look at the meaning of

each of the above term.

Moral hazard is defined as dishonesty or character defects in an individual that

increase the frequency or severity of loss. Morale hazard is defined as carelessness or

indifference to a loss because of the existence of insurance4.

The idea of adverse selection is that the insured knows better about her/his

risk tendency than the insurance company. By not disclosing the information

voluntarily, they may obtain a rate which is lower than their expected rate of loss.

4 Principles of Risk Management and Insurance, George E. Rejda, 2000, pg. 6.

6

Insurance companies can add deductible or coinsurance factor to reduce moral

hazard or morale hazard. It can also design the underwriting policy carefully to

reduce the chance for adverse selection.

In addition to the above factors, there is administration cost of insurance

companies such as the cost of buildings and wages and salaries paid to the employees

of insurance companies.

From the above discussion, we can see that what insurance charges for an

individual should be higher than the expected loss of each individual in the group.

However, we will put those factors aside when we analyze how the existence of the

insurance sector can affect individual economic decision.

7

II. The Importance and the Function of Insurance in an Economy

The importance of the insurance industry in an economy has been well recognized.

In 1964 the United Nations Conference on Trade and Development (UNCTAD) has

stated that “a sound national insurance and reinsurance market is an essential

characteristic of economic growth.” (page 55 )

The following figures also show the important role of the insurance sector in an

economy. According to the research paper of Hess (2002), 7.8% of the world GDP was

spent on insurance products in the year 2000. However, the development of the insurance

industry is different across countries. Insurance seems to have a more important role in

developed countries than in developing countries. This is not surprising since the

insurance sector is part of the financial institutions, which has been viewed to be related

with economic development. According to Hess (2002), the percent GDP spent on

insurance products is between 8.6% and 10.9% among developed countries but is only

between 2.1% to 3.8% among developing countries. “Empirically, there is clear evidence

that differences are dependent on the stage of national economic development.” (Hess,

2002, p. 1) The statistics further supported that economic development is linked with

insurance development.

By reviewing some literatures (Arrow 1965, Albouy and Blagoutine 2001, Hess

2002), we have a brief summarization of the economic role of an insurance sector.

First, the insurance industry is one of the risk sharing institutions. The insurance

industry provides protection to individuals or firms against a large amount of loss with a

small probability (Arrow, 1965). In doing so, the insurance sector can provide more

8

financial security to economic agents. This makes individuals or firms willing to engage

in risky activities, which are impossible when there isn’t such a system. For example,

individuals may reconsider their decisions of buying a car if they cannot buy car

insurance. People will be reluctant to own a house if there is no property and liability

insurance to protect the loss of their house due to fire, flooding etc. Also, we will expect

firms will make different investment decisions whether the risks associated with a new

project are insurable or non insurable. Therefore the production decisions may be altered

when there is such a risk sharing institution.

Second, insurance provides long-term capital in the capital market. Savings is

very important to economic growth. Both total savings and the structure of savings matter.

When there are more long-term savings versus short-term savings, an economy can

finance more long-term projects. Insurance and pension funds provide long term savings

to the capital market, which broadening and deepening the functions of the capital market.

Third, the insurance industry makes risk management more efficient. The

insurance industry is a sector devoted in risk management. They hire experts in risk

management to price the risks so that the market will give signal to the individuals on

which direction to go: “Actuaries calculating the price for earthquake or flood risks give

important signals as to where to build house or factories and where not.” (Hess 2002 p.2)

9

III. Types of Insurance

We will divide insurance into four groups here according to its dealing with four

different groups of loss exposures. The definition is summarized from the book of

Insurance Perspectives by Gibbons, Rejda and Elliott, 1992.

1. Property/Casualty Insurance

Property/casualty insurance protects the insured against accidental losses due to

loss or damage of the property of the insured. One example is that home owner’s

insurance will cover the owner’s damage to his/her property due to a fire. His/her

property here includes all his/her belongs in the house and the house itself.

2. Liability Insurance

Liability insurance protects the insured from any third party claims against the

insured when the insured is proven to be legally liable for injury or damage to the

claimants. The insurer will pay to the claimants directly the damages the insured is liable

to the claimants. One example is the auto liability insurance. It covers the loss and

injuries of other parties due to an insured driver’s allegedly negligent driving.

We will combine property and liability insurance into one group and study its risk

sharing role in an economy in this dissertation.

Property and liability can also be divided into personal line insurance and

commercial line insurance. Personal line insurance covers individuals and families

against property and liability loss. Commercial line insurance covers businesses and other

organizations against property and liability loss. In this dissertation, we do not separate

them into groups.

10

3. Health Insurance (Accident and Sickness Insurance)

Health insurance protects individuals and families against financial losses due to

accidents and sickness. Both medical expense insurance and disability income insurance

belong to the health insurance group. Medical expense insurance pays the cost of medical

care of the insured due to accidents and sickness. Disability income insurance covers the

income loss when the insured is not able to work due to accidents and sickness.

In this dissertation, we will not study the role of health insurance in an economy.

Carmichael, Benoit and Dissou (2000) have developed a model to illustrate the role of

health insurance in an economy.

4. Life insurance

Life insurance policy specifies that upon the death of the insured, the insurance

company will pay the beneficiary a specified amount named in the policy. It can provide

the named beneficiary from the income loss due to the premature death of the insured. It

can be divided into term life insurance and whole life insurance. The former one provides

a temporary protection while the latter one provides a life long protection.

In the dissertation, we will focus on the capital accumulation role of life insurance

companies in an economy.

11

IV. Aims of This Dissertation

Although the contribution of the insurance development to an economy’s

development has been well recognized, the research in this area is not extensive (Albouy

and Blagoutine, 2001). Several empirical studies have found there is link between insurance

growth and income growth in an economy. However, there is lack of theoretical models

which explain why the insurance industry may contribute to economic growth. To my

best knowledge, there is only one paper explaining why health insurance may contribute

to economic growth by setting up a theoretical model. Another research which links life

insurance with economic growth has been done by Soo (1996), an econ PhD student in

his dissertation. I am interested in developing theoretical framework that links economic

development and insurance development, followed by empirical examination on the role

of the insurance sector in an economy.

The dissertation is composed of two sections. Section I gives out a theoretical

framework which explains why the insurance industry may contribute to economic

growth. In this part we will just focus on the first two economic roles of the insurance

sector in an economy—risk sharing and long term capital accumulation. Two theoretical

models will be presented in this chapter. These two models are dealing with these two

roles separately. The first model focuses on the role of property and liability insurance. It

illustrates the risk sharing role of property and liability insurance. We assume economic

agents do not live in risk free environment. But to simplify the situation, we only assume

two possible outcomes. Economic agents face the possibility of huge loss when they

choose a higher productive method. On the other hand, they face no loss when they

12

choose a safer yet lower productive method. We get the conclusion that agents will

choose the lower productive method over the higher productive method without an

insurance sector. After the introduction of an insurance sector, we can prove that agents

will choose the higher productive method. This is due to the risk averse character (which

is shown in the assumed individual function) of economic agents. This gives an

illustration that under uncertainty, individual maximization choice is not the optimal

economic choice for the whole economy. Presence of the insurance sector can improve

the social economic choice.

The second model focuses on the role of life insurance sector. It shows how the

existence of life insurance companies can provide more long term capital to an economy.

Pension funds and life insurance companies are called contractual savings institutions.

The emergence of contractual savings institutions may affect both the total amount of

savings and the saving pattern of individuals. Here the individuals’ savings patterns

change refers to the structure change between liquid savings (used for short term

investment) and illiquid savings (used for long term investment). Therefore, the

emergence of contractual savings institutions may affect economic growth through

providing more long term capital.

The arguments go as follows. Compared with banks, contractual savings

institutions have special knowledge on population life expanse distribution. This makes

the contractual savings institutions able to offer individuals savings plans. These savings

plans can increase individuals’ utility level. Put it another way, there is a demand for

contractual savings institutions. This leads to the emergence of contractual savings

13

institutions. Compared with banks, contractual savings institutions can offer more long

run funds.

At the end of this chapter, a discussion will be presented to show how the

insurance sector can be linked to technological progress, which sustains long run

economic growth.

Following the theoretical illustration is an empirical study of the relationship

between insurance development and economic growth. Several available countries’ data

are examined to see the relationship between economic growth and insurance

development. The data from the following four countries: US, South Korea, Sweden, and

Germany. When I first collected the data, only data from these four countries were

available through our library system.

In this chapter, the property and liability and life insurance data are collected

separately for these four countries. The growth of property and liability insurance

premium is used to measure the development of PCL (property/casualty and liability)

sector for each country. The growth of life insurance in force is used to measure the

development of life insurance sector for each country. We start with a growth model

which includes life insurance and PCL insurance as two factors which contribute to

economic growth. Due to the fact that economic growth may also affect insurance growth,

we used a three-equation simultaneous equation to run the data again and compared with

the result from the simple OLS regression. At the end, we pool all countries’ data

together and run a fixed effect model to compare with the above result. The fixed effect

model allows for different constant terms for each country.

14

Chapter 2 Theoretical Framework

This section will present two models to illustrate the two important functions of

insurance institutions: the risk sharing function and the capital accumulation function.

I. Property/Casualty/Liability Insurance and Economic Growth

i) The Risk Sharing Role of Property/Casualty and Liability Insurance in an Economy

One important contribution of insurance institutions to economic development is

that such institutions can diversify the risks firms exposed to in an economy. Individual

firms make production plans to maximize their profits. If they face uncertainty in their

production, they may make production plans to maximize their expected profits. In

general economics theory, individuals are risk averse. Therefore, individuals may not

choose the social optimal production level when there is risk present in the production

process. This will lead to underproduction problem. The emerging of insurance

institutions can help firms to diversify the risks they face and therefore increase

production level which is social maximum. Put it another way, the existence of the risk

sharing institutions makes the firms undertake some investment they would not engage in

if there were no such risk sharing institutions. The undertaking of such risk activities is

beneficial to the whole society.

As stated by Arrow (1965), “a man’s capacity for running a business will need not

be accompanies by a desire or ability for bearing the accompanying risks, and a series of

institutions for shifting risks has evolved” (p. 221).

15

“At any moment society is faced with a set of possible new projects which are on

the average profitable though one cannot know for sure which particular projects will

succeed and which will fail. If risks can not be shifted, then very possibly none of the

projects will be undertaken; if they can be, then each individual investor, by

diversification, can be fairly sure of a positive outcome, and society will be better off by

the increase production.” (p. 223)

When there is uncertainty and individuals are risk averse, the social optimal

choice is different from the individual optimal choice. This results in market inefficiency.

The introduction of risk sharing institutions can improve market efficiency by allowing

risk-averse individuals to make socially optimal production choices.

In the following part, we will present a model which illustrates the above idea.

Before we do that we will present a literature review of theoretical models that illustrate

how financial institutions contribute to economic growth. We are borrowing some ideas

from these models to construct our model. I found few specific models which address

how insurance sector can contribute to economic growth. At the end of the review, two

research studies that looked at the relationship between insurance and economic growth is

presented at the last.

ii) Literature Review on the Economic Role of a Financial Sector

A lot of works have been done to examine the contribution of financial

intermediations to economic growth. Theoretical models have been set up to explain the

role of financial markets. Main streams of works can be divided into the following groups.

First, financial institutions can reduce the demand for liquid savings of economic agents

and increase investment on illiquid capital which bears higher rate of return. This will

16

increase economic growth. Second, financial institutions can ease transaction of

ownership and therefore influence choice of technologies. Third, financial institutions are

innovation supportive.

The main works can be summarized as follows

1. Financial intermediaries are growth promoting through the capital accumulation

channel.

Benvicenga and Smith (1991) set up an endogenous growth model to explain the

link between economic growth and the development of financial intermediaries. The

model is a three period overlapping generation model. Economic agents can choose to

invest in production of consumption good (liquid assets) or capital good (illiquid assets).

Production of consumption good bears lower rate of return than production of capital

good. However, the production of the latter requires two periods and the production of

the former only requires one period. So investment in liquid assets has no loss in return if

it is liquidated at period 2. On the other hand, investment in illiquid assets will result a

loss if the assets are prematurely removed. The loss makes return on investment on

illiquid assets lower than return on investment on liquid assets. Economic agents save all

their first period income for second and/or third period consumption. The model is

constructed such that there is a liquidity demand (Diamond and Dybvig (1983) preference

structure), i.e. some agents of the whole population at the end of period one (beginning of

period 2) will find they value period 3’s consumption as nothing (there is no utility

associated with this period consumption). The other agents will value the consumption of

period 2’s consumption and period 3’s consumption the same degree. To maximize their

utility, agents who do not value period 3’s consumption wish they had invested all in

17

liquid assets because they want to consume all of them at period 2. Agents who do value

period 3’s consumption wish they had put all investment in illiquid assets because they

bear higher rate of return. But they do not know this at the beginning of period 1, when

they need to make decision on how much to invest on liquid assets and how much on

illiquid assets. At the beginning of period 1, agents only know the possibility of whether

their consumption in period 3 will bring them utility. So what they do is to maximize

their expected utility. They choose to invest part of their period 1 income in liquid assets

and part on illiquid assets. At the end of period 1, their preference type is revealed.

Without financial intermediations, some agents find they do not value period 3’s

consumption. They will have to prematurely liquidate investment in capital good, which

induce a loss of return of their investment and a loss in capital accumulation of the whole

society. With financial intermediations, investment in capital goods will not be

prematurely liquidated. Agents who do not value period 3’s consumption will trade

through the financial intermediaries with the agents who do value period 3’s consumption.

The capital stock of the whole society remains. The production function is constructed in

such a way that there is an externality associated with capital accumulation. The

production function of an individual firm not only depends on individual input in capital

and labor, but it also depends on the total amount of capital accumulated in the society.

Therefore, financial intermediaries are economic growth promoting by preserving the

capital stock of an economy.

Levine (1991) constructs an endogenous growth model to illustrate the function of

stock market in risk allocation. In his model, physical capital accumulation can positively

contribute to the creation of human capital (human capital is a function of total physical

18

capital stock in a firm). And human capital is a production function shifting parameter,

which means the bigger the human capital stock, the higher the output. This links capital

accumulation with economic growth. In his model, there are two risks, one is liquidity

risk, and the other is the productivity risk. The liquidity risk is modeled similarly as in

Benvicenga and Smith (1991), which also uses the preference structure created by

Diamond and Dybvig (1983). The productivity risk is modeled by introducing a

production shock into the production function. Due to the liquidity risk and productivity

risk, risk-averse investors will not invest enough in the production, which reduce the

accumulation of physical capital. Therefore, it also reduces human capital stock and

affects economic growth. Without financial intermediations, liquidity demand will result

in premature removal of physical capital. This will lower capital accumulation. The

emerging of the stock market helps investors to trade their shares when the liquidity

demand is revealed. This will increase the accumulation of physical capital. The other

function of stock markets is that it allows investors to diversify away idiosyncratic

productivity shocks by holding shares from different firms. This will increase the level of

capital investment in firms. Therefore, stock markets are growth promoting.

2. Financial intermediaries are economic growth promoting through the technology

choice channel.

Saint-Paul (1992) developed a model to illustrate the substitution between

financial diversification and technological diversification. The main idea of his paper is

that some technologies are more ‘flexible’ than others. The greater is the division of labor,

the less flexible is the technology. Less flexible technologies are more productive due to

the greater division of labor. However, there is higher risk associated with less flexible

19

technologies. When there is demand shock, it is hard for the less flexible technologies to

change their production. Agents are risk averse. If there are no other institutions to

diversify the risk, more flexible technology will be adopted by an economy. This means

an economy will choose to use technologies with less productivity. The emergence of

financial markets allows economic agents hedge against such risks by holding a

diversified portfolio. So in an economy with well developed financial markets, less

flexible (higher productivity) technologies will be chosen. On the other hand, in an

economy with poor financial markets, more flexible (lower productivity) technologies

will be chosen to diversify the risk. This will hinder productivity growth. In his model, a

technology flexibility parameter is introduced into the production functions of two goods.

Both goods are produced in two villages. However, the technologies in these two villages

are just opposite of each other, i.e. one unit capital can produce the same amount of good

1 in village 1 and good 2 in village 2. The model is constructed so that only one good is

demanded at the second period. At the beginning of the first period, the demand

information is not known. So both goods will be produced. Entrepreneurs chose

technologies to produce two goods and sell shares to the consumer. They will maximize

the utility of shareholders. If there is no financial market, agents in each village can only

buy shares of entrepreneurs in their own village. The result of the model is that more

flexible technologies will be chosen. And the more risk averse are the economic agents,

the more diversified (flexible) technologies will be employed. The conclusion is that

without financial markets, some degree of technology flexibility is required. Then

financial markets are implicitly introduced into the model, i.e. economic agents are

allowed to buy shares of entrepreneurs in both villages. Still entrepreneurs maximize the

20

expected utility of shareholders. The result is that less flexible technologies (with higher

productivity) will be chosen this time. The author also emphasizes the interaction effect

between technologies diversification and financial diversification. Once more flexible

technologies are chosen, there is not much motive for the development of an advanced

financial system. The economy may be trapped in a lower equilibrium. His model

therefore explains why developed financial markets are associated with developed real

sector. On the other hand, we can also observe that underdeveloped financial markets are

associated with underdeveloped real sector.

Bencivenga and Smith (1995) set up a model to explain the connections between

financial system and economic growth by emphasizing that choice of technologies is

influenced by transaction costs of ownership. The main idea of their model is that the

transaction costs of financial markets in an economy will determine the technologies

adopted for this economy. High productivity technologies may require the investment on

highly illiquid capital. Without an efficient financial system to facilitate transaction of

ownerships, high productivity technologies can not be implemented even though they are

available. Their model is a two period overlapping generation’s endogenous growth

model with production. Their model allows the existence of different production

technologies with different gestation period. The higher the productivity is the

technology; the longer gestation period is this technology. Efficiency of financial markets

is measured by transaction costs. Financial markets influence the economic growth rate

through the following factors: technology chosen, transaction costs in financial markets,

savings rate and the composition of savings. With more efficient financial markets, long

gestation period technologies are more likely chosen because these technologies are more

21

“transaction intensive”. This will make economy favor those high productivity

technologies when financial market is more efficient. This is growth promoting. At the

same time, lower transaction cost will enhance the net productivity of all investments,

which is also growth promoting. In their model, this will also increase savings rate and

therefore increase growth rate. But the effect of the last factor, the composition of savings,

may not favor economic growth when financial markets become more efficient. The

reason is that lower transaction costs make capital resale markets more efficient too.

Therefore the current technologies may not be replaced by more productive, long

gestation period technologies. So financial market efficiency enhance may reduce growth

rate if the effect of the fourth factor is large enough to counter the first three factors.

3. Financial intermediaries are economic growth promoting through supporting

innovations.

King and Levine (1993) construct an endogenous growth model to illustrate how

financial intermediaries facilitate innovations in real sector and therefore promote

economic growth. In their model, they emphasized four functions of financial markets:

evaluation of investment projects, pooling of funds for desired projects, risk

diversification, and valuation of expected rewards to innovative projects. In their model,

entrepreneurship must be identified by outsider other than individuals themselves. Also,

the identification (or rating) process is costly. This requires the existence of financial

markets to do the job. The success of identified entrepreneurs to manage a project

depends on chance. Risk is present in the production process. Risk diversification make

implementing projects possible. In addition, an entrepreneur needs investment to initiate

a project, whether he is successful or not. The investment is beyond his personal wealth

22

ability. This requires the fund pooling function of financial intermediaries. Projects with

successful innovation will enjoy profit in the industry, with a mark up over its rival’s

costs. The cost of selection of entrepreneurs and profit from successful innovations will

decide the equilibrium in the financial intermediation. The equilibrium in the production

side sets up the relationship between growth rate and real rate of return, which is

ambiguous. Combined with the preference side growth rate and real rate of return

relationship, which is unambiguous positive relationship, a general equilibrium is decided.

They illustrate that increasing returns in financial efficiency is like a reduction in tax,

which is growth promoting.

4. Theoretical model that links insurance and economic growth.

Carmichael and Dissou (2000) construct a model to state the growth promoting

role of health insurance. Their model shows that the existence of health insurance allows

individuals to insure against health risk. In their model, individuals face the possibility of

disease on the second period of life, which will reduce their utility level if they are ill.

They can spend money for cures to increase their utility on second period or choose to

stay sick. Without health insurance, individuals will save an amount of money for

treatment of disease for the possibility of catching the disease. This amount of money is

liquid assets. This means part of their income can not be used to invest in illiquid assets,

which carry a higher rate of return. In the model, the agents either choose to keep their

liquid asset equal to treatment expense or keep no liquid asset. The treatment expense is

assumed to be a known and fixed amount of money. Probability of sickness, disutility of

non treatment of the disease, interest rate and health care expense are four factors that

will influence the decision on liquid investment for treatment of future possible illness.

23

Higher probability of sickness and disutility of non treatment of disease will result in

investment in liquid assets. Also, lower interest rate and lower treatment expense will

lead to investment in liquid assets. In such a case (a liquid asset will be set aside for

health care purpose), if there is market insurance, individuals will pay an actuarially fair

insurance and not invest in liquid assets. The result is that the total savings of the society

will decrease with the introduction of a health insurance sector. But the savings

components are different when there is market insurance. Total investment on illiquid

investment increases now, which yields higher rate of return. Therefore a health

insurance sector is economic growth promoting by allocating more resource on

productive sector, although total savings decrease.

Soo (1996,) in his dissertation, researched the economic role of life insurance

companies. He first developed a model to show that borrowing individuals and lending

individuals use insurance to maximize life time utility. He examined the effect of

insurance tax on aggregate consumption and savings. He followed his theoretical model

with empirical study to show that there is support that life insurance can promote

economic growth.

Here we can see the basic idea running through most of the above models is that

economic agents face several choices. Individuals will choose the one that maximize their

own utility. Due to the fact that information is unknown when they make their choices,

what is individually optimal is not socially optimal. With the introduction of financial

intermediaries, individuals can make a better choice which will maximize their own

utility and also achieve social optimal. This is the idea that also underlines our model.

24

iii) Theoretical Model Linking Insurance to Economic growth 1. Assumptions:

There are two technologies: the safe one and the risky one. The production

function for the safe technology is specified as follows.

αα KLy *1−=

The production function for the risky technology is specified as follows.

αα KALy *1−= with probability of π

0=y with probability of π−1

Where 10 pp π

Also, the risky technology will have a higher expected output level than the safe

technology for the same amount of input in labor and capital. To meet this requirement,

we can specify that 1fπA . This infers that 1fA too. Individual producer will be

exposed to risk so that their production may either result in a high output or a zero output.

But if all agents in an economy employ the risky technology, there are a proportion of

π producers will not incur loss and there are a proportion of π−1 producers will incur

loss because we specify π as a number known. So for the whole economy there is no risk.

This means that if all agents in the economy employ the risky technology, the total

average output level will be ααπ KLAyr *1−= . If all the agents in the economy employ

the safe technology, the total average output level will be αα KLys *1−= , which is lower

than the expected output level when all the society employs the risky technology. It is

obvious that for the whole economy’s sake, a risky technology with higher expected

output level should be chosen. However, because individuals are exposed to risk of

losing all their investment and incurring a loss, they may not choose to invest all in risky

25

technology when there is no insurance sector in the economic system. This leads to the

under production for the whole economy.

We need some further assumptions to develop the above result.

First, we assume that the safe technology defines the competitive wage rate. So

the wage rate is equal to the marginal product of labor by the safe technology, which

is ααα KLw *)1( −−= . So the return on L units of labor input to the production process is

ααα KLwL *)1( 1−−= . The return of capital depends on the technology an individual

firm chooses. If the firm chooses to invest in safe technology, then the return on capital

is αααααααα ααα KLKLKLKLyr ss ***)1(**)1( 1111 −−−− =−−=−−= . If the firm

chooses to invest in risky technology, then the return on capital is

)(Pr)1(Pr

)1()1()1()1()1(0)1(

1111

111

ππ

αααααα

αααααααα

αααααα

obob

KLAKLKALKLyKLKLKLy

rr

rr

−

⎩⎨⎧

+−=−−=−−=−−=−−=−−=

−−−−

−−−

The expected return on capital invested in risky technology is

αααααααα απαπα KLAKLKLAKLyr rr *)1(*)1(**)1( 111 −−−− +−=−−=−−= .

Although the expected return on risky technology is higher than the return on safe

technology, individual firms may choose to invest in safe technology due to the

possibility of capital loss.

In the following, we will show that due to individuals risk averse, safe technology

may be chosen, although it is good for the whole economy to choose the risky technology

to engage in production.

2. The Model

We specify an overlapping two generation model. Individuals are endowed with

the same amount of labor at the first period of time. We assume labor is supplied

26

inelastically, which means all individuals will work in the first period and earn a market

competitive wage, which is decided by the marginal product from the safe technology.

Then they will consume part of their wage and invest the other part in either safe

technology or in risky technology. Depending on the technology they choose, they will

get a different return on their investment. Individuals will maximize their life time utility.

We assume the individual utility function takes the following format, with a

constant relative risk aversion.

γ

γ−+−=

)~( 21 CCU , where 1−>γ .

2~C is a random variable which is contingent on the realized return on the

investment on the second period. Due to the special format of the individual utility

function, if safe technology will yield a positive return (we will specify this later),

individuals will not value period one’s consumption. They will save all to invest either in

safe technology or risky technology. Therefore, capital accumulation is not a factor

affecting the path of economic growth. Individuals’ desirability for risky technology is

the factor that will affect the path of economic growth.

This specification assumes constant risk aversion. The specification of the utility

function follows Benvicenga and Smith (1991) and Levine (1991). But there is some

difference with their models. They have a three period overlapping generation model. In

their model first period of consumption does not go into the utility function. What we

take from their model is that they suppress the time effect on different period of

consumption. To put it another way, there is no internal and external discount rate. So

there is no coefficient before 2~C . This will make derivation of result much easier.

27

Define q1 as the proportion of wage an individual will consume in the first period

and q2 as the proportion of wage an individual invest in safe technology. The proportion

invested to the risky technology is 1- q1 - q2. Here we need to assume that 10 1 << q ,

10 2 << q , and 10 21 <+< qq . Therefore the consumption contingent on the production

results will be

)*(*)1(*)1(*)1(])1([*~

1121

121

1122

αα

αααααα

αα

αα

KLqqqKLqqKLKLqC

−

−−−

−++−=

−−−−−−= with probability

of π−1 , when investment in risky technology incurs a loss;

And

)*(*)1(

)*)1(**(*)1(])1([*~

121121

1121

1122

αα

αααααααα

αα

αα

KLAqAqqqqA

KLKLAqqKLKLqC−

−−−−

−−−++−+=

−−−−+−−=with

probability of π , when investment in risky technology is successful.

The first item on the above equations shows the return on safe technology and the

second item shows the return on risky technology. When individual firms incur loss, the

output is zero. But firms still need to pay wage to labors employed. This is why the

second item in the first equation is negative.

An individual will maximize his/her expected utility, which is to

maximize ])~([ 221

γ

γ−++−=

rs CCCUExp by choosing 1q and 2q .

Here 1C is the first period consumption, sC2 is the consumption from return of

investment in safe technology and rC2~ is the consumption from return of investment in

risky technology, which can be positive or negative contingent on the probability of

production output.

28

We assume that each individual in the initial old generation is endowed with K

units of capital. At the beginning there is only safe technology. The old generation will

invest only in safe technology, which determines how much they could consume in that

period. They will employ the young generation each of whom we assume will be

endowed with L unit of labor at the beginning of the first period. Each individual in the

young generation will supply all L units of labor. Production is achieved through

combining the capital of the old generation with the labor of the young generation.

We further assume that KKL >− ααα 1 to guarantee a positive return of investment

on the safe technology. Individuals in the young generation will get a wage rate equal to

the marginal product of labor, which is ααα KLw *)1( −−= . Here we assume α is a

positive number and is smaller than 1.

Individuals of the young generation will choose to allocate their wage among

consumption during the first period, save for investment in the safe technology or save

for investment in the risky technology. At the second period, each individual only invest

and does not supply labor to earn wage anymore. Their consumptions at the second

period totally rely on their return on investment on different technologies they choose. So

the total amount of capital invested is equal to wqwqwCw *)1( 111 −=−=− , which will

be invested in safe or risky technology. Here w is a function of L and K, which are

constant numbers. We will keep w in the following derivations. Whether we express w

in terms of L or K or not will not influence our derivation result. Depending on the

allocation of the capital invested in safe or risky technology, an individual will get

different return on their capital investment. wqqwqwq *)1(**)1( 2121 −−+=− . The left

hand side is the total capital investment. The first item of the right hand side is the

29

investment in the safe technology and the second item is the investment in the risky

technology. So the maximization problem becomes maximize the expected utility of an

individual by choosing 1q , which decides the proportion of the wage consumed in the first

period, 2q , which decides the proportion of wage invested in the safe and risky

technologies. The proportion of the wage invested in risky technology, which is equal

to )1( 21 qq −− , is known after 1q and 2q are chosen.

In the following part, we will prove that 2q is not equal to zero if an expected

utility maximization individual has no way to hedge the production risk. This means that

individuals will choose at least part of their wealth to invest in safe but low return

technology when there is no insurance sector5.

Individuals will choose 1q and 2q to

Max γ

α γαα

−++ −− )~]**[*( 2

121

rCwLqwqE

Here πα

πααα

αααα

−=−−−−=−−−−

=−

−−

1]**)1(0)[1(]**)1(**)[1(

{~1

21

1)1(21

2 probwLqqprobwLwLAqq

C r

After combining similar terms, we get

παπα

αα

αα

−=−−−=+−−−

=−

−

1**)1)(1(*)*)1)(1(

{~1

21

)1(21

2 probwLqqprobwLAqq

C r

The expected utility therefore is6

5 Here we assume that there is no population growth. Each individual in the old generation will form a firm. Each firm will combine his/her capital investment with the L units of labor of the young generation to carry out production. So individual and firm is the same concept here. We will use these two terms alternately. 6 Note if we have A and γ− as constant numbers and B is a random variable,

then )1(*)(*)()( 10 πγ

πγγ

γγγ −−+

+−+

=−+ −−− BABABAE . Here

)1(Pr)(Pr

1

0

ππ−⎩

⎨⎧

=ob

obBB

B .

30

)1(*])1)(1([

*])1)(1([

)~]**[*(

121

121

121

121

21

21

πγ

αα

πγ

ααγ

α

γαααα

γαααα

γαα

−−

−−−+++

−+−−−++

=

−++

−−−

−−−

−−

wLqqwLqwq

wLAqqwLqwq

CwLqwqEr

We need to choose 1q and 2q to maximize the expected utility of an individual.

First we will assume that capital investment in safe technology will give a positive return.

This means KKLKLKLKLyr ss >=−−=−−= −−−− αααααααα ααα ***)1(**)1( 1111 .

To meet this requirement, we need to assume that KKL >− ααα 1* .

Due to the special form of the utility function, we can induce that 01 =q if the

expected utility is maximized. So we will choose 2q conditional on 01 =q to maximize

the expected utility. Take first derivative and set it equal to zero, we get

1)1(12 −+

−−=

ADDq α , where 1

1

)1( +−

−−

= γ

πππ

AD . Here D can be viewed as a term represents

the productivity difference between safe technology and risky technology. 1>D and

11

)1(0 <−+

−<

ADD α . Therefore 10 2 << q (see the appendix for the solving process and the

discussions). It means that individuals will not choose to invest all in risky technology

although it has a higher expected product output. So the whole economy faces an

underproduction problem.

Now let’s assume insuring against risk is possible and individuals pay an

actuarially fair premium. When production goes well, the individual firm will have an

output level of αα KALy *1−= . The return on a successful capital investment in risky

technology is

31

premiumKLApremiumKLKALr −+−=−−−= −−− αααααα αα 111 )1(*)1(* . When

production incurs loss, insurance company will compensate for the loss. The

compensation is αα KALy *1−= . So an insured individual, who incurred loss in his /her

investment in risky technology, will have a return on capital investment of

premiumKLKALr −−−= −− αααα α *)1(* 11 too.

Now, let’s decide how large a premium the insurance sector needs to collect.

When we assume an actuarial fair premium, it means that insurance sector will make zero

profit. This means the premium collected is equal to the cost paid to individual firms who

will incur loss. To calculate the actuarial fair premium, we assume there are n firms in the

economy. For the whole economy, there are πn firms which will not incur loss in their

production process. There are )1( π−n firms which will incur loss. For each firm incurred

loss, the insurance company needs to pay them αα KAL *1− . Therefore the total cost to the

insurance company is ααπ KALn *)1( 1−− . The total premium that the insurance company

needs to collect is therefore equal to ααπ KALn **)1( 1−− . Because there are n firms in

the economy, the premium collected from each firm by the insurance company is

therefore equal to ααπ KAL **)1( 1−− . For π proportion of firms, there is no loss and

insurance sector does not need to pay anything. For π−1 of firms, they need to pay

KALy *1 α−= for each. At the end, all premiums will be paid out. Insurance sector does

not make any profit. In addition, each firm will face the same output level, whether they

incur loss or not in their production process.

The output level net of premium cost of each insured firm is

32

αααααα ππ KLAKALKAL ***)1(* 111 −−− =−− , which is same as the expected

output level when a firm employs the risky technology. Because we assume 1fπA , an

individual firm will definitely choose to invest all in the risky technology when there is

an insurance sector. With insurance possible, a risky technology which yields a higher

return will dominate the economy. Due to the special feature of the utility function, the

individual maximization problem will have a corner solution-- 1q and 2q will be zero:

nobody will choose to invest in safe technology. The maximized utility with an insurance

sector is higher than the maximized utility without an insurance sector. Insurance sector

makes the whole economy on the path of choosing the risky technology, which benefits

all agents in the whole economy. The under production problem is solved. Further, we

can link this with economic growth.

From the production functions of two different technologies, we can see the safe

technology result in a lower output level and the risky technology result in a higher

output level if it is employed by the whole economy. In the following discussion, we will

see how this will relate to economic growth.

33

II. The Long Term Capital Accumulation Role of Insurance in an Economy

In this part, we will discuss how insurance institutions affect the economic growth

through the channel of capital accumulation. We will especially concentrate on life

insurance and pension funds because they are viewed as institutions that will influence

the savings pattern of an economy. Health insurance may also influence the pattern of

individual savings. This is illustrated in the model of Carmichael and Dissou (2000).

Their model shows that the introduction of health insurance into an economy may not

change the total amount of savings. However, it will increase the proportion of long term

capital. Therefore, health insurance can contribute to the growth of an economy. In the

following discussions, we will see pension funds and life insurance also can shift part of

short term savings to long term savings. This will help economic growth.

Pension funds and life insurance companies are called contractual savings

institutions. The emergence of contractual savings institutions may affect both the total

amount of savings and the savings pattern of individuals. When we say individuals’

savings patterns change, we mean the structure between liquid savings (used for short

term investment) and illiquid savings (used for long term investment) changes. Therefore,

the emergence of contractual savings institutions may affect economic growth through

the capital accumulation channel.

The arguments go as follows. Compared with banks, contractual savings

institutions have special knowledge on population life expanse distribution. This makes

the contractual savings institutions able to offer individuals savings plans. These savings

34

plans can increase individuals’ utility level. Put it another way, there is a demand for

contractual savings institutions. This leads to the emergence of contractual savings

institutions. Compared with banks, contractual savings institutions can offer more long

run funds. This means contractual savings institutions can provide more illiquid funds to

an economy, which is believed to contribute to economic growth.

First, we will go through some empirical studies on the effect of contractual

savings institutions. Then we will present the above argument.

The empirical study of Murphy and Musalem (2004) from 43 industrial and

developing countries has shown mandatory pension programs may increase national

savings while voluntary pension programs may not affect national savings.

The role of contractual savings institution on economic growth may be through

deepening of capital market. Some empirical studies have been done to show whether

there is relationship between development of contractual savings institutions and

financial market development.

The empirical study of Impavido, Musalem, and Tressel (2003) found that an

increase in the ratio of the assets of contractual savings institutions to domestic financial

assets will increase the depth of domestic stock market and bond markets on average. The

specific effect is dependent on factors such as financial system of a country (whether it is

market based or not), mandatory or voluntary contribution of pension funds.

Another empirical study of Impavido, Musalem, and Tressel (2002) is about how

the development of contractual savings institutions affect bank sector. Their study

showed that the development of contractual savings institutions is positively related to

bank efficiency and “resilience to credit and liquidity risks”.

35

They also examined how the development of contractual savings institutions

affects the firm financing patterns, which may lead to the efficiency gain in firms.

Impavido and Musalem (1999) conducted an empirical analysis using OECD and

developing countries’ data to show how contractual savings institutions affect the

development of stock markets. They concluded that development in contractual savings

institutions is contributing to the development of stock markets in its depth and volatility.

In summary contractual savings institutions may hold a larger proportion of

illiquid assets because they have long term liabilities. Contractual savings institutions are

more stable to the economy. They may not face runs like banks do. Contractual savings

institutions include pension funds and life insurance companies. The emergence of

contractual savings institutions may not increase the total amount of savings but they will

increase the amount of illiquid savings, which are essential to economic growth. Banks

and open-end mutual funds have short term liabilities while pension funds and life

insurance companies have long term liabilities. Banks will finance more investment with

short maturity while contractual savings institutions will finance more investment with

long maturity. According to the author, the percentage of long term investment for

contractual savings institutions is much higher than that of banks.

However, we should be very careful about the above conclusion on contractual

savings institutions. Although the liabilities that contractual savings hold are mostly in

long term, this does not mean they will have long term investment. At least, this may not

be the case for all countries. Different countries have different laws governing the

operation of life insurance, which may regulate what kind of projects the life insurance

36

companies can invest in. But for the theoretical illustration purpose, we will just assume

that life insurance can freely invest in long term projects to achieve higher profit.

The following part will provide a theoretical framework to show the effect of

contractual savings institutions on accumulation of capital and on economic development.

First, we will show why individuals are willing to put their money in the

contractual savings institutions.

i) Individual Savings Behaviors without Contractual Savings Institutions

We assume each individual will work at the first period and earn wage. Labor

supply is inelastic. Each individual will face the probability of death at either end of

period1, 2, or 3. But the specific life expanse for each individual is not known. Each

individual needs to choose a savings plan for his whole life. He will not work in period 2

and period 3. So they need to save period 1’s wage for possibility of period 2’s and 3’s

consumption. There are no contractual savings institutions. They will put their money in

banks and get a market rate of return. We assume banks offer per period interest rate of r.

Now we assume a specific form of utility function for each individual. Because

individuals do not want to end up with nothing when they were old, they must plan for

their longest possible life span. Also, to make things simple, we assume each individual’s

internal rate of return is the same as the market rate of interest. Particularly, we specify

the utility function as follows.

232

1321 )1(*

1*),,(

rLC

rLC

CCCCU++

=

Subject to the constraint that 232

1 )1(1 rC

rC

Cw+

++

+=

37

In the utility function, (1+r) represent the internal rate of preference of individuals,

which is the same as the rate banks will offer individuals if they deposit their money in

banks. The second period’s and third period’s consumptions are discounted to current

value by individuals’ internal rate of preference in the utility function. In the constraint, it

shows that current wage is equal to the sum of current consumption and future

consumptions discounted by the interest rate that bank offers.

The reason for the special form of the utility function is that it rules out the

situation when individuals are alive but have nothing to consume. Notice here the utility

function is the product of consumptions in three periods, given an individual is alive. The

term LC2 means the consumption in period 2 given the individual is alive at period 2.

Similarly, LC3 means the consumption in period 3 given the individual is alive at period

3. If the individual is not alive at period 2 or period 3, the utility will just be the product

of all previous consumption(s). If an individual is alive and has nothing to consume for

any period, the total utility of an individual will be zero.

Because there is a possibility that an individual will live to the end of period 3, he

has to save for that even if he also has a possibility that he will not live that long.

Individuals do not know their specific life expanse. So they have to plan for the longest

life expanse to avoid dying from hunger before their natural death.

The above utility function is not very weird if we recall the following two-period

model in most microeconomics textbooks.

38

The convex shape of the utility function shows an individual’s utility is the

product of the consumption of two periods. The only difference in our model is that the

utility is conditional on whether an individual will be alive in the second and third

periods.

Also, we will illustrate the probability distribution for the death of each individual

in Table 2.2.1. Particularly, we will specify a symmetric distribution although it may not

be matching the true world situation7.

Table 2.2.1 Assumed Life Expectancy Probability Distribution

Time of Death Probability of Death for Each Individual

End of Period 1 π

End of Period 2 1-2π

End of Period 3 π

7 The format of this particular distribution function is just for the convenience of derivation of the final result. It will not affect the theoretical result.

C1

C2

U

39

Due to the special form of the utility function, we can see if an individual will

maximize expected utility function, he must choose to make real consumption same at

each period. If the wage he earns during the first period is w, then he will plan to

consume w/3 in real term (after discounted by the internal rate of preference) during

period 1, 2 and 3.

The above situation can be illustrated by a numerical example. Suppose an

individual will earn 150 units during the first period. What he will do is to consume 50

units during the first period for sure. Then he will save the other 100 units which will

earn per period interest rate of r. If he does not die at the end of period 1, he will draw out

50(1+r) units at period 2 and consume it. Then he leaves 50(1+r) units in the bank. If he

does not die at the end of period of 2, he will draw all the money left, which is 50(1+r)2 ,

and consume it. So the utility of individuals who will die at the end of period 1 is 50; the

utility of individuals who will die at the end of period 2 is 50*50; the utility of

individuals who will die at the end of period 3 is 50*50*50.

This is under the situation when there are no contractual savings institutions. If

there are contractual savings institutions which allow individuals to buy policy and draw

an annuity as long as the individual is alive, the situation will be different.

ii) Individual Savings Behaviors with Contractual Savings Institutions

Obviously, individuals’ utility can be improved when there are contractual

savings institutions. What individuals will do is that they will put their entire wage in the

institutions and exchange for a life long annuity. If we assume these institutions offer

actuarial fair annuity (they will make zero profit), individuals will consume more during

40

each period. Of course, we need to assume that the probability distribution is known to

the contractual savings institutions, which is not known to banks. This assumption is very

reasonable because life insurance companies or pension funds can hire actuaries to

calculate the life table while this is not the case for banks.

Then we see how contractual savings institutions will manage. Due to the

symmetric distribution of the probability function, contractual savings institutions can

afford an annuity with an annual payment of w/2, which is higher than individuals

previously planned consumption. The reason is that the institutions can use the money of

the early death to finance those who live longer than average. The expected life span is

two periods.

Table 2.2.2 summarizes the inflow and outflow of funds of the contractual

savings institutions.

Table 2.2.2 Inflow and Outflow of Funds (Pension)

Inflow of Funds Outflow of Funds

Period 1 wn (w/2)n π

Period 2 (w/2)n(1-2 π) (w/2)n(1-2 π)(1+r)

Period 3 (w/2)n π (w/2)n π (1+r) (w/2)n π (1+r)2

Note: we assume there are n individuals who earn wages in the economy. Also we assume the

fund in the contractual savings institutions will accrue with an interest rate of r per period. Notice here the present value of the outflow of fund is equal to wn.

Using the above numerical example, we can see each individual can have a real

consumption of 75 units per period as long as he is alive. The utility for the individual

who will die at the end of period 1 is 75; the utility of individuals who will die at the end

of period 2 is 75*75; the utility of individuals who will die at the end of period 3 is

41

75*75*75. All individuals can improve their utility. The role of the contractual savings

institutions is to optimize individual’s plan which could not be achieved otherwise due to

individual’s uncertainty of their death dates.

So if there are contractual savings institutions, individuals will put all their

savings to those institutions rather than in banks. The reason is that the existence of

contractual savings institutions can increase individuals’ utility level.

This is a rather simplified illustration. Please note the above argument does not

rule out the existence of banks. In the real world situation, we can assume that there are

two kinds of savings: one is for life long purpose; the other is for routine daily purpose

(We can view the role of the bank as providing liquidity to individuals inside each living

period of above model). The emergence of contractual savings institutions is for the first

purpose. Savings transfer from banks to contractual savings institutions does not mean

banks are of no use anymore. It only means the savings for life long purpose are

transferred from banks to contractual savings institutions. The other role of banks is not

modeled here.

The difference between banks and contractual savings is that individuals can not

draw funds except when they are alive. Banks can not do that because they do not know

the life expanse distribution of the population. Therefore, funds in contractual savings

institutions can engage more in long term production. This engagement may not be direct.

It may be through the deepening of the stock markets, which is also ignored here.

42

iii) Compositions of Savings with and without Contractual Savings Institutions

We can see from the above illustration that the emergence of contractual savings

institutions will increase long term investment. Suppose individuals will choose to invest

in either short term (one period) or long term investment (two periods). If there are no

contractual savings institutions, they will invest 1/3 of their wage in short term and 1/3 in

long term because they planned for three period’s consumption. They will withdraw at

the second period and the third period if they are alive. We assume the fund will be

withdrawn early if the person dies earlier. The long term investment will be pre-

liquidated. The pre-liquidated long term fund will be counted as short term fund.

The total amount of long term investment when there is no contractual savings

institutions (which does not include those interrupted due to their death) is (1/3)*w*π*n.

The total amount of short term investment is (1/3)*w*π*n +(1/3)*w*(1-2π)*n. When

there are contractual savings institutions, we can see the contractual savings institutions

will increase long term and decrease short term capital. This means there is more capital

invested in the production process, which may be a source of growth. We can see the

contractual savings institutions can invest (1/2)*w*π*n in the long term production and

(1/2)*w*π*n + (1/2)*w*(1-2π)*n in the short term investment.

The above discussion is based upon the case which is similar to pension funds.

The assumption is that people will draw funds as long as they are alive. Payments stop at

death. This is just opposite to the case of life insurance. Life insurance pays to

beneficiaries upon policy holder’s death and does not make any payment when the policy

holder is alive. However, the mathematical derivation won’t be much different. We can

43

just assume that the original utility function will have a similar form. But now the second

period and third period consumption is based on the consumption of the beneficiaries

upon the death of the policy holder. The purpose of life insurance is to supply more

financial need upon death of policy holder.

We may have the following format of outflow of funds in Table 2.2.3.

Table 2.2.3 Inflow and Outflow of Funds (Life Insurance)

Inflow of Funds Outflow of Funds

Period 1 wn wn π

Period 2 wn(1-2 π)(1+r)

Period 3 wn π (1+r)2

We can assume the savings due to uncertainty of death is kept liquid all the time

since the unknown date of death when there is no life insurance available. Therefore,

when there is life insurance available, both long term and short term funds increase.

44

III. Discussion: Technological Progress, Insurance and Economic Growth

i) Factors that Affect Technological Progress

In most growth models such as Solow’s (1956) growth model, economic growth

is sustained by technological growth in the long run. Capital investment alone cannot

generate permanent economic growth. However, in those models, technological growth is

treated as an exogenous rate. How new technology is invented is not illustrated in those

models. Recently, more and more economists realized the importance of technological

progress and the factors that determine the progress. Shumpeter was among the earliest

who gives inspiration of later economists the idea of creative destruction. Basically,

capitalism is in the process of generating new products, ideas, etc. to replace the old ones.

Firms are in the process of competition for innovations and gain profit from these

innovations. Based on the ideas of Shumperian model (1934), many economists have

developed models that make technology progress endogenous variable. Among them are

Philippe Aghion and Peter Howitt (1992), Gene Grossman and Elhanan helpman (1991),

and Paul Romer (1990). In these models, technological progress can be explained by

economic incentives rather than being given exogenously. According to the description

above, we can see that economists have two different ways to model technological

progress. One way is to treat technological progress as “an unintentionally by-product, an

externality, of some other activities such as investment and or production.” (Van den

Berg , 2009 forthcoming, p. 37 of chapter 6). However, the other way is to assume that

45

technological progress is motivated by economic incentives to purposely allocate

resource in generating new technology.

In his development textbook, Van den Berg summarized models which make

technological growth an endogenous variable. He also gives out a mathematical version

of the Shumpeterian model to show how entrepreneurs are motivated to innovate. This is

basically based on Paul Romer’s model (1990). In the following part, the basic idea of

this model is summarized as well as the factors that determine technological progress.

In the Shumepeterian technological growth model, we can see that innovations

take time and effort. This makes technological invention very costly. Although the

production cost may not be high once the new invention is successful (usually new

production method will lower production cost), the upfront cost of making that invention

is huge. Therefore, unlike traditional producers who face a horizontal demand curve and

can not influence market price in a competitive market, entrepreneurs who engage in

innovations face a downward demand curve. This makes entrepreneurs charge a higher

price than average cost to make a profit, which can recover the huge upfront cost of

innovations.

The basic idea of the model can be described as follows. Entrepreneurs engage in

costly innovation activities, which cost scarce resources, to seek the profit coming from

the new products from successful innovations, also at the expectation that the new

product can be further replaced by more advanced technology (the creative destruction

process). Then the question is that how many resources entrepreneurs will engage in

innovation activities. Entrepreneurs need to compare the cost of innovation activities and

46

the expected profit from the innovations to decide how many resources should be

allocated to the innovation activities.

The following derivations (Van den Berg, 2009) are illustrated here to show how

the equilibrium rate of innovation is decided. This is a close version of Paul Romer’s

model (1990). Here I will just give out a very brief summarization of the derivation and

the final result.

The model assumes that firms continually create new products and the growth rate

of new products is g. The model is to determine the equilibrium growth rate of new

products, which is technological progress. The model assumes n firms in the economy,

each one will produce a different product. Each firm faces a down-ward sloping demand

curve, which is the same across different firms; therefore they can charge a price higher

than the marginal cost of production (w) to earn a profit. It is assumed that one unit labor

is required to produce one unit of good. Therefore, the cost of the product is w, which is

the wage rate. γ is the ratio of price that is equal to production cost of one unit of product.

Therefore, 1- γ is the price mark up that will give firm profit above marginal cost. The

profit of each firm is equal to total output of the economy multiplying price mark up then

being divided by n. The present value of all the future profit of a firm decides the equity

value of the firm.

According to the above assumptions, we have the following equations.

γwp = Demand function of each firm

nGDP /)1( γπ −= Profit of each firm

47

)(/)1( grnGDPPV +−= γ The present value of a firm when the capital market

is competitive. r is the market interest rate and g is the growth rate of the firm, which is

the technological progress of the firm.

Firms will engage in innovations till the present value of all future profit equals

the cost of innovation. Assume that it takes β unit of labor to develop a new product. The

cost of innovation is βw.

PV= βw. Equilibrium of innovations growth.

From the above equations, we have the following relationship

)()1()(/)1(

grnGDPgrnGDPPVp

+−

=+−

==βγ

γβγγ

βγ

On the other hand, the entrepreneurs decide how to allocate the total resources R

to current product and innovation of new product. This gives

RpGDPng =+ /β

Combine the above two equations, we have

)()1(

grnGDP

ngRGDP

+−

=− βγ

γβ

Therefore,

rnRg γβγ −−= ]/)1([

Here we can see that the growth rate of new products is a function of R (total

resources), β (units of resources taken for each innovation), γ (the ratio of price which

will cover the cost of production), n (the number of firms in the economy) and r (interest

rate).

48

Any change in the above parameters will lead to the change of technological

progress g. This corresponding effect can be shown in the sign of the partial derivatives

of g against the above variables.

nRg βγ /)1( −=∂∂

rnRg−−=

∂∂ βγ

/

γ−=∂∂

rg

nRg

2

)]1([β

γβ

−−=

∂∂

2

)]1([n

Rng

βγ−−

=∂∂

In the later chapter of his textbook, Van den Berg (2009) further discussed the

role of savings in technological progress. In neoclassical Solow growth model, higher

savings rate will lead to a higher steady state income level. In such kind of models,

savings will automatically turn into investment. Two things we need to consider here.

First, savings may not turn into investment automatically. Second, even though savings

can be turned into capital investment, it can not sustain long run economic growth. Only

savings channeled to investment that leads to technological progress will finally result in

economic growth. Economic growth needs ongoing shift out of production function

which requires an ongoing expanding of capital investment. In the Shumpeterian model,

savings effectively turning to finance technological progress is a key role of promoting

economic progress. More savings channeled to investment can lead to higher steady state

income level. This is corresponding to a move on the production frontier. At the same

49

time, more savings channeled to technological progress is corresponding to a shift out of

production function. This leads to further more output in the economy and more savings

in the future. Therefore, the role of financial intermediation is critical in the economic

development. The financial sector of an economy plays the role of channeling savings to

potential investment projects. Innovations usually require huge upfront cost with the

expectation of future profit. Therefore, without funds being channeled to entrepreneurs,

technological progress seems not possible.

A model of financial intermediation and technological progress developed by

Robert King and Ross Levine (1993) shows that the cost of financial intermediation is

negatively related with technological progress. In their model, the main cost of financial

intermediation is to acquire information on promising entrepreneurs. Here we will just

present the derivation result from their model.

In summary, technological progress is driven by many factors which determine

the cost and profit of innovations and further determine the equilibrium innovation rate.

At the same time, innovations also require an efficient financial sector to bring in savings.

In the following part, we will see how the insurance sector, as part of the financial sector

of an economy, can influence technological progress.

ii) Insurance and Technological Progress

1. The Role of Property/Liability Insurance

In the beginning of this chapter, we illustrated that the presence of

property/liability insurance make economic agents in an economy to choose a risky

technology rather than a safe technology. We can view the risky technology as the

50

innovated technology and the safe technology as the current technology. The insurance

sector here helps the economy to forsake the old technology and apply the new

technology. It opens the door for the new technology. Without such institutions to spread

out risk, economic agents are reluctant to take the new technology even though it is

already innovated. For example, compared with possessing horse driven buggies,

possessing automobiles may be subject to more risks due to the possibility of the loss of

the automobiles, although it may bring more productive economic life. Presence of the

insurance sector increases the demand for risky technology. Entrepreneurs get a higher

profit ratio due to more demand of new technology. This is corresponding to a lower γ.

We have 0lg

<∂∂pcγ . From the above mathematical derivation, we have

0/ <−−=∂∂ rnRg βγ

. Therefore, 0lg

*lg

>∂∂

∂∂

=∂∂

pcg

pcg γ

γ, PCL insurance will lead to a

higher g when it can expand demand for new technology from the consumption side. On

the other hand, property insurance on buildings and machines etc. will lower the risk of

property loss that entrepreneurs face and therefore decrease their expected cost. This will

be corresponding to a decrease of β, which is 0lg

<∂∂pcβ From the above mathematical

derivation, we have 0)]1([2 <−−

=∂∂

nRgβ

γβ

. Therefore, 0lg

*lg

>∂∂

∂∂

=∂∂

pcg

pcg β

β, PCL

insurance will lead to a higher g when it can reduce the cost associated with the

producing of new technology. The combination of the two results due to the presence of

an insurance sector will reinforce each other. The total effect is corresponding to an

increase of g, the technological progress growth rate.

51

2. The Role of the Life Insurance Sector in Technological Progress

We have illustrated that life insurance companies can provide more long term

funds into the economy. Innovative activities usually demand for huge upfront cost. Also,

it may take a long time to have new innovations. Therefore, there is the need of long term

funds for innovation activities. Here we can see that more long term funds may increase

the total resource available for innovation activities. We can view this as an increase as

total available resources devoted to innovation. This is corresponding to an increase of R,

which is 0>∂∂lfgR . From the mathematical derivation, we have 0/)1( >−=

∂∂ nRg βγ .

Therefore, 0>∂∂

∂∂

=∂∂

lfgR

Rg

lfgg . Life insurance growth may lead to the technological

progress.

Also, we can illustrate this from the perspective of the cost of financial

intermediation. In King and Levine’s (1993) model, lower cost of financial sector will

increase technological progress. Although in their model the cost is associated with

acquiring information, we can generalize this cost as the general cost of financial

intermediation. More long term funds in the life insurance sector can make their

provision of necessary long term to entrepreneurs less costly. This will increase

technological growth rate.

By the above discussion, we can see that the insurance sector may serve as the

assisting institutions of technological progress. These are the possible reasons how

insurance can contribute to economic growth through promoting technological progress.

However, in the real world situation, there are more costs involved with these institutions

as well as their cooperation with other similar institutions. The final effect will rely on the

52

situation of specific countries. In the following section, we will investigate whether

insurance will contribute to economic growth through the study of four countries’ data.

53

Chapter 3 Empirical Study of Insurance Growth and Economic Growth

In the last section, we built up the theoretical framework to explain how the

insurance sector may contribute to the growth of an economy. In this section, we have

collected several countries’ data that are available to us. We study the data to see whether

they give empirical evidence of the theoretical models we developed in the first section of

the dissertation. We emphasize the role of the insurance sector in an economy, which is

how the insurance sector can help the growth of an economy. However, there is no doubt

that economic growth can also help the development of the insurance sector in an

economy. Therefore, in the empirical analysis, we allow the interaction between

economic growth and insurance growth. The following is a literature review on the

empirical studies on the relationship between economic growth and insurance growth.

Actually, what we find here is that almost all the studies focus on the factors that affect

the development of the insurance sector in an economy. These literatures help us to set up

the growth demand function of either life or non life insurance in an economy.

I. Literature Review

One empirical study of the relationship between economic growth and insurance

is by Beenstock, Dickinson and Khajuria (1988). They used the international property-

liability insurance premiums and income data. They found that the marginal propensity of

insurance is different across countries and “property-liability insurance is a superior good

and is disproportionately represented in economic growth” (pp. 270)

54

Ward and Zurbruegg (2000) used the data of nine OECD countries from 1961 and

1996 to examine the interaction of economic growth and insurance industry development.

They used the VAR to test for the Granger causality between economic growth and

insurance development. Their results showed that the causality relationship is different

across countries. Only three countries have notable causality test results found: Canada,

Japan and Italy. In Canada and Japan, insurance seems Granger cause growth, while in

Italy there is bi-causal relationship.

Browne and Kim (1993) used international data to analyze the factors that may

influence the demand of life insurance in an economy. They include the following factors:

income, social security, inflation, education, life expectancy, price of insurance and

whether the data are from an Islamic Nation. They found that the following factors are

statistical significant in life insurance demand function---dependency ratio, national

income, government spending on social security, inflation and the price of insurance and

whether a country is an Islamic nation.

Outreville (1996) studied the role of life insurance in the financial sector of

developing countries. He found that the development of the life insurance market in

developing countries was highly related with the personal disposable income and the

level of financial development. He also found that inflation expectation is negatively

related with life insurance premiums.

Liu, et al. (2003) found that urbanization in China is a significant source of the

increase in health insurance coverage in rural China. They used an urbanization index to

measure the degree of urbanization. The index includes the following variables:

55

population size, infrastructure variables and industrialization variables. They also found

that income is positively related with the health insurance coverage.

Enz (2000) used the international data to examine the relationship between

insurance penetration (premium/GDP) and per capita income. He found that the income

elasticity of insurance purchase is not linear but presenting an S-curve shape. The data

have shown that penetration of life insurance across countries is more diversified than

that of non-life insurance. The income elasticity of insurance is around one for high and

low level of income and is near two or more for intermediate income levels. The income

elasticity is highest around $10000 for non-life and $15000 for life insurance.

From the above literature review, we can see that there is evidence that economic

development will affect insurance development. Second, development in the insurance

sector is different from country to country. Third, there is a difference between life

insurance development and non life insurance development. In the following section, we

will present the result from four countries’ data.

56

II. Data and Methodology

i) Data

The data for this empirical study are from four countries: The U.S., Korea,

Sweden, and Germany. These four countries’ data are available from our library

resources. For the empirical study, the more countries are included in the study, the better.

However, these are all the data on hand for me to do the time series analysis when I

started this dissertation. Not a lot of countries provided very good data on their insurance

sector. That is part of the reason that there is lack of literature on insurance study.

The real GDP is used to measure the economic growth. For

property/casualty/liability (PCL in the following part throughout this dissertation or non

life) insurance, real written premiums are used as a proxy for the development of PCL

insurance sector. Generally speaking, PCL insurance policies are short term policies.

Most of the policies are renewed in half or one year. Therefore, the time when premiums

are paid is very close to the time period when the risk is under coverage. So the usage of

real written premiums for the PCL insurance sector is a good measurement. For the

analysis of life insurance growth, there are three choices to measure its growth—life

insurance written premiums, life insurance policy reserve and life insurance in force. The

following are the definitions of the four terms.

1. Premium: The payment, or one of the periodic payments, that a policyholder makes to

own an insurance policy or annuity.

2. Reserve: The amount required to be carried as a liability on an insurer’s financial

statement to provide for future commitments under policies outstanding.

57

3. Life Insurance in Force: The sum of face amounts and dividend additions of life

insurance policies outstanding at a given time. Additional amounts payable under

accidental death or other special provisions are excluded.

4. Face Amount: The amount stated on the face of a life insurance policy that will be paid

upon death or policy maturity. The amount excludes dividend additions or additional

amounts payable under accidental death or other special provisions.

(The above definitions are cited from the website of the American Council of Life Insurers)

Most life insurance policies are in much longer term, some of them are in whole

life of the policy holder. The policy holders pay periodically—monthly (most of the time),

quarterly, bi-annually or annually to own a life insurance policy. Obviously, the time

when the premiums are paid is quite different with the time period when the risk is under

coverage. Therefore it is not a good measure of life insurance growth. Life insurance in

force and life insurance policy reserve are correlated with each other. We have to decide

which one to use at last.

Actuaries use life table and other techniques to estimate life insurance policy

reserve, which shows their estimate of future claims on the all current life insurance

policy in force. I chose life insurance in force rather than life insurance policy reserve as

a measure of life insurance growth for two reasons. First, life insurance policy holders

will make their economic decision according to the coverage amount on contingency.

Second, life insurance in force is a better independent variable for a life insurance

demand function.

For the U.S., Germany and Sweden, the data are from their statistical yearbooks,

Penn World Table and IMF financial data disk. The data of Korea are from the website of

the Korean Bureau of Statistics. The U.S. data are from the Statistical Abstract of the

58

United States. The range of the PCL data available to us is from 1963 to 2000. The range

of the life insurance data available for us is from 1956 to 2001. Therefore, we will use the

data from 1963 to 2000. The data of Germany are from 1970 to 1999. The data of

Sweden are from 1972 to 1992.

The data of Korea are from the following website:

http://www.kosis.kr/eng/index.htm. Both the ranges of the life insurance and

property/casualty insurance are from 1980 to 2004.

Premiums collected and life insurance in force both are in nominal terms. They

are discounted by GDP deflator of each country to get real premiums. The real GDP data

are from the publication of IMF.

At the end of the dissertation, a detailed source of each variable is described.

ii) Methodology

Simultaneous equations are used to allow the interaction of GDP growth and

insurance growth. An ordinary least square model will be run first. We then compare the

result from OLS with the results of the simultaneous equation model.

It is well known that non stationary of a variable may lead to the spurious result of

regression. So the unit root of each variable is tested. If a variable is suspected of being

non stationary, the first difference of the data will be used (given the first difference of

the data is stationary). The results will be presented individually for each country because

there is some difference in the inclusion of variables for different countries (due to data

availability)

59

1. Unit Root Test

The unit root test will tell us whether a time-series variable is stationary or non-

stationary, which will decide the appropriate form of the regression model.

Two tests will be used: the augmented Dickey-Fuller test and the Phillips-Perron

test. All the illustration of the methodologies in the following part is from Enders (1995).

The augmented Dickey-Fuller test assumes a time series y follows a pth-order

autoregressive process as follows.

tptpttt yayayaay ε+++++= −−− ......22110

Rearrange the above equation; we can get the following equivalent equation:

tit

p

iitt yyay εβγ +Δ++=Δ +−

=− ∑ 1

210

Where

)1(1∑=

−−=p

iiaγ

∑=

=p

ijji aβ

We are interested in testing the coefficient ofγ . If it is 0, then there is a unit root

in the time series y. The test statistics is based on the Dickey Fuller statistics which is

different with the traditional t test.

One problem with the Dickey-Fuller test is that it assumes that the errors are

independent and have a constant variance, which may not be the case for the true data

generating process. So the Phillips-Perron Test is conducted. In the Phillips-Perron test,

the error terms can be weakly dependent and heterogeneously distributed. The criterion

used to select the appropriate lag length is the Akaike Information Criterion.

60

In the Phillips-Perron test, a drift and a stationary trend is included into the least

square regression. The regression will look as the following equation.

ttt uTtyy ˆ)21(ˆˆˆ 1 +−++= − βαμ

In the Phillips-Perron test, the estimated variance used in calculating the t statistic

is constructed by the Newey and West method. All tests are conducted through

SHAZAM.

2. OLS Regression of the Growth Model

Soo (1996) developed a variant of Solow growth model (Solow 1957) to test the

relationship between life insurance and economic growth. I will base on what he

developed to set up the relationship between insurance and economic growth. This is

consistent with the discussion of chapter two that insurance may contribute to

technological progress.

In this variant of the Solow growth model, productivity growth (technological

progress) is related to factors such as economic institutions, openness of an economy,

information, knowledge etc.

We assume a Cobb-Douglas production function as follows.

)1(),( αα −= LKeLKF gt

gte is the productivity factor that can explain the output growth that can not be

explained by the growth of capital (K) and labor (L).

Take the log of the production function and differentiate it with respect to time we

can get the following

GLGKgGY )1( αα −++=

61

We will take g as an endogenous variable which can be a function of openness of

an economy, existence of risk shielding institutions and the degree of influence by

government activities. We use the export and import growth as the measurement of

openness of an economy, the insurance sector growth as the measurement of the effect of

risk sharing institutions and government expenditure ratio as the measurement of degree

of government influence.

Therefore

ελλλλλλ ++++++= govrnonrlifgRimpgxpgg 543210 lgRe

Here Rexpg, Rimpg, Rlifg, Rnonlg and gov represent real export growth, real

import growth, real life insurance in force growth and real non life insurance in force

growth and government expenditure ratio to GDP respectively.

Put g back to the production function we have the following.

εααλλλλλλ

+−+++++++=

GLGKgovrnonrlifgRimpgxpgGY

)1(lgRe 543210

This will specify our estimated growth function as follows.

εααααααααα

+++++++++=

TIMEGOVREXPGRIMPGRNONLGRLIFGLGINVESTRGDPG

876

543210

Here we use real GDP growth as a proxy of output growth and investment ratio

as a proxy of capital growth.

3. Simultaneous Equations

Simultaneous equations are a system of equations, which allow for the interaction

of variables in the system. The above theoretical framework shows that the insurance

sector’s growth may contribute to economic growth. On the other hand, economic growth

may also demand for insurance growth. When the influence between economic growth

62

and insurance sector growth are mutual to each other, the simultaneous equation system

should give a better estimation.

Here we will give out a simple illustration how ordinary least square may lead to

biased estimation of coefficients. We will use a system of two equations for illustration

purpose, although in our estimation, we will have a system of three equations.

Suppose we have the following structural equations.

ttt yy εαα ++= 2101

ttt uyy ++= 1102 ββ

Here we assume that

0)()( == tt uEE ε

22 )( εσε =tE

22 )( utuE σ=

0)( =ttuE ε

The equilibrium condition is tt yy 21 =

To Estimate the first equation by OLS

∑

∑

∑

∑

=

=

=

=

−

−−+=

−

−−= n

tt

n

ttt

n

tt

n

ttt

yy

yy

yy

yyyya

1

222

122

1

1

222

11122

1

)(

))((

)(

))(( εεα

22

211

12

211

)()(

),()lim(

ut

tt

yVaryCov

apσσσαβ

αε

αε

ε

+−

+=+=

Which is a biased estimator.

In the following part, both the single equation and simultaneous equation system

will be estimated. Results from different estimations will be compared with each other.

63

The single equation is defined as follows.


+++++++++=

TIMERGOVREXPORTRIMPGRPCLGRLIFGPGINVESTRGDPG

876

543210

Here ε is assumed to have a normal distribution with mean zero.

The simultaneous equation model is defined as follows.

11111331221111 ......lg ttkktttt xxrnonrlifgrgdpg εααλλλ =+++++



Here rgdpg, rlifg and rnonlg are endogenous variables and all the other variables

are assumed to be exogenous. The set of x variables are different from country to country

due to the different source and availability of the data for each country. However, the first

equation in the above system is all the same for each country. It is defined the same as the

single estimation equation.

The relevance test of the instruments used for each country will be presented in

Appendix D.

Also, in either the single equation or the simultaneous equation system, if a unit

root is suspected, its nth order stationary difference should be used to run the regression.

In the following parts, each country’s data will be analyzed and presented

individually. Then we will compare the results of the four countries. We will give a

definition of all the variables that will be included in the study of all countries. Some

variables are just country specific.

64

III. Definition of variables

RGDPG--- Real GDP growth, which is nominal GDP deflated by GDP deflator. This

variable serves as a proxy for economic growth.

INVEST--- Ratio of capital investment to GDP. This variable is a proxy of capital growth.

PG--- Population growth. This variable is one of the measures of labor growth in an

economy.

LG--- Labor force growth. This variable is the other measure of labor growth in an

economy.

RIMPG--- Real import growth (nominal import is deflated by GDP deflator)

REXPG--- Real export growth (nominal export is deflated by GDP deflator)

RGOV---the percent of government expenditure in GDP

RLIFG--- Real life insurance in force growth (nominal life insurance in force is deflated

by GDP deflator)

RPCLG--- Real property/casualty/liability insurance growth (nominal term is deflated by

GDP deflator)

RNONLG--- Real non life insurance growth (nominal term is deflated by GDP deflator).

This should be very similar with RPCLG. But when I collect the data for different

countries, they just label the data as non life insurance data.

INF--- Expected inflation

LEXP--- Life expectancy

RSSG--- Real social security growth

65

EDR--- Third level education enrollment ratio. This is a variable to measure the education

development. This variable is only available for the US economy.

ED--- Percentage of high school graduates entering to higher education. This variable is

only available for the Korean economy.

WPART--- Woman participation ratio in the labor force

DRATIO--- Dependant ratio. This is defined as the ratio of the population with age under

15 to the population with age between 15 and 64.

PRATIO--- Profit ratio of the property/casualty/liability insurance industry. This is a

variable which is only available for the US economy.

NLNLR--- Non life insurance industry net loss ratio. This variable is only available for

the Korean economy. It is related with PRARIO with the following relationship 1-

NLNLR--- PRATIO

LNLR--- Life insurance industry net loss ratio. This variable is also available just for the

Korea economy.

URBANR--- Percent of urban population in total population

If FD is added before a variable, it means the first difference of the time series is

used because a unit root is suspected. Similarly, SD and TD represent the second

difference and the third difference of the time series.

Before we present the empirical results from these countries, we will discussion

how expected inflation is constructed. Consumer price index is collected for each country.

The change in consumer price index from one period to the next is calculated as the

inflation of each country. Then the different averages of past inflation are calculated as

the expected inflation variables. We calculated the averages from the most recent two

66

periods up to the most recent eight periods. Then the unit root tests on those expected

inflation variables are conducted. Then the nth order difference which can reject the

existence of a unit root at 90% significance level is chosen. An ordinary least square

between the nth order of these expected inflation variables and real life insurance in force

is run. The one most correlated with real life insurance in force is chosen to be the

expected inflation variable for that country. For the US economy, the average of the last

eight periods of inflation is chosen as the expected inflation. For Korea, Germany and

Sweden, the averages of the last seven, four and seven periods of inflation are chosen as

the expected inflation for these three countries respectively.

Because both population growth and labor force growth are available for each

country, OLS regression is run twice, first with population growth, then with labor force

growth as the measure of labor growth for each country. Labor force growth seems to be

a better measure as labor growth for Korea, Germany and Sweden, where the estimated

coefficients on labor force growth show stronger statistical significance than the ones on

population growth for OLS regressions. However, for the US economy, population

growth seems a better one to use as a measure of labor growth. Also, these two

alternatives as the measure of labor growth are used in simultaneous equation analysis.

67

Chapter 4 Empirical Result from Four Countries

I. Analysis of the US data

i) Unit Root Test Results

Table 4.1.1 presents the unit root test results of all the variables used in the

simultaneous equations of the US data. Both the DF test and the PP test results are

presented here. The null hypothesis of the test is that there is a unit root in the time series.

If the null hypothesis is not rejected in 10% significance level, a unit root is suspected in

the time series. In the DF test and PP test, a drift and a time trend is included in the

regressions.

The regression data range is from 1966 to 2000. However, when the unit root test

is conducted for each time series, a longer period of data is used if the series is available

for a longer period of time. This may result in a more accurate unit root test.

From the Table 4.1.1, we can see for some variables, the DF test and PP test give

out different results regarding the existence of a unit root in the time series. We will

choose according to the test results of PP test, because the error assumption for the PP

test is more flexible.

68

Table 4.1.1 Unit Root Test Results (US Data)

Variables PP Test Statistics DF Test Statistics WPART -0.25 -0.48 PRATIO -3.27* -3.06 INF -0.35 -1.81 EDR -5.40* -5.50* LEXP -1.44 -1.39 RSSG -6.83* -2.29 RGDPG -4.67* -3.39* PG -6.91* -2.21 RLIFG -3.57* -3.30* RPCLG -3.22* -3.42 RGOV -2.48 -2.42 INVEST -2.88 -2.77 RTRADEG -4.80* -4.78 DRATIO -0.71 -3.64 LG -3.28* -2.55* REXPG -3.92* -3.66 RIMPG -6.00* -3.23 URBANR 0.50 -1.48

Note: * shows that unit root test can reject the null hypothesis at 90% significant level.

For the variables that can not reject the null hypothesis of the existence of a unit

root, the first difference of that variable is taken to do the unit root test. All unit root tests

for the first difference of those variables except INF, DRATIO and URBANR reject the

null hypothesis of a unit root at 90% significance level. Then the second difference of

the above three variables are taken and the unit root test on them are conducted. The null

is rejected at 90% significance level for the second difference of the above three variables.

69

ii) OLS Regression

The simple OLS regression will be run first. The results are used to compare with

the simultaneous equation results. The following are the estimated equations.

1.


+++++++++=

TIMERGOVRPCLGRLIFGEXPGIMPGPGFDINVESTRGDPG

876

543210

2.


+++++++++=

TIMERGOVRPCLGRLIFGEXPGIMPGLGFDINVESTRGDPG

87

6543210

The Newey West estimator is used to estimate the variance and covariance of the

estimated coefficients. The estimated coefficients and the t statistics based on the Newy

West estimator are shown in Table 4.1.2 and Table 4.1.3.

As stated before, population growth and labor force growth are used as two

different measures of labor growth in the model.

Table 4.1.2 Estimation Results from OLS (US data) - Population Growth is Used as a Proxy of Labor Growth

R-square=0.7664 Adj R-

square=0.6916 34

Observations Dependent Variable= RGDPG

VARIABLE NAME ESTIMATED

COEFFICIENT T-RATIO P-VALUE FDINVEST 0.697 3.476 0.002 PG 7.556 1.010 0.322 REXPG 0.009 0.333 0.742 RIMPG -0.009 -0.155 0.878 FDRGOV -1.685 -2.364 0.026 RLIFG 0.159 3.223 0.004 RPCLG 0.086 3.131 0.004 TIME -0.033 -0.715 0.481 CONSTANT -5.001 -0.721 0.477

70

From the above results we can see that both life insurance growth and PCL

insurance growth have a positive contribution to GDP growth. Also, both estimated

coefficients show strong statistical significance. Export growth and import growth do not

show very strong statistical relationship with GDP growth. Export growth shows a

positive relationship with GDP growth while import growth shows a negative

relationship with GDP growth. Percent of government expenditure to GDP shows

negative relationship with economic growth with strong statistically significance.

Both capital growth (approximated by investment share in GDP) and labor growth

(approximated by population growth) have shown positive contribution to economic

growth (approximated by GDP growth). But the estimated coefficient on Investment ratio

is statistically significant while the estimated coefficient on population growth is not

statistically significant.

Table 4.1.3 Estimation Results from OLS (US Data) - Labor Force Growth is Used as a Proxy of Labor Growth

R-square=0.7564 Adj R-square=0.6785 34 Observations

Dependent Variable= RGDPG


COEFFICIENT T-RATIO P-VALUE FDINVEST 0.786 3.258 0.003 LG 0.109 0.217 0.830 REXPG 0.003 0.090 0.929 RIMPG -0.021 -0.340 0.737 FDRGOV -1.373 -1.727 0.097 RLIFG 0.188 3.020 0.006 RPCLG 0.071 2.284 0.031 TIME 0.002 0.072 0.943 CONSTANT 1.860 1.342 0.192

When labor force growth is used as a measure of labor growth, the estimated

coefficient on labor force growth is much different than the estimated coefficient on

71

population growth. At the same time, the significance level of the estimated coefficient

on labor force is lowered significantly.

However, the signs and statistical significance level of the estimated coefficients

on all the other variables are very similar. Especially, here we can see the change in the

measure of the labor growth does not affect much the estimated coefficients on both life

insurance growth and PCL insurance growth. In either situation, they showed statistically

significant contribution to economic growth.

In the following part, the simultaneous equations are used to allow for the

interaction between GDP growth and insurance growth. Two sets of simultaneous

equations are run with either PG or LG in the first equation.

iii) Simultaneous Equations

The simultaneous equation system includes three equations.

1.

1876

543210


+++++++++=

TIMEFDRGOVREXPGRIMPGRPCLGRLIFGPGFDINVESTRGDPG

2.

2109876

543210

εβββββββββββ++++++

+++++=TIMEDSDURBANRFDWPARTSDRATIO

EDRRSSGfFDLEXPRGDPGSDINFRLIFG

3.

36

543210

εδδδδδδδ

+++++++=

TIMESDURBANRFDWPARTEDRPRATIORGDPGRPCLG

The estimated results are listed in the following tables (Table 4.1.4 to Table 4.1.6)

72

Table 4.1.4 Estimation Results from Simultaneous Equations—Equation 1 (US Data) – Population Growth is Used as a Proxy of Labor Growth

R-square=0.61098 34 Observations



COEFFICIENT T-RATIO P-VALUE FDINVEST 0.700 2.193 0.028 PG 8.896 1.356 0.175 RLIFG 0.130 1.198 0.231 RPCLG 0.250 3.262 0.001 RIMPG -0.034 -0.673 0.501 REXPG 0.041 0.925 0.355 FDRGOV -1.378 -1.829 0.067 TIME -0.013 -0.413 0.679 CONSTANT -7.157 -1.121 0.262

Here we will compare the results from the OLS and the results from the first

equation in the simultaneous equation system. All the estimated coefficients in the

simultaneous equation system remain the same signs as for those in the single equation

model. However, the statistical significance for some estimated coefficients changed. The

statistical significance of the estimated coefficient on PG increased. While the statistical

significance of the estimated coefficient on RPCLG increases, the statistical significance

of the estimated coefficient on RLIFG decreases a lot.

The statistical significance of the estimated coefficients of both IMPG and EXPG

increases. The statistical significance of the estimated coefficient on FDRGOV decreases

a little.

8 When instrument variables are used, the sum of RSS and ESS is not equal to TSS. The definition of R-square is

ESSRSSRSSR+

=2. It may not be a good measure of goodness fit of the model.

73



Dependent Variable= RLIFG


COEFFICIENT T-RATIO P-VALUE SDINF -2.923 -3.357 0.001 RGDPG 0.061 0.299 0.765 FDLEXP 0.869 0.575 0.565 RSSG -0.155 -1.536 0.125 EDR -13.721 -2.973 0.003 SDRATIO 268.660 2.208 0.027 FDWPART -233.140 -2.118 0.034 SDURBANR 7.631 1.625 0.104 D 1.058 0.986 0.324 TIME 0.157 1.521 0.128 CONSTANT 45.331 3.582 0.000

This is the second equation in the simultaneous equation system. It examines the

factors which affect real life insurance in force growth. We can also view this as a

demand growth function of life insurance.

The negative relationship between expected inflation growth and life insurance in

force growth shows that high expected inflation growth harms the purchase of life

insurance. Higher GDP growth contributes positively to life insurance purchase growth,

although it is not statistically significant. When the income of an economy increases, life

insurance may be more affordable to the agents in this economy. This is why the higher

GDP growth may lead to higher growth in life insurance in force. Life expectancy is

positively related to life insurance purchase but with very low statistical significance.

This means, when people expect to live longer, they purchase more life insurance. Social

security growth has a negative contribution to life insurance purchase growth. This means

74

when social security grows, it will crowd out the need for life insurance purchase. This is

very meaningful. Third level enrollment has a negative contribution to life insurance in

force growth. This is perplexing at the first sight. However, our explanation for this is as

follows. When people get more education, especially higher education (remember EDR is

the third level enrollment rate in proper age group), they tend to have a better paid job

with a better benefit package. This may reduce their need for life insurance. Dependant

ratio has a positive contribution to life insurance purchase growth. This is meaningful

because when there are more dependants for the primary breadwinner, there is a greater

need for life insurance to cover the risk of early death.

Women participation ratio has a negative contribution to life insurance purchase.

The relationship here is also statistically strong. When women join the labor force, it

spreads the risk of the loss due to the death of primary breadwinner, usually the husband

in a household. A higher ratio of urban population in the whole population contributes to

a higher life insurance in force growth. When there are more people living in the urban

area, there is less “family-tie”, which gives family’s members in need help. This probably

explains why higher urban population ratio the growth of life insurance in force.

D is the variable that defines the higher inflation period in the US economy. It is

from 1974 to 1984. During the high inflation period, people seemed to have a higher

demand for more life insurance.

75



Dependent Variable= RPCLG


COEFFICIENT T-RATIO P-VALUE RGDPG 0.887 1.852 0.064 PRATIO -0.261 -1.462 0.144 FDWPART 153.340 0.619 0.536 SDURBANR -10.236 -1.035 0.301 EDR -0.107 -0.016 0.988 TIME -0.091 -0.573 0.567 CONSTANT 3.565 0.183 0.855

The third equation explains the factors that contributes to

property/casualty/liability insurance growth. First, GDP growth has a positive

contribution to PCL insurance growth and the relationship is very strong statistically.

More wealth is accumulated as GDP grows. Therefore there is a greater need for

protection against the loss.

Profit ratio is negatively related to PCL insurance growth. This supports those

literatures stating that there are writing cycles in PCL insurance. Here, third level

enrollment ratio seems to have no effect on the demand for PCL insurance.

Woman participation ratio in labor force is positively related to PCL insurance

purchase. When more women join the labor force, the total income of a household may

increase. There is a higher demand for PCL insurance to protect the increased wealth.

Urban population ratio has a negative contribution to PCL insurance purchase growth.

76

The following part shows the results from the following simultaneous equation

system, which replaces PG with LG in the first equation to see whether there is any

change in the results.

1.

1876

543210


+++++++++=

TIMEFDRGOVREXPGRIMPGRPCLGRLIFGLGFDINVESTRGDPG

2.

2109876

543210

εβββββββββββ++++++

+++++=TIMEDSDURBANRFDWPARTSDRATIO

EDRRSSGfFDLEXPRGDPGSDINFRLIFG

3.

36

543210

εδδδδδδδ

+++++++=

TIMESDURBANRFDWPARTEDRPRATIORGDPGRPCLG

Table 4.1.7 Estimation Results from Simultaneous Equations—Equation 1 (US Data) – Labor Forth Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE FDINVEST 0.781 2.468 0.014 LG -0.063 -0.134 0.893 RLIFG 0.180 1.596 0.110 RPCLG 0.271 3.855 0.000 RIMPG -0.048 -0.980 0.327 REXPG 0.040 0.905 0.365 FDRGOV -0.933 -1.275 0.202 TIME 0.026 0.993 0.321 CONSTANT 1.097 0.903 0.367

First, we will compare Table 4.1.3 with Table 4.1.7. Table 4.1.3 is the OLS

regression results with LG as a proxy of the labor growth. Table 4.1.7 is the regression

results from the first equation in the simultaneous equation system also with LG as a

proxy of the labor growth. We can see all the estimated coefficients remain the same sign

77

except the one on LG, which changes from a positive sign to a negative sign, although

neither one is statistical significant.

The statistical significance level of the estimated coefficients on both RIMPG and

REXPG increases. Here we can see in the simultaneous equation system, the statistical

significance of the estimated coefficient on RLIFG decreases and the statistical

significance of the estimated coefficient on RPCLG increases. This is consistent with

what we found when we compare the results from OLS with the results from the

simultaneous equation system in the case that PG is used as a measure of labor growth.

Therefore, we may make the conclusion that the single equation over estimated

the coefficient on RLIFG but under estimated the coefficient on RPCLG.

Second, we will compare Table 4.1.4 and Table 4.1.7. Both of them are the first

equation in the three equation system. However, Table 4.1.4 is the results when PG is

used as a proxy of labor growth while Table 4.1.7 is the results when LG is used as a

proxy of labor growth. Both tables show that life insurance and PCL insurance contribute

positively to economic growth. Also, the statistical significance level for the estimated

coefficients of RPCLG is higher than the one for the estimated coefficients of RLIFG.

The following two tables (Table 4.1.8 and Table 4.1.9) are the regression results

of the second and third equations when LG is used as a proxy of labor growth.

78


R-square=0.4699 34 Observations Dependent Variable= RLIFG

VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE SDINF -2.974 -3.425 0.001 RGDPG 0.082 0.420 0.674 FDLEXP 0.693 0.455 0.649 RSSG -0.155 -1.526 0.127 EDR -13.970 -3.036 0.002 SDRATIO 272.930 2.231 0.026 FDWPART -220.580 -2.046 0.041 SDURBANR 7.777 1.687 0.092 D 1.065 0.983 0.326 TIME 0.162 1.572 0.116 CONSTANT 45.954 3.645 0.000



Dependent Variable= RPCLG


COEFFICIENT T-RATIO P-VALUE RGDPG 1.095 2.361 0.018 PRATIO -0.263 -1.506 0.132 FDWPART 161.970 0.700 0.484 SDURBANR -8.474 -0.922 0.356 EDR -1.789 -0.279 0.780 TIME -0.067 -0.451 0.652 CONSTANT 7.766 0.425 0.671

We can see that Table 4.1.8 and Table 4.1.9 are very similar with Table 4.1.5 and

Table 4.1.6. The change of PG to LG almost has no effect on the results from the second

and the third equations.

We can make the following conclusion from the US data. The US data support

our theoretical models in the sense that both life insurance and non life insurance

79

contribute to economic growth. Yet, from the simultaneous equation system, the evidence

for life insurance is not as strong as the one for non life insurance.

80

II. Analysis of Korean Data

i) Unit Root Test

Table 4.2.1 Unit Root Test Results (Korean Data)

Variables PP Test Statistics DF Test Statistics

WPART -2.85 -2.8 NLNLR -2.95 -2.95 LNLR -1.61 -0.29 INF -2.25 -2.81 ED -1.61 -1.47 LEXP -1.96 -1.72 RGDPG -4.88* -3.19* PG -1.94 -1.75 RLIFG -5.79* -3.87* RNONLG -3.60* -3.58* RGOV -2.28 -2.34 INVEST -1.91 -1.8 DRATIO -0.79 -2.88 LG -4.47* -4.47* REXPG -4.09* -4.08* RIMPG -4.76* -2.43 URBANR 2.54 -0.92


For the variables that can not reject the null hypothesis of the existence of a unit

root at 90% significant level, the first difference of that variable is taken and a unit root

test is conducted on it in Table 4.2.1. The results show that the null hypothesis can be

rejected at the 90% significant level for the first difference of INVEST, PG, INF, LEXP,

ED, NLNLR, LNLR, RGOV, and WPART. So for any equations to include these

variables, the first difference of those variables will be used for the regressions. For the

81

variables with non-stationary first difference, the second difference is taken and a unit

root test is conducted on it. These include the variables DRATIO, URBANR and INF.

The unit root tests for all three variables show that the second difference can reject the

null of the existence of unit root at 90% significance level.

ii) Simple OLS Regression

The following is the estimated equations.

1.


+++++++++=

TIMEFDRGOVREXPGRIMPGRNONLGRLIFGFDPGFDINVESTRGDPG

876

543210

2.


+++++++++=

TIMEFDRGOVREXPGRIMPGRNONLGRLIFGLGFDINVESTRGDPG

876

543210

The first equation uses PG as a measurement of labor growth and the second

equation uses LG as a measurement of labor growth.

Table 4.2.2 is the estimated coefficients and the t statistics based on the Newy

West estimator.

82

Table 4.2.2 Estimation Results from OLS (Korean Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE FDINVEST 0.505 1.398 0.188 FDPG 0.874 0.390 0.703 RLIFG 0.006 3.968 0.002 RNONLG 0.089 2.702 0.019 REXPG 0.061 0.647 0.530 RIMPG 0.041 0.435 0.671 FDRGOV -2.211 -2.187 0.049 TIME -0.133 -1.642 0.127 CONSTANT 6.255 6.205 0.000

From the above result we can see that both the estimated coefficients on

FDINVEST and FDPG show positive sign, which is what we expect. However, neither

one shows strong statistical significance, especially for the estimated coefficient on

FDPG. Both life insurance growth and non life insurance growth show positive

contribution to economic growth and both of the estimated coefficients are statistically

significant. Both real export growth and real import growth show positive contribution to

the economic growth, but neither of them shows strong statistical significance. The

estimated coefficient on GDRGOV is negative and statistically strong. This means an

increase in the percentage of government expenditure will decrease GDP growth.

The results in Table 4.2.3 show when we use LG in replace of PG.

83

Table 4.2.3 Estimation Results from OLS (Korean Data) - Labor Force Growth is Used as a Proxy of Labor Growth

From the above regression result, we can see that for the Korean economy, labor

force growth is a better proxy of labor growth than the population growth. The

significance level of the estimated coefficient on LG is much higher than the one on PG

from the first table. In this regression, life insurance growth and non life insurance

growth also show a positive contribution to economic growth with strong statistical

significance. At the same time, both regressions show that life insurance growth has a

stronger statistical relationship with GDP growth than non life insurance growth.

The change of PG to LG does not change the results on other estimated

coefficients either.

In the following part, we will present the results from simultaneous equations.

Both LG and PG are used in the simultaneous equation system to compare the

regression result.


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE FDINVEST 0.383 1.130 0.281 LG 0.495 2.565 0.025 RLIFG 0.006 4.558 0.001 RNONLG 0.049 1.918 0.079 REXPG 0.023 0.248 0.808 RIMPG 0.064 0.726 0.482 FDRGOV -2.520 -2.537 0.026 TIME -0.113 -1.736 0.108 CONSTANT 5.686 10.500 0.000

84

iii) Simultaneous Equations 1.

1876

543210 )(/εααα

αααααα++++

+++++=TIMEFDRGOVREXPG

RIMPGRNONLGRLIFGFDPGLGFDINVESTRGDPG

2.

29876

543210

εββββββββββ

++++++++++=

TIMESDINFFDEDFDWPARTSDURBANRSDRATIOFDLEXPFDLNLRRGDPGRLIFG

3.

36

543210

εδδδδδδδ

+++++++=

TIMEFDWPARTFDEDSDURBANRFDNLNLRRGDPGRNONLG

The regression results are shown in the following tables (Table 4.2.4 to Table 4.2.6). Table 4.2.4 Estimation Results from Simultaneous Equations—Equation 1 (Korean Data) - Labor Force Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE FDINVEST 0.435 1.688 0.091 LG 0.486 1.827 0.068 RLIFG 0.004 0.974 0.330 RNONLG 0.049 0.979 0.328 REXPG 0.028 0.464 0.643 RIMPG 0.064 0.912 0.362 FDGOV -2.068 -2.510 0.012 TIME -0.128 -2.391 0.017 CONSTANT 5.833 6.105 0.000

Comparing the result of OLS regression and the one from the first equation of the

simultaneous equation system (Table 4.2.4), we can see that all the estimated coefficient

remain the same sign. However, the statistical significance of most estimated coefficients

changes from one method to the other method. We can notice here, the statistical

85

significance for the estimated coefficients on both life and non life insurance growth is

lower than before. The statistical significance for the estimated coefficient on labor force

growth is also lower than before, although it still remains at a high statistical significance

level. But the statistical significance of the estimated coefficient on FDININVEST

increases. The statistical significance of the estimated coefficients on both RIMPG and

REXPG increases, yet they are still not statistically significant. All the other estimated

coefficients remain at the similar significance level.

Table 4.3.5 Estimation Results from Simultaneous Equations—Equation 2 (Korean Data) - Labor Force Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE RGDPG -4.068 -0.599 0.549 FDLNLR -2.830 -1.276 0.202 FDLEXP -216.340 -1.372 0.170

SDRATIO 178.710 0.986 0.324 SDURBANR 70.325 1.165 0.244 FDWPART -10.136 -0.283 0.777

FDED -2.317 -0.637 0.524 SDINF -53.141 -3.089 0.002 TIME -6.647 -1.727 0.084

CONSTANT 252.440 1.836 0.066

The second equation explains the factors that affect the growth of life insurance in

force. This is the demand growth function of the life insurance. Interestingly, for the

Korean Economy, GDP growth has a negative contribution to life insurance in force

growth. Put it another way, when GDP growth increases, the growth for the demand of

life insurance decreases. We need some explanation here for this result. Life insurance

net loss ratio is negatively correlated with life insurance in force growth. This means

there is no counter writing cycle for the life insurance industry of the Korean economy.

86

Expected life expectance is negatively correlated with growth of life insurance in

force. When expected life expectancy increases, the demand for life insurance grows

slower. Dependant ratio is positively correlated with life insurance in force growth. This

means when dependant ratio increases, the demand for life insurance grows faster. This is

what we expect. The estimated coefficient on SDURBANR is positive, which means

when there are more population living in the urban area, the growth of life insurance in

force will increase. The estimated coefficient on women participation ratio is negative.

This means when more women participate in the labor force, it will decrease the growth

of life insurance in force. This is what we expect. Here, we also see that participation in

higher education will lower the growth rate of life insurance demand. This result is

similar with the result from the US economy.

At last, expected inflation growth will decrease the growth of life insurance in

force. It also shows a great statistical significance. This means high expected inflation

harms life insurance growth.

Table 4.2.6 Estimation Results from the Simultaneous Equations—Equation 3 (Korean Data) - Labor Force Growth is Used as a Proxy of Labor Growth


Dependent Variable= RNONLG


COEFFICIENT T-RATIO P-VALUE RGDPG 0.834 1.808 0.071 FDNLNLR -0.177 -1.170 0.242 SDURBANR -10.007 -1.897 0.058 FDED 0.872 2.560 0.010 FDWPART 6.822 2.221 0.026 TIME -0.710 -2.747 0.006 CONSTANT 11.703 2.208 0.027

87

The third equation explains the factors that influence the growth of non life

insurance. First, we can see that the estimated coefficient on RGDPG is positive and

statistically significant. This means GDP growth in Korean economy contributes to non

life insurance growth. Second, the net loss ratio of non life insurance is negatively related

to non life insurance growth. This is shown by a negative and statistically significant

estimated coefficient on FDNLNLR. This is actually contrary to what we found in the US

economy, where the data shows that there is counter writing cycle in non life insurance.

Usually, a counter writing cycle signals the competitiveness of the insurance market.

Comparing the results from Korean and US data, we may conclude that the US non life

insurance is more competitive than the one in the Korean economy.

The estimated coefficient on SDURBANR is negative and statistically significant.

This means for the Korean economy, when there are more population living in the urban

area, there is a slower growth in demand for non life insurance. Both higher education

participation and women participation in labor force have positive and significantly

strong contribution to the growth of non life insurance demand. These make sense. When

more females join the labor force, the income of each household may increase. This

requires more need for insurance to protect household wealth from risk of loss.

Then LG is replaced by PG in the first equation and we run the whole equation

system again. The results are shown in Table 4.2.7 to Table 4.2.9.

88

Table 4.2.7 Estimation Results from the Simultaneous Equations—Equation 1 (Korean Data) - Population Growth is Used as a Proxy of Labor Growth



VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE FDINVEST 0.565 2.071 0.038 FDPG 2.055 0.636 0.525 RLIFG 0.002 0.518 0.605 RNONLG 0.088 1.816 0.069 REXPG 0.060 0.970 0.332 RIMPG 0.036 0.486 0.627 FDGOV -1.695 -1.943 0.052 TIME -0.151 -2.518 0.012 CONSTANT 6.655 4.644 0.000



Dependent Variable= RLIFG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE RGDPG -4.075 -0.596 0.551 FDLNLR -2.751 -1.234 0.217 FDLEXP -215.320 -1.362 0.173 SDRATIO 178.320 0.980 0.327 SDURBANR 70.197 1.158 0.247 FDWPART -10.923 -0.303 0.762 FDED1 -2.259 -0.619 0.536 SDINF -53.073 -3.074 0.002 TIME -6.628 -1.711 0.087 CONSTANT 251.700 1.820 0.069

89



Dependent Variable= RNONLG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE RGDPG 0.813 1.765 0.078 FDNLNLR -0.173 -1.173 0.241 SDURBANR -9.617 -1.860 0.063 FDED1 0.844 2.500 0.012 FDWPART 7.676 2.553 0.011 TIME -0.705 -2.728 0.006 CONSTANT 11.749 2.216 0.027

What we can see here is that for Korea, the change from LG to PG almost has no

affect on the regression result of the second and third equation in the system.

However the results from the first equation (which represent the economic growth

function of each country) do have some significant change on estimated coefficients.

First, when LG is used, the estimated coefficients on LG are much more

significant than those on PG when PG is used, which prove that LG is a more precise

proxy of labor growth here. Use of PG or LG does not alter any sign on the estimated

coefficients. It only changes the significance level on some estimated coefficients. For the

Korean economy, when PG is used in the economic growth function, the significance

level on the estimated coefficients of non life insurance growth increased. At the same

time, the significance level on the estimated coefficients of life insurance growth

decreased. From the Korean data, we can have the following conclusion. Both life

insurance and non life insurance growth contribute to the growth of the Korean economy.

But the statistical relationship found in the simultaneous equation system is not as strong

as the one from the OLS regression. The change of labor growth proxy does not change

the above conclusion.

90

III. Analysis of Swedish Data

i) Unit Root Test

Table 4.3.1 Unit Root Test Results (Swedish Data)

Variables PP Test Statistics DF Test Statistics WPART 1.39 0.99 INF -1.37 -2.04 LEXP -3.76* -2.73 RGDPG -3.73* -3.63* PG -1.89 -1.49 RLIFG -4.71* -4.71* RNONLG -5.95* -4.24* RGOV -2.28 -2.24 INVEST -3.38* -3.25* REXPG -4.07* -2.18 DRATIO -1.01 -1.38 LG -3.43* -2.39 URBANR -4.15* -3.25*


For the variables that the unit root test can not reject the null hypothesis at 90%

significant level, the first difference is taken and a unit root test on the first difference of

the variable is conducted In Table 4.3.1. These include woman participation in the labor

force, expected inflation, population growth, the ratio of government expenditure to GDP

and dependant ratio.

But the unit root test on the first difference of population growth and dependant

ratio concludes that a unit root may be present in the first difference of both variables. I

conduct the unit root test until I found that the third difference of both variables can reject

91

the null at 90% significance level. Therefore, we include the third difference of both

variables into the regression analysis.



1.

εαααααααα

++++++++=

TIMEFDRGOVREXPGRNONLGRLIFGTDPGINVESTRGDPG

76

543210

2.

εαααααααα

++++++++=

TIMEFDRGOVREXPGRNONLGRLIFGLGINVESTRGDPG

76

543210

The estimated coefficients and the t statistics based on the Newy West estimator are

shown in Table 4.3.2.

Table 4.3.2 Estimation Results from OLS (Swedish Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE INVEST 0.500 7.920 0.000 TDPG 1.847 0.292 0.775 RLIFG -0.083 -2.905 0.012 RNONLG 0.058 2.042 0.062 REXPORTG 0.057 4.914 0.000 FDRGOV -1.839 -11.070 0.000 TIME -0.032 -1.720 0.109 CONSTANT -8.979 -5.239 0.000

Here we can see that the estimated coefficient on TDPG is positive but the

statistical significance is really low. This shows that PG is not a good proxy of labor

growth. For the Swedish economy, the estimated coefficient on real life insurance in

92

force is negative with high statistical significance. It means life insurance growth will

hinder economic growth. This finding is different with the US and Korean economy. It is

also against the theoretical model’s prediction in the first part of the dissertation.

However, the estimated coefficient on real non life insurance has a positive sign with

strong statistical significance. Also the estimated coefficients on both export growth and

FDRGOV show the expected signs with high statistical significance.

Now let’s see the following result when we replace TDPG with LG in Table 4.3.3.

Table 4.3.3 Estimation Results from OLS (Swedish Data) - Labor Force Growth is Used as a Proxy of Labor Growth


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE INVEST 0.430 6.218 0.000 LG 0.268 1.307 0.214 RLIFG -0.077 -2.782 0.016 RNONLG 0.062 2.166 0.049 REXPORTG 0.057 4.290 0.001 FDRGOV -1.791 -9.129 0.000 TIME -0.026 -1.222 0.244 CONSTANT -7.617 -4.571 0.001

After we use LG to replace TDPG, the significance level of the estimated

coefficient on LG increases a lot. All the signs and statistical significance level of the

estimated coefficients on other variables do not change much.

In the following part, we will analyze the data using the simultaneous equation

method. Both LG and PG are used in the simultaneous equation system to compare the

regression result.

93


176

543210 )(/εαα

αααααα+++

+++++=TIMEFDRGOV

REXPGRNONLGRLIFGTDPGLGINVESTRGDPG

2.

26

543210

εβββββββ

+++++++=

TIMEFDWPARTFDINFURBANRLEXPRGDPGRLIFG

3.

343210 εδδδδδ +++++= TIMEFDWPARTURBANRRGDPGRNONLG

The results from the simultaneous equation estimation are reported in Table 4.3.4

to Table 4.3.9. Table 4.3.4 to Table4.3.6 show the results when LG is used in the first

equation; While Table 4.3.7 to Table 4.3.9 show the results when TDPG is used in the

first equation.

Table 4.3.4 Estimation Results from SME—Equation 1 (Swedish Data) - Labor Force Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE INVEST 0.422 4.392 0.000 LG 0.317 1.224 0.221 RLIFG -0.070 -1.060 0.289 RNONLG 0.074 1.698 0.089 REXPORTG 0.059 2.264 0.024 FDRGOV -1.794 -6.509 0.000 TIME -0.022 -0.689 0.491 CONSTANT -7.589 -3.400 0.001

Table 4.3.4 shows the estimation result of the first equation. It reports the factors

that contribute to the growth of the Swedish economy. The estimated coefficients on

94

INVEST and LG are both positive. There are very similar with the results we get from

the single equation estimation. The estimated coefficients on RLIFG and RNONLG

remain the same signs and similar values with the one from the single equation estimation.

However, the statistical significance of the estimated coefficients on both variables is

lowered compared with the single equation result. In the simultaneous equation system,

we still can get the conclusion that real life insurance growth will hinder real GDP

growth while real non life insurance growth will contribute to real GDP growth positively.

Export growth positively contributes to economic growth and the estimated coefficient is

statistically significant, just as shown in the OLS. From the simultaneous equation system

we can also conclude that a higher ratio of government spending to GDP has negative

contribution to GDP growth. This is shown by the negative and statistical significant

estimated coefficient on FDRGOV.





COEFFICIENT T-RATIO P-VALUE RGDPG -0.092 -0.088 0.930 LEXP 5.627 0.903 0.366 URBANR -10.136 -1.937 0.053 FDINF -0.438 -0.131 0.896 FDWPART 982.270 1.347 0.178 QDRATIO 27.144 0.889 0.374 TIME -0.075 -0.057 0.954 CONSTANT 413.680 0.564 0.573

Table 4.3.5 shows the factors that influence life insurance in force growth. The

estimated coefficient on RGDPG is negative and almost has no statistical significance.

This means an increase in real GDP growth has no effect on real life insurance in force

95

growth. The estimated coefficients on LEXP, FDWPART and QDRATIO are all positive.

Therefore, increase in life expectancy, higher woman participation ratio in labor force

and higher dependant ratio all contribute to life insurance in force growth. The estimated

coefficient on URBANR is negative and statistically significant. More people living in

the urban area will decrease the growth of life insurance in force growth. This is different

with what we found in the US and Korean economy. Although the estimated coefficient

on FDINF is negative but it almost has no statistical significance. This means expected

inflation does not affect the growth of life insurance in force. This is also different with

what we found in the US and Korean economy.


R-square=0.1887 21

Observations Dependent Variable= RNONLG


COEFFICIENT T-RATIO P-VALUE RGDPG -1.188 -1.606 0.108 URBANR -8.5209 -1.651 0.099 FDWPART 621.87 0.8116 0.417 TIME 0.46563 0.9329 0.351 CONSTANT 704.12 1.666 0.096

Table 4.3.6 is the regression result of the factors that influence the growth of the

non life insurance growth. The estimated coefficients on RGDPG and URBANR are both

negative and statistically significant. This means both real GDP growth and urban

population growth will lead to a decrease in non life insurance growth. The estimated

coefficient on FDWPART is positive but not statistically significant. An increase in

women participation ratio will increase the growth of non life insurance. This is

consistent with what we found in US and Korean data.

96

The following is the regression result when PG is used as a proxy of labor growth

in replacement of LG from Table 4.3.7 to Table 4.3.9.

Table 4.3.7 Estimation Results from SME—Equation 1(Swedish Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE INVEST 0.501 6.590 0.000 TDPG 3.231 0.483 0.629 RLIFG -0.102 -1.579 0.114 RNONLG 0.055 1.152 0.249 REXPORTG 0.059 2.234 0.025 FDRGOV -1.820 -6.542 0.000 TIME -0.028 -0.947 0.344 CONSTANT -8.950 -4.348 0.000

Table 4.3.8 Estimation Results from SME—Equation 2 (Swedish Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE RGDPG -0.098 -0.094 0.925 LEXP 5.192 0.844 0.399 URBANR -10.448 -2.026 0.043 FDINF6 -0.414 -0.125 0.900 FDWPART 975.830 1.375 0.169 QDRATIO 28.024 0.926 0.354 TIME 0.014 0.011 0.992 CONSTANT 471.740 0.654 0.513

97

Table 4.3.9 Estimation Results from SME—Equation 3 (Swedish Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE RGDPG -1.197 -1.614 0.106 URBANR -8.628 -1.676 0.094 FDWPART 609.020 0.806 0.420 TIME 0.466 0.941 0.347 CONSTANT 713.050 1.692 0.091

What we can see here is that for Sweden, change from LG to PG almost has no

affect on the regression result of the second and third equation in the system.

However the results from the first equation (which represents the economic

growth function of each country) do have some significant change on estimated

coefficients.

First, when LG is used, the estimated coefficient on LG is much more significant

than that on PG when PG is used, which shows that LG is a better proxy of labor growth.

Change from LG to PG does not alter any sign on the estimated coefficients. It only

changes the statistically significance on some estimated coefficients. This is similar with

the result we found in the Korean data. However, when PG is used in the economic

growth function, the statistical significance on the estimated coefficient of life insurance

growth increased. But the statistical significance on the estimated coefficients of non life

insurance growth decreased. This is different with what we have seen in the Korean data.

Here we have to acknowledge that the second and third equations show very low

explanation power. However, I have included all the variables which are available.

98

From the analysis of the Swedish data, we find that life insurance and non life

insurance have opposite effect on the development of the Swedish economy. The

development of life insurance harms the economic growth but the development of the

non life insurance helps the economic growth. Also, the statistical support for non life

insurance’s role in helping the economic growth does not change by the empirical

methods we employed.

99

IV. Analysis of the German Data

i) Unit Root Test Results Table 4.4.1 Unit Root Test Results (German Data)

Variables PP Test Statistics DF Test Statistics WPART -1.79 -1.64 INF -2.19 -2.62 LEXP -2.92 -2.84 RGDPG -3.97* -2.62 PG -1.53 -2.01 LG -4.03* -3.48* RLIFG -4.76* -4.77* RNONLG -4.35* -3.90* RGOV -3.33* -2.8 INVEST -3.03 -2.59 DRATIO -0.12 -0.7 URBANR -1.34 -2.34 REXPG -5.24* -3.02 RIMPG -5.27* -3.27*


For the variables that the unit root test can not reject the null hypothesis at 90%

significant level, the first difference is taken and a unit root test on the first difference of

the variable is conducted in Table 4.4.1. These include the following variables:

population growth, dependant ratio, woman participation in the labor force, expected

inflation, life expectancy ratio, urban population ratio in the whole population and

investment ratio.

But the unit root test on the first difference of population growth, dependant ratio,

urban population ratio and expected inflation concludes that a unit root may still be

100

present in the first difference of the above variables. Then the unit root tests on the

second difference of the above variables are conducted. But the unit root test of the

second difference of population growth and dependant ratio still can not reject the

presence of unit root at 90% significance level. Therefore the third difference of both

variables is taken and the unit root test is conducted on them. The test shows that both

can reject the null at 90% significance level.



1.

εαααααααααα

++++++++++=

TIMEDRGOVREXPGRIMPGRNONLGRLIFGFDINVESTTDPGRGDPG

8876

543210

2.

εαααααααααα

++++++++++=

TIMEDRGOVREXPGRIMPGRNONLGRLIFGFDINVESTLGRGDPG

8876

543210

The estimated coefficients and the t statistics based on the Newey West estimator are

demonstrated in Table 4.4.2.

101

Table 4.4.2 Estimation result from OLS (German Data) – Population Growth is Used as a Proxy of Labor Growth


Dependant Variable=RGDPG


COEFFICIENT T-RATIO P-VALUE FDINVEST 0.139 0.526 0.605 TDPG -9.341 -1.038 0.313 RLIFG -0.632 -3.927 0.001 RNONLG 0.319 4.077 0.001 RIMPG 0.745 3.649 0.002 REXPG -0.725 -3.635 0.002 RGOV -2.270 -6.292 0.000 D -1.354 -1.254 0.226 TIME -0.058 -0.988 0.336 CONSTANT 52.448 6.244 0.000

The estimated coefficient on TDPG is negative, although it is not statistically

significant. This is contrary to economic theory. This shows that population growth is

really not a proper proxy of labor growth for German data. Although the estimated

coefficient on FDINVEST shows the expected sign, its statistical significance level is

really low. The estimated coefficient on RLIFG is negative and the estimated coefficient

on RNONLG is positive. Both of them show strong statistical significance. This is similar

to what we found in the Swedish data--real life insurance shows a negative contribution

to the real GDP growth. The estimated coefficient on RIMPG is positive and is

statistically significant. But the estimated coefficient on REXPG is negative and

statistically significant. This means import growth contribute to economic growth but

export growth harms economic growth in German economy. As in all the other three

countries, higher government expenditure ratio harms economic growth, which is shown

by the negative and statistically significant estimated coefficient on RGOV. D is a

102

dummy variable which define the period after the merge of East and West Germany. The

estimated coefficient on D is negative, which shows the merge may require a period of

adjustment and hinders economic growth.

Table 4.4.3 Estimation Results from OLS (German Data) – Labor Forth Growth is Used as a Proxy of Labor Growth


Dependant variable=RGDPG


COEFFICIENT T-RATIO P-VALUE FDINVEST 0.786 3.224 0.005 LG 0.323 5.311 0.000 RLIFG -0.092 -0.583 0.567 RNONLG 0.097 1.042 0.311 RIMPG 0.151 0.942 0.359 REXPG -0.111 -0.719 0.481 RGOV -1.074 -3.571 0.002 D -1.030 -1.370 0.188 TIME -0.015 -0.332 0.744 CONSTANT 24.630 3.711 0.002

In Table 4.4.3, the estimated coefficients on both FDINVEST and LG are positive

and statistically significant when TDPG is replaced by LG. This is consistent with

economic theory. Therefore, LG is a much better proxy of labor growth than PG. Like in

the first regression, life insurance showed a negative contribution to GDP growth while

non life insurance showed a positive contribution to GDP growth. But neither of them has

shown strong statistical significance. The signs of the estimated coefficients on both

RIMPG and REXPG remain the same but with much lower statistical significance level.

The estimated coefficient on RGOV remains the same sign and similar statistical

significance level as shown in the first equation.

103

The following part shows the results from the simultaneous equation system.

Table 4.4.4 to Table 4.4.6 show the results when LG is used in the first equation; while

Table 4.4.7 to Table 4.4.9 show the results when TDPG is used in the first equation.


198765

43210 )(/εααααα

ααααα+++++

+++++=timeDRGOVREXPGRIMPG

RNONLGRLIFGTDPGLGFDINVESTRGDPG

2.

265

43210

εβββββββ

+++++++=

TIMEFDWPARTSDINFSDURBANRFDLEXPRGDPGRLIFG

3.

343210 εδδδδδ +++++= TIMEFDWPARTSDURBANRRGDPGRNONLG

Table 4.4.4 Estimation Results from SME—Equation 1 (German Data) - Labor Force Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE FDINVEST 0.731 2.538 0.011 LG 0.307 3.398 0.001 RLIFG -0.207 -0.900 0.368 RNONLG 0.152 0.959 0.338 RIMPG 0.156 0.835 0.404 REXPG -0.118 -0.635 0.526 RGOV -1.095 -2.203 0.028 D -0.602 -0.577 0.564 TIME -0.046 -0.690 0.490 CONSTANT 25.894 2.238 0.025

Compared the results in Table 4.4.4 with the result from the single OLS

regression, all the signs of the estimated coefficients remain the same, although the

statistical significance levels change for some variables. The statistical significance of the

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estimated coefficient on RLIFG increases compared with the OLS result. We still have

the same conclusion -- expansion in the life insurance sector shows negative effect on the

GDP growth, although the expansion in the non life sector shows positive contribution to

the economy growth. This is similar with what we found in the Swedish economy. The

statistical significance of the estimated coefficient on D decreases a lot compared with

the OLS result.

Table 4.4.5 Estimation Results from SME—Equation 2 (German Data) - Labor Force Growth is Used as the Proxy of Labor Growth

R-square=0.6126 28

Observations Dependent Variable= RLIFG


COEFFICIENT T-RATIO P-VALUE RGDPG 0.080 0.465 0.642 FDLEXP -0.213 -0.074 0.941 SDURBANR -3.860 -0.986 0.324 SDINF 1.595 2.488 0.013 FDWPART -58.779 -0.477 0.633 D 3.255 2.646 0.008 QDRATIO -8.756 -0.776 0.438 TIME -0.316 -4.399 0.000 CONSTANT 9.652 9.665 0.000

Table 4.4.5 shows the regression result of the factors that affect the growth of life

insurance in force. The estimated coefficient on RGDPG is positive. This means an

increase in real GDP growth will lead to an increase in the growth of life insurance in

force. But the statistical relationship is not significant here. Life expectancy almost has

no influence on the growth of life insurance in force, which is shown by a negative yet

not statistically significant estimated coefficient on FDLEXP. The estimated coefficient

on SDURBANR is negative. This means more population living in the urban area

decrease the growth of life insurance in force. Strangely, here we see that high expected

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inflation does not decrease the growth of life insurance in force but rather increases it.

This is reflected by the positive estimated coefficient on SDINF with strong statistical

significance. When there are more women joining in the labor force, the growth of life

insurance in force decreases. This is consistent with our expectation. After the East and

West Germany merged, there is higher growth in life insurance in force growth. This is

reflected in the positive sign before D with a very strong statistical significance. Probably,

there is much potential demand in East Germany which was not met before the merge.

But dependant ratio shows a negative relationship with the growth of life

insurance in force. This is not consistent with the expectation of economic theory.

Table 4.4.6 Estimation Results from SME—Equation 3 (German Data) - Labor Force Growth is Used as a Proxy of Labor Growth

R-square=0.3565 28

Observations Dependent Variable= RNONLG

VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE

RGDPG 0.788 2.336 0.019SDURBANR -0.757 -0.096 0.923FDWPART -67.131 -0.282 0.778D -1.804 -0.789 0.430TIME -0.041 -0.308 0.758CONSTANT 2.765 1.746 0.081

Table 4.4.6 is the regression result from the third equation. It shows the factors

that influence the growth of non life insurance. The estimated coefficient on RGDPG is

positive and statistically strong. This means economic growth increases non life

insurance growth for German economy. The estimated coefficients on SDURBANR,

FDWPART and D are all negative but not statistically significant. More population living

in urban area and more woman participation in labor force will lead to a decrease in non

life insurance growth. The negative sign of the estimated coefficient on D shows that

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after the merge of two economies, the growth for the demand of non life insurance

decreases.

Table 4.4.7 to Table 4.4.9 are the regression results when PG is used as a proxy of labor

growth.

Table 4.4.7 Estimation Results from SME—Equation 1 (German Data) - Population Growth is Used as a Proxy of Labor Growth




COEFFICIENT T-RATIO P-VALUE FDINVEST 0.105 0.328 0.743 TDPG 0.348 0.027 0.978 RLIFG -0.547 -2.463 0.014 RNONLG 0.773 4.112 0.000 RIMPG 0.553 3.782 0.000 REXPG -0.508 -3.500 0.000 RGOV -1.580 -2.917 0.004 D -0.108 -0.069 0.945 TIME -0.023 -0.242 0.809 CONSTANT 35.445 2.820 0.005





COEFFICIENT T-RATIO P-VALUE RGDPG 0.348 1.570 0.117 FDLEXP 0.287 0.091 0.927 SDURBANR -5.146 -1.227 0.220 SDINF 1.770 2.555 0.011 FDWPART -177.200 -1.237 0.216 D 3.206 2.465 0.014 QDRATIO -16.817 -1.355 0.175 TIME -0.314 -4.131 0.000 CONSTANT 9.156 8.411 0.000

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COEFFICIENT T-RATIO P-VALUE RGDPG 0.39699 0.9851 0.325 SDURBANR 5.4046 0.8113 0.417 FDWPART 174.87 0.6769 0.498 D -1.2815 -0.552 0.581 TIME -6.37E-02 -0.4719 0.637 CONSTANT 3.2233 1.953 0.051

For the German economy, when PG is used in the economic growth function in

stead of LG, the results for all three equations have great change. Although there is no

sign change in the estimated coefficients in the first equation, there is some sign change

in the estimated coefficients of the second and the third equation. When PG is used in the

economic growth equation, the regression results of the first equation shows that there is

almost no statistical relationship between PG and GDP growth. However, when LG is

used in the equation, its estimated coefficient has very strong statistical significance.

Therefore, LG is a better proxy of labor growth than PG. Very interestingly, when PG is

used in the economic growth equation, the statistical significance level on the estimated

coefficients of both life and non life insurance growth increased. However, this may not

be a true picture. It is due to the inability of PG to explain economic growth.

We find very similar empirical results from the German data as from the Swedish

data concerning the role of the insurance sectors on economic growth. From the German

data, life insurance development also harms economic growth while non life insurance

helps economic growth. But the statistical significance for the evidences in either life

insurance or non life insurance is not very strong.

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In the following part, we will use a fixed effect model to pool all four countries’

data together. Then we will compare the result from the fixed effect model with what we

have from OLS and simultaneous equations.

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V. Fixed Effect Model

The fixed effect model allows country differences which are reflected in the

group specific constant.

Because I have an unbalanced panel data set, I used OLS estimation with four

dummy variables to count for the difference in the four countries.

In the original data, there is a dummy variable for the German economy to

show the different periods before and after the merge of East and West Germany. To

make the fixed effect model workable, I choose two ways to estimate. First, I just

ignore the period after merge. This gives a smaller panel data set. Both PG and LG

are used as a proxy of labor growth. The estimated results for this one are shown in

Table 4.5.1 and Table 4.5.2. Second, I ignore the two different periods for Germany

and just put all available data of Germany in the panel data. Of course, in this way,

the two periods of German data are treated as the same. The estimated results are

shown in Table 4.5.3 and Table 4.5.4.

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Table 4.5.1 Estimation Results from FEM (Includes German Data before the Merge) - Population Growth is Used as a Proxy of Labor Growth


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE PG -0.009 -0.096 0.924 INVEST 0.071 7.923 0.000 RNONLG 0.095 4.010 0.000 RLIFG 0.004 1.142 0.257 REXPG 0.045 2.359 0.021 RGOV -0.177 -6.254 0.000 TIME -0.037 -2.009 0.048 US 2.998 6.578 0.000 KOREA 5.576 9.324 0.000 GERMANY 5.838 8.078 0.000 SWEDEN 0.574 1.333 0.186

Table 4.5.2 Estimation Results from FEM (Includes German Data before the Merge) - Labor Force Growth is Used as the Proxy of Labor Growth


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE LG 0.213 1.226 0.224 INVEST 0.068 7.435 0.000 RNONLG 0.087 3.540 0.001 RLIFG 0.004 1.149 0.254 REXPG 0.040 2.106 0.038 RGOV -0.178 -6.360 0.000 TIME -0.030 -1.563 0.122 US 2.526 4.364 0.000 KOREA 5.233 7.989 0.000 GERMANY 5.752 7.991 0.000 SWEDEN 0.487 1.128 0.263

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Table 4.5.3 Estimation Results from FEM (Includes all German Data) - Population Growth is Used as a Proxy of Labor Growth


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE PG 0.079 0.740 0.461 INVEST 0.069 6.005 0.000 RNONLG 0.113 3.717 0.000 RLIFG 0.004 0.761 0.449 REXPG 0.023 0.995 0.322 RGOV -0.190 -5.215 0.000 TIME -0.025 -1.180 0.241 US 2.763 5.023 0.000 KOREA 5.563 7.327 0.000 GERMANY 6.472 7.047 0.000 SWEDEN 0.573 1.051 0.296

Table 4.5.4 Estimation Results from FEM (Includes all German Data) - Labor Force Growth is Used as a Proxy of Labor Growth


Dependent Variable= RGDPG VARIABLE NAME ESTIMATED COEFFICIENT T-RATIO P-VALUE LG 0.375 8.600 0.000 INVEST 0.068 7.904 0.000 RNONLG 0.074 3.202 0.002 RLIFG 0.005 1.185 0.239 REXPG 0.035 2.013 0.047 RGOV -0.178 -6.510 0.000 TIME -0.025 -1.568 0.120 US 2.213 5.341 0.000 KOREA 5.062 8.890 0.000 GERMANY 5.759 8.277 0.000 SWEDEN 0.396 0.972 0.334

From the fixed effect model, we can see that in both case the estimated

coefficients on LG have strong statistical significance. But the estimated coefficients

on PG do not show strong statistical significance. Therefore, LG is a better proxy of

labor growth than PG.

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In all the cases, all the estimated coefficients on RNONLG are positive and

have strong statistical significance. This is consistent with the results from

simultaneous equation—non life insurance growth contributes to economic growth.

Although the estimated coefficients on all RLIFG are positive too but there is no

strong statistical significance. This means that life insurance also shows positive

contribution to economic growth from the fixed effect model. This is different with

the result from the simultaneous equation method. The simultaneous equation method

shows that US and Korean data support the idea that life insurance growth contribute

to economic growth and Swedish and German data shows that life insurance growth

hinders economic growth. The fixed effect model hides the differences here by

forcing a same estimated coefficient on life insurance growth. Actually, because for

the German economy life insurance growth has a negative contribution to economic

growth, when more German data are included in the fixed effect model, the

significance level on estimated coefficient of life insurance growth decreased.

Also, the constant terms, which accounts for country differences, have

estimated coefficients with strong statistical significance. This shows that there are

differences in the economic growth equation across countries.

What we can conclude here is that the fixed effect model supports the

conclusion that non life insurance has positive contribution to economic growth in

these four countries. Yet it does not reveal the difference of non life insurance’s role

from country to country. The difference of growth equation across countries shows

that individual estimation of simultaneous equation for each country is a better

econometric method.

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Note: some time series are non stationary for some countries but are stationary

for other countries. But for the fixed effect model, we have to stack the same time

series together from different countries. For example, PG is stationary for US but not

for all the other three countries. FDPG is stationary for Korea and TDPG is stationary

for Germany and Sweden. To solve the problem, I just stack PG, FDPG and TDPG

for the corresponding countries, although in the regression results it uses the term PG

in the table. I also multiply FDPG and TDPG with 10 and 100 to make the numbers

closer to those in PG.

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VI. Summary and Comparison of the Results across the Four Countries

Table 4.6.1 Effect of Insurance Growth on Economic Growth

OLS Simultaneous Equations

COUNTRY VARIABLE NAME

ESTIMATED COEFFICIENT

T-RATIO

P-VALUE

ESTIMATED COEFFICIENT

T-RATIO

P-VALUE

RLIFG 0.159 3.223 0.004 0.130 1.198 0.231 US(PG) RPCLG 0.086 3.131 0.004 0.250 3.262 0.001

RLIFG 0.188 3.020 0.006 0.180 1.596 0.110 US(LG) RPCLG 0.071 2.284 0.031 0.271 3.855 0.000

RLIFG 0.006 3.968 0.002 0.002 0.518 0.605 Korea (FDPG) RNONLG 0.089 2.702 0.019 0.088 1.816 0.069

RLIFG 0.006 4.558 0.001 0.004 0.974 0.330 Korea (LG) RNONLG 0.049 1.918 0.079 0.049 0.979 0.328

RLIFG -0.083 -2.905 0.012 -0.102 -1.579 0.114 Sweden (TDPG) RNONLG 0.058 2.042 0.062 0.055 1.152 0.249

RLIFG -0.077 -2.782 0.016 -0.070 -1.060 0.289 Sweden (LG) RNONLG 0.062 2.166 0.049 0.074 1.698 0.089

RLIFG -0.632 -3.927 0.001 -0.547 -2.463 0.014 Germany (TDPG) RNONLG 0.319 4.077 0.001 0.773 4.112 0.000

RLIFG -0.092 -0.583 0.567 -0.207 -0.900 0.368 Germany (LG) RNONLG 0.097 1.042 0.311 0.152 0.959 0.338

Table 4.6.1 summarizes the results from both OLS and simultaneous equation

model for the data of all four countries. The left hand side gives us the result from OLS

(with both PG and LG as labor growth). We can see that all four countries data support

the theoretical model that non life insurance (or PCL) insurance growth can promote

economic growth. But not all countries’ data support the theoretical model that life

insurance growth may contribute to economic growth. US and Korean data show that life

insurance can contribute to economic growth. However, Swedish and German data show

that life insurance growth may hinder economic growth.

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Comparing the results from OLS and simultaneous equations, we can see that

OLS may over estimate or under estimated the coefficients on RLIFG or PCLG/NONLG,

if we assume that the simultaneous equation method provides a more precise estimation.

Here we can also see that the sizes of the contribution of the insurance sector to

the economic growth are different across countries. The US insurance sector seems

having the biggest influence on economic growth in these four countries. For example,

from the estimated coefficient on life insurance growth in the output growth function, 1%

increase in life insurance growth rate will lead to around .15% increase in real GDP

growth for the US economy. The German data and the Swedish data show a little bit

smaller influence than the US data. The Korean data shows the lowest level of influence.

For example, 1% increase in life insurance growth only leads to .006% increase in real

GDP growth. The size of the contribution of the insurance sector seems related with the

degree of the development of an economy.

We will compare the effects of economic growth on insurance growth for all four

countries. It is shown in Table 4.6.2.

Table 4.6.2 Effect of Economic Growth on Insurance Growth

VARIABLE NAME

ESTIMATED COEFFICIENT T-RATIO P-VALUE

DEP=RLIFG US RGDPG 0.061 0.299 0.765Korea RGDPG -4.068 0.599 0.549Sweden RGDPG -0.092 0.088 0.930Germany RGDPG 0.080 0.465 0.642 DEP=PCLG/NONLG US RGDPG 0.887 1.852 0.064Korea RGDPG 0.834 1.808 0.071Sweden RGDPG -1.188 1.606 0.108Germany RGDPG 0.788 2.336 0.019

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The results in Table 4.6.2 are based on the second and the third equation of the

simultaneous equations. Here we only show the results from the estimation when the

better proxy of labor growth is used.

For the life insurance sector, two countries’ data (US and Germany) show that

economic growth may promote life insurance growth. One country’s data (Korea) show

that economic growth may hinder life insurance growth. There is almost no statistical

relationship between economic growth and insurance growth for the Swedish data. We

can see here that none of the estimated coefficients on RGDPG is statistical significant in

the life insurance demand growth function.

As for the non life insurance sector, three countries data support the idea that

economic growth may contribute to non life insurance growth. Only Swedish data show

that economic growth may lower non life insurance growth. Also, we can see all the

estimated coefficients on RGDP in the non life insurance growth function show strong

statistical significance. From the four country’s data, it seems that non life insurance

more rely on economic growth than life insurance.

Here we may provide a couple of reasons why life insurance growth does not

promote economic growth as we illustrated in the theoretical framework.

First, in the theoretical model, we assume that when there is more long term fund

in an economy, there is more resource available for technological innovation. However, it

also depends on the institution itself to channel those long term savings to effective

technological innovation. If life insurance companies only invest those savings in short

term, it can not fulfill the role we described in the theoretical model. As we mentioned

earlier that different countries may have different laws governing the operation of

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contractual savings institutions. The development of contractual savings institution can

not promote economic growth if they are only allowed to invest in short term securities or

government bond. One way to see whether this is true is to implore the assets holding

components of life insurance companies in those countries.

Second, it seems that the two countries where life insurance does not contribute to

economic growth are two European countries. The social welfare system of European

countries may be different than other countries. If they already provide protection like life

insurance, life insurance’s effect may not work as predicted. If this is the case, we can

infer that private life insurance may not be a better choice over public social welfare

system which also provides the similar function.

Both of the above reasons require further research work and we will not do that in

this dissertation.

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Chapter 5 Conclusions and Recommendations for Future Research

The importance of the insurance sector in an economy has been well recognized.

This is reflected by the fact that the total world insurance premiums have a significant

portion in total world GDP. In this dissertation, we start with the hypothesis that

insurance industry can promote economic growth by 1) setting up theoretical models to

illustrate how insurance can help economic growth and 2) testing the empirical

relationship between insurance growth and economic growth by using four countries data.

In the theoretical framework, we focus on the risk sharing role of

property/liability insurance and long term capital accumulation role of life insurance. By

providing the instrument for risk sharing, property/liability insurance sector can help

economic agents making a social optimal production choice. By providing savings plans

to increase the utility of the economic agents, contracting savings institution can provide

more long term capital. Both life and non life insurance can contribute to economic

growth by promoting technological progress.

Then we set up empirical models to test our theoretical models. Data from four

countries have been used—US, Korea, Sweden, and Germany. Three empirical methods

are employed—ordinary least square, simultaneous equations and fixed effect model.

Empirical study suggests that property/liability insurance have positive contribution to

economic growth but life insurance may have positive or negative contribution to

economic growth depending on each country’s situation. The following part is the

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summary of the research. Then we discuss the limitation of the research and make

suggestions for future research.

I. Summary of theoretical models

First, we illustrate the economic role of property/liability insurance. We start

the model by assuming two different types of technology are available. Risk is

introduced into the model by assuming one type of technology is “risky” technology

in the sense that investment in this technology may lead to zero output. The other type

of technology is called “safe” technology in the sense that it will produce a certain

output. However, the risky technology is more productive than the safe technology

because it yields a higher expected output given the same amount of labor and capital.

Then we specify an overlapping two generation model with individuals endowed with

a specific amount of labor to decide which technology to invest in. Individuals are

risk averse and maximize their utility function. When there are no institutions to help

diversifying the risk, utility-maximizing-individuals will choose the safe technology.

Because the risky technology has a higher expected output than the safe technology.

The risky technology should be a social optimal choice. This illustrates that when

there is uncertainty associated with economic outcome and economic agents are risk

averse at the same time, individual optimization does not lead to social optimization.

Therefore, there is a need for risk sharing institutions. The insurance industry is such

a kind of institution.

Then we introduce the insurance sector into the economy. This allows

economic agents to insure against the loss when the risky technology is not successful

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by paying a certain amount of money called premium. The model shows that now

individuals will choose the risky technology by maximizing their utility. Now the

individual optimization is the same as social optimization.

Here insurance is illustrated as a door, the open of which allows for a choice

which is non-obtainable or appealing to economic agents because of the risk they

have to bear. In economic growth model, we know that long run economic growth

comes from technology growth. Rather than being innovations themselves, insurance

serves as an institution to help those innovations’ being carried out into economic life.

Second, the life insurance sector is studied. Pension funds and life insurance

companies are called contractual savings institutions. They are different with banks

because they can provide long term savings plans or protection against financial loss

against premature death through contracts. Here we illustrate the role of life insurance

in economic growth by showing how contractual savings institutions can shift short

term capital to long term capital. The main illustration here is to compare banking

with contractual savings institutions. The latter one holds more illiquid assets than the

former one. Illiquid assets can be used to finance long term project which can yield

higher return.

In this part, we start with the argument that there is a need for contractual

savings institutions. Economic agents facing the uncertainty of life expanse are

assumed to work and save for the longest possible life expanse. Their savings

decisions are based on a three-period utility function. Individuals maximize their

utility function by allocating the same amount of real consumption on each period.

Then a contractual savings institution is introduced into the economy. The contractual

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savings institution has knowledge of the life expectancy probability distribution. This

makes economic agents can buy policy to exchange their wage for life long annuity.

By doing so, they can increase their maximized utility. Then the savings structure of

the economy without contractual savings institutions are compared with the ones with

contractual savings institutions. The presence of contractual savings institution in the

economy increase both long term and short term investment in the economy.

Then a discussion about insurance growth and technological progress is

presented. It illustrates how the insurance sector can promote technological

innovations by providing either more resources or lowering the cost of innovation.

II. Summary of Empirical Findings

We examined four country’s data to see whether there is empirical support of

the theoretical illustration about the role of insurance in economic growth in the

second chapter. The four country’s data available at the beginning of this research are

from US, Korea, Sweden, and Germany.

First, we set up the growth model with insurance and other factors to explain

productivity growth (or technological growth). Based on this model, the ordinary

least square is used to estimate the effect of insurance growth on economic growth.

As illustrated in chapter 2, there are two different effects of the insurance sector on

economic growth—risk-diversifying and long term capital accumulation. These two

effects are separately associated with property/liability insurance and life insurance.

Therefore, property/liability insurance growth and life insurance growth are separated

and put into the growth function individually. The result shows that all countries’ data

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support that property/liability insurance can contribute to economic growth. On the

other hand, life insurance growth has mixed results from these four country’s data.

The data of two countries show that life insurance growth has contribution to

economic growth while the data of the other two countries show that life insurance

growth has hindered economic growth. The two countries with negative correlation

are European countries. It is suspected that the social welfare system in European

countries may already provide the role of life insurance companies. The other

possible reason is that life insurance companies in these two countries may not

channel long term capital into technological innovations effectively as the theoretical

model illustrated. But further study is needed to make a specific conclusion on this.

Then we set up simultaneous equations for each country to further study the

effect of insurance growth on economic growth. In Chapter 2 we argued that

insurance growth will contribute to economic growth. On the other hand, economic

growth may also demand for insurance growth. There are interactions between

insurance growth and economic growth. If this is true, ordinary least square

estimation will lead to biased estimation. Simultaneous equations allow for the

interaction between economic growth and insurance growth. Therefore, it will be a

more proper empirical model to use. The result from simultaneous equation is

compared with the one from single equation estimation. The result concerning the

role of insurance growth on economic growth remains unchanged. This means all the

estimated coefficients on RLIFG and RPCLG/RNONLG in the growth function

remain the same signs as in the OLS estimation. However, the statistical significance

level of most estimated coefficients on RLIFG and RPCLG/RNONLG is lowered.

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Also, we found that economic growth has more effect on property/liability insurance

growth than on life insurance growth. Through simultaneous equation analysis, the

factors that affect property/liability insurance and life insurance are identified. The

significance of those factors is different across countries.

Then the results from a fixed effect model is presented. This model combined

all countries data together and estimate a single equation growth model. It allows for

different constant terms for different countries. The result also supports the fact that

property/liability insurance can promote economic growth. But combination of the

data forced a same estimated coefficient on life insurance growth. Therefore, the

result can not show the difference of life insurance actual effect in different countries.

However, by employing different econometric methods, we can test the

robustness of the model.

III. Limitation of the research

In this research, I try to give some theoretical explanation to support the

argument that insurance growth will promote economic growth. In addition to the

theoretical explanation, I hope to support the argument with empirical study.

However, I have to acknowledge that there are some deficiencies in my research. I

will discuss them in this section.

First, we assume that the insurance market is in a very “ideal” state. There is

no loaded premium to cover the extra cost of insurance companies other than pure

loss. Also, the model does not account for those issues of moral hazard and adverse

selection, which may also add more cost to administration cost of the insurance

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industry. When these issues are significant, the theoretical results developed in the

second chapter may be altered. Developing countries with under-developed insurance

market may face such issues.

Second, when we study the role of life insurance on economic growth, we

only focus on its role as contractual savings institutions. Life insurance can also

protect against interruption on human capital investment due to premature death of

the main breadwinner. Life insurance may provide uninterrupted human capital

investment and therefore increase the quality of human capital stock of an economy.

Actually, this is a very important role of life insurance, which can be examined in the

context of the growth model but ignored in this dissertation.

Third, the technological progress model is a very simplified model. For

example, β is a constant term which represents the unit cost of innovation. However,

in the real world situation, the innovation process is much complicated. It is hard to

use a single term to represent the innovation cost. This will also affect the conclusion

on the insurance sector’s contribution to economic growth, which is linked to β.

Fourth, when I started this dissertation, there were only four countries’ data

available for this research. This can not represent all cases in general. Insurance

development may be very country-specific. Examining a broad range of data can help

test the robustness of the theoretical models.

Fifth, only three variables are treated as endogenous in the simultaneous

equation system—GDP growth, Life insurance growth, PCL/Non life insurance

growth. All the other variables are treated as exogenous. Capital growth should be

another important endogenous variable but was treated as exogenous in the

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simultaneous equations. The reason is that I could not obtain the data of capital

growth in each country. Investment to GDP ratio is used as a proxy of capital growth

in the GDP growth function.

Sixth, there are several reasons are proposed for the observations that life

insurance does not contribute to economic growth for two European countries. There

is no further exploration to support the reasons proposed.

IV. Suggestion for Future Research

Based on the above limitations, I have the following suggestions for future

research. In future models, extra cost can be loaded to the pure premium charged by

the insurance sector. By allowing extra cost above pure premium, the limit of the

benefit of an insurance industry can be developed. For some developing countries, I

suspect there would be empirical evidence to support that property/liability insurance

can not promote economic growth. In those markets, the insurance industry may not

be very efficient. And its role in economic growth may be undermined. It would be a

very interesting topic to study.

Second, more countries’ data should be included in the empirical study. As

more and more countries’ data are studied, we may observe more diversified results

from different countries. Studying the difference may lead to some revision of the

theoretical arguments presented here. We observe a wide range of development in the

development of the insurance institutions in the world. For the developed countries,

such as US, there is well developed insurance sector. In contrast, there is very under

developed insurance market in developing countries, such as in some African

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countries. When more country’s data are available, the reason for the difference we

observed may be a very interesting topic to study on. In addition to that, in this model

we do not examine the cost of the insurance institutions. Policy makers may be

concerned whether it is good to subsidize the insurance companies to promote its

development. If there are some positive externalities from the development of the

insurance sector, it may be worthwhile for the government to initiate the

establishment of such institutions.

Third, examine how life insurance could help develop the human capital in an

economy. It seems the model would be more robust if we include this into the growth

model.

Fourth, obtain the capital growth time series for each country and put this into

the simultaneous equations as an endogenous variable to see whether this will change

the result we have here.

127

Appendix A

Solve for 2q

)}1(*])1()1([

*])1()1([

{

)~]***[*(

2111

21

2111

21

221

1

πγ

αα

πγαα

γα

γαααα

γαααα

γα

−−

−−−+++

−−−+−++

=

−++

−−−

−−−

−−

wqqLwLqwq

wqqLAwLqwqMax

CwqLwqMax

r

Conditional on 01 =q

So the maximization problem becomes

)1(*)]1()1([

*)]1()1([ 2

1122

112 π

γαα

πγ

αα αγγαααγγαα

−−

−−++

−−+−+ −−−−−−−− wqLLqwqLALq

Max

Take first order derivative and set it equal to zero.

FOC 0)1(*])1([*)]1()1([

*])1([*)]1()1([111

211

2

1112

112

=−−+−−++

−−+−+−+−−−−−−

−−−−−−

παααα

πααααααγαα

ααγαα

LLqLLqLALqLALq

)1(*])1([*)]1()1([*]))1([*)]1()1([

1112

112

1112

112

παααα

πααααααγαα

ααγαα

−−+−−+=

−++−−+−+⇒−−−−−−

−−−−−−

LLqLLqLALqLALq

)1(**)]1()1([*]))1[(*)]1()1([

112

112

112

112

παα

παααγαα

αγαα

−−−+=

−−+−+⇒−−−−−

−−−−−

LqLLqLAqLALq

πππ

αααα

γαα

γαα

−−

=−−+−+−+

⇒−−−−

−−−−

AqLLqqLALq 1)]1()1([

)]1()1([1

211

2

12

112

11

211

2

211

2 )1()1()1(

)1()1( +−

−−

−−

−−

=−−+−+−+

⇒ γαα

αα

πππ

αααα

AqLLqqLALq

11

22

22 )1()1)(1(

)1)(1( +−

−−

=−−+−+−+

⇒ γ

πππ

αααα

AqqqAq Set 1

1

)1( +−

−−

= γ

πππ

AD

Dqq

qAq=

−−+−+−+

⇒)1)(1(

)1)(1(

22

22

αααα

128

Dq

qAA=

+−−−+−

⇒2

2

1)1(1

αα

22 )1(1 qAADqDD −−+−=+−⇒ αα

αα DDAqADq −++−=−+⇒ 1)1( 22

1)1(1

1)1(1

)1()1()1(

2 −+−

−=−+

−+=

−++−+−

=⇒AD

DADD

ADDDAq ααα

Here we can approve that 10 2 << q .

Note that 11

11

)1

()1( ++−

−−

=−−

= γγ

πππ

πππ A

AD

Also, we have specified that 1>πA so that the expected output level from the risky

technology is higher that the output level from the safe technology.

111 <−−

⇒>ππππ

AA and 0

111 >+

⇒−>γ

γ

1011

)1(1011

)1(01 2 <<⇒<−+

−−<⇒<

−+−

<⇒>⇒ qAD

DAD

DD αα

129

Appendix B

The following is a reproduced illustration why banks (which are subject to runs)

may choose only to invest in short term project while contractual savings institutions will

choose to invest in long term project.

According to Impavido and Musalem (2001), contractual savings institutions have

comparative advantages in financing long term projects compared with banks because

they are not subject to bank runs. They give out a numerical example. Here I will borrow

the numerical example to illustrate why contractual savings institutions are more willing

to finance long term projects than banks.

First, according to Diamond and Bybvig (1983), banks are subject to runs. But

due to the special character of contractual institutions, they are not subject to runs. There

are two kinds of projects to invest for banks--long term projects which give a higher rate

of return and short term projects which give a lower rate of return. Let di , si , li denote

the rate of return required by depositors, the rate of return of short term projects and the

rate of return of long term projects specifically.

Banks are subject to runs with probability p. Banks will choose to invest either in

short term projects and long term projects depending on the expected profits. The

expected profits from short term projects and long term projects are illustrated in Table

AP-1 and Table AP-2.

130

Table AP-1 Profits from Short Term Projects

Investment in

Short Term project

Profit Probability

No bank runs 22 )1()1( ds ii +−+ 1-p

With bank runs )1()1( ds ii +−+ p

Expected profit piipii dsds *)()1(*)1()1( 22 −+−+−+

Table AP-2 Profits from Long Term Projects

Investment in Long

Term Project

Profit Probability

No Bank Runs 22 )1()1( dl ii +−+ 1-p

With Bank Runs - C p

Expected Profit pCpii dl *)1(*)1()1( 22 −−+−+

Here C denotes the cost of banks runs which lead to bankruptcy.

Banks choose to invest in long term projects if only the expected profit from long term

projects are higher than profit from short term projects.

The condition is that

pCpii dl *)1(*)1()1( 22 −−+−+ > piipii dsds *)()1(*)1()1( 22 −+−+−+

To expand to terms on both sides, the condition becomes

131

pCpiiii ddll *)1(*])(*2)(*2[ 22 −−−+ − >

piipiiii dsddss *)()1(*])(*2)(*2[ 22 −+−−−+

Which is equivalent to

pCpii ll *)1(*])(*2[ 2 −−+ > piipii dsss *)()1(*])(*2[ 2 −+−+

0*)(*)1(*])(*2)(*2[ 22 fpiipCpiiii psssll −−−−−−+⇒

If the above condition is not met, banks will choose to invest in short term

projects instead of long term projects.

We can see that the higher the cost of bankruptcy (larger C), the higher the

probability of bank runs (larger p) and the smaller the difference between long term and

short term projects’ rates of return, the less willingness banks will invest in long term

projects.

But for contractual savings institutions, they are not subject to runs so that they

will always to choose to invest in long term projects. The reason is that

22 )1()1( dl ii +−+ > 22 )1()1( ds ii +−+ .

132

Appendix C

Source of Data

Data from the Statistical Abstract of the United States (US): LG, LIFG, PCLG, EDR,

RSSG, INF, PRATIO, WPART, LEXP, URBANR, DRATIO

The data of Korea are from the following website: http://www.kosis.kr/eng/index.htm

except URBANR, LEXP and WPART

World Bank Data: URBANR, LEXP, WPART AND DRATIO (for Korea, Germany and

Sweden)

Penn World Table: Population, INVEST

IMF CD: GDP, EXPORT, IMPORT, GOVERNMENT EXPENDITURE (US)

OECD STATISTICS WEB: GDP, EXPORT, IMPORT, COMSUMER PRICE,

GOVERNMENT EXPENDITURE (GERMANY AND SWEDEN)

Statistical Yearbook of Sweden: LIFG, NONLG

Statistical Yearbook of Germany: LIFG, NONLG

133

Appendix D

Test the Relevance of the Instruments

Regress life insurance growth on all exogenous variables and test the joint

significance of the excluded instruments. If the F test can reject the null, the instruments

are relevant. Otherwise they are not. The results for each country are presented in the

following table.

F test statistics

US Korea Sweden Germany

F P-

Value

F p-

Value

F p-

Value

F p-

Value

Pg 0.532 0.777 0.541 0.770 1.152 0.387 3.522 0.026 RLIFG

Lg 0.413 0.861 0.497 0.742 1.026 0.440 4.295 0.012

Pg 0.711 0.704 5.439 0.018 1.653 0.227 0.580 0.715 RNONLG

Lg 1.066 0.434 7.269 0.008 1.222 0.373 1.590 0.223

134

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Documents

AN INVESTIGATION OF THE INSURANCE SECTOR’S CONTRIBUTION TO ECONOMIC GROWTH