Essays in Macro-Labour Economics

by

Parisa Mahboubi

A Thesis

presented to

The University of Guelph

In partial fulfilment of requirements

for the degree of

Doctor of Philosophy

in

Economics

Guelph, Ontario, Canada

© Parisa Mahboubi, March, 2017

ABSTRACT

ESSAYS IN MACRO-LABOUR ECONOMICS

Parisa Mahboubi Advisor:

University of Guelph, 2017 Dr. Stephen Kosempel

This dissertation consists of three independent chapters. In the first chapter, a life cycle

model of human capital accumulation through learning-by-doing is constructed with

heterogeneity in productivity and age. The model is used to evaluate the impacts of social

security reforms on the welfare of individuals, as well as the distribution of labour supply,

consumption, and physical capital accumulation over the life cycle in the long run. In the

reference economy, retirement is mandatory with a Pay-As-You-Go (PAYG) social security

system. The following policy reforms are considered: (i) terminating the social security system

with mandatory retirement, (ii) terminating the social security system with voluntary retirement,

and (iii) introducing voluntary retirement with the social security. The results from the policy

experiments show that even low earners prefer an economy without a social security system.

Furthermore, the impacts of introducing voluntary retirement on individuals’ decisions vary by

age and productivity. The retirement decision is also affected by the presence of the social

security system, and the amount of income redistribution within the system. In particular, low-

skilled individuals (non-college graduates) decide to retire earlier while high-skilled individuals

(college graduates) remain longer in the workforce. Taxation was shown to exacerbate these

effects. However, these results do not hold if human capital is assumed to be exogenous.

In the second chapter, the impacts of investment-specific and neutral technology shocks

on individuals’ decisions are studied in a life cycle model, populated by heterogeneous

individuals with respect to age. The results show that first the aggregate fluctuations are different in a

life cycle model with an investment-specific technology shock compared to the standard infinitely

lived agent models and in a model with only neutral technology shocks. Specifically, the role of

investment-specific technology shocks as a driving source of fluctuations is weak. The results

also show that the impacts of technology shocks on labour supply, consumption, and physical

capital depend on an individual's age and the nature of shocks. Individuals’ optimal decision is to

increase their current consumption due to a positive neutral technology shock. Therefore, old

individuals work more while young individuals borrow more physical capital. However, more

accumulation of physical capital is optimal for all except the young individuals when a positive

investment-specific technology shock is introduced in to the economy. This leads to a reduction

in consumption of all individuals, and a sharp increase in the labour supply of old workers.

The third chapter studies the labour market outcomes of second generation immigrants

compared to other natives (third generation) in Canada, with an emphasis on cognitive skills and

education. By using survey data from the 2003 International Adult Literacy and Skills Survey,

this paper shows that children of immigrants are more likely to obtain a university degree.

Moreover, they obtain higher test scores in cognitive skills and thus higher earnings compared to

children of non-immigrants in Canada. Educational attainment and literacy skills are found to be

important sources of success in the labour market for second generation immigrants. The positive

association between parental education and human capital of children illustrates how the

Canadian society benefits from the immigration point system in which immigrants with higher

level of human capital are selected through an intergenerational effect.

iv

ACKNOWLEGMENTS

I would like to sincerely thank Dr. Stephen Kosempel, and Dr. Miana Plesca for being

outstanding advisors and mentors throughout my doctoral studies. This thesis and my Ph.D.

degree would have been impossible without their guidance and support.

My sincere thanks also go to Dr. Thenasis Stengos, Dr. Laurent Cellarier, and Dr. Chris

McKenna for their advice and insightful comments.

I would like to express my gratitude to all faculty members and staff in the Department of

Economics.

Finally, I would specially like to thank my beloved family, Vahid and Shayan, for their

love and support throughout my entire doctoral studies.

v

Table of Contents

1 Social Security Reforms in a Life Cycle Model with Human Capital Accumulation and

Heterogeneous Agents .................................................................................................................... 1

1.1 Introduction ...................................................................................................................... 1

1.2 The Model ........................................................................................................................ 4

1.2.1 Household’s problem ................................................................................................ 5

1.2.2 Production ................................................................................................................. 7

1.2.3 Government............................................................................................................... 7

1.2.4 Competitive equilibrium ........................................................................................... 8

1.2.5 Solution methods ...................................................................................................... 8

1.3 Model calibration ............................................................................................................. 9

1.3.1 Demographics ........................................................................................................... 9

1.3.2 Policy parameters ...................................................................................................... 9

1.3.3 Technology and preferences ................................................................................... 10

1.3.4 Human capital ......................................................................................................... 10

1.4 Results and discussions .................................................................................................. 12

1.4.1 Life cycle analysis................................................................................................... 12

1.4.2 Model evaluation .................................................................................................... 13

1.4.3 Social security reforms ........................................................................................... 14

1.5 Conclusion ...................................................................................................................... 22

2 Life Cycle Analysis of Investment-Specific and Neutral Technology Shocks ..................... 36

2.1 Introduction .................................................................................................................... 36

2.2 The Model ...................................................................................................................... 38

2.2.1 Household’s problem .............................................................................................. 38

2.2.2 Production ............................................................................................................... 40

2.2.3 Government............................................................................................................. 40

2.2.4 Competitive equilibrium ......................................................................................... 41

2.2.5 Solution methods .................................................................................................... 41

2.3 Model calibration ........................................................................................................... 42

2.3.1 Demographics ......................................................................................................... 42

vi

2.3.2 Technology and preferences ................................................................................... 43

2.3.3 The human capital profile ....................................................................................... 43

2.3.4 Stochastic parameters.............................................................................................. 44

2.4 Results and discussions .................................................................................................. 45

2.4.1 Steady States Analysis ............................................................................................ 46

2.4.2 Neutral Technology Shocks .................................................................................... 47

2.4.3 Investment-Specific Technological shocks ............................................................. 48

2.4.4 Business Cycle Statistics......................................................................................... 50

2.5 Conclusion ...................................................................................................................... 52

3 Education, Skills and Labour Market Outcomes of Canadian Second Generation Immigrants

60

3.1 Introduction .................................................................................................................... 60

3.2 Data ................................................................................................................................ 63

3.2.1 Descriptive statistics ............................................................................................... 65

3.3 Specification models ...................................................................................................... 67

3.3.1 Key independent variables ...................................................................................... 68

3.4 Estimation results ........................................................................................................... 69

3.4.1 University outcomes ............................................................................................... 69

3.4.2 Literacy outcomes ................................................................................................... 70

3.4.3 Regression results for hourly wages ....................................................................... 70

3.4.4 Regression results from income equation ............................................................... 72

3.4.5 The effect of literacy components on the labour market outcomes ........................ 73

3.5 Conclusions .................................................................................................................... 73

vii

List of Figures

Figure 1.1: Hourly Wages Profiles of College and Non College Graduates and all Individuals . 30

Figure 1.2: Calibrated Efficiency Weights, , and Productivity Sequence,

by Type and Age ........................................................................................................................... 31

Figure 1.3: Steady States Profiles for High Type and Low Type Individuals for Baseline Model

....................................................................................................................................................... 32

Figure 1.4: Ability of the Baseline Model (LBD) to Replicate the Wages, Human Capital and

Hours Worked from the US Data for High Type and Low Type Individuals .............................. 33

Figure 1.5: Impacts of Social Security Reforms on Life Cycle Profiles of Low Type Individuals

....................................................................................................................................................... 34

Figure 1.6: Impacts of Social Security Reforms on Life Cycle Profiles of High Type Individuals

....................................................................................................................................................... 35

Figure 2.1: Steady state outcomes by age ..................................................................................... 54

Figure 2.2: Hours worked comparison between model and actual data ....................................... 55

Figure 2.3: Impulse response functions for aggregate variable after a positive neutral technology

shock. ............................................................................................................................................ 56

Figure 2.4: Impulse response functions after a positive neutral technology shock by age group 57

Figure 2.5: Impulse response functions for aggregate variable after a positive IST shock .......... 58

Figure 2.6: Impulse response function after a positive IST shock by age group .......................... 59

viii

List of Tables

Table 1-1: Calibrated Baseline Model Parameters with Heterogenous Agents ............................ 25

Table 1-2: Steady States Outcomes of Policy Reforms with Endogenous Human Capital

Accumulation ................................................................................................................................ 26

Table 1.3: Average Individual Outcomes of Policy Reforms with Heterogeneous Agents for

Separate Age Groups .................................................................................................................... 27

Table 1.4: Welfare Comparison with the Benchmark Economy .................................................. 28

Table 1.5: Steady States and Welfare Effects of Policy Reforms with Exogenous Human Capital

....................................................................................................................................................... 29

Table 2.1: Calibrated model parameters ....................................................................................... 53

Table 2.2: Business cycle statistics ............................................................................................... 53

Table 3.1: Summary Statistics for the labour market characteristics by gender ........................... 75

Table 3.2: Education, parental education, region of residence, and ethnicity by gender ............. 76

Table 3.3: Marginal effects after probit for the university outcomes ........................................... 77

Table 3.4: Estimation results of the literacy equations for males ................................................. 79

Table 3.5: Estimation results of the literacy equations for females .............................................. 81

Table 3.6: Regression results of the hourly wages by gender ....................................................... 83

Table 3.7: Regression results of the income equations ................................................................. 85

Table 3.8: The effects of the literacy components on the labour market outcomes ..................... 87

Table 3.A1: Distribution of occupation ........................................................................................ 88

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Chapter 1

1 Social Security Reforms in a Life Cycle Model with Human

Capital Accumulation and Heterogeneous Agents

1.1 Introduction

A pay-as-you-go (PAYG) social security system has been adopted in the United States and many

other developed countries, mainly because it guarantees sufficient retirement earnings for the

elderly through redistributing income in the economy. In this system, income is redistributed

from individuals with higher lifetime earnings to those with lower lifetime earnings. In contrast,

there have been some concerns regarding the impacts of social security systems on saving

(Feldstein, 1974; Hubbard et. al, 1995), and labour supply decisions (Diamond and Mirrless,

1978). Following Auerbuach and Kotlikoff (1987), the macroeconomic and welfare implications

of various social security reforms have been extensively analyzed in the literature to cope with

the financial challenges of an aging population on the social security system1. However, in the

existing social security literature, labour productivity is mainly assumed to be exogenous.

Furthermore, the impacts of social security reforms on low-income individuals require more

attention, as the important goal of a social security system is to protect disadvantaged groups

such as low-income retired individuals. Consequently, the assumption of heterogeneity may be

necessary to evaluate policies in a life cycle framework. Conesa and Krueger (1999) also

confirm the importance of heterogeneity to study the political impact of social security reforms,

but the previous studies, even those that considered heterogeneity among individuals, focused on

1 Including Hubbard and Judd (1987); Imrohoroglu, Imrohoroglu and Joines (1995, 1999); Huggett and Ventura

(1999); Conesa and Krueger (1999); Nishiyama and Smetters (2007); Pries (2007); Rojas and Urrutia (2008); and

Chen (2010).

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aggregate outcomes. This study shows that labour supply and retirement decisions significantly

differ by the level of earnings, particularly, when voluntary retirement is an option. Figure 1.1

illustrates that non-college graduates, on average, earn less during their working period

compared to college graduates. Therefore, this study investigates how a social security reform

impacts non-college (low-skilled individuals) and college graduates (high-skilled individuals)

differently over their life cycle in order to distinguish between high and low earners.

This study also contributes to the literature by incorporating a heterogeneous human

capital accumulation mechanism. It is important to account for human capital accumulation

when a change in the economy (e.g. a change to the social security tax rate) is studied since it

impacts the labour market decisions at all ages differently (Shaw, 1986; Heckman et al., 1998;

Imai and Keane, 2004; Hansen and Imrohoroghlu, 2009). In particular, Keane (2015) shows the

assumption of endogenous human capital through learning-by-doing2 (LBD) increases the effects

of permanent tax changes over time. Peterman (2016) also shows that the LBD human capital

accumulation results in different optimal tax policy, particularly due to different response of

young individuals in the economy. Furthermore, Alvarez-Albelo (2004) studied the role of

human capital accumulation through learning-by-doing in a general equilibrium model of social

security with one type of agent to show that the capital-labour ratio and the average hours

worked differ under the model with endogenous human capital compared to a model with

exogenous efficiency units of labour. As such, Alvarez-Albelo indicated that the assumption of

exogenous efficiency units of labour may lead to imprecise results, but it is not clear how social

security reforms influence individual’s decisions differently with heterogeneous human capital

accumulation.

In this study, a life cycle model of labour supply, human capital accumulation and physical

capital accumulation with heterogeneous agents has been constructed. The model has been

developed with the intention of explaining differences in human capital accumulation and labour

supply decisions between high-skilled and low-skilled workers in response to social security

reforms. Consequently, it explains wage differentials and life cycle wage growth in a general

equilibrium setting. In this model, skill is accumulated through past work experience or LBD

2 In general, two forms of human capital accumulation have been mainly adopted in the literature: learning-by-doing

(LBD) or on-the-Job training (OJT). With OJT mechanism, individuals acquire human capital by spending time to

learn while with LBD, individuals accumulate human capital through past experience.

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mechanism3. Heterogeneity derives from two channels in order to capture differences in life

cycle decisions and behavior among individuals. First, the model allows individuals to differ

within an age group as a result of differences in learning abilities and thus productivities.

Second, the model allows learning abilities to vary by age. In the reference economy, it is

assumed that there exists a PAYG social security system and mandatory retirement4. Overall, the

model provides a reasonable fit to the life cycle characteristics observed in the Panel Study of

Income Dynamics 1962-2011 in the US economy.

Furthermore, the quantitative effects of heterogeneous human capital on the evaluation of

social security reforms are investigated in four cases: (i) terminating the social security system

with mandatory retirement, (ii) terminating the social security system with voluntary retirement,

(iii) allowing voluntary retirement with the social security system where pension benefits decline

while the social security tax rate remains unchanged, and (iv) allowing voluntary retirement with

the social security system in which the tax rate rises while pension benefit stays constant.5 The

same exercises with social security reforms have also been done with exogenous human capital

to quantitatively explore how the macroeconomic outcomes are affected by this assumption. It

will be demonstrated that accounting for endogenous human capital is important for the

evaluation of social security reforms with voluntary retirement since it leads to different

outcomes. Differences between the model with endogenous human capital and exogenous human

capital derive from the differences in the price of leisure. In the model with endogenous human

capital, where work experience accumulates human capital, the opportunity cost of the leisure

equals the wage plus the marginal value of work experience. Whereas, in the model with

exogenous human capital, the opportunity cost of leisure equals only the wage.

The results from policy experiments show that distinguishing between high and low income

earners is important and this is particularly true when looking at the effects that these social

3 Hansen and Imrohoroghlu (2009) studied the effect of endogenous human capital on average hours worked by age.

They argued LBD affects labour market decisions at all ages, the assumption of endogenous human capital

accumulation is important for the life cycle analysis, if human capital is accumulated through LBD. 4 In the early 1970s, about half of Americans were covered by mandatory retirement provisions and required to leave

their jobs at a specified age such as 65. Congress amended the Age Discrimination in Employment Act to abolish

mandatory retirement in 1986. 5 Studies that focus on the extending the retirement age as part of social security reforms include Hviding and

Merette (1998) for a number of OECD countries; De Nardi et al. (1999), and Conesa and Garriga (2003) for the

U.S.; Hirte (2002) for Germany; Henin and Weitzenblum (2005) for France; Beetsma et al. (2003) for the

Netherlands; Keuschnigg and Keuschnigg (2004) for Austria; and Koka and Kosempel (2014) for Canada.

` 4

security policies have on the decision to retire. There are significant differences in the optimal

retirement dates between low types and high types in the model. The retirement decision is also

affected by (i) the presence of the social security, and (ii) the amount of income redistribution

within the system. In particular, when retirement becomes voluntary, the labour market

participation of low types declines while high types work longer. In a social security system, low

types prefer voluntary retirement and high types are better off in an economy with mandatory

retirement due to the distributional effects. This is because low types have to work for a longer

period of time with mandatory retirement to make sure a sufficient retirement earnings as high

types are not permitted to work longer and pay more pension tax under mandatory retirement.

Overall, an increase in the tax rate raises the labour force participation of high-skilled individuals

and declines the working life of low types. The welfare outcomes also show that both types of

agents are better off when social security tax is zero. By setting the tax rate to zero, the net

earnings increase which lead to more saving. Consequently, higher physical capital results in a

higher wage rate. Imrohoglue et al. (1995, 1999) and Conesa and Kruger (1999) also found

similar results in which the optimal social security tax rate is zero.

The remainder of this chapter is organized as follows. In section 1.2, the model is developed

and the solution method to obtain the steady states values is described. Calibration of the model

is discussed in section 1.3. Section 1.4 presents the results and discusses the findings of the

model with endogenous human capital accumulation. The results of the policy reform in a model

with exogenous human capital are presented in section 1.5. The conclusions of the first chapter

are provided in section 1.5.

1.2 The Model

A general equilibrium model, based on the pioneering life cycle model developed by Auerbach

and Kotlikoff (1987), is considered with endogenous human capital accumulation and

heterogeneous agents. In the model heterogeneity derives from the initial level of human capital,

ability to learn, and age. There are two types of capital in the model: physical and human.

Physical capital is accumulated during life through investment. Agents begin their life with no

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physical capital and leave no intentional bequests at the end of their life. On the other hand,

agents start their life with positive human capital and human capital is accumulated only by

allocating time to work and learning by doing.

Time is discrete and each period corresponds to one year in reality. Let s denote an

individual’s age and t the time period. A new generation of equal size is born every year.

Individuals face an uncertain life span and may live for a maximum of Tmax periods. All

surviving individuals retire at age Tr. Given the conditional probability, φs, of surviving from age

s to age s + 1, the cohort shares, θs, are obtained by

, where θs= φs-1 θs-1 (1.1)

Equation (1.1) indicates that the sum of the cohort shares equals to one.

1.2.1 Household’s problem

Individuals choose optimal consumption, c, and leisure, l, to maximize their discounted life time

utility:

,

(1.2)

where γ is the disutility of non-leisure activities, η is the coefficient of relative risk aversion, and

β is the discount factor.

In each period, each individual has been provided with one unit of time. During the

working period, time can be allocated among leisure, l, and work, n. Workers receive income

from providing labour services and from renting capital assets to the production sector. Retired

agents provide no labour services and instead, receive public pensions, b, from government. The

budget constraints for working and retired agents, respectively, are as follows:

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(1.3)

(1.4)

where k is physical capital, r is the real rental rate of physical capital, h is worker efficiency or

human capital, τ is the labour income tax rate, and tr is a government transfer of accidental

bequests to the surviving individuals.

The model accounts for two types of heterogeneity in the production of human capital.

First, the levels of productivity are different for individuals within the same cohort such that high

type individuals, H, can accumulate more human capital compared to low types, L, at a given

age. In the model, the fractions of high types and low types are represented by ζ and 1- ζ,

respectively. This type of heterogeneity is necessary to create a group of low and a group of high

income earners. Second, the productivity in learning is different between cohorts and declines

with age. This type of heterogeneity is essential to match the wage profiles. For both types

i , it has been assumed that human capital is accumulated through a LBD mechanism

according to the following equation,

i

sts

i

sts

i

s

i

stsh

i

sts nhhh 1,1,1,,1 )1( (1.5)

here, the parameter h is the depreciation rate of human capital, ϕ is a parameter that affects the

speed of learning by doing, and i

s is a productivity parameter which is assumed to vary by age

and type. Hansen and Imrohoroglu (2009) and Alessandrini and et.al (2015) have used a similar

function for human capital accumulation. However, Alessandrini and et.al (2015) assumed that

human capital is acquired through formal education and Hansen and Imrohoroglu (2009) did not

account for heterogeneity by type in their learning-by-doing human capital accumulation

technology. In both studies, the productivity sequences decline with age but no explanation is

provided for this exogenous decline. One possible explanation might be that for a given

technology, there may exist diminishing returns to learning (Kosempel, 2007). Kosempel

suggests that as agents age they accumulate knowledge and will approach the technology

frontier. As this happens learning will become more difficult, causing a decline in learning

productivity.

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1.2.2 Production

The production sector of the model consists of competitive firms which hire efficiency units of

labour, , and rent physical capital, , to produce output, .. Letting denote the depreciation

rate of physical capital, then the net-of-capital-depreciation production function for the

representative firm is assumed to take the constant returns to scale Cobb-Douglas form:

, (1.6)

where α is the capital share of output.

1.2.3 Government

In this economy, there is a pay as you go system in which government collects labour income

taxes from workers to finance the pension payments to the retired individuals. A balanced

budget is required to be maintained in every period, and the government’s budget constraint is

given by:

maxT

Ts

stttt

r

bLw (1.7)

Furthermore, in every period t, government equally redistributes the confiscated accidental

bequests through government transfer to the survivors:

(1.8)

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1.2.4 Competitive equilibrium

For a given initial distribution of human and physical capital stocks, the stationary competitive

equilibrium in the model consists of a collection of policy rules:

for each type i, and factor prices such that:

1- The policy rules solve the optimization problem of each household in equation

(1.2) subject to (1.3) and (1.5) for , and (1.4) for .

2- Production factors are compensated by their marginal products:

3- Government balances its budget constraint and transfer constraint.

4- Commodity market clears:

α

α

5- In the factor markets, individual decisions and aggregate behaviors are consistent:

1.2.5 Solution methods

The steady state of the model is solved using the computational algorithms inspired by Heer and

Maussner (2005) as follows: First, we make a guess for the initial steady state values for

aggregate physical capital and aggregate labour. Second, the factor prices and pension benefits

are computed. Third, the household optimization problem is solved separately for both types

using backward induction. Then, the new aggregate values for labour and physical capital are

computed. If these values do not match the initial guesses then they are updated and this

procedure is repeated until convergence.

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1.3 Model calibration

Particular values for the parameters of the model must be assigned to obtain numerical solutions

to the model. The parameters are calibrated to match averages in the US data or set to values that

are commonly used in the macroeconomics literature. Table 1.1 summarizes the calibrated values

for the parameters of the model that will be explained in this section.

1.3.1 Demographics

It is assumed that age 1 in the model corresponds to the start of one’s working life, that is, age 18

in reality. Individuals may live up to Tmax=60 years in order to match the life expectancy at age

18 of males born in 1960 estimated by Bell and Miller (2002). The survival probabilities are also

obtained from Bell and Miller (2002). Although human capital is accumulated in the model via

LBD, it is well known that age-earnings profiles differ by education level (see Figure 1.16).

Therefore, the fraction of high types, ζ, is taken to be 0.46 to be consistent with the fraction of

individuals who pursued an education beyond high school from the Panel Study of Income

Dynamics (PSID) for the period of 1969-2011.

1.3.2 Policy parameters

In the benchmark economy, it is assumed that individuals are not allowed to continue to work

when they start collecting their pension benefits. Mandatory retirement age, Tr, is set to 48 to

target the retired to active population ratio of 21.6%. It also matches the normal (or full)

retirement age of 66 at which individuals are eligible to collect their full benefits in the US.

Furthermore, the social security payroll tax rate of 10.1 % in 19787, which implies the gross

6 Figure 1.1 shows the real average hourly earnings by age in 1969 prices from the Panel Study of Income

Dynamics (PSID) 1969-2011. 7 10.1% equals to the US Old Age and Survivors Insurance (OASI) tax rate in 1978

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replacement ratios of pension benefits at 64% and 37% correspondingly for low types and high

types. These ratios are comparable to replacement rates in the data in the way that the

replacement ratio for high earners is lower than low earners. The pension benefit, b, associated

with this tax rate is 0.1935 for the benchmark model.

1.3.3 Technology and preferences

The capital share, α, of 0.36 is taken from Kydland and Prescott (1982) and the depreciation rate

of physical capital, , is set to 10% per year as in Hansen (1985). The discount factor, β, and

disutility from work, ɣ, are chosen to be 0.9747 and 1.819, respectively, to target the return to

physical capital of 6% and the average time spent working of 0.3325 in the steady state. The rate

of return to physical capital is taken from Alessandrini et al. (2015) and the average time spent

working is generated from the Panel Study of Income Dynamics 1969-2011 for individuals aged

18 to 65. In the literature, the coefficient of the risk aversion is commonly assumed to be

between 1 and 2 (e.g. Imrohoroglu and et. al, 1998). Gandelman and Hernández-Murillo (2014)

estimate a constant relative risk aversion (CRRA) function with GMM to obtain the coefficient

of risk aversion for 75 countries using data from Gallup World Poll. The value of 1.384 for the

risk aversion parameter, ɳ, is taken from their estimate for the US.

1.3.4 Human capital

The parameters associated with human capital accumulation technology are calibrated as

follows: By rewriting the human capital accumulation function, the sequence of age-specific

learning abilities,

, for each type is estimated as follows:

ϕ (1.9)

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The average time spent working, and efficiency weights or exogenous human capital,

, for each age s and ability type are obtained using data on real hourly earnings and annual

work hours from the Panel Study of Income Dynamics (PSID) 1969-20118. To do this, first, male

head of households are divided into two groups based on their level of educational attainment

and six age groups (18-24, 25-34, 35-44, 45-54, 55-64 and 65-77) are defined. In particular, low

type individuals are those who achieved at most a high school diploma while high types obtained

further education above high school. Second, the average hours worked, and the real average

hourly earnings, , for each age group and type are obtained. By using the average hourly

earnings, the efficiency weights for each type and for each age group are computed following the

methodology put forward by Hansen (1993). Then, polynomial interpolation method is used to

interpolate the values of average time spent at work and efficiency weights for each age and

type. The parameter ϕ is set to be 0.029 to target the ratio of average efficiency weights between

high types and low types from PSID10

. In particular, the average hourly earnings for each age

group is divided by the average of hourly earnings obtained for all age subgroup by type. In the

model, the initial levels of human capital for low and high types are chosen to be 0.5773 and

0.5855, respectively, to match the calibrated efficiency weights at age 18 (e.g. year 1 in the

model) for each type,

and

, from the data.

Furthermore, the depreciation rate of human capital, , is assumed to be the same across all

individuals regardless of their type. In the literature, there is no consensus on the value of the

depreciation rate of human capital particularly with LBD skill accumulation. In order to select a

value for this parameter, the age-specific learning abilities series are generated with different

values for the depreciation rate of human capital within an acceptable range (e.g. 1%, 5%, 7.5%

and 10%). The wage profile from the data has a humped shape indicating that the wage declines

toward the end of the working period due to human capital deccumulation. In order to obtain

similar profiles in the model, it requires either the learning ability series take negative values or,

8 Data for years 1998, 2002, 2004 and 2008 were missing.

9 Starting with an initial guess for ϕ, the sequence of age-specific learning abilities is generated to run a simulation to

obtain a profile of human capital for each type of agent. If the ratio of average human capital between high type and

low type does not match the ratio of average efficiency weights between high type and low type from the data, the

guess for ϕ is updated until convergence. 10

For example,

.

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more plausibly, a depreciation rate of human capital that is sufficiently high. By setting ,

the model is able to replicate the declines in wage profiles late in life.

Panels (a) and (b) of Figure 1.2 illustrate the estimated human capital ( ) and age-specific

abilities ( i), respectively, over the working years by type and age. The efficiency weights have

a hump shape and are increasing at the beginning of the life and declining as individuals get

older. At any given age, the values of the efficiency weights are higher for high type agents

compared to low type individuals. The calibrated age-specific abilities decline by age for both

types and are higher for high types.

1.4 Results and discussions

This section presents the simulation results of the developed model with learning-by-doing at the

steady state. The simulated life cycle profiles are compared with the observed data from the

PSID for the period of 1969 to 2011. The life cycle profiles of labour supply are illustrated for

each type of agent to evaluate the ability of these models to replicate the life cycle profiles

observed in data. Then, a number of social security policy experiments are conducted and the

impacts of each policy on the variables of interest in the steady states are discussed.

1.4.1 Life cycle analysis

Panels (a) to (d) of Figure 1.3 present the corresponding steady state values of physical capital,

consumption, human capital and hours worked for the benchmark model by age and type.

Results indicate that each type of agent makes different decisions to maximize their utility over

the life cycle. High types devote less time to work and more to leisure when they are young,

compared to low types. This is an optimal response by the high types given the rapid increase in

wages they anticipate over their life cycle. For low types, wages are more constant over the life

cycle. The simulated physical capital-age profiles illustrate that the high types start their life with

borrowing, and hold fewer assets compared to low types in the model when they are young.

` 13

However, the rate of accumulating physical capital is higher for high types so they accumulate

more physical capital at any age above 37 in the model. Capital accumulation and labour

earnings are correlated. For example, high types start their life by spending less time to work and

borrowing to cover their expenses. However, when high types start allocating more time to work,

their earnings accelerate at a higher rate compared to low types due to their higher level of

human capital accumulation and consequently they are able to accumulate more physical capital

too.

Optimal choices by both types result in increasing consumption profiles during the

working periods but consumption declines sharply at the time of retirement which is consistent

with the literature (Bernheim, Skinner, and Weinberg, 2001; Hurd and Rohwedder, 2006).

Nevertheless, the reduction in consumption upon retirement is higher for high types than low

type agents. Human capital and hours worked have hump shapes which are consistent with the

corresponding life-cycle profiles from the actual data. During the working period, high type

agents accumulate a higher level of human capital at any age and allocate more time to work

with the exception of the first few years compared to low types. This is because high types are

more productive in learning compared to low types.

1.4.2 Model evaluation

Figure 1.4 presents the ability of the model to match the empirical life-cycle profiles for both

types for hours worked, wages and human capital. Data on wages and hours worked are from

PSID (1969-2011). Wages in both the data and model have been normalized to one at age 2011

since they have different units. The overall performance of the model is satisfying. The simulated

human capital and hours worked are able to replicate the main characteristics of data from PISD.

In particular, human capital increases quickly and labour supply slowly at the beginning of the

life cycle. On the other hand, the human capital profile is flat later in life while labour supply

declines towards the end of the working period. The calibrated productivity series play important

11

Note that the normalized wages for high type should not be compared to those for low types due to variation in the

wages at age 20 across types. The wage of high type is higher than the wage of low type at age 20.

` 14

roles in the success of the model to imitate the data. Thus, the developed model is capable of

strongly replicating the human capital series and wages across all age ranges. The model is not

fully able to match the life-cycle profile of time spent working, although there is an agreement

between the observed data and model for the shape of the labour supply profile of high type

individuals. The model slightly underestimates the labour supply at the end of working periods

for both types and overestimates it for low types at the beginning of life cycle. These

inconsistencies can be probably explained by the fact that the model does not account for some

features of the data that may impact the labour supply (e.g. indivisibilities in hours worked). In

reality, there is also more heterogeneity among individuals compared to what can be considered

in the model developed here. Other sources of heterogeneity that have not been modeled may

also cause discrepancies between the data and model for life cycle labour supply. That said, the

average hours worked is 31.8% for low types and 34.5% for high types in the data. In

comparison, in the model, low type and high type agents allocate, on average, 31.4% and 35.4%

of their time to work, respectively. Overall, the model provides a reasonable fit to the life cycle

characteristics observed in the data.

1.4.3 Social security reforms

This section provides the quantitative evaluation of the impact of social security reforms on the

economy and individuals’ decisions in the long run with an emphasis on heterogeneity among

agents by age and type. Four reforms are considered to study the economic effects and welfare

implications associated with eliminating the PAYG social security system ( ) and/or

introducing voluntary retirement:

Model 1 represents an economy with mandatory retirement and no PAYG social security

system.

Model 2 characterizes an economy with voluntary retirement and no PAYG social

security system.

In the next two experiments, we introduce voluntary retirement but keep the PAYG social

security system. Note, however, that this reform affects the government revenue. When

` 15

voluntary retirement is studied, in order to satisfy the government budget constraint, it is

necessary to either raise the contribution tax rate or lower the benefit level:

Model 3 corresponds to an economy with a social security system and voluntary

retirement wherein the payroll tax matches the social security tax rate in the benchmark

(BM) economy but the pension benefit is lower.

Model 4 illustrates an economy with a social security system and voluntary retirement in

such a way that the pension benefit is the same as it is in the BM economy while the tax

rate is higher.

Note that for all model economies, we assume that individuals can not start collecting their

pension benefits until they reach the full retirement age and pension benefits are tax exempted.

We study the social security reforms by first examining the life cycle and macroeconomic

effects. Then, we examine the welfare effects.

1.4.3.1 Life cycle and macroeconomic effects

Table 1.2 compares the long run economic outcomes after each policy implementation with the steady

state outcomes of the benchmark (BM) economy in which retirement is mandatory and there

exists a social security system as described in section 1.2. Although macroeconomic outcomes of

social security reforms are well known due to the vast existing literature, the life cycle analysis

of a reform needs more attention to understand how social security reforms impact individuals

differently by age and particularly by type. Figures 5 shows the life cycle profiles for physical

capital, consumption, human capital and hours worked for low type agents in panels (a) to (d),

respectively. Figure 1.6 illustrates the same life cycle profiles for high type agents. Furthermore,

Table 1.3 presents the average individual outcomes of policy reforms for separate age groups and

by type. The life cycle analysis shows that the impact of the social security reforms on labour

supply, physical capital, and consumption depend on an individual's age and type.

In Model 1, the elimination of the social security system with mandatory retirement results

in 14.7% and 6.9% increases in aggregate physical capital and labour, correspondingly,

compared to the benchmark economy. Consequently, the capital labour ratio is higher. The

` 16

increase in the capital-labour ratio causes a 11% reduction in the rental rate of physical capital

and a 2.4% increase in the wage rate. In an economy with no social security in which the sole

source of income during retirement is capital earnings, individuals have an incentive to save

more. Consequently, they accumulate more physical capital to acquire sufficient income to

finance their expenses during the retirement period. Furthermore, elimination of the social

security tax rate coupled with a higher wage rate has a substitution effect and an income effect

on labour supply. Overall, the results indicate that the substitution effect dominates the income

effect in which the average hours worked, , increases when . The increase in hours

worked in each period not only raises the current earnings but it also boosts up human capital

and consequently the future earnings of individuals. However, the impact of the social security

tax on labour-leisure decisions is greater for low types compared to high types. This is because

low types are less productive at work compared to high types. Therefore, without a social

security system, low type individuals need to work more to increase their earnings so that they

have sufficient savings for retirement. Due to a lower interest rate in this economy, both types

accumulate less capital when they are young (high types borrow more). However, middle-aged

and old workers spend more time at work and accumulate more physical capital to guarantee a

sufficient retirement income. Although individuals consume more during their working period,

consumption drops sharply upon retirement and stays below the consumption in the BM during

the retirement period due to lower retirement incomes.

Model 2 expands on the policy experiment in model 1 by allowing for voluntary retirement

in addition to the elimination of social security. The macroeconomic effects are qualitatively

similar to Model 1 in such a way that the aggregate physical capital, labour, consumption and

human capital are higher compared to the benchmark economy. Nevertheless, the elimination of

the social security tax accompanying with higher wage rate has different impacts on each type

and age when retirement is voluntary. Although both types choose to retire later in their life

compared to Model 1, high types’ working life duration (or labour force participation) increases

considerably by 9 periods compared to low types by 2 periods. The explanation for this is that

high types are relatively more productive later in life, and they will work more if given the

opportunity. However, average labour supply during the working period declines for high types

compared to the benchmark economy and Model 1 since they have less incentive to accumulate

more physical capital for their retirement due to being able to work longer. Comparing Model 1

` 17

and Model 2 reveals that a change in the labour force participation has different impacts on

physical capital at the individual level. The accumulation of physical capital is larger under

voluntary retirement for middle-age low types as a result of a relatively higher interest rate in

Model 2 than Model 1. In contrast, middle-age and senior high types accumulate less physical

capital under voluntary retirement since they receive labour earnings for longer periods and

consequently, they have less incentive to accumulate more physical capital for the retirement

compared to Model 1. The results in Table 3 also show a reduction in physical capital for middle

age high types compared to the correspondingly age group in the BM economy.

In Model 3, voluntary retirement is introduced into an economy with a social security

system. In this economy, the social security tax rate matches the benchmark economy. It results

in a 1.5% and 2.4% increase in aggregate physical capital and labour, correspondingly, compared

to the benchmark economy. Subsequently, a relatively lower capital-labour ratio results in a 2%

increase in the rental rate of physical capital and slightly decrease in the wage rate. Given the

same tax rate as benchmark economy, the pension benefits must also decrease by 6% since the

removal of mandatory retirement is associated with early retirement of low types. Furthermore,

the average time spent working for high types declines although they work longer compared to

the benchmark economy. Low types prefer to retire earlier since they are less productive at work

and their productivities decline faster as they age compared to high types. Thus, a reduction in

the wage rate makes working less attractive and discourages low types to work longer. Instead,

their average labour supply increases by 3.5% during their working period so they can save more

due to a higher rate of return compared to the benchmark economy. The decline in low type’s

labour force participation has some impacts on their consumption profile in which young and

middle-age groups consume less compared to the benchmark economy. The consumption during

the retirement is higher for both types in Model 3 since the pension benefits and interest rate are

higher.

Model 4 is similar to Model 3 in that there exits voluntary retirement and social security.

However, in model 4 the benefit level is increased to match its value in the BM economy. The

social security tax rate must increase by about 1.1% with voluntary retirement if the pension

benefit remains unchanged compared to the benchmark economy. This is because low types

leave the labour market earlier than the time they collect pension benefits and average hours

` 18

worked over the working period of high types decline by 7% even though they retire later. In this

economy, a larger decline in aggregate physical capital than in aggregate labour causes a lower

capital-labour ratio compared to the benchmark economy. As a result, the rental rate of capital

rises by 2.7% while the wage rate drops by 0.6%. Young low types accumulate more physical

capital and young high types borrow less due to a higher interest rate. In addition, the changes in

individuals’ labour force participation coupled with an increase in the tax rate are associated with

a negative response of middle-aged individuals on their savings. In particular, low types

accumulate less physical capital due to early retirement and high types need to save less for their

retirement as they work longer given a higher return on capital.

Comparing models 3 and 4, the results show that individuals respond differently in these

economies by type. In particular, an increase in the pension benefits and consequently the tax

rate does not promote an early retirement for high types while encourages low type individuals to

retire earlier. However, higher tax rate is associated with lower aggregate human capital in the

economy. Furthermore as tax rate increases, the average labour supply of high types decline

while low types increase their average hours worked. The results suggest that distinguishing

between high and low skill individuals is important when the social security policies are studied

particularly when these policies impact the decision to retire. These findings may also have some

policy complications for policy makers who seek solutions to alleviate the negative impacts of

population aging on the social security system and labour market.

1.4.3.2 Welfare effects

Following Koka and Kosempel (2014), the welfare benefits are measured as a fixed percentage

of consumption, Δ, that is required to make individuals indifferent between living in the

benchmark economy without compensation, and the alternative economy under a policy reform

with compensation at each age:

` 19

1

0

s

j

j

(1.10)

where the expected discounted life time utilities for each type of agent born in the benchmark

economy and the alternative economy under a given policy reform are denoted by

and

, respectively. Therefore, the percentage consumption compensation for each

type of agent is computed using:

(1.11)

Furthermore, the constant percentage of consumption compensation across all types of

individuals in the economy is obtained from the weighted expected discounted life time utilities

in the economy as it is utilized in Imrohoroglu et al. (1995) to measure the average utility in each

economy, :

1

0

s

j

j

(1.12)

The computed percentage consumption compensations at equilibrium for each type of

agent and for aggregate individuals are provided in Table 4. At the aggregate level, the results

show that individuals prefer the proposed policy changes to the benchmark. For example,

individuals born in Model 1 where social security is eliminated with mandatory retirement

require 0.18% reduction in per period consumption to be indifferent with the outcomes of

benchmark economy. However, the outcomes are interesting when the compensation variation is

computed for each type of agent.

First, the results alter at the individual level by type when voluntary retirement is

introduced with a social security system as in Model 3 and 4. In particular, high types born in the

benchmark economy are better off than high types born in an economy with social security and

voluntary retirement while low types prefer voluntary retirement. In Model 3 and 4, high types

` 20

require 0.008% and 0.015% increases in per period consumption to be as well of as high types in

mandatory retirement while low type require to give up 0.011% and 0.032% of their per period

consumption correspondingly. The reason for these differences is that the redistributional effects

of social security are larger in Model 4 than in the benchmark economy since benefits are not

proportional to taxes paid. In particular, high types bear a larger tax burden compared to the

benchmark economy due to an increase in tax rate. Low types benefit from an increase in the

amount of redistribution since they work for a shorter period of time but they receive the same

annual pension benefits.

Second, low types prefer to live in an economy without social security and pension

benefits during retirement. Although the amount of consumption in each period that low types

are required to sacrifice in order to be indifferent with the outcomes of benchmark economy is

0.05% lower than high types, the magnitude of the compensation variation is still significant for

low types. This is because the social security tax generates a distortion against labour supply, and

the cost associated with this distortion is larger than benefits of income redistribution through the

social security.

Third, both types prefer mandatory retirement when social security is eliminated since the

absolute compensation variation as a percent of consumption in each period is higher for both

types in Model 1 compared to Model 2. Koka and Kosempel (2014) explain that a coordination

problem in the unconstraint economy (the voluntary retirement economy) results in a lower

utility compared to an economy with mandatory retirement. When all high types are forced to

retire early, aggregate employment falls and consequently the capital-labour ratio declines. This

change positively affects the wage rate. The higher wage rate benefits all individuals and offsets

any costs associated with a shorter working life.

Finally, in an economy with social security and voluntary retirement, low types prefer an

economy with higher benefits even though it derives a higher tax rate while high types prefer an

economy with a lower tax rate. This happens because a higher tax rate leads to a shorter working

life for low type individuals and increases their life time utility due to more leisure they obtain,

while the working periods increases for high types. Furthermore, the redistributional effects of

` 21

social security are larger in Model 4 compared to Model 3, since benefits are not proportional to

tax paid. In particular, high types bear a larger tax burden due to an increase in the tax rate since

they retire later.

1.4.3.3 Exogenous human capital

In order to show why it is important to account for endogenous human capital when social

security policies are studied, the impact of social security reforms on the economy and

individuals’ decisions are investigated in an alternative model with exogenous human capital and

heterogeneous agents. Then, the outcomes from the alternative economy are compared with the

benchmark model which is described in section 2. In this economy, the exogenous human capital

for each type is taken from the calibrated human capital series, , in section 1.3.4.

Consequently, equation (1.5) is eliminated in this model. All parameters are taken from the

benchmark model to maintain the same characteristics of individuals for comparison purposes.

Similar to section 4.3, four policy reforms are considered.

Table 1.5 compares the steady states outcomes of this alternative economy with the

outcomes of the benchmark economy in section 4 and the outcomes of all policy models (e.g.

Model A1, Model A2, Model A3 and Model A4) with exogenous human capital. As it is

expected, the aggregate physical capital and aggregate labour are higher in the benchmark

economy with endogenous human capital compared to the alternative economy. However, a

larger increase in the aggregate physical capital compared to an increase in the aggregate labour

pushes the wage rate up by 0.4% while the interest rate declines by 1.9%. The reason is that in

the alternative economy, the wage rate is taken as given and individual’s labour supply decisions

are affected only through the opportunity cost of leisure. In the BM economy, an increase in

labour supply not only raises the current earnings of individuals but it also increases their future

earnings. Consequently, the average time spent working is higher for both types in the

benchmark economy compared to the alternative economy.

Comparing Table 1.2 and Table 1.5, the results show that the assumption of exogenous

human capital not only affects the key variables of the economy, but it predicts different

` 22

outcomes for the labour market participation of individuals in some cases when retirement is

voluntary. For example, after the elimination of social security and mandatory retirement in

Model 2, both high types and low types postpone their retirement by one more period when

human capital is endogenous compared to the corresponding model with exogenous human

capital. This is because first, the increase in the wage rate following the new policy is slightly

lower in the model with exogenous human capital compared to the model with endogenous

human capital. Second, a larger increase in the average labour supply of low types or a lesser

decline in the average labour supply of high types is not associated with higher human capital

accumulation to enhance the future earnings in the alternative economy after the reform. Thus,

individuals have less incentive to provide labour services for one more period.

Furthermore, comparing Tables 1.4 and 1.5 demonstrates how the assumption of exogenous

human capital leads to contradictory outcomes in a model with a social security system and

voluntary retirement. In particular, low types prefer Model 4 to Model 3 with endogenous human

capital due to a higher level of pension benefits and lower labour market participation, while the

results alter when human capital is assumed to be exogenous. Low types prefer Model A3 to

Model A4. This is because low types’ labour force participation declines more in this setting so

they have higher ability with extra leisure. A larger response among high types for their labour

market participation declines the pension benefits at a lower rate and increases the

redistributional effects of social security in Model 3 with the exogenous human capital.

Furthermore, high types are indifferent between Model 3 and Model 4 when human capital is

exogenous while the model of endogenous human capital accumulation leads to a different

outcome for high type since they are worse off in an economy with a higher social security tax

rate when retirement is voluntary.

1.5 Conclusion

In this study, a life cycle model of labour supply and human capital with heterogeneous agents

has been constructed. In the baseline model, human capital is accumulated through learning by

doing. Agents differ in productivity and initial level of human capital. In addition, productivity

` 23

declines by age. Then, two types of social security policies have been considered in constructing

various policy reforms. In one experiment, the PAYG social security system is eliminated and

the social security payroll tax rate and pension benefits are set to be zero with mandatory

retirement. In the second experiment, the PAYG social security system and mandatory retirement

are eliminated. The third and forth experiments represent voluntary retirement policy with a

social security system where either tax rate or pension benefits, respectively, matches the

baseline economy.

The results of these experiments demonstrate that individuals respond to a social security

policy differently by age and type. In particular, the variation in labour force participation with

voluntary retirement is diverse by type. Therefore, it is necessary to account for heterogeneity in

the model to study the social security systems. In general, both types prefer an economy with no

social security and welfare effect is stronger with mandatory retirement although retirement

consumption is lower than the reference economy. In a social security system, low types prefer

voluntary retirement and high types are better off in an economy with mandatory retirement due

to the changes in the distributional effects. Overall, an increase in the tax rate raises the labour

force participation of high-skilled individuals and declines the working life of low types.

Furthermore, the same exercises with social security reforms have been done with

exogenous human capital to explore how quantitatively macroeconomic outcome are affected by

this assumption. The results imply that in addition to aggregate economy, the behavior of

individuals impacted differently when retirement is voluntary. In particular, individuals prefer to

retire earlier due to lower opportunity cost of leisure with exogenous human capital. However, a

change in the tax rate does not have any impact on high types’ decision on when to retire. In

conclusion, the assumption of endogenous human capital is important for evaluation of social

security reforms with voluntary retirement.

` 24

` 25

Table 1-1: Calibrated Baseline Model Parameters with Heterogenous Agents

Parameters set to target Value from

US data

Value from

Model

Life expectancy at age 18 58.99

Retired to active population ratio 21.60% 21.1%

Average annual interest rate 6% 6%

Average time spent working of workers ( ) 0.3325 0.3325

/

1.5079 1.5079

Social security payroll tax rate in 1978 10.1%

` 26

Table 1-2: Steady States Outcomes of Policy Reforms with Endogenous Human Capital Accumulation

BM Model 1

%Δ from

BM Model 2

%Δ from

BM Model 3

%Δ from

BM Model 4

%Δ from

BM

K 1.0011 1.1485 14.7226 1.1614 16.0094 1.0163 1.5174 0.9814 -1.9624

L 0.2829 0.3023 6.8933 0.3161 11.7471 0.2895 2.3518 0.2806 -0.8047

Ha 0.9525 0.9546 0.2138 0.9901 3.9488 0.953 0.0519 0.9360 -1.7328

r 0.0599 0.0532 -11.2039 0.0565 -5.794 0.0612 2.1149 0.0616 2.7391

w 1.0101 1.0348 2.4424 1.0226 1.2426 1.0056 -0.4431 1.0043 -0.5729

b 0.1651 0 -100 0 -100 0.1551 -6.0731 0.1651 0

τ 0.101 0 -100 0 -100 0.101 0 0.1021 1.0505

K/Y 2.2455 2.3494 4.6278 2.2999 2.4246 2.2337 -0.5225 2.2287 -0.7485

K/L 3.5393 3.7985 7.3244 3.6743 3.8142 3.5104 -0.8152 3.4980 -1.1670

C 0.3462 0.374 8.0302 0.3844 11.0226 0.3493 0.8931 0.3488 0.7500

0.2951 0.3144 6.5457 0.3211 8.813 0.2956 0.1908 0.2938 -0.4398

0.4179 0.4498 7.6309 0.4693 12.3082 0.4256 1.8362 0.4272 2.2313

0.3325 0.3537 6.3945 0.3291 -1.028 0.3308 -0.4967 0.3328 0.0907

0.3141 0.3397 8.1497 0.3226 2.6996 0.3251 3.4861 0.3361 6.9966

0.354 0.3702 4.5663 0.3366 -4.911 0.3376 -4.6454 0.3289 -7.1027

47 47

49

43

39

47 47

56

51

53

a. Aggregate level of human capital in the economy; b. The dash over the variables indicates the average; c. The average labour supply

during the working period; d. Duration of working period.

` 27

Table 1.3: Average Individual Outcomes of Policy Reforms with Heterogeneous Agents for Separate Age Groups

Age Groups* Physical Capital

Consumption

Hours Worked

Low type High type

Low type High type

Low type High type

Benchmark Economy

18-35 0.3040 -0.3432

0.2250 0.3062

0.3782 0.3603

36-64 1.7185 1.4597

0.3175 0.4635

0.2743 0.3501

64+ 0.8948 1.5822

0.3421 0.4709

0 0

Model 1

18-35 0.1911 -0.6243

0.2608 0.3590

0.3732 0.3514

36-64 1.9771 1.4748

0.3428 0.5041

0.3190 0.3818

64+ 1.6984 2.4014

0.3252 0.4542

0 0

Model 2

18-35 0.2887 -0.5362

0.2550 0.3519

0.3774 0.3542

36-64 2.1893 1.2266

0.3472 0.5131

0.3009 0.3669

64+ 1.7969 2.0433

0.3542 0.5341

0.0221 0.1411

Model 3

18-35 0.3315 -0.3140

0.2231 0.3040

0.3791 0.3615

36-64 1.7453 1.3826

0.3153 0.4669

0.2467 0.3442

64+ 1.0011 1.6384

0.3522 0.5016

0 0.0558

Model 4

18-35 0.3267 -0.3032

0.2223 0.3028

0.3782 0.3623

36-64 1.6481 1.3863

0.3106 0.4672

0.2173 0.3428

64+ 0.9657 1.5508

0.3553 0.5103

0 0.0744

* Age groups represent the actual age groups in reality.

` 28

Table 1.4: Welfare Comparison with the Benchmark Economy

Model 1 Model 2 Model 3 Model 4

% Consumption Compensation:

Δ

-0.1776 -0.1688 -0.0035 -0.0129

Δl

-0.1568 -0.1509 -0.0113 -0.0320

Δh -0.2073 -0.1944 0.0079 0.0154

29

Table 1.5: Steady States and Welfare Effects of Policy Reforms with Exogenous Human

Capital

Outcomes AL

% Δ from Alternative Economy (AL)

BM

Model

A1

Model

A2

Model

A3

Model

A4

K 0.957 4.627 12.938 17.031 1.648 -1.721

L 0.272 3.882 6.229 12.289 -1.555 -0.673

r 0.061 -1.906 -10.804 -5.609 3.157 2.625

w 1.006 0.409 2.382 1.217 -0.667 -0.556

b 0.159 3.957 -100 -100 -1.696 0

τ 0.101 0 -100 -100 0 1.187

K/Y 2.235 0.458 3.997 2.683 2.070 -0.676

K/L 3.514 0.717 6.315 4.223 3.254 -1.055

C 0.332 4.158 7.432 10.372 1.177 0.983

0.286 3.189 5.974 8.255 0.137 -0.036

0.4 4.568 7.063 11.581 2.625 2.334

* 0.321 3.482 5.603 -0.335 0.505 0.216

0.305 3.095 7.320 3.378 7.835 7.027

0.341 3.888 3.800 -4.233 -7.190 -6.932

Δ

-0.182 -0.173 -0.019 -0.016

Δl

-0.161 -0.155 -0.040 -0.034

Δh

-0.213 -0.199 0.012 0.012

Working Period Duration:

tl 47 47 47 48 38 39

th 47 47 47 55 53 53

* The dash over the variables indicates the average.

30

Figure 1.1: Hourly Wages Profiles of College and Non College Graduates and all

Individuals

22 27 32 37 42 47 52 57 52 671.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Age

Av

era

ge H

ou

rly

Wag

es

Non College individuals

College individuals

All individuals

31

Figure 1.2: Calibrated Efficiency Weights, , and Productivity Sequence,

by Type and Age

0 10 20 30 40 50 600.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Age

(a) Efficiency Weights

0 10 20 30 40 50 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Age

(b) Productivity Sequence

Low Type

High Type

32

Figure 1.3: Steady States Profiles for High Type and Low Type Individuals for Baseline

Model

0 20 40 60-1

0

1

2

3

(a) Physical Capital

0 20 40 60

0.2

0.4

(b) Consumption

0 10 20 30 40 500.5

1

1.4

1.8

Age

(c) Human Capital

0 10 20 30 40 500

0.5

Age

(d) Hours Worked

Low type High type

0 10 20 30 40 500.5

1

1.5

2(e) Wage

0 10 20 30 40 500

0.5

(f) Earnings

33

Figure 1.4: Ability of the Baseline Model (LBD) to Replicate the Wages, Human Capital

and Hours Worked from the US Data for High Type and Low Type Individuals

0 10 20 30 40 500.5

1

1.5

Wages Low Type

0 10 20 30 40 500

0.5

1

1.5

Wages High Type

0 10 20 30 40 500.5

1

1.5

Human Capital Low Type

0 10 20 30 40 500.5

1

1.5

Human Capital High Type

0 10 20 30 40 500

0.3

0.6

Age

Hours Worked Low type

0 10 20 30 40 500

0.3

0.6

Age

Hours Worked High Type

Model

Data

34

Figure 1.5: Impacts of Social Security Reforms on Life Cycle Profiles of Low Type

Individuals

0 20 40 60

0

1

2

3

(a) Physical Capital Low Type

0 20 40 600.15

0.2

0.3

0.4

(b) Consumption Low Type

0 20 40 600.5

0.7

0.9

Age

(c) Human Capital Low Type

0 20 40 600.1

0.2

0.3

0.4

Age

(d) Hours Worked LowType

BM Model 1 Model 2 Model 3 Model 4

35

Figure 1.6: Impacts of Social Security Reforms on Life Cycle Profiles of High Type

Individuals

0 20 40 60

-1

0

1

2

3

4

5

(a) Physical Capital High Type

0 20 40 600.2

0.3

0.4

0.5

0.6

(b) Consumption High Type

0 20 40 60

0.6

0.8

1

1.2

1.4

1.6

Age

(c) Human Capital High Type

0 10 20 30 40 50 600.1

0.2

0.3

0.4

0.5

Age

(d) Hours Worked High Type

BM Model 1 Model 2 Model 3 Model 4

36

Chapter 2

2 Life Cycle Analysis of Investment-Specific and Neutral

Technology Shocks

2.1 Introduction

One of the central issues in business cycle analysis is what the driving sources of fluctuations

are. In the RBC literature pioneered by Kydland and Prescott (1982), neutral technology shocks

are determined as the main source of fluctuations.12

Whereas, Fisher (2006) and Justiniano et al.

(2010) show that the major variability of output and hours are associated with investment-

specific technology shocks as in Greenwood et al. (1988), rather than neutral technology shocks.

Fisher (2006) also suggests that it is important to account for both neutral and investment-

specific technology shocks as they together explain 40% to 60% of fluctuations in output and

hours. However, the role of investment-specific technology shocks in business cycles has not

been studied in a life cycle model, which can account for heterogeneity in responses across ages.

This study incorporates a finitely lived-agent model into a dynamic stochastic general

equilibrium framework to investigate the role of technology shocks as the source of business

cycle fluctuations. Two types of technology shocks are considered: neutral technology (NT) and

investment-specific technology shocks (IST). Greenwood et al (1997 and 2000) documented that

the correlation between relative price and quantity of new equipment is negative. This suggests

that equipment becomes less expensive due to technological improvements and consequently,

more equipment is accumulated. Therefore, the inverse of the relative price of investment has

been used to obtain a measure of IST that accounts for progress in the quality of capital. This

study also uses this measure for the realization of IST shocks. In order to identify the neutral

12

For example, see Hansen (1985), King et al. (1988), and King and Robelo (1999).

37

technology shock, it is important to separate the contributions of neutral technology shock from

other non-neutral technology (Carlaw and Kosempel, 2000; Bocola, Hagedorn, and Manovskii,

2014). In the model, fluctuations in productivity, excluding improvements in the quality of

capital, represent neutral technology shocks.

One of the main contributions of this study is to identify whether the cyclical properties at

the aggregate level are affected differently in a life cycle model when an IST shock hits the

economy compared to the infinity lived-agent models. The RBC literature shows that the

properties of the model after a NT shock remain unchanged when an overlapping generation

model is taken into the account (e.g. Rios-Rull, 1996; Krusell and Smith, 1998). The second

contribution of this study is to explore how technology shocks affect individuals differently by

age.

The results show that first the aggregate fluctuations are different in a life cycle model with

an IST shock compared to the standard infinitely lived agent models and in a model with only

NT shocks. In particular, the role of an IST shock as a driving force of fluctuations is small

where it accounts for only 10% of variation in output. In comparison, IST shocks are reported to

be responsible for about 30% and 50% of fluctuations in output in Greenwood et al. (2000) and

Justiniano et al. (2010) respectively. De Bock (2007) also shows that the importance of IST

declines from 40% to 6% when search and matching frictions are introduced in to the standard

RBC model as matching the new workers is time consuming. In this study, NT conversely

accounts for about 67% variations in output.

The outcomes are different by shock and type of model due to disparities in the nature of NT

and IST shocks and behaviour of individuals by age. The reason that the IST shocks in the life

cycle model are not as important as in the models with infinitely lived agents is that a life cycle

model accounts for differences in individuals decisions by age. Even though consumption

declines at the same rate for all individuals, labour supply and physical capital respond

differently by age with an IST shock. In particular, younger individuals even borrow more and

slightly increase their labour supply due to a reduction in the wage rate. Furthermore, differences

in the NT and IST shocks are due to differences in the nature of the shocks. In particular, a NT

shock directly impacts the production of goods through production sector in the economy and

boosts marginal returns to inputs while an IST shock affects the marginal efficiency of

investment and only triggers accumulation of physical capital directly. As a result, the wage rates

38

decline initially after the IST shocks and the response of labour supply is relatively small

particularly among younger workers. Despite the fact that individuals consume less in order to

accumulate more physical capital with IST shocks, less physical capital is accumulated in the

economy relative to the NT shocks. Therefore, NT shocks are more important than IST shocks in

the business cycle fluctuations

The remainder of the second chapter is organized as follows. In section 2.2, the model is

developed and the solution methods to obtain the steady states values and to calculate business

cycle movements are described. Calibration of the model is discussed in section 2.3. Section 2.4

presents the results and discuses the findings. The conclusions of this chapter are provided in

section 2.5.

2.2 The Model

A life cycle model is considered where time is discrete. Let s denote an individual’s age and t the

time period. It is assumed that a new generation of equal size is born every year. Individuals

begin their lives by working, retire at age Tr, and live up to Tmax periods.

Given the conditional probability, φs, of surviving from age s to age s + 1, the cohort

shares, θs, are given by

, where θs= φs-1 θs-1 (2.1)

Equation (2.1) indicates that the sum of the cohort shares equals to one.

2.2.1 Household’s problem

Individuals choose consumption, c, and leisure, l, to maximize their expected discounted life

time utility:

39

, (2.2)

where γ determines the relative importance of leisure, η is the coefficient of relative risk

aversion, and β is the discount factor.

In each period, each individual has been provided with one unit of time. During the

working period, time can be allocated among leisure, l, and work, n. Workers receive income

from providing labour services and from renting capital assets to the production sector. Retired

agents provide no labour services and instead, receive public pensions, b, from government.

Individuals begin their life with no physical capital and leave no intentional bequests at the end

of their life. Physical capital, k, is accumulated during life through investment, i, according to

(2.3)

where is the depreciation rate of physical capital, and q indicates the current state of

investment-specific technology. It is assumed that q is stationary and represents only the

stochastic component to IST. The stochastic possess for investment-specific shocks is:

(2.4)

with .

The budget constraints for working and retired agents, respectively, are as follows:

(2.5)

(2.6)

where r is the real rental rate of physical capital, h is worker’s efficiency weights or age-specific

human capital, τ is the labour income tax rate, and tr is a lump sum government transfer or tax.

In view of the fact that heterogeneity in the RBC models to some extent improves the predictions

(e.g. Alessandrini et al. 2015; Hansen and Imrohoroglu, 2009; Gomme et al., 2004; Maliar and

Maliar, 2001), age-specific human capital values are imposed.

40

It is worth mentioning that an increase in q or improvement in the quality of new capital

lowers the cost of capital. The reason is that represents the relative price of capital in terms

of consumption in the budget constraints. In other words, an individual can invest in physical

capital, in each period, by sacrificing units of consumption.

2.2.2 Production

The production sector of the model consists of competitive firms which hire efficiency units of

labour, , and rent physical capital, , to produce output, .. The production function for the

representative firm is assumed to take the constant returns to scale Cobb-Douglas form:

(2.7)

where α is the capital share of output and zt denotes the state of neutral technology which follows

the stochastic process

(2.8)

with .

2.2.3 Government

In this economy, there is a pay as you go social security system. The government collects labour

income taxes from workers and accidental bequests from those who die before Tmax. Government

revenue is used to finance pension payments to the retired individuals. A balanced budget is

required to be maintained through a lump sum transfer or tax in every period. The government’s

budget constraint is given by:

(2.9)

41

2.2.4 Competitive equilibrium

For the given initial distribution of physical capital stocks and the government instruments ( ),

the stationary competitive equilibrium in the model consists of a collection of policy rules:

,

and factor prices such that:

6- The policy rules solve the optimization problem of each household in equation

(2.2) subject to (2.5) for , and (2.6) for .

7- Production factors are compensated by their marginal productivity:

8- Government balances its budget constraint.

9- The commodity market clears:

α

α , (2.10)

where the law of motion for aggregate physical capital is:

10- In the factor markets, individual decisions and aggregate behaviors are consistent:

2.2.5 Solution methods

Inspired by Heer and Maussner (2005), the computational algorithms to solve the non-stochastic

steady state of the model are as follows: First, we make a guess for the initial steady state values

for aggregate physical capital and aggregate labour. Second, the factor prices and pension

benefits are computed. Third, the household optimization problem is solved using backward

induction. Then, the new aggregate values for labour and physical capital are computed. If these

42

values do not match the initial guesses then they are updated and this procedure is repeated until

convergence.

Next, positive neutral and investment-specific technology shocks are disjointedly introduced

in the model to study the role of each technology shock on business cycles. To do this, the first

order conditions are log-linearized around the non-stochastic steady state to compute the

transitional dynamics and business cycle statistics. A system of linear equations is numerically

solved in order to study the fluctuations. Note that the model requires being stationary at the

steady states. Then, a positive one percent shock to each type of technology is independently

introduced into the model. The impulse response functions are acquired in order to demonstrate

the time path that directs the economy toward the steady state after the shocks. Lastly, the

average business cycle statistics over 1000 runs, consisting of 100 periods, are generated for each

technology shock as well as when both shocks are combined. These statistics are compared to the

annual business cycle statistics for U.S. economy.

2.3 Model calibration

Values for the parameters of the model must be assigned in order to obtain numerical solutions to

the model. The parameters are set to match averages in the US data or set to values that are

commonly used in the macroeconomics literature. Table 2.1 summarizes the values for the

parameters of the model that will be explained in this section.

2.3.1 Demographics

It is assumed that age 1 in the model corresponds to the start of one’s working life, that is, age 18

in reality. Individuals may live up to Tmax=60 years in order to match the life expectancy at age

18 of males born in 1960 estimated by Bell and Miller (2002). The survival probabilities are also

obtained from Bell and Miller (2002). In the model, it is assumed that individuals are not allowed

to continue to work when they start collecting their pension benefits. Mandatory retirement age,

43

Tr, is set to 48 to target the retired to active population ratio of 21.6%. It also matches the normal

retirement age13

of 65 at which individuals have been eligible to collect their full benefits in the

US for many years. Furthermore, the social security payroll tax rate of 10.7% is taken from

Conesa and Krueger (1999).

2.3.2 Technology and preferences

The capital share, α, of 0.36 is taken from Kydland and Prescott (1982, 1977) to match the US

time series data. The discount factor, β, and disutility from work, ɣ, are chosen to be 0.974 and

1.817, respectively, to target the return to physical capital of 6% and the average time spent

working of 0.3325 in the steady state. The rate of return to physical capital is taken from

Alessandrini et al. (2015) and the average time spent working is generated from the Panel Study

of Income Dynamics (PSID) 1969-2011 for individuals aged 18 to 65. By setting the

depreciation rate of physical capital to 6% per year as in Alessandrini et al. (2015), the average

physical capital to labour ratio of 3 is maintained. In the literature, there is no consensus on the

coefficient of the risk aversion. It is commonly assumed to be between 1 and 2 (e.g. Imrohoroglu

and et. al, 1998). For example, Gandelman and Hernández-Murillo (2014) estimate a constant

relative risk aversion (CRRA) function with GMM to obtain the coefficient of risk aversion for

75 countries using data from Gallup World Poll. The value of 1.384 for the risk aversion

parameter, ɳ, is taken from their estimate for the US.

2.3.3 The human capital profile

The efficiency weights or human capital, , for each age s are obtained using data on real hourly

earnings from the Panel Study of Income Dynamics (PSID) 1969-201114

. To do this, first, male

head of households are divided into six age groups of 18-24, 25-34, 35-44, 45-54, 55-64 and 65-

77. Second, the real average hourly earnings, , for each age group is obtained. By using the

13

It is also known as the full retirement age. 14

Data for years 1998, 2002, 2004 and 2008 were missing.

44

real average hourly earnings, the average efficiency weights for each age group are computed

following the methodology put forward by Hansen (1993). In particular, the average hourly

earnings for each age group are divided by average hourly earnings for all subgroups. Then,

polynomial interpolation method is used to interpolate the values of human capital for each age.

Panel (a) of Figure 2.1 illustrates the calibrated efficiency weights over the working years by

age. The efficiency weights have a slight hump shape. They are increasing quickly at the

beginning of the life and then only decline slightly toward the end of the working period.

2.3.4 Stochastic parameters

The inverse of relative price of investment to consumption,

, is used to estimate the parameters

of the stochastic process for q as follows:

where,

with ) and .

To do this, yearly data on the price index of consumption is divided by the price index for

private fixed investment in structures and equipment in order to obtain the inverse of relative

price of investment to consumption. The price indexes are directly taken from the National

Income product Account (NIPA) for the sample period 1982 to 2012. The estimates for and

are 0.817 and 0.0105 respectively.

Following Greenwood and et al (1997), Fisher (2006) argue that the NIAP investment

deflator is not fully adjusted for quality, particularly, prior to 1982. Consequently, they used a

quality adjusted equipment deflator from Cummins and Violante (2002) which is an update of

Gordon’s 1990 series for the sample period 1955-2000. However, Carlaw and Kosempel (2000)

claim that the procedure for quality adjustment has been improved and the previous estimates are

revised.

45

Following Carlaw and Kosempel (2000), the neutral technology series is obtained from the

production function:

. Then, the parameters of the neutral technology shock

process are obtained as follows:

where,

with ) and .

Several steps need to be taken to generate the neutral technology series. First, the aggregate

labour is obtained using data from Bureau of Labor Statistics (1982-2012), and represents total

non-farm hours worked. Second, the physical capital series is constructed using the real domestic

private investment series from the NIPA and then, iterating over the law of motion provided in

equation (2.3). The initial value for physical capital is chosen to generate a steady state growth

rate of 4.387 for the stock of physical capital in order to match the average annual growth rate of

real domestic private investment in the NIPA data for the sample period 1982 to 2012. Lastly,

the NIPA’s output measure needs to be adjusted to remove the quality component in new capital

goods. This is because as in equation (2.10), output is measured in units of consumption and

therefore, quality improvements are not directly included. However, the components of real

output in data are not measured in units of consumption and contain the quality improvement in

investment.15

Thus, investment component of output (Real Gross Domestic product) from the

data is divided by the measure if IST, q, in order to remove the quality component of investment,

using data from NIPA (1982-2012).Therefore, the parameters and are set to be 0.895 and

0.0133 respectively.

2.4 Results and discussions

The section 2.4.1 presents the simulation results of the model at the non-stochastic steady state

where and are set to one. Then, in sections 2.4.2 and 2.4.3, the impact of neutral and

15

For more details, see Carlaw and Kosempel (2004).

46

investment-specific technology shocks on the economy and individuals’ decisions over the life

cycle are investigated.

2.4.1 Steady States Analysis

Panels (b) to (d) of Figure 2.1 present the corresponding steady state values of labour supply,

physical capital, and consumption by age. Results indicate that individuals make different

decisions to maximize their utility over the life cycle. Labour supply has a hump shape which is

consistent with the corresponding life-cycle profile from the actual data presented in Figure

2.216

. In particular, prime age workers devote more time to work and less to leisure than younger

and older workers. This is an optimal response for individuals given the rapid increase in wages

they anticipate over their midlife period. Overall, the model is more able to predict labour supply

decisions of younger and middle age worker relative to older workers who are paid the most but

work less. In particular, reduction in labour supply among older workers is larger compared to

the data. Furthermore, capital accumulation and labour earnings are correlated. The simulated

physical capital-age profiles illustrate that individuals start their life with borrowing to cover

their expenses as they initially allocate less time to work because they are initially less

productive at work.17

When they start allocating more time to work due, their earnings accelerate

at a high rate due to their higher level of productivity and consequently they are able to

accumulate more physical capital. In particular, they accumulate physical capital at any age

above 2718

. Optimal choices result in increasing consumption profiles during the working

periods but consumption declines sharply at the time of retirement due to reduction in the

earnings upon the retirement and increase in leisure which is consistent with the literature

(Bernheim, Skinner, and Weinberg, 2001; Hurd and Rohwedder, 2006).

The steady state results show how individuals’ decisions over consumption, labour

supply, and the accumulation of physical capital are age-dependent and vary over the course of

16

Data on hours worked are from PSID (1969-2011) 17

If individuals anticipate no change in their wages over time, they start their life with accumulating physical

capital. It happens when human capital is flat and age-independent. 18

It is equivalent to age 10 in the model.

47

their life. Based on this, we also expect individuals will respond differently to a shock by age.

Thus, aggregate outcomes may be different in a life cycle model compared to an infinitely-lived

agent model when a shock is introduced into the economy. Differences in individuals’ decisions

by age and their impacts on the economy by type of technology shock are investigated in the

following subsections.

2.4.2 Neutral Technology Shocks

Figure 2.3 presents the impulse response functions for the aggregate variables to a positive one

percent neutral technology shock. The percent deviations from the steady states after the shock

show that all variables are pro-cyclical. The outcomes are consistent with the typical responses in

the RBC literature and the responses are well understood (e.g. Alessandrini et al., 2015).

Innovations to neutral technology impact output directly, and lead to an increase in the marginal

products of labour and physical capital. Therefore, the boost in the returns to working and

savings, cause physical capital and labour supply to respond positively due to the NT shocks. An

increase in output also leads to a positive response for consumption since it is a normal good.

The marginal rate of transformation between physical capital and consumption goods remains

unchanged since the relative price of consumption goods to physical capital is not affected by the

NT shocks.

One of the advantages of developing a life cycle model is that we are able to provide

insight about how individuals respond differently to a shock by age. Panels (a) to (d) of Figure 4

show the impulse response functions for labour supply, net labour earnings, consumption, and

physical capital, correspondingly, after a positive neutral technology shock. Five age groups are

defined: 18-28, 29-39, 40-50, 51-64 and 65-77 years of age where the last group consists of

retired individuals. Labour supply responds positively to a positive neutral technology shock for

individuals at any age group due to a sharp increase in the wage rate which leads to a positive

response of net labour earnings. However, the increase in labour supply is stronger for senior

workers who are in the age group 51-64 compared to the younger individuals. This is due to the

fact that retirement at age of 65 is mandatory and senior workers face a shorter working horizon

48

and have a limited chance to take advantage of a rise in the wage rate. Thus, it is optimal for this

age group to substitute more leisure for consumption to maximize their discounted life time

utility. Furthermore, senior workers are relatively more productive than younger workers, but

their human capital diminishes as they age. Therefore, current leisure is more expensive than

next period leisure for this age group, whereas the opposite is true for the young.

The consumption boom is mainly driven by working individuals after a positive neutral

technology shock due to simultaneously increases in the wage rate and renal rate of physical

capital. The positive response of consumption is moderate for retired individuals since their

retirement earnings raise only through their capital earnings due to an initial positive response of

the rental rate. In regards to physical capital after a NT shock, a disparity in the behavior of

younger groups is surprisingly observed. In particular, individuals aged 18-27 who were

borrowers at the steady states need to increase their debt in order to compensate for an increase

in their consumption as an increase in their earnings is not adequate. Thus, they maximize their

life time utility by substituting future consumption for current consumption instead of more

current leisure as they are less productive at work and an increase in the wage rate is not

sufficient enough to make leisure less attractive. Conversely, individuals aged above 28

accumulate more physical capital due to a higher return to physical capital. However, physical

capital is more responsive to the NT shocks for individuals aged 28-37 since they face a

relatively longer horizon in their life.

2.4.3 Investment-Specific Technological shocks

Figure 2.5 presents the impulse response functions for the aggregate variables to a positive one

percent IST shock in the model. The adjustment of key variables towards their steady states is

slower after an IST shock compared to a neutral technology shock. The differences between the

dynamic behaviors of the aggregate economy after a neutral technology shock relative to an IST

shock derive from the differences on how the production function is affected by shocks. In

particular, the production of all goods is affected homogenously by neutral technology shocks,

whereas the cost of investment goods relative to consumption goods changes when IST shocks

49

hit the economy. Thus, a positive IST shock directly increases the investment opportunities and

impacts the production of physical capital, but the production technology for consumption goods

is not directly affected.

The percentage deviations from the steady states after an IST shock show that all

variables except wages and consumption are pro-cyclical. Initially, consumption responds

negatively to the IST shock. This is due to the fact that current consumption and leisure are more

expensive compared to future consumption. Thus, current consumption declines while labour

supply initially increases after a shock due to the substitution effects. In particular, individuals

substitute current consumption for future consumption due to the reduced cost of physical

capital. As a result, there is an investment boom. Labour supply responds positively as agents

want to work more to finance capital investment. The positive response of labour supply leads to

a reduction in the wage rate initially. As a result, the return to physical capital initially rises due

to a reduction in capital to labour ratio. Innovations to investment-specific technology results in

the accumulation of more physical capital due to a reduction in the price of investment and,

consequently, output increases. Furthermore, as physical capital is accumulated, the rental rate of

physical capital declines and the wage rate increases in the following periods. Finally,

consumption gradually rises with a fall in the rental rate of physical capital and an increase in

output.

The dynamic behavior of investment and consumption are consistent with outcomes in

Fisher (2006). In particular, investment reaches its maximum level immediately and

consumption drops first before starting to increase while Greenwood et al. (2000) found a

positive response of consumption after an IST shock. The response of output is moderate but

more persistent with IST shocks relative to NT shocks. It increases after the shock due to an

immediate response of labour supply and curves U-shaped similar to the physical capital so IST

affects output through physical capital more than through labour supply in the following periods

after the shock.

Figure 2.6 shows the impulse response functions by age group for labour supply, net

labour earnings, consumption, and physical capital after a positive IST shock in panels (a) to (d),

correspondingly. Similar to neutral technology shocks, labour supply responds positively and

strongly to IST shocks for senior workers who are in the age group 51-64 compared to the

50

younger individuals. Since older workers face a shorter horizon before their retirement, they

want to work more and invest further, so that they can boost their retirement income. However,

the response of labour supply is more moderate for all age groups after an IST shock relative to a

neutral technology shock due to the fact that an IST shock has no direct effect on output and

labour productivity. Despite a positive response of labour supply, net labour earnings respond

negatively to the shock due to negative response of wages.

After a positive IST shock, most individuals accumulate more physical capital except the

youngest individuals. The shock directly improves the production of physical capital, so physical

capital becomes cheap relative to consumption. Therefore, it is an optimal decision to

accumulate more physical capital in order to increase their future consumption after a positive

IST shock except for those young individuals who are least productive at work and have no

capital earnings. The reason is that the youngest workers start their life with no physical capital

and have to borrow as their labour earnings are not high enough to cover their consumption

expenditures due to having low productivity at work. After an IST shock, labour earnings of the

youngest workers declines due to a reduction in the wage rate and insufficient response of labour

supply so they are required to borrow more and consume less to balance their budget constraint.

This is the main difference between finite and infinite horizon models, where all ages invest

more in an infinitely lived agent model. However, similar to NT shocks, individuals aged 28-37

accumulate more physical capital. Consequently, the immediate responses of current

consumption for all individuals are negative due to a slower response of output as IST shock

impacts output indirectly through the accumulation of more physical capital. However,

consumption changes its direction and increases as the formation of new physical capital

improves future output.

2.4.4 Business Cycle Statistics

Table 2 shows the annual business cycle statistics for U.S. economy along with average business

cycle statistics over 1000 runs by different types of technology shocks. To do this, the natural

logarithms of the simulated series are obtained and then, the Hodrick-Prescott filter with the

51

smoothing parameter of 6.25 as in Rvan and Uhlig (2002) is applied to de-trend the series. The

corresponding business cycle statistics for output, investment and consumption for the US

economy are obtained using data from US Bureau of Economic Analysis (1982-2012). Output

represents the real gross domestic product adjusted by removing q as in section 3.4, and

consumption is personal nondurable and services consumption expenditure. Investment stands

for gross private domestic investment which includes investment-specific technology or quality

component in the NIPA series. Therefore, investment series from the model is multiplied by q to

make model-data comparison possible. Labour supply statistics in table 2.2 for the US economy

are obtained using data from CPS, March Supplement (1982-2012). Labour supply indicates

actual hours worked in a week before the time of survey by employed males.

Regarding U.S. data, investment fluctuates about 2.7 times as output while labour supply

and consumption volatilities are 0.3 and 0.4 of output correspondingly. In the model, the

fluctuations in investment are about 4.7 times higher than output when both shocks are

combined. It is not surprising that investment fluctuates more relative to output with IST shocks.

Furthermore, labour supply and consumption volatilities are correspondingly 0.3 and 0.5 of

output in the model. Relative to US data, labour supply and consumption fluctuate less and

investment fluctuate more in the model when both shocks are combined. Therefore, the model

underestimates the fluctuations in consumption and labour supply which is typical in the RBC

literature. Labour supply fluctuations are very low for young workers relative to data.

Overall, Output fluctuates 0.7 times as output in U.S. economy indicating technology shocks

are major sources of fluctuations in output. However, the results show that first the aggregate

fluctuations are different in a life cycle model with an IST shock compared to the standard

infinitely lived agent models. In particular, the role of an IST shock as a driving force of

fluctuations is limited where it accounts for 10% of variations in output whereas, IST shock is

reported to be responsible for about 30% and 50% of fluctuations in output in Greenwood et al.

(2000) and Justiniano et al. (2010) respectively. The reason that fluctuations in output are higher

in a model with infinitely lived agents is that those models ignore different behaviors of

individuals by age. In order to increase output significantly after an IST shock, physical capital

must respond strongly. However, the younger individuals in the model actually borrow more

after an IST shock due to a reduction in the wage rate.

52

In the model with IST shocks, consumption is counter-cyclical but combining the shocks

leads to a positive correlation between consumption and output since the counter-cyclical of

wage rate with an IST shock is offset by pro- cyclical impacts of a NT shock on the wages when

both shocks are combined.

2.5 Conclusion

In this study, a large scale overlapping generation model is constructed to study the role of

neutral and investment-specific technology shocks as driving forces of business cycles.

Furthermore, the model was used to explore the impacts of shocks on individual’s physical

capital accumulation, labour supply, and consumption and how these responses vary over the life

cycle.

The outcome of this study shows that the role of investment-specific technology shocks as a

driving source of fluctuation is not consistent with the IST literature. In particular, investment-

specific technology shocks account for about 10% of variation in output while it is 67% with

neutral technology shocks. The results also show that the impacts of technology shocks on labour

supply, consumption, and physical capital depend on an individual's age and the nature of

shocks. Differences in the response of physical capital and labour supply by age is the reason

that the IST shocks in the life cycle model are not as important as in the models with infinitely

lived agents. In particularly, younger individuals even borrow more and slightly increase their

labour supply due to a reduction in the wage rate after an IST shock. Furthermore, differences in

the NT and IST shocks are due to differences in their impacts on the production sector. In

particular, a NT shock directly impacts the production of goods through production sector in the

economy and boosts marginal returns to inputs while an IST shock affects the marginal

efficiency of investment and only triggers accumulation of physical capital directly.

53

Table 2.1: Calibrated model parameters

Parameters set to target Value from US

data

Value from

Model

Life expectancy at age 18 58.99

Retired to active population ratio 21.60% 21.1%

Average annual interest rate 6% 6%

ɣ 176 Average time spent working of workers 0.3325 0.3326

Table 2.2: Business cycle statistics

X

Corr(X,Y)

Data TFP

shock

IST

shock

Both

shock Data

TFP

shock

IST

shock

Both

shock

Y 1.57 1.05 0.15 1.07 1.00 1.00 1.00 1.00

qI 4.22 4.10 2.71 5.07 0.88 0.99 0.95 0.89

N 0.46 0.29 0.21 0.37 0.74 0.99 0.93 0.87

C 0.66 0.40 0.27 0.49 0.81 0.98 -0.87 0.73

N (18-24) 1.15 0.16 0.21 0.27 0.68 0.93 0.91 0.67

N (25-34) 0.56 0.19 0.18 0.27 0.72 0.97 0.92 0.80

N (35-44) 0.48 0.26 0.19 0.33 0.67 0.99 0.93 0.87

N (45-54) 0.42 0.42 0.29 0.51 0.69 0.99 0.94 0.89

N (55-64) 0.50 0.96 0.57 1.14 0.44 0.99 0.95 0.92

54

Figure 2.1: Steady state outcomes by age

27 37 47 57 670.4

0.6

0.8

1

1.2

1.4

(a) Human Capital

27 37 47 57 670.1

0.2

0.3

0.4

(b) Labour Supply

27 37 47 57 67 77-1

0

1

2

3

4

Age

(c) Physical Capital

27 37 47 57 67 77

0.2

0.45

0.7

Age

(d) Consumption

55

Figure 2.2: Hours worked comparison between model and actual data

22 27 32 37 42 47 52 57 62 670

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Age

Ho

urs

Wo

rked

Data

Model

56

Figure 2.3: Impulse response functions for aggregate variable after a positive neutral

technology shock.

0 10 20 30 40 500

0.5

1

Neutral Technology Shock (z)

0 10 20 30 40 500

0.7

1.5Output (Y)

0 10 20 30 40 50

0

3

6Investment (I)

0 10 20 30 40 500

0.5

1

1.5Physical Capital (K)

0 10 20 30 40 500

0.4

0.8Consumption(C)

0 10 20 30 40 500

0.5

1Wage (w)

Period0 10 20 30 40 50

-1

0

1

2Rental Rate (r)

Period

0 10 20 30 40 50

0

0.3

0.6Labour Supply (N)

57

Figure 2.4: Impulse response functions after a positive neutral technology shock by age

group

0 10 20 30 40 50

-0.2

0

0.4

0.8

(a) Labour Supply

0 10 20 30 40 50

0

0.5

1(d) Consumption

Period

0 10 20 30 40 50-10

-5

0

5(c) Physical Capital

Period

Age 18-27 Age 28-37 Age 38-47 Age 48-64 Age 65-77

0 10 20 30 40 50-0.2

0

0.4

0.8

(b) Net Labour Earnings

58

Figure 2.5: Impulse response functions for aggregate variable after a positive IST shock

0 10 20 30 40 500

0.5

1

Investment-Specific Technology Shock (q)

0 10 20 30 40 50

0

0.2

0.4

Output (Y)

0 10 20 30 40 500

1.5

3

Investment (I)

0 10 20 30 40 500

0.5

1

Physical Capital (K)

0 10 20 30 40 50

-0.3

0

0.4

Consumption(C)

0 10 20 30 40 50-0.2

0

0.4

Wage (w)

Period

0 10 20 30 40 50-1

-0.5

0

0.5Rental Rate (r)

Period

0 10 20 30 40 50-0.1

0

0.3

Labour Supply (N)

59

Figure 2.6: Impulse response function after a positive IST shock by age group

0 10 20 30-0.2

0

0.4

0.8(a) Labour Supply

0 10 20 30-0.5

-0.25

0

0.25

0.5(d) Consumption

Period

0 10 20 30-10

-5

0

5

10(c) Physical Capital

Period

Age 18-27 Age 28-37 Age 38-47 Age 48-64 Age 65-77

0 10 20 30

-0.1

-0.05

0

0.05

(b) Net Labour Earnings

60

Chapter 3

3 Education, Skills and Labour Market Outcomes of

Canadian Second Generation Immigrants

3.1 Introduction

Numerous studies have focused on the labour market outcomes of immigrants and on how

immigrants integrate into the economic and social structure of the host country (Chiswick 1978,

Baker and Benjamin, 1997; Aydemir and Skuterud, 2005; Grant 1999 and McDonald and

Worswick, 1999). The results from these studies show that immigrants suffer a wage penalty at

entry. Moreover, while older cohorts of immigrants were eventually able to catch up with the

native-born in terms of earnings, this is no longer true for more recent cohorts, for whom

assimilation can no longer happen within one generation.

A much less studied question refers to the performance of the children of these

immigrants, whom the literature refers to as “second generation immigrants”. The literature

defines immigrant generations as follows: the first generation are immigrants who were born in a

country rather than the host country, the second generation are those who were born in a country

and have at least one parent born abroad, and the third generation were born in a county from

non-immigrant parents.

The children of immigrants are expected to perform better in the labour market than

immigrants due to having achieved their education and work experience in the host country.

Given that foreign educational credentials and work experiences are often inadequately

recognized and rewarded in the labour market, we should expect that the children of immigrants

fare better than first generation immigrants. Moreover, there is a strong intergenerational

transmission of educational attainment: children of educated parents are more likely to be

61

educated themselves. In countries such as Canada and Australia, where immigrants are selected

based on education according to a points system, we should expect that children of immigrants

will be highly educated themselves. Conditional on education, second generation immigrants

should not experience any differences in the return to their human capital compared to natives,

given that they are born and educated in the host country. Investigating the human capital and

labour market outcomes of second generation immigrants is therefore very important because it

highlights an outcome of immigration policy often overlooked: the benefit to the host country

from selective immigration coming from the intergenerational transmission of human capital.

The aim of this paper is to investigate how the labour market outcomes as well as the

education and skills outcomes differ between second and third generation Canadians. Existing

literature documents that second generation Canadians are more educated than third or first

generation Canadians (e.g. Aydemir and Sweetman, 2006; Tue, 2010; Hum and Simpson, 2007).

Unconditionally, this translates into higher average earnings for second generation Canadians.

Nevertheless, the literature disagrees whether the earning premium persists, conditional on

education and socio-economic background. Using the 2001 Canadian Census, Aydemir and

Sweetman (2006) show that the positive difference in income switches to negative for Canadian

second generation immigrants when socio-economic characteristics are controlled for. They

conclude that second generation immigrants in Canada have advantages in some observed

characteristics associated with higher earnings such as education and region of residence, but the

return on those characteristics is lower than that for the third generation. However, the reason

behind the gaps in the return of return to those characteristics is not addressed. Likewise, Tue

(2010) documents a negative income gap for second generation Canadian immigrants who have

post-secondary education, while finding no significant gap for those with high school or lower

education. Ethnicity, mother tongue and city of residence are mentioned as barriers for

transferring the intellectual ability into productivity among well educated second generation

immigrants. In contrast, Hum and Simpson (2007) use the Survey of Labour and Income

Dynamics (SLID) to show that ethnic differences do not change the conclusions on the relative

performance of second generation immigrants. They find that conditional on education and other

socio-economic characteristics, second generation immigrants do not earn significantly lower

than other native counterpart. This paper contributes to the existing literature by providing

62

evidence that no wage gap exists among Canadian-born individuals based on parental birth of

place.

In terms of the effect of parental education on second generation immigrant wages, Chen

and Feng (2009) find substantial positive correlation between parental education and wages

received by immigrants’ offspring. Moreover, Borjas (1993) shows that the source countries of

immigrant parents strongly affect the earnings of second generation immigrants. Canadian

Studies also documented that parental education extensively explains educational attainment of

second generation (e.g. Bonikowska, 2005; Finnie 2008).

The studies of labour market outcomes for second generation immigrants have focused

almost exclusively only on the formal educational achievements to explain the positive labour

market outcomes of second generation immigrants compared to other natives. Nevertheless, a

very small international literature exists where differences in wage returns by immigrant

generations are examined in relation to literacy skills. While Behrenze and et al. (2007), and

Rooth and Ekberg (2003) show that second generation immigrants in Sweden experience lower

earnings compared to other natives, Nordin and Rooth (2007) apply an achievement test score to

show that it is a skill gap, rather than ethnic discrimination, that causes the income gap. They

argue that schooling is an inappropriate measure of productive skills for second generation

immigrants.19

The Canadian case may be different, because Canada applies a point system to select

educated immigrants. While these immigrants may end up working in occupations below their

education, they should transfer a high level of human capital to their Canadian born children.

Here we measure not only the relationship between parental education and labour market

outcomes of Canadian second generation immigrants, but also how literacy scores embed some

of the intergenerational transmission of human capital. To measure literacy skills, this study

uses the test scores from the Canadian component of the 2003 International Adult Literacy and

Skills Survey (IALS). IALS measures adult literacy skills in four domains: prose literacy,

document literacy, numeracy and problem solving.

19

Green and Riddell (2001) use Canadian data from the International Adult Literacy Survey (IALS) to examine the relationship between labour market success and literacy skills for first generation immigrants. Their findings indicate that literacy has a largely positive effect on immigrants’ earnings. However, they do not examine the labour market outcomes of second generation immigrants.

63

This paper shows that in the long run, Canadian society benefits from the point system in

which immigrants with higher level of human capital are selected. The children of immigrants

are likely to obtain higher educational degree. Moreover, they have higher level of cognitive

skills compared to children of non-immigrants due to higher education and parental education.

The results of the current study are comparable to the results from previous Canadian studies on

unconditional labour market outcomes for second generation immigrants in Canada. Overall,

second generation immigrants, particularly individuals whose parents are both immigrants, have

advantages in the labour market and have higher human capital indicators compared to the other

natives. The results show that education, literacy skills and a set of socio economic

characteristics explain the wage and earnings differentials for second generation immigrants

compared to other natives. In addition to examining the average literacy skills, each of the four

literacy elements were examined, separately, for their impact on labour market outcomes. Within

the elements of literacy skills, numeracy has more effect on the wage earnings potential of males

while, for females, document skills have higher effect. This study concludes that second

generation immigrant earns as well as the third generation after accounting for a set of

controlling variables and no evidence exists to imply that second generation immigrants do not

reach parity with the third generation. Furthermore, compared to other natives, second generation

immigrants not only are more likely to hold a university degree, they attain at least the same test

scores in literacy skills.

The structure of the chapter 3 is as follows: Section 3.2 presents the data and summary

statistics; Section 3.3 describes the model specifications; Section 3.4 presents the results and

discussions for the three outcomes considered in estimation: post-secondary attainment, literacy

skills, and wages; and Section 3.5 provides the conclusions.

3.2 Data

The data used in this study come from the Canadian component of the 2003 International Adult

Literacy Survey (IALS). Besides allowing us to identify the immigrant generation (first, second,

and third), very importantly, the survey provides test scores on a set of literacy skills including

prose, numeracy, document and problem solving. These test scores measure the ability of

64

individuals in implementing skills to work as well as everyday life and differences in skill levels

can be an important source of income inequality, particularly among individuals with the same

level of education. The literacy skills are defined as follows:

Prose includes the knowledge and skills needed to understand and use various kinds of

information from text including editorials, news stories, brochures and instructions

manuals.

Document contains the knowledge and skills required to locate and use information

contained in various formats including job applications, payroll forms, transportation

schedules, maps, tables and charts.

Numeracy comprises the knowledge and skills needed to effectively manage and respond

to the mathematical demands of diverse situations.

Problem solving involves goal-directed thinking and action in situations for which no

routine solution procedure is available. The problem solver has a more or less well-

defined goal, but does not immediately know how to reach it.

In this study, literacy is obtained by averaging over test scores for prose, document,

numeracy, and problem solving.

In addition, the data offers adequate information on other socio-economic information

such as age, parental education, parents’ place of birth and ethnicity. Hence, using IALS

provides an opportunity to investigate the influence of different skills on the wage differential

between second generation and third generation immigrants, while controlling for ethnical

background and parental education. It is well understood in the literature that parental education

plays an important role in educational outcome of children. Consequently, literacy skills are

strongly determined by parental education while ethnicity does not seem to play an important

role when parental education is taken into account. Furthermore, this research provides an

opportunity to benchmark the analysis for second generation immigrants by comparing the

results to the previous studies using Census or SLID data and trying to determine where the

differences come for.

Since the survey provides information on parents’ place of birth, this makes it possible to

explore the heterogeneity among second generation immigrants and to identify the effect of

immigrant parentage depending on whether one or both parents are immigrants. Thus, Canadian

65

born individuals collapse thus into four groups, including: second generation immigrants with

foreign-born father; second generation with foreign-born mother; second generation immigrants

with both parents foreign-born; and, third generation immigrants, who are natives with both

parents Canadian-born.

The sample is restricted to the individuals who have a job during the year of survey with

the age range of 25 to 65 years old for males and females, separately. The students and self-

employed are excluded from sample. Given information on wages and salaries, such as the wage

pay schedule, and the labour market hours of activities for individuals in one year, the hourly

earnings and annual earnings are constructed from the data. Wages and earnings help account for

the variation in unit earnings as well as labour supply. Taking the logarithm of earnings enforces

any observations with zero earnings to be excluded.

3.2.1 Descriptive statistics

Tables 3.1 and 3.2 summarize the descriptive overview of major labour market and human

capital characteristics, separately for each gender. Table 3.1 looks at wages and labour supply, as

well as literacy outcomes, separately by the 4 immigration generations: three categories for the

second generation, and one for the third. Table 3.2 provides educational attainment, parental

education, regions of residence, and ethnicity for each gender, for two categories of immigrants:

second and third generations20

.

The unconditional results show that, on average, second generation immigrants have

better performance in the labour market compared to Canadian individuals born from Canadian

parents. In particular, second generation immigrants with immigrant parents receive the highest

wages, despite also being younger and having fewer years of experience compared to other

groups. The difference in experience can be related to educational attainment, which is also

higher for second generation (Table 3.2), leading to lower potential experience.

20

Since data is provided by Statistic Canada, there is a restriction on the number of observations for releasing the

summary statistics. Therefore, second generation has to be reported in only one group instead of three groups in

Table 3.2 to meet disclosure requirements. It was not also possible to report summary statistics for all ethnicity

categories, but the regression analysis, subject to different disclosure requirements, controls for refined ethnicity

categories.

66

In terms of human capital, literacy score results are described in Table 3.1 and

educational attainment in Table 3.2. Both male and female second generation immigrants,

particularly those whose both parents were born abroad, have higher mean test scores in literacy

and also in its components including prose, numeracy, document and problem solving. While the

gender wage gap is not a main focus of this study, it is notable that, for all generation

immigrants, females receive lower earnings and wages than males, although they achieved

higher literacy test scores in some cases, while, on average, males have higher numeracy skill

compared to females within generation groups. We come back to this point in the regression

analysis.

The summary statistics from Table 3.1 suggest that literacy skills may have an impact on

the labour market outcomes although only education has been used as human capital to predict

the earnings in the Canadian literature. In addition, among literacy skills, numeracy seems to be a

main factor in explaining the labour market success. In order to support these findings from

Table 3.1, literacy is also taken into account in order to explain differences in the earnings

between second generation immigrants and other natives. Table 3.2 shows that second generation

immigrants in Canada are more educated that third generation immigrants. The probability of

having a high level of education, mainly having university degree is lower for third generation

immigrants compared to the second generation. On the other hand, the probability of being less

educated (at most having high school diploma) is highest for third generation immigrants.

Parental education across generations of immigrants is presented separately by the

education of mother and father. The probability of being from low educated families is higher for

third generation immigrants by about 12 to 13 percent. Consequently, second generation are

more likely to be born from educated parents. If there is any positive correlation between

parental education and earnings, second generation will likely have advantages to some extent in

the labour market compared to other natives.

The region of residence is one of the explanatory variables that have been reported to

have a significant effect on earnings. Resources, labour supply and demand vary across the

regions and hence, wages could be different from one place to another. Table 3.2 shows that

distribution of the population over the regions differs across the generation and this may give

misleading results when the region of residence is not controlled for.

67

3.3 Specification models

A probit model is estimated to study the university attainment across immigrant generation

groups. In this model, university is a binary variable that takes the value 1 if individuals obtained

a university degree and 0 otherwise. Canadian studies on education demonstrate immigrants and

their offspring are more likely to attend post-secondary education and to achieve higher levels of

education compared to the children of Canadians. We follow the literature by controlling for age,

parental education and ethnic composition, which can explain a substantial part of education

gaps (Finnie, 2008; Bonikowska, 2005; and Hansen and Kucera, 2004).

However, the skill level of the second generation immigrants compared to the third

generation immigrants, as reflected by literacy scores, has not been analyzed. We investigate the

determinants of the skill gap between second and third generation immigrants using Ordinary

Least Squares (OLS) regression for literacy, with the same controls as in the specifications for

post-secondary outcomes. The foundation for literacy score is set in the K-12 years. In these

formative years, parental education should play a crucial role in literacy outcomes, both through

a direct involvement in the education process as well as through the part of innate ability which

is transmitted genetically from parents to children. Through these mechanisms, literacy scores

for young adults measured at the end of high-school are determinants of post-secondary

enrolment as well as labour market success conditional on education. The IALS literacy skills

are measured here later on in the adult life. Besides K-12 education, ability and parental

involvement, these literacy skills also embed to some extent the outcome of post-secondary

attendance.

Finally, the Mincer earnings function is used to analyze the factors that determine the

labour market outcomes of second generation immigrants in Canada. The logarithm of hourly

wages is used as the main dependent variable for the labour market outcomes. Alternatively, the

logarithm of annual labour income of individuals before tax is also considered, as it embeds both

the productivity channel reflected in the hourly wages as well as the labour supply channel in

terms of hours of work.

68

3.3.1 Key independent variables

Indicators for generation groups based on the immigration status of parents are used in all

equations to investigate the differences in educational and labour market outcomes and skills

between generation groups: 2nd

-mother, 2nd

-father, 2nd

-both, and third generation (default base

category). A vector of the socio-economic variables is controlled for in the most models. These

explanatory variables include age, respondent’s community size (rural), dependent children

present, experience and experience2/100, region of residence, parental education, ethnicity, and

occupation. Furthermore, educational attainment and literacy skills are included as regressors in

the earnings equations. Educational attainment includes five levels of education: less than high

school, high school diploma, some post secondary, bachelor, and postgraduate (default base

category). The variable of literacy skills is the average test scores of various skills including

prose, numeracy, document and problem solving skills.

While educational attainment is known to be a strong predictor of earnings by capturing

an observable component of human capital, remaining wage gaps within a given level of

education, conditional on other observable productivity characteristics, may occur due to

differences in unobserved abilities across the individuals. Using literacy test scores provides a

measure of unobserved abilities which can alleviate to some extent the unobserved ability issues.

Therefore, direct measure of literacy skills can be an appropriate predictor to control unobserved

human capital skills. On the other hand, parental education may influence the academic

achievements and the labour market outcomes of children and it may also be a signal of innate

ability that is inherited by children. Therefore, in the present of test scores to control for skills,

and parental education to control for ability, education is no longer endogenous in the empirical

model.

In addition to above socio-economic variables, more categorical variables are used in

some equations. Region of residence is collapsed into the following categories: Atlantic, Quebec,

Ontario (default), BC, Alberta, Centre, and North. Parental education is a categorical variable

that is divided into three groups: less than high school, high school, and university education

(default) for each parent. Ethnicity is a categorical variable that is collapsed into the following

categories: English (default), French, White, Jewish, Black, Chinese, Aboriginal, and Other. The

first digit of the International Standard Classification of Occupation including 10 categories is

69

used to control for occupation in some specifications. According to table A1, the distribution of

occupation varies between second generation and third generation immigrants. Compared to

third generation, second generation immigrants are more likely to hold managerial or

professional positions, which are associated with higher earnings. This can be likely explained

by the fact that second generation Canadian tend to achieve higher level of education and literacy

skills relative to other native counterpart and consequently, they are more well-equipped to take

over professional positions.

3.4 Estimation results

3.4.1 University outcomes

Education is shown to be the important determinant in the wage regression. The unconditional

results from the summary statistics illustrate that the probability of achieving upper levels of

education is higher for second generation immigrants. In this section, the probability of holding a

university degree across the generation groups is examined.

Tables 3.3 summarizes the marginal effects of having a university degree after probit,

separately, for males and females. Without controls, the results in column (1) for males and

females show that second generation are more likely to obtain a university degree compared to

third generation counterparts21

. After controlling for age, parental education, ethnicity and

location, the statistically significant differences across generation groups disappear only for

males. Overall, the probability of holding a university degree is higher for second generation

immigrants whose parents both are immigrants. These outcomes are not surprising since the

parental backgrounds, particularly parental education, have strong effects on the educational

outcomes of children. Immigrants in Canada are selected from the highly educated applicants

and the university educated parents are more likely to have children with a university degree.

The results also show that individuals who live in the rural area are less likely to obtain a

university degree.

21

When the model is restricted to individuals who have a job, I did not find any significant difference between the

educational outcomes of second generation and third generation males.

70

3.4.2 Literacy outcomes

One could argue that the better educational outcomes for second generation immigrants are

largely the result of high parental expectation and consequently, second generation immigrants

with a university degree might be less skilled than their counterparts. In order to investigate the

differences in skills across the generation groups, literacy is used as an outcome variable in the

regression using the ordinary least square method. The estimation results are reported in Table

3.4 and 3.5, correspondingly, for males and females. In each table, the first two columns present

estimates of literacy for all individuals, respectively, without and with controls for the variables

that could be associated with the higher test scores. The sample is divided then into two

subsamples. The second two sets of results provide the corresponding estimates for those who do

not hold a university degree while last two columns present the estimates for those with a

university degree.

Second generation immigrants unconditionally achieve higher test scores in literacy skills

compared to third generation immigrants in most cases, and the results are stronger for those

without a university degree. After controlling for age, parental education, ethnicity, experience,

and location, second generation immigrants obtain at least the same test score as third generation

immigrants except for high educated second generation females whose only fathers are

immigrants. For those individuals without a university degree, the parents’ birth of place matters.

When mothers are immigrants, only sons achieve statistically significant higher score in literacy.

When fathers are immigrant, daughters attain better score. This might be associated with

differences in parental involvement in children's education by child gender.

The control variables have expected sign and magnitude. Educational attainment has

more impact on literacy than experience does and the role of parental education in achieving

higher test scores is considerable. The literacy decreases with age but the effect is smaller for

highly educated subgroup.

3.4.3 Regression results for hourly wages

71

The results of the summary statistics suggest that the unconditional labour market outcomes are

mostly in favor of second generation immigrants. These outcomes could be explained to some

degree by educational attainment and higher literacy skills since second generation immigrants

achieved higher levels of education and literacy test scores. In this section, the factors that may

explain the earning and wage differentials between second generation and third generation

immigrants will be examined.

Table 3.6 represents the regression results of the hourly wages in three columns by males

and females, separately. The unconditional wage gaps between each group of second generation

and third generation immigrants are provided in column (1) for each gender. Overall, second

generation females receive statistically significant higher hourly wages except for second

generation males whose fathers are immigrants. However, there is no significant wage gap

between second generation and third generation males.

The human capital variables, which are the educational attainment and literacy test scores

in the data, are expected to play important roles in the labour market outcomes. In order to

capture the effect of these variables on the wage gaps between second generation groups and

Canadian born individuals from Canadian parents, these variables are added to the regressions in

column (2) along with a set of basic socio economic variables for males and females, separately.

The set of basic socio-economic variables includes age, rural, dependent children, experience

and experience squared. 22

The results would be useful to investigate how well education and

literacy explain the wage gap between the generation groups because individuals in both

generations have been exposed to the same schooling system. The results indicate that the

magnitude of the positive wage gap diminishes to some extent for those whose mothers are at

least immigrants and the statistically significant positive wage differences disappear for females.

Furthermore, the negative wage gap increases but remains statistically insignificant for those

whose only fathers are immigrant23

. The results suggest that on average, the children of

immigrant do not earn significantly different than the third generation given the same level of

education and skills. Furthermore, second generation immigrants whose mothers are at least

22

Controlling for a set of basic socio-economic characteristics without education does not significantly change the

results and it only wipe out the significant positive wage gaps in favor of second generation males whose mothers

are at least immigrant while the sign of the coefficient remains the same. 23

Without control for education, literacy also captures the effect of education and the results are close to what is

reported in column (2).

72

immigrants have advantages in specific characteristics that are associated to higher wages in

contrast to third generation immigrants.

Parental education, ethnicity groups, region of residence and, occupation are used as

additional controlling variables to explain the wage gap in column (3) for males and females,

separately. Overall, conditional results show second generation immigrants do not earn

significantly less than third generation immigrants when all control variables are taken into the

account.24

The wage differentials remain positive in favor of second generation immigrants

whose mothers are immigrant for males and females, separately, although the positive wage gap

is not statistically significant. However, the results demonstrate that there is a selection bias to

ethnicity, occupation and region of residence for second generation immigrants. In addition,

parental education impacts the earnings of male individuals while has no significant effects on

females earnings.

In addition to specifications provided in Table 3.6, a comprehensive set of specifications

is considered for sensitivity analysis. The results from these specifications show that first,

positive wage gaps in favor of second generation immigrants are driven mainly through

education and literacy skills. Second, controlling for ethnicity does not have any impact on wage

differentials between second and third generation when education is taken into account, even

though some ethnicities may receive relatively higher or lower wages among males and females.

3.4.4 Regression results from income equation

Table 3.7 provides the unconditional and conditional income differentials of second generation

immigrants based on the parental immigration status compared to other natives for males and

females, separately, with an extra specification which is the number of hours of work per week.

The unconditional results from the wage regressions are not consistent with the results from the

earning estimations in all cases. Second generation immigrants whose parents are both

immigrants earn significantly higher income than natives. In addition, second generation females

24

By introducing the ethnicity as an extra control variable in the regression, the wage gap increases slightly in favor

of all second generation immigrants when compared to their native counterparts, but there exists no evidence that

ethnicity plays a significant role on the labour market outcomes of the immigrants’ offspring.

73

whose father is immigrant earn significantly more than third generation females. The sign of

coefficients for the earnings differentials is small and negative for second generation males with

immigrant mothers while it is positive for second generation immigrants whose fathers are

immigrants. These differences could be as a result of work status of individuals or the number of

hours that were contributed to work. Conditional results in column (2) for males and females,

correspondingly, indicate that second generation immigrants do not earn significantly less than

third. Second generation females whose mothers are immigrants receive higher earnings only by

2 percent. The results show that having dependent children has positive impacts on the earnings

even for females. Aging also has statistically significant negative impacts on the females’ income

while has no impact on their wages.

3.4.5 The effect of literacy components on the labour market outcomes

It has been shown that literacy is one of the explanatory variables in wage and income equations

but it is also important to determine which skill has the most important effect. For this reason,

the components of literacy including prose, document, numeracy and problem solving are

controlled in the wage and income equations, and the estimates are summarized in Table 3.8 for

males and females, independently.

The results show that numeracy has statistically significant positive effect on earnings (e.g.

wage or income) and its effect is doubled for males than for females. In addition to numeracy,

Prose skill has significant impact on the earnings for females while the only skill that has

significant positive effect on the earnings for males is numeracy. Surprisingly, problem solving

has statistically significant negative effect on the wages for females.

3.5 Conclusions

In this study, the factors that determine the cognitive skills, educational and labour market

outcomes of Canadian second generation immigrants were analyzed for males and females,

separately. Using the 2003 International Adult Literacy Survey (IALS) provides not only

important determinants of wage and income such as education and experience, but it also gives

74

an opportunity to investigate the role of literacy test scores in the labour market outcomes of

individuals. To account for the heterogeneity among second generation immigrants, they were

divided into three groups based on the immigration statues of each parent. The results confirm

that the immigration status of each parent matters in the analysis. In particular, relatively better

outcomes are observed when mother is immigrant while having only an immigrant father is

associated to a weaker or a negative gap in many cases.

The unconditional results of the summary statistics illustrate that second generation

immigrants, particularly those from foreign born parents, achieve higher earnings as well as

higher levels of schooling and skills. Conditional only on education, second generation

immigrants with post graduate degree have difficulty catching up to the earnings of third

generation immigrants who hold a postgraduate degree.

The conditional results indicate that second generation immigrants do not significantly earn

less than the third generation and second generation immigrants whose mothers are immigrants,

but the coefficients are not statistically significant. Although second generation immigrants with

both migrated parents have advantages in the labour market from unconditional results, these

advantages mostly disappear after controlling for various predictors. In conclusion, Canadian

second generation immigrants have advantages in some characteristics associated with higher

earnings. Furthermore, the impact of literacy skills is also stronger than ethnicity in explaining

the earning differentials. The ethnic differences in the labour market are small.

Furthermore, university outcomes and skill gaps between second generation and third

generation immigrants were examined. Second generation immigrants are not only more likely to

obtain a university degree, they have higher literacy skills. After controlling for the major

determinates of the university outcomes, the higher probability of holding a university degree

remains statistically significant for second generation females. Among non university degree

holders, second generation immigrants have higher literacy skills even after controlling for

parental education and ethnicity. Parental education plays an important role in explaining the

skills and educational outcomes of the individuals. In addition to examining the average literacy

skills, the impact of each skill on labour market outcomes were examined, separately. Within the

elements of literacy skills, numeracy has more effect on the wage earning potential of males

while, for females, document skills have higher effect. These results imply the gender

heterogeneity in skills.

75

Table 3.1: Summary Statistics for the labour market characteristics by gender

2nd Generation 3rd Generation

Mother Only Father Only Both Parents

Males:

Age 44.55 44.09 41.70 43.07

Yearly Income (CAD$) 51548 51619 55231 50673

Hourly Wage (CAD$) 23.69 22.69 25.16 22.87

Hours/week 42.3 43.62 43.9 42.91

Experience 23.79 23.54 20.96 22.07

Prose 297.18 290.07 304.77 282.69

Document 299.39 294.53 309.36 285.74

Numeracy 296.65 291.07 304.12 282.06

Problem solving 289.67 283.17 295.10 276.89

Literacy 295.72 289.71 303.34 281.84

Observations 140 152 158 2616

Females:

Age 43.54 44.27 40.37 42.93

Yearly Income (CAD$) 39308 39402 41059 36070

Hourly Wage (CAD$) 20.44 20.24 21.14 19.30

Hours/week 36.85 37.80 37.33 36.46

Experience 17.75 18.19 17.10 18.06

Prose 308.25 299.91 311.15 292.65

Document 303.06 294.31 304.84 285.79

Numeracy 284.99 280.79 288.36 271.02

Problem solving 297.57 288.03 294.68 280.60

Literacy 298.47 290.76 299.76 282.52

Observations 105 157 148 3149

76

Table 3.2: Education, parental education, region of residence, and ethnicity by

gender

Males

Females

2nd

generation

3rd

generation

2nd

generation

3rd

generation

Education:

Less than HS 12.83 18.43

7.07 13.62

HS 28.81 30.93

30.49 33.34

Post Secondary 30.02 27.64

26.59 27.72

Bachelor’s 23.49 18.65

31.22 21.21

Post Graduate 4.84 4.36

4.63 4.1

Mother’s Education:

Less than HS 0.48 0.58

0.51 0.6

HS 0.32 0.28

0.27 0.26

University 0.2 0.15

0.22 0.14

Father’s Education:

Less than HS 0.52 0.64

0.53 0.67

HS 0.28 0.23

0.3 0.21

University 0.19 0.12

0.17 0.12

Region of Residence:

Atlantic 11.86 21.64

9.76 22.48

Quebec 15.5 21.1

15.37 19.02

Ontario 17.19 19.65

20.24 18.77

Alberta 11.86 4.82

8.05 5.72

BC 10.9 3.71

14.15 3.97

North 15.25 13.3

17.07 12.73

Center 17.43 15.79

15.37 17.31

77

Table 3.3: Marginal effects after probit for the university outcomes

Males

Females

(1) (2)

(1) (2)

2nd _Mother 0.070*** 0.002

0.131*** 0.068**

(0.031) (0.029)

(0.031) (0.028)

2nd _Father 0.057*** 0.019

0.096*** 0.062***

(0.025) (0.024)

(0.025) (0.023)

2nd _Both parents 0.105*** 0.033

0.157*** 0.086***

(0.025) (0.025)

(0.027) (0.025)

Mother-Less than HS

-0.157***

-0.199***

(0.016)

(0.014)

Mother-HS

-0.056***

-0.091***

(0.016)

(0.014)

Father-Less than HS

-0.163***

-0.174***

(0.017)

(0.015)

Father-HS

-0.105***

-0.099***

(0.017)

(0.016)

Age

0.003***

0.000

(0.001)

(0.001)

Rural

-0.118***

-0.046***

(0.013)

(0.012)

French

0.013

0.05***

(0.018)

(0.017)

Jewish

0.252**

0.227***

(0.112)

(0.064)

Chinese

0.338***

0.251**

(0.099)

(0.128)

Black

0.016

0.178

(0.113)

(0.113)

78

White

-0.011

0.045***

(0.016)

(0.016)

Aboriginal

-0.121

-0.043**

(0.023)

(0.02)

Other

-0.041

0.057**

(0.033)

(0.029)

Region of Residence

✓

✓

Observations 4602 4602

6056 6056

pseudo R2 0.006 0.139

0.010 0.143

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%,

and *** for 1 %. The dependent variable takes value of 1 if individuals obtained a university degree and

zero otherwise.

79

Table 3.4: Estimation results of the literacy equations for males

All`

no university degree

university degree

(1) (2)

(1) (2)

(1) (2)

2nd _Mother 21.077*** 3.968

21.459*** 9.707**

4.044 -2.188

(4.216) (3.021)

(4.713) (3.922)

(5.494) (5.274)

2nd _Father 13.126*** 2.665

11.439*** 3.405

5.084 1.758

(3.381) (2.421)

(3.739) (3.114)

(4.559) (4.326)

2nd _Both parents 27.858*** 5.287**

26.905*** 6.804*

8.738** 4.340

(3.523) (2.683)

(4.050) (3.558)

(4.282) (4.490)

Experience

1.249***

2.159***

-0.065

(0.183)

(0.224)

(0.421)

Experience2/100

-1.734***

-3.792***

-0.022

(0.386)

(0.488)

(0.753)

Age

-0.759***

-0.873***

-0.396

(0.100)

(0.122)

(0.245)

Dependent Child

3.988***

4.854***

2.666

(1.094)

(1.375)

(2.132)

Rural

-3.844***

-5.720***

-5.782*

(1.228)

(1.471)

(2.976)

Mother-Less HS

-11.725***

-17.659***

-12.270***

(1.822)

(2.408)

(3.117)

Mother-HS

-2.035

-5.198**

-0.246

(1.802)

(2.486)

(2.726)

Father-Less HS

-12.238***

-19.957***

-1.898

(1.911)

(2.664)

(2.982)

Father-HS

-4.560**

-6.723**

-4.653

(1.953)

(2.766)

(2.919)

French

-3.104*

-3.401

-1.193

80

(1.807)

(2.275)

(3.498)

Jewish

-3.706

7.661

2.575

(11.656)

(38.599)

(11.241)

Chinese

-9.051

-13.399

-7.069

(10.636)

(22.506)

(11.255)

Black

5.891

15.942

-11.528

(10.984)

(14.612)

(17.861)

White

2.741*

3.456

6.014**

(1.665)

(2.127)

(3.021)

Aboriginal

-18.483***

-21.977***

-20.223***

(2.116)

(2.605)

(5.239)

Other

-1.300

-3.943

1.014

(3.147)

(3.878)

(6.662)

Less than HS

-95.405***

(4.365)

Some HS

-56.083***

(3.342)

HS diploma

-30.413***

(3.178)

Post Secondary

-24.795***

(3.162)

Bachelor Degree

-10.412***

(3.060)

Region of Residence

✓

✓

✓

Occupation

✓

✓

✓

Observations 4602 4357

3728 3491

874 866

R-squared 0.020 0.501

0.018 0.331

0.006 0.201

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and *** for 1%.

The dependent variable is literacy.

81

Table 3.5: Estimation results of the literacy equations for females

All

No University Degree

University Degree

(1) (2)

(1) (2)

(1) (2)

2nd _Mother 23.936*** 6.222**

19.253*** 4.612

11.155** 4.917

(3.976) (2.876)

(4.681) (3.853)

(4.954) (4.746)

2nd _Father 14.577*** 2.244

15.100*** 7.592**

-4.105 -6.540*

(3.113) (2.275)

(3.546) (2.981)

(4.154) (3.911)

2nd _Both parents 24.529*** -0.781

20.702*** 0.333

6.601* 1.752

(3.345) (2.556)

(4.038) (3.462)

(4.006) (4.168)

Experience

0.787***

1.284***

0.769**

(0.131)

(0.151)

(0.358)

Experience2/100

-1.370***

-2.092***

-2.797***

(0.307)

(0.351)

(0.922)

Age

-0.353***

-0.529***

-0.213

(0.064)

(0.079)

(0.141)

Dependent Child

3.509***

3.694***

3.206*

(0.960)

(1.222)

(1.867)

Rural

0.033

-0.117

-1.117

(1.055)

(1.266)

(2.322)

Mother-Less than HS

-12.268***

-15.587***

-11.098***

(1.530)

(2.090)

(2.557)

Mother-HS

-3.006*

-4.676**

-2.975

(1.542)

(2.199)

(2.324)

Father-Less than HS

-13.230***

-16.583***

-11.031***

(1.619)

(2.290)

(2.539)

Father-HS

-7.689***

-7.633***

-8.088***

(1.681)

(2.442)

(2.468)

82

French

-5.221***

-5.063***

-9.943***

(1.597)

(1.962)

(3.276)

Jewish

-7.963

-4.761

-11.904

(7.041)

(13.502)

(8.593)

Chinese

19.052

9.385

17.285

(14.898)

(35.562)

(16.371)

Black

-9.744

-7.821

-18.109

(11.024)

(15.918)

(16.393)

White

3.234**

4.981***

0.237

(1.469)

(1.833)

(2.888)

Aboriginal

-15.889***

-19.440***

-18.800***

(1.841)

(2.238)

(4.103)

Other

0.547

4.866

-13.129**

(2.775)

(3.519)

(5.158)

Less than HS

-91.908***

(4.746)

Some HS

-54.728***

(2.992)

HS diploma

-29.334***

(2.784)

Post Secondary

-23.037***

(2.739)

Bachelor Degree

-7.827***

(2.661)

Region of Residence

✓

✓

✓

Occupation

✓

✓

✓

Observations 6056 5318

4773 4072

1283 1246

R-squared 0.017 0.467

0.012 0.311

0.007 0.192

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and ***

for 1 %. The dependent variable is literacy.

83

Table 3.6: Regression results of the hourly wages by gender

Males

Females

(1) (2) (3)

(1) (2) (3)

2nd_Mother 0.083 0.018 0.024

0.085* 0.018 0.008

(0.05) (0.045) (0.042)

(0.051) (0.043) (0.038)

2nd_Father -0.004 -0.053 -0.046

0.036 -0.016 -0.045

(0.042) (0.037) (0.035)

(0.044) (0.037) (0.033)

2nd_Both parents 0.071 0.003 -0.026

0.130*** 0.012 -0.009

(0.046) (0.037) (0.038)

(0.044) (0.038) (0.035)

Less than HS

-0.267*** -0.205***

-0.439*** -0.221**

(0.077) (0.074)

(0.099) (0.088)

Some HS

-0.344*** -0.249***

-0.617*** -0.358***

(0.048) (0.047)

(0.046) (0.043)

HS diploma

-0.297*** -0.208***

-0.491*** -0.261***

(0.043) (0.043)

(0.041) (0.038)

P.S. Non University

-0.202*** -0.142***

-0.329*** -0.156***

(0.043) (0.042)

(0.040) (0.037)

Bachelor Degree

-0.042 -0.002

-0.090** -0.050

(0.043) (0.040)

(0.040) (0.036)

Literacy

0.003*** 0.002***

0.003*** 0.002***

(0.000) (0.000)

(0.000) (0.000)

Experience

0.017*** 0.016***

0.017*** 0.013***

(0.003) (0.003)

(0.002) (0.002)

Experience2 /100

-0.028*** -0.024***

-0.012** -0.010**

(0.006) (0.006)

(0.005) (0.004)

Age

0.006*** 0.005***

-0.000 0.001

(0.002) (0.002)

(0.001) (0.001)

Dependent Child

0.062*** 0.052***

0.061*** 0.056***

84

(0.017) (0.016)

(0.016) (0.014)

Rural

-0.047** -0.046**

-0.041** -0.050***

(0.018) (0.018)

(0.017) (0.016)

Mother-Less than HS

-0.028

-0.025

(0.025)

(0.022)

Mother-HS

0.050**

-0.005

(0.025)

(0.022)

Father-Less than HS

0.028

-0.023

(0.026)

(0.023)

Father-HS

0.048*

0.003

(0.027)

(0.024)

French

0.051**

0.062***

(0.026)

(0.023)

Jewish

0.359*

0.010

(0.199)

(0.116)

Chinese

-0.223*

0.032

(0.135)

(0.269)

Black

-0.032

0.028

(0.162)

(0.154)

White

-0.009

0.022

(0.024)

(0.021)

Aboriginal

0.022

0.059**

(0.032)

(0.028)

Other

0.103**

-0.027

(0.048)

(0.041)

Region of Residence

✓

✓

Occupation

✓

✓

Observations 2723 2723 2722

3260 3260 3259

R-squared 0.002 0.213 0.319

0.003 0.299 0.467

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and ***

for 1 %. The dependent variable is the logarithm of hourly wages.

85

Table 3.7: Regression results of the income equations

Males

Females

(1) (2)

(1) (2)

2nd_Mother -0.007 -0.073

0.093 0.020

(0.086) (0.057)

(0.065) (0.049)

2nd_Father 0.024 -0.028

0.096* -0.004

(0.050) (0.047)

(0.056) (0.042)

2nd_Both parents 0.107** -0.023

0.168*** -0.006

(0.044) (0.050)

(0.050) (0.046)

Less than HS -0.169*

-0.403***

(0.100)

(0.115)

Some HS

-0.197***

-0.435***

(0.064)

(0.056)

HS diploma -0.147**

-0.283***

(0.058)

(0.050)

post Secondary -0.107*

-0.214***

(0.057)

(0.049)

Bachelor Degree 0.018

-0.077*

(0.055)

(0.046)

Literacy

0.002***

0.002***

(0.000)

(0.000)

Experience 0.015***

0.019***

(0.004)

(0.003)

Experience2 /100 -0.020**

-0.015***

(0.008)

(0.006)

Age

0.005**

-0.004***

(0.002)

(0.001)

Dependent Child 0.075***

0.039**

(0.021)

(0.018)

Rural

-0.041*

-0.069***

86

(0.024)

(0.020)

Hour/Week 0.017***

0.026***

(0.001)

(0.001)

Mother-Less than HS 0.014

-0.016

(0.034)

(0.028)

Mother-HS 0.068**

0.013

(0.033)

(0.028)

Father-Less than HS 0.037

-0.007

(0.035)

(0.029)

Father-HS 0.052

0.012

(0.036)

(0.031)

French

0.052

0.065**

(0.035)

(0.030)

Jewish

0.368

0.045

(0.267)

(0.149)

Chinese

-0.146

0.112

(0.182)

(0.346)

Black

0.049

-0.146

(0.219)

(0.198)

White

0.015

0.000

(0.032)

(0.027)

Aboriginal

0.014

0.059*

(0.043)

(0.035)

Other

0.116*

-0.019

(0.064)

(0.053)

Region of Residence

✓

✓

Occupation

✓

✓

Observations 2740 2740

3283 3283

R-squared 0.001 0.325

0.003 0.527

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%,

and *** for 1 %. The dependent variable is the logarithm of annual income.

87

Table 3.8: The effects of the literacy components on the labour market outcomes

Males

Females

Dependent Variable: ln(Wage) ln(Income)

ln(Wage) ln(Income)

2nd_Mother 0.034 -0.056

0.042 0.040

(0.045) (0.060)

(0.043) (0.053)

2nd_Father -0.037 -0.010

-0.017 0.021

(0.037) (0.050)

(0.037) (0.046)

2nd_Both parents 0.025 0.035

0.045 0.054

(0.039) (0.053)

(0.039) (0.049)

Prose 0.000 -0.000

0.002*** 0.002**

(0.001) (0.001)

(0.001) (0.001)

Document 0.001 0.001

0.001 0.001

(0.001) (0.001)

(0.001) (0.001)

Numeracy 0.002*** 0.002***

0.001*** 0.001**

(0.000) (0.001)

(0.000) (0.000)

Problem Solving -0.000 -0.001

-0.001** -0.001

(0.000) (0.001)

(0.000) (0.001)

Control ✓ ✓

✓ ✓

Observations 2723 2740

3260 3283

R-squared 0.230 0.239

0.316 0.429

NOTES: Standard errors are in parentheses. Significance levels are indicated by * for 10%, ** for 5%, and

*** for 1 %. Controls include Education, Parental Education, Region of Residence, Ethnicity, Rural,

Experience, and Dependent Child. Hours per Week is only controlled in Earnings equations

88

Table 3.A1: Distribution of occupation

Second generation Third generation

Managers 13.31 10.82

Professionals 20.86 16.77

Technicians and associate professionals 15.92 14.2

General support workers 13.4 13.13

Service and sales workers 12.41 14.84

Skilled agricultural, forestry and fishery workers 1.62 2.16

Craft and related trades workers 10.34 10.03

Plant and machine operators and assemblers 6.74 9.62

Elementary occupations 5.4 8.43

Total 100 100

Occupation groups are based on the first digit of the International Standard Classification of

Occupations (ISCO). The Armed forces occupations are excluded from this table.

89

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