Macroeconomics Slide SET 2Slide 1 Macroeconomics LECTURE SLIDES SET 2 Professor Antonio Ciccone

Macroeconomics Slide SET 2 Slide 1

Macroeconomics

LECTURE SLIDES SET 2

Professor Antonio Ciccone


5. SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM—OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE

1. Investment and savings meet in the credit (also loan) market

Households may have a PREFERENCE to save for consumption tomorrow. This is captured by the following extremely simple SAVINGS FUNCTION:

(E19) ( ) ( )S t sY t

Households simply save a constant fraction s of their total income Y (this includes labor and capital income).

Savings are deposited in banks that use them to make loans to firms. Firms use credit to buy NEW machines. INVESTMENT refers to the total purchases of NEW MACHINES and ALSO TO THE VOLUME OF LOANS IN THE ECONOMY.

Firms can therefore buy machines or instead rent them. This will give rise to the rent-or-buy decision which determines the real interest rate.


HOUSEHOLDS (aggregate labor endowment L(t) plus property rights in firms;

preferences for consumption today and savings)

FIRMS (technology of production; capital owned at the beginning of the period K(t))).

GOODS MARKET(consumption and investment goods)

LABOR MARKET

RENTAL MARKETFOR CAPITAL GOODS

CREDIT/LOANMARKET(credit/loans forinterest)

FIGURE 7


How firms finance purchase of new machinery

(1)Loans: firms ask banks for loans and banks make these loans

with the savings of households

(2)Retained earnings: firms ask their owners whether they can

retain some of their earnings in order to fund purchases of new

machinery

(3) Issues of new shares: they purchases new machines and issue

property titles to the machines (shares) directly to households

In the Solow environment these ways of financing machinery

are all EQUIVALENT.

We can therefore just think of firms financing the purchase of new

machinery by asking banks for loans.


2. The rent or buy decision

1. The user cost of capital definition in discrete time

Firm can demand credit/loans to purchase capital goods:- in principle, this gives them an alternative to the rental market for capital - instead of renting the capital good next year, for example, you could buy it

on credit today, use it for one year and then sell it off.

The cost of doing so is the USER COST OF CAPITAL

User Cost One-year-Period t

1 ( 1) * ( ) 1 ( 1)K Kr t p t p t

-higher real interest rate and depreciation rate increase user cost-high future price for capital goods relative to current price reduces user cost


2. The user cost in one-sector growth models (which includes, among many, the Solow model)

Assume that consumption goods and investment goods can be produced with identical technologies.

In this case, the price of the investment goods relative to the capital good is always unity. If investment goods were more expensive only investment goods would be produced by profit maximizing firms. And vice versa.

User Cost One-year-Period t

1 ( 1) 1

( 1)

r t

r t

(E21)


3. The credit/loan market equilibrium

The CREDIT/LOAN MARKET is in equilibrium at time t when:

SAVINGS(t)=INVESTMENT(t)

S(t)=I(t)

As we will see, the CREDIT/LOAN market is brought into equilibrium by adjustments of the REAL INTEREST RATE.

How does the real interest rate bring about credit/loan market equilibrium?

What is the effect of the real interest rate on INVESTMENT?And on SAVINGS?


THE EFFETC ON INVESTMENT The firm’s investment decision at time t: Compare future MPK of capital MPK(t+1) with user cost of capital r(t+1)+δ

K(t+1)

MPK(t+1)=MARGINAL BENEFIT (PROFIT) OF INVESTING

0

r(t+1)+δ

K*(t+1)


0

r(t+1)

I(t)=INVESTMENT THAT FIRMS WANT FOR EACH REAL INTEREST RATE

CREDIT/LONA MARKET EQUILIBRIUM

INVESTMENT,SAVINGS

SAVINGS

EQUILIBRIUM

S*=I*


Summarizing the credit market equilibrium

MPK r

(E25) I S

(E24)


Summarizing ALL equilibrium conditions at time t

( ) ( )MPK t r t

(E25) ( ) ( )I t S t

(E24)

PLUS EQUILIBRIUM CONDITIONS,

-in the LABOR MARKET

- in RENTAL CAPITAL MARKET

GENERAL EQUILIBRIUM AT TIME t

( ) ( )MPK t R t

( ) ( )MPL t w t


4. The credit market equilibrium and the link between present and future (or the capital accumulation equation in equilibrium)

As far as the economics of the Solow model are concerned we are done!

-We know how to determine output at a given moment in time given L and K; we also how to obtain factor prices and the real interest rate.

- Now we know how to determine tomorrow’s capital stock given today’s capital stock and employment:

( )( ) ( ) ( ) ( ) ( )

K tK t I t K t S t K t

t

(E26)

Net Investment GrossInvestment

Depreciation


Making use of HH SAVINGS behavior in (E19) S(t)=sY(t)

(E27) ( ) ( ) ( )K t sY t K t

Making use of the fact that aggregate income=aggregate output:

( , )Y F K EL

(E28) ( , )K sF K EL K

this is the EQUILIBRIUM CAPITAL ACCUMULATION EQUATION


6. THE DYNAMICS OF THE SOLOW MODEL

1. The dynamics of capital accumulation

To solve the Solow model completely, we need to specify the evolution over time

of some EXOGENOUS factors like EFFICIENCY E and LABOR SUPPLY L

We will assume that labor supply grows at (exogenous) rate n:

( ) (0) ntL t L e

(E30) ( ) ( )L t nL t

(E29)

(E31) ( )( )L t

nL t


Similarly, we will assume that exogenous efficiency E we will assume growth at

(exogenous) rate a:

( ) (0) atE t E e

(E33) ( ) ( )E t aE t

(E34) ( )( )

E ta

E t

(E32)


SUMMARIZING THE DYNAMIC EQUATIONS OF THE SOLOW MODEL

( , )t t t t tK sF K E L K

(E36) t tE aE

(E37) t tL nL

Following all 3 (so-called state) variables separately over time is somewhat cumbersome and inconvenient.

And WE DO NOT HAVE TO, because as we have seen many things depend on capital per efficiency worker, NOT separately on K, L, and E.

(E35)


More convenient to focus on the change over time of CAPITAL PER EFFICIENCY WORKER

tt

t t

Kk

E L

- determines output per efficiency worker through the production function in efficiency form t

t t tt t

Yy f k k

E L

- getting to the quantities we are interested in is simple

t t ty y E

(E39) 1'( ) ( )t t tr f k k

(E40) (1 ) ( ) (1 )tt t

t

wf k k

E

(E38)

WHY?


From TIME CHANGES OF K,L,E to TIME CHANGES in capital per efficiency worker

(E41)

( )

( )

K E Lkt t t tK E Lk t t tt

k K L Et t ttK L Ek t t tt

k Ktt n aKk tt

Ktk n a kt tE Lt t

( ) ( ) ( )Growth ab Growth a Growth b

( )ab a b

ab a b

( / ) ( ) ( )Growth a b Growth a Growth b

( / )

/

a b a b

a b a b


(E42) ( , )t t t t tt t t t t

t t t t

sF K E L KKk k n k a k n k a

E L E L

(E43) ( , )t t tt t t t

t t

sF K E Lk k k n k a

E L

(E44)

ACTUAL SAVINGS BREAK-EVENAND INVESTMENT INVESTMENT

( ) ( )t t tk sf k n a k

Using the equilibrium capital accumulation equation (E28):


This equation gives us the change in tk as a function of the present tk

Therefore, given a starting point (0)k , it allows to study the whole time path of

.tk

SO NOW WE ARE DONE WITH THE “MECHANICAL” DYNAMIC ASPECTS OF THE SOLOW MODEL TOO.

Now is the time to remember: What is it we want to know about?


What we want to know:

“INTERMEDIATE” QUESTIONS

- Will capital per efficiency worker INCREASE or FALL over time?

- Will capital per efficiency worker GROW FOREVER?

- Will the GROWTH RATE of capital per efficiency worker INCREASE or DECREASE in time?

“FINAL” QUESTIONS

- What does this imply for INCOME, WAGES, and INTEREST RATES.

The questions are most easily approached graphically.


k

y f k

FIGURE 8a Following capital per efficiency worker in time:THE PRODUCTION FUNCTION

0


k

y f k

sf k

FIGURE 8b Following capital per efficiency worker in time:SAVINGS AND THEREFORE INVESTMENT

0


k

( )n a k

sf k

FIGURE 8c Following capital per efficiency worker in time:THE EFFECTIVE DEPRECIATION LINE

0


( )k t

( )n a k

sf k

(0)k

FIGURE 8d Following capital per efficiency worker in time:CAPITAL GROWTH

0tk

0


( )k t

( )n a k

sf k

FIGURE 8e Following capital per efficiency worker in time:THE CAPITAL GROWTH ZONE

BGPk0


( )k t

( )n a k

sf k

(0)k

FIGURE 8f Following capital per efficiency worker in time:FALLING CAPITAL ZONE

0


( )k t

( )n a k

sf k

BGPk

FIGURE 8g Following capital per efficiency worker in time

0


Some important terminology

- BALANCED GROWTH PATH (also called STEADY STATE sometimes)

An equilibrium where all variables grow at constant rates (this growth rate can be 0)

- GLOBALLY STABLE BGP

A BGP is globally stable if the economy ends up in the BGP in the long run NO MATTER WHERE THE ECONOMY STARTS.

- CONVERGENCE

A somewhat fuzzy concept. Many people seem to say that there is convergence if the growth rate of income per capital decreases as the country grows richer.


The growth rate of capital per efficiency worker over time

ACTUAL SAVINGS BREAK-EVENAND INVESTMENT INVESTMENT


(E46)

AVERAGE PRODUCTOF CAPITAL

( ) ( )t t

t t

f kks n a

k k

(E45)


( )k t

y f k ( )y t

MPK

(0)k0


( )k t

y f k ( )y t

1( )k t(0)k 2( )k t0


y f k ( )y t

(0)k

APK=AVERAGEPRODUCT OF CAPITAL

( )k t0


y f k ( )y t

(0)k

APK

( )k t0


The growth rate of capital per efficiency worker over time

(E46)

AVERAGE PRODUCTOF CAPITAL

( ) ( )t t

t t

f kks n a

k k


( )k t

f ksk

0


( )k t

f ksk

n a

0


( )k t

f ksk

n a

(0)k

t

t

kk

0


1( )k t

f ksk

n a

(0)k

t

t

kk

0


(0)k

f ksk

n a

BGPk

t

t

kk

0


- Result 1: Over time capital per efficiency worker tends to its balanced growth path value, which we have denoted by (as long as the initial capital stock is strictly positive)

BGPk

- hence, the economy will end up at the same level of capital per efficiency

worker, no matter what the initial values for E,K,L

- Result 2: The closer capital per efficiency worker to its BGP value, the lower its growth rate

-in the absence of SHOCKS to preferences or technology, the GROWTH RATE of capital per efficiency workers is therefore falling over time

Result 3: In the balanced growth path, growth of capital per efficiency worker is ZERO

We have therefore shown the three following results:


( )k t

BGPk

(0)k

Time t

FIGURE 11 RESULT 1: over time capital per efficiency worker tends to its balanced growth path value

0


Time t

( )( )k tk t

FIGURE 12 RESULT 2 and 3: the closer capital per efficiency worker to its BGP value, the lower its growth rate; in the long-run the growth rate is ZERO

0


2. From capital accumulation to growth of output per worker

(E47) 1t t t tY K E L

where 0 1 is the elasticity of output with respect to capital:

t t

t t

Y K

K Y

or

Percentage increase in

*Percentage increase in Kt

t

Y

(E48)


The Cobb-Douglas production function in efficiency unit form is

(E49) t t

t t t t

Y K

E L E L

or

(E50) t ty k

0 1 hence is also the elasticity of output per efficiency worker with respect to capital per efficiency worker.


Growth in output per worker

- ouput per worker is output per efficiency worker times efficiency

(E51) t t t t ty E y E k

- differentiating therefore yields

ELASTICITYOF OUTPUTTO CAPITAL

EFFICIENCYGROWTH CAPITAL PER

EFFICIENCY GROWTH

t tt t

t t t t

y yE ka

y E y k

(E51)


ln ( )y t

ln (0)y

ln *( ) ( )BGPy t y E t

Time t

FIGURE 13 Evolution of output per worker (on LN scale)

ln ( )y t

0


Time t

( )( )y ty t

a

FIGURE 14: growth of output per worker

0


3. Real wage growth and changes in the real interest rate

Again, the easiest case is to assume the production function takes the so-called Cobb-Douglas form

- the real wage is 1t t t

t tt

K E Lw MPL

L

(E53) 1(1 ) (1 ) t t t

t t t t tt

K E Lw E K E L

L

(E54) (1 ) (1 )tt t

t

Yw y

L

t t

t t

w y

w y

the real wage is simply A CONSTANT FRACTION of income per capita and real wage growth is EQUAL TO output per worker growth

(1 )t tw y


ln ( )w t

ln (0)w

ln *( ) ( )BGPw t w E t

Time t

FIGURE 15a Evolution of REAL WAGE (on LN scale)

ln ( )w t

0


- the real interest rate is the net marginal product of capital

(E55)

1t t tt t

t

K E Lr MPK

L

hence

(E56) 1

1 1 tt t t t

t t

Kr K E L

E L

the real interest rate FALLS as capital per efficiency worker increases

1t tr k

NEGATIVENUMBER!


Time t

( )r tFIGURE 15b real interest rate over time

BGPr

0


7. THE EFFECTS OF AN INCREASE IN SAVINGS ON INCOME

1. Growth in the long run (in the balanced growth path)

After having analyzed the DYNAMICS of growth for all moments in time we will now focus on the long-run, i.e. the balanced growth path

- we already have shown that

(E57) 0t t

t tBGPBGP

ykk y

and therefore(E58) GROWTH LABOR-EFFICIENCYt t

t tBGP BGP

yka

k y


Result: The long-run growth rate output per worker of a country is determined by the GROWTH RATE OF LABOR EFFICIENCY ONLY.

-In particular, the long-run growth rate of output per worker does NOT depend on the SAVINGS RATE at all.

-This is because of DECREASING RETURNS TO CAPITAL IN PRODUCTION. Recall that

(E59) ACTUAL SAVINGS BREAK-EVENAND INVESTMENT INVESTMENT


Because of decreasing returns to capital, SAVINGS per efficiency worker rises less than proportionally with capital. But BREAK-EVEN INVESTMENT rises proportionally. So they will be eventually equal NO MATTER what the SAVINGS RATE may be. At that point growth in income per capita is equal to growth in labor-efficiency.


2. Output per worker in the long run (in the balanced growth path)

The savings rate does, however, affect the LEVEL OF OUTPUT PER WORKER

- having a simple expression for output per worker in the BGP is easiest with a Cobb-Douglas production function

- note that in the BGP:

(E60) ACTUAL SAVINGS BREAK-EVENAND INVESTMENT INVESTMENT

0 ( ) ( )t tsf k n a k

(E61) t

t BGP

k sy n a


- the Cobb-Douglas production function in intensive forms is t ty k which yields:

(E62) t

t BGP

k sn ak

solving for the BGP amount of capital per efficiency worker:

(E63)

11

BGPs

kn a

the amount of capital per worker can be obtained by multiplying by efficiency A

(E64)

11

,t BGP ts

k En a


- substituting in the production function yields output per efficiency worker and output per worker

(E65) 1

BGPs

yn a

(E66) 1

,t BGP ts

y En a

,

,

t BGP

t BGP

k sy n a


Hence, if efficiency growth is constant in time, as assumed, we get that income per capita growth in the BGP is constant in time.

We also get that the CAPITAL-OUTPUT (k/y) ratio is constant in time.

A constant capital-output ratio and steady growth of income per capita is often seen to describe the U.S. well, especially for a longer time period. (Solow developed his model thinking of the U.S. economy.)


JONES Slide1: US IN BGP?


( )k t

HIGHs f k

( )n a k

LOWs f k

LOW SAVINGS HIGH SAVINGS

FIGURE 16 Effect of SAVINGS RATE on capital per efficiency worker

0


Time t

( )( )y ty t

a

INCREASE IN SAVINGS RATE

FIGURE 17 Effect of SAVINGS RATE INCREASE on growth (starting from BGP)

0


Time t

( )( )y ty t

a

INCREASE IN SAVINGS RATE

0


8. QUANTITATIVE IMPLICATIONS OF THE SOLOW MODEL

1. Effect of savings on long run income

We have seen that the effect of the savings rate on long run output per worker can be obtained very easily when the production function is Cobb-Douglas

(E67) 1

,t BGP ts

y En a

-- the PERCENTAGE INCREASE in long-run income that comes from a ONE-PERCENT INCREASE in the savings rate is the

(E68) ,

,1t BGP

t BGP

y ss y


- the greater the elasticity of output with respect to capital, the greater the effect of savings on long run income

-- HOW LARGE IS THIS ELASTICITY? It turns out that under the assumption of the Solow model there is a simple way to estimate

- the definition of is: t t tt

t t t

Y K KMPK

K Y Y

- equilibrium in the capital market implies that t tr MPK

- hence ( )

share of CAPITAL in incomet t

t

r K

Y

- constant returns to scale implies that all income is paid to capital or labor; therefore

(E69) 1 share of LABOR in income


- the LABOR INCOME SHARE in industrialized countries is around 1/3:

(E70) 1 2 /3 1/3 1

1 1 (1 2 /3) 2 /3 2

-- hence, increasing the savings rate by 1% raises long-run income per capita by only 0.5% under the assumptions of the Solow model

-- HOW MUCH CAN DIFFERENCES IN SAVINGS RATE OF CAPITAL EXPLAIN?

(E71) 1

,t BGP ts

y En a


- take two countries that are identical in everything but SAVINGS/INVESTMENT rates

-denote their savings rates by s1 and s2 respectively; what is then the difference in long-run incomes between the two countries?

(E72) 11,

2,

12

COUNTRY BGP

COUNTRY BGP

y sy s

(E73)

1/ 21,

2,

0.279 3

0.03COUNTRY BGP

COUNTRY BGP

y

y

- rather small given the enormous differences in savings rates differences in savings rates alone cannot explain enormous differences in income between rich and poor countries


2. Income per capita versus output per worker

The Solow model is about OUTPUT PER WORKER; how do we get from there to OUTPUT PER CAPITA?

As L=NUMBER OF WORKER, we get

(E74) Y WORKER Y

POPULATION POPULATION L

this can be written further as ((E75))

YPOPWORKINGAGE POP LABORFORCE EMPLOYMENT Y

POP WORKINGAGE POP LABORFORCE L


hence

(E76)

INCOME or OUTPUT per CAPITA =

DEMOGRAPHIC FACTOR

X LABOR FORCE PARTICIPATION RATE

X (1-UNEMPLOYMENT RATE)

X OUTPUT PER WORKER

Income or output per capita may therefore be low because of

- LOW output per worker

- HIGH unemployment among those who do participate

- LOW participation of the population in the labor market

- HIGH share of children and retired persons


With information on OUTPUT PER HOUR WORKED, we can do even better and decompose output per worker into:

(E80) Y HOURS YL WORKERS HOURS

where

Hours= total hours worked in the economy

Hours/Workers= hours worked per employed person


The next table, from

“International comparisons of laborproductivity and per capita income”

by van Ark and McGuckin, Monthly Labor Review, July 1999

illustrates the effect of the different components for the US, Japan, and the EU (all relative to the OECD average)


US EU JAPAN

OUTPUT PER HOUR 120 103 82OUTPUT PER WORKER 118 98 92OUTPUT PER PERSON IN LABOR FORCE 121 94 96OUTPUT PER WORKING-AGE PERSON (age 15-64) 130 90 102OUTPUT PER PERSON 128 90 106

TABLE 1

FIGURES ARE RELATIVE TO OECD AVERAGE, data refer to 1997

Hence factors other than output per hour play an important role in explaining differences in income per capita between these rich countries/regions.


Gap in GDP per Capita decomposed in Participation Gap and Labour Productivity Gap, 2004

-20

0

20

40

60

80

100

World WesternEurope

NorthAmerica

Oceania EastEurope/Central

Asia

Asia LatinAmerica

MiddleEast

Africa

Productivity gap Participation gap

FIGURE 18 But the main explanation for differences in INCOME PER CAPITA are differences in OUTPUT PER WORKER (country or region relative to US)


9. EMPIRICAL APPLICATIONS

1. Growth accounting

The aggregate production function makes clear that GROWTH in OUTPUT can be written in terms of GROWTH in INPUTS plus GROWTH OF EFFICIENCY

(E81)

1

1 1

EFFICIENCY ALL INPUTSOF ALL INPUTS

t t t t

t t t t

Y K E L

Y E K L

The EFFICIENCY FACTOR multiplying all inputs is called TOTAL FACTOR

PRODUCTIVITY (TFP=A)

(E82) 1t t t tY A K L


(E83)

ELASTICITYELASTICITYOF OUTPUTOF OUTPUTTO LABORTO CAPITAL

AGGREGATE AGGREGATE CAPITAL GROWTH LABOR GROWTH

(1 )t t t t

t t t t

Y A K LY A K L

Re-arranging allows us to see how TFP growth can be estimated:

(E84) (1 )t t t t

t t t t

A Y K LA Y K L

- OUTPUT (Y), CAPITAL (K), and EMPLOYMENT (L) are easy to estimate for many countries


- but to calculate TFP growth we ALSO need to know the ELASTICITY OF OUTPUT TO CAPITAL AND TO LABOR

- we know that, in equilibrium, the MARGINAL PRODUCT of a factor is equal to the PRICE OF THAT FACTOR and therefore

(E85) CAPITAL SHARE OF INCOMEt t tt

t t t

Y K KMPK

K Y Y

(E86) 1 LABOR SHARE OF INCOMEt t tt

t t t

Y L LMPL

L Y Y

- data on these INCOME SHARE is available for many countries


TFP growth and the SOLOW RESIDUALWe can therefore estimate TFP growth as

(E87)

SOLOW RESIDUAL

_SHARE _SHAREt t t t

t t t t

A Y K LK L

A Y K L

under CONSTANT RETURNS TO SCALE, K_SHARE+L_SHARE=1 and

(E88)

GROWTH OF GROWTH OFOUTPUT PER CAPITAL PERWORKER WORKER

1 _SHAREt t t t t

t t t t t

A Y L K LL

A Y L K L


AVERAGE ANNUAL GROWTH (OVER 1960-1990 PERIOD)

GDP CAPITAL STOCK

EMPLOYMENT SHARE OF LABOR ININCOME

TECHNOLISTAN 8% 10% 4% 0.5

SAVISTAN 8% 12% 4% 0.5

TABLE 2 macroeconomic growth data for 2 countries

- note that in both countries output per worker was growing at 8%-4%=4%Suppose that based on this figures you are asked to make best possible forecast of LONG-RUN INCOME PER WORKER GROWTH in SAVISTAN relative to TECHNOLISTAN


TABLE 3

ANNUAL CONTRIBUTION OF

ANNUAL GDP

GROWTH

CAPITAL STOCK

EMPLOYMENT TFP

TECHNOLISTAN 8% 5% 2% 1%

SAVISTAN 8% 6% 2% 0%

What implications for long-run growth does this TFP growth difference have according to the SOLOW MODEL?

(E89)

,,

tt

t tCOUNTRY BGPCOUNTRY BGP

y Ey E


(E90) 1t t tTFP A E EFFICIENCYOF ALL INPUTS

(E91) t t

t t

TFP ELABOR SHARE

TFP E

(E92)

,

t

tt

tCOUNTRY BGP

TFPTFP

y

y LABOUR SHARE


TABLE 4 LONG-RUN OUTPUT PER WORKER FORECAST

ANNUAL CONTRIBUTION OF

ANNUAL TFPGROWTH

SHARE OF LABOR ININCOME

LONG-RUNOUTPUT PER WORKER

FORECAST

TECHNOLISTAN

1% 0.5 2%

SAVISTAN 0% 0.5 0%

- one would expect TECHNOLISTAN to grow faster because it has proven capable to improve efficiency (adopt or invent better technologies)

- SAVISTAN has been growing by brute force--they were savings a lot and therefore accumulating capital rapidly; the SOLOW model says that this cannot lead to growth in the long run because of decreasing returns to capital


1. Output and TFP growth of the Asian “Tigers”

The Asian “Tigers”, South Korea, Taiwan, Hong Kong, and Singapore have had very rapid growth of OUTPUT and OUTPUT PER CAPITA

What are the PROXIMATE CAUSES of that?:

- increases in labor force participation- capital accumulation- TFP

IMPORTANT TO KNOW because increases in participation and capital intensity CANNOT FUEL GROWTH FOREVER.

Alwyn Young has analyzed this issue in

“The Tyranny of Numbers: Confronting the Statistical Realities of the East-Asian Growth Experience” Quarterly Journal of Economics, 1995


Young estimates:

" " in next figures " " in next figures

GDP per CAPITA GROWTH GDP GROWTH POP GROWTHN D

" " in next figures " " in next figures

GDP per WORKER GROWTH

GDP GROWTH EMPLOYMENT GROWTHN D

GROWTH ON INPUTS, OFTEN WEIGHTED BY “QUALITY”

TFP GROWTH


YOUNG SLIDE 1: growth of income and output all 4 countries


YOUNG SLIDE 2: TFP growth HK


YOUNG SLIDE 3: TFP growth SINGAPORE


YOUNG SLIDE 4: TFP growth in other countries


2. US versus EU growth: when did the EU stop to catch up (and why)?

The US has higher levels of output per worker than the EU, but the EU has been CATCHING UP for most over the post World-War II period.

This process of CATCHING-UP has stopped in the late 1990s Has the EU stopped catching up because of:

- TFP growth?- CAPITAL ACCUMULATION?

Robert Gordon from Northwestern University and co-authors have researched this in much detail; they argue that the process stopped because of both TFP and capital growth and that new INFORMATION and COMMUNICATION TECHNOLOGIES (ICT) played a role


GORDON SLIDE 1 catch up of GDP per worker stops in 1998


GORDON SLIDE 2 catch up TFP also stops in 1998


GORDON SLIDE 3 catch up capital intensity also stops in 1998


2. Productivity level accounting

It is also interesting to ask how much of the difference in the LEVEL of OUTPUT PER WORKER (AVERAGE LABOR PRODUCTIVITY) are driven by:

- CAPITAL (physical and human)- TFP

This can be done working with the Cobb-Douglas production function

1t t t tY K E L or t t tt t

t t t

Y K KTFP A

L L L

implies that we can estimate the level of TFP as

CAP SHARE at t

Output per Worker at t

(Output per Worker at t)t

tt

yTFP

k


Labour Productivity gaps (Output per hour, Market economy 2001)

60

70

80

90

100

110

120

130

140

US UK GER FR


Explanations for labour productivity gapsCapital per hour, market economy

60

70

80

90

100

110

120

130

140

150

US

UK

GER

FR


Table 5 For US, UK, FRANCE, and GERMANY we get

OUTPUT perHOUR

CAPITAL perHOUR

US BENCHMARK BENCHMARK

FRANCE&GERMANY

Minus 20% approximately

Similar to US

UK Minus 30-35%approximately

Minus 30%approximately


Hence:

US versus France & Germany

- the productivity gap between US on one hand and France and Germany on the other CANNOT be explained by PHYSICAL CAPITAL

- biggest part of the gap is due to TFP

UK

- appears to be behind in TFP and PHYSICAL CAPITAL relative to both US and France and Germany


3. Convergence

1. Definition and mechanisms

Convergence: - When poorer countries grow faster than rich countries.

Mechanisms:- Higher average and marginal productivity of capital in poor countries (the flip side of decreasing returns to capital)- Technological convergence


2. Was there convergence among today’s rich countries?

Many of today’s rich countries have data on output per person going back to the 19th century.

This allows us to ask:

Did those that started poorer grow faster since the 19th century?

For the period 1870-1980, this is the question asked by

Baumol “Productivity, Convergence, and Welfare” American Economic Review, 1986


Baumol Slide1: Convergence among ex-post rich


The figure suggests a clear pattern of convergence among today’s rich countries.BUT there are problems with this approach:

Problem 1: The sample we have are only countries that eventually became rich.Maybe there were some countries that were as rich as, say, Finland, in the 19th century, but then did poorly. These countries would then BREAK the pattern of convergence of the figure.

What countries would that be?-Chile-Argentina-Portugal-…

DeLong considers a sample consisting of the richest countries in the 19th century (not today) and follows them over the same time period.

DeLong “Have Productivity Levels Convergence?” American Economic Review, 1988.



Problem 2: Related to data quality. If the data for the 19th century is worse than that of today, we may conclude based on this data that there is convergence when in reality there is none.

Imagine:- In 1870: all countries really have income the same

income, equal to y(1870)- In 1980: all countries have STILL the same income

Now imagine that the data we have is wrong and underestimates 1870 income for some countries and overestimates it for others. I.e. there is measurement error.

Then we get the following figure.


Time t

y*

1870 1980

Figure 19: Measurement error and (fictitious) convergence


DeLong argues that if this measurement problem is taken into account than the pattern of growth 1870-1980 actually indicates DIVERGENCE among rich countries in the 19th century.

Probably not too surprising because:- the forces of convergence are most likely stronger in

market economies, i.e. economies with economic freedom and protected property rights

- many economies did not conform to this pattern over long periods of time because of communisms, expropriatory dictatorships etc.


3. Convergence among regions

We can also look at the pattern of convergence across regions of one country. The following two figures are about long-term income convergence and output convergence across the STATES of the UNITED STATES.

This question is analyzed in Barro and Sala-i-Martin “Convergence” Journal of Political Economy, 1990.




Advantages and disadvantages of looking for convergence across regions

Advantages: • Regions in the same country tend to share the same

political framework. Differences in income are therefore more likely to be driven by economics.

Disadvantages:• Income of a region is closely related to what the region

specializes in (agriculture?, gold mining?, car manufacturing?, financial services?) and to the process of migration of city-formation (urbanization).

• Growth theory has little to say about all that.


4. Convergence world-wide after World War II

• What if we look at the relation between output growth and initial output per worker for as broad a sample as possible in the post WWII period?

• As has been documented by many economists, we get no indication of convergence. Rich countries may on average even have been growing faster than poor countries.



Or for the 1965-1985 period:


It looks like poor countries have been falling behind in output per worker

But does this prove the absence of the two convergence mechanisms:

- decreasing returns to capital?- technological convergence?

Not necessarily, because BAD ECONOMIC POLICIES in many poor countries have hindered growth.

For example:• not protecting even most basic human and economic rights• not investing in critical factors like infrastructure (roads, electricity

etc.) and human capital (primary and secondary education)


1. Cross-country convergence in the Solow model

CASE 1:-- poor country: poor only because SCARCE

CAPITAL: LOW K(0)/L(0)-- rich country: rich only because ABUNDANT

CAPITAL: HIGH K(0)/L(0)

in all other dimensions the two countries are identical (s,,n,a,E(t))


( )k t

f ksk

n a

BGPk

t

t

kk

rich kpoor k


CASE 2:

-- poor country: poor because SCARCE CAPITAL and LOW SAVINGS RATE

-- rich country: rich because ABUNDANT CAPITAL and high SAVINGS RATE


( )k t

LOW f ks

k

n a

t

t

kk

,BGP richk,BGP poork

HIGH f ks

k

poor k(0) rich k(0)


2. Conditional convergence

The basic idea is that there is CONDITIONAL CONVERGENCE if

poorer countries would have grown faster than richer countries had they adopted the same “ECONOMIC POLICIES”.


How could we check in practice? By running a regression.

For example, estimate the parameters a, b, c below

,1960 ,1985

,1960

ln ln

* *

*ln

country country

country country

country

y y

a SchoolingInvestment b PoliticalStability

c y

GROWTH “EXPLAINED”BY “POLICIES”

GROWTH “EXPLAINED” BY“CONDITIONAL CONVERGENCE”

This is done in Barro “Economic Growth in a Cross-Section of Countries”, Quarterly Journal of Economics 1989.


Growth 1960-1985 assuming same schooling and political stability in all countries

Income in1960


Approach makes sense but also has problems. Because ECONOMIC POLICIES are not exogenous and maybe at least in part due to low initial incomes.

For example:- The approach says that low growth in poor countries may

be due to low investment in schooling. But maybe low investment in schooling is a consequence (not cause) of the poverty of countries.

- The approach says that low growth in poor countries may be due to political instability. But maybe political instability is a consequence (not cause) of the poverty of countries.

- Etc.


5. Forecasting growth of the BRICS

1. The who?

- Brazil, Russia, India, and China- Large countries that are still quite poor but have shown

periods of rapid growth in recent times- Could soon represent a huge part of world GDP, leading

to important changes in international politics and economics (which is why Goldman Sachs is interested in forecasting their future growth)


2. Forecasts

Let us consider the Goldman-Sachs forecast of when total GDP in these countries will overtake the GDP of Germany.




As you know there are many things that must analyzed to get a forecast of total GDP.

Among them:

- working-age population and labor-force participation

- output per worker

….




Avoid that by building in a process of convergence (or growth slowdown):

This can be done by building the forecasts of growth in these countries around the Solow model.

, 1 ,

,

,1960

ln ln

*

0.02*ln

country t country t

country t

country

y y

a

b X

y



Can one check the reliability of these forecasts?

One approach is to do WITHIN SAMPLE FORECASTING.

- Pretend it is 1960.

- Use the approach used to forecast GDP of the BRICs to predict growth of countries 1960-2000.

- Compare to the realized 1960-2000 growth rates.


Documents

Macroeconomics Slide SET 2Slide 1 Macroeconomics LECTURE SLIDES SET 2 Professor Antonio Ciccone