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1Empirical Evidence on EconomicGrowth

Econ302, Fall 2004

Prof. Lutz Hendricks, November 17, 2004

1 The Questions

Why are some countries (USA) so much richer than oth-ers (India)?

Why do some countries grow fast (Japan) while othersdo not (India)?

How important are education, investment, "institutions,"...?


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2 Key Development Facts

.


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2.1 Fact #1: Large income gaps

The richest countries are at least 20 times richer thanthe poorest countries.

Compare real GDP per capita :

USA: $20,000

Uganda: $700

How to compare real GDP across countries?

Real GDP = [Nominal GDP] / [Price index]

Use the same price index for all countries.

Note: Do not use exchange rates to convert JapaneseGDP into USD.


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Should we compare GDP per capita or GDP per worker?

GDP per capita measures how rich countries are.

GDP per worker measures how productive countriesare.

The diff erence is due to labor force participation.


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2.1.1 The world income distribution

More than half of world population earns less than 10%of U.S.

China and India account for 40% of world population.


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2.1.2 Change in the world income distribution

The world income distribution has become somewhat moreequal since 1960.

Large disparities remain.


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2.1.3 Poor countries do not grow faster

1960 real income per worker


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2.1.4 Geographic patterns

All poor countries are in Africa and Asia.

All of South/Latin America is middle-income.

Almost all rich countries are in North America and West-ern Europe. Why?


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2.2 Fact #2: Growth rate di ff erences

BS Figure 1.3

Average post-war growth rates range from below 0 to 8%p.a.

Most rich countries grow at 1.5 to 2% per year.

It takes 40-50 years to double income per person.


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2.2.1 Growth Miracles and Disasters

There are growth miracles with growth rates above 5%.

It takes 12 years to double income per person.

All of the growth miracles were middle income coun-tries in 1960.

There are growth disasters with negative growth rates.

All of these are in Africa and South America.

Growth miracles are usually middle income.

Growth disasters are in Africa and South America.


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Source: Temple (1999)


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2.3 Fact #3: Persistent growth is a mod-

ern phenomenon

Maddison (1991) estimates that per capita incomes roughly

doubled in Western Europe between 1500 and 1800. Thatamounts to a growth rate of 25 percent per century, com-pared with 500 percent for the centuries after 1800.

One reason: innovation is a modern phenomenon (recallGalileo).


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.

2.3.1 The world was poor for nearly all history

Source: Jones (2003)


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Large income dispersion is a modern phenomenon.Prior to about 1800 a more or less common standardof living characterized all major civilizations (Prescott1998).

Fact #4: Country growth rates vary over time Im-plication: Some countries that were rich in the past are

poor today.

Argentinas per capita income in 1900 was about thesame as that of the U.S.


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U.S. GDP since 1870 .

The U.S. growth rate has been constant for 130 years

Source: Jones (2003)

.


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4 Growth Accounting

How large are the contributions of capital and labor tooutput growth?

Growth accounting provides and accounting answer, butdoes not identify the sources of growth.

Assume an aggregate production function: Y t = F (K t , L t , z t

Then the growth rate of GDP is given by:

g (Y ) = E F,z g (z) + E F,K g (K ) + E F,L g (L ) (1)

where E F,z is the elasticity of Y w.r.to z (a parameterof the production function).

In words: GDP growth is a weighted average of inputgrowth rates and productivity growth.


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Cobb-Douglas example: Y t = zt K t L1 t .

Take logs: ln Y t = ln zt + ln K t + (1 ) ln L t .

Take the time derivative:d ln Y t

dt =

d ln ztdt

+ d ln K t

dt + (1 )

d ln L tdt

(2)

Note that the growth rate is about the same as the timederivative of the log:

g (Y t ) d ln Y t

dt (3)

Then

g (Y ) = g (z) + g (K ) + (1 ) g (L) (4)

Growth rate of GDP per worker:

g (Y/L ) = g (Y ) g (L )

= g (z) + g (K/L ) (5)


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4.0.2 Estimating the variables

Capital stock: Estimate from past accumulated invest-ment (perpetual inventory method).

Start from an arbitrary K 0 way back in the past.

Compute K t+1 = (1 ) K t + I t by forward iteration.

Quality adjustments can be made to account for the factthat newer vintages of K are more productive.

Labor input: Estimate from aggregate hours worked.

Quality adjustment can be made to account for the factthat more educated workers are more productive (etc.)

Factor income shares: Should use social marginal prod-ucts when calculating E F,K and E F,L . These are notobservable.

With Cobb-Douglas, exploit the fact that capital receivesfraction of total income: rK/Y = and wL/Y =

1 .


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TFP: z is unobservable. Estimate this as the residual :

g (z) = g (Y ) (rK/Y ) g (K ) (wL/Y ) g (L)

Note: This means that TFP growth captures all omittedfactors (everything other than K and L)!


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4.1 Empirical Results

4.1.1 U.S data

Roughly half of U.S. growth is due to productivity. The

rest is mostly due to capital accumulation.

Note the productivity slowdown after 1973.


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4.1.2 Other countries

The Newly Industrialized Countries (NICs) grew at spec-tacular rates. Why?

TFP growth is not unusually high.


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4.1.3 TFP growth around the world

TFP growth in SGP is negative! OAN is below COL.


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4.1.4 How did the NICs sustain high growth?

The key is high and rising investment.

Recall

g (Y/L ) = g (z) + g (K/L ) (6)

In the long-run, K and Y must grow at the same rate(why?).


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For any constant I/Y, eventually output growth is deter-mined by TFP growth:

g (Y/L ) = g (z)1 (7)

Temporarily , countries can sustain faster growth by rais-ing I/Y .


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4.3 Limitations of Growth Accounting

Growth accounting assumes that factors are paid theirsocial marginal products.

Externalities bias the calculations.

Examples of externalities:

1. Learning by doing: investment improves TFP.

2. Human capital spillovers.

.


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4.3.1 Learning by doing example

Firm i produces output according to: Y i = A K

K i L

1 i =A K ki Li .

K re ects learning by doing (an externality).

Firms pay factors their private marginal products: R = Y i /K i and w = (1 ) Y i /L i .

In equilibrium: all rms choose the same ki = K/L = k.

Therefore: Y = P i Y i = A K k L = A K + L1 .

The correct growth accounting equation is: g (Y ) =g (A) + ( + ) g (K ) + (1 ) g (L ).

The standard growth accounting approach weights g (K )

with and therefore attributes part of capitals eff

ect toTFP.

.


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4.3.2 Growth accounting does not identify sourcesof growth

Factor accumulation responds to technical change.

Example: Solow model with constant population. Allgrowth is ultimately due to technical change.

But in steady state, growth accounting attributes fraction of g (Y ) to g (K ) .

.


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5 Growth Regressions

Why do some countries grow fast or slow?

A large literature addresses that question by regressing acountrys growth rate on

initial conditions: y,k,h .

control variables: investment, government spending,institutions, etc.

.


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Poorer countries grow faster (conditional convergence).

.


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Weak relationship between institutional measures and growth

.


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5.1 Problems

1. Robustness (Levine and Renelt 1993):

Nearly all regressors become insigni cant when someother regressors are added to the equation.

2. Interpretation.

Regressions show that growth rates are correlatedwith investment, but cannot resolve causality.

Regressors may proxy for other omitted variables.Example: Low government spending could re ectlow taxes.

Only quantitative theory can resolve the questionwhy some countries grow faster than others.

3. Do long-run growth rates really diff er across countries?

Long-run data cast doubt on that assertion.


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Perhaps the regressions capture transitional dynam-ics.

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