chapter 16 endogenous growth theory. 2 introduction the neoclassical growth model was constructed in...

Chapter 16

Endogenous Growth Theory

2

Introduction

• The neoclassical growth model was constructed in the 1950s to accommodate some stylized facts about the U.S. economy.

• Now, data on most countries that extends back to 1960 is available.

• It is found that a number of predictions of the simplest version of the neoclassical model are inconsistent with the evidence.

3

Introduction

• Both the neoclassical and endogenous growth theories make the simplifying assumption that each country in the world produces the same homogenous commodity – no international trade in commodities.

• However, both of the models allow for trade in capital as countries borrow from and lend to each other.

4

Introduction• Endogenous and exogenous growth theories

explain growth as increases in the efficiency of labor, Q.

• The neoclassical model assumes that Q is exogenous, but endogenous growth theory explains why Q increases from one year to the next.

• As the economy builds more complicated machines and workers learn to operate new machines, they acquire knowledge which accumulates over time and contributes to the growth process.

5

The Neoclassical Model and the International Economy

• The major motive for international trade is the diversity in the abilities of different countries to produces the goods and services.

• The neoclassical growth model excludes the trade in commodities because the model deals with a world in which there is only one good.

6


• A second kind of trade is intertemporal trade

-- trade between different points in time.

• Intertemporal trade occurs when one country’s consumption plus investment is greater than its GDP.

• Possible reasons :

1. People in one country might be more patient than those in another which implies a higher saving rate.

7


• Possible reasons :

2. One country may have a higher rate of growth rate of population than another. The high-population-growth country needs to invest at a faster rate in order to maintain a fixed capital-labor ratio.

3. One country is richer than the others.

4. Different countries may use different production function. (This is not the case.)

8


• In this chapter, we model the world as a collection of countries, each of which produces the same homogenous commodity using the same production function.

• Countries differ for only three reasons :

1. Different saving rates;

2. Different rate of population growth;

3. Different initial stocks of capital.

9

Modeling World Trade

• Two ways :

1. Assume that world capital markets are completely open.

2. Assume that world capital markets are closed.

• Reality is somewhere in between the two extremes but difficult to model.

10

The Neoclassical Growth Model with Open Markets

• The first task in amending the neoclassical model is to allow for the fact that countries can borrow and lend internationally.

World saving equals world investment.

f fS S I I

11


• Figure 16.1 shows that domestic saving in each of these countries is very close to domestic investment.

• The neoclassical model cannot explain.

• This gives us to question the assumptions of the theory.

f fS S I I

12


• A second implication of the neoclassical model is that investment in a perfect capital market should flow freely between countries to equalize the interest.

• If one country has a higher interest rate, capital should flow to the high-rate country as the MPK is higher.

• As capital flows into a country, the MPK will fall and the rates of return are equalized.

13


• For the neoclassical production function, the rate of return depends only on the ratio of capital to labor.

• If the rate of return is equal in different countries, the capital-labor ratio must also be equal.

11 ff

f

K KMPK A MPK A

NQ N Q

14


• How to test whether the marginal product of capital is equalized across countries ?

• Equalization of capital-labor ratios implies equalization of GDP per person :

1Y K QN K

A AQN QN QN QN

15


• Figure 16.2 presents evidence from five countries : the U.S., the U.K., Mexico, Turkey, and India.

• In reality, we see that poor countries, like India, tend to stay poor, and rich countries, like the U.S. tend to stay rich.

Y KA

QN QN

16Figure 16.2©2002 South-Western College Publishing

GDP Per Person Relative to U.S. GDP Per Person for a Selection of Five Countries

17

The Neoclassical Growth Model with Closed Capital Markets

• Evidence suggests that capital does not flow freely between countries. Can a different version of the neoclassical model, zero capital mobility, explain the facts ?

• Consider two countries that are different in only one aspect -- the saving rate, s.

1

1 1t t t t t tsY sAK Q N K K

Saving Investment

18


• If we let gE represent the growth rate of labor in efficiency units, the steady state value of capital per efficiency unit of labor is

which depends on the four factors, the saving rate, the depreciation rate, the growth rate of labor in efficiency unit and the capital elasticity of output.

1

1

E

K sA

QN g

19


• For the same production function, the depreciation rate and the capital elasticity are ruled out as possible factors that differ across countries.

• Two factors left : the saving rate and the growth rate of labor in efficiency unit.

1

1

E

K sA

QN g

20


• This equation predicts that countries saving more will accumulate more capital per unit of labor in the steady state and have higher level of GDP per person.

1/(1 )

E

K sA

QN g

1

E

Y sAA

QN g

21


• If country A has a higher saving rate than country B, (with the same level of Q)

1E

Y sAA

QN g

A B

A B

Y Y

N N

Steady state level of GDP per person

22


• As a test of this prediction, panel A of BOX 16.1 plots average GDP per person from 1960 to 1998 against the average investment-GDP ratio for 17 countries.

• Panel B corrects for population growth rate.

• In fact, there is little or no correlation between them !!

or Y Y

sN NQ

23

©2002 South-Western College Publishing

Box 16.1A

FOCUS ON THE FACTSInvestment and GDP Per Person

24

©2002 South-Western College Publishing

Box 16.1B

FOCUS ON THE FACTSInvestment and GDP Per Person

25


• The neoclassical model predicts that GDP per person should be correlated with saving rates, but the data does not supports this.

• The model also falls short in its predictions about growth rates of GDP per person.

• The model maintains that the growth rates of GDP per person should be the same because the model states that all growth is ultimately due to exogenous technical progress.

26


• Consider two countries A and B that have different saving rates and growth rates of population growth, then the output per unit of labor are

• and the growth rate of GDP per person are

, ,A AA B

A B

Y Yy y

N Q N Q

/ /, .

/ /A A B B

A A B B

Y N Y NQ Q

Y N Q Y N Q

27


• This equation shows that in the steady state, output per person will grow at the same rate in each country because countries that have the same production function should experience the same increases in the efficiency of labor.

• Figure 16.3 : the prediction of the simple neoclassical model does not do a good job!

/ /, .

/ /A A B B

A A B B

Y N Y NQ Q

Y N Q Y N Q

28

Convergence

• Some economists note that the prediction that countries will grow at the same rate, only holds if all the countries in the world have attained their steady state.

• With the same saving rate and population growth rate, countries with lower capital stock should grow faster.

• Evidence : Japan, Germany and Italy grew rapidly in the postwar period.

• This idea is called reconstruction hypothesis.

29

Convergence

• A second way : test whether countries with low levels of GDP per person grow faster.

• This is called convergence hypothesis.• Most studies conclude that this hypothesis does

not hold across all of the countries in the world.• Conditional convergence : if we include

variables such as education, political stability and etc., we can explain some of the differences in growth rates.

• However, the convergence occurs at a much slower rate than the simplest model predicts.

30

The Model of Learning by Doing• The neoclassical theory attributes growth to

increases in labor efficiency which are not explained by other economic variables and is so called exogenous growth theory.

• More recently, economists have begun to study alternative approach that assumes workers acquire skill, human capital, as they learn a new technology.

• The accumulation of human capital is responsible for growth in GDP per person. (Endogenous Growth Theory)

31

Endogenous and Exogenous Theories of Growth

• The acquisition of human capital allows a worker to operate complicated machinery or join a team of other skilled workers.

• Human capital can be accumulated in the same way that physical capital is accumulated by devoting resources to the act of investment.

Physical capital : building factories and machines

Human capital : acquiring knowledge (skills)

32

Endogenous and Exogenous Theories of Growth

• Human capital is acquired through

-- the active pursuit of learning (or education)

-- the act of production itself (learning by doing)

• Learning by Doing :

-- The cost of production declines as companies learn the best way to produce.

-- Workers acquire this knowledge through their experiences in the workplace.

33

The Technology of Endogenous Growth

• Endogenous grow theory makes a relative minor change to the neoclassical production function.

• It assumes that the aggregate (social) production function is described by a C-D technology :

1

1

Y AK L

AK

34


• If the capital elasticity of output is equal to 1 (rather than 1/3), this means that the economy is no longer subject to a diminishing marginal product of capital.

Y AK

( a constant )MPK A

35


• In the neoclassical theory, the capital elasticity, α=1/3, is proposed to be consistent with the evidence.

• How does endogenous growth theory explain this alternative value, α=1, can be made consistent with the fact ? (constant returns to capital )

--- This is the social technology !!

Y AK

36

Social and Private Technology

• The acquisition of human capital is a social process whose effects go beyond the individual’s own productivity. (Externality)

-- As one firm produces a idea, another firm copies it.

-- As one individual learns a quick and easy way of solving a problem, another individual can duplicate it.

-- The technological progress, Q, is a function of the level of industrialization of the society.

37


• Suppose an economy consists of M firms and each firm produces output using a private technology that is identical that in the neoclassical growth mode.

• Let Y, K, L be the aggregate GDP, capital and labor, respectively, the private production function is given by

1

1

Y K LQA

M M M

Y AK LQ

38


• The new element in the theory of learning by doing is what determines Q !!

-- The aggregate level of industrialization.

-- The aggregate stock of capital per worker, K/N, is a good proxy.

-- Q is assumed to be proportional to K/N.

For simplicity, we assume

, the knowledge function.

KQ

N

39


• The accumulation of capital has two effects :

1. The private effect that gives rise to the term Kα in the social production function.

2. The second effect is called “externality” which gives rise to the term K1-α.

1Y A K L Q

The private effect Externality (Spillover Effect)

40

Externality

• As workers learn to use the new technology in one firm, they acquire skills that can transferred to another firm.

• The learning was acquired from the workers’ exposure to ideas over the course of their work history.

• The degree of exposure grows with the social acquisition of capital.

• It’s almost free.

41

The Social Production Function

/Q K N

1L

Y A K Q NN

1 (for simplicity)L

N

1

The Social Technology

Y AK K A K Aggregate

GDP

Aggregate

Capital

42

©2002 South-Western College PublishingFigure 16.4B

The Private Production Functions

1Y AK LQ

MPK

43©2002 South-Western College PublishingFigure 16.4A

The Social and Private Production Functions Compared

(constant)

Y AK

MPK A

44


• The economic meaning :

1. When an individual firm expands its use of capital, it captures only the private impact of this additional capital.

2. As the firm trains its workers in the use of new equipment, most of this benefit is lost when the worker leave to take new jobs.

Their new skills are widely disseminated to friends and colleagues who work at other firms.

45


• An important implication

A firm will be more productive if it is part of a society with a high level of capital.

Contrast this with the neoclassical model, which assumes that if a firm were transported from the U.S. to Ghana, it would still employ the same technology.

Learning by doing argues that the firm would be less productive because the skills of the Ghanaian workforce are lower.

46

Learning by Doing and Endogenous Growth

• Because evidence suggests that there is relatively little international borrowing and lending, we examine the extreme case that the capital market is closed.

domestic investment equals domestic savingt tI S

47


• Saving is assumed to be a fixed fraction of GDP

• Capital is accumulated with the identity :

• The social production function :

1 1(1 )t t tK I K

t tS sY

t tY AK

48


• In a learning by doing economy, the solution to the growth equation is a straight line.

1 (1 )

(1 )

(1 )

(1 )

t t t

t t

t t

t

K I K

sY K

sAK K

sA K

49


• Notice that because the population is assumed to be constant, the dynamics of Y (or K) and y ( or k) are almost the same.

1 1 (1 )

(1 )t t t

t

Y AK A sA K

sA Y

1

1

(1 )

(1 )t t

t t

k sA k

y sA y

51

Predictions of Comparative Growth Rates

• Consider two economies that have the same saving rates, country A and B, but country A begins with an higher initial level of capital lower than that of country B.

The learning-by-doing model predicts that country B will always remain ahead of country A, but both countries’ capital will grow at the same rate.

This explain why countries like India, U.K., Mexico, which have similar saving rates, grow at about the same rate.

52Figure 16.6 ©2002 South-Western College Publishing

Two Economies with the Same Growth Rate But Different Initial Conditions

53

Predictions of Comparative Growth Rates

• A second piece of evidence concerns two countries with different saving rates.

• Consider two economies begin with the same initial capital stock, but have different saving rates.

1

1

1 1

(1 ) ,

(1 ) ,

,

.

At t

Bt t

A B

A B

t t

t t

K s A K

K s A K

s s

K K

K K

54©2002 South-Western College Publishing

Figure 16.7

Two Economies with the Same Initial Condition But Different Savings Rates

56

Endogenous Growth and Economic Policy

• One issue that concerns contemporary policymakers is the fact that GDP growth per capita was a little slower in the 1970s than it was in the immediate postwar period.

-- If the neoclassical growth theory is correct, not much can be done about this.

-- The learning-by-doing suggests that growth is related to investment- both public and private.

57


• Q=K/N is indeed a too simplified assumption!!

• In the real world, a poor country can just invest and copy the technologies from the other countries to raise the level Q.

• However, for a rich country like the U.S., Q is extreme high, and can only be raised through new invention or more education of workers.

(the growth rate of Q may be smaller than the growth of capital per person)

58


• Policy :

-- Investment in human capital can have great public benefits.

-- Research & Development (R&D)

59

Modified Theories of Learning by Doing

• Although economists agree that the neoclassical model does not do a good job of explaining the cross-country evidence, they do not accept the extreme from of the learning-by-doing hypothesis.

• They believe as a country gets close to the frontier of world knowledge, part of its investment will spillover over and improve growth in other world countries.

the externalities can cross international boundaries.

60

Modified Theories of Learning by Doing

• A weaker form of the learning-by-doing hypothesis argues that the knowledge function for each country may display decreasing returns.

• This leads to a model behaves much like the NGT.

• GDP per capital is predicted to converge across countries, but the speed at which it converges is much slower.

(1 )

. / ,0 1.Ex Q K N

y Ak

(1 )1 1t tk k sAk

61

Homework

Question 8, 11, 14

In question 14, the production function is corrected to be

1/(1 ) .Y aK a N