Explaining High Growth– Supply-side Analysis –

Prof. Michael Smitka

Winter 2002

Washington and Lee University

Growth Accounting Framework

• Underlying this approach is a production function for the macroeconomy

• Furthermore, Say’s Law* holds:– This is a wholly supply-side model

– In the long run all capacity is utilized – or disappears!

*Say’s Law: supply creates its own

demand.

Other implicit assumptions

• This is a “classical” model– Demand does not matter (as above)

– Prices don’t matter - real output is independent of the price level

• In other words, AS is vertical and AD doesn’t matter or is horizontal

• The Phillips curve is vertical / there’s no unemployment tradeoff

• It does not explain events within a 2-3 yr horizon– It’s the wrong model for analyzing business cycles!

Production Function

• Y = f (K, L, tech, etc)= AKL

• In per capita terms, we want to look at Y/L– Hence AKL /L = AKLL

= AKL = A(K/L)

How does K/L grow?

• Demographics!– Read Mason & Ogawa “Population, Labor

Force, Saving, and Japan’s Future” in Japan’s New Economy

• Investment– In our simple model, there is neither

government nor trade– Hence (since nothing is wasted) S=I

Savings and Investment

• We use the simplest possible savings function– S = sY (a fixed share of income) so I = sY

• Capital doesn’t last forever:– subtract depreciation each year from K

• So the net addition is I- K = sY - K• Growth rate is (I- K)/K = sY/K -

The (long) Long-run

• To simplify further, assume technology fixes the capital-output ratio K/Y=k

• Then capital grows at gK=s/k-• Remember that logs give:

– Growth rate of x: gx = d(log x) = dx/x

– So if we take logs of our initial equation:log Y = log A + ( log K + () log L we get:

– gY = gA + gK + ()gL

Growth Accounting

• Hence in growth terms:

• gY = gA + gK + ()gL

• To implement we (just) need to know– past or likely future growth rates or values of:

• Inputs: capital stock, labor force

• factor shares • productivity growth gA

Marginal Rules

• How do we find income and so on?– In a micro model, wages w = ??

– Similarly, real interest rates r = ??• Hint: marginal product of capital … or:

• r = d(Y)/dK = d(AKLAKL

• Now we should have wL + rK = Y, right?– Let’s plug in and check!

– So the exponent has a clear meaning: the share of output that accrues to capital.

Long-run

• What would you expect to happen as K rises, ceteris paribus?– Diminishing returns set in, right?!

• What then do growth dynamics look like?– Well, if returns diminish, so does growth!– Eventually investment equals depreciation

• Cf. a simple Excel spreadsheet effort…or the following chart.– Can readily extend to see what happens with population

growth, productivity growth

Applying the model empirically

• Find values of our parameters– Use regression analysis, check against other

information on labor and capital shares of income

• Find values of K and L– Can decompose, consider vintage effects,

education…

• Plug in and see what we find….

Historical digression

• Original work was done by the Nobel Laureate Robert Solow (MIT) in pre-computer days

• Continued by Dale Jorgenson at Harvard, and a whole stream of grad students / colleagues

• Robust results, but new growth theory today with fancier statistical tools

Growth Accounting for Japan

• Contributions, 1961-71• 1.78 Labor

• +0.11 Hours • +1.09 Workers • +0.58 Educ etc

• 2.57 Capital• 2.78 Structural

(agri, EOS, trade)

• 2.43 “Knowledge”• 9.56 Total

• Contributions, 1970s

• 0.68 Labor• -0.15 Hours

• +0.68 Workers

• +0.50 Educ etc

• 0.86 Capital

• 0.42 Structural (agri, EOS,

trade) 1.28“Knowledge”

• 3.24 Total

Interpretation

• The contribution of labor to growth is:– 1.8 out of 9.6% per annum

• Thus explains about 20% of the total• Is roughly ()gL

• Ditto for capital– a bit over 25% of the total

• Structural change represents one-time shifts– From agriculture to higher productivity sectors– From low to higher size & economies of scale– From near-autarky to more international trade

Interpretation: “Knowledge”

• Solow, in his original work, found that he could only account for about half of growth

• The residual here is gA since productivity can’t be measured directly:

gA = gY - gK - ()gL

• Better & more data ought to reduce, but doesn’t by much

• So calling it “knowledge” may be appropriate– Certainly that fits story of Japan’s (and the EU’s) post-

WWII race to “catch-up” with new US technologies

Interpretation (cont.)

• In the more recent period– Input growth slowed– Output growth slowed

• In short, maybe the slowdown in Japan’s growth is entirely predictable

• But what about a decade of really low growth?

A predictive tool

• What of the future?

• Here are charts of:• Labor force growth

• Changes in quality / education

• Capital stock growth

• Returns to capital

Labor Force (November)

3000

4000

5000

6000

7000

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001

Labor Force

Not in Labor Force

So…

• No labor force growth• Education is widely diffused

– Further gains reduce the labor force– Diminishing returns here, too

• Returns on assets are very low• Let’s plug into our growth accounting

model

• Sources, 1961-71

• 1.78 Labor• Hours +0.11

• Workers +1.09

• Educ etc +0.58

• 2.57 Capital

• 2.43

Knowledge

• 2.78 Structural

(agri, EOS,

trade)

• 9.56 Total

• Sources, 1970s

• 0.68 Labor• Hours -0.15

• Workers +0.68

• Educ etc +0.50

• 0.86 Capital

• 1.28

Knowledge

• 0.42 Structural

(agri, EOS,

trade)

• 3.24 Total

Growth Accounting Applied

• Sources, 2000s

• -0.20 Labor• Hours -0.20

• Workers -0.10

• Educ etc +0.10

• -0.10 Capital

• 1.20

Knowledge

• -0.20 Structural

(services,

trade)

• 0.70 Total

Growth Accounting% pa contribution: an alternate study

similar findings, despite different time periods etc

1960s 1970s 1980s 1990s

Kapital 6.9 3.8 2.8 1.9

Labor 0.4 0.0 0.4 -0.3

TFP 3.7 0.7 1.0 0.0

GDP growth

11.1 4.5 4.2 1.6

Yoshikawa, Hiroshi (2000). Technical Progress and the Growth of the Japanese Economy – Past and Future. Oxford Review of Economic Policy. 16:2, 36.

Zero Growth

• So maybe the Japanese economy simply cannot grow much from now into the future

• But if labor force growth is negative– Real wages can still rise!!– So no problem??!

Causation: Sources of GrowthBasic Historical Queries

• Our long-run model isn’t a full explanation

• Where did demand come from?– Was growth export-led?– Did the government do it?– How about investment?– How about domestic demand?

• Consumers

• Urbanization

Model Refinements• In these models labor-force growth is exogenous.

– So we need to look at demographics

– And the structure of labor markets & skill formation

• Capital growth is another element.– So we need to model savings, or at least try to make it

at least endogenous in our thinking.

• Productivity growth looms large– Structural reforms!

– Corporate management

So we have a map of where we go next

• Examine the nature of key input markets!

• But remember:– The long run isn’t everything

• We also must turn eventually to short-run variations in growth:

Japanese Real GDP Growthseasonally adjusted, 1993 SNA

-12%

-9%

-6%

-3%

0%

3%

6%

9%

1980/ 1- 3.1981/ 1- 3.1982/ 1- 3.1983/ 1- 3.1984/ 1- 3.1985/ 1- 3.1986/ 1- 3.1987/ 1- 3.1988/ 1- 3.1989/ 1- 3.1990/ 1- 3.1991/ 1- 3.1992/ 1- 3.1993/ 1- 3.1994/ 1- 3.1995/ 1- 3.1996/ 1- 3.1997/ 1- 3.1998/ 1- 3.1999/ 1- 3.2000/ 1- 3.2001/ 1- 3.

Growth over Previous Quarter Growth over previous Year

Average 4.0%

Average 1.1%

The End

January 2002

Economics 285

Prof. Smitka