Transcript Growth Models - Washington and Lee University

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)
= AKaL(1-a)
• In per capita terms, we want to look at Y/L
– Hence AKaL(1-a) /L = AKaL(1-a) L-1
= AKaL-a
= A(K/L) a
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 + (a log K + (1-a) log L we get:
– gY = gA + agK +
(1-a)gL
Growth Accounting
• Hence in growth terms:
• gY = gA + agK + (1-a)gL
• To implement we (just) need to know
– past or likely future growth rates or values of:
• Inputs: capital stock, labor force
• factor shares a
• 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(AKaL(1-a))  aAKa-1L(1-a)
• Now we should have wL + rK = Y, right?
– Let’s plug in and check!
– So the exponent a 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 precomputer 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
• Contributions, 1970s
• 0.68
Labor
• +0.11 Hours
• +1.09 Workers
• +0.58 Educ etc
• 2.57
• 2.78
Capital
Structural
• -0.15 Hours
• +0.68 Workers
• +0.50 Educ etc
• 0.86
• 0.42
(agri, EOS, trade)
• 2.43
• 9.56
“Knowledge”
Total
Capital
Structural
(agri, EOS, trade)
1.28
• 3.24
“Knowledge”
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 (1-a)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 - agK - (1-a)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) postWWII 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)
7000
6000
Labor Force
5000
Not in Labor Force
4000
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
3000
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
Growth Accounting Applied
•
Sources, 1961-71
•
Sources, 1970s
•
Sources, 2000s
•
1.78 Labor
•
0.68 Labor
•
-0.20 Labor
• Hours +0.11
• Hours -0.15
• Hours -0.20
• Workers +1.09
• Workers +0.68
• Workers -0.10
• Educ etc +0.58
• Educ etc +0.50
• Educ etc +0.10
•
2.57 Capital
•
0.86 Capital
•
-0.10 Capital
•
2.43 Knowledge
•
1.28 Knowledge
•
1.20 Knowledge
•
2.78 Structural
•
0.42 Structural
•
-0.20 Structural
(agri, EOS, trade)
•
9.56 Total
(agri, EOS, trade)
•
3.24 Total
(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 Growth
Basic 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:
The End
January 2002
Economics 285
Prof. Smitka