1. Explaining High Growth – Supply-side Analysis – Prof. Michael Smitka Winter 2002 Washington and Lee University

2. 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.

3. 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!

4. Production Function Y = f (K, L, tech, etc) = AK  L  In per capita terms, we want to look at Y/L –Hence AK  L  /L = AK  L  L  = AK  L  = A(K/L) 

5. 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

6. 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 - 

7. The (long) Long-run To simplify further, assume technology fixes the capital-output ratio K/Y=k Then capital grows at g K =s/k-  Remember that logs give: –Growth rate of x: g x = d(log x) = dx/x –So if we take logs of our initial equation: log Y = log A + (  log K + (  ) log L we get: – g Y = g A +  g K + (  )g L

8. Growth Accounting Hence in growth terms: g Y = g A +  g K + (  )g L 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 g A

9. 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(AK  L   AK  L  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.

10. 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

12. 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….

13. 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

14. Growth Accounting for Japan Contributions, 1961-71 1.78Labor +0.11 Hours +1.09 Workers +0.58 Educ etc 2.57Capital 2.78Structural (agri, EOS, trade) 2.43“Knowledge” 9.56Total Contributions, 1970s 0.68Labor -0.15 Hours +0.68 Workers +0.50 Educ etc 0.86Capital 0.42Structural (agri, EOS, trade) 1.28“Knowledge” 3.24Total

15. 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 (  )g L 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

16. Interpretation: “Knowledge” Solow, in his original work, found that he could only account for about half of growth The residual here is g A since productivity can’t be measured directly: g A = g Y -  g K - (  )g L 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

17. 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?

18. A predictive tool What of the future? Here are charts of: Labor force growth Changes in quality / education Capital stock growth Returns to capital

23. 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

24. Sources, 1961-71 1.78Labor Hours +0.11 Workers +1.09 Educ etc +0.58 2.57Capital 2.43Knowledge 2.78Structural (agri, EOS, trade) 9.56Total Sources, 1970s 0.68Labor Hours -0.15 Workers +0.68 Educ etc +0.50 0.86Capital 1.28Knowledge 0.42Structural (agri, EOS, trade) 3.24Total Growth Accounting Applied Sources, 2000s -0.20Labor Hours -0.20 Workers -0.10 Educ etc +0.10 -0.10Capital 1.20Knowledge -0.20Structural (services, trade) 0.70Total

25. Growth Accounting % pa contribution: an alternate study similar findings, despite different time periods etc 1960s1970s1980s1990s Kapital6.93.82.81.9 Labor0.40.00.4-0.3 TFP3.70.71.00.0 GDP growth 11.14.54.21.6 Yoshikawa, Hiroshi (2000). Technical Progress and the Growth of the Japanese Economy – Past and Future. Oxford Review of Economic Policy. 16:2, 36.

26. 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??!

27. 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

28. 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

29. 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:

31. The End January 2002 Economics 285 Prof. Smitka