Solow Growth Accounting

Transcription

1 Econ 307 Lecture 3

2 Solow Growth Accounting Let the production function be of general form: Y = BK α L (1 α ) We call B `multi-factor productivity It measures the productivity of the composite of labour and capital

3 Labour Productivity Let the production function be of general form: Y L α K = B = L Bk α

4 Growth Accounting Solow growth accounting dy = dk (1 ) dl db Y α + K α + L B As before, assume CRS, Competitive Markets This allows us to transform above equation so that all but the last term is observable

5 Growth Accounting CRS Y = MPL * L + MPK * K Competitive mkts MPL = W, MPK = R Implies capital share (labour share) is α,(1 α )

6 So TFP growth is obtained by re-arranging g = g α g (1 α ) g Bt yt t Kt t Lt Note that factor shares will be constant in Cobb-Douglas economy, but not more generally doesn t matter if you have data on factor shares anyway

7 This is a useful empirical equation Growth in Y, K, L are observable productivity growth is the residual Does not imply particular type of technical progress (as in the specific Solow model above) Labour productivity growth: g = g + α ( g g ) ( = g g ) PLt Bt t Kt Lt yt Lt

8 Example. Take data on US Japan US and Japan Growth rates US Japan Output Capital Employment Japanese GDP growth was much higher: on average more than 2% per annum Contributions to Growth Factor US Japan Capital Employment Productivity Total But, assuming share of capital=.33, only half of this was due to higher Japanese productivity growth

9 Productivity slowdown Post 1973 worldwide slowdown in TFP and labour productivity growth e.g. US 50 s 60 s 70 s 80 s Productivity recovered in 1990 s investment in new technologies? But in Canada neither TFP nor labour P. growth recoveredlagged significantly behind US

10 Big differences in manufacturing; mostly due to `high tech differences in US over Canada Output per Hour Manufacturing United States Canada

11 Canadian experience Canada TFP LP US TFP LP Currently a major debate in Canada. But great controversy over data

12 Recent Experience Growth in Labour Productivity US Canada

13 Growth Accounting and East Asia Many of the fast growing East Asian countries had TFP growth no higher than OECD countries In particular, Singapore had very low, and even negative TFP Implies most or all growth comes from capital and labour Productivity growth required for long run

14 Back to Solow growth model Can it account for the growth and income differentials across countries? See Jones chap 3 plus Mankiw article Growth of Nations (first part) 3 facts to be explained The scale of international GDP pc differentials The rate of convergence among countries (differences in growth rates) The implied differentials in rates of return to capital among countries

15 International differentials How big will be steady state Y differences given differences in s, n? Remember equation: dy* α ds dn n = ( ) y* 1 α s n n+ g+ δ So an increase in savings rate will raise GDP by proportion α 1 α

16 International differentials Share of capital is about.33 So by standard estimates this proportion about 0.5. Differences in s of factor of 4 differences in y of factor of 2 Same for population growth elasticity of y wrt population growth About 0.08 α n (( 1 α )( n + g + δ )) So cannot explain differences in y of factor of 30

17 The rate of convergence Convergence regressions growth is faster, the further away from steady state Two economies with same steady state: lowest k(0) economy will grow faster Regression Average growth = a+bgdppc(1960) b <0 should hold

18 Motivation for convergence regression Recall from the previous lecture: dlnk dt = (1 α)( n+ g+ δ)(ln( k) ln( k*)) This gives the solution ln kt ( ) ln k* = Cexp( (1 α)( n+ g+ δ) t) = Cexp( λt) This implies that: C= ln k(0) ln k*

19 Same holds for y ln y =α ln k ln yt ( ) ln y* = (ln y(0) ln y*)exp( λt) So that: = λ ln y( t) ln y(0) (ln y* ln y(0))(1 exp( t)) Leads to convergence estimation equation (cross country estimation) ln( yt ( )/ y(0)) (1 exp( λt )) i i = a ln y (0) + u i i T T

20 Evidence is mixed OECD economies clear convergence All economies no convergence But problem is that economies don t have same steady states. If poor economies have low savings rate (e.g.), they ll converge to lower s. state, and therefore have lower growth Conditional convergence Average growth (60-90) = a+bgdppc(1960)+cx Where X is other factors (savings, education, political stability,etc.)

21 lny Same steady state: absolute convergence rich poor time

22 lny Different steady states: conditional convergence rich poor time

23 Estimates of speed of convergence Root of differential equation λ = (1 α)( n+ g+ δ) Root is about 0.04 or 0.05 But estimates of Barro X.Y. Martin and others is about So empirical half life (0.7/0.02) is 35 years Theoretical prediction is (0.7/0.05) -14 years much too fast

24 Rate of returns differentials between rich and poor should be gigantic in Solow model Remember dr R = (1 α ) α dy y So income differences of magnitude 10 produce returns differences magnitude 100 (if α=.33) - much larger than anything observed

25 How to fix up these problems? Mankiw and Mankiw Romer and Weil Need to amend Solow model to allow for human capital There are differences in innate productivity of labour across countries due to investment in education, skills etc.

26 How to fix up these problems? In the simplest model (Jones) α 1 α Y = K ( AhL), h= exp( ψ u) Allows for agents to invest in human capital Leads to SS equation ŷ = kˆ α h

27 This can add to the explanation of income differentials across countries Jones estimates that differences in h of order of 2 between richest and poorest countries average 8 more years of schooling, with return 10 percent, we get: h = exp(.1 8) 2.2

28 But does not get far enough In combination with savings differentials, can explain differences by factor of 4 Jones argues that different `A s can explain the rest But these are unexplained within the model

29 Alternative approach to human capital (Mankiw paper) Allow for a higher share of capital. If α = 0.67 differences in s of magnitude 4 imply y differences magnitude 16. Convergence speed of 0.02 Differences in y of magnitude 10 imply rates of return differences 3.2 much smaller

30 y Basic Solow Model k

31 y Amended Solow Model Much less diminishing returns, so that the impacts of changes in s is much greater. And the dynamics of transition are much slower k

32 How to get higher capital share in Solow model? Externalities: the social return to capital exceeds the private return y = Bk α B = k b Perceived private return to capital is α, but social return is b+α.

33 So if human capital share is 0.4 or higher, can account for the anomalies in the Solow model