1. Economics 216: The Macroeconomics of Development Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.) Kwoh-Ting Li Professor of Economic Development Department of Economics Stanford University Stanford, CA 94305-6072, U.S.A. Spring 2000-2001 Email: ljlau@stanford.edu; WebPages: http://www.stanford.edu/~ljlau

2. Lecture 5 Cross-Country Growth Regressions Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.) Kwoh-Ting Li Professor of Economic Development Department of Economics Stanford University Stanford, CA 94305-6072, U.S.A. Spring 2000-2001 Email: ljlau@stanford.edu; WebPages: http://www.stanford.edu/~ljlau

3. Lawrence J. Lau, Stanford University3 The Basic Methodology of Cross-Country Regressions u Real output (GDP) (per capita) at a given time t is assumed to depend and only depend on initial conditions (per capita) (including initial real GDP, endowments (capital stock), etc., perhaps even savings and investment rates) at time 0, policy and environmental variables (e.g., degree of openness), possibly external variables, and elapsed time u The explanatory variables are assumed to be pre-determined or exogenous u Variables that may be regarded as endogenous, e.g., the levels and the rates of growth of the population and the capital stock, etc. are in general not included in the list of explanatory variables

4. Lawrence J. Lau, Stanford University4 The Basic Methodology: A Dynamic Reduced Form Approach u Thus, for example, ln Y t = F(Y 0, X 0, Z 0, t) u where Y t and Y 0 are the real GDP per capita of a country at time t and time 0 respectively, X 0 is a vector of variables reflecting initial conditions, and Z 0 )is a vector of variables reflecting government policy and the environment (Z 0 may contain some variables that reflect developments after time 0 to the extent that they are exogenous to the country itself) u Given the level equation, the growth rate of real output per capita between time 0 and time t may be derived as: u g t = (ln Y t - ln Y 0 )/t = F(Y 0, X 0, Z 0, t) u The average rate of growth over t periods therefore depends on the same variables u It is reasonable to assume that the average rate of growth is independent of the length of the period under consideration

5. Lawrence J. Lau, Stanford University5 The Basic Methodology: The Growth Rate Equation u In a typical cross-country regression study, it is the growth rate equation that is actually estimated, even though in principle the level equation can also be estimated u g t = (ln Y t - ln Y 0 )/t = G(Y 0, X 0, Z 0 ) u t is typically chosen to be a decade or longer

6. Lawrence J. Lau, Stanford University6 Implicit Assumptions Required by Pooling across Countries u The economic structures of the different economies are identical or at least similar up to at most a multiplicative factor, e.g., conditional on the exogenous policy and environmental variables: u the production functions must be identical up to multiplicative factors across countries u the consumption, saving and investment behavior must be identical across countries u no external variables are available if all countries are included (except sunspots) u no individual country fixed effects are allowable (although group fixed effects based on geography--latitude, land-lockedness, cultural or language affinity, common colonial heritage, etc. are possible)

7. Lawrence J. Lau, Stanford University7 Implicit Assumptions Required by Pooling across Countries u The dynamic structure, that is, the leads and lags in the economies are also identical u The differences in institutions across countries are either unimportant or can be captured through explanatory variables u The stochastic structure is such that the stochastic disturbances at each instant of time have no permanent or lasting impact u Individual fixed country effects cannot be identified unless there are truly long time-series so that there can be several non-overlapping decade-long growth rates for the same country

8. Lawrence J. Lau, Stanford University8 The Formulation of Robert Barro u g t = (ln Y t - ln Y 0 )/t = F(ln Y 0, ln Y*) u where Y t and Y 0 are the real outputs per capita at time t and 0 respectively, and Y* is the target or steady-state value of real output per capita, which in turn depends on other explanatory variables u The (initial) savings rate is not included as an exogenous variable u Endogeneity of the exogenous/predetermined variables u Evidence of conditional convergence

9. Lawrence J. Lau, Stanford University9 The Hypothesis of Conditional Convergence u Other things being equal, countries with lower levels of per capita real GDP tend to grow faster

10. Lawrence J. Lau, Stanford University10 The Barro Formulation (Estimation Results)

11. Lawrence J. Lau, Stanford University11 The Barro Formulation (Figure)

12. Lawrence J. Lau, Stanford University12 Differences between Production Function- Based Approaches and Growth Regressions u The questions addressed u Effects of alternative economic development strategies and policies versus the relationship between output and inputs u The assumptions u A high degree of similarity of technology and tastes (conditional) u Exogeneity of policy and environmental variables u The existence of a steady state u The functional form

13. Lawrence J. Lau, Stanford University13 Alternative Concepts of Convergence u Convergence in the levels of real output per capita u Convergence in the rates of growth of real output per capita u Convergence in the levels eventually implies convergence in the rates of growth, but not vice versa u Conditional convergence (given initial conditions, policy variables and environmental variables) u Convergence in technology (given the same measured inputs, outputs of different countries converge to the same levels)

14. Lawrence J. Lau, Stanford University14 Convergence in the Levels of Real Output per Capita

15. Lawrence J. Lau, Stanford University15 Convergence in the Levels of Real Output per Capita

16. Lawrence J. Lau, Stanford University16 The Term Rate of Growth & the Initial Level of Real GDP per Capita

17. Lawrence J. Lau, Stanford University17 Convergence in the Rates of Growth of Real Output per Capita

18. Lawrence J. Lau, Stanford University18 Convergence in the Rates of Growth of Real Output per Capita

19. Lawrence J. Lau, Stanford University19 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1960)

20. Lawrence J. Lau, Stanford University20 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1970)

21. Lawrence J. Lau, Stanford University21 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1980)

22. Lawrence J. Lau, Stanford University22 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1990)

23. Lawrence J. Lau, Stanford University23 Convergence in Technology: Hypothetical Levels of Real Output (Boskin & Lau (2000))

24. Lawrence J. Lau, Stanford University24 Convergence in Technology: Relative Productive Efficiencies (Boskin & Lau (2000))

25. Lawrence J. Lau, Stanford University25 Tests of the Maintained Hypotheses of Growth Regressions u Identical across countries, e.g., division into groups and tests of identical parameters across groups u Non-existence of fixed country effects u Replicability over time, e.g., origin-shifting growth regressions u Linearity (or logarithmic linearity) of the functional form

26. Lawrence J. Lau, Stanford University26 The Negative Relationship between the Growth Rate & Initial Real GDP u Is it true? u What are possible explanations of the negative relationship?

27. Lawrence J. Lau, Stanford University27 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? u Problems of measurement u At low levels of real GNP/GDP per capita, marketization alone can result in larger measured increases in real GNP; however, the marketization effect is a one-time phenomenon and is expected to disappear as an economy completes its process of marketization (e.g., monetization of in kind compensation and consumption; market transactions instead of barter; household work) u With the onset of economic development, the price of land tends to rise rapidly; to the extent that profits from the appreciation of land values are not separated or separable from total profits, there will be an over-estimation of value added or GNP/GDP. Again, this is expected to be less of a problem as an economy matures, asset prices stabilize, and accounting practices improve.

28. Lawrence J. Lau, Stanford University28 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? u The law of diminishing returns u Given a stationary or slowly growing labor force, and a much faster rate of growth of the tangible capital stock, the law of diminishing returns is going to set in for additional tangible investments--the marginal productivity of capital may be expected to decline. Since the investment rate cannot be increased indefinitely to offset the decline in the marginal productivity of capital, the rate of growth is therefore likely to decline over time.

29. Lawrence J. Lau, Stanford University29 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? u The rising demand for leisure u At high levels of real GNP/GDP per capita, more and more leisure is likely to be consumed voluntarily (leisure has a high income elasticity of demand). Since leisure is not directly valued in GNP and only goods and services are included, the growth of measured GNP in terms of the value of goods and services (other than leisure) produced is likely to slow. u The importance of the quality of life u At high levels of real GNP/GDP per capita, more and more resources are likely to be devoted to the improvement of the quality of life (education, public health, environmental protection and preservation, etc.) rather than to the direct increase of real GNP.

30. Lawrence J. Lau, Stanford University30 Is a Slowdown Inevitable? The Catching-Up Factor u The “Late-Comer” advantage--the further away an economy is from the technological frontier, the more potential improvements in technical efficiency (total factor productivity) are possible u Economies with low levels of real GNP/GDP per capita are most likely operating well within the production possibilities frontier and hence have greater potential for a higher rate of economic growth, exploiting innovations made by more advanced economies. Economies with high levels of real GNP/GDP per capita can grow more rapidly only by pushing out the production possibilities frontier, which in turn requires significant investment of new resources u This effect depends on technology being freely available and exploitable by low-income countries

31. Lawrence J. Lau, Stanford University31 Interpretation of the Negative Relationship between the Growth Rate & Initial Real GDP u Two economies have identical exogenous and policy variables, differing only in initial real GDP per capita u Assumption: Aggregate production functions exhibit constant returns to scale and neutral technical progress and are identical up to a positive multiplicative constant (Thus, the rates of technical progress are also identical). u Case 1: Suppose initial capital stocks per capita and savings rates are the same u Case 2: Suppose initial capital stocks per capita are different but savings rates are the same u Case 3: Suppose both initial capital stocks per capita and savings rates are different, but the growth regressions are not controlled for savings rates

32. Lawrence J. Lau, Stanford University32 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical u Then initial real GDP per capita is higher in one economy than the other because of either (1) stochastic disturbances (transient) or (2) unmeasured factor of production or technical efficiency (permanent) u Under scenario (1), the economy with a higher initial real GDP per capita will have a higher capital stock per capita in the second period and hence a higher real output per capita in the second period, other things being equal

33. Lawrence J. Lau, Stanford University33 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical

34. Lawrence J. Lau, Stanford University34 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical u For an economy with a higher initial real GDP per capita but the same initial capital stock per capita and savings rate, the elasticity of output per capita with respect to capital stock per capita should be the same and the rate of growth of capital should be higher, thus the rate of growth of per capita real GDP should not be lower u It can be lower only if either the elasticity of output with respect to capital stock declines sufficiently sharply with the higher rate of growth of capital (which is unlikely) or it is simply the statistical artifact of a higher initial level of real GDP per capita and hence a lower measured rate of growth

35. Lawrence J. Lau, Stanford University35 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical u Under scenario (2), the higher initial real GDP per capita can be attributed to permanent factors, I.e., a higher level of A(0). However, since the relative efficiency between the two economies remains the same over time, the rates of growth (as opposed to the levels) of the two economies should also remain the same.

36. Lawrence J. Lau, Stanford University36 Case 2: Savings Rates are Identical u Since initial capital stocks per capita need not be the same, it is reasonable to assume that the economy with the higher initial real GDP per capita is also the one with the higher initial capital stock per capita u Growth could well be slower in the economy with the higher initial real GDP per capita if its initial capital stock were sufficiently high to result in a lower elasticity of output with respect to capital

37. Lawrence J. Lau, Stanford University37 Case 2: Savings Rates are Identical

38. Lawrence J. Lau, Stanford University38 Case 3: Initial Capital Stocks per Capita and Savings Rates are Different u It is assumed here that the differences in the savings rate are not controlled for in the growth regressions. In this case it is reasonable to suppose that the higher initial real GDP per capita is associated with higher initial capital stock per capita and higher savings rate. A sufficiently rapid decline in the output elasticity of capital with respect to increases in the capital stock per capita can result in a negative correlation with the rate of growth and the initial level of real GDP per capita