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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: [email protected]; WebPages: http://www.stanford.edu/~ljlau 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: [email protected]; WebPages: http://www.stanford.edu/~ljlau The Basic Methodology of Cross-Country Regressions 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 The explanatory variables are assumed to be pre-determined or exogenous 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 Lawrence J. Lau, Stanford University 3 The Basic Methodology: A Dynamic Reduced Form Approach Thus, for example, ln Yt = F(Y0, X0, Z0, t) where Yt and Y0 are the real GDP per capita of a country at time t and time 0 respectively, X0 is a vector of variables reflecting initial conditions, and Z0 )is a vector of variables reflecting government policy and the environment (Z0 may contain some variables that reflect developments after time 0 to the extent that they are exogenous to the country itself) Given the level equation, the growth rate of real output per capita between time 0 and time t may be derived as: gt = (ln Yt - ln Y0)/t = F(Y0, X0, Z0, t) The average rate of growth over t periods therefore depends on the same variables It is reasonable to assume that the average rate of growth is independent of the length of the period under consideration Lawrence J. Lau, Stanford University 4 The Basic Methodology: The Growth Rate Equation 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 gt = (ln Yt - ln Y0)/t = G(Y0, X0, Z0) t is typically chosen to be a decade or longer Lawrence J. Lau, Stanford University 5 Implicit Assumptions Required by Pooling across Countries 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: the production functions must be identical up to multiplicative factors across countries the consumption, saving and investment behavior must be identical across countries no external variables are available if all countries are included (except sunspots) 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) Lawrence J. Lau, Stanford University 6 Implicit Assumptions Required by Pooling across Countries The dynamic structure, that is, the leads and lags in the economies are also identical The differences in institutions across countries are either unimportant or can be captured through explanatory variables The stochastic structure is such that the stochastic disturbances at each instant of time have no permanent or lasting impact 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 Lawrence J. Lau, Stanford University 7 The Formulation of Robert Barro gt = (ln Yt - ln Y0)/t = F(ln Y0, ln Y*) where Yt and Y0 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 The (initial) savings rate is not included as an exogenous variable Endogeneity of the exogenous/predetermined variables Evidence of conditional convergence Lawrence J. Lau, Stanford University 8 The Hypothesis of Conditional Convergence Other things being equal, countries with lower levels of per capita real GDP tend to grow faster Lawrence J. Lau, Stanford University 9 The Barro Formulation (Estimation Results) Lawrence J. Lau, Stanford University 10 The Barro Formulation (Figure) Lawrence J. Lau, Stanford University 11 Differences between Production FunctionBased Approaches and Growth Regressions The questions addressed Effects of alternative economic development strategies and policies versus the relationship between output and inputs The assumptions A high degree of similarity of technology and tastes (conditional) Exogeneity of policy and environmental variables The existence of a steady state The functional form Lawrence J. Lau, Stanford University 12 Alternative Concepts of Convergence Convergence in the levels of real output per capita Convergence in the rates of growth of real output per capita Convergence in the levels eventually implies convergence in the rates of growth, but not vice versa Conditional convergence (given initial conditions, policy variables and environmental variables) Convergence in technology (given the same measured inputs, outputs of different countries converge to the same levels) Lawrence J. Lau, Stanford University 13 Convergence in the Levels of Real Output per Capita Figure 1.1: GDP per Capita of the Group-of-Seven (G-7) Countries 30,000 Canada 25,000 France W. Germany 20,000 Japan U.K. U.S.A. 15,000 10,000 5,000 0 19 50 19 52 19 54 19 56 19 58 19 60 19 62 19 64 19 66 19 68 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 U.S. Dollars per Person Italy Year Lawrence J. Lau, Stanford University 14 Convergence in the Levels of Real Output per Capita Figure1.1: GDP per Capita of the Group-of-Seven (G-7) Countries Relative to U.S.A. 1.1 1 0.9 0.8 0.6 0.5 Canada France W. Germany Italy Japan U.K. U.S,A. 0.4 0.3 0.2 0.1 Lawrence J. Lau,Year Stanford University 1997 1995 1993 1991 1989 1987 1985 1983 1981 1979 1977 1975 1973 1971 1969 1967 1965 1963 1961 1959 1957 1955 0 1953 U.S.A.=1.0 0.7 15 The Term Rate of Growth & the Initial Level of Real GDP per Capita Lawrence J. Lau, Stanford University 16 Convergence in the Rates of Growth of Real Output per Capita Average Annual Rate of Growth of Real GNP per Capita over Each Decade vs. Real GNP per Capita at the Beginning of That Decade (in 1995 US$) 15 Percent per annum 10 5 0 100 1000 10000 100000 -5 1960-1970 1970-1980 1980-1990 1990-1998 -10 Lawrence J. Lau, US$ Stanford University 17 Convergence in the Rates of Growth of Real Output per Capita Average Annual Rate of Growth of Real GNP per Capita over Various Periods vs. Real GNP per capita at 1960 (in 1995 US$) 16 1960-1970 1960-1980 1960-1990 1960-1998 Percent per annum 12 8 4 US$ 0 100 1,000 10,000 100,000 -4 Lawrence J. Lau, Stanford University 18 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1960) The Instantaneous Annual Rate of Growth of Real GNP per Capita versus Real GNP per capita of 1960 (in 1995 US$) 30 20 Percent per annum 10 0 0 5000 10000 15000 20000 25000 US$ 30000 -10 -20 -30 Lawrence J. Lau, Stanford University 19 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1970) The Instantaneous Annual Rate of Growth of Real GNP per Capita versus Real GNP per capita of 1970 (in 1995 US$) 30 20 Percent per annum 10 0 0 10000 20000 30000 40000 50000 60000 US$ 70000 -10 -20 -30 Lawrence J. Lau, Stanford University 20 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1980) The Instantaneous Annual Rate of Growth of Real GNP per Capita versus Real GNP per capita of 1980 (in 1995 US$) 30 20 Percent per annum 10 0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 US$ 50000 -10 -20 -30 Lawrence J. Lau, Stanford University 21 Instantaneous Rate of Growth & the Initial Level of Real GDP per Capita (1990) The Instantaneous Annual Rate of Growth of Real GNP per Capita versus Real GNP per capita of 1990 (in 1995 US$) 30 20 Percent per annum 10 0 0 10000 20000 30000 40000 50000 US$ 60000 -10 -20 -30 Lawrence J. Lau, Stanford University 22 Convergence in Technology: Hypothetical Levels of Real Output (Boskin & Lau (2000)) Hypothetical Output Level of Countries with Measured Inputs of the U.S. 8 6 CAN FRA WGER JAP UK US ITA 5 4 3 2 1 Lawrence J. Lau, Stanford University 1996 1994 1992 1990 1988 1986 1984 1982 1980 1978 1976 1974 1972 1970 1968 1966 1964 1962 0 1960 Trillions of Constant 1990 US Dollar 7 23 Convergence in Technology: Relative Productive Efficiencies (Boskin & Lau (2000)) Productive Efficiency Relative to the U.S. (U.S.=100) 110 100 90 70 60 50 CAN FRA WGER ITA JAP UK US 40 Lawrence J. Lau, Stanford University 1996 1994 1992 1990 1988 1986 1984 1982 1980 1978 1976 1974 1972 1970 1968 1966 1964 1962 30 1960 Percent 80 24 Tests of the Maintained Hypotheses of Growth Regressions Identical across countries, e.g., division into groups and tests of identical parameters across groups Non-existence of fixed country effects Replicability over time, e.g., origin-shifting growth regressions Linearity (or logarithmic linearity) of the functional form Lawrence J. Lau, Stanford University 25 The Negative Relationship between the Growth Rate & Initial Real GDP Is it true? What are possible explanations of the negative relationship? Lawrence J. Lau, Stanford University 26 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? Problems of measurement 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) 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. Lawrence J. Lau, Stanford University 27 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? The law of diminishing returns 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. Lawrence J. Lau, Stanford University 28 Is a Slowdown of the Measured Rate of Growth of Real GNP Inevitable? The rising demand for leisure 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. The importance of the quality of life 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. Lawrence J. Lau, Stanford University 29 Is a Slowdown Inevitable? The Catching-Up Factor 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 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 This effect depends on technology being freely available and Lawrence J. Lau, Stanford University 30 exploitable by low-income countries Interpretation of the Negative Relationship between the Growth Rate & Initial Real GDP Two economies have identical exogenous and policy variables, differing only in initial real GDP per capita 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). Case 1: Suppose initial capital stocks per capita and savings rates are the same Case 2: Suppose initial capital stocks per capita are different but savings rates are the same Case 3: Suppose both initial capital stocks per capita and savings rates are different, but the growth regressions are31 Lawrence J. Lau, Stanford University not controlled for savings rates Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical 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) 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 Lawrence J. Lau, Stanford University 32 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical Y/L = A(t)f(K/L) y = A(t) f(k) ln y = ln f(k) + ln A(t) d ln y d ln f d ln k d ln A( t ) dt d ln k dt dt Lawrence J. Lau, Stanford University 33 Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical 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 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 Lawrence J. Lau, Stanford University 34 growth Case 1: Initial Capital Stocks per Capita and Savings Rates are Identical 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. Lawrence J. Lau, Stanford University 35 Case 2: Savings Rates are Identical 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 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 Lawrence J. Lau, Stanford University 36 Case 2: Savings Rates are Identical y11 = A(1) f(k11) y21 = A(1) f(k21) y11/y10 = A(1) f(k11)/y10 y21/y20 = A(1) f(k21)/y20 (y11/y10)/(y21/y20) = [f(k11)/f(k21)]/(y10/y20) Now, k11>k21; y10>y20; thus, f(k11)>f(k21). In order for the rate of growth of economy 1 to be less than the rate of growth of economy 2, it must be the case that the proportional increase in output due to the higher savings per capita is less than the proportional difference in initial real output per capita. Lawrence J. Lau, Stanford University 37 Case 3: Initial Capital Stocks per Capita and Savings Rates are Different 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 Lawrence J. Lau, Stanford University 38