APPENDIX: Data Used in the Study
Becker, G., K. Murphy, and R. Tamura, “Human Capital, Fertility, and Economic Growth,” Journal of Political Economy, Vol. 98 (1990), pp. S12–37.
Chen, E., Hyper-Growth in Asian Economies: A Comparative Study of HongKong, Japan, Korea, Singapore, and Taiwan (New York: Holmes and Meier, 1979).
Conlisk, J., “A Modified Neo-Classical Growth Model with Endogenous Technical Change,” Southern Economic Journal, Vol. 34 (1967), pp. 199–208.
Edwards, S., “Trade Orientation, Distortions and Growth in Developing Countries,” Journal of Development Economics, July 1992, pp. 31–58.
Grossman, G. and E. Helpman, “Comparative Advantage and Long-Run Growth,” American Economic Review, Vol. 80 (1990), pp. 796–815.
Inada, K., “On a Two-Sector Model of Economic Growth: Comments and Generalization,” Review of Economic Studies, Vol. 30 (1963), pp. 119–27.
Khan, M. and D. Villanueva, “Macroeconomic Policies and Long-Term Growth: A Conceptual and Empirical Review,” (International Monetary Fund, Washington, D.C.) Working Paper (March 1991).
Khang, C., “Export-Led Economic Growth: The Case of Technology Transfer,” Economic Studies Quarterly, Vol. 38 (1987), pp. 131–47.
Knight, M., N. Loayza, and D. Villanueva, “Testing the Neoclassical Theory of Economic Growth: A Panel Data Approach,” forthcoming, International Monetary Fund, Staff Papers.
Orsmond, D., “The Size of Government and Economic Growth: A Methodological Review,” (International Monetary Fund, Washington, D.C.) unpublished manuscript (1990).
Rivera-Batiz, L. and P. Romer, “International Trade and Endogenous Technical Change,” (National Bureau of Economic Research, Washington, D.C.) Working Paper 3594 (1991).
Sato, Ryuzo, “Fiscal Policy in a Neo-Classical Growth Model--An Analysis of the Time Required for Equilibrium Ajustment,” Review of Economic Studies, Vol. 30 (1963), pp. 16–23.
Summers, R. and A. Heston, “A New Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950-85,” Review of Income and Wealth, Vol. 34 (1988), pp. 1–25.
Thirlwall, A., “The Balance of Payments Constraint as an Explanation of International Growth Rate Differences,” Banca Nazionale del Lavoro Quarterly Review, Vol. (1979), pp. 45–53;
The author is grateful to Donald Mathieson and Julio Santaella for useful comments and to Brooks Dana Calvo and Ravina Malkani for efficient research assistance.
Such a slow adjustment would render somewhat irrelevant the equilibrium behavior of the model because of the likelihood that the other parameters of the system would have changed in the interim.
Equilibrium growth in Arrow’s (1962) learning-by-doing model, although a function of the “learning coefficient,” nevertheless remains independent of the saving rate and the depreciation rate. See footnote 1 on page 5 for details.
lim ∂F/∂K = ∞ as K→0; lim ∂F/∂K = 0 as K→∞; f(0) ≥ 0; f' (k) > 0; and f''(k) < 0.
Arrow’s (1962) learning-by-doing model has a steady-state solution for the growth rate of output equal to (λ+n)/(1-α), wherein the technical change function is (dT/dt)/T = α(dK/dt)/K + λ, 0 < α < 1. Although steady-state growth is thus a multiple of λ+n, growth remains independent of s and δ; besides, this model has the property that ∂(g*-n)/∂n = α/(1−α) > 0, that is, an increase in population growth raises equilibrium rate of per capita growth! This proposition is rejected by the empirical finding reported in Section IV that an increase in the rate of population growth depresses the average growth rate of per capita output during 1975-86 in a sample of 36 developing countries from five regions.
See the discussion on the production linkage summarized in Khan and Villanueva (1991). Edwards (1992) and Knight et al. (forthcoming) present evidence on the relationship between trade openness and economic growth.
The transfer of efficient technologies and the availability of foreign exchange have featured prominently in recent experiences of rapid economic growth (Thirlwall (1979)).
For a degree β homogeneous production function Y = F(K,N), π(k) = kf' (k)/βf(k). The sign of π' (k) follows the sign of ϵ (k) - 1, where ϵ(k) = f' (k)[βf(k)-kf'(k)]/k[(β-l)f'(k)2-βf(k)f''(k)] is the elasticity of substitution. If F is Cobb-Douglas, π(k) = α, where α is the constant exponent of K, and ϵ (k) = 1. If F is CES, π(k) = 1/[1+ (1-α) (1/α)k-σ] and ϵ(k) = 1/(1-σ). Notice that if σ = 0, CES reduces to Cobb-Douglas.
The opposite sequence of events is true for points to the right of ke*, implying negative values of (dk/dt)/k).
The effects of a reduction in the rate of depreciation--exogenously in the SS model and endogenously in the EG model via a higher growth rate of real expenditures on operations and maintenance--are similar.
The transitional growth rate of output, (dY/dt)/Y, is equal to λ + n + π(k)k/k, where π(k) = kf' (k)/f (k). Now, both π(k) and k/k are positive anywhere between ks* and ks*'. It follows that (dY/dt)/Y > λ + n during the transition from B to C. At either B or C, π > 0 and k/k = 0, so that (dY/dt)/Y = λ + n at either equilibrium point. The convergence property of neoclassical growth models, including both SS and EG models, can be demonstrated with the aid of Figure 2. As the initial capital intensity (or initial income per worker) moves farther to the left of ks*' (or ke*'), i.e., gets smaller, the average growth rate of per capita income rises, i.e., the length of the line increases between C (or D) and any point on the K' curve corresponding to the initial level of capital intensity.
And thus the equilibrium level of real income per efficient worker.
Except for the exogenous rate of technical change λ, whose effects on capital intensity and per capita growth are similar in the two models.
As noted earlier, as the public sector dissaves less resources will be available to accumulate capital. Moreover, the ensuing large government borrowings from financial markets would tend to raise interest rates or lower available credit, adversely affecting private capital accumulation.
Equations (11), (15) and the definition π = k*f'(k*)/f(k*) are used to derive this result. When α = 0, the proportionality factor assumes a value of unity, and the standard neoclassical result holds. In terms of the parametric values assumed in the simulations reported in Table 2 below (Section IV), when the learning coefficient α is greater than zero, the optimal saving rate should be set at about three quarters of the assumed income share of capital π, or at 0.3 when π = 0.4. The simulations also show that the higher the learning coefficient, the lower the optimal saving rate as a proportion of capital’s income share. According to the standard model, the optimal saving rate should always be set equal to π, which is at 0.4 in the numerical examples. The higher saving rate implied by the standard model owes to its neglect of endogenous growth and positive externalities through learning-by-doing associated with saving and capital accumulation. By contrast, in the EG model the economy benefits from such endogenous growth and positive externalities, so that a smaller saving-investment rate is all that is required (relative to the rate required by the standard model).
The constant k* is the unique root of (18) equated to zero: sk*a −αk*2 − (n+λ+δ)k* = 0. Given s = 0.2, a = 0.4, α = 0.01, n = 0.025, λ = 0.005, and δ = 0.04, k* assumes the value of 3.00, and the balanced growth path is equal to an annual rate of 0.06. If α = 0, as in the SS model, and assuming the other parameters unchanged, k* solves to a higher level at 5.75, and balanced growth to a lower rate of 0.03 per annum.
As mentioned in the preceding footnote, for values of the parameters and of k* assumed therein, a particular value for A equal to -0.0886 is obtained for α = 0.01.
Note that as t goes to infinity, the second term on the right-hand side of (21) goes to zero (since A < 0), and thus k approaches k*.
See footnote 2 on page 9.