Appendix: Data Sources and Description of Variables
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An earlier version of this paper appears as Chapter 1 of my Ph.D. dissertation completed at Yale University. I thank Xavier Sala-i-Martin, T.N. Srinivasan, Gustav Ranis, Willem Buiter, William Brainard, Ken Kletzer, Malcolm Knight and Sena Eken for their comments and suggestions. The financial support of a Doctoral Dissertation Fellowship from the Alfred P. Sloan Foundation is gratefully acknowledged.
More accurately, the standard neoclassical growth model assumes that the marginal product of each factor goes to zero as use of that factor increases, holding all other factors constant (that is, the Inada conditions hold).
In the traditional optimal growth models of Ramsey (1928), Cass (1965), and Koopmans (1965), time-varying savings rates were derived from the optimization of an intertemporal social welfare function. In this normative (or planning) use, these models were designed to calculate the required savings rate to be attained to achieve a given target rate of growth, rather than provide guidance for the appropriate role for government in promoting growth.
In the Solow-Swan neoclassical growth model, fiscal policies (taxation and government spending) can affect the rate of growth only during the transition to steady state, as the steady-state rate of growth is determined by the exogenous rate of technological progress. This is also the case in the Arrow-Kurz (1970) model of the influence of public investment on growth, where as in this paper the stocks of private and public capital enter into the private production function, but unlike this paper they assume diminishing returns to scale in private and public capital inputs for a given exogenous population. As in Solow-Swan, for Arrow-Kurz exogenous technical progress drives the rate of growth, and the marginal returns to public and private capital are not bounded away from zero.
Equivalently, aggregate production, Y(t)=Ny(t), exhibits constant returns with respect to K(t)=Nk(t), G(t) and T(t), yet diminishing returns to K(t) for given G(t) and T(t) due to increases in congestion from the use of public capital and the consumption of transfers.
Competitive producers take r1, r2, G(t)/K(t), T(t)/K(t) and Ġ(t) as given, because each agent is small relative to the aggregate, and so do not believe their actions affect the behavior of government. Accordingly, they do not take into account the externality arising when, as described above, higher private output raises the revenue obtained by the government from its constant tax rates (r1 and r2), thus raising public investment and transfers, and so the marginal product of private capital of all producers.
It can also be argued that by including the flow of services from publicly provided goods as an input to private production functions, the Barro and Sala-i-Martin formulations are implicitly assuming full depreciation of the existing stock of public capital at the end of each production period. Alternatively, Barro (1990, at p.sl07) argues that in his set up the government can be envisaged as carrying out no production and owning no capital, but acts as a middleman in purchasing a flow of output from the private sector and redistributing it to private firms.
The assumption that the accumulation of private capital is a perfect substitute for consumption differs from the models proposed by Srinivasan (1964) and Kurz (1968), where different production processes for consumption and capital goods were assumed. The present model resembles that of Jones and Manuelli (1990), where a single production process is used for consumption and capital goods, as here public and private capital are basically the same good.
Mulligan and Sala-i-Martin (1993) discuss transitional dynamics in two-capital good models of endogenous growth, and argue that if there are initial imbalances among any of the sectors in an economy (due perhaps to a war or large price shock), then there may be a transitional period when these variables do not behave as would be predicted by steady-state analysis. For example, a war may have destroyed a large fraction of the private capital stock, leaving public capital relatively unaffected, and so the economy will have to get back to the steady-state ratio of G/K by higher (lower) than steady-state rates of growth for the private (public) stock of capital. Such issues do not arise in one capital good (or AK) models of growth (Barro 1990, Rebelo 1991), which do not exhibit transitional dynamics and are always in steady-state.
For linear homogenous production functions, a steady-state equilibrium will be attained only if the utility function features constant intertemporal elasticity of substitution, and the technology for capital, A(.), exhibits constant returns to scale. These requirements yield a constant elasticity of marginal utility of -σ=-[c(t)U’’(c(t))/U’(c(t))] and
In this model γc = σ-1[(1-r1-r2A(G(t)/K(t))α(T(t)/K(t))β - ρ] and γk = (1-r1-r2)A(G(t)/K(t))α(T(t)/K(t))β - c(t)/k(t). It is assumed that: A(1-r1-r2)(G(t)/K(t))α(T(t)/K(t))β > ρ (for positive steady-state growth of consumption, private capital, public capital, and income) and that the parameters of
If the production function is not Cobb-Douglas, then the utility-maximizing size of government exceeds (is smaller than) the growth-maximizing size of government if the elasticity of substitution between the inputs is greater (less) than one.
The 23 countries involved, all members of the Organization for Economic Cooperation and Development (OECD), are: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Iceland, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the United States of America.
The initial level of income has a strong influence on the growth experience of countries in the neoclassical (Solow-Swan) model of economic growth. Similarly, here by including INIT in the regressions we are holding constant the influence of initial income, and concentrate on explanations involving the endogenous growth explanators of growth. In effect in this empirical estimation we are testing the transition to steady state, rather than steady-state growth itself, as it is unlikely the OECD countries were in steady state over the entire sample period. INIT is accordingly included to take into account that income may not initially be at its steady-state level, which if so will affect the observed growth rate. By not including INIT in the regressions, the results obtained would be subject to omitted variables bias, due to a failure to account for initial incomes in analyzing the conditional convergence of countries to their respective steady states.
The classical disturbance term vit is assumed to be iid over i and t, uncorrelated with the explanatory variables. The latent country-specific effect αi is assumed to be iid over i, distributed independently across countries.
To the extent that many of the previous analyses of the interrelationship between government spending, taxation, and growth used time-series analysis alone or cross-sectional analysis alone, then in the presence of such correlation these studies would have yielded biased and inconsistent estimates of the parameters.
In the absence of measurement errors if the assumed E(αi|Xit) = E(ηi|Xit) = 0 is violated, due for example to omitted variables, the RE estimator is biased and inconsistent, while the FE estimator is unbiased and consistent. However, the FE estimator is particularly sensitive to the presence of measurement errors, and if E(vit|Xit) ≠ 0 due to such errors then it may well be a worse estimator than either the RE or ordinary least squares (OLS) specifications (Hausman 1978).
As noted above, the specification bias which arises from ignoring parameter heterogeneity among cross-sectional or time-series units can result in the erroneous application of pooled least-squares regression techniques to all NT observations, yielding inconsistent estimates of parameters. Hsiao (1986) suggests that given we assume the parameters are constant over time, but differ between individual countries, then the two possible cases are: (i) either heterogeneous intercept and homogeneous slope parameters, or (ii) heterogeneous intercept and slope parameters. The first case is examined here. An F-test for homogeneous intercepts (given homogeneous slope parameters) yields an F-statistic of 2.05, while the critical value for F0.95 (22,63)=1.68, and so the null is not accepted.
Lagged endogenous variables cannot be used as instruments in the presence of endogeneity, due to potential biases in the presence of either fixed effects or serially correlated error terms. See Bowden and Turkington (1984) for details of GIV estimation.
GIV estimation has advantages over the more traditional two-stage least squares (2SLS) estimator in that: (i) the 2SLS estimator will be inconsistent (even as the sample size grows) if not all the exogenous variables in the structural and reduced form equations are included in the reduced form regression - the GIV estimator will still be consistent should such an omission be made; and (ii) the standard errors obtained from least squares estimation of the structural equation need to be corrected - this is not the case for GIV (see White 1982).
In traditional cross-sectional tests for the presence of convergence, when the initial level of GDP per capita is mis-measured, then the subsequent rate of growth will be biased toward acceptance of the convergence hypothesis (Romer 1989). However, when TSCS data are used then such measurement errors are less important, as the initial levels of GDP per worker are here used in each of the four sub-periods to calculate each sub-period’s GRWKR, rather than one measure of the rate of growth as is typically done in cross-sectional studies.
Easterly and Rebelo’s (1993) cross-sectional study of 100 countries between 1970-88 found that the ratio of public investment in transport and communication to GDP was positively correlated with growth.
Indeed BE estimation (without accounting for the endogeneity of IGOV and SOCSEC) yields a positive and significant coefficient on EDUC, as in Barro (1991).