PAUL EVANS Ohio State University

Columbus, Ohio

GEORGIOS KARRAS University of Illinois at Chicago

Chicago, Illinois

Is Government Capital Productive? Evidence from a Panel of Seven Countries

Using panel data for seven countries in each year between 1963 and 1988, this paper investigates the extent to which government capital contributes to production. No statistically significant evidence is found that government capital is productive.

1. Introduction The Clinton Administration advocates a large increase in infrastructure

investment on the grounds that government capital is highly productive and underprovided in the United States. Several studies in the literature support this view; see for example, Ratner (1983); da Silva Costa, Elson and Martin (1987); Deno (1988); Aschauer (1989,199O); and Munnell (1990a,1990b). Other studies find little evidence that government capital is productive and underprovided; see for example, Hulten and Petersen (1984); Eisner (1991); Evans and Karras (1991); Hulten and Schwab (1991); Jorgenson (1991); Rubin (1991); and Tatom (1991). Apparently, estimates of the productivity of government capital in the United States are fragile. Minor specification changes can produce appreciable shifts in estimated coefficients.

The purpose of this paper is to investigate how productive government capital is using panel data for Belgium, Canada, Finland, Germany, Greece, the United Kingdom, and the United States in each year between 1963 and 1988.l Using data that vary across countries as well as over time may enable

‘Ashauer (1990) has also investigated data for a panel of countries. His estimates, however, are flawed in two ways. First, his estimation equation is valid only under the assumption that the ratios of private capital and government capital to output are constant over his sample period. This assumption is untenable since capital-output ratios have varied considerably over time and especially across countries. Second, he does not allow for fixed or random time and country effects in estimation. Our empirical analysis below shows that estimates are severely biased if one does not allow for time and country effects.

&wnal of Macroeconomics, Spring 1994, Vol. 16, No. 2, pp. 271-279 271 Copyright 0 1994 by Louisiana State University Press 0164-0704/94/$1.50

Paul Evans and Georgios Karras

us to obtain robust and precise estimates of the productivity of government capital.

2. Empirical Analysis To our data we fit Cobb-Douglas production functions of the form

with

Eit = P&i-l + Yt > -l<pi<l; (2)

where i and t index countries and years; Y is the average annual gross domestic product; N is average annual employment; KP is the beginning-of-year private net capital stock; KG is the beginning-of-year government net capital stock;2 A is the difference operator; K, a, p, y, and p are parameters; f~ is a country effect; IL is a time effect; and II is a zero-mean, constant-variance error term that is uncorrelated both across countries and over time.

We consider three specifications for the country and time effects: all of them are constrained to be zero; they are fixed effects; and they are random effects. We also consider three specifications for the ps: all of them are constrained to be zero; they equal a common value p; and they differ across countries. The specification (1) and (2) implicitly assumes that multifactor productivity [that is, (p+h+e)/A] h as a stochastic rather than deterministic trend. The need to model economic variables as driven by stochastic trends rather than deterministic trends has been widely appreciated since the work of Nelson and Plosser (1982).

Table 1 reports estimates of a, p, and y for several of these specifi- cations. In all cases, the error term v is assumed to be uncorrelated with the regressors. Row (a) presents estimates assuming no country and time effects and no serial correlation. According to these estimates, gross domestic prod- uct is essentially linear homogeneous in employment and private capital, and the coefficients on the growth rates of these two inputs are roughly the shares of those two factors in gross income. This fact suggests that government capital may be a nonrival input. 3 The coefficient on the growth rate of government capital is large and highly significant and implies that the mar-

2The data on real gross domestic product, employment, and capital come from National Accounts: Main Aggregates, L.abour Force Statistics, and Flows and Stocks of Fixed Capital. The countries included in the sample are all those for which data on both private and government net capital stocks are available over the entire sample period 1963-1987. The manufacturing data mentioned below also come from these sources.

%ee Romer (1990) for a persuasive argument that production functions should be linear homogeneous in the rival factors of production.

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Is Government Capital Productive?

ginal product of government capital is 2.38 times the marginal product of private capital at the sample means. * Row (a) would therefore seem to provide strong evidence that government capital is underprovided.

This evidence, however, is fragile. Row (b) shows that allowing for a fixed time effect wipes out the estimated productivity of government capital. Apparently, governments tended to increase their capital stocks most rapidly (slowly) in the years during which multifactor productivity grew most rapidly (slowly). With these effects removed, one can find no evidence that gov- ernment capital is productive. Row (c) shows that allowing for both fixed time and country effects wipes out the estimated productivities of both govem- ment and private capital. Apparently, private firms tended to increase their capital stocks most rapidly in those countries for which multifactor produc- tivity grew most rapidly (slowly). With these effects also removed, one can find no evidence that private capital is productive.

The estimates depend somewhat on whether one allows for fixed effects or for random effects, Row (d) reports the estimates obtained when one allows for fixed time and random country effects. Private capital is again estimated to be productive with a coefficient that is within a standard error of private capitals share in gross income. Government capital continues to be estimated to be unproductive, however. Row (e) reports estimates ob- tained when one allows for both random individual and country effects. The coefficients on employment and private capital are now within a standard error of their shares in gross income, and the estimated coefficient on government capital is small and statistically insignificant at the 0.05 level.

Finally, the estimates depend appreciably on whether and how one accounts for serial correlation in the error term. Rows (f) and (g) report the estimates that we obtained by allowing for random time and country effects and fitting first-order autoregressive processes to e5 When a common au- toregressive process is assumed for all countries, we obtained the estimates in row (f). The estimates are similar to those reported in row (e) except that private capital is no longer estimated to have a positive coefficient. By contrast, when we fitted a different autoregressive process for each country, we obtained estimates similar to those in row (e) although the coefficient on private capital does decline somewhat.

In fitting the regressions reported in Table 1, we used annual average employment rather than annual hours worked as our measure of the labor input N. The reason is that aggregate hours data are not available to the best

‘9he ratio of marginal products is [y(Y/KG)]I[P(YKP)] or (yI~)(KP/KG). Plugging in the estimates for y and p and evaluating this expression at the sample means for Kp and KG yields the figure in the text.

“Fitting autoregressive processes to the error term has qualitatively the same effect on the coefficients, however one chooses to account for time and country effects.

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TABLE 1. Estimated Cobb-Douglas Production Functions for Gross Domestic Production

Equation N KP KG ri

(a)

(b)

(c)

(d)

(e)

(f)

k)

0.637* (0.103) 0.387"

(0.099) 0.499" (0.126) 0.394"

(0.103) 0.538"

(0.117) 0.651"

(0.131) 0.589"

(0.119)

0.348* (0.110) 0.251

(0.140) -0.120 (0.176) 0.230

(0.146) 0.269

(0.140) -0.106 (0.189) 0.188

(0.141)

0.182" (0.085)

-0.103 (0.097)

-0.175 (0.107)

-0.108 (0.100) 0.033 (0.098) 0.059 0.298 (0.116) (0.097) 0.079 -0.282

(0.104) 0.391

NOTES: Standard errors appear in parentheses, and asterisks indicate statistical signif- icance at the 0.05 level. If a single p is estimated, the last column reports its estimate and standard error. If a separate p is estimated for each country, the last column reports its minimum and maximum values.

(a) OLS on growth rates. (b) OLS on growth rates less estimated fired time effects. (c) OLS on growth rates less estimated hxed time and country effects. (d) OLS on growth rates less estimated Ilxed time and random country effects. (e) OLS on growth rates less estimated random time and country effects. (i) AR1 on growth rates less estimated random time and country effects. (g) AR1 on growth rates less estimated random time and country effects.

of our knowledge. It is possible, however, to use a measure of annual hours worked if we confine ourselves to the manufacturing sectors of the countries in our sample. We therefore fitted Equation (l), where N, is the product of average annual manufacturing employment and average annual hours ofwork per week in year t, ICI’, is the net private capital stock in manufacturing at the beginning of year t, and KG, is the net government capital stock at the beginning of year t. Table 2 reports the estimates for the same specifications as in Table 1. The estimated coefficients on N are uniformly higher and those on Kp and KG are uniformly lower than those in Table 1. As a result, Table 2 provides even less evidence that government capital is productive than does Table 1. Moreover, the estimates of Table 2 are virtuahy as fragile as those of Table 1.

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IS Government Capital Productive?

TABLE 2. Estimated Cobb-Douglas Production Functions for Real Value Added in Manufacturing

Equation N KP KG b

(a)

(b)

Cc)

(4

(e)

(f)

k)

0.795* (0.116) 0.583" (0.134) 0.706"

(0.151) 0.595"

(0.139) 0.778*

(0.136) 0.746"

(0.147) 0.762*

(0.140)

0.100 (0.130) 0.101

(0.164) -0.106 (0.242) 0.088

(0.172) 0.084

(0.166) -0.015 (0.215) 0.042 (0.175)

0.039 (0.195)

-0.397 (0.255)

-0.465 (0.294)

-0.403 (0.264)

-0.069 (0.238)

-0.219 0.228 (0.291) (0.093)

-0.087 -0.183 (0.255) 0.681

NOTES: Standard errors appear in parentheses, and asterisks indicate statistical signif- icance at the 0.05 level. If a single p is estimated, the last column reports its estimate and standard error. If a separate p is estimated for each country, the last column reports its minimum and maximum values.

(a) OLS on growth rates. (b) OLS on growth rates less estimated hxed time effects. (c) OLS on growth rates less estimated fixed time and country effects. (d) OLS on growth rates less estimated fixed time and random country effects. (e) OLS on growth rates less estimated random time and country effects. (f) AR1 on growth rates less estimated random time and country effects. (g) AR1 on growth rates less estimated random time and country effects.

If firms or governments can anticipate the error terms in the production functions fitted in Table 1, we should expect the estimates reported there to be inconsistent. The reason is that profit-maximizing firms raise private inputs in anticipation of increased multifactor productivity and governments may also choose to make more government capital available when they anticipate multifactor productivity to be higher. Since fixed and random effects can no doubt be anticipated, only the estimates in row (c) that allow for fixed time and country effects can reasonably be considered to be consistent. Further- more, to the extent that E is predictable as it will be if p # 0, even the estimates in row (c) are inconsistent. Finally, our estimates may be inconsistent because labor may be hoarded and capital underutilized when multifactor produc- tivity is low, thereby contaminating the regressors with measurement error.

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Because using instrumental variables is not a viable way of eliminating potential simultaneity,6 we adopted an alternative approach that can yield consistent estimates of the elasticity of output with respect to government capital even if employment and private capital are correlated with produc- tivity shocks. This benefit comes at the cost of having to make assumptions about how factor markets work.

Suppose that output is produced according to the technology

Yu = F(N&Pg;i)KG;Y,exp[(~ + i$ + Eit)/A] , (3)

where F(o) is increasing and twice continuously differentiable in N and KP and is homogeneous of degree q. Differencing the natural logarithms of both members of equation (3) yields

AInYit = (FlNiJF)AhNit + (F&P~~/F)AhKP~~ + yAh.KGit + A+ + b + et(4)

to a first approximation. We assume that all output, including the return to government capital, is paid to the private factors. Specifically, we assume that the real wage W and real rental rate R are l/q times the marginal products of labor and private capital:7

and

Wit = (l/~>F~(Nit,KPit;i)~G~e~[(~ + & + EJ/A] , (5)

4, = (1/71>Fz(Ni,,KPi,;i)~G~e~[(~ + L + e&A] .

Substituting Equations (5) and (6) into Equation (4) yields

(6)

The left-hand member of Equation (7) is the Solow residual if 11 = 1.a We

6we tried estimating Equation (1) using instrumental variables for All and/or AhrKP and allowing for hxed time and country effects. These efforts were fruitless because none of the instruments that we were willing to specify as exogenous were well correlated with Ah# and AlnKP As a result, our estimates had enormous standard errors and were not robust to minor specification changes.

‘The parameter 11 might also reflect market power as Hall (1988) has shown. ‘In our data, WN+RKP differs from Y by real indirect business taxes less real subsidies. We

assume that the recipients of income from labor and capital consume the same baskets of goods and hence that the tax is shifted forward equally onto the two factors. We therefore measure the left-hand member of Equation (7) as

AhrY - ~[COMPAhriV+(CFC+OS)AlnKP]I(COMP+CFC+OS) , where COMP, CFC, and OS are nominal wage and salary compensation, consumption of fixed capital, and operating surplus from National Accounts: Main Aggregates.

Is Government Capital Productive?

TABLE 3. Moda$ed Solow-Residual Regressions for Gross Domestic Product

OLS Estimates of the Coefficient on KG with

rl Fixed Effects Random Effects

0.8 -0.072 0.109 (0.102) (0.079)

1.0 -0.045 0.157 (0.102) (0.081)

1.2 -0.019 0.145 (0.103) (0.090)

NOTE: Standard errors appear in parentheses

do not impose this condition because N and Kp may not be pure rival factors and KG may not be a pure nonrival factor.

For any given r~, Equation (7) can be estimated consistently if Ah&G is uncorrelated with the error term E and if we treat lt and h as fixed effects. If instead we treat them as random effects, they must also be uncorrelated with Al&G. These conditions are much less stringent than those necessary for the estimates reported in Table 1 to be consistent.

Table 3 reports estimates of Y for values of q ranging between 0.8 and 1.2.g Because data on W,,N,JY,, and l&&/Y,, are not available for the manufacturing sectors of all of the countries in our sample, we fit Equation (7) only to data for the aggregate economy and use employment as our measure of the labor input N. In obtaining these estimates, we allow l.t and h to be not only fixed effects but also random effects. We find no evidence that government capital is productive. Moreover, our point estimates are fragile since they differ appreciably depending on whether we allow for fixed or random effects.

3. Summary and Conclusions We end this paper by summarizing our results and drawing some

conclusions. We found that government capital is estimated to have large and highly significant productivity only if we misspecify the production function by ignoring time effects in productivity growth. Under the most plausible specifications, the estimates are not statistically significantly different from zero at conventional levels. Moreover, the estimates are fragile in the sense

9his range of qs includes the ordinav least squares estimates of q

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Paul Evans and Georgios Karras

that minor changes in specification can appreciably affect them. We therefore conclude that there is no evidence that government capital is highly pro- ductive and underprovided in the seven countries in our sample.

Received: December 1992 Final version: May 1993

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