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SOLOW AND THE STATES: CAPITAL ACCUMULATION, PRODUCTIVITY, AND ECONOMIC GROWTH DOUGLAS HOLTZ-EAKIN

Abstract - National, state, and local policymakers have increasingly focused their attention on policies toward economic growth, especially efforts to raise the rate of investment. Recent studies of economic growth have raised a debate over the role played by the investment rate in the long-run performance of the economy and, thus, over the impact of tax and other policies to alter investment incen- tives. Evidence from the states suggests that the effects of capital accumulation on growth are consistent with the predictions of the neoclassical growth model. At the same time, the estimates indicate a substantial role for human capital as well in raising productivity. Also, even in the context of a neoclassical growth model, changes in the rate of investment have a sustained impact on the pace of economic growth.

INTRODUCTION

Issues

Policymakers at all levels of government have increasingly focused their attention on means by which to raise the rate of

Syracuse Umverslty, Syracuse, NY 13244-l 090

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economic growth. In doing so, however, they are confronted by the conflicting policy implications of alternative views of the growth process. In the traditional, neoclassical approach, government tax and budget policies primarily affect the accumulation of capital; labor force growth is largely determined by demographic factors, while technical progress stems from the flow of scientific advances. Further, while the stance of fiscal policy affects the long- run level of productivity, it has only a tran- sitory impact on the pace of economic growth per se. For example, preferential tax policies may raise investment and increase the growth rate in the short run; but the economy ultimately adjusts to a higher level of capital per worker, and the long-term growth rate reverts to that dic- tated by the growth of the labor force and technology. Thus, in the neoclassical model of growth developed by Solow (1956), the long-run level of output per worker de- pends upon the rate of investment in the economy, but tts growth rate does not.

The traditional view of economic growth

has recently come under fire. Critics argue that there is no tendency for growth rates

to revert to the pace indicated by labor and technological considerations. Instead,

differences In growth rates appear to be sustained and generate large disparities In Income per caplta that are Inconsistent with the neoclassicail model. As an alterna- tlve, Romer (1986, 19891, for example, suggests an “endogenous growth” model tn whtch output per worker expands even in the absence of technological advances and thie rate of growth is determined by t:he rate of Investment. Such a model car- ries with it a very different view of the Im- pact of changes In investment, predicting no tendency for economic condltlons to equalize amo~ig nations and yielding per- manent differences In output per worker.

13~ implication, policies tt-at foster more rapid accumulation of capital have a direct, Immediate, and lasting impact on the rate of economic growth ’ The importance and Influence of tax and budget decisions are accordingly magnlfled. In this way, the endogenous growth literature suggests a dra- matlcally different context for policy toward private investment. In addition, these studies have Ibroadened Ihe menu of growth-related policies presented to policymakers, calling into question the focus on private capital accumulation. Lucas (1988), for example, singles out human capital accumulation as the focus of the growth process, while Barro (1990) emphasizes the role of government (capital accumulation.

In this context, It appear’; useful to assess the degree to whtch the contnbutlon of In- vestment to growth In the United States IS consistent wI th the neoc assical model and, thus, the traclitional view of economic policy. This paper revisits th:~ empirical performance of the Solow model using data dravvn from the U.S stales. Focusing on the states has natural advantages. The results from the states are of direct Impor- tance to the design of policies by state and local governments. further, there are research design considerallons as well. Em- pirical analyses of growth models typically assume that (all economies have access to identical production technologies. The free

flow of technology across state borders is consistent with this assumption unlike, for example, r,tudles using international data. Moreover, there are no1 large variations in the legal r,ettlng, political Institutions, or tastes across states. FInally, states offer the opportunity to analyze reasonably large samples of data collected on a consistent basis.

State data present difficulties as well. In particular, states are open economies with relatively free mobility of factors The potential erdogenelty of labor force growth and investment patterns that mobility en- genders I!, Ignored II-I the basic, closed- economy growth model. Empirical analyses, however, mJst guard against InapproprIate inferences generated by such influences I discuss these Issues below.

Previous Studies

Mankiw, Romer, and Well (1992) use the Solow mI:)del to explain international differences In ouiput per worker in a cross section of countries. Their results suggest that any move to write off the Solow model is a bit premature, although the model must be modified to acknowiedge a substantial role for human capital. Barro and Sala i MartIn (1990, 1991) also examine the growth characteristics cf the states, focusing on the convergence of output per worker that IS predlctecl by the basic growth model. They do not, however, control explicitly for cross-state variation in the steady state toward vvhich each state econ- orny converges. As shown below, this steady state IS characterized in PIart by the parameters of the state productlon function. In the absence of direct esr.imates of these par(jmeters, Barre and SaIlI i Martin must Infer the characteristics of state production IndIrectly frorn an estim&ed speed of adjustment coefficient. Thus, the guid- ance to policy provided by these estimates IS indirect aj well. In contrast, the empirical work below specifies explicitly the steady state in i~~rrns of a small number of ob-

I SOLOW AND THE STATES

servable variables, thereby permitting direct estimation of the parameters of the production technology. Further, the techniques employed impose consistency between the estimated characteristics of production and the estimated speed of convergence.

The remainder is organized in three parts. The next section reviews the major predictions of the neoclassical growth model. Data sources, estimation issues, and empirical findings are presented in the third section, and the final section discusses the implications of the econometric findings. To preview the results, I find that the rate of investment contributes to growth in a manner consistent with the neoclassical growth model. The implied speed of convergence to the study state suggests, however, that variations in the rate of investment, induced by policy changes or from other sources, will have noticeable effects on economic growth over a substantial period. Finally, the estimates highlight the need for a deeper understanding of the role of human capital accumulation in the growth process.

THE SOLOW GROWTH MODEL: THEORY AND EMPIRICAL IMPLICATIONS

The striking feature of the Solow growth model is its prediction that all economies with the same investment and labor force growth rates will converge to an identical steady state level of output per worker. The next subsection makes precise the nature of this prediction. The second subsection covers the notion of convergence, dis- cussing the circumstances under which states will approach the same level of output per worker and situations in which economies that start with lower initial levels of output per worker will grow faster, ceteris paribus, than similar economies with higher initial levels of output. I then turn to the implications of incorporating public- sector capital or human capital into the analysis. The final subsection addresses the

complications posed by the open features of state economies.

Steady States

The growth model begins with a constant- returns-to-scale production function.* With an eye toward the empirical analysis to fol- low, assume that this takes the Cobb- Douglas form:

81 Y, = K$lqt)‘-a

where Y, is output, Kt is capital inputs, @ is a technical efficiency index, and L, is labor inputs. @,L, represents effective labor inputs. Equation 1 may be written in “in- tensive form”:

yet = k:t

where the subscript e denotes quantities per effective labor unit. Assume that Qi, and L, grow at constant rates A and 7, re- spectively:

q L, = Loeqt

From equation 2, growth in ye is propor- tional to growth in k,, which is the difference between the growth rate of K and the growth rate of effective labor (7 + A):

l;,t k -= - 0 k Kt - (q + A) et

The growth rate of the capital stock is determined by the difference between the

fraction of output that represents investment (0) and losses due to depreciation (6) :

In the context of a closed economy, the focus is on the saving rate, which will co- incide with the Investment rate. In open economies, such as the states, saving and investment may differ due to capttal flows. Thus, the key policy parameter is the rate of investmenl. Collecting the results in equations 5 and 6 gives

Predictions concerning the steady state levels of output and productivity come from setting the growth rate of capital per effective worker in equation 7 equal to zero. The steady state value for effective capital

Substituting k,” Into the production function gives the steady state value of effec- trve-labor productivity,

It IS not possible to observe effective labor units; however, one may develop predictions concerning the observable output per worker. Letting y denote output per worker, usrng equatron; 3 and 9, and tak- ing logarithms yields

In yr = ;--& [In 0 - In(q + A + S)]

Equation IO displays the means by which policy affects economic performance. In the long run, those policies that increase the rate of investment will, ceteris paribus, raise productrvity and incomes. The equation also suggests a straightforward test of the model. In a cross section of observa- ttons on the U.S. states, the (IO(J) difference between the investment rate and the sum (A -t 17 + 6) should predict (log) output per worker.

Figure 1 displays the 1986 distribution of output per worker (scaled by the mean) for the 48 states used in the empirical analysis below. As a glance at the figurle indicates, there is considerable variation in productivrty across the states; even excluding the outliers at each end suggests a range of roughly 30 percent. The state&y-state dispersion In productrvity stems from two sources: the growth characteristics of each state and chocks idiosyncratic to 1986. The basic statement of the Solow model IS that the variation due to the former should be explicable In terms of a narrow set of variables. Output per worker should be posi- tively correlated with the investment rate in each state and negatively correlated with (A + 7 -t @--this sum representing the “caprtal requirements”’ generated by growth in the effective amount of labor and the ccnsumptron of capital--and the coefficrents should be of equal magnitude. To the extent that the narrow (set of variables explains a large fraction of cross-state variation in productivity in a manner consistent wrth these predictions, 1 he data are not at odes with the traditional focus on capital accumulation in policy development.

Adjustment to Steady States

One reason the data rnay not 1,upport the predictions of equation 10 is the assump-


FIGURE 1

Distribution of Productivity, 1986 160.0%

150.0%

140.0%

B 130.0%

$

2 8 120.0%

b a

a .g 110.0%

$

f 100.0%

90.0%

80.0%

70.0%

tion that the data are observations of steady state behavior. While useful as a benchmark, this restrictive assumption may be relaxed by considering the characteristics of convergence toward the steady state. Further, as noted by Lucas (1988) and Romer (1989), the steady state of a neoclassical growth model will be indistin- guishable from the balanced growth path of an endogenous growth model. For this reason, equation 10 may not distinguish among the alternatives. The neoclassical growth model, however, predicts that economies will tend to converge during the transition steady states.

In the simplest case, one might imagine that all economies converge toward an identical steady state level of productivity. If so, one should observe a decline in the absolute dispersion of productivity over

429

time. Figure 2 displays evidence suggestive of this phenomenon using the data for this study. As the figure shows, the dispersion (measured by the coefficient of variation in each year) of output per worker falls fairly steadily over the period 1973-1986.

While the data appear broadly consistent with this simple form of convergence, the predictions of the model are more modest. The Solow model predicts only that “identical” economies-those with equal investment rates, labor force growth rates, etc.-will have Identical steady states; all states will not evolve toward the same level of productivity. For those with the same steady state, however, output per worker will converge regardless of initial conditions. Accordingly, the model predicts that when observing the transition to (the same) steady state, growth will be faster in

FIGURE 2

13 04.

Coefficient of Variation - Productivity

those economies that start off at a lower level. Figure 3 contains suggestive evidence on this front, plotting the average annual growth rate for 1973-86 vs. the initial productivity level. The negative correlation predicted by the convergence process is plainly evident in the raw data.

The difficulty, of course, is that Figure 3 does not control for variations In the steady state. It is possible to employ the basic model to develop a regression analy- 86s of convergence toward the steady state. Using discrete time, and approximating in the vicinity of the steady state yields

In yet - In ye0 = (1 -- (1 - y)‘)(ln ye* - In ye,)

where ye0 is the initial level of productivity

1980 1994 1 Year

The parameter y, which governs the speed of convergence, is given by

y = (1 -' a)(7 + A + 6).

Transformirlg equation 11 into observable variables yields

Iny, - Iriy, = (1 - (I .- Y)f)

( -+J--Jln 8 - In (77 + h + (S)]

+ In @IO - In yO )

-t At.

As equatron 13 indicates, the growth rate of yt durrng the transition to the steady

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FIGURE 3

Growth Rate versus Initial Productivity

lOd.O% udos do% 1973 Productivity - Percent of Mean

state is inversely related to the initial level of output per worker (yO). The speed of adjustment toward the steady state de- pends upon the underlying parameters for technology, tastes, and population growth. For example, assume that (Y is 0.33 and that (A + 7 + 6) = 0.075. As a result, y = 0.05, and the economy requires 13.5 years to adjust one-half of the way toward the steady state. Higher values of (Y lower the speed of adjustment; with a = 0.67 the economy will require 27 years to adjust one-half of the way toward the steady state.3 As policy toward 8 affects the growth rate of the economy only during the transition to the steady state, estimates of y may provide some insight into the horizon over which policy will have a noticeable effect on the economy. Finally, consider the impact of policies that raise 8 at t = 0. From equation 13, one can see that

431

the impact on the average growth rate between t = 0 and t = t is

1 a(ln yet - In yea) (1 - (1 - Y)‘)CU

t ae = (1 - a)et

For 0 < (Y < 1, the growth rate effect declines as t rises.

The policy implications are quite different in simple models of endogenous growth. For example, the linear production technology ye = Ak, (corresponding to (Y = 1) yields a simple model of endogenous growth. In this case, the model predicts

-=-= ye k,

8A - (7 + A + 6)

that is, a constant rate of growth with no tendency to converge. instead, similar


ysis of transitions to the steady state to yield5

In yt - In y0 = (1 - (1 - $‘)

c & [In 19 - In (q + A + S)]

P +-Inh*+In@,-Iny, +ht

l-CY 1

where the adjustment speed, y, is now given by

y = (1 - a - P)(q + A + 6).

Open-Economy Considerations

The discussion thus far has treated each state in isolation. In practice, however, states are open to flows of capital, labor, and, hence, human capital. How do these considerations affect the analysis? To the extent that tax and budget policies alter the rate of investment by attracting inflows of capital, the policy implications are identical to those in which the additional capital is generated internally. Hence, the focus is on the rate of investment, not the rate of saving. However, to the extent that high-productivity states attract greater investment, the direction of causality will be reversed and econometric inferences con- taminated. Similarly, labor may flow from low-productivity to high-productivity regions. Thus, the empirical work that follows attempts to gauge the degree to which the results reflect these influences.

EMPIRICAL ANALYSES

Econometric Specification

Equation 16 embodies the discussion of steady state behavior in the second section, indicating the relationship between steady state output per worker and the investment rate, the labor force growth rate, the rate of technical progress, the rate of

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depreciation, and the stock of human caprtal. Thus, the initial econometric objective is to estrmate the parameters of equation 16: LY, p, A, and Go.’

One approach to the estimation would be to estimate the model using a single cross section of data. In the current context, one could use (log) output per worker in any given year as the dependent variable. Aver- ages for all preceding years would serve as emptrical proxies for the right-hand-side variables. As a result, one would estimate the (nonlinear) relationship between, say, 1986 productivrty and the average rates of investment and labor force growth rate between 1973 and 1986.

Indeed, one could construct such a regres- s/on for each year in the sample. Utilizrng the panel structure of the data provides one way to simultaneously exploit the information in the data. Thus, below I estimate equation 16 using all the years available. In these analyses, Y,~ is productivity for state i in year t, 8,, is the average In- vestment rate in state i between the start of the sample (1973) and year t, and T,~ is average labor force growth for state i between 1973 and year t.7 As noted below, the data available do not permit the estimation procedures to use time-series variation in h,.

As noted earlier, a possible objection to this procedure IS that annual observations of output per worker may not reflect steady state behavior. The second major message of the previous section, however, concerns the behavior out of the steady state, i.e., convergence. Equation 17 shows the relationship between output per worker and Investment rates, labor force growth rates, productivity growth, and the initial level of productivity. As in the case of the estimates of the steady state, I pool data for all the available years in the estimation .8

Estimation is done via nonlinear least squares. The estimated standard errors are

corrected for heteroskedasticity using the rnethod of White (1980).

Data

Output for each state is taken from the estimates of the Gross State Product (GSP) produced by the Bureau of Economic Anal- ys~s (BEA). The labor force for each state was obtained from the ESEA.’ Productivity is defined as the ratio of output to the labor force.

IReal investment was based on the estimates of private-sector capital in Munnell (1990).‘” The information on GSP and investment was used to compute the investment rate (0) in each state. To estimate the Investment rate inclusive of government capital, information on real capital investment for state and local governments was taken from Holtz-Eakin 1(1993).” Each van- able was computed on an annual basis for the period 1973-1986 and, where appro- priate, the average value for each state employed in the analysis.

Human capital per worker is proxied by the fraction of individuals, aged 25 or older, having completed 4 or more years of college.12 Data for each state is taken from the 1980 Census of the Population. As a result, there is no variation over time in the measure of human capital Sample statistics are shown in Table 1.

Estimation Results

The parameter estirnates are presented in Table 2. Consider the results for equation 16 (the steady state), which are contained in column 1 of Table 2. As the theory indicates, output per worker rises with the difference between the investment share and capital requrements. The estimated elasticity of output with respect to capital is roughly 0.115, somewhat below rule-of- thumb estimates of capital’s share in output.13 The elasticity with respect to human capital is of comparable magnitude, 0.18, and is also Iprecisely estimated.14 Thus, the data suggest that physical and human cap-

ital enter the production function in a roughly symmetric fashion.‘* Finally, the estimate of A suggests a slow, but statistically significant, rate of labor-augmenting technical progress over this period.

Thus, the irlitial pass provides plausible estimates of the production process. As shown at the bottom of column 1, however, the adjusted R2 Indicates that a rather small fraction of the variation is explained by the variables central to the model. It could be the case that this simply reflects a large influence of year-specific shocks.“’ Another possibility, however, is that the low explan- atory power stems frorn deviations from the assumptions of steady state behavior. To investigate the latter, I turn ‘to the transition process and present estimates of equation 1’7 In column 2 of Table 2.

Explicitly modeling the transition from initial conditions to the steady state raises the estimates elf both cy and p. The estimated elasticity wtth respect to physical capital is 0.24, while that for human capital is 0.32.” Both are precisely estimated. Fur- ther, as with the steady state estimates, the results indicate only a small role for technical progress during the sample period. Because the adjustment toward the steady state modeled in column 2 incorpo- rates cross-state variation in the initial level of productivity in each state, the fraction of the variation explained by the equation rises; the adjusted R* is now 0.91. These results suggest support for the traditional view of the role of investment In the growth process: an econometric equation specified in accordance with the neoclassical model ,ylellds parameter estimates of a realistic magnitude that are simultaneously capable of explaining a large fraction of the time and spatial variations tn growth rates.

How robust are these results? Thus far, the analysis has assumed that all states share a common level of initial productivity, QO. Clearly, there is the potential for differ-

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TABLE 1 SAMPLE STATISTICS

Mean Standard Deviation

Investment rate (@) (Percent)

Labor force growth rate (v) (Percent)

Percent college (h*) (Percent)

Productivity (y) (1982 Dollars)

Area (square miles)

Urban area (square miles)

Mineral (1986 metal mining + nonmetallic minerals)

Coal (demonstrated reserves, 1984)

Oil (proven reserves, 1988)

Gas (proven reserves, 1988)

3.81 4.93

2.27 3.40

15.9 2.83

3.54 0.156

61,499 46,452

964 868

177 179

9,758 22,876

358 1,208

2,813 7,105

TABLE 2 PARAMETER ESTIMATES”

Converaence

Steady State Basic Parametize G0 State Effects

a 0.1549 0.2354 0.2880 0.1608

P

a3

Areab

Urban Areab

Mineral x 1O-6

Coal x 10m6

Oil

Gas

fi2

(0.03257) (0.02363) 0.1781 0.3165

(0.02656) (0.03169) 0.007376 0.001966

(0.002441) (0.001723) 2.833 2.106

(0.1108) (0.1457)

-

-

-

-

-

0.12-

-

-

-

-

0.91

(0.02669) (0.04311) 0.3333 0.6502

(0.02155) (0.04111) 0.01555 0.03432

(0.002547) (0.02456) 1.487

(0.1936) - 0.003128

(0.009520) - 0.02652

(0.009149) - 182.0 (46.22) -

0.1450 (0.4550) -

-0.3140 (7.736) -

2.113 (1.307) - 0.92 0.96

‘Standard errors are shown in parentheses. All variables are defined In the text. bEntered as a logarithm.

ences across states in productivity stem- differences are both important and corre- ming from varying endowments of land lated with typical rates of investment in and minerals, for example, or from a host each state, the exclusion of these factors is of other factors. To the extent that these inappropriate and the estimated parame-

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ters may be quite misleading. The estimates presented in columns 3 and 4 ad- dress this issue.

i begin by parameterizing the heterogene- ity In Q0 as a function of cross-sectional information for each state; i.e.,

where the vector X’, contains the land area (in logs), urblan land area (in logs), and endowments of minerals, coal, 011, and natural gas in each state.18 (Sample statistics for these data are also shown In Table I.) Following this approach, one finds in column 3 that urban land area and endowments of minerals and natural gas are sig- nificantly correlated with cross-sectional differences in initial levels of productivity. Explicitly controlling for these differences, however, has little effect on the estimated values of (Y and p. In contrast, the estimated value of h rises substantially. Taken as a whole, however, there is only a small difference irl the overall performance of the model.

Column 4 Investigates an alternative means by which to control for differences among states. Specifically, I augment the model with a dichotomous variable for each state. These variables permit one to control for unobserved characteristics of states that do not change through time, thus controlling for dffferences in initial productivity levels, as well as other idtosyncratic features of each state.“’ As the table indicates, the impact is to sharply increase the estimated value of p to 0.65, while the estimate of o! declines somewhat to 0.1 6.20 Both estimates are statistically significant at conven- tional levels These results focus attention on the limited informatron available on human capital At a heuristic level, the inclu- sion lof the state-specific effects implies that the identification of p does not derive from cross-state variation in h,. Instead, p

is identified largely by its contribution to y. In effect, this approach does not impose as tight a consistency between the speed of the transition and the nature of the steady state. (It IS interesting to note that Barro and Sala i Martin (1991) also estimate relatively small values for y in similar circumstances.) Still, while the point estimates differ, the overall characteristic of the results remains consistent with the neoclassical model, especially with regard to the role of 8.

A final econometric Issue is the degree to which the Iparameter estimates are subject to simultaneity bias. Recall that factor mobility across states might lead to circumstances in which relatively high.productivity states attract inflows of capital and labor, thus implying that causation runs from y to 6, and r), not the reverse. Consider first the effects of differences in productivity across states that do not change through time. In these circumstances, controlling for initial differences will lead to consistent estimates of the parameters, thus leading one to prefer the estimates presented in columns 3 and 4

Of course, it may be that changes in productivity subsequently attract c,3pital inflows. Reasoning in this way suggests that the history of productivity changes in a state should improve one’s ability to predict the future path of both 0 and 7. That is, one shcluld find that productivity “Granger-causes” these variables. I investigate this possibility using the estimation and testing procedures developed by Holtz- Eakin, Newey, and Rosen (1988) for vector autoregressions in panel data. Specifically, I specify an equation for the change in 8,, that contains a dummy variable for each year, four lags of the change in 8,t, four lags of the change in qit, and four lags of the change in Y,~. The parameters are estimated using instrumental variables to control for the difficulty presented by serial correlation In the error term and the pres- ence of lagged dependent vari,3bles.2’ I

436


then conduct two tests on the equation. First, I reduce simultaneously the lag length for each variable In the equation until the data reject the restrictions Imposed by the shorter lag length. Following this procedure results in an equation with a lag length of one year.” Using this specification, I test the null hypothesis that past changes in Y,~ may be excluded from the equation. The test statistic for this hypothesis, distributed as a chi-square with eight degrees of freedom, is only 4.3. Thus, I fail to reject the null hypothesis of no causal relation between past changes in states’ productivity and the rate of investment.

In the same way, I specify an equation using the change in T,~ as the dependent variable and including the same right- hand-side variables. The same testing procedure again leads to an equation contain- ing only one lagged value of changes in each of the variables.23 Again, using this specification, I test the null hypothesis that past changes in Y,~ may be excluded from the equation. The resulting test statistic, distributed as a chi-square with eight degrees of freedom, is 6.6. Once more, I fail to reject the null hypothesis of no causal relation.

Thus, within the context of this empirical analysis, the data do not suggest that the parameter estimates-especially those in columns 3 and 4-are plagued to a great degree by simultaneity bias. Of course, these diagnostics do not constitute a com- plete investigation of factor mobility across states, which lies beyond the scope of this paper.

lmplica tions

Taken at face value, the characteristics of the estimated production function are rea- sonable. Is the same true for the convergence behavior that these estimates imply? The key parameter governing the speed of adjustment to the steady state is y. Using the estimated parameters in column 3 and data for 1986, the mean value is y =

437

0 045, Indicating that the typrcal state economy adjusts toward the steady state by roughly 4 percent In a given year. Put differently, the estimates and 1986 data imply that on average it requires 15.1 years for states to adjust one-half of the distance toward the steady state.

Comparable estimates from InternatIonal data In Mankiw, Romer, and Weil (1992) imply the same adjustment requires 38 years. The estimates in Barro and Sala I

Martin (1990), also based on U.S. state data, rndtcate that the time required for this adjustment IS 31 years.24 These com- parisons suggest two lessons. First, adjustment is somewhat faster in the environ- ment of free factor mobility provided by the United States. Second, econometric estimates that include information on both the steady state and the adjustment process suggest very different qualitative results. From a policy perspective, however, these results suggest that the “debate” between proponents of alternative views may be overstated. In both cases, policies to raise the rate of capital accumulatron WIII affect the growth rate of the economy over any realistic political horizon.

Concluding Remarks

The empirical analysis reported above provides qualitative support for the Solow model of economic growth. The average investment rate, the labor force growth rate, and the rate of technological progress, depreciation, and human capital accumulation are good predictors of output per worker and yield plausible estimates of the parameters of the production function. Fi- nally, the strong evidence in favor of convergence argues against simple models of endogenous growth.

Still, the key role played by human capital in the estimates equation suggests the need to examine directly the growth of human capital in each state. Further, a better understanding of the links between physr- cal capital investment and human capital


nods Thus, the speclflcatlon IS not subject to the bias In models with flxed effects using lagged dependent varl- ables (NIckelI, 1981) I also expenmented with a spectflca- tlon In which the growth of labor efficiency, A. IS permlt-

ted to vary across states The results for a and p are quite slmllar to those In column 4

2o An F-test rejects the null hypothesis that the state effects are simultaneously equal to zero at the one percent level of signrftcance

2’ See Holtz-Eakln, Newey, and Rosen (1988) for details I used lags 2-5 of B,,, Q, and ylr (In levels) as Instrumental variables

22 The chl-square tests statistics, each dlstrlbuted with 24 degrees of freedom, are as follows 3-year lag length, 16 4, 2-year lag length, 7 7, l-year lag length, 26 88, and no lags, 354 2

23 In this case, the chl-square tests statlstlcs, each distributed with 24 degrees of freedom, are as follows 3-year lag length, 8 7, 2-year lag length, 28 3, l-year lag length,

13 1, and no lags, 42 3

24 If one uses the parameter esttmates In column 4 for these computations, the mean time IS 26 3 years Given the slmllarlty In the parameter estimates (see above), It IS not surprising that the Impllcatlons are closer to those of Barro and Sala I MartIn

REFERENCES

Aschauer, David. “Is Publtc Expenditure Productive,” jour nal of Monetary Economics 23 (March, 1989) 177 200

Barre, Robert. “Government Spending In a Simple Model of Endogenous Growth ” burnal of Po/~t~.a/ Economy 98 No 5 (October, 1990) s103%s125

Barro, Robert and Xavier Sala i Martin. “Economic Growth and Convergence across the United States ” Working Paper No 3419, Nat/ona/ Bureau of Econom/c Research, 1990

Barro, Robert and Xavier Sala i Martin. “Convergence across States and Regions ” Brookngs Papers on Econom/c Act/v/ty (No 1, 1991) 107-82

Bartik, Timothy. Who Benefits from State and Local Eco- nom/c Development Po//aes Kalamazoo, Ml W E Upjohn In- statute, 1991

Holtz-Eakin, Douglas. “State Speclflc Estimates of State and Local Government Capital ” RegIona/ Saence and Urban Eco- nom(cs 23 (1993) 185 209

Holtz-Eakin, Douglas. ’ Public Sector Capital and the Pro- ductlvlty Puzzle ” Review of Econom/cs and Stat/ct,cs, forth- coming

Holtz-Eakin, Douglas, Harvey 5. Rosen, and Whitney Newey. “Estlmatlng Vector Autoregresslons with Panel Data ” tconometrica 56 (November, 1988) 1371 96

Holtz-Eakin, Douglas and Amy Ellen Schwartz. 1993 In- frastructure in a Structural Model of Economic Growth Syra- cuse University Mime0

H&en, Charles and Robert Schwab. 1991 Publtc Capital FormatIon and the Growth of Reglonal Manufacturing Indus- tries Untverslty of Maryland, Mlmeo

Lucas, Robert. “On the Mechanics of Economic Develop- ment ” lournai of Monetary Economics 22 (1988) 30 42

Mankiw, N. Gregory, David Romer, and David Weil. “A Contrlbutlon to the Emplrlcs of Econom!c Growth ” Quarter/y

louma/ of fconomrs (May, 1992) 407-38

Munnell, Alicia. “How Does PubtIc Infrastructure Affect Re- gional tconomic Performance,” In Is There a Shortfa// in Pub/~ CapCal Investment? edlted by A Munnell Boston

Federal Reserve Bank of Boston, 1990

Nickell, Stephen. “Biases In Dynamic Models with Fixed Ef- fects ” Econometnca 49 No 6 (November, 1981) 1417 26

Romer, Paul. “Increasing Returns and Long Run Growth ” /ourna/ of Pa/it/cd/ Economy 97 (1986) 1002-37

Romer, Paul. “Crazy Explanations for the Productlvlty Slow- down ” NBER Macroeconomics Annuai (1987) 163 201

Romer, Paul. “Capital Accumulation In the Theory of Long- Run Growth ” In Modern Euslness Cycie Theory, &ted by R Barro Cambridge, MA Harvard University Press, 1989

Solow, Robert. “A Contrlbutlon to the Theory of Economic Growth ” Quarterly Journal of Economrcs (February, 1956) 65-94

Tamura, Robert. “Income Convergence In an Endogenous Growth Model ” /ournai of Po/ft/ca/ Economy 99 (June, 1991) 522 40

White, Halbert. “A Hrteroskedastlclty-Conststent Covarlance Matrix Estimator and a Direct Test for Heteroskedasticlty ” Econometrlca 48 (1980) 817-38

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