Growth, taxes, and government expenditures: growth hills for U.S. states.

INTRODUCTION

Do taxes and government expenditures enhance or impede economic growth? This question lies at the heart of public finance and taxation policy, both at the national and sub-national levels. In an extensive summary of empirical studies of the effects of taxes on economic growth, Poot (2000) finds that most estimates are either insignificant or negative, though a small number are positive. Similarly, estimates of the effects of government investment expenditures on economic growth also tend to be insignificant, though some studies find positive effects, particularly for expenditures on physical infrastructure and education (e.g., Cohen and Paul (2004) and Pereira (2000)).

Recently, Bleaney, Gemmell, and Kneller (2001) tested Barro (1990) and Barro and Sala-i-Martin (1992, 1995) style endogenous growth models for Organisation for Economic Co-operation and Development (OECD) countries over the period 1970-95, extending tests in earlier Barro (1989, 1990) cross-country studies. Based on a full specification of the government budget constraint, including distinctions between economically productive and nonproductive government expenditures, their results are consistent with the endogenous growth model, in that taxes reduce the long-run growth rate and productive government expenditures increase it, all else the same.

While the studies surveyed by Poot (2000) and the recent Bleaney et al. (2001) study are based primarily on cross-country data, there are also a number of cross-state (or cross-county) studies for the United States, including, for example, Helms (1985), Mofidi and Stone (1990) and, more recently, Mark, McGuire, and Papke (2000) and Holcombe and Lacombe (2004). Helms (1985) and Mofidi and Stone (1990) find that taxes spent on publicly provided productive inputs tend to enhance growth, while Holcombe and Lacombe (2004) and Mark et al. (2000) find that increases in taxes tend to impede growth. Which conclusion is correct?

Ironically, the Barro-style models of endogenous growth suggest that all could be right, depending on the level of taxes, the composition of expenditures, and other factors. In Barro-style models, increases in taxes can enhance, have no effect on, or impede growth depending, in particular, on the initial level of taxes--as well as on how the tax revenues are spent. For example, an incremental dollar of tax revenue spent on productive government services has a much more positive effect on growth in the Barro model when taxes are initially low than when they are already high, when the effect may even be negative. This kind of "growth hill" arises because a rising tax share invested in productive public services initially increases but ultimately decreases the net (i.e., after-tax) return to private capital, crowding out private capital investment (as in Barro and Sala-i-Martin (1992)).

Surprisingly, no study, at least to our knowledge, has attempted to estimate the growth hills arising from Barro-style models. (1) This is the task we set out for ourselves in this paper. Based on data for 49 of the 50 U.S. states (Alaska is excluded), our results provide insights not only for some of the conflicting findings of positive, insignificant, or negative effects in other studies, but also for the extent to which U.S. states have tax and expenditure structures conducive to economic growth.

A well-specified examination of the long-term effects of state and local taxes and expenditures on the growth in state per-capita income requires, at a minimum, that: i) the potential for growth hills inherent in Barro-style models of endogenous growth be incorporated into empirical specifications; ii) the government budget constraint be fully specified, i.e., all revenues, expenditures and deficits/surpluses be specified, explicitly or implicitly, since the effect of an additional dollar of tax revenue presumably will vary depending on what it is used for (Helms, 1985; Mofidi and Stone, 1990); iii) unobserved differences across states, which are likely to be correlated with both the dependent and independent variables, be accounted for (Mofidi and Stone, 1990; Mark et al., 2000); and iv) the period of analysis be sufficiently long and the dynamics adequately specified to ensure that steady-state effects are identified separately from shorter-term, cyclical effects (Mofidi and Stone, 1990; Bleaney et al., 2001; and Gray and Stone, 2006).

Our findings suggest, consistent with Barro-style models, that increases in taxes spent on publicly provided productive inputs initially increase the growth rate of state real personal income per capita, but do so at a declining rate sufficient to induce a growth hill. Hence, the impact of taxes depends both on the initial level of taxes, as well as on how they are spent. We also provide empirical assessments of the extent to which state and local taxes and corresponding public investments are optimal, too low, or too high in terms of growth in state real personal income per capita, though we urge caution in interpreting our particular point estimates.

In the next section, we set out the theoretical context for our empirical specifications, and describe the data and estimation strategies in the third section. In the fourth section, we present the empirical estimates, along with a number robustness tests. In the fifth section, we assess the implications of the non-monotonic tax effects--growth hills--for whether or not tax and expenditure structures are conducive to economic growth. In a final section, we summarize our findings and offer some suggestions for future directions.

THEORETICAL BACKGROUND

Unlike the neoclassical growth model, where fiscal effects alter the level of the long-run output path, the endogenous growth model permits fiscal effects to alter the slope of the long-run output path, as illustrated, for example, in Barro (1990). Here, we employ an adaptation of the Bleaney et al. (2001) presentation of the Barro and Sala-i-Martin (1992, 1995) model of endogenous growth. There are n producers, each producing output (y) according to the production function

[1] y = A[k.sup.(1-a)][g.sup.a],

where A is a positive constant, k is private capital, g is a publicly provided input, and a is a parameter between zero and one. (2) The government funds its budget with a proportional tax on output at the rate r. (3) The government budget constraint is, therefore,

[2] ng + C = rny,

where C is government-provided consumption (or "non-productive") goods. (4)

Bleaney et al. (2001) note that with an isoelastic utility function, the long-run growth rate (V) in this variant of the Barro and Sala-i-Martin (1992) model can be expressed as

[3] V = w(1 - r)(1 - a)[A.sup.1/(1-a)][(g/y).sup.a/(1-a)] - u,

where w and u are constants reflecting parameters in the utility function. Note that private capital is endogenously determined in the model and, hence, does not appear in equation [3]. Thus, output growth in the steady state depends only on structural parameters for production and utility (w, u, a, and A), the tax rate (r), and the ratio of productive government expenditures to output (g/y). (5)

Equations [2] and [3] together are typically used to motivate a static or dynamic linear regression equation, despite the nonlinearity of equation [3]. Here, however, we are concerned with the intrinsic nonlinearities, in particular the potential for Barro-style growth hills for tax-financed expenditures on productive government services. Using equation [2] to substitute for productive government expenditures (g) in equation [3], one obtains a nonlinear equation in the production and utility parameters (w, u, a, and A), the tax rate (r) and government consumption expenditures (as a fraction of output, C/ny):

[4] V = w(1 - r)(1 - a)[A.sup.1/(1-a) [(r - C / ny).sup.a/(1-a)] - u.

The incremental effect of taxes (r) is initially positive in equation [4], as taxes are implicitly spent on productive government services. (6) However, the effect eventually turns negative, as private capital is increasingly crowded out by the depressing effect of the rising tax share on the net return to private capital. (7) If C/ny is zero, the growth peak occurs where the rate of taxation equals the productivity parameter for publicly provided inputes in equation [1], i.e., where r = a (Barro and Sala-i-Martin, 1992). If C/ny is non-zero, the typical case, then the growth peak occurs where

[5] r - a = (1 - a)(C/ny).

Hence, as public spending shifts away from publicly provided productive inputs toward publicly provided consumption goods, the tax rate consistent with maximum growth rises relative to a, but proportionately less than the increase in C/ny. The effect of an increment in C/ny is negative in equation [4], all else the same, as it reflects a shift of expenditures from productive to nonproductive government expenditures.

DATA AND EMPIRICAL METHODOLOGY

Our model for growth in equation [4] can be approximated for estimation by a second-order expansion, which is linear in parameters, but nonlinear in the variables:

[6] V = [[omega].sub.0] + [[omega].sub.1] r + [[omega].sub.2] [r.sup.2] + [[omega].sub.3] (C/ny) + [[omega].sub.4] [(C/ny).sup.2] + [[omega].sub.5] (r)(C/ny) + [[omega].sub.6] z + e,