The robust relationship between taxes and U.S. state income growth.

INTRODUCTION

A long-standing research enterprise has been devoted to estimating the effect of taxes on economic growth in U.S. states. To the extent a consensus exists, it is that taxes used to fund transfer payments have small, negative effects on economic activity. When used to fund productive expenditures, the associated tax effects are often estimated to vanish, or even become positive (Helms, 1985; Bartik, 1991; Phillips and Goss, 1995; Wasylenko, 1997). However, even this modest conclusion is disputed, since estimated effects vary widely across studies (Bartik, 1991; McGuire, 1992; Wasylenko, 1997).

Given the scores of studies that have investigated this issue, it is surprising that many important estimation issues are often not addressed. My study takes up several of these, and re-estimates the relationship between taxes and income growth. I find that taxes used to fund general expenditures are associated with significant, negative effects on income growth. Further, I show that these effects are generally robust across estimation procedures, alternative specifications of the regression equation, different time divisions of the data, and across time periods and Bureau of Economic Analysis (BEA) regions. I also provide a possible explanation for why previous research has had difficulty identifying these effects.

My analysis addresses the following estimation issues. First, it uses economic theory to derive an estimable equation. With respect to specification of the regression equation, theory has consequences for the following: (1) the inclusion/exclusion of labor, capital, and population variables along with, or instead of, underlying parameters such as saving, depreciation, and population growth rates; (2) the inclusion/exclusion of a lagged dependent variable; and (3) whether to include other explanatory variables in level or differenced forms.

The Cobb-Douglas production function has now become a standard point of departure for models of economic growth. Studies that have analyzed U.S. state fiscal policy (1) within this framework include Merriman (1990), Garcia-Mila and McGuire (1992), Evans and Karras (1994), Holtz-Eakin (1994), Garcia-Mila, McGuire, and Porter (1996), Aschauer (2000), Yamarik (2000), and Shioji (2001). My study follows suit by employing a general version of the Cobb-Douglas production function that includes the textbook Solow model and the augmented, human capital model of Mankiw, Romer, and Weil (1992) as special cases.

A second specification issue concerns the role of time. Much of the previous literature has restricted taxes to have only contemporaneous effects on economic activity. When dynamic effects are incorporated, it is usually done indirectly, through the inclusion of a lagged income variable (e.g., Helms, 1985). My regression specifications allow taxes to have both contemporaneous and lagged effects. (2)

A related issue concerns how to define the length of a time period for time series observations of states. Previous research on state-level taxes and growth has relied almost exclusively on either cross-sectional (e.g., Romans and Subrahmanyam, 1979; Mullen and Williams, 1994; Yamarik, 2000) or annual panel data (e.g., Helms, 1985; Crain and Lee, 1999).

Cross-sectional data is undesirable because it ignores time-varying behavior in the explanatory variables. This is particularly a problem for taxes: The average state tax burden in 1999 was very close to its level in 1970 (cf. Reed, 2006, Figure 1), despite large variation over time. Cross-sectional analyses also suffer from omitted variable bias due to uncontrolled fixed effects--to the extent these are not picked up in initial income levels.

On the other hand, annual data is particularly vulnerable to measurement error bias. This is, again, of particular relevance for tax studies. Using two very different approaches, Reed and Rogers (2006, 2007) estimate that roughly one-half of the annual variation in tax burden is due to factors other than tax policy. This bias is exacerbated by the inclusion of state fixed effects. Further, annual state-level income data are characterized by substantial serial correlation (cf. Evans and Karras, 1994). The combination of serial correlation with a lagged dependent variable produces inconsistent estimates.

Multi-year interval data also suffer from these problems, but to a lesser degree: Measurement errors are more likely to cancel out over longer time periods. Serial correlation is less severe when observations are distanced further in time. A few studies have analyzed the effects of fiscal policy using multiple-year interval data. These include Garcia-Mila et al. (1996), Aschauer (2000), Shioji (2001), Chemick (1997), Tomljanovich (2004), and Bania, Gray, and Stone (2007), though only the latter three directly study taxes. My analysis estimates tax effects over 30 years using five-year interval data.

A third issue is the selection of "control variables." Growth theory is sufficiently general that many variables are potential determinants of growth. Despite this, many studies of tax effects include no, or only a few, non-fiscal variables other than initial/lagged income, time, and/or state-fixed effects (cf. Becsi, 1996; Tomljanovich, 2004; Yamarik, 2000). Helms (1985) includes variables for state wages, percent unionization, and population density. Mullen and Williams (1994) include variables for growth of the civilian labor force, and the growth rates of private and public capital. Bania et al. (2007) employ the unemployment rate, percentage of the population that is working age, and union membership rates. Only Chernick (1997) and, notably, Crain and Lee (1999) have a broad set of control variables. My study includes an extensive set of control variables to avoid problems of bias associated with omitted variables.

That being said, it is well known that coefficient estimates are often highly dependent upon the particular set of variables included in the regression equation (Leamer, 1985; Levine and Renelt, 1992; Crain and Lee, 1999; Sala-i-Martin, 2004). To address this problem, I employ model selection criteria to determine variable selection. Further, I investigate the robustness of my results to alternative specifications.

A fourth issue concerns the choice of estimation procedure. Panel data are potentially characterized by complex error structures. Most previous research on fiscal policy uses Ordinary Least Squares (OLS) (e.g., Garcia-Mila and McGuire, 1992; Chernick, 1997; Crain and Lee, 1999), or OLS with standard errors corrected for general heteroscedasticity (e.g., Aschauer, 2000; Tomljanovich, 2004) or serial correlation (Evans and Karras, 1994). A few studies employ feasible Generalized Least Squares (FGLS) to address random effects (Garcia-Mila et al., 1996; Helms, 1985; Holtz-Eakin, 1994), though this procedure is usually rejected in favor of OLS with fixed effects. Dynamic panel data (DPD) estimators have occasionally been used to obtain consistent estimates when the regression specification includes both a lagged dependent variable and fixed effects (Holtz-Eakin, 1994; Shioji, 2001; and Bania et al., 2007). My analysis allows for a variety of serial correlation, heteroscedasticity, and cross-sectional correlation behaviors in the error term. It investigates the robustness of estimating tax effects using alternative OLS, FGLS, and DPD estimators.

A fifth issue addresses the role of influential observations. Point estimates may mask the fact that results can be driven by just a few time periods, or just a few states. This is of particular importance to policymakers who are interested in extrapolating the results of empirical studies to their own states and time periods. With only a few exceptions, previous research on tax effects reports only average effects: Mullen and Williams (1994) and Chernick (1997) check for (1) robustness across different time periods and (2) the effect of omitting some states from their samples. My analysis goes further by interacting tax variables with time, region, and state dummy variables to check for robustness across these dimensions.

The paper proceeds as follows. The second section derives a model of income growth that is general enough to encompass many of the models that have been used in previous research. The third section describes the data and discusses associated specification issues. The fourth section presents the initial empirical results. The fifth section checks for robustness across (1) alternative variable specifications, (2) alternative estimation procedures, (3) different time divisions of the data, and (4) different time periods, regions, and states. The sixth section provides a possible explanation for why my study finds a robust relationship between taxes and income growth while previous studies have not. The seventh section concludes.

A MODEL OF INCOME GROWTH

I assume that state income ([Y.sub.t]) is determined by the following general version of the Cobb--Douglas production function,

[1] [Y.sub.t] = [A.sub.t] [K.sub.t.sup.[alpha]] [(([L.sub.t][Q.sub.t]).sup.[beta]] = [A.sub.t] [Q.sub.t.sup.[beta]] [K.sub.t.sup.[alpha]] [L.sup.[beta].sub.t],

where [K.sub.t] and [L.sub.t] are capital and employment, [Q.sub.t] is the efficiency of labor, and [A.sub.t] represents other factors that influence state incomes (e.g., human capital variables, factor neutral productivity determinants). The textbook Solow model and the augmented human capital model of Mankiw et al. (1992) are both special cases of equation [1]. (3)

Dividing both sides by population, [N.sub.t], gives