Economic growth regressions for the American states: a sensitivity analysis.

Crain, W. Mark ; Lee, Katherine J.

I. INTRODUCTION

Researchers motivated by a variety of questions turn to data on the economic performance of the American states to analyze their ideas empirically. The appeal of cross-state empirical analysis derives from the fact that while states differ in relevant dimensions, they are not so different as to make omitted variables an overwhelming source of error. For example, the state economies operate under the same monetary regime (The Federal Reserve), comparable legal institutions (The U.S. Constitution), and borders open to the flow of productive factors, knowledge and products. Cross-state analysis avoids the myriad structural differences that encumber cross-national empirical analysis. Thus, investigators feel secure in considering a relatively small number of control variables in attempting to establish a statistical relationship between state economic performance and a particular variable of interest. The availability of uniform and accurate time-series data for the states adds to the appeal of cross-state regression models.

Despite the advantages associated with evaluating institutionally similar economies, researchers who rely on state regressions find little systematic guidance concerning which variables to include and other basic specification issues. For instance, do demographic and geographic characteristics vary sufficiently across states to require independent controls? Do cultural or climatic conditions affect growth, or are these variables correlated with other factors that may affect growth such as labor force participation rates or education levels?

A review of the extensive literature reveals that few studies control for the variables analyzed by other researchers. These specification differences make it hard to evaluate and compare the results of existing studies. Bartik [1991] and Phillips and Goss [1995] illustrate this problem as they attempt to garner the effect of taxes on state economic development from dozens of studies that employ alternative specifications and methodologies. They use Meta Regression Analysis (MRA) to test whether specification changes and alternative variables significantly affect the estimated elasticity of state growth with respect to taxes. The MRA technique focuses on the sensitivity of the estimated coefficients for state tax variables to model variation. In this paper we employ a technique to assess the sensitivity of numerous control variables identified in the state growth literature. We also introduce several new control variables. The approach identifies which variables are robust to small changes in the conditioning information set.

Our procedure closely follows that in Levine and Renelt [1992] which for its part relies on the Extreme-Bounds Analysis (EBA) suggested by Learner [1983; 1985].(1) The main difference is that we employ annual panel data on the American states (pooling cross-sectional and time-series data) whereas Levine and Renelt employ cross-country data averaged over 20-year or even longer time intervals. The cross-country studies such as those assessed in Levine and Renelt that average long time periods generally seek to identify factors associated with long-run, steady state growth. The U.S. state studies using annual panel data do not share a comparable unifying purpose. Relationships estimated from yearly data reveal short-term responses and pick-up business cycle effects which confounds drawing implications about growth theory. With this qualification in mind the results presented below indicate which variables included in past studies are robust and provide a set of core variables as a starting point for future research that relies on state growth regressions and annual panel data. Finally, the findings demonstrate that several important conclusions in the literature depend on how variables are measured. For example, the relationship between state growth and government size reverses sign depending on whether we denominate government size in per capita terms or as a share of state income.

II. SPECIFICATION ISSUES, SAMPLE, AND SENSITIVITY TECHNIQUE

Adopting the convenient notation in Levine and Renelt [1992], the EBA uses equations of the general form:

(1) Y = [[Beta].sub.i] I + [[Beta].sub.m] M + [[Beta].sub.z] Z + u, where

Y = real per capita personal income;

I = a set of core variables always included in the regressions;

M = the variable of interest;

Z = a subset of variables chosen from a pool of variables identified by past studies as potentially important explanatory variables of state growth; and

u = a random disturbance term.

Annual observations on the 48 contiguous American states serve as the basic unit of measurement. The Appendix tables provide complete definitions of the variables, data sources, and summary statistics.

Equation (1) specifies real per capita personal income, a common indicator of state economic performance, as the dependent variable.(2) Two variables constitute I, the set of core variables always included in the EBA: the share of the state population between the ages of 18 and 64, and the share of the state population with a bachelor's degree or better.(3) The two core variables target a fundamental element of growth, the size and skill of the labor force.(4) Using a common core specification to compare across models makes the analysis tractable, while leaving most of the variables open to the sensitivity analysis.

The EBA evaluates 29 variables identified by past studies as potentially relevant to state economic performance, i.e., we examine 29 "M variables" as defined in Equation (1).(5) The procedure first regresses Y on I and M, producing a "base" regression result for each M variable. We then regress Y on I, M, and linear combinations of a set of six Z variables taken two at a time (further described below). The ten regressions generated for each M variable using the subsets of Z variables allow us to identify the highest and lowest values for the coefficient on M (denoted [[Beta].sub.m]), and thereby define the upper and lower bounds of [[Beta].sub.m]. The extreme upper bound is the highest value of [[Beta].sub.m] plus two standard deviations; the extreme lower bound is the lowest value of [[Beta].sub.m] minus two standard deviations.(6) If [[Beta].sub.m] remains significant and of the same sign at the extreme bounds, we label the partial correlation between Y and the M variable "robust." If [[Beta].sub.m] does not remain significant or if it changes signs at the extreme bounds, we label the partial correlation "fragile."

We select the set of Z variables for the EBA from the pool of 29 variables. The selection process involves two steps. First we group the 29 variables into seven general categories. For example, three variables represent alternative ways to proxy a state's industrial composition, and seven variables represent alternative ways to proxy fiscal policy indicators. The Appendix identifies the seven categories, and the variables associated with each. Second we use univariate regressions to identify one variable from within each category that best proxies that particular dimension.(7) To illustrate, among the three variables that proxy a state's Industrial Composition, the univariate regression for the "Industry Diversity" variable exhibits a much higher R-square than the regressions for the other two variables in that category; we thus use it to represent the Industrial Composition group in the set of Z variables. We likewise select one variable from the other categories to obtain a set of six Z variables.(8) The Appendix identifies the Z variables. Again, the EBA for each of the 29 M variables varies the subset of Z variables by running regressions that include all linear combinations of the Z variables taken two at a time. These Z-variable combinations exclude the representative variable from the same category as the variable of interest.(9) This procedure thus yields ten regressions for the EBA of each M variable.

Samples and Preliminary Diagnostics

The samples consist of panel data for the 48 contiguous states for a 16-year period, except for the category of variables measuring the stocks of public and private capital (we explain the exception in more detail below). The sample period commences with 1977 data, the initial year for which we could obtain a consistent series on all variables. The sample period ends with 1992 data, the most recent year for which all data are available (excepting the capital stock variables as noted in footnote 8).

Preliminary specifications using the logged-levels of the variables indicated first-order positive serial correlation, yielding Durbin-Watson statistics well below the lower limit critical values. Furthermore, Dickey-Fuller unit root tests failed to reject the hypothesis that the series follow random walks. As a remedial strategy we first-difference all of the variables (first-differencing makes the model stationary). Of course, first-differencing the variables frames the analysis in terms of growth rates. As it turns out, employing growth rates as the dependent variable coincides with the majority of past studies.(10) In summary we use a Generalized Least squares estimation procedure on logged, first-differenced data to correct for nonstationarity, serial correlation, and heteroscedasticity. Finally we include a constant term in the first-differenced model to pick up the effect of any time trend.(11)

III. RESULTS OF THE EXTREME BOUNDS ANALYSIS

The core model of the EBA yields the following regression results (t-statistics are in parentheses):

PPY = 0.008 + 1.401 LABOR + 0.210 EDUC, (3.91) (8.36) (2.76)

where PPY is real per capita personal income, LABOR is the share of the population between the ages of 18 and 64, and EDUC is the share of the population with a bachelor's degree or better.(12) The signs of the estimated coefficients are consistent with theory and significant at the 1% level. The core specification explains 20% of the variation in the dependent variable. The EBA Uses this core specification as a starting point to evaluate the effect of small changes in the conditioning information on the variable of interest.

Table I presents the EBA results for 29 variables. The table organizes the results into the seven variable categories, and the discussion proceeds in that order. Table I reports three regression results for each variable: the base model (which includes only the variable of interest and the core variables); the extreme upper bound model; and the extreme lower bound model. The columns list: the estimated coefficient for [[Beta].sub.m]; its t-statistic; the R-square; and the Control Variables (i.e., the subset of the Z variables) included in the upper- and lower-bound models. The far right column reports the results of the EBA, identifying the variable of interest as either fragile or robust.

State Industrial Composition

Growth regressions often include a variable controlling for a state's industrial composition. For instance, Mofidi and Stone [1990] include the percentage of non-agricultural employment in durable goods industries, and Romans and Subrahmanyam [1979] include the ratio of non-agricultural to agricultural income. Glaeser et al. [1992] explicitly test the effect of industrial composition using data on American cities, finding that a diversified economy tends to promote growth more than a homogeneous economic base.

We evaluate three variables that proxy a state's industrial composition: Industry Diversity; Manufacturing Share of Gross State Product (GSP); and Service Share of GSP.(13) Two variables, the Service Share of GSP and Industry Diversity, yield robust results. The growth rate in per capita income decreases as the Service Share of GSP grows more rapidly, and increases as the industrial base diversifies [TABULAR DATA FOR TABLE I OMITTED] more rapidly.(14) These results indicate that while state growth regressions appropriately include a control for a state's industrial composition, it would be beneficial to use Industry Diversity or the Service Share of GSP rather than the Manufacturing Share of GSP.

Fiscal Policy Indicators

The effects of fiscal policy and public sector growth on state economic performance have received considerable attention since the late-1970s.(15) While this relationship had been examined at the national level, researchers turned to the diverse revenue and expenditure policies of the states to add a new dimension to empirical research. State data provide an opportunity to identify the alternative effects of taxes and expenditures and to test fairly specific hypotheses concerning fiscal policy. Romans and Subrahmanyam [1979] find that tax progressivity and expenditure policies affect growth to a larger extent than the overall level of taxes. Plaut and Pluta [1983] find that states relying more heavily on the property tax exhibit higher rates of industrial growth than states relying more heavily on other revenue sources. Helms [1985] finds that taxes used to finance transfers reduce state incomes, but the net effect of tax-financed spending in other areas may be positive.

We include seven broad measures of fiscal policy in the EBA: Total Revenue Share of Personal Income; Tax Revenue Share of Personal Income; Total Revenue Per Capita; Tax Revenue Per Capita; Expenditure Share of Personal Income; Expenditure Per Capita; and the Government Share of GSP. Although the public finance literature offers evidence that particular tax and expenditure policies matter, we evaluate broad measures of fiscal balance for two reasons. First, as a practical matter this approach offers guidance to researchers primarily interested in non-fiscal variables, and who simply want a reasonable set of control variables. Second, introducing narrow fiscal variables such as the state income tax or state spending on welfare invites an endogeneity problem. For example, the demographic or economic composition of a state may influence the tax structure.(16) Finally, the analysis informs the empirical question of whether alternative measurements of fiscal policy affect the results. For instance, do the results change if measures of revenue include all sources of revenue or only tax revenue?(17) Does it matter if we denominate taxes as a share of personal income, or in per capita terms?

Six of the seven fiscal policy variables evaluated exhibit robust results; only Expenditure Per Capita proves fragile.(18) We find that using total revenue versus tax revenue affects the results. The signs of the estimated coefficients are consistent, but the magnitudes (even after accounting for different means) yield different implications for the marginal effect of revenue changes.

More importantly, we find that the signs of the coefficients on the robust fiscal policy variables generally depend on whether such variables (expenditures, total revenue, or tax revenue) are measured in per capita terms or as a share of the state's economy. The estimated coefficients exhibit positive signs for Total Revenue Per Capita and Tax Revenue Per Capita. The estimated coefficients exhibit negative signs for Total Revenue Share of Personal Income, Tax Revenue Share of Personal Income, Expenditure Share of Personal Income, and the Government Share of GSP. Here the opposite signs highlight an underlying source of difficulty in evaluating the results from different areas of fiscal policy research. For instance, studies estimating the relationship between state fiscal policies and economic performance typically measure the size of government as a share of the economy.(19) Alternatively, studies of the determinants of public sector growth typically measure the size of government in per capita terms.(20)

Public and Private Capital

A flurry of studies investigating the impact of public and private capital on state economic output appeared in the 1990s. The conventional approach estimates a state-level production function, regressing output against public capital, private capital, labor, and other conditioning variables such as the unemployment rate.(21) The extensive efforts by Munnell [1990] and Holtz-Eakin [1993] to assemble previously unavailable state-level measures of capital stocks represent a valuable by-product of this research program.

In their cross-country sensitivity analysis Levine and Renelt find investment as a share of GDP to be the most important factor in explaining variations in long-run growth rates. We evaluate this result at the state level using the variables produced by Munnell and Holtz-Eakin. As noted above, these data series end in 1987, as opposed to 1992 for the other variables analyzed in this study.(22)

We evaluate five variables created from the capital stock data, each lagged one period. Of course, first-differencing the capital stock measures generates variables that reflect investment rates, comparable to the investment measure examined by Levine and Renelt. The EBA identifies these five variables as robust, although the estimated coefficients are opposite of the expected sign. The confounding state results suggest that updating the Munnell and Holtz-Eakin data series would not enhance growth rate regressions employing panel data. Levine and Renelt conclude investment rates are key components of growth models, but their analysis focuses on long-term growth rates. This analysis of short-term responses and business cycles in the state economies finds nothing comparable.

Cultural/Ethnic Characteristics

In addition to the age and education controls in our core model, we include three demographic variables in the analysis intended to capture cultural and ethnic differences across states: Religious Affiliation Diversity; Church Membership; and the Black Population Share.(23) Of the subset of econometric studies evaluating the relationship between economic performance and fiscal policy, Mofidi and Stone [1990] are the only researchers controlling for a state's demographic characteristics. Mofidi and Stone find a negative coefficient on the percent of population that is nonwhite. We find a positive, but insignificant coefficient on the percent of the population that is black, and overall this variable is fragile.(24) The other cultural and ethnic characteristics variables also produce fragile results. These findings indicate neglecting cultural and ethnic differences does not appear to bias existing studies.

Public Choice Variables

The variables in this section draw from concepts addressed in studies of state growth but with foundations in the public choice literature. They generally proxy factors that affect government structure and the performance of public policy, forces that in turn affect individual and firm location decisions. These factors include agglomeration economies, availability of public services, government influence, and market access.(25) Studies employing cross-state regressions commonly control for population density: Plaut and Pluta [1983], Smith and Smith [1984], Helms [1985] and Garand [1988]. As Garand [1988] points out, population density may affect government performance through its relationship to the demand for public services. We evaluate Population Density in the EBA and four other Public Choice Variables: Local Share of Government Tax Revenue; Urbanization; Interstate Commuting; and Owner-Occupied Housing. While Population Density or Urbanization appear in a number of econometric studies, three of the five measures included under the Public Choice category are not widely used in the state growth literature (Local Share of Government Tax Revenue, Interstate Commuting, and Owner- Occupied Housing), warranting a brief discussion of their potential impact on growth. These three measures each relate to factors that may restrain, or at least influence, state and local government policy and may ultimately affect the availability or cost of public services. As the empirical public finance literature suggests, these measures also may affect growth if they affect the tax structure adopted by a state. For instance, local governments rely more heavily than state governments on property taxes, which we control for with the variable Local Share of Government Tax Revenue.26 The Interstate Commuting variable may be tied to growth because a state with a high percentage of its workers crossing state boundaries suggests residents have jurisdictional choices available to them. The state government may be more constrained in fiscal-policy decisions and may be more likely to implement policy consistent with constituent preferences. In many areas, labor market participants must jointly make residential and labor market mobility decisions. In areas conducive to interstate commuting, individuals may choose to work in high wage, high tax areas, but live in low wage, low tax areas.(27) Finally, as discussed by Bartik [1991] the effect of development policies on households partially depends on whether they are renters or owners, which we control for with the Owner-Occupied Housing variable.

The EBA identifies only Local Share of Government Tax Revenue as robust. The estimated negative relationship indicates that a decline in local government relative to state government tax revenues facilitates economic growth. Further research is required to determine whether this result derives from the resulting tax structure, factors relating to inter-jurisdictional competition, or some other factor.

Pressure Groups

George Stigler's seminal [1971] article that framed economic regulation in an interest group perspective inspired a large empirical literature on the effects of political pressure groups on economic development. Olson [1982] initiated the use of American state data to test the interest group theory, followed by a host of studies that both support and refute the thesis that pressure groups significantly affect growth.(28) Becker's [1983] theoretical elaboration of the pressure group framework mediates these opposing empirical results. While each pressure group may seek efficiency-reducing policies, competition among multiple pressure groups drives the policy process toward outcomes that minimize excess burden.

We evaluate four measures of pressure group activity: Business Association Revenue Share of Personal Income; Business Association Revenue Per Capita; Number of Business Associations; and Union Membership.(29) The EBA finds the Business Association Revenue Share of Personal Income and Business Association Revenue Per Capita variables robust, but the Number of Business Associations and Union Membership variables fragile. As with the fiscal policy variables, we find that the signs of the coefficients on the robust measures of interest group activity depend on the measurement method. The per capita variable exhibits a positive sign consistent with Becker's hypothesis, whereas the share of personal income variable exhibits a negative sign in support of the Stigler-Olson hypothesis.(30) In short, empirical conclusions concerning the impact of pressure groups on state economic performance appear quite sensitive to variable measurement.

Energy Prices

Many researchers explore the thesis that sunbelt and frostbelt states exhibit different growth paths, primarily because of differences in energy and labor costs; these include Plaut and Pluta [1983] and Wasylenko and McGuire [1985]. Although the two temperature variables we considered could not be used because they lacked time-series variation (see footnote 5), we examine one variable that controls for differences in energy prices across states. The EBA identified Real Energy Prices as fragile. The estimated coefficient is insignificantly different from zero, and it switches signs at the extreme bounds.

IV. ROBUST REGRESSION MODELS RECOMMENDED FOR FUTURE RESEARCH

Table II seeks to consolidate and refine the results from the sensitivity analysis into a format useful for future empirical research. Table II includes only the core variables and select "robust" variables as determined by the extreme bounds analysis. We sift the robust variables and nominate five model specifications for reasons described below.

First, for categories yielding more than one robust variable, we allot these robust variables into separate model specifications; for example Models 1, 3, and 5 contain Industry Diversity and Models 2 and 4 contain Service Share of GSP. The exception is the Fiscal Policy group from which we include revenue and expenditure variables within a single specification (Model 3).(31) Second, from the Fiscal Policy and Pressure Groups categories Table II extracts only the robust variables denominated as a share of the state's economy; we pan the robust variables from these categories denominated in per capita terms. We base this choice on the principle that the share-denominated variables reflect the economically relevant allocation of resources more appropriately than the population-denominated variables.(32) Likewise Table II extracts from the Pressure Group category one of the variables measured in relation to a state's economy; Business Association Revenue Share of Personal Income is included in Models 4 and 5. A conceptual principle stands behind this choice. Growth implications derive from the relative allocation of private sector resources within a state between redistributive versus productive activities. Finally, the recommended models in Table II adopt the "Total Revenue Share of Income" variable instead of the related "Tax Revenue Share of Income" [TABULAR DATA FOR TABLE II OMITTED] variable. The EBA results in Table I indicate that the marginal effect of total revenue shares exceed the marginal effect of tax revenue shares; in other words, changes in non-tax revenue sources as well as changes in taxes affect economic growth.(33)

The overall explanatory power of the models in Table II ranges from 0.469 to 0.622. By comparison, the core cross-country model of long run growth identified by Levine and Renelt [1992] yields an R-square of 0.46. In the five recommended models the estimated coefficients of the variables evaluated in the EBA retain the sign, significance and magnitude that one would expect from the sensitivity analysis on the variables individually. Of the core variables, Share of the Population with a BA or Better retains a positive sign in four of the five models, but is not significant. The other core variable, Share of the Population Ages 18-64, remains positive and significant.

Finally, we note that these models rely on a common intercept term for each cross-section. As discussed by Bartik [1991] this restriction may attribute to one of the included variables an effect deriving from an omitted variable. To test for an omitted variable bias, we re-estimate the models with state fixed effects. We then evaluate the coefficients in the restricted and unrestricted models to determine [TABULAR DATA FOR TABLE III OMITTED] whether the change in model specification changes the explanatory power of the variables found to be robust in the EBA. As shown in Table III, Wald tests restricting the coefficients in the fixed effects models to the coefficients in the common intercept models generally fail to reject the null hypothesis that the coefficients are the same. The common intercept restriction does not appear to bias the results.34

V. CONCLUSION

The 1992 watershed study by Levine and Renelt inventoried cross-country growth regressions and provided an important baseline for subsequent empirical research. This paper emulates their purpose and approach, drawing on the voluminous literature that estimates growth equations using panel data for the American states. Like Levine and Renelt we discover that many commonly used control variables are fragile to small changes in model specification. We also find that the sign of the estimated coefficient for critical variables depends on how a variable is transformed, for example whether state government revenue or political pressure groups are denominated in per capita terms or as a share of state income. This helps to explain the array of incongruent results in the literature.

The extreme bounds sensitivity analysis provides a starting point for future research that relies on panel data and state growth regressions. We identify robust control variables including proxies for industrial composition, fiscal policy, the relative cost of state versus local government services, and pressure group activity. Limitations of the analysis merit recognition, however. Identifying robust correlations with growth does not necessarily imply an interpretable or important economic relationship; issues such as causality and coefficient size remain. Further, a fragile correlation does not automatically imply an unimportant economic relationship; rather the variation among two control variables may simply be too close to identify an independent link with growth. Extreme bounds analysis furnishes a useful guide for analysis, but it alone does not define what is a valuable result.

[TABULAR DATA FOR APPENDIX TABLE A1 OMITTED]

[TABULAR DATA FOR APPENDIX TABLE A2 OMITTED]

ABBREVIATIONS

EBA: Extreme-Bonds Analysis

GSP: Gross State Product

MRA: Meta Regression Analysis

We are grateful to Bob Tollison, Tom Saving, Nicole Crain and an anonymous referee for helpful comments and to the Center for Study of Public Choice for financial support.

1. Its large number of citations indicates the influence of the work by Levine and Renelt [1992]. Like Levine and Renelt we do not estimate a structural model, establish causal links, identify growth determinants, or conduct other analyses discussed in Leamer [1985] and McAleer et al. [1985]. Rather we examine whether estimated relationships are robust or fragile to small changes in model specification.

2. Some studies use Gross State Product (GSP) or state employment to measure economic performance. The simple correlation coefficient between real per capita personal income and real per capita GSP is 0.80; the correlation coefficient between real per capita personal income and employment is 0.63. Note that these correlations reflect logged, first-differenced transformations of the variables for the period 1977-1992. Although GSP and personal income tend to exhibit similar trends, these alternative measures of economic performance differ in important ways. For instance GSP includes allowances for depreciation and indirect business taxes. The preferred measure to use depends on the particular question being evaluated.

3. We follow the procedure in Levine and Renelt [1992] and use a small set of core variables (they also include a country investment variable, reflecting the long-run growth model underlying their analysis). Unlike many growth studies we do not include the initial level of income as an independent variable. The validity of using lagged values of the level of income has received considerable attention in models that test the convergence hypothesis (e.g., Friedman [1992], Quah [1993], Hart [1995], and Barro [1996]). This debate notwithstanding, our model considers annual observations on performance, and does not address the convergence hypothesis.

4. We note that a related measure of educational attainment - the high school graduate share of a state's population - exhibits little variation across the American states, and in a preliminary estimation (not reported in the text) it did not perform as well as the population share with a bachelor's degree. Another sometimes-used variable, engineering degrees, is not readily available for our entire sample period. We also do not include a wage variable in the analysis despite its use by some researchers because of an endogeneity problem: the influence of growth on wages. The core model includes two variables that affect labor market conditions and thus wage costs. We also examine union membership, another commonly-used proxy for labor costs, as an M variable.

5. Beyond the 29 M variables described in the Appendix we discarded three other M variables prior to the EBA analysis: Miles of Common Border, Average Temperature, and Average Deviation from the Average Temperature. These variables do not exhibit time-series variation, and regression models including these variables as panel data fail to yield non-singular matrices.

6. We consider only statistically significant equations to identify the upper and lower bounds of [[Beta].sub.m].

7. The univariate analysis regressed Y against each M variable and a constant term. We identified one variable from each of the general categories based on an overall assessment of three criteria: the regression R-square, the significance of the estimated coefficient, and the Durbin-Watson statistic.

8. We do not include a representative variable from the Public and Private Capital group in the set of Z variables because these data only spanned two-thirds of the sample period available for the other variables.

9. For example, in the EBA for the variable "Manufacturing Share of GSP," we exclude the Industry Diversity variable from the subset of Z variables. Both variables proxy a state's Industrial composition.

10. A notable exception is the Helms study [1985] that specifies the level of real personal income as the dependent variable. Many of the studies examining the productivity of public capital such as Aschauer [1989a] and Munnell [1990] also use levels (GDP) as the dependent variable. These studies have been criticized, for example by Tatom [1991], for failing to correct for nonstationarity.

11. Performing the analysis with state fixed effects generates similar results. This is not surprising because first-differencing and fixed effects offer alternative techniques to control for problems caused by omitted variables. (Bartik [1994] and Phillips and Goss [1995] reach this same conclusion.) We rely on a common intercept for the EBA as way to attribute as much explanatory power as possible to the variable of interest. We then evaluate whether our final model specifications based on the EBA results suffer from omitted variable bias. Section 4 describes the method and results of this test. The non-fixed effects models provide an additional benefit: sometimes researchers have limited time series data on a particular variable of interest, which renders fixed effects models infeasible.

12. We reiterate that all variables enter the regression analysis as logged first-differences.

13. The Industry Diversity variable is calculated as the sum of the squared share of private, non- farm GSP originating in eight industries: agricultural services; mining; construction; manufacturing; transportation and utilities; wholesale and retail trade; finance, insurance, and real estate; and services.

14. This measure of industrial diversity does not assess the effect of competition within particular industries. The degree of competition represents a different dimension as described in Glaeser, et al. [1992].

15. Bartik [1991; 1994], Phillips and Goss [1995], and Wasylenko [1997] survey most of this literature.

16. The Public Choice Variables group tangentially addresses the effects of alternative tax and expenditure policies. Several variables in that group intend to capture factors that may influence government policy choices.

17. In 1993 tax revenue accounted for 47% of total revenue on average across states, and ranged from 35% to 59%. Intergovernmental transfers in the form of federal grants account for most of the non-tax portion of state revenue.

18. We enter the fiscal policy variables contemporaneously, although lagging these variables made no difference in the signs of the estimated coefficients. In an effort to keep the number of reported specifications to a manageable level, we simply report the contemporaneous models. At first blush, contemporaneous fiscal policy indicators may seem unreasonable. However, note that the enactment of fiscal policy legislation typically precedes implementation by six to 12 months. For instance, tax legislation in Virginia that becomes law in, say, January of 1999 would typically affect the 2000 Fiscal Year, beginning in July of 1999 and ending in June 2000, and subsequent years because tax policy changes are often phased-in. The state government finance statistics produced by the U.S. Bureau of the Census relate to fiscal years, typically beginning in July.

19. An exception is the state growth study by Dye [1980] that includes taxes as a percentage of personal income, but expenditures in per capita terms.

20. For example, Abrams and Dougan [1986] and Shadbegian [1996] evaluate the effects of constitutional constraints on per capita expenditures.

21. The seminal, if controversial work by David Aschauer [1989a and 1989b] surely spurred research using state level data. Aschauer estimates a high marginal product of public capital relative to private capital using aggregate U.S. data. Morrison and Schwartz [1996] recently employ a cost function approach. For comprehensive literature surveys see Munnell [1992] and Gramlich [1994].

22. We are grateful to Alicia Munnell and Douglas Holtz-Eakin for making their data available. One motivation for evaluating the robustness of the capital stock data is to assess the usefulness of updating the Munnell and Holtz-Eakin data series, no small task.

23. The Religious Affiliation Diversity variable is calculated as the sum of the squared share of total adherents comprising four broad denominations: Baptists, Catholics, Methodists, and all others.

Barro [1996] investigates the impact of religion on political freedom and economic growth using cross-country regressions. His estimated coefficients show weak results, but Barro argues that religious creeds carry indirect effects (e.g., religious tenets affect female schooling that in turn affects growth and political freedom).

24. The conflicting signs with Modifi and Stone [1990] may result from our inclusion of an education variable in the core model.

25. Schmenner, Huber and Cook [1987] broadly characterize similar factors as relating to the "attractiveness of the state."

26. Local Share of Government Tax Revenue also may proxy the independence of localities relative to the state or the degree of fiscal centralization within a state. If factor mobility within a state exceeds factor mobility between states, a state with less centralized decision-making may offer attractive alternatives to individuals and firms. A higher Local Share of Government Tax Revenue also may be correlated with more intergovernmental competition.

27. Additionally, states with a higher value for Interstate Commuting may rely more heavily on sales taxes as a mechanism to export the tax burden to non-residents.

28. Conceptually, the Stigler-Olson thesis states that interest groups move the policy process toward unproductive, redistributional outcomes at the expense of market-driven activities that promote efficiency and lower prices. For examples of the empirical studies, see Mueller and Murrell [1986], Gray and Lowery [1988], and the survey articles by Tollison [1988] and Mitchell and Munger [1991].

29. A variable controlling for union membership appears in many state growth regression models, for example, in Dye [1980], Newman [1983], and Helms [1985]. We use this variable as a measure of pressure group activity, but some researchers use union membership as a proxy for labor costs. In this context, we alternatively categorized Union Membership as an Industrial Composition variable or a Public Choice variable in results not reported in the text. The results of the EBA did not change when we re-categorized the Union Membership variable; Union Membership proves fragile regardless of its categorization.

30. The positive signs on the per capita interest group measures are consistent with Becker's hypothesis that competition among pressure groups minimizes inefficient policy outcomes, but do not validate his hypothesis. These measures reflect only a crude proxy for the degree of pressure group competition.

31. Helms [1985] pioneered this approach in state growth regressions using panel data, stressing the relevance of both taxes and the expenditures financed by these taxes.

32. A simple case illustrates. Government revenue per capita in Massachusetts exceeds government revenue per capita in Michigan. At the same time, state government revenues absorb a smaller share of state income in Massachusetts than in Michigan. The extent to which the public sector exercises control over a state's resources is thus greater in Michigan than in Massachusetts, although the per capita revenue variables would suggest otherwise. Recall that the EBA results in Table I show opposite signs on the fiscal policy coefficients depending on how the variables are measured, rendering this choice a non-trivial decision.

33. This finding supports Vedder's [1982] hypothesis that the methods of distributing intergovernmental transfers affect states' policy decisions. For example, federal intergovernmental transfer programs may encourage states to adopt growth-retarding revenue policies.

34. The Wald test on the Pressure Groups variable rejects the null hypothesis that the estimated coefficient suffers from omitted variable bias, but the results are opposite of what would be expected if the common coefficient restriction were attributing to pressure groups an effect deriving from another source. The estimated coefficient in the unrestricted model retains a negative and significant coefficient, but the effect of pressure groups in the unrestricted model exceeds the effect in the restricted model. This finding offers reassurance that the estimated negative relationship between Pressure Groups and Personal Income growth is not spurious.

REFERENCES

Abrams, Burton A., and William R. Dougan. "The Effects of Constitutional Restraints on Government Spending." Public Choice, 49(2), 1986, 101-6.

Aschauer, David A. "Is Public Expenditure Productive?" Journal of Monetary Economics, March 1989a, 177-200.

-----. "Does Public Capital Crowd Out Private Capital?" Journal of Monetary Economics, September 1989b, 171-88.

Barro, Robert J. "Determinants of Economic Growth: A Cross-Country Empirical Study." National Bureau of Economic Research Working Paper No. 5698, 1996.

Bartik, Timothy J. Who Benefits from State and Local Economic Development Policies? Kalamazoo, Michigan: W. E. Upjohn Institute for Employment Research, 1991.

-----. "Jobs, Productivity, and Local Economic Development: What Does Economic Research Have for the Role of Government?" National Tax Journal, December 1994, 847-61.

Becker, Gary S. "A Theory of Competition Among Pressure Groups for Political Influence." Quarterly Journal of Economics, August 1983, 371-400.

Dye, Thomas R. "Taxing, Spending, and Economic Growth in the American States." Journal of Politics, November 1980, 1,085-107.

Friedman, Milton. "Do Old Fallacies Ever Die?" Journal of Economic Literature, December 1992, 2, 129-32.

Garand, James C. "Explaining Government Growth in the U.S. States." American Political Science Review, September 1988, 837-49.

Glaeser, Edward L., Hedi D. Kallal, Jose A. Scheinkman, and Andrei Shleifer. "Growth in Cities." Journal of Political Economy, December 1992, 1,126-52.

Gramlich, Edward. "Infrastructure Investment: A Review Essay." Journal of Economic Literature, September 1994, 1,176-96.

Gray, Virginia, and David Lowery. "Interest Group Politics and Economic Growth in the American States." American Political Science Review, March 1988, 109-31.

Hart, Peter E. "Galtonian Regression Across Countries and the Convergence of Productivity." Oxford Bulletin of Economics and Statistics, August 1995, 287-93.

Helms, L. Jay. "The Effect of State and Local Taxes On Economic Growth: A Time Series-Cross Section Approach." Review of Economics and Statistics, November 1985, 574-82.

Holtz-Eakin, Douglas. "State-Specific Estimates of State and Local Government Capital." Regional Science and Urban Economics, April 1993, 185-209.

Leamer, Edward E. "Let's Take the Con Out of Econometrics." American Economic Review, March 1983, 31-43.

-----. "Sensitivity Analyses Would Help." American Economic Review, June 1985, 308-13.

Levine, Ross, and David Renelt. "A Sensitivity Analysis of Cross-Country Growth Regressions." American Economic Review, September 1992, 942-63.

McAleer, Michael, Adrian Pagan, and Paul A. Volker. "What Will Take the Con Out of Econometrics?" American Economic Review, June 1985, 293-307.

Maitland, Ian. "Interest Groups and Economic Growth Rates." Journal of Politics, February 1985, 44-58.

Mitchell, William, and Michael Munger. "Economic Models of Interest Groups: An Introductory Survey." American Journal of Political Science, May 1991, 512-46.

Mofidi, Alaeddin, and Joe A. Stone. "Do State and Local Taxes Affect Economic Growth?" Review of Economics and Statistics, November 1990, 686-91.

Morrison, Catherine J., and Amy Ellen Schwartz. "State Infrastructure and Productive Performance." American Economic Review, December 1996, 1,095-111.

Mueller, Dennis C., and Peter Murrell. "Interest Groups and the Size of Government." Public Choice, 48(2), 1986, 125-45.

Munnell, Alicia H. "How Does Public Infrastructure Affect Regional Economic Performance?" New England Economic Review, September/October 1990, 11-32.

-----. "Infrastructure Investment and Economic Growth." Journal of Economic Perspectives, Fall 1992, 189-98.

Newman, Robert J. "Industry Migration and Growth in the South." Review of Economics and Statistics, February 1983, 76-86.

Olson, Mancur. The Rise and Decline of Nations: Economic Growth, Stagflation, and Social Rigidities. New Haven, Conn.: Yale University Press, 1982.

Phillips, Joseph M., and Ernest P. Goss. "The Effect of State and Local Taxes on Economic Development: A Meta-Analysis." Southern Economic Journal, October 1995, 320-33.

Plaut, Thomas R., and Joseph E. Pluta. "Business Climate, Taxes and Expenditures, and State Industrial Growth in the U.S." Southern Economic Journal, July 1983, 99-119.

Quah, Danny. "Galton's Fallacy and Tests of the Convergence Hypothesis." Scandinavian Journal of Economics, December 1993, 427-43.

Romans, Thomas, and Ganti Subrahmanyam. "State and Local Taxes, Transfers, and Regional Economic Growth." Southern Economic Journal, October 1979, 435-44.

Schmenner, Roger W., Joel C. Huber, and Randall L. Cook. "Geographic Differences and the Location of New Manufacturing Facilities." Journal of Urban Economics, January 1987, 83-104.

Shadbegian, Ronald J. "Do Tax and Expenditure Limitations Affect the Size and Growth of State Government?" Contemporary Economic Policy, January 1996, 22-35.

Smith, Janet K., and Richard L. Smith II. "State and Local Fiscal Policy: Implications for Property Values and Economic Growth." Public Finance Quarterly, January 1984, 51-76.

Stigler, George J. "The Theory of Economic Regulation." Bell Journal of Economics and Management Science, Spring 1971, 1-21.

Tatom, John A. "Public Capital and Private Sector Performance." Federal Reserve Bank of St. Louis Review, May/June 1991, 3-15.

Tollison, Robert D. "Public Choice and Legislation." Virginia Law Review, March 1988, 339-71.

Vedder, Richard K. "Rich States, Poor States: How High Taxes Inhibit Growth." Journal of Contemporary Studies, Fall 1982, 19-32.

Wasylenko, Michael. "Taxation and Economic Development: The State of the Economic Literature." New England Economic Review, March/April 1997, 37-52.

Wasylenko, Michael, and Therese McGuire. "Jobs and Taxes: The Effect of Business Climate on States' Employment Growth Rates." National Tax Journal, December 1985, 497-511.