Economic Growth Regressions for the American States: A Sensitivity Analysis
Crain, W. Mark, Lee, Katherine J., Economic Inquiry
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  and Phillips and Goss  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  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. …