A MATCHED PAIRS ANALYSIS OF STATE GROWTH DIFFERENCES

I. INTRODUCTION The American states have been and continue to be a useful laboratory for testing influences on economic growth, including convergence, physical capital, human capital, and a variety of policy variables. Routinely, all 50 states or regional subsets of them are grouped together, and regression analysis is performed to estimate parameters of the models. Implicitly, this practice generates coefficients by comparing states with widely divergent populations such as California and Wyoming, widely divergent incomes such as Connecticut and Mississippi, widely divergent historical and cultural backgrounds such as Pennsylvania and Utah, and states with other extreme differences. Although these regressions take into account a variety of "control" variables, they omit or use proxy measures of important, long-run differences between the states. Regional subsamples or regional dummy variables are used as a means to "soak up" some of the variability because of these omitted factors. In this article, we offer an alternative methodology to estimate state growth models by using matched pairs based on common geographic characteristics. The intuition behind matching is straightforward. Matching of birth twins, for example, can eliminate or reduce genetic differences as a source of variation so that other factors can be isolated and estimated with greater accuracy. Although matching can be used, and may be most frequently considered, as a pre-treatment experimental design method, it has also been developed as a post-treatment method. (1) Although the method is not a panacea to cure all observational study problems, under certain conditions, the post-treatment matching imitates the results of randomizing treatments among observations. Statistical investigators in a variety of disciplines--including economics, finance, statistics, psychology, and biomedicine--have made use of post-treatment matched pairs to improve estimates. In economics, the methods have been used where the observational units ranged from individual employees or borrowers to financial institutions and the subjects studied ranged from bank problems to risk, wage rates, and firm size. (2) Although the theoretical links have not been worked out, creating subsamples of data based on common socio-demographic characteristics is a closely related method that has been shown to improve estimates. For example, Barro and Sala-i-Martin (1991, 1992) show that while the Solow growth model's prediction of convergence in growth rates does not hold for a large sample of countries, it does hold for a reduced sample containing only OECD countries. The practice of reducing samples based on Chow test's rejecting coefficient equality is closely related to ex post matching methods because the objective, as in pairwise matching, is to better align the sample to the underlying process generating outcomes. In spite of the growing use of matching methods in statistical studies in economics, their use at a state level of analysis has largely been limited to time series studies of a particular pair of states or small groupings of states. (3) The U.S. states provide an attractive basis for matching. State-based, pairwise matches compare observational units generated, at least in part, by similar underlying processes, doing so on the front end of the estimation process using similar characteristics of the data rather than on the back end of the estimation process (as with a Chow-type sample partitioning method). State matching pairs states that share important similarities and, therefore, can implicitly eliminate differences that are difficult to measure, in particular, we pair states by location, and these pairs also capture historical, political, climatic, topographic, and transportation similarities. Many states share similar geographic and historical backgrounds and trails. For example, Kentucky and Tennessee or Arizona and New Mexico provide specific examples of states that are near ^twins'' when viewed from a long-run historical, political, and geographic perspective. …