BAYESIAN INFERENCE FOR COMPARATIVE RESEARCH

RV egression analysis in comparative research suffers from two distinct problems of statistical inference. First, because the data constitute all the available observations from a population, conventional inference based on the long-run behavior of a repeatable data mechanism is not appropriate. Second, the small and collinear data sets of comparative research yield imprecise estimates of the effects of explanatory variables. We describe a Bayesian approach to statistical inference that provides a unified solution to these two problems. This approach is illustrated in a comparative analysis of unionization. A widely used tool in quantitative comparative politics is the linear regression model, estimating relationships between institutional and economic variables observed for a set of countries constituting some population of interest. A brief survey of recent comparative research finds no shortage of work of this type. For instance, Remmer (1991) identifies economic crisis as a source of electoral volatility in Latin American countries in the 1980s; Robertson (1990) presents evidence that institutions moderating the transaction costs of negotiations between capital and labor reduce industrial conflict; and Golden (1993) finds that union wage moderation in industrialized democracies results from coordinated collective bargaining. Although the methodological advantages are well documented (Jackman 1985), we identify two distinct problems of statistical inference endemic to this type of quantitative comparative research. First, because the data constitute all the available observations from a population, conventional inference based on the long-run behavior of some repeatable data mechanism is not appropriate. Second, because data sets tend to be small and collinear, the effects of explanatory variables are estimated imprecisely. In most applications the first problem is generally ignored and the second is solved by imposing restrictions on the regression model to obtain "sensible" results. The Bayesian model of statistical inference provides a unified solution to these two distinct problems of quantitative comparative research. Two features of Bayesian inference are important in this context. First, probability is conceived subjectively as characterizing a researcher's uncertainty about the parameters of a statistical model. This subjective probability concept seems particularly useful in comparative settings, where the data are typically convenience samples not generated by a known probability mechanism such as random sampling. Second, Bayesian inference allows the inclusion of other information, in addition to the quantitative sample information. Again, this seems useful in the comparative context where rich historical material is commonly available, sparking ideas for researchers, but formally discarded in the final analysis. In the Bayesian approach, this historical material can be formally incorporated into the analysis. We begin by detailing why the nonstochastic and weak data typical of comparative research are problematic for conventional linear regression analysis. We next introduce some ideas about Bayesian inference and describe Bayesian regression analysis. These ideas are applied to a comparative analysis of unionization-the subject of a recent exchange in the American Political Science Review between Michael Wallerstein and John Stephens (Stephens and Wallerstein 1991; Wallerstein 1989). The Bayesian regressions we present are supplemented with a sensitivity analysis that investigates how our conclusions depend upon the sample data and our prior beliefs. Although we survey some ideas in Bayesian statistics, a full introduction to the Bayesian approach to statistical inference is beyond our scope here. (Good book-length treatments are Pollard 1986, Lee 1989 and, at a slightly higher level, Press 1989.) Our intention here is to spotlight problematic but ignored issues of statistical inference in a common area of application. The Bayesian alternative that we present represents just one way forward to address these inferential problems.