Political Analysis Advance Access published online on June 24, 2009
Political Analysis, doi:10.1093/pan/mpp009
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Dealing with Weak Instruments: An Application to the Protection for Sale Model
Bush School of Government and Public Service, Texas A&M University, College Station, TX 77843-4220 e-mail: kgawande{at}tamu.edu (corresponding author)
Department of Economics, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920 e-mail: hli{at}eiu.edu
Endogeneity of explanatory variables is now receiving the concern it deserves in the empirical political science literature. Instrumental variables (IVs) estimators, such as two-stage least squares (2SLS), are the primary means for tackling this problem. These estimators solve the endogeneity problem by "instrumenting" the endogenous regressors using exogenous variables (the instruments). In many applications, a problem that the IV approach must overcome is that of weak instruments (WIs), where the instruments only weakly identify the regression coefficients of interest. With WIs, the infinite-sample properties (e.g., consistency) used to justify the use of estimators like 2SLS are on thin ground because these estimators have poor small-sample properties. Specifically, they may suffer from excessive bias and/or Type I error. We highlight the WI problem in the context of empirical testing of "protection for sale" model that predicts the cross-sectional pattern of trade protection as a function of political organization, imports and output. These variables are endogenous. Importantly, the instruments used to solve the endogeneity problem are weak. A method better suited to exact inference with WIs is the limited information maximum likelihood (LIML) estimator. Censoring in the dependent variable in the application requires a nonlinear Tobit LIML estimator.
Author's note: We thank two anonymous referees, the editor (Christopher Zorn), and an associate editor (Robert Franzese) for insightful comments that have improved the paper. Responsibility for any remaining errors is ours. Kishore Gawande acknowledges financial support from the Helen and Roy Ryu Chair at the Bush School. Data set and programs are available on the POLMETH Web site.