Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-11T21:44:40.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Dealing with Weak Instruments: An Application to the Protection for Sale Model

Published online by Cambridge University Press:  04 January 2017

Kishore Gawande  and
Hui Li
Kishore Gawande*
Affiliation:
Bush School of Government and Public Service, Texas A&M University, College Station, TX 77843-4220
Hui Li
Affiliation:
Department of Economics, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920. e-mail: hli@eiu.edu
*
e-mail: kgawande@tamu.edu (corresponding author)
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Political Analysis , Volume 17 , Issue 3 , Summer 2009 , pp. 236 - 260
Copyright
Copyright © The Author 2009. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Authors' 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.

References

Acemoglu, Daron, Johnson, Simon, Robinson, James A., and Yared, Pierre. 2008. Income and democracy. American Economic Review 98: 808–42.Google Scholar
Anderson, T. W., Kunitomo, N., and Sawa, T. 1982. Evaluation of the distribution function of the limited information maximum likelihood estimator. Econometrica 50: 1009–27.CrossRefGoogle Scholar
Anderson, T. W., and Rubin, H. 1949. Estimators of the parameters of a single equation in a complete set of stochastic equations. The Annals of Mathematical Statistics 21: 570–82.Google Scholar
Anderson, T. W., and Sawa, T. 1979. Evaluation of the distribution function of the two-stage least squares estimate. Econometrica 47: 163–82.Google Scholar
Angrist, Joshua D., and Krueger, Alan B. 1991. Does compulsory school attendance affect schooling and earnings. Quarterly Journal of Economics 106: 979–1014.CrossRefGoogle Scholar
Baldwin, Robert. 1985. The political economy of US import policy. Cambridge, MA: MIT Press.Google Scholar
Bartels, Larry M. 1991. Instrumental and ‘quasi-instrumental’ variables. American Journal of Political Science 35: 777–800.Google Scholar
Bawn, Kathleen, and Rosenbluth, Frances. 2006. Short versus long coalitions: Electoral accountability and the size of the public sector. American Journal of Political Science 50: 251–65.Google Scholar
Beaulieu, Eugene, and Magee, Chris. 2004. Campaign contributions and trade policy: New tests of Stolper-Samuelson. Economics and Politics 16: 163–87.Google Scholar
Bombardini, Matilde. 2008. Firm heterogeneity and lobby participation. Journal of International Economics 75: 329–48.Google Scholar
Bound, J., Jaeger, D. A., and Baker, R. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variables is weak. Journal of the American Statistical Association 90: 443–50.Google Scholar
Calvo, Ernesto, and Murillo, Maria V. 2004. Who delivers? Partisan clients in the Argentine electoral market. American Journal of Political Science 48: 742–57.Google Scholar
de Melo, Jaime, and Tarr, David. 1990. Welfare costs of U.S. quotas in textiles, steel and autos. Review of Economics and Statistics 489–97.Google Scholar
Eicher, Theo, and Osang, Thomas. 2002. Protection for sale: An empirical investigation: Comment. American Economic Review 92: 1702–10.Google Scholar
Facchini, Giovanni, Van Biesebroeck, Johannes, and Willmann, Gerald. 2003. Protection for sale with imperfect rent capturing. University of Kiel Economics Working Paper.Google Scholar
Feenstra, Robert, and Branstetter, Lee. 2002. Trade and foreign direct investment in China: A political economy approach. Journal of International Economics 58: 335–58.Google Scholar
Fuller, Wayne A. 1986. Measurement error models. New York: John Wiley.Google Scholar
Gabel, Matthew, and Scheve, Kenneth. 2007. Estimating the effect of elite communications on public opinion using instrumental variables. American Journal of Political Science 51: 1013–28.Google Scholar
Gallaway, Michael P., McDaniel, Christine A., and Rivera, Sandra A. 2003. Short-run and long-run industry-level estimates of U.S. Armington elasticities. North American Journal of Economics and Finance 14: 49–68.CrossRefGoogle Scholar
Gao, Chuanming, and Lahiri, Kajal. 2000. Further consequences of viewing LIML as an iterated Aitken estimator. Journal of Econometrics 98: 187–202.CrossRefGoogle Scholar
Gawandem, Kishore, and Hoekman, Bernard. 2006. Lobbying and agricultural policy in the United States. International Organization 2006: 527–61.Google Scholar
Gawande, Kishore, and Krishna, Pravin. 2003. The political economy of trade policy: Empirical approaches. In Handbook of international trade, eds. Harrigan, J. and Kwan Choi, E. Oxford: Blackwell Publishers.Google Scholar
Gawande, Kishore, and Bandyopadhyay, Usree. 2000. Is protection for sale? A test of the Grossman-Helpman theory of endogenous protection. Review of Economics and Statistics 89: 139–52.Google Scholar
Greene, William H. 2000. Econometric analysis. 4th ed. New York: Prentice Hall.Google Scholar
Goldberg, Pinelopi, and Maggi, Giovanni. 1999. Protection for sale: An empirical investigation. American Economic Review 89: 1135–55.Google Scholar
Grossman, Gene M., and Helpman, Elhanan. 1995. Protection for sale. American Economic Review 4: 833–50.Google Scholar
Grossman, Gene M., and Helpman, Elhanan. 1995. Electoral competition and special interest politics. Review of Economic Studies 63: 265–86.Google Scholar
Hahn, Jinyong, and Hausman, Jerry. 2002a. A new specification test for the validity of instrumental variables. Econometrica 70: 163–89.Google Scholar
Hahn, Jinyong, and Hausman, Jerry. 2002b. Notes on bias in estimators for simultaneous equation models. Economics Letters 75: 237–41.Google Scholar
Hiscox, Michael J. 2002. Commerce, coalitions, and factor mobility: Evidence from congressional votes on trade legislation. American Political Science Review 96: 593–608.Google Scholar
Hufbauer, Gary C., Berliner, Diane T., and Elliott, Kimberly A. 1986. Trade protection in the United States: 31 case studies. Washington, DC: Institute of International Economics.Google Scholar
Kelejian, Harry H. 1971. Two stage least squares and econometric systems linear in parameters but non-linear in the endogenous variables. Journal of the American Statistical Association 66: 373–4.Google Scholar
Kleibergen, Frank. 2002. Pivotal statistics for testing structural parameters in instrumental variables regressions. Econometrica 70: 1781–804.Google Scholar
Konisky, David M. 2007. Regulatory competition and environmental enforcement: Is there a race to the bottom? American Journal of Political Science 51: 853–72.Google Scholar
Lassen, David D. 2005. The effect of information on voter turnout: Evidence from a natural experiment. American Journal of Political Science 49: 103–18.Google Scholar
Lebo, Matthew J., McGlynn, Adam J., and Koger, Gregory. 2007. Strategic party government: Party influence in congress, 1789–2000. American Journal of Political Science 51: 464–81.Google Scholar
Lewbel, Arthur. 1997. Constructing instruments for regressions with measurement error when no additional data are available, with an application to patents and R&D. Econometrica 65: 1201–14.Google Scholar
Lewis-Beck, Michael S., Nadeau, Richard, and Elias, Angelo. 2008. Economics, party, and the vote: Causality issues and panel data. American Journal of Political Science 52: 84–95.Google Scholar
McCalman, Phillip. 2004. Protection for sale and trade liberalization: An empirical investigation. Review of International Economics 12: 81–94.Google Scholar
McGillivray, Fiona. 1997. Party discipline as a determinant of the endogenous formation of tariffs. American Journal of Political Science 41: 584–607.Google Scholar
Mitra, Devashish. 1999. Endogenous lobby formation and endogenous protection: A long-run model of trade policy determination. American Economic Review 89: 1116–34.Google Scholar
Mitra, Devashish, Thomakos, Dimitrios D., and Ulubasoglu, Mehmet A. 2002. Protection for sale’ in a developing country: Democracy versus dictatorship. Review of Economics and Statistics 84: 497–508.CrossRefGoogle Scholar
Moreira, Marcelo J. 2003. A conditional likelihood ratio test for structural models. Econometrica 71: 1027–48.Google Scholar
Nelson, Charles R., and Startz, Richard. 1990. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58: 967–76.Google Scholar
Olson, Mancur. 1965. The logic of collective action: Public goods and the theory of groups. Cambridge: Harvard University Press.Google Scholar
Phillips, Peter C. B. 1983. Exact small sample theory in the simultaneous equations model. In Handbook of econometrics. Vol. 1, eds. Griliches, Z. and Intrilligator, M. D., 449–516. Amsterdam, The Netherlands: North-Holland.Google Scholar
Prakash, Aseem, and Potoski, Matthew. 2006. Racing to the bottom? Trade, environmental governance, and ISO 14001. American Journal of Political Science 50: 350–64.CrossRefGoogle Scholar
Reinhardt, Eric, and Busch, Marc. 1999. Industrial location and protection: The political and economic geography of U.S. nontariff barriers. American Journal of Political Science 43: 1028–50.Google Scholar
Rothenberg, T. 1975. Bayesian analysis of simultaneous equations models. In Studies in Bayesian econometrics and statistics, eds. Fienberg, S. E. and Zellner, A. Amsterdam, The Netherlands: North-Holland.Google Scholar
Rudra, Nita. 2005. Globalization and the strengthening of democracy in the developing world. American Journal of Political Science 49: 704–30.Google Scholar
Smith, R. J., and Blundell, R. W. 1986. An exogeneity test for a simultaneous equation Tobit model with an application to labor supply. Econometrica 54: 679–86.Google Scholar
Staiger, Douglas, and Stock, James H. 1997. Instrumental variables regression with weak instruments. Econometrica 65: 557–86.Google Scholar
Stock, James H., Wright, J. H., and Yogo, Motohiro. 2002. A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20: 518–29.Google Scholar
Stock, James H., and Yogo, Motohiro. 2004. Testing for weak instruments in linear IV regression. In Identification and inference in econometric models: Essays in honor of Thomas J. Rothenberg, eds. Andrews, D. W. K. and Stock, J. H. Cambridge: Cambridge University Press.Google Scholar