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Estimating Regression Models in Which the Dependent Variable Is Based on Estimates

Published online by Cambridge University Press:  04 January 2017

Jeffrey B. Lewis  and
Drew A. Linzer
Jeffrey B. Lewis*
Affiliation:
Department of Political Science, University of California, Los Angeles, 4289 Bunche Hall, Los Angeles, CA 90095
Drew A. Linzer
Affiliation:
Department of Political Science, University of California, Los Angeles, 4289 Bunche Hall, Los Angeles, CA 90095. e-mail: [email protected]
*
e-mail: [email protected] (corresponding author)
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Abstract

Researchers often use as dependent variables quantities estimated from auxiliary data sets. Estimated dependent variable (EDV) models arise, for example, in studies where counties or states are the units of analysis and the dependent variable is an estimated mean, proportion, or regression coefficient. Scholars fitting EDV models have generally recognized that variation in the sampling variance of the observations on the dependent variable will induce heteroscedasticity. We show that the most common approach to this problem, weighted least squares, will usually lead to inefficient estimates and underestimated standard errors. In many cases, OLS with White's or Efron heteroscedastic consistent standard errors yields better results. We also suggest two simple alternative FGLS approaches that are more efficient and yield consistent standard error estimates. Finally, we apply the various alternative estimators to a replication of Cohen's (2004) cross-national study of presidential approval.

Type
Research Article
Information
Political Analysis , Volume 13 , Issue 4: Special Issue on Multilevel Modeling for Large Clusters , Autumn 2005 , pp. 345 - 364
Copyright
Copyright © The Author 2005. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: We thank Chris Achen, Barry Burden, Michael Herron, Gary King, Eduardo Leoni, and Lynn Vavreck for comments on earlier drafts of this article. Any remaining errors are ours alone.

References

Anderson, Christopher J., and Tverdova, Yuliya V. 2003. “Corruption, Political Allegiances, and Attitudes toward Government in Contemporary Democracies.” American Journal of Political Science 47: 91–109.Google Scholar
Banducci, Susan A., Karp, Jeffrey A., and Loedel, Peter H. 2003. “The Euro, Economic Interests and Multilevel Governance: Examining Support for the Common Currency.” European Journal of Political Research 42: 685–703.Google Scholar
Bryk, Anthony, and Raudenbush, Stephen W. 1992. Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park, CA: Sage.Google Scholar
Burden, Barry, and Kimball, David. 1998. “A New Approach to the Study of Ticket Splitting.” American Political Science Review 92: 533–544.CrossRefGoogle Scholar
Clarke, Harold D., and Stewart, Marianne C. 1994. “Prospections, Retrospections, and Rationality: The ‘Bankers’ Model of Presidential Approval Reconsidered.” American Journal of Political Science 38: 1104–1123.CrossRefGoogle Scholar
Cohen, Jeffrey E. 2004. “Economic Perceptions and Executive Approval in Comparative Perspective.” Political Behavior 26: 27–43.Google Scholar
DeGroot, Morris H., and Schervish, Mark J. 2002. Probability and Statistics, 3rd ed. New York: Addison Wesley.Google Scholar
Efron, Bradley. 1982. The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar
Greene, William H. 2003. Econometric Analysis, 5th ed. Englewood, NJ: Prentice Hall.Google Scholar
Guerin, Daniel, Crete, Jean, and Mercier, Jean. 2001. “A Multilevel Analysis of the Determinants of Recycling Behavior in the European Countries.” Social Science Research 30: 195–218.Google Scholar
Hanushek, Eric A. 1974. “Efficient Estimators for Regressing Regression Coefficients.” American Statistician 28: 66–67.Google Scholar
Hanushek, Eric A., and Jackson, John E. 1977. Statistical Methods for Social Scientists. New York: Academic.Google Scholar
Herron, Michael C., and Shotts, Kenneth W. 2003. “Using Ecological Inference Point Estimates as Dependent Variables in Second-Stage Linear Regressions.” Political Analysis 11: 44–64.Google Scholar
Jusko, Karen Long, and Shively, Phillips W. 2005. “Applying a Two-Step Strategy to the Analysis of Cross-National Public Opinion Data.” Political Analysis. doi:10.1093/pan/mpi030.Google Scholar
Kaltenthaler, Karl C., and Anderson, Christopher J. 2001. “Europeans and Their Money: Explaining Public Support for the Common European Currency.” European Journal of Political Research 40: 139–170.CrossRefGoogle Scholar
King, Gary. 1997. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton, NJ: Princeton University Press.Google Scholar
Long, J. Scott, and Ervin, Laurie H. 2000. “Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model.” American Statistician 54: 217–224.Google Scholar
Lubbers, Marcel, Gijsberts, Mérove, and Scheepers, Peer. 2002. “Extreme Right-Wing Voting in Western Europe.” European Journal of Political Research 41: 345–378.CrossRefGoogle Scholar
MacKinnon, James G., and White, Halbert. 1985. “Some Heteroscedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties.” Journal of Econometrics 29: 305–325.Google Scholar
MacKuen, Michael B., Erikson, Robert S., and Stimson, James A. 1989. “Macropartisanship.” American Political Science Review 83: 1125–1142.Google Scholar
MacKuen, Michael B., Erikson, Robert S., and Stimson, James A. 1992. “Peasants or Bankers? The American Electorate and the U.S. Economy.” American Political Science Review 86: 597–611.CrossRefGoogle Scholar
Maddala, G. S. 2001. Introduction to Econometrics, 3rd ed. West Sussex: John Wiley and Sons.Google Scholar
Norpoth, Helmut. 1996. “Presidents and the Prospective Voter.” Journal of Politics 58: 776–792.Google Scholar
Oppenheimer, Bruce. 1996. “The Importance of Elections in a Strong Congressional Party Era.” In Do Elections Matter? eds. Ginsberg, Benjamin and Stone, Alan. Armonk, NY: M. E. Sharpe, pp. 120–139.Google Scholar
Patel, Jagdish K., and Read, Campbell B. 1996. Handbook of the Normal Distribution. New York: Marcel Dekker.Google Scholar
Peffley, Mark, and Rohrschneider, Robert. 2003. “Democratization and Political Tolerance in Seventeen Countries: A Multi-level Model of Democratic Learning.” Political Research Quarterly 56: 243–257.Google Scholar
Rohrschneider, Robert, and Whitefield, Stephen. 2004. “Support for Foreign Ownership and Integration in Eastern Europe; Economic Interests, Ideological Commitments, and Democratic Context.” Comparative Political Studies 37: 313–339.Google Scholar
Saxonhouse, Gary R. 1976. “Estimated Parameters as Dependent Variables.” American Economic Review 66: 178–183.Google Scholar
Steenbergen, Marco R., and Jones, Bradford S. 2002. “Modeling Multilevel Data Structures.” American Journal of Political Science 46: 218–237.Google Scholar
Taylor, D. Garth. 1980. “Procedures for Evaluating Trends in Public Opinion.” Public Opinion Quarterly 44: 86–100.Google Scholar
White, Halbert. 1980. “A Heteroscadastically-Consistent Covariance Matrix Estimator and a Direct Test for the Heteroscasticity.” Econometrica 48: 817–838.CrossRefGoogle Scholar