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

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.

[1]  Michael D. Martinez.  Partisan Reinforcement in Context and Cognition: Canadian Federal Partisanships, 1974-79 , 1990 .

[2]  Jonathan N. Katz,et al.  What To Do (and Not to Do) with Time-Series Cross-Section Data , 1995, American Political Science Review.

[3]  Marcel Lubbers,et al.  Extreme right-wing voting in Western Europe , 2002 .

[4]  Robert S. Erikson,et al.  Peasants or Bankers? The American Electorate and the U.S. Economy , 1992, American Political Science Review.

[5]  Gregory A. Caldeira,et al.  Mailing In the Vote: Correlates and Consequences of Absentee Voting , 1985 .

[6]  Leland Gerson Neuberg,et al.  A solution to the ecological inference problem: Reconstructing individual behavior from aggregate data , 1999 .

[7]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[8]  J. S. Long,et al.  Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model , 2000 .

[9]  Michael W. Giles,et al.  David Duke and Black Threat: An Old Hypothesis Revisited , 1993, The Journal of Politics.

[10]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[11]  D. Voss,et al.  Beyond Racial Threat: Failure of an Old Hypothesis in the New South , 1996, The Journal of Politics.

[12]  Robert Rohrschneider,et al.  Support for Foreign Ownership and Integration in Eastern Europe , 2004 .

[13]  J. Cohen.  Economic Perceptions and Executive Approval in Comparative Perspective , 2004 .

[14]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[15]  B. Oppenheimer.  The Representational Experience: The Effect of State Population on Senator-Constituency Linkages , 1996 .

[16]  H. Theil.  Introduction to econometrics , 1978 .

[17]  Eric A. Hanushek,et al.  Efficient Estimators for Regressing Regression Coefficients , 1974 .

[18]  Jstor.  The American political science review , 2022 .

[19]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[20]  D. Garth Taylor.  Procedures for Evaluating Trends in Public Opinion , 1980 .

[21]  Kenneth W. Shotts,et al.  Using Ecological Inference Point Estimates as Dependent Variables in Second-Stage Linear Regressions , 2003, Political Analysis.

[22]  M. Peffley,et al.  Democratization and Political Tolerance in Seventeen Countries: A Multi-level Model of Democratic Learning , 2003 .

[23]  J. Patel,et al.  Handbook of the normal distribution , 1983 .

[24]  Gary King,et al.  Enhancing Democracy Through Legislative Redistricting , 1994, American Political Science Review.

[25]  Lillian Cohen,et al.  Statistical Methods for Social Scientists. , 1954 .

[26]  Christopher J. Anderson,et al.  Corruption, Political Allegiances, and Attitudes Toward Government in Contemporary Democracies , 2003 .

[27]  H. Norpoth.  Presidents and the Prospective Voter , 1996, The Journal of Politics.

[28]  W. P. Shively,et al.  Applying a Two-Step Strategy to the Analysis of Cross-National Public Opinion Data , 2005, Political Analysis.

[29]  Bradford S. Jones,et al.  Modeling Multilevel Data Structures , 2002 .

[30]  Gary R. Saxonhouse,et al.  Estimated Parameters as Dependent Variables , 1976 .

[31]  H. White,et al.  Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties☆ , 1985 .

[32]  S. Banducci,et al.  The euro, economic interests and multi‐level governance: Examining support for the common currency , 2003 .

[33]  J. Crété,et al.  A Multilevel Analysis of the Determinants of Recycling Behavior in the European Countries , 2001 .

[34]  Karl C. Kaltenthaler,et al.  Europeans and their money: Explaining public support for the common European currency , 2001 .

[35]  B. Efron,et al.  The Jackknife: The Bootstrap and Other Resampling Plans. , 1983 .

[36]  David C. Kimball,et al.  A New Approach to the Study of Ticket Splitting , 1998 .

[37]  H. Clarke,et al.  Prospections, Retrospections, and Rationality: The "Bankers" Model of Presidential Approval Reconsidered , 1994 .