Scholars often assume that the danger posed by omitted variable bias can be ameliorated by the inclusion of large numbers of relevant control variables. However, there is nothing in the mathematics of regression analysis that supports this conclusion. This paper goes beyond textbook treatments of omitted variable bias and shows, both for OLS and for generalized linear models, that the inclusion of additional control variables may increase or decrease the bias, and we cannot know for sure which is the case in any particular situation. The last section of the paper shows how formal sensitivity analysis can be used to determine whether omitted variables are a problem. A substantive example demonstrates the method.
Achen, Christopher H.1992. Social psychology, demographic variables, and linear regression: Breaking the iron triangle in voting research. Political Behavior14 (September): 195-211.
2.
Achen, Christopher H.2002. Toward a new political methodology: Microfoundations and ART. Annual Review of Political Science5: 423-450.
3.
Achen, Christopher H.2005. Let's put garbage-can regressions and garbage-can probits where they belong. Conflict Management and Peace Science22(4): 327-339.
4.
Akaike, H.1973. Information theory and an extension of the likelihood ratio principle. In Second International Symposium of Information Theory, eds B. N. Petrov and F. Csaki, pp. 267-281. Budapest: Minnesota Studies in the Philosophy of Science.
5.
Altonji, Joseph G., Todd E. Elder, and Christopher R. Taber.2005. Selection on observed and unobserved variables: Assessing the effectiveness of Catholic schools . Journal of Political Economy113 (February): 151-184.
6.
Ansolabehere, Stephen, Alan Gerber, and Jim Snyder.2002. Equal votes, equal money: Court-ordered redistricting and public expenditures in the American states. American Political Science Review96 (December): 767-777.
7.
Bailey, Michael A., Brian Kamoie, and Forrest Maltzman .2005. Signals from the Tenth Justice: The political role of the Solicitor General in Supreme Court decision making . American Journal of Political Science49 (January): 72-85.
8.
Brady, Henry E., and John E. McNulty .2004. The costs of voting: Evidence from a natural experiment. Paper presented at the annual meeting of the Society for Political Methodology, Stanford University.
9.
Breiman, Leo.1992. The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error. Journal of the American Statistical Association87 (September): 738-754.
10.
Buhaug, Halvard, and Scott Gates.2002. The geography of civil war. Journal of Peace Research39 (July): 417-433.
11.
Clarke, Kevin A.2001. Testing nonnested models of international relations: Reevaluating realism. American Journal of Political Science45 (July): 724-744.
12.
Clarke, Kevin A.2003. Nonparametric model discrimination in international relations . Journal of Conflict Resolution47 (February): 72-93.
13.
Clarke, Kevin A.2005. The phantom menace: Omitted variable bias in econometric research. Conflict Management and Peace Science22 (Winter): 341-352.
14.
Clarke, Kevin A.2007. A simple distribution-free test for nonnested hypotheses . Political Analysis15 (Summer): 347-363.
15.
Cornfield, J.W.Haenszel, E.C.Hammond, A.M.Lilienfeld, M.B. Shimkin, and E.L. Wynder .1959. Smoking and lung cancer: Recent evidence and a discussion of some questions. Journal of the National Cancer Institute22(1): 173-203.
16.
Cox, David R.1961. Tests of separate families of hypotheses. Proceedings of the Fourth Berkeley SymposiumI: 105-123.
17.
Cramer, J.S.2003. Logit models. Cambridge: Cambridge University Press.
18.
Davidson, Russell, and James G. MacKinnon .1993. Estimation and inference in econometrics. Oxford: Oxford University Press.
19.
Gail, M.H., S. Wieand, and S. Piantadosi.1984. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates . Biometrika71 (December): 431-444.
20.
Gelpi, Christopher, and Peter D. Feaver .2002. Speak softly and carry a big stick? Veterans in the political elite and the American use of force. American Political Science Review96 (December): 779-793.
21.
Greene, William H.2003. Econometric analysis, 5th edn. New Jersey: Prentice Hall .
22.
Griliches, Zvi.1977. Estimating the results to schooling: Some econometric problems. Econometric45(January): 1-22.
23.
Gujarati, Damodar N.2003. Basic econometrics, 4th edn. New York: McGraw-Hill.
24.
Hanushek, Eric A., and John E. Jackson .1977. Statistical methods for social scientists. New York: Academic Press .
25.
Hegre, Havard, Tanja Ellingsen, Scott Gates, and Nils Petter Gleditsch .2001. Toward a democratic civil peace? Democracy, political change, and civil war, 1816-1992. American Political Science Review95(March): 33-48.
26.
Hendry, David F., and Jean-Francois Richard .1982. On the formulation of empirical models in dynamic econometrics. Journal of Econometrics20(October): 3-33.
27.
Holland, Paul W.1986. Statistics and causal inference. Journal of the American Statistical Association81(December): 945-960.
28.
Imbens, Guido W.2003. Sensitivity to exogeneity assumptions in program evaluation . American Economic Review93(May): 126-132.
29.
Johnston, Jack, and John DiNardo.1997. Econometric methods, 4th edn. New York: McGraw-Hill.
30.
Judge, George G., W.E. Griffiths, R. Carter Hill, Helmut Lutkepohl, and Tsoung-Chao Lee .1985. The theory and practice of econometrics, 2nd edn. New York : John Wiley and Sons.
31.
King, Gary, Robert O. Keohane, and Sidney Verba.1994. Designing social inquiry: Scientific inference in qualitative research. Princeton, NJ: Princeton University Press.
32.
King, Gary, James Honaker, Anne Joseph, and Kenneth Scheve.2001. Analyzing incomplete political science data: An alternative algorithm for multiple imputation. American Political Science Review95(March): 49-69.
33.
Kmenta, Jan.1986. Elements of econometrics, 2nd edn. New York: Macmillan.
34.
Krause, George A.2003. Coping with uncertainty: analyzing risk propensities of SEC budgetary decisions, 1949-97. American Political Science Review97(February): 171-188.
35.
Maddala, G.S.1977. Econometrics. New York: McGraw-Hill.
36.
Mallows, C.L.1973. Some comments on Cp. Technometrics15(November): 671-676.
37.
McCullagh, P., and J.A. Nelder.1989. Generalized linear models, 2nd edn. New York: Chapman and Hall.
38.
Meyer, Bruce D.1995. Natural and quasi-experiments in economics. Journal of Business and Economic Statistics13(April): 151-161.
39.
Neuhaus, John M.1993. A geometric approach to assess bias due to omitted covariates in generalized linear models. Biometrika80(December): 807-815.
40.
Rosenbaum, Paul R.1986. Dropping out of high school in the United States: An observational study. Journal of Educational Statistics11(Autumn): 207-224.
41.
Rosenbaum, Paul R.2002. Observational Studies, 2nd edn. New York: Springer-Verlag .
42.
Rosenbaum, P.R., and D.B. Rubin.1983. Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society, Series B 45(2): 212-218.
43.
Rudolph, Thomas J., and Jillian Evans.2005. Political trust, ideology, and public support for government spending. American Journal of Political Science49(July): 660-671.
44.
Schwarz, G.1978. Estimating the dimension of a model. Annals of Statistics6: 461-464.
45.
Sims, Christopher A.1980. Macroeconomics and reality. Econometrica48(January): 1-48.
46.
Stein, C.1955. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability , pp. 197-206.
47.
Vuong, Quang.1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica57(March): 307-333.
48.
Welch, Finis.1975. Human capital theory: Education, discrimination, and life-cycles . American Economic Review65(May): 63-73.
49.
Wooldridge, Jeffrey M.2002. Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press .
