Quantitative Marketing and Economics

, Volume 3, Issue 4, pp 365–392 | Cite as

Solving and Testing for Regressor-Error (in)Dependence When no Instrumental Variables are Available: With New Evidence for the Effect of Education on Income

  • Peter Ebbes
  • Michel Wedel
  • Ulf Böckenholt
  • Ton Steerneman


This paper has two main contributions. Firstly, we introduce a new approach, the latent instrumental variables (LIV) method, to estimate regression coefficients consistently in a simple linear regression model where regressor-error correlations (endogeneity) are likely to be present. The LIV method utilizes a discrete latent variable model that accounts for dependencies between regressors and the error term. As a result, additional ‘valid’ observed instrumental variables are not required. Furthermore, we propose a specification test based on Hausman (1978) to test for these regressor-error correlations. A simulation study demonstrates that the LIV method yields consistent estimates and the proposed test-statistic has reasonable power over a wide range of regressor-error correlations and several distributions of the instruments.

Secondly, the LIV method is used to re-visit the relationship between education and income based on previously published data. Data from three studies are re-analyzed. We examine the effect of education on income, where the variable ‘education’ is potentially endogenous due to omitted ‘ability’ or other causes. In all three applications, we find an upward bias in the OLS estimates of approximately 7%. Our conclusions agree closely with recent results obtained in studies with twins that find an upward bias in OLS of about 10% (Card, 1999). We also show that for each of the three datasets the classical IV estimates for the return to education point to biases in OLS that are not consistent in terms of size and magnitude. Our conclusion is that LIV estimates are preferable to the classical IV estimates in understanding the effects of education on income.


instrumental variables latent instruments testing for endogeneity mixture models identifiability estimating the return to education 


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  1. Al-Hussaini, E.K. and K.E.-D. Ahmad. (1981). “On the Identifiability of Finite Mixtures of Distributions.” IEEE Transactions on Information Theory 27, 664–668.CrossRefGoogle Scholar
  2. Angrist, J.D. and A.B. Krueger. (1991). “Does Compulsory School Attendance Affect Schooling and Earnings?” The Quarterly Journal of Economics 56, 979–1014.Google Scholar
  3. Bekker, P.A. (1994). “Alternative Approximations to the Distributions of Instrumental Variable Estimators.” Econometrica 62, 657–681.Google Scholar
  4. Belsley, D.A., E. Kuh, and R.E. Welsch. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons, Inc.Google Scholar
  5. Bound, J. and D.A. Jaeger. (1996). “On the Validity of Season of Birth as an Instrument in Wage Equations A Comment on Angrist and Krueger's Does Compulsory School Attendance Affect Schooling and Earnings?” Technical Report 5835, NBER.Google Scholar
  6. Bound, J., D.A. Jaeger, and R.M. Baker. (1995). “Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variable is Weak.” Journal of the American Statistical Association 90, 443–450.Google Scholar
  7. Bowden, R.J. and D.A. Turkington. (1984). Instrumental Variables. New York: Cambridge University Press.Google Scholar
  8. Bronnenberg, B.J. and V. Mahajan. (2001). “Unobserved Retailer Behavior in Multimarket Data: Joint Spatial Dependence in Market Shares and Promotion Variables.” Marketing Science 20, 284–299.CrossRefGoogle Scholar
  9. Card, D. (1995). “Using Geographical Variation in College Proximity to Estimate the Return to Schooling.” In L.N. Christofides, E. Grant, and R. Swidinsky (eds.), Aspects of Labour Market Behaviour: Essays in Honour of John Vanderkamp, Toronto: University of Toronto Press, pp. 201–222.Google Scholar
  10. Card, D. (1999). “The Causal Effect of Education on Earnings.” In Ashenfelter, O.C. and D. Card (eds.), Handbook of Labor Economics volume 3A, North-Holland: Elsevier Science B.V., pp. 1801–1863Google Scholar
  11. 11 Card, D. (2001). “Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems.” Econometrica 69, 1127–1160.CrossRefGoogle Scholar
  12. Chamberlain, G. and Z. Griliches. (1975). “Unobservables with a Variance-Components Structure: Ability, Schooling, and the Economic Success of Brothers.” International Economic Review 16, 422–449.Google Scholar
  13. Cook, R.D. and S. Weisberg. (1982). Residuals and Influence in Regression. New York: Chapman and Hall.Google Scholar
  14. Dijk, van, A., H.J. van Heerde, P.S.H. Leeflang, and D.R. Wittink. (2004). “Similarity-Based Spatial Methods for Estimating Shelf Space Elasticities From Correlational Data.” Quantitative Marketing and Economics 2, 257–277.Google Scholar
  15. Ebbes, P. (2004). “Latent Instrumental Variables: A New Approach to Solve for Endogeneity.” Ph D thesis, SOM Research School, University of Groningen ({}).Google Scholar
  16. Erickson, T. and T.M. Whited. (2002). “Two-Step GMM Estimation of the Errors-in-Variables Model Using High-Order Moments.” Econometric Theory 18, 776–799.CrossRefGoogle Scholar
  17. Fahrmeir, L. and G. Tutz. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. New York: Springer-Verlag.Google Scholar
  18. Fox, J. (1991). Regression Diagnostics. London: Sage Publications, inc.Google Scholar
  19. Greene, W.H. (2000). Econometric Analysis. New Jersey: Prentice-Hall, Inc., Upper Saddle River.Google Scholar
  20. Griliches, Z. (1977). “Estimating the Returns to Schooling: Some Econometric Problems.” Econometrica 45, 1–22.Google Scholar
  21. Hahn, J. and J. Hausman. (2003). “Weak Instrumens: Diagnosis and Cures in Empirical Econometrics.” American Economic Review 93, 118–125.Google Scholar
  22. Harmon, C. and I. Walker. (1995). “Estimates of the Economic Return to Schooling for the United Kingdom.” American Economic Review 85, 1278–1286.Google Scholar
  23. Hartog, J. (1988). “An Ordered Response Model for Allocation and Earnings.” Kyklos 41, 113–141.Google Scholar
  24. Hausman, J.A. (1978). “Specification Tests for Econometrics.” Econometrica 46, 1251–1271.Google Scholar
  25. Hennig, C. (2000). “Identifiability of Models for Clusterwise Linear Regression.” Journal of Classification 17, 273–296.CrossRefGoogle Scholar
  26. Hertz, T. (2003). “Upward Bias in the Estimated Returns to Education: Evidence from South Africa.” The American Economic Review 93, 1354–1368.CrossRefGoogle Scholar
  27. Judge, G.G., W.E. Griffiths, R.C. Hill, H. Lütkepohl, and T.-C. Lee. (1985). The Theory and Practice of Econometrics. New York: John Wiley & Sons Inc.Google Scholar
  28. Madansky, A. (1959). “The Fitting of Straight Lines When Both Variables are Subject to Error.” Journal of the American Statistical Association 54, 173–205.Google Scholar
  29. Manchanda, P., P.E. Rossi, and P.K. Chintagunta. (2004). “Response Modeling with Non-Random Marketing Mix Variables.” Journal of Marketing Research 41, 467–478.CrossRefGoogle Scholar
  30. McLachlan, G.J. and D. Peel. (2000). Finite Mixture Models. New York: John Wiley & Sons, Inc.Google Scholar
  31. Mroz, T.A. (1987). “The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions.” Econometrica 55, 765–799.Google Scholar
  32. Pagan, A. (1984). “Econometric Issues in the Analysis of Regressions with Generated Regressors.” International Economic Review 25, 221–247.Google Scholar
  33. 33 Ploeg, van der, J. (1997). “Instrumental Variable Estimation and Group-Asymptotics.” Ph D thesis, SOM Research School, University of Groningen ( Scholar
  34. Redner, R.A. and H.F. Walker. (1984). “Mixture Densities, Maximum Likelihood and the EM Algorithm.” SIAM Review 26, 195–239.CrossRefGoogle Scholar
  35. Ruud, P.A. (2000). An Introduction to Classical Econometric Theory. New York: Oxford University Press.Google Scholar
  36. Staiger, D. and J.H. Stock. (1997). “Instrumental Variables Regression with Weak Instruments.” Econometrica, 65, 557–586.Google Scholar
  37. Stock, J.H., J.H. Wright, and M. Yogo. (2002). “A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments.” {Journal of Business & Economic Statistics} 20, 518–529.Google Scholar
  38. Teicher, H. (1963). “Identifiability of Finite Mixtures.” The Annals of Mathematical Statistics 34, 1265–1269.Google Scholar
  39. Titterington, D.M., A.F.M. Smith, and U.E. Makov. (1985). Statistical Analysis of Finite Mixture Distributions. Chichester: John Wiley & Sons Ltd.Google Scholar
  40. Uusitalo, R. (1999). “Essays in Economics of Education.” Ph D thesis, University of Helsinki.Google Scholar
  41. Verbeek, M. (2000). A Guide to Modern Econometrics. Chichester: John Wiley & Sons Ltd.Google Scholar
  42. Wald, A. (1940). “The Fitting of Straight Lines if Both Variables are Subject to Error.” The Annals of Mathematical Statistics 11, 284–300.Google Scholar
  43. White, H. (1980). “A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity.” Econometrica 48, 817–838.Google Scholar
  44. Wooldridge, J.M. (2002). Econometric Analysis of Cross Section and Panel Data. Cambridge: Massachusetts Institute of Technology.Google Scholar
  45. Yakowitz, S.J. and J.D. Spragins. (1968). “On the Identifiability of Finite Mixtures.” The Annals of Mathematical Statistics 39, 209–214.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Peter Ebbes
    • 1
  • Michel Wedel
    • 2
  • Ulf Böckenholt
    • 3
  • Ton Steerneman
    • 4
  1. 1.Smeal College of BusinessThe Penn State UniversityUniversity ParkUSA
  2. 2.Ross School of BusinessUniversity of MichiganAnn ArborUSA
  3. 3.Faculty of ManagementMcGill UniversityMontrealCanada
  4. 4.Department of EconomicsUniversity of GroningenGroningen

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