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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


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 relations hip 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.

Original languageEnglish (US)
Pages (from-to)365-392
Number of pages28
JournalQuantitative Marketing and Economics
Issue number4
StatePublished - Dec 2005


  • Estimating the return to education
  • Identifiability
  • Instrumental variables
  • Latent instruments
  • Mixture models
  • Testing for endogeneity

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)
  • Marketing

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