Solving and Testing for Regressor-Error (in)Dependence When no Instrumental Variables are Available: With New Evidence for the Effect of Education on Income |
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Authors: | Peter Ebbes Michel Wedel Ulf Böckenholt Ton Steerneman |
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Institution: | (1) Smeal College of Business, The Penn State University, University Park, PA 16802-3603, USA;(2) Ross School of Business, University of Michigan, Ann Arbor, MI 48109-1234, USA;(3) Faculty of Management, McGill University, Montreal, PQ, H3A 1G5, Canada;(4) Department of Economics, University of Groningen, P.O.Box 800, 9700AV Groningen, NL |
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Abstract: | 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.
JEL Classification: C12, C13, C21, J3, M3 |
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Keywords: | instrumental variables latent instruments testing for endogeneity mixture models identifiability estimating the return to education |
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