Asymptotic bias reduction for a conditional marginal effects estimator in sample selection models

Abstract

In this article we discuss the differences between the average marginal effect and the marginal effect of the average individual in sample selection models, estimated by the Heckman procedure. We show that the bias that emerges as a consequence of interchanging the measures, could be very significant, even in the limit. We suggest a computationally cheap approximation method, which corrects the bias to a large extent. We illustrate the implications of our method with an empirical application of earnings assimilation and a small Monte Carlo simulation.

Acknowledgements

We are indebted to Lennart Flood, Marcela Ibanez, Florin Maican and Kerem Tezic for their benefitting comments. We would also like to specially thank an anonymous referee for his valuable suggestions. All mistakes and misprints are exclusively ours.

Notes

¹ A more precise terminology would require defining it as conditional marginal effect, since it refers only to the individuals who actually work.

² The expected second order of magnitude is larger than the third one (Nguyen and Jordan, 2003).

³ We define an immigrant as an individuals who was born abroad (first generation).

⁴ The exact functional forms for age and years since migration are quadratic. The second order terms are omitted for notation simplicity purposes.

⁵ The exclusion restriction adopted in this article is that the nonlabour income affects the probability of being employed but not the earnings.

⁶ The entry age in the present study is assumed to be constant across immigrants and equal to 20.