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2.3 Sample selectivity bias  (Page 6/6)

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Inverse mills ratio comparison.
Observation As calculated from probit estimate As reported by the Heckman two-step
1 1.2821240 1.2821240
2 0.9313837 0.9313837
3 1.1269680 1.1269680
4 0.9079438 0.9079438
5 0.5900134 0.5900134
6 0.4652062 0.4652061
7 0.2974918 0.2974918
8 0.5300468 0.5300469
9 0.7864666 0.7864666
10 0.6024283 0.6024283

Exercise

We are interested in understanding the decision of married Portugese women to enter the labor force. We have available data from Portugal. The data set is a sample from Portuguese Employment Survey, from the interview year 1991, and has been provided by the Portuguese National Institute of Statistics (INE). The data are in the Excel file Martins. This file is organized in the following way. There are seven columns, corresponding to seven variables, and 2,339 observations.

a) Estimate the following equation using OLS: W a g e s = f ( a g e , a g e 2 , e d u c a t i o n ) using the observations for women actually working.

b) What is the potential source of selection bias?

c) Estimate a wage equation for the Portuguese data three ways: (1) using OLS, (2) using the Heckman two-step method, and (3) using the ML method. Report all three estimates in a single table. For consistency, we will assume that the appropriate explanatory variables for wages are (1) age, (2) the square of age, and (3) the years of education. Further, assume that women do not enter the labor force because (1) presence of children under the age of 3, (2) presence of children between 3 and 18, (3) husband's wage level, (4) the level of education of the woman, and (5) the age of the woman.

Appendix a.

z~N(0, 1). Φ ( z 0 ) = ∫ − ∞ z 0 ϕ ( z ) d z = 0.5 + Pr ( 0 ≤ z ≤ z 0 ) MathType@MTEF@5@5@+=feaagyart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdy0aaeWaaeaacaWG6bWaaSbaaSqaaiaaicdaaeqaaaGccaGLOaGaayzkaaGaeyypa0Zaa8qmaeaacqaHvpGzdaqadaqaaiaadQhaaiaawIcacaGLPaaacaWGKbGaamOEaaWcbaGaeyOeI0IaeyOhIukabaGaamOEamaaBaaameaacaaIWaaabeaaa0Gaey4kIipakiabg2da9iaaicdacaGGUaGaaGynaiabgUcaRiGaccfacaGGYbWaaeWaaeaacaaIWaGaeyizImQaamOEaiabgsMiJkaadQhadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGLPaaaaaa@5715@
Normal distribution.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990

The normal distribution

Picture of the Normal distribution.

References

Bourguignon, François, Martin Fournier, and Marc Gurgand (2007). Selection Bias Corrections Based on the Multinomial Logit Model: Monte Carlo Comparisons. Journal of Economic Surveys 21 (1): 174-205.

Chiburis, Richard and Michael Lokshin (2007). Maximum Likelihood and Two-Step Estimation of an Ordered-Probit Selection Model. The Stata Journal 7 (2): 167-182.

Dahl, G. B. (2002). Mobility and the Returns to Education: Testing a Roy Model with Multiple Markets. Econometrica 70 (6): 2367-2420.

Dubin, Jeffrey A. and Douglas Rivers (1989). Selection Bias in Linear Regression, Logit and Probit Models. Sociological Methods and Research 18 (2&3): 360-390.

Heckman, James (1974). Shadow Prices, Market Wages and Labor Supply. Econometrica 42 (4):679-694.

Heckman, James (1976) “The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models,” The Annals of Economic and Social Measurement 5 : 475-492.

Heckman, James (1979). Sample Selection Bias as a Specification Error. Econometrica 47 (1): 153-161.

Jimenez, Emanuel and Bernardo Kugler (1987). The Earnings Impact of Training Duration in a Developing Country: An Ordered Probit Model of Colombia's Servicio Nacional de Aprendizaje (SENA). Journal of Human Resources 22 (2): 230-233.

Lee, Lung-Fei (1983). Generalized Econometric Models with Selectivity. Econometrica 51 (2): 507-512.

McFadden, Daniel L. (1973). Conditional Logit Analysis of Qualitative Choice Behavior. In P. Zarembka Frontiers in Econometrics (New York: Academic Press).

Newey, W. K. and Daniel L. McFadden (1994). Large Sample Estimation and Hypothesis Testing. In R. F. Engle and D. L. McFadden (eds.) Handbook of Econometrics (Amsterdam: North Holland).

Schmertmann, Carl P. (1994). Selectivity Bias Correction Methods in Polychotomous Sample Selection Models. Journal of Econometrics 60 (1): 101-132.

Vella, Francis (1998). Estimating Models with Sample Selection Bias: A Survey. The Journal of Human Resources 33 (1):127-169.

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Source:  OpenStax, Econometrics for honors students. OpenStax CNX. Jul 20, 2010 Download for free at http://cnx.org/content/col11208/1.2
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