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From |
Ewa Cukrowska <e.cukrowska@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Multinomial logit selection correction using -selmlog-. Interpretation of the estimates? |

Date |
Tue, 17 Dec 2013 18:46:39 +0100 |

Dear Statalist users, Recently I have come across some interpretation problems and I would like to ask you for your help. I estimated an updated version of the selection correction model by Dubin and Mc Fadden (1984). The improvement of the initial model was recently proposed by Bourguignon, Fournier and Gurgand (2007). The model is based on the estimation of the multinomial logit selection model, derivation of the correction terms and then their inclusion in the outcome equation. For the estimation I used –selmlog- command provided by Gurgand and Fournier. I run the model using the DMF(2) specification from –selmlog- command, which is the Bourguignon’s et al. modification of Dubin and Mc Fadden’s model. I wanted to estimate wage equations for private, public and self-employed and correct for their selection. In my model each individual can choose from: 1) working in the public sector, 2) working in the private sector, 3) working as self-employed and 4) not working at all. In the end, I obtained the estimates for 3 wage equations (for public, private and self-employed) that besides standard demographic characteristics include selection correction terms. The number of selection terms is equal to the number of multinomial logit alternatives (in my case 4). Below I report the estimates of the coefficients on the correction terms I obtained for the public sector wage equation. m_1 (private) 0.160*** (0.037) m_2 (public) -0.080*** (0.012) m_3 (self-employed) 0.166*** (0.035) m_4 (not working) 0.316*** (0.044) I would like to interpret the coefficients that relate to selection terms but I am confused. Firstly, according to Bourguignon, Fournier and Gurgand (2007) the estimates on the correction terms represent sigma*rho_1 to sigma*rho_s, where s stands for the number of alternatives from the multinomial logit selection model and r_s represents the correlation coefficient between the error terms in the wage equation and s-alternative from the selection equation (page 179). So when the estimated coefficient on the correction term is positive it indicates that error terms are positively correlated. Referring to my estimates, the positive coefficient on the private/self-employed/not-working sector selection equation in the public sector wage equation implies that some unobserved skills that cause an individual who is working in the public sector to have higher probability to choose one of these sectors are positively correlated with some unobserved skills that influence the wage in the public sector. Does it mean that those individuals, who are more able to choose these specific sectors have so-called “better” unobserved skills? That would make sense, since the correction variables (I mean the derived variables m_1, m_3 and m_4) are negative and the higher the probability of choosing these sector the lower the average wage for the public sector workers. Above interpretation seems appealing to me, but I got very confused by the interpretation that I have recently found in Dimova and Gang (2007). They run the same model as I do using the same estimation method. The interpretation they give is however the following: "For instance, a positive bias correction coefficient related to the private sector selection equation in the public sector wage equation highlights higher wages of individuals in the public sector compared to individuals taken at random, due to the allocation of people with worse unobserved skills out of the public sector into the private sector." (page 616). Which seems to be quite the opposite… My questions are: Is the interpretation of Dimova and Gang (2007) the right one (I assume yes…) and if yes from where it stems from? Below I post the references to the papers I mention: Bourguignon, F., Fournier M. and Gurgand M. (2007) Selection Bias Corrections Based On The Multinomial Logit Model: Monte Carlo Comparisons. Journal of Economic Surveys 21(1): 174-205. (available at: http://onlinelibrary.wiley.com/doi/10.1111/j.1467-6419.2007.00503.x/abstract?deniedAccessCustomisedMessage=&userIsAuthenticated=false – need to login) Dubin, J. A. and McFadden, D. L. (1984) An econometric analysis of residential electronic appliance holdings and consumption.Econometrica 52: 345-362. (available at: http://econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/mcfaddendubin.pdf) Dimova, R. and Gang, I. N. (2007) Self-selection and wages during volatile transition. Journal of Comparative Economics 35(3): 612-629. (full text for ScienceDirect subscribers: http://www.sciencedirect.com/science/article/pii/S0147596707000492; working paper is available at: http://ideas.repec.org/p/edb/cedidp/06-03.html) Selmlog command may be found here: http://www.parisschoolofeconomics.com/gurgand-marc/selmlog/selmlog13.html I would appreciate your help. Kind regards, Ewa * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

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