Selectivity & Treatment Heckman 2-Step Correction The data set select.dta contains information on a sample of married women taken from the 2003 General Household Survey. . su Variable | Obs Mean Std. Dev. Min Max -+- age | 4270 47.20047 11.89064 17 69 sex | 4270 2 0 2 2 ndepchld | 4270 .8386417 1.118618 0 8 hw | 2296 884.8653 870.429 .0061538 21875 treated | 4270 .5377049 .4986347 0 1 -+- married | 4270 1 0 1 1 lhw | 2296 6.6076 .6470898 -5.090678 9.9931 educ | 4270 12.10023 2.658739 6 35 the variable treated takes the value 1 if the women are observed in work and 0 otherwise. Hence the summary statistics show that around 53.8% of the sample of married women are in work. This may be a non-random sample of all married women if there are variables which affect participation in the labour force. If so, then OLS on the sample of working women will be biased and inconsistent. Suppose we are interested in the determinants of wages for married women. The uncorrected OLS regression on the sample of working women is . reg lhw educ age Source | SS df MS Number of obs = 2296 -+- F( 2, 2293) = 119.83 Model | 90.9340802 2 45.4670401 Prob F = 0.0000 Residual | 870.040215 2293 .379433151 R-squared = 0.0946 -+- Adj R-squared = 0.0938 Total | 960.974295 2295 .418725183 Root MSE = .61598 - lhw | Coef. Std. Err. t P|t| 95% Conf. Interval -+- educ | .0791092 .005117 15.46 0.000 .0690748 .0891435 age | .0037069 .0013281 2.79 0.005 .0011024 .0063113 _cons | 5.468114 .0960707 56.92 0.000 5.279719 5.656508 - If selectivity exists then these coefficients may not be applicable to all married women (working and non-working). To determine whether selection is a problem, first estimate the probability of being in work, (the probability of being treated) as a function of the original control variables and an additional identifying variable in this case the number of dependent children. This variable is assumed to affect the probability of participation in work (negatively), but is assumed not to influence wages on offer once in work, (in practice this assumption should be tested). A probit estimate of the probability of being treated gives . probit treated educ age ndepchld Iteration 0: log likelihood = -2947.5859 Iteration 1: log likelihood = -2698.3709 Iteration 2: log likelihood = -2696.5695 Iteration 3: log likelihood = -2696.5692 Probit regression Number of obs = 4270 LR chi2(3) = 502.03 Prob chi2 = 0.0000 Log likelihood = -2696.5692 Pseudo R2 = 0.0852 - treated | Coef. Std. Err. z P|z| 95% Conf. Interval -+- educ | .0116392 .0077145 1.51 0.131 -.003481 .0267595 age | -.0442952 .0022067 -20.07 0.000 -.0486202 -.0399702 ndepchld | -.1714651 .0219398 -7.82 0.000 -.2144664 -.1284638 _cons | 2.19459 .1614445 13.59 0.000 1.878165 2.511015 - Remember these coefficients have no direct interpretation (being simply the values that maximize the likelihood function), but the marginal effects = (Z) jdo and are given by . dprobit treated educ age ndepchld Iteration 0: log likelihood = -2947.5859 Iteration 1: log likelihood = -2698.3709 Iteration 2: log likelihood = -2696.5695 Iteration 3: log likelihood = -2696.5692 Probit regression, reporting marginal effects Number of obs = 4270 LR chi2(3) = 502.03 Prob chi2 = 0.0000 Log likelihood = -2696.5692 Pseudo R2 = 0.0852 - treated | dF/dx Std. Err. z P|z| x-bar 95% C.I. -+- educ | .0046198 .003062 1.51 0.131 12.1002 -.001382 .010621 age | -.0175815