Question

How does fertility affect labor supply? That is, how much does a woman's labor supply fall when she has an additional child? We would like to estimate this effect using data for married women from the 1980 U.S. Census. The data set contains information on n = 254654 married women aged 21-35 with two or more children. In particular, the variable weeksworked is equal to the number of weeks a mother has worked in 1979; morekids is a dummy variable that is equal to 1 if a mother has more than two kids, and equal to 0 otherwise; age is age; and afam, hispanic, and other are dummy variables for race. We run the following regression weeksuorked,-A) + β,morekids, + β2age, + Asafarní + β4hispanicit ßsot her i + ui. (1) (a) Explain why the variable morekids, could be correlated with the error term u. If this is the case, what would happen to the OLS estimator in this model?

Answer 1

a.

As kids will be more woman's working weeks will be reduced as it is evident that a woman has to spend more time with kids. Here the causal relationship between the explanatory variable and the dependent variable goes in both directions (a case of 'Simultaneity'). Hence the variable 'morekids_i' could be correlated with the error term u_i

If the explanatory variable x is correlated with the error term $\epsilon$ then it would result in inconsistent parameter estimates