GR5412 Ron Miller Assignment 1: Due Feb. 3 1) This problem uses female lfp.dta, which contains data from a sample of married white women in the US, in 1975. We are interested in determinants of female labor force participation. Take a look at the variables in the data set and their means before getting started. a) Estimate a linear probability model for lfp, as a function of all the other variables in the model. Be sure to allow for heteroskedasticity with the robust option. All else equal: are older or younger women more likely to be in the workforce? College educated woman or non-college educated women? Look at the results for inc and discuss including economic intuition. For each observation, predict the probability of having labor force participation. Are there any problems with these predictions? b) Re-estimate the model from part a) using a probit and then with a logit, focusing on the marginal effects. Are there meaningful differences in the implications among the three different models? If so, discuss these differences. For each observation, for the probit, predict the probability of labor force participation. How do these predictions differ from those of part a)? c) For the probit model, compare the marginal effect of inc for women who have attended college as compared to women who have not attended college. Interpret your results. d) For the probit model, test the joint hypothesis that both college attendance variables have no effect. Do it using each of the three ML tests and compare the results. 2) Assume that the distribution of x is f(x) = 1/θ, 0≤x≤θ. If you have a random sample from this distribution, show that the sample maximum is a consistent estimator of θ. It is possible to show that this is also the MLE, but the usual properties do not apply here. Please explain why they do not. (Consider the expectation of the score.) 3) Suppose that x is distributed Weibull: α f (x |α , β ) = αβ (−α ) x (α −1)e −( x/β ) a) Find the log-likelihood function for a random sample of N observations. b) Find the likelihood equations (that is first order conditions) with respect to α and β. The first should offer an explicit solution. But after substituting that into the equation for β, the solution is only implicit. How would you find the MLE? c) Find the second derivative matrix of the log-likelihood with respect to α and β. The expectations of this matrix are difficult to derive analytically. But your results GR5412 Ron Miller should suggest an empirical estimator of it. How would you estimate the asymptotic covariance matrix for your estimators in (b)?
