Q2. Why is it desirable to use a smoothed estimator of the probabilities?
On account of .nite sample performance, however, it may be desirable to use a smoothed estimator of the probabilities, or to drop cells that contain very few observations (as the authors do in the empirical application).
Q3. How many probability functions are required to maximize the probability of the data given byLi?
since p1 enters the restriction E( i) = 11 p1 + 1 2 (1 − p1) = 0, the authors maximized the full likelihood of the data given byLi × (p1)yi1 (1− p1)(1−yi1):10
Q4. What is the.nite sample property of the MD estimates?
Since both yTi and x T i have .nite supports the model is fully parametric and the asymptotic distribution of the estimators can be obtained using standard GMM asymptotic theory.
Q5. What is the reason for the linear index?
The reason is that the coeOcients in the linear index, like 2 and , will be typically parameters of interest in econometric applications in which the index is related to the agents’ objective functions evaluations.
Q6. Why do the GMM estimates have a smaller MSE than with T = 4?
With T = 6, the GMM estimates always have a smaller MSE than with T = 4, but this is due to reductions in variance that o1set larger biases in all the experiments.
Q7. What is the likelihood function in this case?
The likelihood function is particularly simple in this case since the conditioning variables are binary, and only the probabilities speci.ed by the model are required in the evaluation of the t−1j .
Q8. How many white married women were included in the Panel Study of Income Dynamics?
Weused data on 384 white married women from the random sub-sample of the Panel Study of Income Dynamics (PSID), for the years 1971, 1973, 1975, and 1977.
Q9. What is the simplest way to explain the relationship between vit and wti?
Since the history will a1ect the shape of the conditional distributions i |wti , their assumption implies that in general vit will only be mean independent of wti , which is a limitation of this approach.
Q10. What is the motivation behind the e1ect of children?
This particular speci.cation is motivated by the factthat most of the children’s e1ects on participation appear to depend on the presence of very young children, more so than, for example, on the total number of children living in the household (see Browning, 1992).
Q11. What is the likelihood function for a given individual?
Assuming that the conditional random variables i |yi1 = 1 and i |yi1 = 0 are discrete with .nite support given by m mass points e1; : : : ; em, the likelihood for one individual given the initial observation in this case isLHi = m∑‘=1 T∏ t=2 Git(e‘)yit [1− Git(e‘)](1−yit) Pr( i = e‘ |yi1 = 1); (3.4)whereGit(e‘) = F( + 2yi(t−1) + e‘): (3.5)LHi is a function of ; 2, the mass points e1; : : : ; em and the conditional probabilities Pr( i = e‘ |yi1 = 1).