2. Suppose you are interested in studying labor force participation (LFP) of adult women in the U.S. You have access to a cross-sectional sample of women that contains variables about their characteristics and participation in the labor force. Using this data you construct the following cross table relating motherhood status to LFP. Table 1: Motherhood status and LFP. LFP Mother No Yes Total No 0.13 0.24 Yes 0.27 0.36 Total (a) Based on the table, what is the probability that a woman drawn randomly from your sample is a mother? (b) What about the probability that a woman drawn randomly from your sample is in the labor force? (c) Based on the data, is the probability of being in the labor force greater or smaller for mothers? Show your calculations. (d) Suppose you write the following equation LFP, = Bo + 8, motherhood, + e; (1) and run a simple regression of LFP on motherhood status using the same sample used to construct the table above. That is, use the Linear Probability Model (LPM) to estimate the relationship between LFP and motherhood status. What are the estimated values of B, and 81? You suspect that equation (1) is too simple to correctly capture the relationship between motherhood and LFP. So you move to a more complex model where the variable of interest is not only a dummy indicating motherhood status but also the number of children a women has (which can of course be zero). You also add other regressors to your equation and estimate the model by LPM and Logit as show in the Table 2 (e) Focusing on the LPM output, holding everything else constant, what is the expected change in the probability of being in the labor force for a woman that just had her second child? Can you perform the same calculation for the Logit model? If yes, calculate the expected change. If not, explain why you cannot. (f) Focusing again on the LPM, what is the predicted probability of being in the labor force for a 40 year old woman who is not married and not a mother? (g) Focusing now on the Logit estimates in the second column, what is the predicted probability of being in the labor force for the woman considered in part f? (h) Focusing now on the Logit estimates, how would you test whether the underlying models in columns two and three are the statistically equivalent? (i) Discuss how the number of children is predicted to affect LFP, based on the results in the third column