1. Based on a smaple of 100 couples with young babies, Jack considers a probit model...

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1. Based on a smaple of 100 couples with young babies, Jack considers a probit model for couples' decisions on whether going to a restaurant to celebrate wedding anniversary. Variables are defined as: Y INCOME BABY SIT = 1 if the couple went to a restaurant the couple's annual income in thousands of dollars = 1 if the couple needed a baby-sitter for babies The proposed probit model is Y = (31 + 32 INCOME; +33 BABY SIT;) +e; where is the probit function (cumulative density function of the standard normal distribution). The estiamted coefficients are: Independent Variables CONSTANT Coefficient Estimates 0.50 0.02 -0.40 INCOME BABY SIT The CDF of the standard normal distribution is attached and its PDF is listed in the following table: 2 Probablilty density function (PDF) of the standard normal distribution 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 (2) 0.40 0.40 0.39 0.38 0.37 0.35 0.33 0.31 0.29 0.27 0.24 0.22 0.19 (a) Consider a specific couple with INCOME = 50 and BABY SIT: 1. What is the estimated probability that the couple would go to a restaurant? (b) (Continued from (a)) For this specific couple, what is the marginal effect on the probability that they would go to a restaurant when their income increases? (c) (Continued from (a)) If this couple's parents can help and they no longer need to hire a babysitter, will the probability increase or decrease? And by how much? (d) If Jack uses the same sample to estimate a linear probability model below: Y = 1+2 INCOME; +3 BABY SIT; +ui What are your comments to his model specification? (e) With the same sample, Jack defines a new variable NOBABY SIT to be used in an alternative probit model: Y = (a1+ a2 INCOME; +03 NOBABY SIT;) + e where NOBABY SIT; = 1 if the couple DOES NOT need a baby-sitter. Provide esimates of a1, a2 and 3, respectively. 1. Based on a smaple of 100 couples with young babies, Jack considers a probit model for couples' decisions on whether going to a restaurant to celebrate wedding anniversary. Variables are defined as: Y INCOME BABY SIT = 1 if the couple went to a restaurant the couple's annual income in thousands of dollars = 1 if the couple needed a baby-sitter for babies The proposed probit model is Y = (31 + 32 INCOME; +33 BABY SIT;) +e; where is the probit function (cumulative density function of the standard normal distribution). The estiamted coefficients are: Independent Variables CONSTANT Coefficient Estimates 0.50 0.02 -0.40 INCOME BABY SIT The CDF of the standard normal distribution is attached and its PDF is listed in the following table: 2 Probablilty density function (PDF) of the standard normal distribution 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 (2) 0.40 0.40 0.39 0.38 0.37 0.35 0.33 0.31 0.29 0.27 0.24 0.22 0.19 (a) Consider a specific couple with INCOME = 50 and BABY SIT: 1. What is the estimated probability that the couple would go to a restaurant? (b) (Continued from (a)) For this specific couple, what is the marginal effect on the probability that they would go to a restaurant when their income increases? (c) (Continued from (a)) If this couple's parents can help and they no longer need to hire a babysitter, will the probability increase or decrease? And by how much? (d) If Jack uses the same sample to estimate a linear probability model below: Y = 1+2 INCOME; +3 BABY SIT; +ui What are your comments to his model specification? (e) With the same sample, Jack defines a new variable NOBABY SIT to be used in an alternative probit model: Y = (a1+ a2 INCOME; +03 NOBABY SIT;) + e where NOBABY SIT; = 1 if the couple DOES NOT need a baby-sitter. Provide esimates of a1, a2 and 3, respectively.