Question 4 Suppose the dependent variable Xi = 1 the drivers licence applicant passed the driving test, and 0, otherwise. The vector of explanatory variables x; includes the constant and driving experience. The probability of outcome 1 conditional on x; is modeled as Pr(); = 1x:) = F(x;3), i = 1,...n where FC) is some cdf. a) Write the joint likelihood function for estimation of 8. Based on the random sample of 400 applicants, in which the average driving experience is 5 years, the following estimates have been obtained: Logit LPM Const 1.059 0.774 (0.221) 0.034) Exper 0.040 0.006 (0.016) (0.002) b) Is Exper significant at 5% level in both models? c) Interpret the coefficient on Exper. Hint: the cdf and pdf of the logistical distribution are, respectively, F(x) = 1 and f(3) = Ite d) Explain why the LPM (linear probability model) is generally not a good model to study binary choice. e) John has 10 years of driving experience. Using the logit model, calculate the probability that John will pass the driving test. By how much will this probability change if his experiences increases by 1 from 10 to 11 years? Question 4 Suppose the dependent variable Xi = 1 the drivers licence applicant passed the driving test, and 0, otherwise. The vector of explanatory variables x; includes the constant and driving experience. The probability of outcome 1 conditional on x; is modeled as Pr(); = 1x:) = F(x;3), i = 1,...n where FC) is some cdf. a) Write the joint likelihood function for estimation of 8. Based on the random sample of 400 applicants, in which the average driving experience is 5 years, the following estimates have been obtained: Logit LPM Const 1.059 0.774 (0.221) 0.034) Exper 0.040 0.006 (0.016) (0.002) b) Is Exper significant at 5% level in both models? c) Interpret the coefficient on Exper. Hint: the cdf and pdf of the logistical distribution are, respectively, F(x) = 1 and f(3) = Ite d) Explain why the LPM (linear probability model) is generally not a good model to study binary choice. e) John has 10 years of driving experience. Using the logit model, calculate the probability that John will pass the driving test. By how much will this probability change if his experiences increases by 1 from 10 to 11 years