The following estimates were calculated from a sample of 753 women respondents. The dependent variable takes the value 1 if the woman was in labor force, and 0 otherwise. educ Huswage Age age2 kidsl16 Constant OLS 0.051 (0.008) -0.014 (0.004) 0.008 (0.004) -0.022 (0.004) -0.292 (0.037) 0.197 (0.519) Logit 0.244 (0.040) -0.069 (0.020) 0.012 (0.007) -0.075 (0.129) -1.409 (0.198) -0.938 (2.507) Probit 0.148 (0.023) -0.042 (0.012) 0.010 (0.006) -0.049 (0.078) -0.855 (0.115) -0.620 (1.516) Where educ is education in years, huswage is husband's hourly wage in dollars; age is age in years; age2 is (age)/100; kidslt6 is the number of children less than 6 years of age. Conventionally calculated standard errors are in brackets for the ordinary least squares (OLS) results, asymptotic standard errors are in brackets elsewhere. (a) Explain fully the problem with OLS estimation Using all three sets of estimates, test the null hypothesis that the coefficient of age is zero at 5% and at 1% significance level. Which test statistics would you consider more reliable? Explain. (5 marks) (c) Using OLS and Probit estimates, calculate the estimated probabilities of being in employment for a woman aged 30 with 10 years of education, two children who are less than 6 years old and whose husband earns 5 dollars per hour. (4 marks) (d) Test the null hypothesis that all the slope coefficients of the probit model are jointly equal to zero. It is given that In LR=-514.87 In LU = -459.90, where In LR and In LU are the log of the likelihood from the restricted and the unrestricted probit models respectively. (2 marks)