We want to study the effect of financial record on mortgage application. The binary variable to be explained is approve, which equals one if a mortgage loan to an applicant i was approved, and zero otherwise. The key variable is pubrec which equals 1 if i filed bankruptcy before. Some covariates were also observed, including hrat (housing expenditure to total income), self (equals 1 if i was self employed), white (equals 1 for white applicants), and black (equals 1 for black applicants). The coefficient estimates (and standard errors in parentheses below the coefficient estimates) for Linear Probability Model (LPM), Probit and Logit models are reported in Table below (which can be downloaded for a better view).

1)What are the advantages of using Probit to analyze binary dependent variables, such as approve?

2)Logit and Probit are estimated by the Maximum Likelihood Estimator (MLE). Outline the important properties of MLE in general, and the key assumptions necessary for those properties.

3)Based on the estimation results for Probit (1) in the Table, what is the approximate partial effect of being self employed on the probability of mortgage application approval?

4) Test the null hypothesis that financial condition has no effect on approval using the likelihood ratio test at 1% significance level. The Probit (3) model in the Table presents the estimation results for the restricted model, when the variables about financial condition ( pubrec and hrat ) are excluded.

Dependent Variable: approve LPM Logit pubrec hrat self - 304 (.028) -.003 (.0009) - .045 0.025) .122 (.031) -.072 (.037) 1,9869 -1.776 (.199) -.028 (.0035) -.423 (.149) 1.002 (251) -.371 (287) 1,989 Probit (1) Probit (2) Probit (3) 3 -1.026 -1.147 (.118) (115) -.014 -.015 (.005) (.005) -242 -.199 --226 (.079) (.107) (.109) .547 .617 (.141) (.131) -219 -269 (.166) (.166) 1,989 1,989 1,989 -656.28 -685.52 -697.16 white black Observations (n) Log-Likelihood (LLF) BIC -656.92 1359.403 1358.149 1401.418 1424.703 Dependent Variable: approve LPM Logit pubrec hrat self - 304 (.028) -.003 (.0009) - .045 0.025) .122 (.031) -.072 (.037) 1,9869 -1.776 (.199) -.028 (.0035) -.423 (.149) 1.002 (251) -.371 (287) 1,989 Probit (1) Probit (2) Probit (3) 3 -1.026 -1.147 (.118) (115) -.014 -.015 (.005) (.005) -242 -.199 --226 (.079) (.107) (.109) .547 .617 (.141) (.131) -219 -269 (.166) (.166) 1,989 1,989 1,989 -656.28 -685.52 -697.16 white black Observations (n) Log-Likelihood (LLF) BIC -656.92 1359.403 1358.149 1401.418 1424.703