Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Quantitative Methods II

Problem Set 5

Due on Friday, December 2nd

When using STATA for portions of this assignment: Make sure to hand in 1) a print out of a do-file containing all the commands that you used; and 2) written answers to the questions.  Each question is worth 2 points unless stated otherwise (20 pts total).  

Exercise 1 GMM Estimation and Limited Dependent Variable models:

You are working with a data set of loan applications for mortgages, loanapp.dta.  You want to understand the determinants of loan approval.  You have the following variables in the data set:

 – dummy variable for loan approval

 – dummy variable for married or not

 – dummy variable for race

 – loan amount scaled by the house price

 – whether your credit assessment satisfies the guideline for a loan

 – amount of consumer loans outstanding

 – number of credit cards

Before running any analysis, you look at the outcome variable and find the following.

a) You begin with running the following analysis.  

. gmm (approve - {b1}*married - {b2}*black - {b3}*loanprc - {b4}*gdlin - {b5}), instruments(married black loanprc gdlin) nolog

What type of a model are you estimating above using GMM?  Could you obtain identical results using a different approach?  If so, what is it?

b) Interpret the coefficients on /b1 and /b2 above.  Make sure to note statistical significance as appropriate.

c) You next decide to run the following model.

. gmm (approve - {b1}*married - {b2}*black - {b3}*loanprc - {b4}*gdlin - {b5}), instruments(married black loanprc cons lines) nolog

How does this model differ from that you estimated in a)?  Replicate the above results using the ‘ivregress gmm’ command.  Show the Stata syntax and the output.

d) Although you used a different approach in c), you find that the estimated coefficients are not much changed from those in a).  What is your explanation for this finding?

e) You next decide to try and estimate the above model using 2SLS.  You obtain the following results.

You noticed that the regression results have changed a little bit from those shown above in c).  Explain why you think occurred.  Is there any reason to prefer one model to another or are they simply results from different approaches?

f) In the remained of this Exercise, you decide to use Limited Dependent Variable approaches to examine the determinants of loan approval.

You decide to begin by estimating a logit model to look at partial effects.

You first look at the margins with respect to  and obtain the following:

Explain what the above marginal coefficient reports?  Discuss its statistical difference.

g) Finally, you decide to approach this problem by looking at the implied odds ratios from the logit regression.  You obtain the following results:

What does the coefficient on  tell you about the presence of racial biases in mortgage approvals?

Exercise 2 Time Series Forecasting:

a) Your undergraduate friend has run a time series regression for unemployment on a set of regressors and is very excited to have gotten an R²of 82% with some of the regressors significant at conventional levels.  Your friend is excited about this result and keen on using it to forecast unemployment.  Should you share your friends excitement?  Discuss.

b) We evaluate time series forecasts using the root mean squared error (RMSE) and the mean absolute error (MAE).  Explain how you construct each of these measures.

c) You want to compare a forecast for unemployment with a forecast for inflation.  You think that using RMSE and MAE will tell you which forecast is performing better.  Your friend notes that this runs into a problem.  What is it?