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ETF3200-ETF5320-BEX3200: APPLIED ECONOMETRICS

Assignment 2, Semester 2, 2022

This assignment is worth 10% of the overall assessment for this unit. It is due by 9.30am, Monday September 19th, and must be submitted electronically via the "sub- mit assignment" button on Moodle by that time. It will be essential for you to accept the Universityís submission statement, so please make sure that you do this. Completing this assignment will take some time, so you are advised to start working on it early. Exten- sions (to be approved by Heather Anderson) will only be granted under exceptional and documented circumstances.

The written components of your answers can be neatly handwritten or typed, but must be submitted as a pdf Öle, and should include printouts of the requested output and graphs. You must also submit your EViews workÖle, with all output that you have included in your written report labled with the same names as the corresponding output in the workÖle. Make sure that you include your student ID number on the Öle names for all Öles that you submit.

This is NOT a group assignment and you are expected to do your own work. Any evidence of copying and/or extensive collusion could lead to a zero mark on the relevant assignment(s).

1. The objective is to use our data to understand what determines if a property-loan application is approved or not. In particular, we would like to investigate if there is any discrimination against non-white applicants in the loan market. We have a data set (loanapp.csv) comprising 824 independent observations on medium property loan applications (for loan amount between 100 and 150 thousand dollars) that includes the following variables:

Variable Code	Description
approve	1 if application is approved, 0 otherwise
white	1 if applicant is white, 0 otherwise
male	1 if applicant is male, 0 otherwise
married	1 if applicant is married, 0 otherwise
dep	number of dependents
bankrupt	1 if applicant has ever declared bankruptcy, 0 otherwise
appinc	applicantís annual income in 1000 dollars
down	down-payment as a fraction of total price

(a) (4 marks) As a Örst pass, estimate a logit model for the binary variable ap- prove, with a constant and white as explanatory variables. Does the observation that the coe¢ cient of the white dummy variable is statistically signiÖcant pro- vide conclusive evidence for discrimination? Your answer should provide brief reasoning, using no more than three sentences.

(b) (4 marks) Add all other variables in the data set as explanatory variables, and estimate the logit model. Test the overall signiÖcance of the model.

(c) (2 marks) Using the p-values, list the explanatory variables that are statistically signiÖcant at the 5% level of signiÖcance (you do not need to write the null, alternative, test statistic, etc.).

(d) (4 points) Discuss the plausibility of the sign of the estimates for each of the parameters that are statistically signiÖcantly di§erent from zero.

(e) (3 marks) Test that all of the (non-intercept) parameters that were individually insigniÖcant, are also jointly insigniÖcant. If the hypothesis is not rejected, drop all of those insigniÖcant variables from the list of explanatory variables for the remainder of Question 1.

(f) (7 points) Is there any evidence of racial discrimination? Derive the probabilities that a loan application is approved for two applicants, one white and one black, whose other characteristics are all at the median value for the sample. Compare your two results in a sentence or two.

(g) (6 marks) Probabilities are hard to explain. To present your results in a way that most people can understand, consider two applicants, one white and the other black, with exactly the same (median) characteristics (other than race), applying for the exactly the same (median) property. Determine how many percentage points the black applicant should put as down-payment more than the white applicant in order to have the same chance of approval.

2. (a) (7 marks) The binary variable HD is equal to 1 if the student obtains a high distinction in Applied Econometrics, and is equal to 0 otherwise. We want to estimate the parameter p which is the probability that HD = 1. We have a random sample of eight students who took Applied Econometrics in 2021, and we observe the following HD values: {1, 0, 0, 0, 0, 0, 0, 1} . Write down the log- likelihood function of p based on this sample, and derive the maximum likelihood estimator of p, as well as the maximum likelihood estimate .

(b) (4 marks) We expect that the probability of obtaining a high distinction in Ap- plied Econometrics depends on the studentís mark in second year econometrics (denoted by z1 ). Suppose we record the value of this variable for each of the eight people for whom the HD value was observed in part (a). Explain why the use of OLS to estimate 8 1 and 82 in the following model might not be appropriate.

E (HD|z1 ) = 81 + 82z1

(c) Suppose that we have data on N=4642 infant births and we estimate a pro- bit model with dependent variable LBWEIGHT=1 if the baby is a low birth- weight baby and 0 otherwise, MAGE is the motherís age, PRENATALI = 1 if the motherís Örst prenatal visit is in the Örst trimester and 0 otherwise, and MBSMOKE=1 if the mother smokes and 0 otherwise. The probit coe¢ cient estimates (and standard errors in brackets) are as follows:

C MAGE PRENATAL1 MBSMOKE MAGE2

0.1209 -0.1012 -0.1387 0.4061 0.0017

(.4972) (0.0385) (0.0716) (0.0672) (0.007)

(i) (5 marks) Calculate the impact of smoking on the probability of a low birth- weight baby for a 30 year old mother with PRENATALI =0, and interpret your result.

(ii) (4 marks) Calculate the marginal e§ect on the probability of a low birth- weight baby, given a one year increase in the motherís age, for a non-smoking thirty year old mother with PRENATALI=0. Interpret your result.