econ6511

Advanced Applied Econometrics (Econ 6511) Assignment 2

Due Thursday, Febraury 4 at 6:30pm. Students may discuss answers in groups but must submit unique answers.

1. (10 points) (Wooldridge, Chapter 17, Problem 3(ii)) Suppose in the Tobit model that x1 = z1 and x2 = z

2 1, show that

∂E(y|y > 0,x) ∂z1

= (β1 + 2β2z1) (1 −λ(xβ/σ)[xβ/σ + λ(xβ/σ)])

where β1 is the coefficent on z1 and β2 is the coefficent on z 2 1.

2. (From Winter 2015 Midterm Exam) Consider the bank failure logit results on the next page. The dependent variable is 1 if the bank failed in 2008 or 2009 and 0 if it survived. The regressors are balance sheet variables as of December 2007 as a proportion of total assets.

(a) (5 points) Which of the two specifications fits the data better? How can you tell?

(b) (5 points) Using the first specification, calculate the fitted probality of failure for a bank with equity = .1, ltdep = .15, past30 = .01, and income = invsec = nonacc = oreo = 0. (Hint: the cumulative distribution for logit is G(z) = e

z

1+ez .)

(c) (5 points) The variable ltdep measures large time deposits. Are large time deposits associated with higher or lower risk of bank failure? How can you tell?

(d) (5 points) What is one advantage of running a logit regression instead of estimating a linear probability model with OLS?

(1) (2) fail0809 fail0809

equity -12.67∗∗∗ -11.85∗∗∗

(3.267) (3.166)

income -16.78∗∗ -17.43∗∗

(5.594) (5.418)

invsec -1.352 -1.697 (0.894) (0.882)

ltdep 2.933∗∗ 3.425∗∗∗

(0.922) (0.870)

past30 53.63∗∗∗

(7.716)

past90 66.43∗∗∗

(19.27)

nonacc 43.69∗∗∗ 57.28∗∗∗

(5.893) (5.721)

oreo 12.19 23.10∗

(11.94) (11.06)

cons -3.563∗∗∗ -3.565∗∗∗

(0.417) (0.401) N 7671 7671 Log-likelihood -526.81926 -545.87596

Standard errors in parentheses ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

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