Assignment: Advanced Applied Econometrics
1. Suppose in the Tobit model that x1 = z1 and x2 = z21, show that
∂E(y|y > 0, x)/∂z1 =(β1 + 2β2 z1 ) (1 - λ(xβ/σ)[xβ/σ + λ(xβ/σ)])
where β1 is the coefficent on z1 and β2 is the coefficent on z21.
2. Consider the bank failure logit results given below. 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) Which of the two specifications fits the data better? How can you tell?
(b) 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.
(c) 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) What is one advantage of running a logit regression instead of estimating a linear probability model with OLS?
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(1)
fail0809
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(2)
fail0809
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equity
|
-12.67∗∗∗
(3.267)
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-11.85∗∗∗
(3.166)
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income
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-16.78∗∗ (5.594)
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-17.43∗∗ (5.418)
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invsec
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-1.352
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-1.697
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(0.894)
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(0.882)
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ltdep
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2.933∗∗ (0.922)
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3.425∗∗∗ (0.870)
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past30
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53.63∗∗∗ (7.716)
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|
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past90
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|
66.43∗∗∗ (19.27)
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nonacc
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43.69∗∗∗ (5.893)
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57.28∗∗∗ (5.721)
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oreo
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12.19
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23.10∗
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|
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(11.94)
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(11.06)
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cons
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-3.563∗∗∗ (0.417)
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-3.565∗∗∗ (0.401)
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N
|
7671
|
7671
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Log-likelihood
|
-526.81926
|
-545.87596
|
Standard errors in parentheses
∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001