PS5+answer+sheet2009 - Department of Economics University...

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Department of Economics Spring 2009 University of California Prof. Woroch Economics 140: Problem Set 5 ANSWER SHEET Instructions: Include the names/SIDs of members of your study group (maximum of 3) and the name of your common GSI. Staple your answer sheets—otherwise it will not be accepted. I. True/False/Uncertain and Explain. Below are statements that may be true or false, or possibly ambiguous. State which one you believe to be the case, and more importantly, give a detailed but concise explanation for your answer. 1. Suppose that using data on mortgage application decisions, estimation of a probit model of denial generated the following results: Pr( deny = 1| P/I Ratio , black ) = (–2.26 + 2.74 P/I ratio + 0.71 black ). Given this probit specification, and the probit coefficient estimates, the effect of increasing the P/I (“payment to income”) ratio from 0.3 to 0.4 for a white person amounts to 2.74 percentage points. Answer : False. It is found by evaluating the estimated probit model at the two hypothesized situations: Pr( deny =1| P/I =0.4, white ) - Pr( deny =1| P/I= 0.3, white ) = (–2.26 + 2.74×0.4) - (–2.26 + 2.74×0.3) = (–1.164) - (–1.143) = 0.1222 - 0.0752 = 0.046995, or 4.7% increase in probability of mortgage denial. (Alternatively, one could approximate the effect of this change using the derivative of the denial probability with respect to P/I: Pr( deny =1| P/I , white )/ (P/I)× Δ (P/I) = / (P/I)× Δ (P/I) = φ (–2.26+2.74×0.3)×2.74× Δ (P/I) = 0.1419×2.74×0.1 = 0.03889, or about 3.9%. This is quite a bit different than the discrete comparison we made because the denial probability is highly nonlinear in the vicinity of the change in P/I .) 2. When calculating the standard errors of TSLS coefficient estimates you do not have to worry about heteroskedasticity because it will be taken into account in the first stage OLS estimation. You cannot, however, be certain that the standard errors reported by OLS estimation of the second stage regression where fitted values of endogenous regressors from the first stage are used in place of the regressors’ original values are consistent. Answer : True and false. Heteroskedasticity robust estimation in the first stage of TSLS will accommodate heteroskedasticity of the error in the relation between the instruments and the endogenous regressors. However, it does not address possible heteroskedasticity in the error of the relation between the fitted values from that first stage and the dependent variable, i.e., the second stage. It is true, however, that when the research simply runs that second regression taking the fitted values as exogenous, the standard errors are not good estimates of the standard deviation of the original regressor. After all, the second stage regression ignores the sampling error introduced into those fitted values, instead taking those values as exogenous in the second stage. A good econometric software package will not make that mistake; it will generate standard errors that take account of sampling error introduced in first stage.
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This note was uploaded on 02/02/2012 for the course ECON 140 taught by Professor Duncan during the Spring '08 term at Berkeley.

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PS5+answer+sheet2009 - Department of Economics University...

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