Final Exam Review Questions - Applied Econometrics | ECON 508, Exams of Introduction to Econometrics

Download Final Exam Review Questions - Applied Econometrics | ECON 508 and more Exams Introduction to Econometrics in PDF only on Docsity! University of Illinois Department of Economics Fall 2006 Professor R. Koenker ECON 508 Final Exam Review Questions 1. In the seminal paper of Thurman and Fisher (1988) evidence is presented to resolve the long- standing conundrum: Which came first, the chicken or the egg? (a) Explain briefly the conclusion of the paper and the nature of the empirical evidence used to support it. (b) Do the statistical methods used by Thurman and Fisher constitute a reasonable method for assessing causation? Why and/or why not? 2. Consider a fictional, balanced panel data model for household demand for gasoline, yit = αi + xitβ + z′iγ + uit where i = 1, . . . , n and t = 1, . . . , T , and yit = log of household demand for gasoline in gallons/month xit = log of average price of gasoline paid by household i in month t zi = a vector of time invariant household characteristics including income, family structure, etc. A serious potential problem with the model is that the price variable, xit, may be correlated with the individual specific effect αi. This problem arises because the price paid by household i must 1 be inferred by dividing recorded expenditure on gasoline by the number of gallons purchased – since some households may search more intensively than others for a lower price, some of the observed price variation may be due to this endogenous “shopping-effect” rather than purely exogenous market variability. In particular one might expect that this endogeneity would be correlated with the household specific demand effect αi. (a) Explain briefly why OLS is an unsatisfactory method of estimating this model. (b) Since the primary objective in estimating this model is to recover an accurate estimate of the price elasticity, β, suggest a way to accomplish this which avoids the problems alluded to above regarding the endogeneity of the price variable. (c) Suppose you now estimate the model by the technique recommended in part (b.) and obtain β̂ = −.70 with a standard error of .08. Then, ignoring the endogeneity effect, you also estimate the model using the random effects estimator, i.e., treating the αi’s as a random sample with mean α0 and variance σ2α. From this you obtain β̂ = −.40 with a standard error of .06. Someone suggests using these results to test for bias due to the endogeneity. Explain the test briefly and carry it out. (d) How do the conclusions drawn in part (c.) affect your ability to estimate the parameter vector γ. Explain briefly how the availability of a new time varying covariate, say, household income, would affect your estimation strategy. 3. You have estimated the logit model logit(pi) = −4.5 + 1.7xi − .25x2i where pi is the probability that a paper submitted to the Phuzics Review is accepted for publication and xi is the natural logarithm of the length of the paper in pages. (a) If you would like to maximize the probability of acceptance, how long should your paper be? (b) By how much do you change the probability of acceptance when you cut the length of a 50 page paper to 40 pages, assuming the content is undamaged? 4. Consider the linear model y = X1β1 + X2β2 + u where u is assumed to be iid N (0, σ2). An investigator suggests using the test statistic T = (β̂1 − β̃1)1V −1(β̂1 − β̃1) where β̂1 = (X ′1M2X1) −1X ′1M2y and β̃1 = (X ′1X1) −1X ′1y 2