课程名称︰计量 课程性质︰选修 课程教师︰刘锦添 开课学院： 开课系所︰经济系 考试日期（年月日）︰2013.5.2 考试时限（分钟）：120mins 是否需发放奖励金：yes （如未明确表示，则不予发放） 试题 : 1. Let S*t be the desired savings of a household and Y*t be its expected income. The relationship between these two variables is of the form S*t = α + βY*t. According ti the partial adjustment and adaptive expectations rules, St= S(t-1)+ λ(S*(t-1)-S(t-1)) Y*t= Y*(t-1)+ μ(Y(t-1)-Y*(t-1)) where St is actual saving and Yt is actual income. You have data on only St and Yt, and none on S*t and Y*t. (a) State the signs and other restrictions you would expect for the unkonwn parameters α, β , λ, and μ. Explain your reasons. (b) Derive a relationship that can be used to estoimate α, β , λ, and μ. Add an error tern ut at the end. (c) State all the assumptions on ut that will make OLS you got in part (b) consistent. Are the estimates BLUE? Why or why not? (d) Can α, β , λ, and μestimated? If not, explain why. If yes, describe how they can be estimated: that is, express α , β , λ, and μ in terms of the estimates of the model in part (b). 2. Suppose annual earnings and marijuana usage are determined jointly by log(earnings) = β0 + β1 gMINt+β2educ + u1 marijuana = γ0 +　γ1 log(earnings)　+ γ2 educ + γ3 fine + γ4 prison + u2 where fine is the typical fine for people possessing small amounts of marijuana and prison is a dummy variable equal to one if a person can serve prison time for being in possession of marijuana. Assume fine and prison can vary with the country of residence. (a) If educ, fine, and prison are exogenous, what do you need to assume about the parameters in the system in order to consistently estimate beta s? (b) Explain how would you estimate the beta s, assuming the parameters are identified. (c) Do you have over identification? 3. Suppose that, for a given state in the United States, you wish to use annual time series data to estimate the effect of the state-level minimum wage on the employment of those 18 to 25 years old (EMP). A simple model is gEMPt=β0+β1gMINt+β2gPOPt+β3gGSPt+β4gGDPt+ut, where MINt is the minimum wage, in real dollars, POPt is the population from 18 to 25 years old, GSPt is gross state product, and GDPt is U.S. gross domestic product. The g prefix indicates the growth rate from year (t-1) to year t, which would typically be approximated by the difference in the logs. (a) If we are worried that the state chooses its minimum wage partly based on unobserved (to us) factors that affect youth employment, what is the problem with OLS estimation? (b) Let USMINt be the U.S. minimum wage, which is also measured in real terms. Do you think gUSMINt is uncorrelated with ut? (c) By law, any state’s minimum wage must be at least as large as the U.S. minimum. Explain why this makes gUSMINt a potential IV candidate for gMINt. 4. Suppose that, for one semester, you can collect the following data on a random sample of college juniors and seniors for each class taken: a standardized final exam score, percentage of lectures attended, a dummy variable indicating whether the class is within the student’s major, cumulative grade point average prior to the start of the semester, and SAT score. (a) Why would you classify this data set as a cluster sample? Roughly how many observations would you expect for the typical student? (b) Write a model that explains final exam performance in terms of attendance and the other characteristics. Use s to subscript student and c to subscript class. Which variables do not change within a student? (c) If you pool all of the data together and use OLS, what are you assuming about unobserved student characteristics that affect performance and attendance rate? What roles do SAT score and prior GPA play in this regard? (d) If you think SAT score and prior GPA do not adequately capture student ability, how would you estimate the effect of attendance on final exam performance? --

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