課程名稱︰計量經濟學二 課程性質︰選修 課程教師︰劉錦添 開課學院：社會科學院 開課系所︰經濟系 考試日期（年月日）: 2004.6.18 考試時限（分鐘）：180 分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 計量經濟學(二) 期末考 台大經濟系 2004.6.18 9:00-12:00 1.Suppose the probability of getting a student load is determined by a student's grade point average (GPA), age, sex, and level of study-udergraduate, MA or PhD student. (a) Explain how to use the logit model to represent this. (b) Given data on 45 students, 25 of whom were offered a loan, explain how to estimate the parameters of your model. (c) How would you estimate the probabilty that a 23year-old, male, undergraduate student, with a GPA of 3.2, will obtain a loan? Be explicit. 2. (Required calculus) Let patents be the number of patents applied for by a firm during a given year. Assume that the conditional expectation of patents given sales and RD is E(patents|sales, RD)=exp(b0+b1log(sales)+b2RD+b3RD^2) where sales is annual firm sales and RD is total spending on research and development over the past 10years. (i) How would you estimate the bj? Justify your answer by discussing the nature of patents. (ii)How do you interpret bi? (iii)Find the partial effect of RD on E(patents|sales, RD) 3. Consider a family saving function for the population of all families in the United States: sav=b0 + b1inc+ b2hhsize + b3educ + b4age + u, where hhsize is house hold size, educ is years of education of the household head, and age is age of the household head. Assume the E(u|inc, hhsize, educ, age) = 0 (i) Suppose that the sample includes only families whose head is over 25year old. If we use OLS on such a sample, do we get unbiased estimators of the bj? Explain. (ii) Now, suppose our sample includes only married couples without children. Can we estimate all of the parameters in the saving equation? Which ones can we estimate? (iii) Suppose we exclude from our sample families that save more than $25000 per year. Does OLS procedure consitent estimators of the bj? 4. Consider a simple model to estimate the effect of personal computer(PC) ownership on college grade point average for graduating seniors at a large public university: GPA = b0 + b1PC +u, where PC is a binary variable indicating PC ownership. (i) Why might PC ownership be correaleted with u? (ii) Explain why PC is likely to be related to parents' annual income. Does this mean parental income is a good IV for PC? Why or why not? (iii)Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming student, and the students who recieved grants were randomly chosen. Carefully explain how you would use this information to construct an instrumental variable for PC. 5. Suppose S: q= ap + u and D: q= bp + v are two relations operating simultaneously, where the errors u and v have zero convariance and q and p are quantity and price measured in logs. (a) Show that the plim of the least squares regression coefficient of q on p is equal to a weighted average of a and b, the weights being the variance of u and v, respectively. (b) Show why this estimate could be interpreted as a lower limit on the absolute values of the supply and demand elasticities. (c) If σv=kσu^2, where k is a known constant. show how a and b can be estimated. Hint: Two regressions are needed. (d) What does this question illustrate about identification? -- Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog. --

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