课程名称︰计量经济学二 课程性质︰经济学系选修 课程教师︰刘锦添 开课学院：社会科学院 开课系所︰经济学系 考试日期（年月日）︰2010.4.29 考试时限（分钟）：170分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : d 1. Demand function: Q = βP +u t t t s Supply function: Q = αP +u t t t 2 2 2 Assume Var(u )=σ ,Var(v )=σ , Cov(u ,v )=σ t u t v t t uv (a) Show that the plim of the OLS coefficient of Q or P is equal to a t t weighted average of α and β, the weighted being the variances of u and v , respectively. (b) What does this question illustrate about identification? 2. Table 1 is a model in five equations with five endogenous variables Y and four exogenous variables X: Table1 ─────────────────────────────── Coefficients of the variables Equations no. Y1 Y2 Y3 Y4 Y5 X1 X2 X3 X4 ─────────────────────────────── 1 1 β12 0 β14 0 γ11 0 0 γ14 2 0 1 β23 β24 0 0 γ22 γ23 0 3 β31 0 1 β34 β35 0 0 γ33 γ34 4 0 β42 0 1 0 γ41 0 γ43 0 5 β51 0 0 β54 1 0 γ52 γ53 0 ─────────────────────────────── Determine the identifiability of each equation with the aid of the order and rank conditions of identification. e 3. Suppose p is determined linearly by p and two ther explanatory variance x e e e e and w, with p determined adaptively as p = p +λ(p - p ). t t-1 t-1 t-1 (a) Derive the estimating equation and discuss its estimating problems. (b) Consider the following two ways of estimating this equations, both of which assume a spherical error term (i) OLS; and (ii) OLS in conjunction with a "search" over λ. Will these estimates be essentially the same? If not, which would you prefer, and why? 4. Consider the binomial variable y, which takes on the values zero or one according to the probability density function (pdf) y (1-y) f(y)=θ (1-θ) 0≦θ≦1 , y= 0, 1 Thus the probability of a "success"(y=1) is given by f(1)=θ, and the probability of a "failure"(y=0) is given by f(0)= 1-θ. Verify that E(y)=θ, and var(y)=θ(1-θ). If a random sample of n observations is drawn from this distribution, find the MLE of θ and the variance of its sampling distribution. Find the asymptotic variance of the MLE estimator. 5. In order to determine the effects of collegiate athletic performance on applicants, you collect data on applications for a sample of Division I colleges for 1985, 1990, and 1995. (i) What measures of athletic success would you include in an equation? What are some of the timing issues? (ii) What other factors might you control for in the equation? (iii) Write an equation that allows you to estimate the effects of athletic success on the percentage change in applications. How would you estimate this equation? Why would you choose this method? 6. The following is a simple model to measure the effect of a school choice program on standardized test performance [see Rouse(1998) for motivation]: score = β0 +β1*choice +β2*faminc + u1 where score is the score on a statewide test, choice is a binary variable indicating whether a student attended a choice school in the last year, and faminc is family income. The IV for choice is grant, the dollar amount granted to students to use for tuition at choice schools. The grant amount differed by family income level, which is why we control for faminc in the equation. (i) Even with faminc in the equation, why might choice be correlated with u1? (ii) If within each income class, the grant amounts were assigned randomly, is grant uncorrelated with u1? (iii) Write the reduced form equation for choice. What is needed for grant to be partially correlated with choice? (iv) Write the reduced form equation for score. Explain why this is useful. (Hint: How do you interpret the coefficient on grant?) --

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