[試題] 98下 劉錦添 計量經濟學二 期中考
課程名稱︰計量經濟學二
課程性質︰經濟學系選修
課程教師︰劉錦添
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰2010.4.29
考試時限（分鐘）：170分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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?)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.7.59
推
04/29 22:15, , 1F
04/29 22:15, 1F