[試題] 99上 張勝凱 計量經濟理論一 期中考
課程名稱︰計量經濟理論一
課程性質︰必修
課程教師︰張勝凱
開課學院：社會科學院
開課系所︰經濟學研究所
考試日期（年月日）︰2010/11/10
考試時限（分鐘）：120mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Problem 1.(25 points (5,10,10))
︿ ︿ ︿
Let θ=(θ1,θ2)' be a √N-asymptotically normal estimator for θ=(θ1,θ2)'.
︿ ︿ ︿
Let γ=2*θ1*θ2^2 be an estimator of γ=2*θ1*θ2^2.
︿
1. Is γ a consistent estimator of γ ? Explain.
︿ ︿
2. Find Avar(γ) in terms of θ and Avar(θ).
︿ ︿
3. If, for a sample of data,θ=(1,2)' and Avar(θ) is estimated as
┌ ┐
│1 -0.5│
│-0.5 2 │
└ ┘ ︿
Find the asymptotic standard error of γ.
Problem 2. (30 points (10,10,10))
Let E(y|x,q)= x*β+γ* q , thus y=x*β+γ* q+ v, where E(v|x,q)=0.
1. Suppose that we can observe y and both x and q, would OLS estimators of y
on x and q provide an unbiased estimators of β ? Why or why not? Would
OLS estimators of y on x and q provide an best linear unbiased estimator(
BLUE) ofβ ? Why or why not?
2. Suppose we do not observe q, under what conditions , would OLS estimators
of y on x provide an unbiased estimators ofβ ? Why?
3. Suppose there is a variable z where E(q|z)=δ*z. Suppose also that
E(y|z,q,z)=E(y|x,q), would OLS estimators of y on x and z provide an
unbiased estimators ofβ ? Why or why not?
Problem 3. (45 points (8,8,5,8,8,8))
-1
Recall the long regression model y=X1*β1+X2*β2+ε. Let N1≡X1(X1'X1) X1',
* *
M1≡I-N1, X2 ≡M1*X2 and y ≡M1*y.Let b1 and b2 be an OLS estimatiors ofβ1
andβ2 in equation (1),e is the residual term correspondingly. That is
︿
y=X1*b1+X2*b2+e, y =X1*b1+X2*b2
1. Write down the normal equations (first order conditions) for OLS estimators
b1 and b2.
*' *-1 *'
2. Show that b2=(X2 X2 ) X2 y.
3. Show M1e=e.
︿ ︿
4. Show y'y= y'y +e'e.
*
5. Find the residual term of the regression y on X1.
* *
6. Find the residual term of the regression y on X2 .
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01/22 14:38, , 1F
01/22 14:38, 1F