[試題] 94下 劉錦添 計量經濟學(二) 期末考
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︰經濟學系
考試日期（年月日）︰2006年 6 月 23日
考試時限（分鐘）：180分鐘 (0900 - 1200)
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
國立台灣大學經濟學系 劉錦添 教授
考試時間: 2006年6月23日(五) 早上 9:00-12:00
1. (30%) y*i = β1 + β2x2i + ui 式中，ui~N(0,σ^), 請分別寫出下列各小題的
概似函數(log likelihood function), score function, 以及參數的估計過程。
(1) y* is latent variable, if y*i>0 then yi =1, else yi=0.
(2) if y*i = 0, then yi = 0; if yi*>0, then yi = y*i.
(3) 若* 為Box-cox Transformation, i.e. y*i = y
2. (40%) 針對下面各種問題，寫出經濟理論、計量模型與估計方法。
(1) y1 = β1 + β2x2i + ui式中，y1 為受訪者在過去一個月生病天數，x2i為受訪者
教育程度。回歸式需要再引進哪些變數? 可否利用OLS估計？
(2) ln waget = β1 + β2x2i + β3x3i +...+βkxki + ui 式中，waget 為有偶結婚
婦女的工資率，清說明回歸式需包括哪些解釋變數，why? 可否利用OLS估計？
(3) 新生兒出生時的體重可能會受到母親健康的影響，如果我們有新生兒出生時的體重
與母親當年出生時的體重，請問該如何估計母親健康對新生兒健康的影響？利用OLS
估計有何缺陷？如何補救?
(4) 探討教育的工資報酬，如利用單一年度橫斷面資料估計有何缺陷？利用同卵雙胞胎
資料有何優點？why?
(5) 1995年台灣全民健保的實施之後，民眾門診看病價格下跌，門診需求量上升。如政
府想請您評估健保的實施對門診量的影響，您應該如何進行？
3.(20%) Suppose the probability that a person is a smoker is given by the logit
model, namely exp(α+βx)[1+exp(α+βx)]^-1 where x is a dummy variable
taking the value one for males and zero for female. We have 100 observations,
of which 10 are smoking males, 15 are smoking females, and 35 are nonsmoking
males.
(1) What is the Maximum Likelihood Estimation (MLE) of the probability
that a person is a smoker, under null that β=0.
(2) What are the MLEs of αβ.
(3) What is the MLE of the probabilty that a male is a smoker, and of the
probabilty that a female is a smoker? Compare these answer to those
obtained by estimating the probability by the fraction of smokers in the
data in the relevant category.
4.(10%) Suppose the price of a stock is determined by p =α+βx+εwhere ε
is distributed normally with mean zero and variance σ^2. On some days the
stock does not trade, so the bid and ask price(Pb and Pa, respectively)
are reported instead of the actual price (which if it were to have been
determined, would lie between the bid and ask prices). Given a year's worth
of daily data, including days on which the stock did not trade, explain how
you would estimate.
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exchange of one bone for another with another dog.
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