EMPIRICAL STUDY AND FORECASTING II April 19, 2013
Suggested Answers for Midterm Exam.
1 (b) 2 (a) 3 (d) 4 (b) 5 (d) 6 (d) 7 (c) 8 (b) 9 (b) 10 (d) 11 (b) 12 (a) 13 (c) 14 (d) 15 (c)
二、非選擇題:
1a Letn1 =#(Y =1), the number of observations on the random variable Y which equals 1; andn2 =#(Y =2).
Then #(Y =3)=n−n1 −n2. The joint probability distribution ofY1, ...,Ynis Pr(Y1 = y1, ...,Yn = yn)=
n
Y
i=1
Pr(Yi = yi)= pn1qn2(1− p−q)n−n1−n2
The likelihood function is the above joint probability distribution treated as a function of the unknown coefficients (pandq).
1b The MLEs of pandqmaximize the likelihood function. Let’s use the log-likelihood function L =ln[Pr(Y1 = y1, ...,Yn = yn)] =n1lnp+n2lnq+(n−n1−n2)ln(1− p−q) Using calculus, the partial derivatives ofL are
∂L
∂p = n1
p − n−n1−n2 1− p−q
∂L
∂q = n2
q − n−n1−n2 1− p−q
Setting these two equations equal to zero and solving the resulting equations yield the MLE of pandq: pˆ = n1
n ,qˆ = n2 n . 5
2 2003年立法院對 「總統副總統選舉罷免法」 中增修對無效票的定義。 實驗組為「不識字比例高」的鄉鎮;對照組 為「不識字比例低」的鄉鎮。
3a The coefficient is -5.387, which indicates that women with more than 2 children work 5.387 fewer weeks per year than women with 2 or fewer children.
3b Both fertility and weeks worked are choice variables. A woman with a positive labor supply regression error (a woman who works more than average) may also be a woman who is less likely to have an additional child. This would imply that Morekids is positively correlated with the regression error, so that the OLS estimator ofβmor eki ds
is positively biased.
3c The linear regression of morekids on samesex (a linear probability model) yields morekids= 0.346
(0.001)
+ 0.066 (0.002)
samesex
so that couples withsamesex= 1 are 6.6% more likely to have an additional child that couples withsamesex= 0.
The effect is highly significant (t-statistic = 35.2)
3d samesexis random and is unrelated to any of the other variables in the model including the error term in the labor supply equation. Thus, the instrument is exogenous. The first stageF-statistic is large (F = 1238) so the instrument is relevant. Together, these imply that samesex is a valid instrument.
3e No, see the answer to (2d).
3f See column (2) of the table. The estimated value ofβmor eki ds = −6.313.
3g The results do not change in an important way. The reason is that samesex is unrelated toagem1,black,hispan, othrace, so that there is no omitted variable bias in IV regression in (2).
4a 本省籍為實驗組,外省籍為對照組。 因為在實驗中,對照組理論上僅能受控制變數影響而不能受實驗變數影響。
在本題中,外省人本來就少說台語,相較之下比較不會受政策影響,故為對照組。
4b i mpact為本省籍與1976年的交乘項。 不考慮其他變數之下,政策效果使的台語能力下降0.767。 4c 如下表:
台語能力
1976前 1976後 Differences
族群 (1) (2) (2)-(1)
(a)本省籍 8.854 7.293 -1.561
(b)外省籍 6.052 5.313 -0.739
Differences (a)-(b) 2.802 1.98 -0.822
4d 一個1980年出身的外省籍公務員其台語能力比一個同年紀的本省籍私人公司員工差了2.145−0.532+0.540= 2.153。
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