计量经济学 实验二

浙江财经大学
实验（实训）报告
项目名称邹检验（Chow test）
所属课程名称计量经济学（统计）
项目类型验证性实验
实验(实训)日期15年03月27 日
班级
学号
姓名
指导教师
浙江财经大学教务处制
实验二报告
Chow 检验（验证性实验）
实验类型：验证性实验
实验目的：
学会用虚拟变量进行项目评价分析；理解Chow 检验的本质，掌握Chow 检验的方法，并体会其局限性；掌握用Stata产生多分类变量的虚拟变量的使用技
巧；掌握Stata 的bysort 和regress 相结合使用来估计不同组的回归方程。

通过此题体会Stata 的优越性。

实验内容：
Chow 检验。

实验要求：
掌握Chow 检验,按具体的题目要求完成实验报告,并及时上传到给定的FTP ！
实验题目：
[abstracted from << Introductory Economerics >>chapter7 C7.11] Use the data in 401KSUBS. DTA for this exercise.
(i)Compute the average, standard deviation, minimum ,and maximum values of nettfa in the sample.
(ii)Test the hypothesis that average nettfa does not differ by 401(k) eligibility status; use a two-sided alternative .
[Hint: regress nettfa on e401k ]
(iii) Estimate a multiple linear regression model for nettfa that includes income, age, and e401k as explanatory variables. The income and wage variables should appear as quadratics. Now ,what is the estimated dollar effect of 401(k) eligibility.
(iv)To the model estimated in part(iii) ,add the interactions e401k*(age-41) and e401k*(age-41)2.Note that the average age in the sample is about 41,so that in the new model ,the coefficient on e401k is the estimated effect of 401(k) eligibility at the average age. Which interaction term is significant?
(v)Comparing the estimates from parts(iii) and (iv) ,do the estimated effects of e401(k ) eligibility at age 41 differ much? Explain.
(vi)Now, drop the interaction terms from the model ,but define five family size dummy variables:fsize1,fsize2,fsize3,fsize4 and fsize5.The variable fsize5 is unity for families with five or more members. Include the family size dummies in the model estimated from part(iii) ;be sure to close a base group .Are the family dummies significant at 1%level?
(vii)Now, do a Chow test for the model
μββββββ++++++=k e age age inc inc nettfa 40152432210
across the five family size categories ,allowing for intercept differences. The restricted sum of squared residuals, SSRr ,is obtained from part(vi) because that regression
assumes all slopes are the same. The unrestricted sum of squared residuals is 521SSR SSR SSR SSR ur +++= ,wher SSR f is the sum of squared residuals for equation estimated using only family size f. You should convince yourself that there are 30 parameters in the unrestricted model(five intercepts plus 25 slopes)
and 10 parameters in the unrestricted model(five intercepts plus 5 slopes).
Therefore, the number of restrictions being tested is q=20,and the df for the unrestricted model is 9275-30=9245.
实验题目分析报告：
(i)
sum nettfa
Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------
nettfa | 9275 19.07168 63.96384 -502.302 1536.798
(ii) reg nettfa e401k
ˆ18.858 and 14.01.e401k e401k t β== 因此拒绝原假设，平均值无明显差距。

系数的意思是平均一个合格401（k ）计划的家庭有更多的$18,858总的净金融资产
(iii)
reg nettfa e401k inc age incsq agesq
nettfa =23.09+9.705 e401k- 0.278 inc + 0.0103 inc2- 1.972 age + 0.0348 age2
(9.96) (1.277) (.075) (.0006) (.483) (.0055)
n = 9,275, R2 = .202
保持收入和年龄不变，401（k）资格的家庭估计有9705美元的财富超过一个非符合资格的家庭。

这只刚超过$18,858的一半
(iv)
gen a=e401k*(age-41)
gen b=e401k*(age-41)^2
reg nettfa e401k inc age incsq agesq a b
只有e401k*(age-41)交互作用是显著的，系数是0.654（t=4.98），结果表明随着年龄增长401（k）合格对金融财富的影响，另一种认为年龄对401（k）合格的总资产净额有较强的积极作用，e401k*(age-41)^2的系数为-0.0037886（t=-0.33），
所以放弃这个交互。

(v)
在（iii）中401（k）对所有年龄的影响都是相同的，9705。

在（iv）的回归方程中401（k）的系数是9960，在平均年龄41的影响。

包括相互作用增加e401k估计效果，但是只有$255。

如果我们观察（IV）的影响在很宽的年龄范围，我们会看到更多的戏剧性的差异。

(vi)
tabulate fsize,gen(fsize)
drop fsize5 fsize6 fsize7 fsize8 fsize9 fsize10 fsize11 fsize12 fsize13
gen fsize5=1- fsize1- fsize2- fsize3- fsize4
reg nettfa e401k inc age incsq agesq fsize2 fsize3 fsize4 fsize5
test fsize2 fsize3 fsize4 fsize5
nettfa=16.34 + 9.455 e401k- 0.240 inc + 0.0100 inc2- 1.495 age + 0.0290 age2 (10.12) (1.278) (.075) (.0006) (.483) (.0055)
- 0.859 fsize2 - 4.665 fsize3- 6.314 fsize4- 7.361 fsize5
(1.818) (1.877) (1.868) (2.101)
n = 9275, R2 = 0.204, SSR= 30215207.5
四种家庭的F统计量为5.44，p值0.0002，所以这四个虚拟变量联合显著(vii)（vi）中约束模型的SSR是30215207.5，无约束模型的SSR是通过增加五个
SSR=29985400，F （20,9245）= [(30,215,207.5 单独的家庭规模回归的SSR得到，ur
- 29,985,400)/ 29,985,400]*(9245/20) ≈ 3.54. P值接近0，有强有力的证据表明斜率变化在家庭大小。

允许单独改变截距是不够的。

如果你看看个别的回归，你会看到在收入变量的迹象，实际上改变了整个家庭的大小。