计量虚拟变量讲解
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
9 October 2010 4
Interacting Dummies with Other Explanatory Variables
For what? To allow differences in slopes. Now suppose that we wish to test whether the return to education is the same for men and women, allowing for a constant wage differential between men and women. We need a model that allows for a constant wage differential as well as different returns to education.
9 October 2010
7
(a) women earn less than men at all levels of education, and the gap increases as educ gets larger.(b) women earn less than men at low levels of education, but the gap narrows as education increases.
9 October 2010 5
Interacting Dummies with Other Explanatory Variables
To be more specific, we wish to model to be log(wage)=β0+ β1 educ+u for male, log(wage)=β’0+ β’1 educ+u for female, where β0 ≠ β’0 as we have already found evidence that there exists wage differential between male and female. Let β’0= β0+δ0 , β’1= β1+δ1 , then we can combine the above two equations using a dummy female: log(wage)= β0+δ0 female+(β1+δ1 female) educ+u, rearranging, log(wage)= β0+δ0 female+β1educ+δ1 female educ+u, where we observe the dummy, and the interaction of the dummy with other explanatory variables.
9 October 2010 6
Interacting Dummies with Other Explanatory Variables
The equation log(wage)= β0+δ0 female+β1educ+δ1 female educ+u, shows that δ0 measures the difference in intercepts between women and men, and δ1 measures the difference in the return to education between women and men. After we estimate the above equation using OLS, we can perform hypothesis about return to education and wage differential. Holding other factors unchanged, we can use figures to show the impacts of different combinations of δ0 and δ1 on log(wage).
9 October 2010
2
Interactions Among Dummy Variቤተ መጻሕፍቲ ባይዱbles
Interactions of dummy variables with other dummy variables and/or other explanatory variables makes the regression analysis much more powerful. We start with the interaction of a dummy with another dummy. Interactions of dummies allows another way to observe and test group difference among different groups.
9 October 2010 12
Example: Effects of race on baseball player salaries
The following equation is estimated for the 330 major league baseball players for which city racial composition statistics are available. black and hispan : binary indicators for the individual players. (The base group is white players.) percblck :percentage of the team’s city that is black, perchisp is the percentage of Hispanics. Other variables measure aspects of player productivity and longevity. The interactions blackpercblck and hispanperchisp are added in to observe race effects.
中级计量经济学
INTERMEDIATE ECONOMETRICS
多元回归虚拟变量之二
Chapter Outline
Describing Qualitative Information A Single Dummy Independent Variable Using Dummy Variable for Multiple Categories Interactions Involving Dummy Variables A Binary Dependent Variable: The Linear Probability Model
9 October 2010
3
Interactions Among Dummy Variables
Consider the wage model with female-married interaction with the base group still be single men:
This model also allows us to obtain the estimated wage differential among all four groups, but here we must be careful to plug in the correct combination of zeros and ones. Comment: no real advantage over using multiple dummy variables. Just another possible way.
9 October 2010 13
female female educ fedu
9 October 2010
educ 1 0.0832
fedu
1 -0.085 0.9636
1
11
Example: Log hourly wage equation
What to do? Notice the wage differential between women and men is estimated when educ=0. Not interesting. More interesting would be to estimate the gender differential at, say, the average education level in the sample (about 12.5). To do this, we would replace female educ with female(educ -12.5) and rerun the regression; this only changes the coefficient on female and its standard error.
9 October 2010
10
Example: Log hourly wage equation
Caution: interacting dummy with other explanatory variables can cause multicollinearity problem. Evidence 1: The standard error the dummy female is 0.036 without interaction term, it is 0.168 with it. 5 times larger. Evidence 2: the correlation matrix directly measures the degree of correlation:
9 October 2010 9
Example: Log hourly wage equation
The wage equation is estimated with tenure:
Interpretation: The estimated return to education for men in this equation is .082, or 8.2%. For women, it is .082 -.0056=.0764, or about 7.6%. The difference, .56%, or just over one-half a percentage point less for women, is not economically large nor statistically significant. No evidence against the hypothesis that the return to education is the same for men and women.
9 October 2010
8
Hypothesis testing
H0: the return to education is the same for women and men. This amounts to test H0: δ1 =0. That is, the wage differential should be the same for all levels of education level. H0:Average wages are identical for men and women who have the same levels of education. This is to test H0: δ 0=0, δ1 =0. F test can be used in this case.
Interacting Dummies with Other Explanatory Variables
For what? To allow differences in slopes. Now suppose that we wish to test whether the return to education is the same for men and women, allowing for a constant wage differential between men and women. We need a model that allows for a constant wage differential as well as different returns to education.
9 October 2010
7
(a) women earn less than men at all levels of education, and the gap increases as educ gets larger.(b) women earn less than men at low levels of education, but the gap narrows as education increases.
9 October 2010 5
Interacting Dummies with Other Explanatory Variables
To be more specific, we wish to model to be log(wage)=β0+ β1 educ+u for male, log(wage)=β’0+ β’1 educ+u for female, where β0 ≠ β’0 as we have already found evidence that there exists wage differential between male and female. Let β’0= β0+δ0 , β’1= β1+δ1 , then we can combine the above two equations using a dummy female: log(wage)= β0+δ0 female+(β1+δ1 female) educ+u, rearranging, log(wage)= β0+δ0 female+β1educ+δ1 female educ+u, where we observe the dummy, and the interaction of the dummy with other explanatory variables.
9 October 2010 6
Interacting Dummies with Other Explanatory Variables
The equation log(wage)= β0+δ0 female+β1educ+δ1 female educ+u, shows that δ0 measures the difference in intercepts between women and men, and δ1 measures the difference in the return to education between women and men. After we estimate the above equation using OLS, we can perform hypothesis about return to education and wage differential. Holding other factors unchanged, we can use figures to show the impacts of different combinations of δ0 and δ1 on log(wage).
9 October 2010
2
Interactions Among Dummy Variቤተ መጻሕፍቲ ባይዱbles
Interactions of dummy variables with other dummy variables and/or other explanatory variables makes the regression analysis much more powerful. We start with the interaction of a dummy with another dummy. Interactions of dummies allows another way to observe and test group difference among different groups.
9 October 2010 12
Example: Effects of race on baseball player salaries
The following equation is estimated for the 330 major league baseball players for which city racial composition statistics are available. black and hispan : binary indicators for the individual players. (The base group is white players.) percblck :percentage of the team’s city that is black, perchisp is the percentage of Hispanics. Other variables measure aspects of player productivity and longevity. The interactions blackpercblck and hispanperchisp are added in to observe race effects.
中级计量经济学
INTERMEDIATE ECONOMETRICS
多元回归虚拟变量之二
Chapter Outline
Describing Qualitative Information A Single Dummy Independent Variable Using Dummy Variable for Multiple Categories Interactions Involving Dummy Variables A Binary Dependent Variable: The Linear Probability Model
9 October 2010
3
Interactions Among Dummy Variables
Consider the wage model with female-married interaction with the base group still be single men:
This model also allows us to obtain the estimated wage differential among all four groups, but here we must be careful to plug in the correct combination of zeros and ones. Comment: no real advantage over using multiple dummy variables. Just another possible way.
9 October 2010 13
female female educ fedu
9 October 2010
educ 1 0.0832
fedu
1 -0.085 0.9636
1
11
Example: Log hourly wage equation
What to do? Notice the wage differential between women and men is estimated when educ=0. Not interesting. More interesting would be to estimate the gender differential at, say, the average education level in the sample (about 12.5). To do this, we would replace female educ with female(educ -12.5) and rerun the regression; this only changes the coefficient on female and its standard error.
9 October 2010
10
Example: Log hourly wage equation
Caution: interacting dummy with other explanatory variables can cause multicollinearity problem. Evidence 1: The standard error the dummy female is 0.036 without interaction term, it is 0.168 with it. 5 times larger. Evidence 2: the correlation matrix directly measures the degree of correlation:
9 October 2010 9
Example: Log hourly wage equation
The wage equation is estimated with tenure:
Interpretation: The estimated return to education for men in this equation is .082, or 8.2%. For women, it is .082 -.0056=.0764, or about 7.6%. The difference, .56%, or just over one-half a percentage point less for women, is not economically large nor statistically significant. No evidence against the hypothesis that the return to education is the same for men and women.
9 October 2010
8
Hypothesis testing
H0: the return to education is the same for women and men. This amounts to test H0: δ1 =0. That is, the wage differential should be the same for all levels of education level. H0:Average wages are identical for men and women who have the same levels of education. This is to test H0: δ 0=0, δ1 =0. F test can be used in this case.