ECON Introductory Econometrics. Seminar 4. Stock and Watson Chapter 8

Transcription

1 ECON Introductory Econometrics Seminar 4 Stock and Watson Chapter 8

2 empirical exercise E8.2: Data 2 In this exercise we use the data set CPS12.dta Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the Current Population Survey (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected U.S. households are surveyed each month. The file CPS12.dta contains the data for 2012 (from the March 2013 survey). These data are for full-time workers, defined as workers employed more than 35 hours per week for at least 48 weeks in the previous year. Data are provided for workers whose highest educational achievement is (1) a high school diploma, and (2) a bachelor s degree.

3 empirical exercise E8.2: Data 3 Series in Data Set: FEMALE: 1 if female; 0 if male YEAR: Year AHE : Average Hourly Earnings BACHELOR: 1 if worker has a bachelor s degree; 0 if worker has a high school degree

4 empirical exercise E8.2: Data 4 Tuesday March 3 14:58: Page 1 (R) / / / / / / / / / / / / Statistics/Data Analysis 1. sum Variable Obs Mean Std. Dev. Min Max year ahe bachelor female age

5 Tuesday March 3 15:01: Page 1 empirical exercise E8.2 part a) (R) / / / / / / / / / / / / Statistics/Data Analysis 5 1. regress ahe age female bachelor, robust Linear regression Number of obs = 7440 F( 3, 7436) = Prob > F = R-squared = Root MSE = Robust ahe Coef. Std. Err. t P> t [95% Conf. Interval] age female bachelor _cons If age increases from 25 to 26, earnings are expected to increase by $0.51 per hour. If age increases from 33 to 34, earnings are expected to increase by $0.51 per hour.

6 empirical exercise E8.2 part b) (R) 6 / / / / / / / / / / / / Statistics/Data Analysis 1. gen lnahe=ln(ahe) 2. regress lnahe age female bachelor, robust Linear regression Number of obs = 7440 F( 3, 7436) = Prob > F = R-squared = Root MSE = Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] age female bachelor _cons If age increases from 25 to 26, earnings are expected to increase by 2.55%. If age increases from 33 to 34, earnings are expected to increase by 2.55%. These values, in percentage terms, are the same because the regression is a linear function relating ln(ahe) and age.

7 Tuesday March 3 15:11: Page 1 empirical exercise E8.2 part c) (R) / / / / / / / / / / / / Statistics/Data Analysis 7 1. gen lnage=ln(age) 2. regress lnahe lnage female bachelor, robust Linear regression Number of obs = 7440 F( 3, 7436) = Prob > F = R-squared = Root MSE = Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] lnage female bachelor _cons ln(ahe) = 0.75 (ln(26) ln(25)) = so if age increases from 25 to 26, earnings is expected to increase by 2.9%. ln(ahe) = 0.75 (ln(34) ln(33)) = so if age increases from 25 to 26, earnings is expected to increase by 2.2%.

8 empirical exercise E8.2 part d) 1. gen age2=age^2 2. regress lnahe age age2 female bachelor, robust (R) / / / / / / / / / / / / Statistics/Data Analysis 8 Linear regression Number of obs = 7440 F( 4, 7435) = Prob > F = R-squared = Root MSE = Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] age age female bachelor _cons ln(ahe) = ( ) ( ) = so if age increases from 25 to 26, earnings is expected to increase by 3.7%. ln(ahe) = ( ) ( ) = so if age increases from 25 to 26, earnings is expected to increase by 1.7%.

9 empirical exercise E8.2 part e) 9 The regressions differ in their choice of one of the regressors. They can be compared on the basis of the adjusted R 2 Part b): display e(r2_a) Part c): display e(r2_a) Regression in part c) has a marginally higher adjusted R 2, but the differences are very small.

10 empirical exercise E8.2 part f) 10 The regression in (d) adds the variable age 2 to regression (b). The coefficient on age 2 is not statistically significant at the 5% level (t = 1.72<1.96) and the estimated coefficient is very close to zero. This suggests that (b) is preferred to (d) (note: conclusion would be different at 10% level)

11 empirical exercise E8.2 part g) 11 The regressions differ in their choice of the regressors (ln(age) in (c) and age and age 2 in (d)). They can be compared on the basis of the adjusted R 2. Part c): display e(r2_a) Part d) display e(r2_a) The regression in (d) has a (marginally) higher adjusted R 2, so it is slightly preferred.

12 empirical exercise E8.2 part h) ln(ahe) age part b) log-linear part d) log-quadratic part c) log-log The regression functions for women with a college degree will look just like these, but they will be shifted by the amount of the coefficient on the binary regressors female and bachelor.

13 Tuesday March 3 16:14: Page 1 empirical exercise E8.2 part i) (R) / / / / / / / / / / / / Statistics/Data Analysis gen interaction=female*bachelor 2. regress lnahe age age2 female bachelor interaction, robust Linear regression Number of obs = 7440 F( 5, 7434) = Prob > F = R-squared = Root MSE =.4777 Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] age age female bachelor interaction _cons The coefficient on the interaction term shows the difference between men and women in the association between having a bachelor degree and log hourly earnings.

14 empirical exercise E8.2 part i) 14 Predicted values of ln(ahe): Alexis: x = 3.00 Jane: = 2.51 Alexis-Jane= = 0.49 Bob: = 3.15 Jim: = 2.75 Bob-Jim= = 0.4

15 empirical exercise E8.2 part j) Tuesday March 3 16:41: Page 1 15 (R) / / / / / / / / / / / / Statistics/Data Analysis 1. gen age_female=age*female 2. regress lnahe age female age_female bachelor, robust Linear regression Number of obs = 7440 F( 4, 7435) = Prob > F = R-squared = Root MSE = Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] age female age_female bachelor _cons

16 empirical exercise E8.2 part k) Tuesday March 3 16:42: Page 1 16 (R) / / / / / / / / / / / / Statistics/Data Analysis 1. gen age_bachelor=age*bachelor 2. regress lnahe age female age_bachelor bachelor, robust Linear regression Number of obs = 7440 F( 4, 7435) = Prob > F = R-squared = Root MSE = Robust lnahe Coef. Std. Err. t P> t [95% Conf. Interval] age female age_bachelor bachelor _cons

17 empirical exercise E8.2 part l) 17 The estimated regressions suggest that earnings increase as workers age from 25 35, the range of age studied in this sample. Can we say more...?