Labor Force Participation and the Wage Gap Detailed Notes and Code Econometrics 113 Spring 2014

Transcription

1 Labor Force Participation and the Wage Gap Detailed Notes and Code Econometrics 113 Spring 2014 In class, Lecture 11, we used a new dataset to examine labor force participation and wages across groups. To do so, we pooled cross- sections of the Current Population Survey, Outgoing Rotational Groups, with 5 year gaps between each cross- section to keep the dataset manageable. Specifically, we merged the cross- sections from 1983, 1988, 1993, 1998, 2003, 2008, and 2013, and used the survey for the fourth month of each group (they were surveyed at multiple points). To begin our study of labor markets, we will focus on labor force participation, which is characterized by a group of dummy variables: empl: 1 if employed, 0 otherwise. unem: 1 if unemployed but in the labor force, 0 otherwise nilf: 1 if not in labor force, 0 otherwise. We use the summarize command to take a first look at these variables:. su empl unem nilf Variable Obs Mean Std. Dev. Min Max empl unem nilf It is also interesting to look at the fraction of the population that is unemployed or underemployed, as in working part- time. The dummy variable unempt is equal to one when the respondent is unemployed or part- time employed.. su unempt Variable Obs Mean Std. Dev. Min Max unempt We can evaluate how these variables have changed over time using the tabstat command:. tabstat empl unem unempt nilf, by(year) Summary statistics: mean by categories of: year (Year) year empl unem unempt nilf Total

2 Since most labor market statistics are conditioned on the set of the population that is in the labor force, we can condition the tabstat command using if nilf==0, which will calculate the means only using the sample of the pooled cross section for which workers are in the labor force.. tabstat empl unem unempt nilf if nilf==0, by(year) Summary statistics: mean by categories of: year (Year) year empl unem unempt nilf Total Not surprisingly, the recent unemployment rate of 6-7% is reflected in the mean of unem, conditional on labor force participation. As this is how unemployment rates are calculated, this suggests that our dataset is a pretty meaningful representation of the US Labor Force and participation within. 1 Labor Force Participation Regressions In Lecture Module 11, we specified a linear probability model to study labor force participation rates as a function of education, age, age^2, gender, and demographic characteristics. We first need to code our demographic characteristics from the survey results (in the variable wbho ):. gen age2 = age^2. gen black = 0. replace black = 1 if wbho==2. gen hispanic = 0. replace hispanic = 1 if wbho==3. gen other = 0. replace other = 1 if wbho==4 The outside group is white. We will also include year fixed effects, which we will estimate using the i.year command within the regression specification. The code and results for the regression are listed in Regression 1A. However, year fixed effects may not be sufficient if there are reasons why education levels, the age of the workforce, and composition of the population may change within states across time. As this is a 30- year collection of cross- sections 5 years apart, large changes that are differential to states could happen. So, to control for these possibilities, or more specifically absorb state- year specific shocks, we will treat state- year combinations as groups and estimate using fixed effects. To define state year groups, we use:. egen state_year = group(state year) Then, we run a fixed effects regression with xtreg, but using i(state_year) as an option (after the fe ). The precise code and results are below in Regression 1B.

3 REGRESSION 1A. reg nilf educ age age2 i.year female black hispanic other Source SS df MS Number of obs = F( 13, ) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = nilf Coef. Std. Err. t P> t [95% Conf. Interval] educ age age e year female black hispanic other _cons REGRESSION 1B. xtreg nilf educ age age2 female black hispanic other, i(state_year) fe Fixed-effects (within) regression Number of obs = Group variable: state_year Number of groups = 357 R-sq: within = Obs per group: min = 1262 between = avg = overall = max = F(7, ) = corr(u_i, Xb) = Prob > F = nilf Coef. Std. Err. t P> t [95% Conf. Interval] educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(356, ) = Prob > F =

4 To add contrast to our results related to labor force participation, we now condition the sample to only those in the workforce, and evaluate the same factors and their relationship to unemployment status. We allow for state- year fixed effects, since unemployment rates across states due to local shocks and other factors that are not national. The code and regression results are below in Regression 1C. REGRESSION 1C. xtreg unem educ age age2 female black hispanic other if nilf==0, i(state_year) fe Fixed-effects (within) regression Number of obs = Group variable: state_year Number of groups = 357 R-sq: within = Obs per group: min = 785 between = avg = overall = max = 9663 F(7,730806) = corr(u_i, Xb) = Prob > F = unem Coef. Std. Err. t P> t [95% Conf. Interval] educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(356, ) = Prob > F = Review Questions for Final 1a. Within state-year groups, calculate the age at which labor force participation is maximized or minimized. Is this a maximum or minimum? How do we know? Be careful about the definition of nilf (not in labor force) when answering this question. 1b. Within state-year groups, calculate the age at which unemployment is maximized or minimized. Is this a maximum or minimum? How do we know? 1c. Going from Regression 1A to Regression 1B, some coefficients change a bit, while others do not (educ, female). What do you think the state-year fixed effects are controlling for in this case? Think omitted variables here. 1d. In Regression 1C, please interpret the coefficients on educ, female and black.

5 2 Wage Gap Regressions In this section, we present the detailed code and related questions for our discussion of wage gaps. We use the same dataset as above. To begin, we use the real wage, rw, which is the wage of the respondent divided by a local price index, and transform using natural logs:. gen ln_rw = ln(rw) After transforming the variable into natural logs, we regress the real wage of each respondent on their education, age, and demographics, using year fixed effects. The code and results are in Regression 2A. REGRESSION 2A. xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(year) fe warning: existing panel variable is not year Fixed-effects (within) regression Number of obs = Group variable: year Number of groups = 7 R-sq: within = Obs per group: min = between = avg = overall = max = F(7,598141) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(6, ) = Prob > F = Next, we use state_year fixed effects as above rather than year fixed effects to absorb changes in wages attributable to state- year groups that are also correlated to demographic changes. The code and results are below in Regression 2B. REGRESSION 2B. xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(state_year) fe warning: existing panel variable is not state_year Fixed-effects (within) regression Number of obs = Group variable: state_year Number of groups = 357 R-sq: within = Obs per group: min = 638 between = avg = overall = max = 7478

6 F(7,597791) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(356, ) = Prob > F = Review Questions for Final 2a. Please interpret precisely the coefficient on female for both regressions 2A and 2B. 2b. Using Regression 2B, please calculate and interpret precisely the difference in wage for a black female compared to a white male. Next, we will evaluate how the wage gap has changed over time. We will focus on the male- female wage gap for now. Though this can be done in a variety of ways, the plan will be to first define a year specific dummy variable for females. That is, we are now (for example) allowing for the male- female gap to be different in 1983 from its value in The code for this is below:. gen female83 = female. gen female88 = female. gen female93 = female. gen female98 = female. gen female03 = female. gen female08 = female. gen female13 = female. replace female83 = 0 if year!=1983. replace female88 = 0 if year!=1988. replace female93 = 0 if year!=1993. replace female98 = 0 if year!=1998. replace female03 = 0 if year!=2003. replace female08 = 0 if year!=2008. replace female13 = 0 if year!=2013 The gen command assigns a variable identical to female, and then the replace command gives a zero to all observations not of that stated year. The results of replacing female with these seven variables in the within state- year regression is below in Regression 2C.

7 REGRESSION 2C. xtreg ln_rw educ age age2 female83 female88 female93 female98 female03 female08 female13 black hispanic other if nilf==0, i(state_year) fe Fixed-effects (within) regression Number of obs = Group variable: state_year Number of groups = 357 R-sq: within = Obs per group: min = 638 between = avg = overall = max = 7478 F(13,597785) = corr(u_i, Xb) = Prob > F = educ age age e female female female female female female female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(356, ) = Prob > F = Review Questions for Final 2c. Please comment on the direction of the wage gap over time. Precisely, please interpret the change in the wage gap from 1983 to 2013, as evidenced in Regression 2C. 2d. Suppose, that I want to test precisely the difference between the coefficient on female83 and female13. Please derive a regression that allows me to do this. Show your work! Next, we d like to evaluate these results by looking not just within state- year groups, but adding industries and occupations to the mix. Within the dataset, we use the two- digit industry classification, ind_2d, and the two digit occupational classification, docc03, for this purpose. Since the industry and occupational classifications are available only for 2003 onward, we drop observations for which either are not available using drop if ind_2d==. docc03==.. Then, we define industry- state- year groups, occupation- state- year groups, and then industry- occupation- state- year groups:.egen ind_state_year = group(ind_2d state year).egen occ2_state_year = group(docc03 state year).egen ind_occ2_state_year = group(ind_2d docc03 state year)

8 REGRESSION 2D xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(state_year) fe Fixed-effects (within) regression Number of obs = Group variable: state_year Number of groups = 153 R-sq: within = Obs per group: min = 638 between = avg = overall = max = 6935 F(7,258561) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(152, ) = Prob > F = REGRESSION 2E. xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(ind_state_year) fe Fixed-effects (within) regression Number of obs = Group variable: ind_state_~r Number of groups = 7208 R-sq: within = Obs per group: min = 1 between = avg = 35.9 overall = max = 750 F(7,251506) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(7207, ) = 5.54 Prob > F =

9 REGRESSION 2F. xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(occ2_state_year) fe Fixed-effects (within) regression Number of obs = Group variable: occ2_state~r Number of groups = 3361 R-sq: within = Obs per group: min = 1 between = avg = 77.0 overall = max = 1039 F(7,255353) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(3360, ) = Prob > F = REGRESSION 2G. xtreg ln_rw educ age age2 female black hispanic other if nilf==0, i(ind_occ2_state_year) fe Fixed-effects (within) regression Number of obs = Group variable: ind_occ2_s~r Number of groups = R-sq: within = Obs per group: min = 1 between = avg = 5.5 overall = max = 402 F(7,211990) = corr(u_i, Xb) = Prob > F = educ age age e female black hispanic other _cons sigma_u sigma_e rho (fraction of variance due to u_i) F test that all u_i=0: F(46723, ) = 2.40 Prob > F =

10 Review Questions for Final 2e. Do industries and occupations contribute to the wage gap (ie. different genders and races selecting into different industries and occupations), or is the wage gap amplified when looking within industries or occupations? 2f. Suppose that I claim within industry-occupation-state-year groups, the male-female wage gap is exactly twice as large as the white-black wage gap. Please write this hypothesis, and a suitable alternative. Please derive an estimating equation that allows for one to test this hypothesis. 2g. Write out code that does the following. Within industry-state-year groups, evaluate the differences in the male-female wage gap as a function of having a college degree. Put differently, does having a college degree affect the size/direction of the wage gap? Write out the regression specification you wish to estimate, and the code that will do it (including any variables that you need to generate).