Lab 6: Internal validity and LPM

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Materials

• acs2024_4pct.dta
• Do-file template econ3500_lab_template.do

Objectives

Today we’re going to work with acs2024_4pct.dta, which contains information from the 2024 American Community Survey.

By the end of this lab, you should be able to complete the following tasks in Stata:

• Think about sample selection issues
• Estimate and interpret linear probability models
• Reason about omitted variable bias and measurement error

Data context

Each row in acs2024_4pct.dta is an individual from the 2024 ACS microdata. The file includes demographics, education, labor-force status, work hours, and earnings variables. We will restrict our sample to married adults and explore the gender wage gap, labor force participation, and how sample selection affects our estimates.

Tip: use describe, codebook, and tab ... , nolabel to check labels and coding for any variables you plan to use.

Variables we’ll use

Key commands

Linear Probability Models

What happens when our dependent variable is binary? We can use it anyway! Using OLS with a binary dependent variable is called a linear probability model. There is plenty of debate about whether (and when) this is an okay idea, as it can lead to predictions that are below zero or greater than 1, and it violates homoskedasticity assumptions. We can fix the latter by estimating heteroskedasticity-robust standard errors, and the general consensus seems to be that usually, we’re okay using a LPM. (Though we can do better!)

What about interpretation? We interpret coefficients in percentage points (not percents!)

Consider the following:

$Married_i = \beta_0 + \beta_1 age_i + \beta_2 educ_i + u_i$

$\beta_1$ means that a 1-year increase in age is associated with a 100*$\beta_1$ percentage-point change in the probability of being married. So if $\beta_1$ is 0.05, that means that being one year older is associated with a 5 percentage point increase in the likelihood of being married.

regress lf female, robust

For great slides on this (and a deeper dive), check out this resource!

Lab Video

** Note that this video is from an earlier version of the lab that used 2016 data from the Current Population Survey. Details may vary, but the implelmentation is the same!**

Workflow overview

1. Load the dataset and start your log file.
2. Restrict the sample (married adults only).
3. Inspect and clean variables (codebook, tab, replace N/A codes).
4. Generate binary indicators (female, lf).
5. Run regressions, adding controls sequentially and interpreting results.
6. Construct new variables (hourly wages, log wages) and analyze outliers.
7. Answer the worksheet questions about internal validity throughout.

Lab 6 Worksheet

What do I submit?

• Your written up answers to exercise questions (1) - (18). This can be typed or written out then scanned (or photographed), in any reasonable format.
• The do-file you’ve created that runs this analysis
• A log file that contains the results from this exercise.

Use robust standard errors in all regressions.

Example:

regress incwage female, robust

Questions

1. Open Stata, start a new do-file (or use the template). Make sure you add code to start (and end) a log.

2. Open acs2024_4pct.dta and restrict the sample to adults (age 18+) who are married (spouse present or absent). Use tab marst, nolabel to identify the correct codes. Confirm that you have 59,039 observations.

3. Check work hours (uhrswork), weeks of work (wkswork1), and wage income (incwage) for any N/A codes. In this dataset, uhrswork == 0 means “did not work last year” (N/A) — replace these with missing. Also check whether incwage has any topcode values (999999). Use the codebook command to help (e.g. codebook uhrswork). Ensure you have the correct means and number of observations:

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
    wkswork1 |     59,039    30.70257    24.59739          0         52
    uhrswork |     37,796    39.18065    12.56177          1         99
-------------+---------------------------------------------------------
     incwage |     59,039    50505.14    84753.23          0     907000

4. Generate a binary variable female equal to one if sex == 2. Estimate the impact of female on wage income (incwage) among your sample of married individuals. What is the interpretation of the coefficient?

5. If our objective is to measure the impact of gender on wage income among married people, is sample selection bias likely to be important? Why or why not? Is measurement error likely to be important? Why or why not? If so, what is the likely impact of measurement error on your estimated coefficients?

6. Create a binary variable lf equal to 1 if an individual is in the labor force (labforce == 2), and 0 otherwise. Estimate the impact of gender on labor force status. What is the interpretation of the coefficient?

7. What is the impact of being in the labor force on wage income? Based on this and the previous question, what is the implication for the direction of omitted variable bias when you estimated $incwage = \beta_0 + \beta_1 female + u$ without controlling for labor force participation status?

8. Re-estimate the previous regression, including a control for lf: $incwage = \beta_0 + \beta_1 female + \beta_2 lf + u$. Was your prediction in part (7) correct?

9. Now, add your cleaned variable for usual hours worked to estimate $incwage = \beta_0 + \beta_1 female + \beta_2 lf + \beta_3 uhrswork + u$. What is the interpretation of each coefficient?

10. Why does your regression not include all 59,039 people? What type of bias might this introduce?

11. Is measurement error likely to be important in the previous regression, and if so, for which variables? What is the likely impact of measurement error on your estimated coefficients?

12. Generate a new variable uhrsNZ that recodes all missing work hours values as zeros. You can expedite this with the clonevar command, which retains variable labels. Re-estimate the impact of gender, labor force status and uhrsNZ on wage income (incwage). That is, you’re replacing uhrswork with uhrsNZ. What is the interpretation on each coefficient? Why did it change?

13. Now, re-estimate but exclude lf: $incwage = \beta_0 + \beta_1 female + \beta_3 uhrsNZ + u$. How do your results change? Conditional on including female and uhrsNZ, does it make sense to include lf?

14. Create a new variable that estimates log wages: gen l_incwage = log(incwage). Estimate the impact of gender on logged wage income, including a control for uhrswork. How does the sample size change, and why? What is the interpretation of each coefficient?

15. Using the cleaned variables, calculate hourly wages: gen hourwage = incwage / (uhrswork * 50). We assume that people work 50 weeks in one year. What are mean hourly wages for men and women?

16. Estimate the impact of gender on hourly wages for those with positive hourly wages, controlling for usual hours worked (uhrswork). Then, replace missing hourly wages with 0 for those who worked but earned no wages, and re-estimate. How does the impact of gender on earnings compare between the two regressions? Why does the sample size change?

17. Do outliers affect your results? Exclude observations that exceed the 99th percentile in wages based on incwage, and re-estimate both equations from the previous question. How do your results change?

_pctile incwage, per(99)
ret list

18. Is measurement error likely to affect your dependent variable, hourwage? Why or why not? If so, what are the implications?