Lab 6: Internal validity and LPM

Due by 2:50 PM on Thursday, April 7, 2022

Materials
Objectives
Key commands
Linear Probability Models
Lab Video
Lab 6 Worksheet
- What do I submit?
- Exercises

Materials

cps_2016.dta
Do-file template labtemplate_f21.do

Objectives

Today we’re going to keep working with cps_2016.dta, which contains information from the 2016 Current Population 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

Key commands

command	description
`codebook var1`	Look at key details for `var1`
`clonevar var1 = var2`	Make a new variable, `var1` that duplicates `var2` (including labels!)
`_pctile hourwages,per(99)`	Calcualte the 99th percentile of hourly wages, and store as a local variable
`ret list`	Show locally stored variables (handy!)

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 probablity model. There is plenty of debate about whether (and when) this is an okay idea, as it can lead to predcitions 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 intrepret coefficients are in percentage points (not percents!)

Consider the following to see:

$M a r r i e d_{i} = β_{0} + β_{1} a g e_{i} + β_{2} e d u c_{i} + u_{i}$

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

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

Lab Video

Lab 6 Worksheet

What do I submit?

Your written up answers to the exercise questions. 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.

Exercises

Open Stata, start a new do-file (or bring in a template). Make sure you add code to start (and end) a log.
Open cps_2016.dta and restrict the sample to adults (age 18+) who are married (spouse present or absent). Drop anyone who reports “NIU” (not in universe) for labor force status. Confirm that you have 73,950 observations
Check work hours, weeks of work, and wage income for any weird recodes (that is, replace any 999999 values with missing values) for the following variables. Ensure you have the correct means and number of observations. You may want to use the codebook command to help (i.e. codebook uhrsworkly)


    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
    wkswork1 |     73,950     34.0054     23.5977          0         52
  uhrsworkly |     51,921    40.19379    11.33071          1         99
-------------+---------------------------------------------------------
     incwage |     73,950    38947.58    64901.47          0    1259999

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 interpretaion on the coefficient?
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?
Create a binary variable lf equal to 1 if an individual is in the labor force, and 0 otherwise. Estimate the impact of gender on labor force status. What is the interpretation of the coefficient?
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 $i n c w a g e = β_{0} + β_{1} f e m a l e + u$ without controlling for labor force participation status?
Re-estimate the previous regression, including a control for lf: $i n c w a g e = β_{0} + β_{1} f e m a l e + β_{2} l f + u$ . Was your prediction in part (7) correct?
Now, add your cleaned variable for usual hours worked to estimate $i n c w a g e = β_{0} + β_{1} f e m a l e + β_{2} l f + β_{3} u h r s w o r k l y + u$ . What is the interpretation of each coefficient?
Why does your regression not include all 73,950 people? What type of bias might this introduce?
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?
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 lables. Re-estimate the impact of gender, labor force status and uhrsNZ on wage income (incwage). That is, you’re replacing uhrsworkly with uhrsNZ. What is the interpretation on each coefficient? Why did it change?
Now, re-estimate but exclude lf: $i n c w a g e = β_{0} + β_{1} f e m a l e + β_{3} u h r s N Z + u$ . How do your results change? Conditional on including female and uhrsNZ, does it make sense to include lf?
Create a new variable that estimates log wages: l_incwage = log(incwage). Estimate the impact of gender on logged wage income, including a control for uhrsworkly. How does the sample size change, and why? What is the interpretation on each coefficient?
Using the cleaned variables, calculate hourly wages, hourwage, based on incwage and uhoursworkly. Assume that people work 50 weeks in one year. What are mean hourly wages for men and women?
Estimate the impact of gender on hourly wages for those with non-zero hourly wages, controlling for weekly work hours. Repeat to include all adults by replacing hourly wages with 0 for non-earners. How does the impact of gender on earnings compare between the two regressions?
Do outliers affect your results? Exclude observations that exceed the 99th percentile in wages based on incwage, and re-estimate both equations. How do your results change?
Is measurement error likely to affect your dependent variable, hourwage? Why or why not? If so, what are the implications?

Last updated on March 28, 2022

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