Lab 4: Multivariate Regression

Creating binary variables

Recall that there are two easy ways to make binary variables out of categorical or continuous variables. Consider the variable race, where 100 = White, 200 = Black, 300 = Native American, 651 = Asian, etc. Suppose you want to generate a binary indicator for whether a person is White.

• gen white = race == 100: generates a variable equal to 1 if race is 100, and 0 otherwise

• gen white = 1 if race == 100: generates a variable equal to 1 if race is 100, and missing otherwise. To complete this you need two lines of code:
  gen white = 1 if race == 100
replace white = 0 if race != 100

Working with loops

Loops can help us (1) avoid errors and (2) code super fast!

I’ve uploaded a sample from our class here, as lab4_sample.do

Stata has two types of looping setups, using the forval or foreach command. The first is simpler, and the second is more versatile. Recall that you can always use help forval or help foreach if your code isn’t working or if you have a vision you’re not sure how to realize.

forvalues lname = range {
                Stata commands referring to `lname'
        }

forval i = 0/2{
gen labfor`i' = labforce == `i'
}

foreach x in "rice wheat corn rye barley oats" {
          display "`x'"
        }

    foreach num of numlist 1 4/8 13(2)21 103 {
        display `num'
 }

foreach var of varlist inc* {
      summarize `var',d
        }

Working with binary independent variables

When you are representing a categorical variable with a set of binary variables, there is a slow way and a fast way to integrate them.

• Slow way: generate the binary variables you want, and include them. This is good when you want to be precise about your omitted variable, or when you want to create complicated binary categories

gen white_nh = race == 100 & hisp == 0 
gen black_nh = race == 200 & hisp == 1
gen hisp = hisp == 1
gen other = white_nh == 0 & black_nh == 0 & hisp == 0 
regress incwage black_nh hisp other

Here, white, non-Hispanic is the omitted “reference” category.

• Fast way: tell Stata to create a binary variable for each value of a categorical variable. This is good when you aren’t trying to do anything complicated and when you want to be quick - very useful if you want something like state-level dummies.

regress incwage i.statefip

Note that this will work only if your categorical variable is numeric. If it’s a string you’ll get an error. You can fix it by adding a xi: prefix, like so:

xi: regress incwage i.statefip

When we include a dummy variable for every value of a categorical variable, like above, we call those “fixed effects.” We’ll talk about these more soon.

What do I submit?

• Your written up answers to exercise questions (1) - (13). 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.

Questions

Download the do-file template and data files. Personalize the file paths so that you can run it and open your cps_2016.dta file. You can also work with a blank data file if you’re more comfortable - just make sure you remember to include commands to start and close your log file.

Use robust standard errors in all regressions

1. Let’s practice with loops! Download loop_example.do and paste the code into your sample. Run it and look at the output. In your do-file, write comments that describe what each loop is going.

2. Now, go back to your cps_2016.dta file and do-file template. Adjust your do-file template so that it loads cps_2016.dta and starts a log.

3. Restrict your sample to individuals ages 25-54.

4. Create a new variable, birthyr, equal to each individual’s year of birth. Is there any potential imprecision or error in this variable?

5. Then, write a loop to generate a dummy variable for each possible value of birth year.¹

6. Look through the available list of data (note, IPUMS has full documentation of all variables). Based on this data, think of a research question for your lab of the form, “What is the relationship between .… and ...?”. Pick a dependent variable that is continuous. (Because a later question asks you to explore race/ethnicity controls, please do not use a race/ethnicity variable for \(X\).)

   Research question:
   

   Dependent variable (\(Y\)):
   

   Key independent variable (\(X\)):
   

7. Using the data available, write a reasonable population model, including your key independent variable along with a set of likely relevant independent variables (somewhere between 2 and 5 additional variables). Before estimating your regression, you should tabulate each variable to make sure you are interpreting it correctly.

8. In words, what exactly will your estimated regression tell us?

9. What do you hypothesize the answer to your research question is? (i.e. strong positive, weak negative, none)

10. Before you estimate your model, make sure you don’t have any N/A values coded. For example, if incwage is not applicable, it is coded as 9999999. Tabulate or summarize your data to check for any values like this. Replace any values as missing if they are equal to some N/A code (see above).

11. Estimate the relationship between \(X\) and \(Y\) using simple linear regression (excluding any other covariates). Write your results in equation form and report the \(R^2\). How many degrees of freedom do you have?

12. Estimate the relationship between \(X\) and \(Y\) using multiple linear regression (including other covariates). That is, estimate the population model you wrote earlier. Write your results in equation form and report the \(R^2\). How many degrees of freedom do you have?

13. Using your multivariate linear regression from the previous step, set up a hypothesis test for your parameter of interest, the \(\beta\) associated with your key independent variable, \(X\). What do you find? What is the p-value? What is the interpretation?

14. Besides your key independent variable, which other variables are statistically significant at the five-percent level?

15. A lot of student research papers will look at differences in outcomes by gender and by racial/ethnic groups. U.S. surveys like the CPS, ACS, and Census treat race and ethnicity a little strangely, and it can take some practice to get comfortable.

    There are two variables commonly used to identify a person’s race and ethnicity: the race and the hispan variable.

    1. What share of the sample is White, non-Hispanic?

    2. What share of the sample is Hispanic/Latino?

    3. A common way to summarize the racial/ethnic make-up of the U.S. is the following categories:

       • White, non-Hispanic

       • Black, non-Hispanic

       • Hispanic/Latino

       • Asian, non-Hispanic

       • Other

       Make a table that shows the distribution of the population into these five groupings.

16. Estimate your multiple linear regression model from earlier, but include the race/ethnicity variables that you created in the previous part. How do the inclusion of these factors affect your estimates of the relationship between \(Y\) and \(X\)?

17. Now, add “birth-year fixed effects” to your regression that you generated earlier. Because there is a set of binary 0/1 variables, one for each year of birth, they will essentially pull out any mean differences in your dependent variable at the birth-year level - so if your outcome variable is different for people born in 1971 vs 1971 on average, these variables will take care of it. What is the omitted birth year? How do the inclusion of these factors affect your estimates of the relationship between \(Y\) and \(X\)?