Lab 8: Instrumental variables

Due by 2:20 PM on Wednesday, December 8, 2021

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It’s our final lab of the semester! 🙌 🏆 💃 👏

Materials

Objectives

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

  • Estimate instrumental variable specifications and interpret them.

  • Output regression results using outreg2

Key commands

Conducting instrumental variables regressions with ivregress

We can estimate an instrumental variables regression with ivregress

General form:

ivregress estimator depvar [varlist1] (varlist2 = varlist_iv) [if] [in] [weight] [, options]
  • estimator is where we will type 2sls
  • depvar is your dependent variable
  • You can include other explanatory variables before or after the parentheses, `[varlist1]
  • In the parentheses, write you endogenous (\(x\)) then your instrument (\(z\)) - these can be lists!
  • The rest of it is just as you’re used to

Example:

To estimate the following two-stage least squares equation: \[ rent = \beta_0 + \beta_1 \widehat{hsngval} + \beta_2 pcturban + u\] where \(\widehat{hsngval}\) is predicted from the following first-stage equation \[ hsngval = \alpha_0 + \alpha_1 faminc + \alpha_2 pcturban + v \]

webuse hsng2

ivregress 2sls rent  (hsngval = faminc ) pcturban, robust

You can add , first to report the first-stage results:

`ivregress 2sls rent  (hsngval = faminc ) pcturban, robust first`

Outputting your results with outreg2

We are very good at reading raw Stata output. But, raw stata output has no place in our papers. How do we make it pretty? There are lots of ways, including putexcel, which lets you create customizable excel tables with your outputs (good for descriptive statistics), and estout, which does the same thing but is more regression oriented.

Personally, I like outreg2, because it’s easy to set up and use. So that’s what we’ll use!

outreg2 is a user-created package, which means you have to install it:

ssc install outreg2

You only have to do this once.

You’ll run outreg2 after estimating a regression. It takes your results and saves them to a table. You can run it multiple time and generate columns of results within the same excel sheet, which is pretty handy! The general format of outreg2 is this:

// You can copy and paste this into stata, and it should work! But note that it will save to your working directory

sysuse auto,clear

// Specification 1
regress mpg foreign weight headroom trunk length turn displacement
outreg2 using myfile.xls, replace 

// Specification 2  (add on)
regress mpg foreign weight headroom trunk length turn displacement,robust
outreg2 using myfile.xls, append

You can customize, with lots of options! (see help outreg2, or check out these resources)

What sort of things?

  • Export directly to Word
    • outreg2 using myfile, word replace
  • Add summary statistics and p-values
    • See here for more details
  • Add notes
    • outreg2 using myfile, addnote(Dummy variables not shown)
  • Report only some variables
    • outreg2 using myfile, keep(mpg foreign)
  • Modify number of decimal places
    • outreg2 using myfile, dec(5)
  • You can use a loop to make a whole set of columns!

An example:


 sysuse auto,clear
 local r "replace"
   forval num=1/5 {
       regress mpg weight headroom if rep78==`num'
       sum mpg if rep78 == `num'
       local mean = `r(mean)'
       outreg2 using myfile.xls, `r' keep(headroom) title("Sample Graph") nocons addtext("Rep78", `num') addstat("Mean", `mean') auto(2) bracket
   
   local r "append"
   }

Exercises

Today we’re going to work with voucher.dta, a data set of student performance from Rouse (1998). She measures the impact of private school vouchers on student achievement. The final measure of student performance we’re interested in is mnce, their math test scores in 1994 (after up to four years in the private school). We also have some measures of baseline performance, their math test score in 1990 (mnce90). The variable choiceyrs is the number of years enrolled in a private school, and selectyrs is the number of years a student was selected to receive a voucher to fund enrolling in a private school.

  1. In your do-file, start a log and open voucher.dta.

  2. Summarize your data. Of the 990 students in the sample, how many were never awarded a voucher? How many had a voucher for all four years? How many actually attended a choice school for four years?

  3. Predict the relationship between choice school attendance and math scores by regressing math scores mnce (dependent variable) on number of years enrolled in a choice school choiceyrs (independent variable). What do you find? Is this what you expect? What happens if you add in the variables black, hispanic, and female? Write your results in equation form.

  4. Why might choiceyrs be endogenous? Explain:

  5. Now, estimate a regression of \(choiceyrs\) (dependent variable) on \(selectyrs\) (independent variable), including race/ethnicity and gender controls. Why is this a reasonable choice of an instrument? What is the F-statistic on selectyrs? (Hint: You can use the testparm command for a hypothesis test with just one coefficient)

  6. Based on the previous regression, use the predict command to generate a predicted \(\widehat{choiceyrs}\). Estimate the regression of \(mnce\) on \(\widehat{choiceyrs}\), including race/ethnicity and gender controls. Write the estimated equation. How does your result compare to your OLS estimate?)

  7. Re-estimate a regression of \(mnce\) (dependent variable) on \(choiceyrs\) (independent variable) using \(selectyrs\) as an instrument for \(choiceyrs\). However, this time, estimate the equation in one command line using ivregress 2sls. How do your results change, if at all?

  8. Repeat your IV analysis, but this time include a control for baseline achievement by adding \(mnce90\). Write the results in equation form below. Do you find these results convincing? Explain.

  9. We can also use multiple instruments for multiple endogenous variables. The variables \(choiceyrs1\), \(choiceyrs2\), etc. are dummy variables indicating the different number of years a student could have been in a choice school. Similarly, \(selectyrs1\), \(selectyrs2\), etc. have a similar definition, but for being selected from the lottery.

    Estimate the following equation using IV. \[\begin{split} mnce &= \beta_0 + \beta_1 choiceyrs_1 + \beta_2 choiceyrs_2 + \beta_3 choiceyrs_3 + \beta_4 choiceyrs_4 + \\ & \beta_5 black + \beta_6 hispanic + \beta_7 female + \beta_8 mnce90 + u \end{split}\]

  10. Finally, go back through your regressions in your do-file. After each regression (there should be six: OLS without controls, OLS with controls, IV by hand, IV using ivregress, IV with \(mnce90\), and IV with multiple instruments), add a line of code to output the results to a word or excel file using outreg2.

    Include a table with your results with your submission - there should be six columns in one table. Note that you can use the append option to add each regression as a new column, rather than a new file.

References: Rouse, Cecilia Elena (1998), “Private School Vouchers and Student Achievement: An Evaluation of the Milwaukee Parental Choice Program,” The Quarterly Journal of Economics 113(2), 553-602.

Last updated on December 1, 2021

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