Lab 7: Difference in differences

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Materials

• banks.dta
• nsly_marijuana.dta
• Do-file template econ3500_lab_template.do

Objectives

There are two separate parts to this lab — a set of data for working with difference-in-differences models, and another set for working with fixed-effects models.

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

• Estimate and interpret difference-in-differences models

• Estimate panel data models using dummy variables

• Interpret panel data models

What is panel data?

Up to now, we’ve worked with cross-sectional data — one observation per person (or state, or county) at a single point in time. In this lab, we’ll work with panel data (also called longitudinal data), where we observe the same individuals or units across multiple time periods.

Panel data lets us control for characteristics of each unit that don’t change over time — even ones we can’t directly measure — by comparing each unit to itself over time. This is the key idea behind fixed effects models.

What is difference-in-differences?

Difference-in-differences (DiD) is a method for estimating causal effects when one group is exposed to a treatment and another is not. The idea: compare how the outcome changed over time for the treatment group vs. the control group. The first difference removes time-invariant characteristics of each group; the second difference removes common time trends. What’s left is the estimated treatment effect — if the two groups would have trended the same way absent the treatment.

Key commands

Using xtset and xtreg

The xtset command tells Stata that you have panel data. For example, if you have individual and year data, then you would enter xtset id year, or whatever the appropriate variable names are.

General format: xtset panelvar timevar

After declaring your panel with xtset:

• Use xtreg instead of regress for panel regression. Everything else proceeds as normal.
• Add ,fe to estimate a fixed effects model, where the fixed effects are the panelvar variable you declared.
• Add cluster(panelvar) to cluster standard errors at the panel level (accounts for correlation within units over time).

For example: xtreg income education i.year, fe cluster(id) regresses income on education with individual fixed effects (from xtset) and year fixed effects (from i.year), clustering standard errors at the individual level.

Adding other fixed effects

You can add fixed effects to a model more generally with the i. prefix or areg. A few examples:

xi: reg income i.educ i.bpl, robust
reg income i.educ i.bpl, robust

areg income i.educ, robust absorb(bpl)

1. xi: — this prefix is necessary for adding i. variables if the variables are in string form. You can also use it to do fancier interactions with fixed effects, like xi: reg income i.educ*i.bpl, robust
2. You can exclude the prefix and just do i.var to create indicator variables so long as your variable is numeric
3. You can use areg to “absorb” a set of fixed effects — they will not be reported in your output, but they will be estimated. This method is less efficient than xtreg because you use up degrees of freedom.

Workflow overview

1. Load a dataset and start your log file.
2. Explore the data structure (describe, browse, tab).
3. For Part A: Calculate the DiD estimator by hand, then estimate it as a regression.
4. For Part B: Declare your panel data and estimate fixed-effects models.
5. Compare results across specifications and interpret.
6. Answer the worksheet questions.

Lab 7 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(s) you created that run this analysis
• A log file that contains the results from this exercise.

Part A: Difference-in-differences

This part looks at a simple difference-in-differences model based on Richardson and Troost (2009).¹

Data context

Mississippi is split between two Federal Reserve Districts. During the early years of the Great Depression, each district took a different approach to bank runs. The Sixth District increased lending, while the Eighth District responded by restricting lending to threatened banks. We look at the impact of these policies on bank survival rates using difference-in-differences.

Each row in banks.dta represents a Federal Reserve district in a given year. The dataset is small — use browse to see the full thing.

Variables (Part A)

Tip: use describe and browse to confirm the variable names in your dataset.

Questions

Use robust standard errors in all regressions.

1. Start a new do-file and change directory to your working directory.

2. In your do-file, start a log and open banks.dta.

3. Using pencil & paper or electronic means of your choosing (you don’t need to do this in Stata), plot a graph of the number of banks in business, by district, by year.

   • Plot number of banks in business on the y-axis and year on the x-axis.
   • Include only the years 1930 and 1931.
   • Draw separate lines for the numbers of banks in District 6 and District 8.
   • Draw a dotted “counterfactual” line based on your understanding of the change in bank policies.
   • Mark all four actual values clearly.