5 Panel Data and Difference-in-Differences

When we can observe and measure potentially confounding factors, we can recover causal effects by controlling for these factors. Often, however, confounders may be difficult to measure or impossible to observe. If this is the case, we need alternative strategies for estimating causal effects. One approach is to try to obtain data with a time dimension, where one group receives a treatment at a given point in time but the other group does not. Comparing the differences between pre- and post-treatment periods for these two groups allows us to control for unobserved omitted variables that are fixed over time. Under certain assumptions, this can produce valid estimates of causal effects.

Chapter 5 in MHE gives a very good treatment of the main empirical issues associated with difference-in-differences analysis, and with panel data more generally. The relevant chapter in Mastering ’Metrics is especially good for this week, so both are worth consulting.

The papers by Card (1990) and Card and Krueger (1994) are classics in the diff-in-diff literature, and give a very intuitive overview of the basics behind the method. More advanced applications can be found in the paper by Ladd and Lenz (2009), which also provides a useful demonstration of how difference-in-difference analyses can be combined with matching in order to strengthen the parallel trends assumption, and the recent paper by Dinas et al (2018), which we will replicate in part below.

An example of using fixed-effect regression to estimate a difference-in-differences type model can be found in the paper by Blumenau (2019).

For those of you who are feeling very committed, an important paper on statistical inference for difference-in-difference models is this one by Bertrand et. al. (2004). Be warned, however, that essentially no-one has ever enjoyed time spent reading a paper that is almost entirely about standard errors.

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