Jessie asks: Is there a nonparametric (or parametric) test that can be
used to test whether the treatment and control group are similar in
difference-in-difference before the treatment occurs?
For example, in the Card-Krueger minimum wage example (Figure 5.2.1),
would there be a test to check whether the trend in the employment
rate was statistically similar between PA and NJ before the 1992
minimum wage change?
I can only think of doing a linear regression (or perhaps another
parametric form?) on the 2 series and testing whether the coefficient
on the time variable in the NJ regression pre-1992 is statistically
different from that of the PA regression pre-1992.
Thank you!
Good question jessie. You can think of
the "Granger Causality" approach taken in Autor (2003)
and described in chapter 5 as version of the
test you have in mind. If there appears to be
a treatment effect before treatment, that's evidence of
diverging trends.
Ultimately, what matters most is whether allowing for differential
trends changes results in a meaningful way, not whether the trends
themselves are statistically significant. Chapter 5 suggests
adding linear group-specific trends (e.g., state-specific trends)
as a spec test.
Note that this won't work in the original NJ/PA min wage study.
Why not?
JA
Testing DD
Jessie asks: Is there a nonparametric (or parametric) test that can be used to test whether the treatment and control group are similar in difference-in-difference before the treatment occurs? For example, in the Card-Krueger minimum wage example (Figure 5.2.1), would there be a test to check whether the trend in the employment rate was statistically similar between PA and NJ before the 1992 minimum wage change? I can only think of doing a linear regression (or perhaps another parametric form?) on the 2 series and testing whether the coefficient on the time variable in the NJ regression pre-1992 is statistically different from that of the PA regression pre-1992. Thank you! Good question jessie. You can think of the "Granger Causality" approach taken in Autor (2003) and described in chapter 5 as version of the test you have in mind. If there appears to be a treatment effect before treatment, that's evidence of diverging trends. Ultimately, what matters most is whether allowing for differential trends changes results in a meaningful way, not whether the trends themselves are statistically significant. Chapter 5 suggests adding linear group-specific trends (e.g., state-specific trends) as a spec test. Note that this won't work in the original NJ/PA min wage study. Why not? JA