Diff-in-Diff with log or non-log prices

[Oliver WB]

Hi,

I have conducted a Difference-in-Difference regression to study the impact of establishing of a factory on the housing prices in a certain region. I have used log-prices as my dependent variable. I get parallel trends, and a significant effect post-treatment.

However, when doing the same DID-regression with non-log prices, I get parallel trends, but no significant effect post-treatment.

Should I include both of these regressions in my thesis for the sake of transparency and discussion? Or should I use only the one with logged prices, since similar studies often only look at logged prices?

//Oliver

[Jeff Wooldridge]

The parallel trends assumption is not invariant to the transformation used for Y, as recently discussed by Roth and Sant'Anna (2023, Econometrica). In my own work on nonlinear Diff-in-Diff, I've found that tests for pre-trends need not have lots of power. So, it's not too surprising you can't reject PT using Y or log(Y). But that doesn't mean your estimated effect will be significant.

If you want to try something else to check robustness, you might try an exponential model for Price [not log(Price)] and estimate it using the Poisson QMLE. I discuss this in my 2023 Econometrics Journal paper. In simulations, I find the Poisson regression can be much more efficient than a linear model. And it's almost as easy as a linear model.