Help for endogenous treatment variable in DID estimation

[Richa jain]

How can endogenous treatment variable be used in the DID estimation with multiple periods and groups

[Maxence Morlet]

Do you have an instrument for it?

You can try the community-contributed

ssc install sdid

command to conduct matching if the parallel trends assumption is violated, but there is one problem: matching is unfortunately not a magic wand, and if treatment is endogenous... well the best you can do is run your estimations and just state that they have to be interpreted with caution...

Here is Wooldridge's (2021) amazing paper on two way fixed effects and difference-in-difference - I recommend you give it a read.

https://papers.ssrn.com/sol3/papers....act_id=3906345

[Richa jain]

I don't have an instrument for it. I am following did_multiplegt approach given by Chaisemartin(2021). The only problem is that my treatment variable is an endogenous variable. Can we simply use the DID estimation an interpret the results without looking for endogenity concern

[Maxence Morlet]

Your results will be inevitably biased if you cannot identify the source of endogeneity and control for it. Therefore, you cannot interpret your results in a causal manner.

If you're an economist, I suggest you include this endogeneity as "disclaimer", and discuss it at length.

I would not try to "camouflage" it and not highlight it in the limitations or results interpretation.

[Richa jain]

Yes, I am an economist. My work is macro based and therefore endogeneity is a big concern. Is there no way to control for it while using DID estimation?

[Maxence Morlet]

Here's an example I've encountered in macroeconomics, that may apply to your problem:

I wanted to evaluate the effects of negative interest rate policy (NIRP) on consumption in the eurozone using difference-in-difference.

Here's the thing though: the European Central Bank chose to implement NIRP endogenously in 2014, arguably this decision was driven by the outcome, so nonrandom selection into treatment occurred.

I tried propensity score matching (not necessarily the best form of matching, see Hainmueller (2012) or Arkhangelsky et al. (2021)) and included all observables that drove the ECB to implement NIRP in the propensity score estimation equation.

I ran weighted equations and graphed my newly constructed control group (with certain countries given more weight than others as they were more "resemblant" to Eurozone countries).

The trends looked more parallel after matching than before, but bottom line: I still did not have exogenous variation, even if I had used the most fancy matching techniques in the world. Angrist and Pischke (2009) discuss this at length.

My results were therefore arguably biased, also because the decision to implement NIRP was based not only on observables. I had no choice but to include this as a disclaimer, and hope that journal editors will be show understanding when they read the paper.

Perhaps interested readers could comment on your situation if you share details.

[Richa jain]

My objective is to evaluate the effect of capital controls on financial stability of emerging economies. Now most of the emerging economies apply these controls to maintain their financial stability, and therefore these capital controls are endogenous in nature. I am trying to employ DID estimation with heterogeneous treatment effect ( Developed by Chaisemartin et al (2021)).

Now my problem is that whether I take capital control data as my treatment variable and do the analysis. Or I have to take some lag of it to control for endogenous but then purpose of DID might get voilated.

[Maxence Morlet]

Ok, thanks for clarifying.

Indeed, the adoption of capital controls will likely be driven by a pre-existing trend in financial stability.

Either you search the literature for a valid, exogenous, instrument, or you have to accept that your results will comprise bias, whatever you do. You may mitigate this bias, but bottom line, the variation is not exogenous...

Two recommendations from my side:

- give the community-contributed

sdid

command a go.

- give Wooldridge's (2021) paper: https://papers.ssrn.com/sol3/papers....act_id=3906345 for a flexible way of running two way fixed effects with difference-in-difference methodology.