Triple differences, multiple treatment effects.

[Daniel Bukstein]

Hello Stata community,
I am working in a impact evaluation of firms that asked public support for innovation programs. To do so I am running a differences-in-differences model. I have information on which year the firms asked for the public support so I want to go further of the classic diff-in-diff model and test whether a longer exposure to treatment causes a larger treatment effect. The latter would fall under a differences-in-differences-in-differences approach (triple difference). I have data on years 2009 to 2015. Baseline year is 2009, first treatment year is 2010. This is a tab of firms by treatment year:


anio_tratam |
iento | Freq. Percent Cum.
------------+-----------------------------------
0 | 581 58.04 58.04
2010 | 245 24.48 82.52
2011 | 56 5.59 88.11
2012 | 28 2.80 90.91
2013 | 28 2.80 93.71
2014 | 21 2.10 95.80
2015 | 42 4.20 100.00
------------+-----------------------------------
Total | 1,001 100.00


To run the standard diif-in-diff model I run:

gen t=year>=2010
gen tratamiento=innova_2010==1
reg ln_gastoneto t##treatment

Suppose I want to estimate the differential treatment effect for the firms that ask for public support for innovation if year>=2011. Theoretically I would want to estimate ATT=(Treated_2011_after-treated2011_before)-(treated2010_after-treated2010_before)-(control_after-control_before).

I tried running this regression using:

gen t=year>=2010
gen treatment=innova_2010==1
gen tratamiento2=tratamiento==1&anio>=2011
reg ln_gastoneto t##tratamiento##tratamiento2

But the output is full of empty/ommited interaction variables.

I also tried generating a continuous treatment exposure variable:

g duracion=year-year_treated
replace duracion=0 if duracion<0
replace duracion=0 if treatment==0

And then running the regression

reg ln_gastoneto tratamiento##t##duracion

But also in this way all the tripple interaction variables are empty or ommited. Any suggestions? What should I be doing differently? Is there another model that captures the different treatment effects when there are starting points of the intervention?

This is my first post so I hope to have followed the guidelines listed in the FAQs. Many thanks in advance.

Regards,

Daniel

[Phil Bromiley]

You didn't get a quick answer. You have included Stata code in code delimiters, but you would increase your chances of a useful answer if you include Stata output, and sample data using dataex - see FAQ on asking questions. Also, simplify what you post to the minimum needed to demonstrate the problem.

Your post is long and complex. I also don't know what the sample size is. Whenever you do triple interactions, you're creating a very complex set of results. As you found, with discrete variables, you often have empty or small number of observations categories. With continuous variables, it becomes extremely difficult to interpret.

One thing you might try is to include the main effects separately and then set up the interactions using # instead of ##. This may result in fewer empty outcomes. Also, try to be more consistent with your terms - for example, ATT=(Treated_2011_after-treated2011_before)-(treated2010_after-treated2010_before)-(control_after-control_before). then ATT doesn't appear in your regressions.