Region-specific linear trends, a good option?

[Daniel Perez Parra]

Hello Statausers,

I'm currently working on the impact of some specific legislation on female education for my master thesis. This is the first time I apply diff-in-diff (staggered) and I have some doubts concerning how to control for region-specific trends in order to relax the pararell trends assumption. First of all, I have already read other posts with similar questions and what I'm gonna show is based on them, which it doesn't mean that it necessarily correct since I'm not quite sure whether I have a good understanding on the issue. My econometric specification is the following:

where i are girls in a region r in a year t (2000, 2005, 2011), including household controls Z (ethnicity, religion, wealth...) and region, year of birth and survey fixed effects.

My question is the next: would it make sense to add an interaction term between years and regions to control for region-specific trends? Someting like (region x year)? Would that cause any problem estimating the equation in Stata considering that I'm using a pooled cross section and most likely the Callaway and Sant'Anna method for applying diff-in-diff?

Sorry for this pretty basic question, I'm also open to any LR concerning this topic!!

Thanks a lot in advance.

Daniel.

[Jared Greathouse]

You can do this (I think), but it only makes sense if you think there are really religion-year specific trends.



I do have a much better idea about how you can relax the parallel trends assumption, though.

[Daniel Perez Parra]

You can do this (I think), but it only makes sense if you think there are really religion-year specific trends.



I do have a much better idea about how you can relax the parallel trends assumption, though.

Thanks a lot for your response Jared.

Any idea for relaxing the PTA within my econometric equation is welcome!! I thought that including regional-specific trends were the most widely accepted way.

Daniel.

[Jared Greathouse]

Wait, before I answer, are your data 2000-2011? How many time periods do you have per unit? Like how many treated units are we talking about, how many control units and, more importantly, how many pre-intervention time periods are there?

[Daniel Perez Parra]

Wait, before I answer, are your data 2000-2011? How many time periods do you have per unit? Like how many treated units are we talking about, how many control units and, more importantly, how many pre-intervention time periods are there?

I have data for 2000, 2005, and 2011, a total of 3 time periods. The intervention is staggered, so some regions adopted the law at the end of the year 2000, some in 2003-2004 (early-adopters, 2000 observations) and some after 2005 (2006 and 2007 concretely) (late-adopters, 760 observations). Also, there are some regions that have not passed the law yet (never-adopters, 350 observations).

I hope this answers your questions. Thanks a lot for the help.

[Jared Greathouse]

Oh. Then, in that case, I think your best bet is the use Calloway's method. The main issue I see here (unavoidable, I know) is the lack of data.

Unit-specific trends I think are good when you wanna model long term unit-specific trends. I don't think 3 intervention periods are really enough to solve this.

Another solution.... I was originally going to suggest synthetic controls, but now I'd suggest a matched difference-in-differences design.

[Daniel Perez Parra]

Oh. Then, in that case, I think your best bet is the use Calloway's method. The main issue I see here (unavoidable, I know) is the lack of data.

Unit-specific trends I think are good when you wanna model long term unit-specific trends. I don't think 3 intervention periods are really enough to solve this.

Another solution.... I was originally going to suggest synthetic controls, but now I'd suggest a matched difference-in-differences design.

Thanks Jared. Any LR recommendations on matched DiD design? I've never heard about it.

Also, I didn't specify but taking into account the three surveys I reach a total of 6000, 2100, and 1000 observations depending on the treatment group I previously mentioned. However, this still may be a small sample of obs.

[Jeff Wooldridge]

Is the year 2000 a control year so that no units were treated in that year? It's easy and robust to use regression methods that allow staggering, different treatment effects by cohort and period, and it's easy to include trends in the analysis. Here's a link to a shared Dropbox with a version of my paper on this and some Stata code and simulations:

https://www.dropbox.com/sh/zj91darud...bgsnxS6Za?dl=0

[Daniel Perez Parra]

Is the year 2000 a control year so that no units were treated in that year? It's easy and robust to use regression methods that allow staggering, different treatment effects by cohort and period, and it's easy to include trends in the analysis. Here's a link to a shared Dropbox with a version of my paper on this and some Stata code and simulations:

https://www.dropbox.com/sh/zj91darud...bgsnxS6Za?dl=0

Thanks a lot for your response Mr. Wooldridge.

Well, there are 2 regions treated on that year (after data collection of the 2000 survey). Therefore, my plan is to use 2000 survey as pre-treatment data, and get the post-treatment data from the 2005 and 2011 surveys, comparing observations in early-, late- and never-treated regions in a staggered context. I avoided carryng out my empirical strategy using cohorts since I face several limitations regarding the inclusion of some important control variables, such as household wealth (because I don't have data on each year between 2000 and 2011, and I would need to assume that hh wealth of my observations were constant between survey years), being the outcome variable various female education outcomes. I don't know whether this is a good idea or not, I'm very open to suggestions.

Thanks a lor for sharing the link!

[Daniel Perez Parra]

Thanks a lot for your response Mr. Wooldridge.

Well, there are 2 regions treated on that year (after data collection of the 2000 survey). Therefore, my plan is to use 2000 survey as pre-treatment data, and get the post-treatment data from the 2005 and 2011 surveys, comparing observations in early-, late- and never-treated regions in a staggered context. I avoided carryng out my empirical strategy using cohorts since I face several limitations regarding the inclusion of some important control variables, such as household wealth (because I don't have data on each year between 2000 and 2011, and I would need to assume that hh wealth of my observations were constant between survey years), being the outcome variable various female education outcomes. I don't know whether this is a good idea or not, I'm very open to suggestions.

Thanks a lor for sharing the link!

I meant that I'm not using yearly cohorts, just girls between 14 and 17 (the ones theoretically affected by the law), and comparing this age group across regions and throughout the years.