Synthetic control method using imbalanced time periods (a theoretical question)

[Eddie Brighton]

Hi statlist:

I wonder how I can use two different time periods (year and quarter) in modeling a synthetic control model.
The intervention of my research interest occured in 2013. I have yearly data from 2006 to 2016, and quarterly data from 2017 to 2022. Is there a way I can accommodate both year and quarters in the model? Thanks.

[Jared Greathouse]

I'm not understanding the problem. You can run two iterations of SCM using the respective yearly and quarterly intervention dates.


Suppose I have a variable that's about total imports of alcohol. In 2011q 1 2 3 4, we imported 10, 20, 70, and 100 bottles.

if intervention begins at q3, we can just calculate the total for each year (200 for 2011) and run scm on that, or use the quarterly date. Am I understanding right?

[Eddie Brighton]

@Jared Greathouse You are right. I want to use the more granular level (quarter periods) for more observations. But, I only have those for observations after the intervention. In this case, the lapse would be imbalanced (years for the pre-intervention period and quarters for the post-intervention period). I guess I'll have to run it anyways and see what happens.

[Jared Greathouse]

You can't use years for both?

[Eddie Brighton]

@Jared Greathouse I can, or course, but I want to use quarters where those are available.

[Jared Greathouse]

How come you have data for two different time units? Are they from the same data source?

[Eddie Brighton]

@Jared Greathouse They are from the same source, and it's publicly available. My best guess is that they decided to release quarterly data from some point.

[Dimitriy V. Masterov]

In principle, you can define your own integer time variable that mixes annual and quarterly data. If the quarterly data started before treatment, you could do a false placebo test to make sure that nothing went awry by doing SC on the pre-treatment period only and pretending the treatment took place when the annual-to-quarterly transition took place. But if your treatment effect changes over time and the quarterly data starts during treatment, it will be hard to disentangle the two. If you do decide to do this, I would watch for changes in the treatment effect when the data switch happens. I would get nervous if you see a jump or the pattern of effects changes (oscillations, slope changes, etc.).

Your inclination to use quarterly data is natural but not always optimal. Annual data will often be less noisy than quarterly, so the loss in sample size will be offset by reduced variance from smoothing over seasonality. It can also allow you to match units with offset seasonalities. For example, when it's winter in the Northern Hemisphere, it's summer in the Southern Hemisphere, so agricultural output timing will not align at a quarterly level. The weights that work at the annual level may not work well at the quarterly level because of that.