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I am trying to make a small impact evaluation, using the synthetic control method. The outcome variable is a monthly time series, whereas a potential predictor variable is only available on the yearly basis. What would be the best approach in this case? To take the yearly predictor variable as constant for each year or to use an average of this predictor variable for the whole period? I am fairly new to this approach, so I would be very thankful if someone could provide me with some advice.

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  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Apr 30 at 22:14

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I am going to interpret "best" in terms of using the level of aggregation for the predictors that optimizes your ability to track the trajectory of the outcome variable for the treated unit for an extended pre-intervention period.

I think this partially depends on theory or domain knowledge rather than statistical considerations. If this is an important variable with very heterogeneous trends across units, I would try the most disaggregated version you can: "average" the constant annual predictor across the 12 months of the corresponding year. If it's less important or there is a lot of co-movement across units, the averaging over the entire pre-treatment period would be acceptable. You can also do something intermediate, like averaging over pre-treatment decades or lustrums (5-year periods) and so on. You can even mix durations. Using more aggregated versions will generally select sparser donor groups (fewer control units with non-zero weights). Ideally, you want to show that the level of aggregation does not matter for the estimate.

With enough data, you could adopt a data-driven method for variable selection. The procedure divides the pre-intervention periods into an initial training period and a subsequent validation period. Synthetic control weights are computed using data from the training period only. The validation period can then be used to evaluate the predictive power of the resulting synthetic control. This procedure can be used to select predictors or to evaluate the predictive power of a given set of predictors or different ways of aggregating them. Section 7 of Abadie, Alberto. 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects." Journal of Economic Literature, 59 (2): 391-425 goes into more detail.

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  • $\begingroup$ Thank you for your extensive reply! $\endgroup$
    – M.J.
    Commented May 3 at 19:38

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