5 Synthetic Control Weights
The synthetic control methodology described in Section 3.1 consists of an optimisation process with two parts: (i) finding a combination of countries in the donor pool that best resembles the pre-treatment predictor values of the US (inner optimisation), and (ii) finding the optimal weights on these predictors so as to best resemble the export value of the US (outer optimisation). In practice, we end up with a set of weights put on both countries and predictors.
The various sets of specifications tested – quarterly and monthly specifications with or without a first or seasonal lagged dependent variables included – all lead to slightly different country and predictor weights. The weights for the 'headline' (quarterly first-lagged) specifications are presented here (with value, quantity, or price as the dependent variables).
|Dependent variable||Top country weights||Top predictor weights|
|Value||Canada||24.8%||Lagged dep. var.||> 99.9%|
|France||22.8%||GBP exchange rate||< 0.01%|
|Further 9 countries||35.9%||Other predictors||0.0%|
|South Korea||15.3%||Lagged dep. var.||21.2%|
|Australia||9.8%||Interest rate||< 0.01%|
|Further 8 countries||18.9%||Other predictors||< 0.01%|
|Price||Switzerland||37.9%||Lagged dep. var.||96.3%|
|Australia||13.6%||GBP exchange rate||3.3%|
|Further 7 countries||36.7%||Other predictors||< 0.01%|
Note that not all countries in the donor pool (or predictors) will necessarily have a weight associated with them.
In many cases, the weights obtained were similar between these specifications and those with other lagged dependent variables. A more complete set of weights associated to the quarterly specifications can be found in Annex B – Intermediate Synthetic Control Outputs.
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