# Aggregating Matching Variables Over Time

#### Michael Robbins and Steven Davenport

#### 2023-06-29

This is a brief discussion of how microsynth allows the user to aggregate outcome variables (passed to `match.out` or `match.out.min`) over time, either before or after matching, and how that can affect the workings of two other arguments: `period` and `start.pre`.

## Declaring outcome variables as a vector or list

microsynth will match treatment and control based on the variables passed to `match.out` and `match.out.min`. But there are two different ways to input parameters to `match.out`, and they have different implications for how the arguments work.

The simple way to pass variables to match.out is with a simple vector of variable names (e.g., `match.out=c("Y1", "Y2")`. A more complex way is to pass a list, containing a set of vectors with named corresponding to variable names and elements corresponding to instructions for how to aggregate those variables over time before matching, e.g. `match.out = list('Y1' = c(1, 3, 3), 'Y2'= c(2,5,1))`. Under this specification, if the intervention occurs at time 10, then matching will proceed across a) The value of Y1 at time 10; b) the sum of Y1 across times 7, 8 and 9; c) the sum of Y1 across times 4, 5 and 6; e) The sum of Y2 across times time 9 and 10; e) the sum of Y2 across times 4, 5, 6, 7, and 8; f) the value of Y2 at time 3.

## Interactions with other arguments

The choice between the simple and the complex input method is important, and it alters how other arguments work.

`period` specifies the granularity of the data used by microsynth. When provided simple input from match.out (i.e., a vector of variable names), `period` indicates that those variables should be aggregated into the duration equal to the value of `period`. E.g., if data are provided monthly and `period=3`, then variables will be aggregated to the year-quarter before matching. But when provided complex input from match.out (i.e., a list of names and integers), then the user has already manually specified how the variables should be aggregated prior to matching; in this case, `period` will only affect the appearance of charts and how results are reported (but not the matching procedure).

`start.pre` is also affected. When match.out is provided the simple input (a vector of variable names), start.pre will identify the time of the beginning of the pre-intervention data to be used for matching, plotting, and displaying results. Data observed any time before the `start.pre` will be ignored entirely. If provided the complex (list) input, then `start.pre` will merely affect plotting behavior and suppress some of the results. But observations before the `start.pre` will still be used for matching.

In conclusion, passing a list to `match.out` will lock into place the parameters around the matching procedure; arguments such as `period` and `start.pre` will only alter how results are reported and how charts are plotted. But when `match.out` is passed only variable names, then `period` and `start.pre` will also govern the matching procedure.