# Aggregating Matching Variables Over Time

#### 2021-02-26

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.