6  Which accounts answer the question

A flat line carries no information about a slope

A slope answers one question: when the treatment moves, how much does the outcome move?

So an account whose treatment never moves has no answer to give. It sat at raised = 0 in every single month, and after subtracting its own average it sits at zero in every month still. Multiply that by anything and you get zero. It cannot push the slope up or down.

That is not a quirk of the software. It is what “compare an account with itself” means: an account that was never treated has no itself before and itself after to compare.

Figure 6.1: Ten accounts. The demeaned treatment is what the regression actually multiplies against the outcome.

The left panel is five flat lines on zero. Those accounts are in the regression, they are counted in the sample size, and they move the estimate by exactly nothing.

Table 6.1: How much of the data has anything to say about the slope 
                Group Share of all rows Rows where treatment moves
               <char>            <char>                     <char>
1: limit never raised             94.7%                       none
2:   limit was raised              5.3%                    181,291

So 94.7% of the panel is along for the ride. The whole estimate rests on the other 5.3%.

Two things follow, and both matter later.

This is an effect on the treated. It describes what happened to accounts that actually got an increase. It is not a claim about what would happen if you raised limits at random across the book — those are different quantities, and only the first one is in this data.

The never-treated accounts are not a comparison group here. They are not what the treated accounts are being measured against; each treated account is measured against its own past. The never-treated earn their keep in the next chapter, for a different job entirely.

Everything above runs from 06-which-accounts.qmd. Shared setup <80><94> the data loader, the plot theme and the inline formatters <80><94> is in R/_common.R. The panel itself is built by R/01-build.R.