2  Why the groups were never comparable

What the regression is actually holding up against what

raised is 1 for account-months running on an increased limit and 0 for everything else. “Everything else” is mostly other accounts — ones that never had an increase at all. So the comparison is between accounts, and it carries every difference between them.

before <- d[post == 0L, .(accounts = uniqueN(SK_ID_PREV),
                          dpd30_pct = 100 * mean(dpd30)), by = treated]
Table 2.1: 30+ day delinquency in the months BEFORE any increase happened 
                    Group Accounts 30+ dpd
                   <char>   <char>  <char>
1:     limit never raised   69,945  1.669%
2: limit was later raised   13,819  0.022%
Figure 2.1: The two groups, before anything happened to either of them.

2.1 The same gap, seen a different way

The chart above splits by calendar month. Split instead by the one behavioural variable the panel carries — how much of the limit an account was actually using — and the picture is the same.

acc <- d[post == 0L, .(util = mean(utilization, na.rm = TRUE),
                       dpd  = mean(dpd30),
                       months = .N,
                       treated = treated[1]), by = SK_ID_PREV][months >= 3]

breaks_ <- c(-0.001, 0.001, seq(0.1, 1.0, 0.1), 2)
acc[, bin := cut(util, breaks_)]
binned <- acc[, .(x = mean(util), y = 100 * mean(dpd), n = .N), by = .(treated, bin)]
binned <- binned[n >= 50]
Figure 2.2: One point per bin of accounts. Point size is the number of accounts behind it.

Take any vertical slice. At 25% utilisation the never-raised accounts sit at 2.55% and the later-raised ones at 0.00%. The same holds all the way across.

The blue series is flat against the floor. Accounts the lender chose to reward were barely ever in arrears, no matter how heavily they were borrowing — which is presumably why it chose them.

The accounts that later got an increase were already 75 times less likely to be in arrears — before anyone raised anything.

That is not a coincidence and it is not a data problem. It is the lender’s policy: limits go up for customers it already trusts. The regression sees healthy accounts on raised limits, troubled accounts on flat ones, and reports the difference as if the limit caused it.

The standard response is to control for the difference. Next.

Everything above runs from 02-not-comparable.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.