When One Stress Model Fits the Wrong Bank
The subject here is the Federal Reserve’s FLARE stress-testing model and its treatment of regional banks. The specific question is whether relationships estimated across all banks describe a group whose funding, lending, and revenue mix differs from the institutions that dominate the industry by assets. Understanding that distinction lets a reader judge what a regional-bank model can improve—and recognize when neither model answers an individual bank’s local or granular risk question.
What a top-down model is built to answer
A stress test is not a crystal ball. It is a structured way to ask what a specified economic path would imply for a bank’s income, losses, and capital if historical relationships remain informative. The Federal Reserve’s Forward-Looking Analysis of Risk Events, or FLARE, makes that question concrete with bank-level financial-statement data and macroeconomic variables.
Three outputs organize the exercise. Pre-provision net revenue, usually shortened to PPNR, captures revenue and expenses before provisions for expected loan losses. Net charge-offs, or NCOs, measure loans that are removed from the balance sheet as losses after recoveries are considered. Common Equity Tier 1, or CET1, is a capital measure that shows how the bank’s loss-absorbing equity position changes relative to risk-weighted assets. The model does not jump directly from “the economy is weak” to a capital number. It estimates operating and loss components, then carries them into the capital projection.
FLARE estimates separate equations for PPNR components and loan-loss rates by type. The equations use past values, or autoregressive terms, along with financial-market indicators, macroeconomic variables, and bank-specific controls. A past value matters because bank income and loss rates often persist from one quarter to the next. A market or macro variable supplies a possible driver. A bank-specific control helps the model distinguish a common environment from differences among institutions. The result is a set of estimated sensitivities that can be applied to a scenario path.
The level of the data determines the level of the answer. FLARE is top-down because it begins with broad macroeconomic and financial conditions and estimates their relationship with bank-level outcomes. A bottom-up model would use more granular information, such as loan-level or security-level data, to examine the particular exposures inside an institution. Top-down and bottom-up tools are not competing labels for the same exercise. A top-down model is well suited to asking whether broad stress creates correlated losses across a group. It is not designed, by itself, to determine the solvency of one named bank.
That distinction matters for regional banks. A regional-bank stress exercise can estimate how the group responds to a national rate path, changes in unemployment, or broad property-price movements. It may not see that one bank’s office loans are concentrated in a city with a more severe vacancy problem, or that its deposits behave differently from the group average. The model can be relevant at the group level without being complete at the institution level.
The Federal Reserve study therefore estimates FLARE twice. The “All Banks” model uses the full bank sample. The “Regional Banks” model restricts the estimation sample to regional banks, defined in the study as firms with at least $10 billion but less than $100 billion in consolidated assets throughout the sample period. The comparison changes the estimated relationships, not the basic model architecture. Both versions use the same general kind of inputs and produce the same general kinds of outputs; the question is whose history determines the coefficients.
The sequence has an important stopping point. Validation can show that one set of coefficients explains or forecasts regional-bank aggregates better than another. It cannot prove that every regional bank will follow that path in the next crisis. Nor can it convert an aggregate model into a substitute for asset-level examination. A model’s usefulness depends on matching its population, variables, and output to the decision at hand.
Why the population changes the estimate
Large banks represent most of the banking industry’s assets. That gives them substantial influence in an all-bank statistical relationship even when the question concerns a smaller group of institutions. The issue is not that the all-bank sample contains no information about regional banks. It is that the dominant observations may reflect a different combination of deposits, loans, capital-markets activity, consumer credit, and geographic reach.
Consider the economic meaning of an estimated interest-rate relationship. A diversified large bank may adjust its income through trading, investment banking, fee businesses, wholesale funding, and a broad loan portfolio. A regional bank may rely more on interest income from loans and lower-cost deposits, with a much higher share of CRE. If the short-term rate rises, the two groups can experience different timing and magnitude of changes in asset yields, deposit costs, fair values, and credit losses. A coefficient estimated mainly from the first balance-sheet pattern may be a poor description of the second even if both banks operate in the same national economy.
This is a population-calibration problem. The model is not merely asking, “What happens to a bank when unemployment rises?” It is asking, “How has this type of bank’s interest income, expenses, or loss rate moved when unemployment, rates, spreads, or prices changed, after accounting for its own history and controls?” If the type of bank changes, the relevant relationship may change too.
The study first compares in-sample fit. For each equation, the R-squared statistic indicates how much of the observed variation the model accounts for within the estimation sample. The regional-bank model’s fit was comparable to or better than the all-bank model in many equations, including important components. Interest-income R-squared was 0.94 for the regional model and 0.95 for the all-bank model. Interest-expense R-squared was 0.97 versus 0.96. Salary ratio fit was 0.96 versus 0.88, and fee ratio fit was 0.88 versus 0.87. Investment-banking and brokerage fit was 0.94 in both models.
Those figures support a limited but meaningful conclusion: restricting the sample to regional banks does not make the model obviously less coherent. In several equations, it fits the regional-bank data at least as well. That is evidence against the assumption that an all-bank relationship is automatically the best available description for every bank group.
But R-squared is not a causal certificate. A high value can reflect persistence, common trends, or variables that move together without identifying a structural cause. A regional model can fit historical data and still fail under a new policy, a new funding behavior, or a shock outside the sample. Some equations fit better in the all-bank model. The correct reading is that population-specific calibration is plausible and empirically useful, not that the regional model is universally superior.
The stronger test is what happens outside the estimation sample. The Federal Reserve compares forecasting errors for aggregate regional-bank PPNR, NCO rates, and CET1 ratios across different episodes. The exercise starts forecasts at selected pre-stress or pre-event quarters and uses the actual paths of macroeconomic and financial variables that followed. That design asks how well each model would have projected regional-bank aggregates when the environment became calmer or more distressed.
The contrast is clearest in the Global Financial Crisis episode. For PPNR, the root mean squared error was 0.818 when regional-bank coefficients were used, compared with 0.899 with all-bank coefficients. For NCO rates, the corresponding errors were 0.981 and 1.274. The regional calibration therefore produced lower errors for both reported outcomes during a period of severe macroeconomic and financial distress.
The result is not uniform across episodes or outcomes. In the pre-COVID exercises, PPNR error was 0.304 for the regional model and 0.686 for the all-bank model, but NCO error was 0.045 and 0.041, respectively. In the episode beginning just before the SVB failure and adding a funding shock, PPNR error was 0.328 versus 0.366 and CET1 error was 0.622 versus 0.710; NCO error was 0.121 versus 0.111. In the calmer cases, the NCO difference was slight, and the Diebold–Mariano test indicated equal forecasting accuracy.
These exceptions improve the evidence rather than weaken it. They show that model choice can matter greatly for one output and only marginally for another. PPNR may be especially sensitive to the different persistence and rate pass-through of regional banks, while aggregate NCO rates can be difficult to distinguish when losses are low or when the broad variables do not explain local credit conditions. A reader should therefore ask which output is being validated, over what episode, and against which benchmark.
The SVB-era exercise also shows why shock definition matters. The additional funding shock was represented within FLARE’s fixed-balance-sheet framework as a higher cost of uninsured deposit funding. It was not modeled as a replacement of uninsured deposits by more expensive funding. That assumption isolates one effect, but it does not reproduce every possible deposit run, asset sale, management response, or confidence feedback. A lower forecast error under that setup is evidence about that setup, not a complete historical reconstruction.
Why aggregate variables can still be the right variables
A natural objection remains. If individual regional banks have concentrated local footprints, why not replace national macroeconomic variables with state or regional indicators? The study gives two reasons to retain aggregate variables in the regional version of FLARE. First, its purpose is to model the propagation of system-wide stress. Broad macroeconomic conditions are the more direct drivers of losses that can occur across many banks at once. Second, the regional-bank sector’s deposits are geographically distributed even though individual banks are less diversified than large institutions.
The Federal Reserve’s deposit analysis illustrates the distinction. The median regional bank operated in about four states, and around 20 percent operated in only one. Yet the five states with the largest shares of regional-bank deposits accounted for about 34 percent of the sector’s deposits, close to their share of national economic output. A Herfindahl–Hirschman Index well below 1,000 also points to broad sector distribution. Local shocks can remain important for a particular bank, but a single local event is less likely to represent the dominant systemic risk for the entire regional-bank sector.
This is a question of correlation and scale. If a downturn affects employment and property markets across the country, aggregate variables can capture the common movement that links many regional banks. If a city’s office market collapses while the national economy remains stable, a national variable may not capture the bank-specific loss. The same dataset can be appropriate for one question and inadequate for another because the question changes from correlated system stress to local heterogeneity.
The practical implication is not to choose between “macro” and “local” analysis once and for all. It is to layer them. A regional-bank model can provide the group-level response to a common macro scenario. A supervisor, manager, investor, or analyst then needs local and granular evidence to test whether a particular institution departs from that average. The evidence required might include property type and location, loan maturity, borrower quality, deposit concentration, securities duration, and operational conditions—information that this top-down comparison does not supply.
That boundary also protects the meaning of the results. The study’s regional model is more closely matched to regional-bank history, and its forecast results generally favor that calibration, especially for PPNR in stressed episodes. It does not show that regional banks are broadly safe, that every regional bank has lower losses, or that an all-bank model has no value. The all-bank model remains a benchmark for the system and can perform as well or better for particular outcomes. The evidence shows why the benchmark should not be mistaken for the only relevant lens.
The next question is therefore quantitative: once the two models have different coefficients, how much do those differences change a common stress scenario’s projected earnings, loan losses, and capital? That step moves from whether the lens fits the population to what the lens changes in the resulting picture.