Summary Statistics
| Variable | N | Mean | Std | 1% | 25% | 50% | 75% | 99% |
|---|
Baseline
Within & BetweenThe within-bank model estimates the size penalty using bank fixed effects. The between-bank model confirms the cross-sectional relationship using bank-level means. The growth model adds asset and deposit growth dynamics.
| Model | Term | Coef | SE | p | CI Low | CI High | N | R² |
|---|
The within-bank model shows a size penalty of −0.090. The between-bank model confirms the cross-section at −0.085. The growth model shows asset growth is positively associated with NIM (+0.71) but the asset×deposit growth interaction is strongly negative (−3.64) — growth without matching deposit growth hurts margins.
NIM Decomposition
Asset yield vs funding costThe baseline within-bank FE is rerun with interest income and interest expense as separate outcomes to isolate whether the NIM penalty comes from lower asset yields, higher funding costs, or both.
| Model | Term | Coef | SE | p | CI Low | CI High | N | R² |
|---|
Loading decomposition results.
Franchise Dilution
Growth quality| Model | Term | Coef | SE | p | CI Low | CI High | N | R² |
|---|
The branch-growth interaction is negative and significant (−0.58): rapid franchise expansion dilutes margins.
Rate Cycle
Heterogeneity| Model | Term | Coef | SE | p | CI Low | CI High | N | R² |
|---|
Size×FedFunds = −0.012 (p<0.001): each 1 pp rate hike amplifies the size penalty. A steeper yield curve partially offsets this (+0.015).
Acquisition Event Study
23,837 obsNIM Around Acquisitions
Event-time coefficients (relative to t−1) for acquiring banks. 95% confidence intervals shown as shaded band.
Reference period is t−1 (coefficient = 0). Positive coefficients mean higher NIM relative to the quarter before the deal.
NIM declines into acquisitions (coefficients fall from +0.11 at t−8 to +0.02 at t−2 vs. t−1), then rebounds post-deal peaking at t+2 (+0.12) before fading. Acquirers may be buying when their own margins are under pressure.
Threshold Crossing
Regulatory cutoffsEvent-study coefficients around the quarter a bank first crosses a regulatory asset threshold. Reference period is t−1.
148 banks crossed $10B. $50B (41 banks) and $100B (26 banks) samples are too small for reliable inference.
Robustness
6 specificationsSize Coefficient Across Specifications
Point estimates and 95% confidence intervals for the log-assets coefficient under six alternative specifications. Dashed red line marks zero.
Raw NIM (no winsorization) shows the size effect is insignificant (−0.01, p=0.87). The result depends on trimming extreme NIM outliers. The first-difference spec (−0.11, p<0.001), which removes bank-specific trends, and the lagged-controls spec (−0.12, p<0.001) are the most reassuring robustness results.
Time-Varying Coefficients
Rolling 20-quarter FEThe baseline within-bank FE specification is re-estimated in rolling 20-quarter windows to show how the size penalty evolves over time rather than assuming one constant coefficient for the full 2010–2025 sample.
Rolling Size Penalty on NIM
Each point is the log-assets coefficient from the baseline FE model centered on the labeled quarter. The shaded band shows the 95% confidence interval.
Window length is 20 quarters. More negative values imply a steeper within-bank size penalty.
Loading rolling coefficient path.
Extensions
8 analyses| Model | Term | Coef | SE | p | CI Low | CI High | N | R² |
|---|
NIM Volatility: null result (p=0.19). Size doesn’t predict NIM volatility.
H6 Fee Offset: ROA rises with size (+0.20, p<0.001). Noninterest margin +0.31 (p<0.001). Large banks offset lower NIM with higher fee income — a different earnings model, not a worse one.
Market Power: null result. Local deposit HHI doesn’t predict NIM (p=0.70).
Lagged Controls: strengthens baseline (−0.119 vs. −0.090).
Loading equity-ratio extension.
Loading efficiency extension.
Loading loan-composition extension.
Loading distress model.