Bank Consolidation and Uniform Pricing: Granja & Paixão (2026)

What this is. The paper’s core results, the structural model of deposit demand and bank pricing, and the identifying empirical specifications: enough to know what it found and how, without reading all 27 pages. To replicate or extend it, read the full source at the original.

TL;DR

Granja and Paixão document that U.S. banks set deposit and loan rates with a high degree of uniformity across their branch networks, and show that this practice fundamentally shapes the evolution of interest rates at acquired branches following a merger. Building on the earlier documentation of Radecki (1998) and Park and Pennacchi (2009) that U.S. banks price uniformly, they use a broader dataset and more products to confirm the pattern and trace its consequences for mergers and antitrust policy. Using branch-level RateWatch data on roughly 100,000 branches and 2,006 acquired banks over 2006-2019, they find that the absolute rate difference between acquired and acquirer branches falls by 40-70% within twelve months of a deal, regardless of changes in local market concentration. Pre-merger rate differences between the acquirer and acquired branches explain far more of the cross-sectional variation in post-merger rate changes than HHI-based concentration indicators. A structural model of monopolistic competition in banking that features uniform pricing fits the observed rate changes significantly better than a local-pricing model, even for acquirer branches in markets where the two banks never competed. Counterfactual welfare analysis shows that forced branch divestitures, which antitrust authorities commonly require, reduce consumer welfare by about 7% on average in markets where the acquirer offered better deposit rates than the acquired bank, raising questions about the adequacy of concentration-only merger review.

Core results

Magnitudes are as reported; ***/** = 1%/5%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	After a bank merger, the absolute difference in 12-month CD rates between acquired and acquirer branches falls by ~11 bps on average	Table 3, col. 1, p. 11	Post-Acquisition coeff = -0.108*** (SE=0.009); pre-merger average absolute difference 25.7 bps
R2	Rate convergence holds across all four products: savings deposits, HELOCs, and personal loans show declines of 3.7 bps, 43 bps, and 139 bps in absolute rate differences	Table 3, cols. 2-4, p. 11	Post-Acquisition coefficients: SAV100K -0.037*** (SE=0.003), HELOC -0.429*** (SE=0.047), Personal -1.385*** (SE=0.142)
R3	Rate adjustments are driven primarily by the acquired branches, not the acquirer; both higher-rate and lower-rate acquired branches converge toward the acquirer’s median	Table 5, p. 14	CD: higher-rate acquired branches fall 12.2 bps***; acquirer median rises 3.3 bps***. Lower-rate acquired branches rise 9.5 bps***; acquirer median falls 2.9 bps***
R4	Acquired branches lose 7-11% of their deposit volume after a merger; deposit losses are larger when the acquired branch had higher rates than the acquirer	Table 6, cols. 1-2, p. 15	Post-Acquisition on ln(total deposits): 12MCD10K -0.109*** (SE=0.012), SAV100K -0.069*** (SE=0.014); 1-SD higher pre-merger rate diff adds -2.5% (CD) and -3.8% (SAV)
R5	Pre-merger rate differences between acquired and acquirer branches explain 27.6% of residual variation in post-merger deposit rates; HHI changes explain near-zero additional variation	Table 7, Panel A, p. 16	CD rate top quintile (highest pre-diff) falls 28.5 bps*** (SE=0.026); bottom quintile rises 24.2 bps*** (SE=0.031); adj. R2 rises from 0.783 to 0.843 vs 0.784 for HHI bins
R6	The structural uniform pricing model fits observed post-merger rate changes significantly better than the local pricing model, including for acquirer branches that never competed with the acquired bank	Fig. 11, Panel A-C, p. 25	Uniform pricing slope beta=0.0818 (SE=0.0296, sig.); local pricing beta=0.0144 (SE=0.0365, insig.) for all branches; beta=0.0766 (sig.) vs 0.000 (insig.) for non-overlapping acquirer branches
R7	Forced branch divestitures required by antitrust authorities reduce consumer welfare by 7.2% on average in markets where the acquirer offered lower deposit rates (and where uniform pricing would have benefited depositors)	Table 9, p. 26	DeltaW^{Divestitures} = -7.209 pp in markets with Pre-Merger Rate Dif<0 (39 markets); no-divestiture welfare gain approx. 0.77%; in 5 markets with higher acquirer rates, divestitures add +2.167 pp

Overall (paper’s conclusion). Standard merger review based on local market concentration (HHI) fails to capture the most consequential channel through which bank mergers affect deposit rates: the convergence of rates at acquired branches toward the acquirer’s uniform network rate. This uniform pricing practice means that pre-merger rate differences between banks are far stronger predictors of post-merger deposit rate changes than local concentration indices. Antitrust regulators who require branch divestitures without accounting for uniform pricing risk imposing welfare losses on depositors in markets where the merger would have been beneficial.

Theory / model

The paper models demand and supply in the retail deposit market. On the demand side, consumers in each local banking market choose among available bank branches to maximize utility. On the supply side, the bank chooses deposit rates under one of two pricing regimes.

Consumer preferences. Each consumer in zip code $z$, banking market $m$, derives total indirect utility from depositing with branch $j$ of bank $b$ (p. 21, Eq. 3):

$$V_{j,z,m,b,t} = a_m r_{j,t} + \beta_0 X_{j,t} + \beta_1 H_{b,m,t} + \beta_2 W_{b,t} + \xi_b + \gamma_z \tag{3}$$

where $a_m$ is the market-specific deposit-rate semi-elasticity (the rate coefficient allowed to vary by market to capture heterogeneous depositor clienteles), $r_{j,t}$ is the branch deposit rate, $X_{j,t}$ is the branch age (capturing local relationship capital), $H_{b,m,t}$ is a vector of bank characteristics in market $m$ (branch network density, years of experience), $W_{b,t}$ captures time-varying bank-wide attributes (size, ROA, NPL ratio, Tier 1 capital), $\xi_b$ is a bank fixed effect (capturing unobserved service quality and brand), and $\gamma_z$ is a zip code fixed effect.

Market shares. Following the standard discrete-choice procedure of Berry et al. (1995), with Type-I extreme-value utility shocks, the aggregate share of branch $j$ in market $m$ is (p. 21, Eq. 4):

$$s_{j,z,m,b,t} = \frac{\exp(V_{j,z,m,b,t})}{\sum_{k \in \Gamma^m} \exp(V_{k,z,m,b,t}) + \exp(V_{O,m,t})} \tag{4}$$

where $\Gamma^m$ is the set of branches available in market $m$ and $V_{O,m,t}$ is the outside option value (normalized so $\xi_O = 0$).

Bank profit and pricing regimes. A multi-market bank $b$ owns branches $j$ across markets $m \in \Omega_b$, paying marginal cost $c_b$ per unit of deposits and fixed cost $C_{jbm}$ per branch. Let $R_{bm} = \tilde{R}_{bm} - c_b$ denote bank-market returns net of marginal costs. Bank profits are (p. 22, Eq. 6):

$$\Pi_b = \sum_{m \in \Omega_b} \sum_{j \in m} \left[ (R_{bm} - r_{jbm}) \, s_{jbm} \, D_m - C_{jbm} \right] \tag{6}$$

Under local pricing, each branch rate $r_{jbm}$ is chosen independently. The first-order condition sets the deposit spread equal to the inverse of the local demand semi-elasticity (p. 23, Eq. 7):

$$R_{bm} - r_{bm} = \frac{1}{a_m \bigl(1 - s_{bm}(r_{bm},\, \mathbf{r}_{b'/m})\bigr)} \tag{7}$$

Under uniform pricing, the bank sets a single rate $r_b$ across all branches and markets. The optimal uniform rate satisfies (p. 23, Eq. 8):

$$R_b - r_b = \frac{1}{\displaystyle\sum_{m \in \Omega_b} a_m \bigl(1 - s_{bm}(r_b,\, \mathbf{r}_{b'/m})\bigr)\, \xi_{b,m}} \tag{8}$$

where $\xi_{b,m} = s_{bm} D_m \big/ \sum_{m' \in \Omega_b} s_{bm'} D_{m'}$ is the share of bank $b$‘s total deposits held in market $m$. The uniform rate thus equals the inverse of the deposit-weighted average of local demand semi-elasticities. This has the key implication that any merger changes $r_b$ for all markets where bank $b$ operates, including markets that have no overlap with the acquired bank. In contrast, the local pricing model predicts no adjustment in non-overlapping markets.

Consumer welfare. Following Small and Rosen (1981), the change in consumer welfare in market $m$ induced by a policy intervention is (p. 24):

$$\Delta W_m = \ln\!\left(\sum_{j \in \Gamma_m^{post}} \exp V_j^{post}\right) - \ln\!\left(\sum_{j \in \Gamma_m^{pre}} \exp V_j^{pre}\right)$$

where $V_j^{pre}$ and $V_j^{post}$ are pre- and post-policy indirect utilities. This formula is applied to evaluate two counterfactuals: (i) merger approved without divestitures, and (ii) merger with the divestitures antitrust authorities actually required.

Method

Demand estimation. The market-specific rate semi-elasticities $a_m$ in Eq. (3) are estimated by taking logarithms of market shares relative to the outside option and writing the logit share equation in a linear specification (p. 22, Eq. 5):

$$\ln s_{j,z,m,b,t} = \sum_m (a_m \, r_{j,t} \times I_m) + \beta_0 X_{j,t} + \beta_1 H_{b,m,t} + \xi_b + \gamma_z + \chi_{m,t} \tag{5}$$

where $I_m$ are market indicator variables and $\chi_{m,t}$ are year-market fixed effects that absorb the unobservable outside-option characteristics $r_{O,t}$ and $H_{O,m,t}$. The specification restricts the sample to banking markets with at least 200 observations to obtain reliable market-level elasticity estimates.

The key endogeneity concern is that deposit rates $r_{j,t}$ are chosen by banks in response to local demand conditions, creating a simultaneity bias. Following the Hausman (1996) instrument approach used by Dellavigna and Gentzkow (2019) and Egan et al. (2017), the paper instruments the deposit rate offered at a branch with the average rate offered by other branches of the same bank in other markets. This instrument is strong because branches of the same bank share an equilibrium uniform rate, but it is excludable because the rate differences across markets are driven by the bank-wide uniform rate, not local demand.

Estimated market-specific semi-elasticities average 0.134 (standard deviation 0.111) and are Winsorized and empirical-Bayes-shrunk to reduce sampling noise in thin markets (Fig. 10, p. 23). This average semi-elasticity is lower than estimates from Abrams (2019) (approximately 0.3) and Egan et al. (2017) (0.16-0.60), partly reflecting different sample selection and the use of a finer market-level identification.

Counterfactual simulation. The structural model is used to simulate all mergers in the sample and compute post-merger equilibrium deposit rates under both pricing regimes. The procedure: (i) recover bank-market net returns $R_{bm}$ from the pre-merger first-order conditions; (ii) reassign acquired branches to the acquirer; (iii) solve the fixed-point system of first-order conditions (Eq. 7 or 8) for all banks under the new ownership structure. In both counterfactuals, acquired branches adopt the non-price characteristics of the acquirer, so quality convergence is held constant and the equilibrium rate differences reflect only pricing conduct.

Empirical specifications

Rate convergence around mergers (Table 3, p. 11, R1-R2). The main reduced-form specification is OLS on the panel of acquired branches (p. 9, Eq. 1):

$$Y_{i,t,s} = \gamma_{s,t} + \theta_i + \beta \cdot \text{Post-Acquisition}_{i,t,s} + \varepsilon_{i,t,s} \tag{1}$$

where $Y_{i,t,s}$ is the absolute value of the difference between the acquired branch rate and the acquirer’s median rate, $\gamma_{s,t}$ are state-by-month fixed effects, $\theta_i$ are branch fixed effects, $s \in \{0, 1, \ldots, 12\}$ post-merger and $s \in \{-12, \ldots, -1\}$ pre-merger. The coefficient $\beta$ measures the average impact on the absolute rate difference in the twelve months after acquisition. Standard errors are clustered at the merger level. Results shown for four products (12MCD10K, SAV100K, HELOC, Personal) and for both levels and percent differences.

Deposit volume around mergers (Table 6, p. 15, R4). To assess how uniform pricing affects branch deposits over a five-year window, Eq. (2) interacts the post-merger indicator with the pre-merger percent rate difference (p. 14, Eq. 2):

$$Y_{i,t,s} = \gamma_{s,t} + \theta_i + \beta_0 \cdot \text{Post-Acq}_s + \beta_1 \cdot \text{Post-Acq}_s \times \left(\frac{\text{Acquired Branch Rate} - \text{Acquirer Rate}}{\text{Acquirer Rate}}\right)^{\!\text{Pre}} + \varepsilon_{i,t,s} \tag{2}$$

where $Y_{i,t,s}$ is the natural logarithm of total deposits at acquired branch $i$ in year $t$, $s$ years from the merger. The coefficient $\beta_1$ measures the average percent change in deposits per one-unit increase in the pre-merger rate difference. Branch- and state-by-year fixed effects are included throughout.

Rate convergence decomposition by HHI and pre-merger rate quintile (Tables 7-8, p. 16, R5). To compare the predictive power of HHI changes versus pre-merger rate differences, the following flexible specification is estimated:

$$Y_{i,t,s} = \gamma_{s,t} + \theta_i + \sum_{k=1}^{5} \beta_k \cdot \text{Post-Acq}_s \times \mathbf{1}[\text{Pre-Diff Rate}_i \in Q_k] + \varepsilon_{i,t,s}$$

where $\mathbf{1}[\text{Pre-Diff Rate}_i \in Q_k]$ are dummy variables for each quintile of pre-merger rate differences $(\text{Branch Rate} - \text{Acq Median Rate}) / \text{Acq Median Rate}$. A parallel specification interacts $\text{Post-Acq}$ with indicators for HHI change bins (zero, 0-200, 200+ basis points). The incremental adjusted $R^2$ from adding quintile interactions is 0.060 (0.783 to 0.843), explaining 27.6% of the unexplained variation from the base specification; the HHI bins add only 0.001. Following Liebersohn (2020), the same pattern holds for the subsample of mergers with predicted post-merger HHI between 1,300 and 1,800 (Table 8), which are below the antitrust trigger threshold and thus free from selection by regulatory intervention.

Robustness includes: large vs. small acquirer partitions (Table 4 Panel B), market overlap vs. non-overlap partitions (Panel C), matched-control difference-in-differences using branches not involved in mergers (Internet Appendix E), and extending the analysis to two and three years post-merger (Internet Appendix F).

Datasets used

Dataset	Role in paper	Wiki page
RateWatch (S&P Global Market Intelligence)	Branch-level weekly posted rates for CDs, savings, HELOC, personal loans (4 products); primary source for all interest-rate analysis	RateWatch
FDIC Summary of Deposits (SOD)	Annual branch-level deposit balances; used to compute market shares, deposit volumes, and bank market shares for the structural model	FDIC Summary of Deposits
FFIEC Call Reports	Quarterly bank balance-sheet data (total assets, deposits, ROA, NPL, Tier 1 capital); used as bank-level characteristics in demand estimation	Call Reports
Federal Reserve NIC (public structure data)	Panel of all bank M&A events with dates and FDIC branch identifiers; used to identify ownership transfers and the sample of mergers; only the public BHC ownership and merger-history layer was used, not confidential CAMELS ratings	No page yet (public NIC structure data)

Sample: January 2006 to December 2019 (merger analysis); 2,177 M&A deals for 12MCD10K, 9,370 acquired branches across 49 states. Uniform pricing documentation (Section 3) uses 2004-2019.

When to read the full paper

Use the original if you are: designing antitrust review procedures that account for uniform pricing (Section 7.5, Table 9); calibrating a structural model of retail deposit demand and estimating market-specific semi-elasticities (Section 7.1-7.2); assessing the empirical prevalence of uniform pricing in banking (Section 3 and Fig. 2-4); or extending the event-study convergence analysis to other banking products or jurisdictions. The Internet Appendices contain robustness tests on alternative product definitions, sample restrictions, alternative estimation approaches (Appendix G), and the role of HHI at longer horizons (Appendix F).

Attribution and rights

Source: peer-reviewed, Journal of Financial Economics 176 (2026) 104204. DOI: 10.1016/j.jfineco.2025.104204. This distillation was extracted by an LLM on 2026-06-24 and is not human-verified or independently reproduced. The article is paywalled (Elsevier B.V., 2025); this page reproduces only short extracts for academic commentary under fair use. No verbatim PDF is hosted here.

Granja, João, and Nuno Paixão. “Bank consolidation and uniform pricing.” Journal of Financial Economics 176 (2026) 104204. DOI: 10.1016/j.jfineco.2025.104204. © 2025 Published by Elsevier B.V. All rights reserved. Extract-only. This page is an LLM-distilled summary by the Institute for Automated Research.