## 2.1 Cost-benefit analysis (CBA) of regulation

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### Research approach and model
- Revealed-preference approach: infer regulatory costs from distortions (bunching) in the cross-sectional size distribution of banks around regulatory thresholds.
- Structural model features:
  - Regulatory costs modeled as a tax on banks’ profits with discrete jumps at regulatory thresholds.
  - Banks optimally choose size and may shrink assets to avoid crossing thresholds, generating local excess densities (bunching).
  - Maximum likelihood estimator uses magnitude and shape of excess densities to identify regulatory costs.
- Identification advantage: captures strategic regulatory avoidance and implicit costs not observable in financial statements.

### Key empirical estimates (Dodd–Frank Act)
- Direct regulatory costs (revealed-preference estimates):
  - Regulatory costs triggered at the $10 billion threshold: 0.41% of average annual profits. (Standard error: 0.066%)
  - Additional regulatory costs triggered at the $50 billion threshold: 0.11% of average annual profits. (Standard error: 0.046%)
  - Total Dodd–Frank burden for a $50 billion bank: 0.41% + 0.11% = 0.52%.
- Dollar interpretation for a $50 billion bank:
  - Profits ≈ 1.6% of assets.
  - Dollar cost = $50,000M × 1.6% × 0.52% = $4.16M per year.
  - Example equivalence: $4.16M ≈ salary expenses of hiring 52 compliance officers at $80,000 average annual compensation.
- Indirect regulatory costs (general equilibrium simulation):
  - Indirect costs of the Dodd–Frank Act are equivalent to a 0.02% tax on the output of bank-dependent firms (Counterfactual simulation: Output change = -0.020%).

### Counterfactual and market-structure implications
- Contribution to decline in bank franchise value:
  - Estimated regulatory costs explain only a small fraction of the decline in bank franchise value in the post-crisis period; other contributors likely include ultra-low interest rates, market reassessment of risks, and removal of too-big-to-fail subsidies.
- Market share and concentration effects (counterfactual simulation results):
  - Predicted effects after Dodd–Frank (percentage changes relative to baseline):
    - Mass of banks: -0.184%
    - Market-to-book: -0.221%
    - Lending quantity: -0.065%
    - Lending rate: 0.046%
    - Output: -0.020%
  - By size group (percentage changes in annual profits and asset/share metrics):
    - Annual profits: Small banks +0.068%, Medium banks -0.399%, Big banks -1.268%
    - Asset shares: Small banks -0.061%, Medium banks -0.216%, Big banks +0.022%
    - Shares of banks: Small banks -0.012%, Medium banks +0.089%, Big banks +0.075%
  - Mechanisms:
    - Medium banks ($10B–$50B) engage in regulatory avoidance and shrink average asset size.
    - Heightened regulatory costs reduce bank values and entry of small banks (<$10B), reducing competition from below.
  - Suggests size-based regulation can have unintended consequence of increasing industry concentration.

### Comparison with other methods and evidence
- Reduced-form methods (difference-in-differences, regression discontinuity):
  - Likely to underestimate direct regulatory costs because banks can strategically avoid regulation.
  - Empirical reduced-form findings: generally little evidence of changes in regulation-related expenses after Dodd–Frank.
  - Difference-in-differences Treat * Post coefficients (selected; normalized by assets):
    - # employees: -0.012 [0.012]
    - Salaries: -0.043 [0.081]
    - Total admin expenses: -0.012 [0.018]
    - Communications: -0.009 [0.004] ∗∗
  - Regression discontinuity treatment effects (selected; 2010Q3–2018Q2):
    - Auditing: 0.021 [0.010] ∗∗
    - Communications: -0.010 [0.005] ∗
- Self-reported estimates by banks and surveys:
  - Bank Director Magazine survey: 9.9% of banks’ annual profits.
  - American Action Forum estimate: 1.8%.
  - These survey estimates are typically much larger than revealed-preference estimates and may be biased upward.
- Advantages of revealed-preference structural approach:
  - Less prone to self-reporting bias.
  - Captures implicit regulatory burdens not recorded in financial statements.
  - Enables simulation of indirect costs in full market equilibrium.

### Robustness checks and extensions
- Regulatory relief in 2018 (Economic Growth, Regulatory Relief, and Consumer Protection Act of 2018):
  - Excess densities around Dodd–Frank thresholds decreased after 2018 relief.
  - Estimated regulatory costs in post-relief period are significantly smaller:
    - Post-2018 $10 billion τ = 0.219 [0.095]; post-2018 $50 billion τ = 0.003 [0.012].
  - Steady-state number of banks increases after 2018 relief, consistent with increased bank entry.
- Distributional and specification robustness:
  - Baseline MLE assumes undistorted bank assets follow a power law; log-normal alternative yields similar τ estimates (e.g., $10 billion τ = 0.342 [0.062] under log-normal).
  - Local abnormal densities around thresholds drive identification; global distributional form has limited influence.
- Transition dynamics and placebo tests:
  - Dropping first several post-Dodd–Frank years yields similar estimates, implying relatively fast bank size adjustment.
  - Placebo tests on pre-Dodd–Frank samples and non-regulatory round numbers yield null τ estimates (e.g., pre Dodd–Frank $10B τ = 0.005 [0.003]).

### Estimation strategy, data, and sample statistics
- Two-stage estimation:
  1. Stage 1: estimate direct regulatory costs via maximum likelihood using bunching distortion in size distribution.
  2. Stage 2: estimate indirect regulatory costs by comparing equilibrium output of bank-dependent firms with and without regulation.
- Data and sample:
  - Sources: Call Reports and FR Y-9C reports; total consolidated assets used.
  - Sample period for structural estimation: 2010Q3 to 2018Q2 (overall data 2001–2019 for descriptive moments).
  - Exclude banks with assets less than $1 billion.
  - Sample covers around 40,000 bank-quarter observations.
- Selected sample moments (Table 1):
  - Average asset size = $28 billion.
  - Mean annual asset growth rate = 7.7%; standard deviation = 8.7%.
  - Average profits per dollar of assets = 1.6%.
  - Average administrative expenses = 0.2 cents per dollar of assets.
  - Number of employees per million of assets = 0.2.
  - Average salaries = 1.6 cents per dollar of assets.
- Stage 1 estimation specifics:
  - Observed log assets a = q + u, with u ∼ N(0, σ^2).
  - Undistorted assets follow power-law: exp(q) ∼ c exp(q)^(−β).
  - Parameters Θ = (τ, β, σ) estimated by maximizing log-likelihood over sample windows around thresholds.
  - Point estimates (Table 2):
    - $10 billion threshold: β = 1.112 [0.001]; σ = 4.258 [0.386]; exp(q) = 10.973 [0.086]; τ = 0.405 [0.066].
    - $50 billion threshold: β = 1.083 [0.002]; σ = 2.290 [0.498]; exp(q) = 52.393 [0.517]; τ = 0.106 [0.046].

### Policy-relevant takeaways
- Measured direct regulatory burden from Dodd–Frank is economically meaningful but substantially smaller than many self-reported industry estimates (revealed-preference: 0.41%–0.52% of profits vs. surveys up to 9.9%).
- Indirect macroeconomic costs, measured as lost output of bank-dependent firms, appear modest (output -0.020% under baseline counterfactual).
- Size-based regulatory thresholds generate strategic responses (bunching) that reshape bank size distribution and can have unintended effects on market concentration and entry.
- Regulatory CBA should account for strategic avoidance and implicit costs; revealed-preference methods provide complementary evidence to surveys and reduced-form approaches.

*Source: wpiea2022041-print-pdf - 2.1    Cost-benefit analysis (CBA) of regulation.*

### 2.1 Cost-benefit analysis (CBA) of regulation ..........................................................................

### 2.1 Cost-benefit analysis (CBA) of regulation

### Research approach and model
- Revealed-preference approach: infer regulatory costs from distortions in the cross-sectional size distribution of banks (bunching) around regulatory thresholds.
- Structural model features:
  - Regulatory costs modeled as a tax on banks’ profits with discrete jumps at regulatory thresholds.
  - Banks optimally choose size and may shrink assets to avoid crossing thresholds, generating local excess densities (bunching).
  - Maximum likelihood estimator derived from the model uses the magnitude of excess densities to identify regulatory costs.
- Identification advantage: captures strategic regulatory avoidance and implicit costs not observable in financial statements.

### Key empirical estimates (Dodd–Frank Act)
- Direct regulatory costs estimated from U.S. bank data:
  - Regulatory costs triggered at the $10 billion threshold: equivalent to a 0.41% tax on banks’ average annual profits.
  - Additional regulatory costs triggered at the $50 billion threshold: equivalent to a 0.11% tax.
  - Total Dodd–Frank burden for a $50 billion bank: 0.41% + 0.11% = 0.52%.
  - Dollar interpretation for a $50 billion bank: $50,000M × 1.6% × 0.52% = $4.16M per year.
    - Example equivalence: $4.16M ≈ salary expenses of hiring 52 compliance officers at $80,000 average annual compensation (Feldman, Heinecke, and Schmidt, 2013).
- Indirect regulatory costs (general equilibrium simulation):
  - Indirect costs of the Dodd–Frank Act are equivalent to a 0.02% tax on the output of bank-dependent firms.

### Counterfactual and market-structure implications
- Contribution to decline in bank franchise value:
  - Estimated regulatory costs explain only a small fraction of the decline in bank franchise value in the post-crisis period.
  - Other likely contributors: ultra-low interest rate environment, market reassessment of risks, removal of too-big-to-fail subsidies.
- Market share effects:
  - Counterfactual simulation predicts market share of big banks (>$50 billion) would expand after Dodd–Frank.
    - Mechanisms: medium banks ($10B–$50B) engage in regulatory avoidance and shrink average asset size; heightened regulatory costs reduce bank values and entry of small banks (<$10B), reducing competition from below.
  - Suggests potential unintended consequence of size-based regulation on industry concentration.

### Comparison with other methods and evidence
- Reduced-form methods (difference-in-differences, regression discontinuity):
  - Likely to underestimate direct regulatory costs because banks can strategically avoid regulation.
  - Typically find little evidence of changes in regulatory costs after the Dodd–Frank Act.
- Self-reported estimates by banks:
  - Generally much larger than revealed-preference estimates; susceptible to inflation for lobbying/regulatory relief purposes.
  - Anecdotal and prior work (Parker, Hinkes-Jones) indicate self-reports may be biased upward.
- Advantages of the revealed-preference structural approach:
  - Less prone to bias from self-reporting.
  - Captures implicit regulatory burdens not recorded in financial statements.
  - Enables simulation of indirect costs in full market equilibrium.

### Robustness checks and extensions
- Regulatory relief in 2018 (Economic Growth, Regulatory Relief, and Consumer Protection Act of 2018):
  - Empirical finding: excess densities around Dodd–Frank thresholds decreased after 2018 relief.
  - Estimated regulatory costs in post-relief period are significantly smaller than in the post-Dodd–Frank period.
  - Steady-state number of banks increases after 2018 relief, consistent with increased bank entry.
- Distributional assumptions:
  - Baseline MLE assumes undistorted bank assets follow a power law; alternative distribution assumptions produce robust estimates.
  - Local abnormal densities around thresholds drive identification; global distributional form has limited influence.
- Transition dynamics and adjustment speed:
  - Dropping the first several post-Dodd–Frank years yields similar estimates, suggesting relatively fast bank size adjustment and limited downward bias from transition dynamics.
- Placebo and falsification tests:
  - Applying estimator to pre-Dodd–Frank samples yields null regulatory-cost estimates.
  - Placebos at non-regulatory round numbers in the post-Dodd–Frank period also yield null results.
- Other robustness checks:
  - Allowing size-dependent profit margins and using alternative measures of bank regulatory assets do not materially change results.

### Policy-relevant takeaways
- Measured direct regulatory burden from Dodd–Frank is economically meaningful but substantially smaller than many self-reported industry estimates.
- Indirect macroeconomic costs, measured as lost output of bank-dependent firms, appear modest (0.02% tax equivalent).
- Size-based regulatory thresholds generate strategic responses (bunching) that reshape bank size distribution and can have unintended effects on market concentration and entry.
- Regulatory CBA should account for strategic avoidance and implicit costs; revealed-preference methods provide complementary evidence to surveys and reduced-form approaches.

*Source: "Watch what they do, not what they say: Estimating regulatory costs from revealed preferences" (January 21, 2022).*

### 2.1    Cost-benefit analysis (CBA) of regulation

### 2.1    Cost-benefit analysis (CBA) of regulation

### CBA: purpose and challenges
- Regulators are mandated by law to conduct a cost-benefit analysis (CBA) on regulations.
- CBA entails an economic or statistical assessment of the social benefits of the regulation and the compliance costs borne by the regulated parties.
- Goal of CBA:
  - Advance regulators’ ability to increase welfare.
  - Allow the public to detect and push back against regulations that fail to increase welfare.
- Institutional role:
  - CBA often forms the basis for judicial review and Congressional oversight of regulatory actions.
- CBA of financial regulations: policy debate
  - Since the passage of the Dodd–Frank Act, CBA of financial regulations has become an important policy debate.
  - Proponents: financial regulators should be held accountable to more-stringent CBA to ensure discretion on rule-making is not abused (Posner and Weyl, 2013).
  - Critics: inherent difficulties in CBA of financial regulations due to complexity of financial institutions and lack of reliable data (Coates, 2014; Cochrane, 2014).

### Dodd–Frank Act: tiered regulation and empirical evidence of bunching
- Dodd–Frank Wall Street Reform and Consumer Protection Act of 2010 (Dodd–Frank) is the centerpiece of post-crisis financial reform.
- Tiered regulatory approach:
  - Banks are classified into size categories based on regulatory thresholds.
  - Banks in larger size categories are subject to stricter regulations.
- Specific requirements for threshold-crossing banks:
  - Banks whose assets exceed$10 billion are required to:
    - (1) conduct annual stress tests,
    - (2) comply with the Durbin Amendment, which puts a cap on the fees charged to merchants for debit card transactions,
    - (3) report to the Consumer Financial Protection Bureau (CFBP), a government agency created as part of Dodd–Frank, and
    - (4) create risk committees with independent directors.
  - Banks whose assets exceed$50 billion are subject to additional risk-based capital and liquidity requirements, stress tests, and annual resolution plans.
- Behavioral response to thresholds:
  - The tiered regulation creates discontinuities in regulatory burden at the regulatory thresholds.
  - Banks around the thresholds strategically downsize assets to avoid regulation.
  - Empirical evidence: cumulative distribution function of bank size displays abnormal bulges around the$10 billion and$50 billion thresholds after passage of Dodd–Frank (red solid line in Figures 1a and 1b), suggesting bank bunching to avoid regulation.
  - This pattern is absent in the pre-Dodd–Frank period (blue dashed line in Figures 1a and 1b).
  - No excess density is found around round numbers that are not regulatory thresholds (e.g.,$20 billion or$40 billion), supporting the interpretation that excess densities around$10 billion and$50 billion arise from strategic responses to regulation.
  - Related findings: Bouwman, Hu, and Johnson (2018) find banks around the Dodd–Frank thresholds substantially reduce their assets; Eisenbach, Lucca, and Townsend (2021) find regulators spent considerably more work hours on banks above$10 billion in the post-crisis period.

### Bank size determination for regulatory purposes
- Dodd–Frank does not provide a uniform methodology to determine bank size for regulatory purposes; implementation left to separate rule-making processes producing different methodologies:
  - Annual stress test uses the average assets in the past four quarters;
  - Durbin Amendment uses the end of the calendar year assets;
  - CFPB reporting requirement uses the minimum of the last four consecutive quarters with the exception that all institutions above$10 billion as of the June 30, 2011 would be required to report to CFPB, and would only stop to be if they reported total assets below$10 billion for four consecutive quarters.
- Empirical approach in paper:
  - Uses the simplest measure—the quarter-end assets—to construct size distribution.
  - Conducts robustness checks with other methodologies and allows a measurement error term in estimation to account for regulatory-measurement intricacies.

### Theoretical model: bank size choice and direct regulatory cost
- Setup:
  - Banks heterogeneous by productivity z with density g(z); z interpreted broadly as non-regulatory factors affecting preferred size.
  - Banks raise funding from depositors at cost r(q|z), where q is log quantity of funds; r_q > 0 and r_z < 0.
  - Lending to firms occurs at rate R. Initially R and g(z) taken as exogenous.
- Size-based regulation:
  - Banks classified into I+1 categories based on size thresholds q_i, i = 1,...,I.
  - If assets cross threshold q_i, bank incurs additional regulatory cost equivalent to τ_i fraction of its profits.
  - τ_i interpreted as a proportional tax (tax-equivalent regulatory cost) or fraction of bank value loss due to present value of future regulatory costs.
- Banks maximize profits:
  - max_q π(q|z) = max_q (R − r(q|z)) exp(q) · Π_{i=1}^I (1 − τ_i 1_{q ≥ q_i}).
- Undistorted optimal size (all τ_i = 0):
  - q_0(z) ≡ arg max_q (R − r(q|z)) exp(q).
  - First-order condition: R − r(q_0(z)|z) = r_q(q_0(z)|z).
  - Example with r(q|z) = (1/θ)(q − z) gives q_0(z) = z + θR − 1, where θ ≡ 1/r_q is the semi-elasticity of funding supply.
- Optimal size with regulation:
  - Regulation creates discrete jumps in costs at thresholds; banks may bunch below thresholds to avoid τ_i but incur bunching costs (foregone profits).
  - Optimal asset choice as function of productivity:
    - q*(z) = { q_i  for z ∈ [z_i, z_ī];  q_0(z) for z ∉ ∪[z_i, z_ī] }.
    - z_i defined by q_i = q_0(z_i).
    - z_ī defined by q_i ≡ q_0(z_ī).
  - Marginal bank indifference condition:
    - (R − r(q_i | z_i)) exp(q_i) (1 − τ_i) = (R − r(q_i | z_i)) exp(q_i).
- Sufficient-statistic formula for direct regulatory cost (Proposition 1):
  - Proposition 1: The direct regulatory costs τ_i that come into effect at threshold i is given by the following sufficient statistic formula:
    - τ_i '1− ( q_i − q_i + 1 ) exp ( q_i − q_i ).
  - Notes:
    - The approximation is exact when the funding supply function has a constant semi-elasticity.
    - τ_i depends only on the difference between the marginal bank’s log assets q_i and the regulatory threshold q_i; it does not depend on R or r.
    - Intuition: regulatory cost is measured as a percentage of profits; lending and deposit rates scale profits but do not change relative magnitudes of regulatory costs versus bunching costs.
    - To translate τ_i into a dollar value, lending and deposit rates (to compute profits) are required.
    - The sufficient-statistic formula still works with heterogeneous semi-elasticities; heterogeneity matters only when calculating dollar values of regulatory costs (can be captured by multiplying τ_i with bank-specific profits).

### General equilibrium: firms, lending rate, and indirect costs
- Firms:
  - Firm problem: max_K Π = A K^α − R K, where Y = A K^α.
- Aggregate supply of capital:
  - K_s(R) ≡ N ∫ exp(q*(z|R)) g(z) dz, where N is number of banks.
- Market-clearing lending rate:
  - K_s(R) = (R / A α)^{1/(α−1)}.
- Bank entry, productivity distribution, and stationarity:
  - Productivity z evolves as Brownian motion: dz_t = μ_z dt + σ_z dB_t.
  - Bank value: v(z_0) ≡ E[ ∫_0^∞ e^{−(ρ+λ)t} π(q*(z_t)|z_t) dt | z_0 ], where ρ is discount rate and λ is exogenous exit rate.
  - Entry condition: m = m_exp( η( ∫ v(z) ψ(z) dz − c_e ) ), where c_e is entry cost, ψ(z) distribution of potential entrant productivity, η entry elasticity, m long-run entry mass when expected value equals cost.
  - For simplicity new entrants have starting productivity z_n.
  - Productivity distribution evolves per Kolmogorov forward equation:
    - ∂g(z,t)/∂t = −∂[μ_z g(z,t)]/∂z + (1/2) ∂^2[σ_z^2 g(z,t)]/∂z^2 − λ g(z,t) + (m/N) ψ(z).
  - Stationary equilibrium defined by incumbent choices q*(·), entry decisions, firm credit demand, aggregate credit market clearing, and ∂g/∂t = 0 for all z.
  - With constant semi-elasticity, stationary bank assets follow a power-law distribution (proportional random growth intuition).

- Indirect cost of regulation:
  - Defined as percentage output change between regulated and unregulated economy:
    - τ_indirect = (Y(0) − Y(τ)) / Y(0).
  - Equilibrium outputs:
    - Y(τ) = A ( N(τ) ∫ exp(q*(z | R(τ), τ)) g(z | τ) dz )^α.
    - Y(0) = A ( N(0) ∫ exp(q*(z | R(0), 0)) g(z | 0) dz )^α.
  - Indirect costs arise from:
    - Intensive margin: reduced credit supply from incumbent banks q*(·).
    - Extensive margin: regulation’s effect on entry and thus number of banks N; sign ambiguous (reduced incumbent supply can increase entry incentive, while higher expected regulation can deter entry).
  - Whether regulation increases or decreases entry is an empirical question.

### Estimation strategy and data
- Two-stage estimation:
  1. Estimate direct regulatory costs using a maximum likelihood estimator based on bunching distortion in size distribution.
  2. Estimate indirect regulatory costs by comparing total output of bank-dependent firms in counterfactual economies with and without regulation.
- Rationale:
  - Estimating direct costs requires only bank size distribution data.
  - Estimating indirect costs requires stronger assumptions and calibration of parameters for banks and firms; these are calibrated to prior literature or data moments.
  - The paper avoids using changes in bank values or entries pre/post Dodd–Frank to estimate regulatory costs because those moments can be influenced by other factors (low-interest-rate environment, market perception of risks, size of too-big-to-fail subsidy).
  - Instead uses distortion in size distribution around Dodd–Frank thresholds, argued to be unlikely driven by other factors.
- Data:
  - Combined data sources: Consolidated Reports of Condition and Income (“Call Reports”) and Consolidated Financial Statements for Holding Companies (“FRY-9C reports”).
  - Consider total consolidated assets (Dodd–Frank applies to highest holding entity); a bank refers to either a standalone commercial bank or a bank holding company.
  - Sample period: 2001–2019.
  - Exclude banks with assets less than$1 billion from sample.
- Sample summary statistics (Table 1):
  - Sample covers around 40,000 bank-quarter observations.
  - Average asset size is$28 billion.
  - Mean and standard deviation of annual asset growth rate are 7.7% and 8.7%, respectively.
  - Average profits per dollar of assets is 1.6%.
  - Administrative expense items reported (legal, data processing, advisory, printing and supplies, auditing, communications, labor) are not used in structural estimation because they do not capture all regulatory costs; used for comparison in Section 4.5.
  - In sample:
    - Average administrative expenses are 0.2 cents per dollar of assets.
    - Number of employees per million of assets is 0.2.
    - Average salaries are 1.6 cents per dollar of assets.

*Italic: Content derived from "wpiea2022041-print-pdf - 2.1    Cost-benefit analysis (CBA) of regulation".*

### 4.2    Stage 1:  direct regulatory costs

### 4.2    Stage 1:  direct regulatory costs

### Model setup and assumptions
- Observed log assets a are modeled as a structural error around true log assets q: a = q + u, with u ∼ N(0, σ^2).
- Undistorted assets follow a power-law distribution: exp(q) ∼ c exp(q)^(−β).
- The semi-elasticity of funding supply is assumed constant locally around thresholds so that equation (8) holds exactly.
- The scale parameter c of the power-law distribution is treated as a constant and is unidentified by the data.
- Sample period used for estimation: 2010Q3 to 2018Q2.
- Sub-samples around regulatory thresholds:
  - For the $10 billion threshold: banks in the $3 billion to $40 billion interval.
  - For the $50 billion threshold: banks above $40 billion.

### Estimation method
- Parameters estimated by maximum likelihood:
  - Θ = (τ, β, σ), where
    - τ is the direct regulatory cost,
    - β determines curvature of undistorted asset distribution,
    - σ is the standard deviation of the structural error.
- Log-likelihood maximized: max_Θ L(Θ) = Σ_{j=1}^J ln f(a_j | Θ) (equation (17)), with f derived in Appendix A.5.
- Identification intuition:
  - Larger τ → larger abnormal mass (bunching) around regulatory thresholds.
  - Larger σ → more diffused abnormal mass around thresholds.
  - β pinned down by global shape of distribution (observations far from thresholds).

### Empirical estimates (point estimates and inference)
- Point estimate for annual regulatory costs triggered by the $10 billion threshold: 0.41% of average annual profits.
  - Standard error: 0.066%.
  - This estimate captures additional regulatory cost imposed by the Dodd–Frank Act triggered at the $10 billion threshold (does not include pre-existing regulations).
  - Implied undistorted assets of the marginal bank at this threshold, exp(q): around $11 billion (using equation (8)).
- Point estimate for additional regulatory costs crossing the $50 billion threshold: 0.11% of average annual profits.
  - Total regulatory cost imposed by the Dodd–Frank Act on banks above $50 billion (sum of $10b and $50b-triggered costs): 0.52%.
  - Implied undistorted assets of the marginal bank at the $50 billion threshold, exp(q): around $52 billion.
- Robustness notes:
  - Results robust to alternative sample ranges (Online Appendix Table OA.2).
  - Estimation robust to adding pre Dodd–Frank data (Online Appendix Table OA.3).
  - Goodness-of-fit tests in Online Appendix Table OA.1 find the power-law distribution fits well.

### Dollar cost interpretation and comparisons
- For a bank with $50 billion assets:
  - Profits are around 1.6% of total assets (Table 1).
  - Estimated regulatory cost implies a dollar value of regulatory costs around $4.16 million per year.
  - This dollar estimate is equivalent to the annual expense of hiring 52 additional compliance officers, assuming average annual compensation per compliance officer is around $80,000 (Feldman, Heinecke, and Schmidt, 2013).
- Comparative literature:
  - Kisin and Manela (2016) estimate the shadow cost of bank capital requirements before the 2008 financial crisis to be around 0.4% of banks’ annual profits; while regulations differ, the magnitudes are similar.

*Italic: Source: 4.2 Stage 1: direct regulatory costs (wpiea2022041-print-pdf)*

### 4.5    Comparisons with existing methods

### 4.5    Comparisons with existing methods

### Survey
- The cost estimates surveyed in this section are about the direct compliance costs for banks and should be compared with the direct regulatory costs estimated in Section 4.2, which are 0.41%-0.52% of banks’ profits.
- Many surveys only provide qualitative indications of high regulatory costs but no quantitative estimates.
- Among surveys that provide quantitative estimates:
  - Bank Director Magazine survey suggests annual regulatory costs are around 9.9% of banks’ annual profits.
  - American Action Forum survey estimates regulatory costs around 1.8%.
- The survey estimates are usually much larger than the estimates obtained from the revealed preference approach used in this paper.

### Difference-in-differences
- Methodology described:
  - Regression model: Expenses_{i,t} = α_i + α_t + β Treat_i × Post_t + γ X_{i,t} + ε_{i,t}.
  - Expenses includes regulation-related expenses such as legal, data processing, advisory, printing, stationery and supplies, auditing, and communication costs.
  - α_i and α_t are bank and time fixed effects. X_{i,t} includes the log number of branches. Expenses normalized by assets. Also include number of employees and total salaries.
  - Sample: banks with assets between $3 billion and $40 billion as of 2010Q2.
  - Sample period: 2003Q1 to 2018Q2.
  - Treat = 1 if bank’s total assets > $10 billion as of 2010Q2; Post = 1 for years after the Dodd–Frank Act (after 2010Q3).
- Empirical findings:
  - Table 7 reports that none of the expenses increases significantly for the treated banks.
  - Some expenses, such as communication expenses, have the wrong sign.
  - Rolling four-quarter average annualized expenses plotted for treated and control groups (Figure 8) show no significant increase for the treated group after the Dodd–Frank Act.
- Caveats:
  - Measurement challenge: not all regulatory costs are reflected in income-statement expenses (e.g., increased capital requirement).
  - Endogeneity: banks can endogenously bunch below thresholds to avoid regulatory costs, potentially biasing difference-in-differences estimates downward.
  - Thus, the lack of significant increases in expenses should not be interpreted as evidence that the Dodd–Frank Act imposes no costs on banks.

### Regression discontinuity
- Methodology described:
  - Regression model: Expenses_{i,t} = β_0 + β_1 1{Q_{i,t} ≥ Q} + β_2 f(Q_{i,t} − Q) + β_3 1{Q_{i,t} ≥ Q} f(Q_{i,t} − Q) + ε_{i,t}.
  - Expenses_{i,t} same regulation-related expenses as in difference-in-differences; Q_{i,t} is assets; f(·) is a polynomial function of degree one. β_1 measures the increase in regulation-related expenses when assets exceed threshold Q.
  - Sample period: 2010Q3 to 2018Q2.
- Empirical findings:
  - Table 8 and Figure 9 show most expenses do not exhibit significant changes above and below the thresholds.
  - There is a small increase in auditing costs for treated banks and a small decrease in communication costs.
- Caveats:
  - Subject to the same measurement and endogeneity concerns as the difference-in-differences approach.

### Summary
- Existing methods yield inconsistent evidence on the regulatory costs of the Dodd–Frank Act:
  - Surveys typically suggest extremely large regulatory costs (e.g., 9.9%, 1.8%), and may be inflated (consistent with anecdotal evidence and lobbying incentives).
  - Reduced-form methods (difference-in-differences and regression discontinuity) find virtually no evidence of additional regulatory costs, subject to endogeneity and measurement caveats.
  - The paper’s structural revealed preference approach finds a modest level of regulatory costs.
- Advantages and limitations:
  - Reduced-form approaches do not require modeling the data generating process but require some observations to be randomly assigned; anticipated regulatory changes allow regulated parties to engage in regulatory avoidance, undermining random assignment and creating selection issues.
  - Finding valid instruments could address selection but limits scope to settings with available instruments.
  - The structural approach allows analysis of equilibrium responses to big and highly anticipated regulatory changes, enables counterfactual policy experiments and welfare analysis with additional assumptions on the data generating process.
- Key quantifications reported elsewhere in the paper:
  - Estimated regulatory costs triggered at the $10 billion threshold are equivalent to a 0.41% tax on banks’ average annual profits.
  - Regulatory costs triggered at the $50 billion threshold are equivalent to a 0.11% tax.
  - In total, the regulatory costs introduced by the Dodd–Frank Act for a $50 billion bank amount to $4.16 million per year.
- Overall conclusion:
  - The revealed preference approach complements existing methods by focusing on banks’ actions rather than self-reported estimates, and can be applied in settings with big, anticipated regulatory changes.

*Source: 4.5 Comparisons with existing methods, wpiea2022041-print-pdf*

### References

### References

### Key empirical estimates of regulatory cost (revealed-preference estimates)
- Maximum likelihood estimation, power law (Table 2), $10 billion threshold:
  - β (Exponent of the power law distribution) = 1.112 [0.001]
  - σ (Measurement error volatility (in %)) = 4.258 [0.386]
  - exp(q) (Assets of marginal bank ($Billion)) = 10.973 [0.086]
  - τ (Cost of regulation (% of profit)) = 0.405 [0.066]
- Maximum likelihood estimation, power law (Table 2), $50 billion threshold:
  - β = 1.083 [0.002]
  - σ = 2.290 [0.498]
  - exp(q) = 52.393 [0.517]
  - τ = 0.106 [0.046]
- Post-2018 regulatory relief estimates (Table 9), $10 billion threshold:
  - exp(q) = 10.701 [0.159]
  - τ = 0.219 [0.095]
- Post-2018 regulatory relief estimates (Table 9), $50 billion threshold:
  - exp(q) = 50.138 [3.707]
  - τ = 0.003 [0.012]
- Log-normal specification (Table 10), $10 billion threshold:
  - μ_q (Average undistorted log(asset)) = 1.999 [0.007]
  - σ_q (Undistorted log(asset) std.) = 0.674 [0.005]
  - σ (Measurement error volatility (in %)) = 4.027 [0.378]
  - exp(q) = 10.888 [0.086]
  - τ = 0.342 [0.062]
- Log-normal specification (Table 10), $50 billion threshold:
  - μ_q = 5.040 [0.022]
  - σ_q = 1.062 [0.016]
  - σ = 2.355 [0.533]
  - exp(q) = 52.552 [0.533]
  - τ = 0.120 [0.048]
- Placebo tests (Table 11) show negligible τ estimates in pre-Dodd–Frank or non-regulatory thresholds:
  - $10 billion threshold, pre Dodd–Frank: τ = 0.005 [0.003]
  - $50 billion threshold, pre Dodd–Frank: τ = 0.029 [0.034]
  - $20 billion threshold, post Dodd–Frank: τ = 0.004 [0.003]
  - $40 billion threshold, post Dodd–Frank: τ = 0.008 [0.071]

### Counterfactual and model-based quantitative results
- Counterfactual simulation results (Table 5): values are percentage changes with respect to the baseline economy (Columns report Baseline / Dodd–Frank / Regulatory relief):
  - Panel (a): all banks
    - Mass of banks: 11.836, -0.184 %, -0.094 %
    - Market-to-book: 1.228, -0.221 %, -0.104 %
    - Lending quantity: 257.805, -0.065 %, -0.032 %
    - Lending rate: 0.049, 0.046 %, 0.023 %
    - Output: 42.313, -0.020 %, -0.010 %
  - Panel (b): annual profits by size group
    - Small banks: 0.023, 0.068 %, 0.033 %
    - Medium banks: 0.358, -0.399 %, -0.221 %
    - Big banks: 6.150, -1.268 %, -0.593 %
  - Panel (c): asset shares by size group
    - Small banks: 0.057, -0.061 %, -0.034 %
    - Medium banks: 0.073, -0.216 %, -0.123 %
    - Big banks: 0.870, 0.022 %, 0.013 %
  - Panel (d): shares of banks by size group
    - Small banks: 0.878, -0.012 %, -0.006 %
    - Medium banks: 0.072, 0.089 %, 0.042 %
    - Big banks: 0.050, 0.075 %, 0.042 %
- Robustness of counterfactuals (Table OA.4) — alternative parameter scenarios (all entries are percentage changes from baseline to Dodd–Frank):
  - Lower discount rate scenario:
    - Mass of banks: -0.236 %
    - Market-to-book: -0.234 %
    - Lending quantity: -0.085 %
    - Lending rate: 0.060 %
    - Output: -0.026 %
  - Higher entry cost scenario:
    - Mass of banks: -0.193 %
    - Market-to-book: -0.223 %
    - Lending quantity: -0.067 %
    - Lending rate: 0.047 %
    - Output: -0.020 %
  - Lower exit rate scenario:
    - Mass of banks: -0.512 %
    - Market-to-book: -0.167 %
    - Lending quantity: -0.255 %
    - Lending rate: 0.179 %
    - Output: -0.077 %

### Difference-in-differences and regression discontinuity estimates of regulation-related expenses
- Difference-in-differences estimates (Table 7), Treat * Post coefficient (with bank and quarter FE, dependent variables normalized by assets):
  - # employees: -0.012 [0.012]
  - Salaries: -0.043 [0.081]
  - Total admin expenses: -0.012 [0.018]
  - Legal: 0.008 [0.008]
  - Data processing: 0.001 [0.014]
  - Advisory: -0.003 [0.008]
  - Printing: 0.001 [0.004]
  - Auditing: 0.000 [0.005]
  - Communications: -0.009 [0.004] ∗∗
  - Adjusted R-squared ranges from 0.006 to 0.515 across specifications.
- Regression discontinuity estimates (Table 8), Treatment Effect (sample: U.S. banks with assets between 8.62 and 11.38 billion, 2010Q3–2018Q2; dependent variables normalized by assets):
  - # employees: 0.010 [0.024]
  - Salaries: 0.222 [0.182]
  - Total admin expenses: 0.025 [0.030]
  - Legal: 0.011 [0.021]
  - Data processing: 0.007 [0.023]
  - Advisory: -0.003 [0.015]
  - Printing: -0.005 [0.005]
  - Auditing: 0.021 [0.010] ∗∗
  - Communications: -0.010 [0.005] ∗

### Summary statistics and model fit
- Sample summary (Table 1) — selected metrics (N, mean, sd, percentiles):
  - Assets: N = 39,228; mean = 27.905; sd = 163.363; p5 = 1.056; p25 = 1.376; p50 = 2.232; p75 = 5.845; p95 = 81.776 (Assets reported in billions)
  - Assets growth rate: N = 336,167; mean = 1.655; sd = 11.504; p5 = -7.081; p25 = 1.484; p50 = 5.809; p75 = 11.632; p95 = 29.310
  - Profits: N = 39,228; mean = 1.624; sd = 1.328; p5 = 0.223; p25 = 1.074; p50 = 1.503; p75 = 1.948; p95 = 3.063 (Profits and expenses annualized and reported as a percentage of the assets)
  - # employees: N = 39,228; mean = 0.217; sd = 0.106; p5 = 0.070; p25 = 0.148; p50 = 0.206; p75 = 0.271; p95 = 0.398 (reported as per million of assets)
- Model fit (Table 4) — selected untargeted moments, data vs. model:
  - Share of banks: small banks (pre DF) Data = 89.609, Model = 87.787; (post DF) Data = 89.318, Model = 87.777
  - Share of assets: big banks (pre DF) Data = 79.142, Model = 86.958; (post DF) Data = 82.887, Model = 86.978
  - Imbalance ratio at $10 billion (pre DF) Data = 1.091, Model = 0.881; (post DF) Data = 0.421, Model = 0.558

### Institutional and theoretical derivations (appendix highlights)
- Institutional background (Appendix A.1) lists statutes relevant to cost-benefit analysis of financial regulation:
  - Paperwork Reduction Act (PRA): Pub. L. No. 104–13, 109 Stat. 163 (1995) (codified at 44 U.S.C.§§3501-3520).
  - Regulatory Flexibility Act (RFA): Pub. L. No. 96-354, 94 Stat. 1164 (1980) (codified at 5 U.S.C.§§601–612).
  - Congressional Review Act (CRA): Pub. L. No. 104–121, 110 Stat. 847 (1996) (codified as amended in 5 U.S.C.§801 et seq.).
  - Court example: Chamber of Commerce v. SEC, 412 F.3d 133 (D.C. Cir. 2005) (rule struck down in part for insufficient cost quantification).
- Analytical results and derivations:
  - Derivation of regulatory cost τ from the profit indifference condition (Appendix A.2), yielding approximation:
    - 1 − τ ' ( (q̄ − q + 1) exp (q − q̄) ) when q is close to q̄ (equations (20)–(24))
  - Robustness to heterogeneous semi-elasticity of funding supply (Appendix A.3):
    - The mapping between proportional regulatory tax τ and marginal bunching bank size q does not depend on semi-elasticity θ; heterogeneity in θ affects dollar value τ · (1/θ) exp(q) but not τ (equations (25)–(32))
  - Stationary distribution derivation (Appendix A.4):
    - Productivity stationary distribution g(z) is a double power law distribution (equation (36)); in absence of regulatory distortion, bank size distribution is also double power law.
  - Maximum likelihood estimators for observed size densities derived for both power law (Appendix A.5) and log-normal (Appendix A.6) undistorted distributions, leading to explicit likelihood expressions used for parameter estimation (equations (43)–(47)).

### Survey-based and literature evidence (selected entries)
- Table 6 summarizes survey-based estimates of regulatory costs (translated into percentages of net income where quantitative):
  - Bank Director Magazine, Survey of 10 banks, Estimate = 9.9, Date = 1/1/2017
  - American Action Forum, Estimation from Federal Register, Estimate = 1.8, Date = 7/1/2016
  - JPMorgan and Citigroup, Survey of 2 banks, Estimate = 0.9, Date = 2012, 2014
  - Federal Reserve Bank of Minneapolis, Estimation of cost of new hires, Estimate = 1.1, Date = 3/1/2013
  - Several other surveys reported as Qualitative (dates and sample sizes listed in Table 6)

*Source: wpiea2022041-print-pdf - References.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022041-print-pdf.pdf_