## Appendix I.

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---

### Figures and Tables (listing)
- Figures included in this appendix:
  - 1. Stochastic Frontier Analysis Representation
  - 2. Histogram of the Size of Central Banks' Staff and Overall Contributions (by Income Group)
  - 3. Staffing and Population
  - 4. Average Salary per Headcount and GDP per Capita
  - 5. Distribution of Cost to GDP (by Income Group)
  - 6. Efficiency Estimates with Tangible and Intangible Assets: Dispersion across Countries
  - 7. Efficiency Estimates with Tangible and Intangible Assets: Dispersion across Income Groups
  - 8. Efficiency Estimates: By Number of Central Bank Objectives
- Tables included in this appendix:
  - 1. Descriptive Statistics
  - 2. Operational Expenses
  - 3. Stochastic Frontier Estimates with Tangible Assets Only
  - 4. Stochastic Frontier Estimates with Tangible and Intangible Assets
  - 5. Summary Statistics of Efficiency Estimates
  - 6. Determinants of Central Bank Operational Efficiency

### Robustness tests — overview and approaches
- Purpose:
  - Examine determinants of central bank operational efficiency by testing robustness of three factors: central bank independence, real GDP growth, financial system depth.
- Approaches:
  - Split sample by exchange rate regime (floating vs. nonfloating).
  - Introduce additional controls for operating environment (control of corruption, rule of law, financial freedom).
  - Use alternative measure of financial depth (public international debt-to-GDP instead of financial system deposit-to-GDP).
  - Split sample by trade balance sign (trade surpluses vs. trade deficits).

### Findings — By exchange rate regimes (Table A.1)
- Sample sizes and fit:
  - Observations: 178 (Floats), 350 (Nonfloats)
  - Number of central banks: 18 (Floats), 45 (Nonfloats)
  - R-squared: 0.181 (Floats), 0.394 (Nonfloats)
- Key coefficients (dependent variable = operating expense efficiency):
  - (X+M)/GDP:
    - Floats: -0.000808*** (0.000198)
    - Nonfloats: -0.0100** (0.00457)
  - Central bank independence:
    - Floats: 0.000723* (0.000415)
    - Nonfloats: 0.00132*** (0.000180)
  - Real GDP growth:
    - Floats: 0.000135 (0.000611)
    - Nonfloats: -0.000161 (0.000148)
  - Financial system deposit/GDP:
    - Floats: 0.000381 (0.000389)
    - Nonfloats: 0.000592*** (9.33e-05)
  - Capital account openness:
    - Floats: 0.00589 (0.0534)
    - Nonfloats: -0.00400 (0.00802)
- Interpretation:
  - Central bank independence, real GDP growth, and financial system depth retain the same sign as baseline.
  - Trade balance effect differs by regime: negative and significant for nonfloaters; negative and significant (smaller magnitude) for floaters as well.

### Findings — Controlling for operating environment (Table A.2)
- Sample splits and fit:
  - Observations: 520 (ALL), 196 (AEs), 213 (EMs), 111 (LIDCs)
  - Number of central banks: 63 (ALL), 20 (AEs), 28 (EMs), 15 (LIDCs)
  - R-squared: 0.332 (ALL), 0.259 (AEs), 0.549 (EMs), 0.406 (LIDCs)
- Key coefficients (dependent variable = operating expense efficiency):
  - (X+M)/GDP:
    - ALL: -0.000693*** (0.000121)
    - AEs: -0.000743*** (0.000129)
    - EMs: -0.00585 (0.00424)
    - LIDCs: -0.0118 (0.00830)
  - Central bank independence:
    - ALL: 0.00125*** (0.000164)
    - AEs: 0.000848** (0.000382)
    - EMs: 0.00136*** (0.000224)
    - LIDCs: 0.000961** (0.000422)
  - Real GDP growth:
    - ALL: -0.000166 (0.000208)
    - AEs: 0.000313 (0.000412)
    - EMs: 1.75e-06 (0.000286)
    - LIDCs: -3.70e-05 (0.000234)
  - Financial system deposit/GDP:
    - ALL: 0.000543** (0.000214)
    - AEs: 0.000441* (0.000228)
    - EMs: 0.000812*** (0.000149)
    - LIDCs: 0.00107** (0.000416)
  - Control of corruption:
    - ALL: -0.0144** (0.00708)
    - AEs: -0.0224 (0.0150)
    - EMs: -0.00843 (0.00708)
    - LIDCs: -0.00494 (0.0136)
  - Rule of law:
    - ALL: -0.00943 (0.00839)
    - AEs: -0.0112 (0.0182)
    - EMs: -0.0189** (0.00807)
    - LIDCs: 0.0207* (0.0115)
  - Financial freedom:
    - ALL: -7.64e-06 (0.000347)
    - AEs: -0.000185 (0.000504)
    - EMs: 0.000382 (0.000490)
    - LIDCs: 9.59e-06 (0.000757)
- Interpretation:
  - Results remain consistent after adding operating-environment controls.
  - Financial system deposit/GDP shows positive and often significant association with operating expense efficiency across groups.
  - Control of corruption and rule of law show heterogeneous signs and significance across country groups.

### Findings — Alternative financial depth measure: public debt/GDP (Table A.3)
- Sample splits and fit:
  - Observations: 511 (ALL), 197 (AEs), 207 (EMs), 107 (LIDCs)
  - Number of central banks: 59 (ALL), 19 (AEs), 26 (EMs), 14 (LIDCs)
  - R-squared: 0.326 (ALL), 0.277 (AEs), 0.467 (EMs), 0.433 (LIDCs)
- Key coefficients:
  - (X+M)/GDP:
    - ALL: -0.00103*** (4.10e-05)
    - AEs: -0.00103*** (4.12e-05)
    - EMs: -0.00117 (0.00314)
    - LIDCs: -0.0110 (0.00792)
  - Central bank independence:
    - ALL: 0.00122*** (0.000208)
    - AEs: 0.000767** (0.000341)
    - EMs: 0.00147*** (0.000240)
    - LIDCs: 0.000642 (0.000478)
  - Real GDP growth:
    - ALL: -0.000209* (0.000123)
    - AEs: 1.94e-05 (0.000321)
    - EMs: -0.000249 (0.000219)
    - LIDCs: -7.94e-05 (0.000153)
  - Capital account openness:
    - ALL: 0.00899 (0.0168)
    - AEs: 0.0583*** (0.0154)
    - EMs: -0.0158 (0.0203)
    - LIDCs: 0.0273 (0.0266)
  - Public debt/GDP:
    - ALL: 0.000422*** (9.60e-05)
    - AEs: 0.000598*** (0.000159)
    - EMs: 0.000470*** (0.000147)
    - LIDCs: 0.000363** (0.000128)
- Interpretation:
  - Using public debt/GDP as an alternative measure of financial depth yields broadly similar results.
  - Public debt/GDP is positively associated with operating expense efficiency across groups.

### Findings — Trade deficit vs. trade surplus (Table A.4)
- Sample sizes and fit:
  - Observations: 279 (Trade Deficit Group), 176 (Trade Surplus Group)
  - Number of central banks: 46 (Deficit), 29 (Surplus)
  - R-squared: 0.358 (Deficit), 0.216 (Surplus)
- Key coefficients:
  - (X-M)/GDP:
    - Trade Deficit Group: 0.0791*** (0.0150)
    - Trade Surplus Group: -0.000989*** (0.000112)
  - Central bank independence:
    - Trade Deficit Group: 0.00102*** (0.000227)
    - Trade Surplus Group: 0.000623** (0.000246)
  - Real GDP growth:
    - Trade Deficit Group: 0.000180 (0.000135)
    - Trade Surplus Group: 0.000214 (0.000167)
  - Financial system deposit/GDP:
    - Trade Deficit Group: 0.000531*** (0.000140)
    - Trade Surplus Group: 0.000294 (0.000242)
- Interpretation:
  - Trade deficit subgroup shows a strong positive coefficient on (X-M)/GDP, consistent with an aggregate demand channel.
  - Trade surplus subgroup shows a negative and statistically significant coefficient on (X-M)/GDP, consistent with an imported inflation channel.
  - Central bank independence remains positively associated with operating expense efficiency in both groups.

### Additional summary statistics and tests
- Table A.5 — Summary statistics of central bank operating environment (observations shown):
  - Central bank independence: Mean 77.10; Median 77.70; Standard Deviation 6.67; Kurtosis 3.59; Skewness -1.18; Observations 688.00
  - Control of corruption: Mean 0.44; Median 0.26; Standard Deviation 1.04; Kurtosis -1.23; Skewness 0.29; Observations 714.00
  - Rule of law: Mean 0.42; Median 0.30; Standard Deviation 0.97; Kurtosis -1.27; Skewness 0.16; Observations 714.00
  - Financial freedom: Mean 57.59; Median 60.00; Standard Deviation 16.18; Kurtosis -0.55; Skewness -0.22; Observations 677.00
- Table A.6 — Difference between IFRS and Non-IFRS group means of operational expenses:
  - 0 (non-IFRS): Obs. 425; Mean 19.30; Std. err. 0.11; Std. dev. 2.30; 95% conf. Interval 19.07914 to 19.51801
  - 1 (IFRS): Obs. 291; Mean 17.66; Std. err. 0.10; Std. dev. 1.73; 95% conf. Interval 17.46306 to 17.86335
  - Combined: Obs. 716; Mean 18.63; Std. err. 0.08; Std. dev. 2.24; 95% conf. Interval 18.46973 to 18.79811
  - Mean difference (non-IFRS − IFRS): 1.64; Std. err. 0.16; 95% conf. Interval 1.32317 to 1.947563
  - t = 10.2842; Degrees of freedom = 714
  - Pr(T < t) = 1.0000; Pr(T > t) = 0.0000
- Figure A.1:
  - Efficiency estimates with price stability output: dispersion across exchange rate regime (visual distribution labeled 0 . 2 . 4 . 6 . 8 1 on axis).

### Robustness-summary conclusions (as reported)
- Core results are robust to:
  - Splitting samples by exchange rate regime.
  - Controlling for the operating environment (control of corruption, rule of law, financial freedom).
  - Using alternative measures of financial depth (public debt/GDP).
  - Splitting samples by trade balance sign (trade deficits vs. trade surpluses).
- Consistent relationships observed:
  - Central bank independence: positive and often statistically significant association with operating expense efficiency across specifications.
  - Financial depth (measured by deposits/GDP or public debt/GDP): positive association with operating expense efficiency across specifications.
  - Trade openness or trade balance measures: sign and significance vary by subgroup and regime; evidence consistent with both aggregate demand and imported inflation channels depending on trade balance status.
- Additional empirical notes:
  - IFRS adopters display a lower mean of operational expenses (Mean 17.66) than non-IFRS group (Mean 19.30), with mean difference 1.64 (t = 10.2842).

*Source: IMF Working Paper — Estimation and Determinants of Cost Efficiency: Evidence from Central Bank Operational Expenses (Working Paper No. WP/2023/195), Appendix I.*

### Appendix I. ............................................................................................................

### Appendix I.

### Figures
- 1. Stochastic Frontier Analysis Representation .................................................................................................... 6
- 2. Histogram of the Size of Central Banks' Staff and Overall Contributions (by Income Group) ........................... 8
- 3. Staffing and Population ..................................................................................................................................... 9
- 4. Average Salary per Headcount and GDP per Capita ........................................................................................ 9
- 5. Distribution of Cost to GDP (by Income Group) .............................................................................................. 10
- 6. Efficiency Estimates with Tangible and Intangible Assets: Dispersion across Countries ............................... 14
- 7. Efficiency Estimates with Tangible and Intangible Assets: Dispersion across Income Groups ...................... 15
- 8. Efficiency Estimates: By Number of Central Bank Objectives ........................................................................ 15

### Tables
- 1. Descriptive Statistics ......................................................................................................................................... 7
- 2. Operational Expenses ..................................................................................................................................... 11
- 3. Stochastic Frontier Estimates with Tangible Assets Only ............................................................................... 12
- 4. Stochastic Frontier Estimates with Tangible and Intangible Assets ................................................................ 13
- 5. Summary Statistics of Efficiency Estimates .................................................................................................... 16
- 6. Determinants of Central Bank Operational Efficiency ..................................................................................... 18

*Source: wpiea2023195-print-pdf - Appendix I.*

### 7. Central Bank Operational Efficiency and De Jure Central Bank Independence ...........................................

### 7. Central Bank Operational Efficiency and De Jure Central Bank Independence

### Overview and objectives
- Purpose of the chapter:
  - Measure cost efficiency of central banks.
  - Investigate determinants of efficiency.
- Key dataset and sample:
  - Constructed dataset includes 90 central bank income statements, objectives, and staffing information from 2008 to 2021.
  - Final sample retained: 75 central banks with 712 observations (average of eight observations per central bank).
  - Initial classification: 24 LIDCs, 42 EMs, and 24 AEs (from initial 90).
  - Accounting standards: 30 central banks apply IFRS; others apply generally accepted local standards.

### Methodology: stochastic frontier analysis (SFA) and model specification
- Chosen method: stochastic frontier analysis (SFA) (advantages over DEA: separates random noise and inefficiency; allows measurement errors; less sensitive to outliers).
- Cost function (log-linear Cobb-Douglas form): log(C) modeled as function of log(outputs) and log(inputs) plus a two-part error term (v noise, μ inefficiency where μ = ln(ξ)).
- Inputs:
  - Number of staff (labor).
  - Equity (capital).
- Tangible outputs:
  - Total assets, interest income.
- Intangible output (used in extended specifications):
  - Price stability proxied by inflation; monetary policy cost proxied by interest expenses; inflation targeting indicator.

### Data descriptive statistics (selected exact figures)
- Central bank income statement items (all values in USD except staff, population, inflation, GDP per capita):
  - Net interest income: Mean 5.4E+09; Median 7.6E+07; Standard Deviation 2.1E+10; Observations 749.
  - Noninterest income: Mean 2.0E+09; Median 6.4E+07; Standard Deviation 7.8E+09; Observations 746.
  - Operating expenses: Mean 1.7E+09; Median 8.8E+07; Standard Deviation 6.3E+09; Observations 749.
  - Asset: Mean 6.3E+11; Median 1.9E+10; Standard Deviation 2.5E+12; Observations 749.
  - Equity: Mean 2.2E+10; Median 8.4E+08; Standard Deviation 8.7E+10; Observations 749.
  - Number of staff: Mean 1848; Median 679; Standard Deviation 3261; Observations 749.
- Macroeconomic variables:
  - GDP per capita: Mean 2.5E+04; Median 2.0E+04; Standard Deviation 2.2E+04; Observations 749.
  - Population: Mean 2.9E+07; Median 7.4E+06; Standard Deviation 5.3E+07; Observations 749.
  - Inflation: Mean 3.9; Median 2.4; Standard Deviation 5.3; Observations 749.
  - Country size: Mean 3.5E+07; Median 1.08E+05; Standard Deviation 1.76E+08; Observations 749.

### Key empirical results — cost function and SFA estimates
- Baseline OLS and fixed-effects (dependent variable = log operational expenses):
  - Table 2 coefficients (Pooled OLS; Fixed Effects):
    - Log (asset): 0.385*** (0.0315); 0.333*** (0.0481).
    - Log (interest income): 0.303*** (0.0240); 0.206*** (0.0367).
    - Log (staff): 0.182*** (0.0458); 0.539*** (0.0993).
    - Log (equity): 0.0919*** (0.0289); 0.0463 (0.0311).
    - Observations 712; R-squared 0.886 (OLS) and 0.681 (FE); Number of central banks 75.
- SFA tangible-assets-only (Table 3, Models 1–2 selected entries):
  - Model 1:
    - Log (asset) 0.3692*** (0.0383).
    - Log (interest income) 0.2187*** (0.0328).
    - Log (number of staff) 0.3196*** (0.0624).
    - Log (equity) 0.0551*** (0.0279).
    - Share of inefficiency explained: 72% (휎휎휇/(휎휎휇+휎휎푣) = 72%).
  - Model 2:
    - Log (asset) 0.4860*** (0.0401).
    - Log (interest income) 0.2355*** (0.0335).
    - Log (number of staff) 0.4479*** (0.0831).
    - Log (equity) 0.0600*** (0.0276).
    - Share of inefficiency explained: 73.3%.
- SFA with tangible and intangible assets (Table 4, Models 3–4 selected entries):
  - Model 3:
    - Log (asset) 0.4684*** (0.034).
    - Log (interest income) 0.2515*** (0.0399).
    - Log (number of staff) 0.4757*** (0.0349).
    - Log (equity) 0.0843*** (0.0285).
    - Share of inefficiency: 83% (휎휎휇 = 0.998; 휎휎푣 = 0.21).
    - Observations 673; Time FE No.
  - Model 4:
    - Log (asset) 0.4580*** (0.0346).
    - Log (interest income) 0.3033*** (0.0344).
    - Log (inflation) 0.0101 (0.0283).
    - Log (number of staff) 0.4953*** (0.0727).
    - Log (equity) 0.0762*** (0.0278).
    - Dummy (inflation targeting) 0.3535** (0.1457).
    - Log (interest expense) -0.0357*** (0.0116).
    - Share of inefficiency: 81%.
    - Observations 673; Time FE No.
- Cost efficiency score statistics (from SFA models):
  - Overall efficiency levels range from 0.15 to 0.8 in one summary; elsewhere range from 0.15 to 0.89 for models with intangible output.
  - Estimated average inefficiency for whole sample: 0.4 (implying central bank could improve cost efficiency by 60 percent).
  - Model summary (Table with Models 1–4):
    - Model 1 mean 0.42; Sd 0.23; Median 0.47; Max 0.90; Min 0.05; Share of inefficiency 75%.
    - Model 2 mean 0.45; Sd 0.20; Median 0.44; Max 0.92; Min 0.08; Share of inefficiency 73%.
    - Model 3 mean 0.50; Sd 0.26; Median 0.53; Max 0.91; Min 0.03; Share of inefficiency 83%.
    - Model 4 mean 0.55; Sd 0.25; Median 0.63; Max 0.92; Min 0.04; Share of inefficiency 82%.

### Patterns across income groups and mandates
- Cost-to-GDP and staff findings:
  - Operational expenses to GDP tend to be higher in LIDCs than in EMs, and higher in EMs than in AEs.
  - Emerging markets exhibit the highest number of staff per million inhabitants among sample groups.
- Efficiency by income group (Model 4, Figure 7 results):
  - Median cost-efficiency scores:
    - AEs: 0.63.
    - EMs: 0.38.
    - LIDCs: 0.2.
  - Currency unions in LIDCs display higher cost efficiency compared with regional peers.
- Efficiency by number of objectives (Figure 8):
  - Central banks with a single objective tend to be more cost efficient than those with multiple objectives.
  - Sample coverage: 60 percent of central banks in sample have a single objective, representing 465 observations.

### Determinants of operational efficiency (regression of efficiency scores; Table 6)
- Regression specification: efficiency score regressed on trade openness (X+M)/GDP, central bank independence, real GDP growth, financial system deposit/GDP, capital account openness; country fixed effects included.
- Table 6 coefficients (exact values and robust standard errors):
  - Column (1) ALL (Observations 528; Number of central banks 63; R-squared 0.288):
    - (X+M)/GDP: -0.000762*** (0.000128).
    - Central bank independence: 0.00118*** (0.000165).
    - Real GDP growth: -0.000276 (0.000226).
    - Financial system deposit/GDP: 0.000480** (0.000225).
    - Capital account openness: -0.00351 (0.0105).
    - Constant 0.339*** (0.0198).
  - Column (2) AEs (Observations 196; Number of central banks 20; R-squared 0.185):
    - (X+M)/GDP: -0.000842*** (0.000134).
    - Central bank independence: 0.000652 (0.000386).
    - Financial system deposit/GDP: 0.000350 (0.000253).
    - Constant 0.517*** (0.0444).
  - Column (3) EMs (Observations 221; Number of central banks 28; R-squared 0.463):
    - (X+M)/GDP: -0.00649 (0.00460).
    - Central bank independence: 0.00126*** (0.000238).
    - Financial system deposit/GDP: 0.000798*** (0.000164).
    - Constant 0.300*** (0.0188).
  - Column (4) LIDCs (Observations 111; Number of central banks 15; R-squared 0.368):
    - (X+M)/GDP: -0.0110 (0.00883).
    - Central bank independence: 0.000957** (0.000443).
    - Financial system deposit/GDP: 0.00113** (0.000408).
    - Constant 0.143*** (0.0309).
- Interpretation of determinants:
  - Central bank independence: positive and statistically significant across pooled and many subgroup specifications (higher independence → higher operational efficiency).
  - Financial depth (bank deposits/GDP): positive relationship with cost efficiency, particularly for EMs and LIDCs.
  - Trade openness (X+M)/GDP: negative and statistically significant in pooled estimates, indicating greater trade openness associated with lower operational efficiency.
  - No robust statistically significant role found for capital account openness and real GDP growth in the main specifications.

### De jure central bank independence: Romelli index and dimensions (Table 7)
- Alternative independence measure: dynamic de jure central bank independence index (Romelli, 2022) scaled 0–1.
- Table 7 estimates (dependent variable = operating expense efficiency):
  - Column (1) CBI (Observations 329; Number of central banks 53; R-squared 0.189):
    - CBI: 0.180*** (0.0288).
    - Constant 0.295*** (0.0288).
  - Column (2) CBI dimensions (Observations 321; Number of central banks 52; R-squared 0.259):
    - CBI board: 0.0253*** (0.00765).
    - CBI policy: -0.0519 (0.0321).
    - CBI objective: 0.0399*** (0.00411).
    - CBI finances: 0.00853 (0.0206).
    - CBI lending: 0.315*** (0.0882).
    - Constant 0.179*** (0.0332).
- Summary: de jure central bank independence index positively and significantly associated with higher operational efficiency; most index dimensions positive and significant except monetary policy/conflict resolution dimension (CBI policy) which is not statistically significant.

### Main findings and policy-relevant messages
- Significant variation in operational cost efficiency across central banks and income groups.
- Central banks with single objectives are, on average, more cost efficient than those with multiple objectives.
- When including price stability as an output:
  - Operational efficiencies are lower in LIDCs than EMs, and lower in EMs than AEs.
  - Median cost-efficiency scores: AEs 0.63; EMs 0.38; LIDCs 0.2.
- Determinants with consistent positive relationships to efficiency:
  - Central bank independence (both de facto freedom measure and de jure Romelli index).
  - Financial depth measured by deposits/GDP.
- Trade openness linked to lower operational efficiency in pooled results.
- Cost-efficiency gains are potentially large: average inefficiency 0.4 suggests scope to reduce operational costs by 60 percent to match best practice.

### Policy recommendations and implications (drawn from chapter conclusions)
- Emphasize well-defined objectives and concentration on core activities to reduce inefficiency.
- Regular external efficiency reviews and benchmarking to identify sources of inefficiency and improve transparency and decision making.
- Consider reforms enhancing central bank independence (institutional design, financial independence, limits on lending to government) as part of strategies to improve operational efficiency.
- Strengthen financial depth and intermediation to reap efficiency benefits for central bank operations.
- Account for trade openness and external shock exposure when designing central bank organizational and operational resilience measures.

*Source: IMF Working Paper — “Estimation and Determinants of Cost Efficiency: Evidence from Central Bank Operational Expenses” (chapter 7 content).*

### Appendix I

### Appendix I

### Robustness Tests — Overview
- Purpose: Examine determinants of central bank operational efficiency by testing robustness of three factors (central bank independence, real GDP growth, financial system depth) using alternative specifications and samples.
- Approaches:
  - Split sample by exchange rate regime (floating vs. nonfloating).
  - Introduce additional controls for operating environment (control of corruption, rule of law, financial freedom).
  - Use alternative measure of financial depth (public international debt-to-GDP instead of financial system deposit-to-GDP).
  - Split sample by trade balance sign (trade surpluses vs. trade deficits) to explore aggregate demand vs. imported inflation channels.

### Findings — By Exchange Rate Regimes (Table A.1)
- Sample sizes and fit:
  - Observations: 178 (Floats), 350 (Nonfloats)
  - Number of central banks: 18 (Floats), 45 (Nonfloats)
  - R-squared: 0.181 (Floats), 0.394 (Nonfloats)
- Coefficients (dependent variable = operating expense efficiency):
  - (X+M)/GDP:
    - Floats: -0.000808*** (standard error 0.000198)
    - Nonfloats: -0.0100** (standard error 0.00457)
  - Central bank independence:
    - Floats: 0.000723* (0.000415)
    - Nonfloats: 0.00132*** (0.000180)
  - Real GDP growth:
    - Floats: 0.000135 (0.000611)
    - Nonfloats: -0.000161 (0.000148)
  - Financial system deposit/GDP:
    - Floats: 0.000381 (0.000389)
    - Nonfloats: 0.000592*** (9.33e-05)
  - Capital account openness:
    - Floats: 0.00589 (0.0534)
    - Nonfloats: -0.00400 (0.00802)
- Interpretation:
  - Central bank independence, real GDP growth, and financial system depth retain same sign as baseline.
  - Trade balance effect differs by regime: positive (close to zero) and statistically significant for floaters; negative and statistically significant for fixed/nonfloaters.

### Findings — Controlling for Operating Environment (Table A.2)
- Sample splits and fit:
  - Observations: 520 (ALL), 196 (AEs), 213 (EMs), 111 (LIDCs)
  - Number of central banks: 63 (ALL), 20 (AEs), 28 (EMs), 15 (LIDCs)
  - R-squared: 0.332 (ALL), 0.259 (AEs), 0.549 (EMs), 0.406 (LIDCs)
- Key coefficients (dependent variable = operating expense efficiency):
  - (X+M)/GDP:
    - ALL: -0.000693*** (0.000121)
    - AEs: -0.000743*** (0.000129)
    - EMs: -0.00585 (0.00424)
    - LIDCs: -0.0118 (0.00830)
  - Central bank independence:
    - ALL: 0.00125*** (0.000164)
    - AEs: 0.000848** (0.000382)
    - EMs: 0.00136*** (0.000224)
    - LIDCs: 0.000961** (0.000422)
  - Real GDP growth:
    - ALL: -0.000166 (0.000208)
    - AEs: 0.000313 (0.000412)
    - EMs: 1.75e-06 (0.000286)
    - LIDCs: -3.70e-05 (0.000234)
  - Financial system deposit/GDP:
    - ALL: 0.000543** (0.000214)
    - AEs: 0.000441* (0.000228)
    - EMs: 0.000812*** (0.000149)
    - LIDCs: 0.00107** (0.000416)
  - Control of corruption:
    - ALL: -0.0144** (0.00708)
    - AEs: -0.0224 (0.0150)
    - EMs: -0.00843 (0.00708)
    - LIDCs: -0.00494 (0.0136)
  - Rule of law:
    - ALL: -0.00943 (0.00839)
    - AEs: -0.0112 (0.0182)
    - EMs: -0.0189** (0.00807)
    - LIDCs: 0.0207* (0.0115)
  - Financial freedom:
    - ALL: -7.64e-06 (0.000347)
    - AEs: -0.000185 (0.000504)
    - EMs: 0.000382 (0.000490)
    - LIDCs: 9.59e-06 (0.000757)
- Interpretation:
  - Results remain consistent after adding controls, reinforcing robustness of primary findings.
  - Financial system deposit/GDP shows positive and often significant association with operating expense efficiency across groups.
  - Control of corruption and rule of law show heterogeneous signs and significance across country groups.

### Findings — Alternative Financial Depth Measure (Public Debt/GDP) (Table A.3)
- Sample splits and fit:
  - Observations: 511 (ALL), 197 (AEs), 207 (EMs), 107 (LIDCs)
  - Number of central banks: 59 (ALL), 19 (AEs), 26 (EMs), 14 (LIDCs)
  - R-squared: 0.326 (ALL), 0.277 (AEs), 0.467 (EMs), 0.433 (LIDCs)
- Key coefficients:
  - (X+M)/GDP:
    - ALL: -0.00103*** (4.10e-05)
    - AEs: -0.00103*** (4.12e-05)
    - EMs: -0.00117 (0.00314)
    - LIDCs: -0.0110 (0.00792)
  - Central bank independence:
    - ALL: 0.00122*** (0.000208)
    - AEs: 0.000767** (0.000341)
    - EMs: 0.00147*** (0.000240)
    - LIDCs: 0.000642 (0.000478)
  - Real GDP growth:
    - ALL: -0.000209* (0.000123)
    - AEs: 1.94e-05 (0.000321)
    - EMs: -0.000249 (0.000219)
    - LIDCs: -7.94e-05 (0.000153)
  - Capital account openness:
    - ALL: 0.00899 (0.0168)
    - AEs: 0.0583*** (0.0154)
    - EMs: -0.0158 (0.0203)
    - LIDCs: 0.0273 (0.0266)
  - Public debt/GDP:
    - ALL: 0.000422*** (9.60e-05)
    - AEs: 0.000598*** (0.000159)
    - EMs: 0.000470*** (0.000147)
    - LIDCs: 0.000363** (0.000128)
- Interpretation:
  - Using public debt/GDP as an alternative measure of financial depth yields similar results; public debt/GDP positively associated with operating expense efficiency across groups.

### Findings — Trade Deficit vs. Trade Surplus (Aggregate Demand vs. Imported Inflation) (Table A.4)
- Sample sizes and fit:
  - Observations: 279 (Trade Deficit Group), 176 (Trade Surplus Group)
  - Number of central banks: 46 (Deficit), 29 (Surplus)
  - R-squared: 0.358 (Deficit), 0.216 (Surplus)
- Key coefficients:
  - (X-M)/GDP:
    - Trade Deficit Group: 0.0791*** (0.0150)
    - Trade Surplus Group: -0.000989*** (0.000112)
  - Central bank independence:
    - Trade Deficit Group: 0.00102*** (0.000227)
    - Trade Surplus Group: 0.000623** (0.000246)
  - Real GDP growth:
    - Trade Deficit Group: 0.000180 (0.000135)
    - Trade Surplus Group: 0.000214 (0.000167)
  - Financial system deposit/GDP:
    - Trade Deficit Group: 0.000531*** (0.000140)
    - Trade Surplus Group: 0.000294 (0.000242)
- Interpretation:
  - Trade deficit subgroup shows a strong positive coefficient on (X-M)/GDP, consistent with an aggregate demand channel.
  - Trade surplus subgroup shows a negative and statistically significant coefficient on (X-M)/GDP, consistent with an imported inflation channel.
  - Central bank independence remains positively associated with operating expense efficiency in both groups.

### Additional Tables and Figures — Summary Statistics and Tests
- Table A.5 — Summary statistics of central bank operating environment (observations shown):
  - Central bank independence: Mean 77.10; Median 77.70; Standard Deviation 6.67; Kurtosis 3.59; Skewness -1.18; Observations 688.00
  - Control of corruption: Mean 0.44; Median 0.26; Standard Deviation 1.04; Kurtosis -1.23; Skewness 0.29; Observations 714.00
  - Rule of law: Mean 0.42; Median 0.30; Standard Deviation 0.97; Kurtosis -1.27; Skewness 0.16; Observations 714.00
  - Financial freedom: Mean 57.59; Median 60.00; Standard Deviation 16.18; Kurtosis -0.55; Skewness -0.22; Observations 677.00
- Table A.6 — Difference between IFRS and Non-IFRS group means of operational expenses:
  - Group means and dispersion:
    - 0 (non-IFRS): Obs. 425; Mean 19.30; Std. err. 0.11; Std. dev. 2.30; 95% conf. Interval 19.07914 to 19.51801
    - 1 (IFRS): Obs. 291; Mean 17.66; Std. err. 0.10; Std. dev. 1.73; 95% conf. Interval 17.46306 to 17.86335
    - Combined: Obs. 716; Mean 18.63; Std. err. 0.08; Std. dev. 2.24; 95% conf. Interval 18.46973 to 18.79811
  - Mean difference (non-IFRS − IFRS): 1.64; Std. err. 0.16; 95% conf. Interval 1.32317 to 1.947563
  - t = 10.2842; Degrees of freedom = 714
  - Pr(T < t) = 1.0000; Pr(T > t) = 0.0000
- Figure A.1 — Efficiency estimates with price stability output: dispersion across exchange rate regime
  - Visual indicates distribution of cost efficiency scores for "Float" and "Non float" categories ranging from 0.0 to 1.0 (denoted as 0 . 2 . 4 . 6 . 8 1 on axis).

*Source: IMF Working Paper — Estimation and Determinants of Cost Efficiency: Evidence from Central Bank Operational Expenses (Working Paper No. WP/2023/195), Appendix I.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023195-print-pdf.pdf_