## wpiea2019192-print-pdf - Sections II–V and Annex I (summary)

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---

### Review of the literature
- Main strands:
  - Statistical properties of prices and exchange rates: law of one price / Purchasing Power Parity (PPP) often rejected in short-to-medium term; departures persistent and adjustment likely non-linear; short- to medium-term volatility of prices smaller than that of nominal exchange rates (references cited).
  - Exchange rate determination drivers: traditional factors confirmed—Balassa-Samuelson effect, fiscal variables, commodity prices, trade openness; difficulty linking exchange rates to macro variables via standard asset pricing.
  - Cross-sectional level RER literature: Penn Effect links income per capita and price levels; renewed work following ICP 2011.
  - Micro-data studies of price levels: supermarket/retailer/online datasets.

### Data and methodology
- Construction of level REER measure:
  - Two-step process: (1) cross-sectional ICP GDP-based price level relative to the United States for benchmark year 2011; (2) extend 2011 cross-section over 1990-2016 using IMF-INS CPI-based REER indices re-scaled to 2011.
  - Increase in REER level measure indicates a real appreciation.
  - Formal construction follows equation (1) combining ICP GDP-based price level (benchmark 2011) and Fund’s INS REER index (CPI-based) for year t using 2011 base.
  - Alternative level REER measures include time-series variation based on GDP deflators.
- Benchmark regression specification:
  - REER_it = α + β X_it + γ P_it + ε_it
  - Determinants grouped: macroeconomic, supply-side, cyclical, financial, structural, and policy variables.
- Estimation approach:
  - Linear OLS benchmark; two-stage least squares IV for FXI.
  - Many regressors expressed as deviations from trading partners’ weighted average.
  - No fixed effects in benchmark to exploit cross-sectional price-level REER dimension.
  - Robust inference: Newey-West HAC standard errors if stationary; cointegration tests applied if nonstationary (cointegration passed).
  - Sample: 39 countries over 1990-2016 (panel unbalanced).

### Key empirical findings (benchmark specification and fit)
- Selected benchmark coefficients (coefficient (robust pval in parentheses)):
  - Lag Demeaned PPPGDP/Top3(PPP)]: 0.17*** (0.00)
  - Log Commodity ToT (43) levels in 2011 vs trading partner: 0.06*** (0.00)
  - NFA/GDP: 0.06*** (0.00)
  - Expected GDP growth of medium-term (5 years out), WEO project (rel to TRD PRT): 1.96** (0.05)
  - Share of the country's currency held as FX reserve by central banks worldwide: -0.36*** (0.00)
  - Lag Capital stock per employed person at current PPPs (2005US$) (rel to TRD PRT): 0.11*** (0.00)
  - Lag Ratio Traded/Non Traded relative to trd part (in logs): 0.18*** (0.00)
  - Dependency Ratio (rel to TRD PRT): 0.36* (0.09)
  - ICRG-12 (rel to TRD PRT): 0.65*** (0.00)
  - Lag of Trade Openness (avg. of exports and imports to GDP) (rel to TRD PRT): -0.34*** (0.00)
  - Share of administered prices in CPI: -2.81*** (0.00)
  - Real interest rate differential demeaned interacted with K openness (rel to TRD): 0.59* (0.08)
  - Lag of Public health exp. (The new series) (rel to TRD PRT): 4.20*** (0.00)
  - Change in reserves to GDP * capital controls (The new series) (rel to TRD PRT): -3.56* (0.06)
  - Private credit/GDP gap (Detrended) (rel to TRD PRT): 0.03 (0.65)
  - Lag of VIX * capital account openness: -0.15 (0.25)
  - Lag of VIX * capital account openness * share of own currency in global reserve: 0.83 (0.13)
  - Constant: 0.19*** (0.00)
- Benchmark fit and sample diagnostics:
  - Observations: 990
  - Number of Countries: 39
  - R-squared: 0.90
  - Overall R-sq: 0.90
  - Between R-sq: 0.96
  - Within R-sq: 0.11
  - RMSE: 0.1456
  - Robust significance notation: *** p<0.01, ** p<0.05, * p<0.1

### Explanatory power and role of cross-sectional variation (Section IV)
- Overall explanatory power:
  - R-squared of benchmark model is 0.9.
  - Cointegration results indicate the relationship captures a long-run equilibrating relation; deviations are persistent but cointegrated with regressors.
- Cross-sectional variation:
  - About 90 percent of variance in level REER comes from the cross-sectional dimension.
  - Relative output per worker (to top 3 economies) is the most important single regressor:
    - Relative output per worker alone explains almost 80 percent of overall level REER variation (Table 3) and of the between-country variation (Appendix Table 3).
  - Fitted values closely match original level-REER patterns; residuals have a much more compressed range (order of 1) versus original cross-country REER range (about 2).
  - Some idiosyncratic country-level factors remain unaccounted for.

### Robustness to alternative methodologies and REER measures (Section V)
- Alternative estimation methods (Table 4) summary:
  - Methods compared: OLS (col. 1), fixed effects (col. 2), random effects (col. 3), benchmark (col. 4), and IV with fixed effects (col. 5).
  - OLS (col. 1) is close to benchmark in coefficients and significance.
  - Fixed/random effects absorb cross-sectional variation, downplaying variables whose main contribution is cross-sectional (e.g., capital stock, dependency ratio) and altering NFA coefficient.
  - IV with fixed effects (col. 5) returns some variables (reserves, real interest rates) close to benchmark; VIX and private credit become significant in col. 5, suggesting those mainly explain time-series variation.
  - Coefficients for variables capturing both time-series and cross-sectional variation are stable across methods.
- Alternative REER constructions (Annex I, Tables 5–7):
  - Cross-sectional alternatives (Table 5): PWT GDP-based, ICP Consumption-based, PWT Consumption-based, PWT Domestic Absorption-based.
    - Baseline results robust: coefficients retain sign and usually magnitude and significance; fit measures similar.
    - NFA to GDP robust except column 1 (insignificant).
    - Sensitive variables to dependent-variable choice: dependency ratio, VAT revenue, expected GDP growth in medium-term, and real interest rate differential interacted with capital controls.
    - Country rank by preferred ICP GDP-based REER consistent with alternatives, especially PWT domestic absorption.
  - Time-series alternatives (Table 6): CPI-based benchmark vs GDP deflator-based indices.
    - Coefficients retain basic sign and significance, including key coefficients from Table 2.
    - Dependency ratio, VAT revenue, real interest rate differentials interacted with capital controls not robust.
    - Within-R2 is much higher for GDP-deflator-based REER than CPI-based REER, implying better explanation of time-series variation with GDP deflator-based REER.
    - Recommendation: complement CPI-based external assessment with GDP-deflator-based REER.
  - Full-panel alternatives (Table 7): combining TS and XS alternatives.
    - Most coefficients retain sign and significance; few remain not fully robust, largely overlapping with previously identified sensitive variables.
- Sequential variable introduction (Appendix Table 3):
  - Lag Demeaned PPP GDP/Top3(PPP) coefficient progression: 0.54*** → 0.53*** → 0.37*** → 0.28*** → 0.29*** → 0.27*** → 0.14 → 0.12 across columns 1–8.
  - R-squared progression across columns 1–8: 0.79, 0.89, 0.91, 0.93, 0.94, 0.95, 0.95, 0.96.
  - RMSE progression across columns 1–8: 0.2012, 0.1515, 0.1349, 0.1265, 0.1165, 0.1104, 0.1064, 0.09985.

### Diagnostics: unit root and cointegration (selected results)
- Panel unit root/ stationarity diagnostics (selected entries):
  - REER-Level: Fisher test Z-statistic -2.27**; Hadri test Z-statistic 26.31*** — inference: inconclusive.
  - Output per worker (lagged, rel. top 3 economies): Fisher 4.24; Hadri 49.41*** — inference: yes.
  - FXI*capital controls (instrumented): Fisher -11.65***; Hadri 6.64*** — inference: inconclusive.
  - VIX*capital account openness * reserve currency status (lagged): Fisher -4.17***; Hadri -3.64 — inference: no.
- REER-Level model residual diagnostics:
  - Fisher unit root on residuals: -4.10***.
  - Dickey-Fuller t-statistic: -3.52***.
  - Modified Dickey-Fuller (adjusted for serial autocorrelation): -3.33***.
  - Augmented Dickey-Fuller (1 lag, adjusted): -3.66***.
  - Note: alternative hypothesis — all panels are cointegrated.

### Annex I: alternative REER variables and data sources (summary)
- Twelve alternative REER constructions by combining:
  - REER index time-series source: IMF-INS CPI; IMF-INS ER and WEO GDP deflator; PWT9 time-series.
  - PPP cross-section (2011) source: WB-ICP or PWT9 (GDP-based, Consumption-based, Absorption-based).
- Alternatives listed verbatim include Benchmark and Alternative 1 through Alternative 12 mapping TS and XS choices.
- Selected data sources used: Lane and Milesi-Ferretti (NFA), World Economic Outlook (output per worker, expected growth), COFER (reserve currency status), CBOE VXO (global risk aversion), FEENSTRA/INKLAAR/TIMMER (capital stock), BIS (credit), WB-ICP (price level), Quinn Database (capital controls).

### Policy implications and recommendations
- Methodological and operational implications:
  - The methodology’s ability to explain large cross-country differences in level REER suggests the EBA framework can incorporate the proposed level-REER measure to improve external assessments.
  - Given superior time-series explanatory power for GDP-deflator-based REERs, consider complementing CPI-based assessments with GDP-deflator-based REER measures.
  - Structural policy drivers of cross-country REER variation require more detailed data; progress depends on overcoming data constraints.
- Specific policy-relevant empirical findings:
  - Higher lagged public health spending associated with a higher level REER (coefficient 4.20*** (0.00) in benchmark).
  - Increases in reserves interacting with capital controls associated with lower level REERs (coefficient -3.56* (0.06) in benchmark), though magnitude and significance vary across specifications.
  - Greater share of a currency held in global FX reserves associated with a lower level REER (coefficient -0.36*** (0.00)).

### Conclusions
- The paper develops an empirical model of drivers of the level REER and incorporates it into the IMF’s EBA methodology.
- Key contributions:
  - Construction of a new level-REER measure combining cross-sectional and time-series components.
  - An empirical framework, guided by theoretical/empirical studies, to gauge cross-sectional and time-series determinants of the level REER.
- Main findings:
  - Large cross-sectional variation of the level REER is mostly accounted for by the methodology itself.
  - Results robust to alternative econometric methods and alternative level-REER measures.
  - Framework explains time-series variation better for GDP-deflator-based REERs than for CPI-based REERs.
  - Recommendation: consider complementing external assessments with GDP-deflator-based REER measures; further work needed to capture structural policy drivers pending data availability.

*Source: IMF working paper content (wpiea2019192-print-pdf; sections II–V and Annex I as provided).*

### Section IV expands on the explanatory power of the benchmark regression. Section V

### wpiea2019192-print-pdf - Section IV expands on the explanatory power of the benchmark regression. Section V

### Review of the literature
- Main strands:
  - Statistical properties of prices and exchange rates: law of one price / Purchasing Power Parity (PPP) often rejected in short-to-medium term; departures are persistent and adjustment likely non-linear; short- to medium-term volatility of prices smaller than that of nominal exchange rates (references: Burstein and Gopinath (2014); Rogoff (1996); Engel (1993); Sarno and Taylor (2002)).
  - Exchange rate determination drivers: traditional factors confirmed—Balassa-Samuelson effect, fiscal variables, commodity prices, trade openness; difficulty linking exchange rates to macro variables via standard asset pricing (Engel and West (2005)); panel extensions (Sarno and Schmeling (2014)).
  - Cross-sectional level RER literature: Penn Effect links income per capita and price levels; renewed work following ICP 2011 vintage (Fischer and Hossfeld (2014); Berka et al. (2015); Mano (2017); Cheung et al. (2017); Fujii (2015); Fischer (2019)).
  - Micro-data studies of price levels: supermarket/retailer/online datasets (Gopinath et al. (2011); Burstein and Jaimovich (2012); Haskel and Wolf (2002); Baxter and Landry (2017); Cavallo et al. (2015)).

### Data and methodology
- Construction of REER level measure:
  - Two-step process: (1) cross-sectional ICP GDP-based price level relative to the United States for benchmark year 2011; (2) extend 2011 cross-section over 1990-2016 sample using IMF-INS CPI-based REER indices re-scaled to 2011 value to ensure basket comparability.
  - Increase in REER level measure indicates a real appreciation.
  - Formal construction follows equation (1) combining ICP GDP-based price level (benchmark 2011) and Fund’s INS REER index (CPI-based) for year t using 2011 base.
  - Alternative level REER measures include time-series variation based on GDP deflators.
- Benchmark specification: regress (log) REER level on constant α, macroeconomic fundamentals X, and policies P:
  - Equation (2): REER_it = α + β X_it + γ P_it + ε_it
  - Determinants grouped: macroeconomic, supply-side, cyclical, financial, structural, and policy variables.
- Key determinants and expected signs (empirical findings noted where stated):
  - Macroeconomic fundamentals:
    - Net Foreign Asset position (lagged): coefficient expected positive; empirical results consistent.
    - Expected Real GDP growth 5 years ahead: coefficient expected positive; empirical consistency noted.
  - Supply-side fundamentals:
    - Output per worker relative to top 3 economies (lagged): positive (Balassa-Samuelson); strong empirical support.
    - Capital-labor ratio (lagged): positive (Bhagwati-Kravis-Lipsey); empirical positive coefficient.
    - Ratio of traded/non-traded sector productivity (lagged): positive (Balassa-Samuelson); empirically positive.
  - Cyclical fundamentals:
    - Commodity Terms of Trade (commodity export prices / commodity import prices): positive coefficient.
  - Financial fundamentals:
    - Global Financial Conditions / Risk Aversion (VIX deviations from historical average, interacted with capital account openness and reserve currency status, lagged): increased risk aversion tends to depreciate most currencies but appreciate reserve currencies; effects vary with capital account openness.
  - Structural fundamentals:
    - Demographics (population growth, old-age dependency ratio): population growth associated with appreciation; higher OADR associated with appreciation; empirical results consistent.
    - Institutional quality (lower risk → higher REER): coefficient expected positive; supported.
    - Trade openness (lagged, exports+imports/GDP): expected negative; empirical negative sign.
    - VAT revenue (share of GDP): proxy for indirect taxation; expected positive; estimated positive but at times insignificant.
    - Share of administered prices in CPI: expected negative; empirical results corroborate.
  - Policy variables:
    - Monetary policy (real short-term interest rate differential interacted with capital account openness): higher differential → REER appreciation; empirical support.
    - Health spending (lagged): proxy for social safety net; estimated coefficient positive.
    - Foreign Exchange Intervention (FXI/GDP, interacted with capital controls): FXI measured broadly (reserves changes and derivatives); instrumented due to endogeneity with instruments: (a) global accumulation of reserves (peers), (b) reserve adequacy linked to M2 defined as (M2-reserves)/GDP relative to emerging market average, (c) emerging market and developing economy dummy. Results: FX purchases of foreign currency lead to a real depreciation, with smaller effects where capital is more mobile.
    - Financial excesses (credit booms via private credit-to-GDP above trend): increase domestic demand → more appreciated REER; effect not statistically significant.
    - Capital controls included via interactions with fundamentals and policies.
- Estimation approach:
  - Linear specification estimated via OLS; two-stage least squares IV used to instrument FXI.
  - Many regressors expressed as deviations from trading partners’ weighted average.
  - No fixed effects in benchmark (enabled by cross-sectional price-level REER dimension).
  - Robust inference approach: Newey-West HAC standard errors if stationary; cointegration tests applied if nonstationary (cointegration passed; Appendix Table 2 referenced).
  - Sample: covers 39 countries over the 1990-2016 period (panel unbalanced).

### Explanatory power of the benchmark regression (Section IV)
- Benchmark regression results (Table 2):
  - Most variables statistically significant with expected signs.
  - R-squared of the model is very high: 0.9.
  - Cointegration results indicate the relationship captures a long-run equilibrating relation—nonstationary levels can be cointegrated with regressors, so deviations are persistent but not permanent.
- Cross-sectional variation explained:
  - About 90 percent of variance in level REER comes from the cross-sectional dimension.
  - Relative output per worker (to top 3 economies) is the most important single regressor:
    - Provides strong empirical support for the Balassa-Samuelson effect.
    - Relative output-per-worker alone explains almost 80 percent of overall level REER variation (Table 3) and of the between-country variation (Appendix Table 3).
  - Figures 2-8 (described):
    - Fitted values from benchmark regression closely match original level-REER patterns.
    - Residuals exhibit a much more compressed range (order of 1) compared to original cross-country REER range (about 2) when plotted on the same vertical scale.
    - Some idiosyncratic country-level factors remain unaccounted for.

### Robustness to alternative methodologies and REER measures (Section V)
- Alternative estimation methods (Table 4):
  - Methods compared: OLS (col. 1), fixed effects (col. 2), random effects (col. 3), benchmark (col. 4), and IV with fixed effects (col. 5).
  - OLS (col. 1) is close to benchmark in coefficients and significance.
  - Fixed/random effects absorb cross-sectional variation, downplaying variables whose main contribution is cross-sectional (e.g., capital stock, dependency ratio) and altering NFA coefficient.
  - Adding fixed effect to preferred methodology (col. 5) returns some variables (reserves, real interest rates) close to benchmark; VIX and private credit become significant in col. 5, suggesting those mainly explain time-series variation.
  - Coefficients for variables expected to capture both time-series and cross-sectional variation are stable across methods.
- Alternative measures of REER (Tables 5–7 and Table 6 analysis):
  - Cross-sectional alternatives (Table 5): PWT GDP-based REER (col 1), ICP Consumption-based REER (col 2), PWT Consumption-based REER (col 3), PWT Domestic Absorption-based REER (col 4).
    - Baseline results remarkably robust: coefficients retain sign and usually magnitude and significance; fit measures similar.
    - NFA to GDP robust across regressions except column 1 (insignificant).
    - Variables sensitive to choice of dependent variable include dependency ratio, VAT revenue, expected GDP growth in medium-term, and real interest rate differential interacted with capital controls.
    - Country rank by preferred ICP GDP-based REER is consistent with alternatives, especially PWT domestic absorption measure.
  - Time-series alternatives (Table 6): CPI-based benchmark complemented with GDP deflator-based indices for time-series dimension.
    - Coefficients retain basic sign and significance, including key coefficients from Table 2.
    - Same exceptions as above: dependency ratio, VAT revenue, and real interest rate differentials interacted with capital controls not robust.
    - Within-R2 is much higher for GDP-deflator-based REER than CPI-based REER, implying better explanation of time-series variation with GDP deflator-based REER.
    - Suggestion: complement CPI-based external assessment with GDP-deflator-based REER.
  - Full alternative REERs differing in both cross-sectional and time-series dimensions (Table 7):
    - Most coefficients retain sign and significance; only a few remain not fully robust, overlapping with those previously identified as sensitive.
- Overall robustness conclusion:
  - Benchmark findings are generally robust across estimation methods and alternative REER constructions, with the strongest and most stable result being the dominant role of relative output per worker (Balassa-Samuelson effect) in explaining cross-country level REER variation.

*Source: IMF working paper content (sections II–V as provided).*

### Appendix Figures 3 and 4 show that even across these different measures of REER there is a

### wpiea2019192-print-pdf - Appendix Figures 3 and 4 show that even across these different measures of REER there is a

### Conclusions
- The paper develops an empirical model of the drivers of the level of the REER, incorporated into the IMF’s EBA methodology.
- Key contributions:
  - Construction of a new measure of the level REER combining cross-sectional and time-series components.
  - An empirical framework, guided by theoretical/empirical studies, to gauge cross-sectional and time-series determinants of the level REER.
- The study finds that a large cross-sectional variation of the level REER is mostly accounted for by the methodology itself — described as a novel finding.
- Results are robust to alternative econometric methods and alternative level-REER measures.
- Framework explains time-series variation better for GDP-deflator-based REERs than for CPI-based REERs.
- Recommendation: consider complementing external assessments with REER measures based on the GDP-deflator; further work needed to capture structural policy drivers, contingent on data availability.

### Measure construction and methodology
- Level REER measure:
  - Cross-sectional dimension: countries’ price level relative to the U.S. in a given year based on the World Bank’s 2011 International Comparison Program (ICP 2011) ("bilateral” relative price) converted to an effective measure using the IMF multilateral weighing system.
  - Time-series dimension: IMF CPI-based REER to maintain comparability with existing studies.
- Alternative level-REER measures are constructed and tested using combinations of PWT and ICP datasets and alternative price definitions (GDP deflators, CPI, absorption).
- Benchmark regression aligns closely with prior IMF EBA methodology specifications (Phillips et al, 2013; Cubeddu et al, 2019) and borrows from Penn-effect literature and supply-side determinants (Mano, Mano and Castillo).

### Main empirical results (Benchmark specification)
- Selected benchmark coefficients (coefficient (robust pval in parentheses)):
  - Lag Demeaned PPPGDP/Top3(PPP)]: 0.17*** (0.00)
  - Log Commodity ToT (43) levels in 2011 vs trading partner: 0.06*** (0.00)
  - NFA/GDP: 0.06*** (0.00)
  - Expected GDP growth of medium-term (5 years out), WEO project (rel to TRD PRT): 1.96** (0.05)
  - Share of the country's currency held as FX reserve by central banks worldwide: -0.36*** (0.00)
  - Lag Capital stock per employed person at current PPPs (2005US$) (rel to TRD PRT): 0.11*** (0.00)
  - Lag Ratio Traded/Non Traded relative to trd part (in logs): 0.18*** (0.00)
  - Dependency Ratio (rel to TRD PRT): 0.36* (0.09)
  - ICRG-12 (rel to TRD PRT): 0.65*** (0.00)
  - Lag of Trade Openness (avg. of exports and imports to GDP) (rel to TRD PRT): -0.34*** (0.00)
  - Share of administered prices in CPI: -2.81*** (0.00)
  - Real interest rate differential demeaned interacted with K openness (rel to TRD): 0.59* (0.08)
  - Lag of Public health exp. (The new series) (rel to TRD PRT): 4.20*** (0.00)
  - Change in reserves to GDP * capital controls (The new series) (rel to TRD PRT): -3.56* (0.06)
  - Private credit/GDP gap (Detrended) (rel to TRD PRT): 0.03 (0.65)
  - Lag of VIX * capital account openness: -0.15 (0.25)
  - Lag of VIX * capital account openness * share of own currency in global reserve: 0.83 (0.13)
  - Constant: 0.19*** (0.00)

- Benchmark fit and sample:
  - Observations: 990
  - R-squared: 0.90
  - RMSE: 0.1456
  - Number of Countries: 39
  - Within R-sq: 0.11
  - Between R-sq: 0.96
  - Overall R-sq: 0.90

### Robustness and alternative estimations
- Sequential variable introduction (Table 3) shows stable coefficients for core variables as the specification expands; final RMSE reported as 0.1456 and R-squared stabilizing near 0.90.
- Alternative estimation methods (Table 4) — OLS, FE, RE, IV-Reg — produce broadly consistent coefficient signs and many significant estimates (e.g., Log Commodity ToT: 0.06*** to 0.09**; Lag Demeaned PPPGDP/Top3: 0.17*** to 0.35*** in some methods).
- Alternative LHS variables and XS dimensions (Tables 5–7):
  - Results hold across TS: INS-CPI and TS: WEO GDP deflator REER indices and across XS inputs from ICP-2011 and PWT 9.0 with various price definitions (GDP-based, consumption-based, absorption).
  - Coefficients for key fundamentals (Lag Demeaned PPPGDP/Top3, Share of administered prices, Lag capital stock per employed person, Lag Ratio Traded/Non Traded) remain significant and of similar magnitude in most specifications.
  - Some policy-variable coefficient magnitudes vary with alternative TS/XS choices (e.g., Change in reserves to GDP * capital controls shows larger negative coefficients in GDP-deflator TS and full-panel XS specifications).

### Policy implications and recommendations
- The methodology’s ability to explain large cross-country differences in the level REER suggests the EBA framework can incorporate the proposed level-REER measure to improve external assessments.
- Given superior time-series explanatory power for GDP-deflator-based REERs, consider complementing CPI-based assessments with GDP-deflator-based REER measures.
- Structural policy drivers of cross-country REER variation require more detailed data; progress depends on overcoming data constraints.
- Specific policy-relevant empirical findings:
  - Higher lagged public health spending is associated with a higher level REER (coefficient 4.20*** (0.00) in benchmark).
  - Increases in reserves interacting with capital controls are associated with lower level REERs (coefficient -3.56* (0.06) in benchmark), though magnitude and significance vary across specifications.
  - Greater share of a currency held in global FX reserves is associated with a lower level REER (coefficient -0.36*** (0.00)).

### Key statistics and model diagnostics
- Observations: 990
- Number of Countries: 39
- R-squared: 0.90
- Overall R-sq: 0.90
- Between R-sq: 0.96
- Within R-sq: 0.11
- RMSE: 0.1456
- Robust significance notation used: *** p<0.01, ** p<0.05, * p<0.1

*Source: IMF staff calculations and empirical results as presented in the document.*

### ANNEX I: ALTERNATIVE REER VARIABLES

### ANNEX I: ALTERNATIVE REER VARIABLES

### Definitions of alternative level REER variables
- Table A1 enumerates benchmark and 12 alternative REER constructions by combining:
  - REER index time-series source: IMF-INS CPI based; IMF-INS ER and WEO GDP deflator based; PWT9 time-series.
  - PPP cross-section (2011) source: WB-ICP or PWT9 (GDP-based, Consumption-based, Absorption-based).
- Alternatives listed (verbatim mapping):
  - Benchmark: IMF-INS CPI based (time series) — WB-ICP GDP-based (cross section, 2011)
  - Alternative 1: IMF-INS CPI based — PWT9 GDP-based
  - Alternative 2: IMF-INS CPI based — WB-ICP Consumption-based
  - Alternative 3: IMF-INS CPI based — PWT9 Consumption-based
  - Alternative 4: IMF-INS CPI based — PWT9 Absorption-based
  - Alternative 5: IMF-INS ER and WEO GDP deflator based — WB-ICP GDP-based
  - Alternative 6: IMF-INS ER and WEO GDP deflator based — PWT9 GDP-based
  - Alternative 7: IMF-INS ER and WEO GDP deflator based — WB-ICP Consumption-based
  - Alternative 8: IMF-INS ER and WEO GDP deflator based — PWT9 Consumption-based
  - Alternative 9: IMF-INS ER and WEO GDP deflator based — PWT9 Absorption-based
  - Alternative 10: PWT9 GDP-based (time series)
  - Alternative 11: PWT9 Consumption-based (time series)
  - Alternative 12: PWT9 Absorption-based (time series)

### Data sources used in the analysis (selected)
- Net Foreign Assets (NFA) position: EWN: Lane and Milesi-Ferretti
- Output per worker, relative to top 3 economies: World Economic Outlook
- Productivity (Output per worker interacted with capital openness): World Economic Outlook and Quinn Database
- Expected Real GDP growth 5 years ahead: World Economic Outlook
- Commodity Terms of Trade Gap (interacted with trade openness): World Economic Outlook and World Integrated Trade Solution (WITS)
- Reserve Currency Status: Currency Composition of Official Foreign Exchange Reserves (COFER)
- Global Financial Conditions (interacted with capital controls): Haver, and Quinn Database
- Health Spending: OECD, WDI, CEPAL, FAD, and ADB
- Foreign Exchange Intervention (FXI): World Economic Outlook, EWN: Lane and Milesi-Ferretti, Data Template on International Reserves and Foreign Currency Liquidity, and Quinn Database
- Credit Gap: BIS (Credit statistics) and World Bank (Global Financial Development Database)
- Price Level: World Bank’s International Comparison Program, 2011
- Capital Stock per employed person: Feenstra, Inklaar and Timmer (2013), "The Next Generation of the Penn World Table"
- Ratio of Traded/Non-Traded Sector Productivity: Rui C. Mano and Marola Castillo (2015), and World Bank's WDI Database
- Share of administered prices: European Bank of Reconstruction and Development (Structural Changes Indicators)

### Variable definitions in the EBA models — key variables and measurement
- NFA-to-GDP: enters directly in level terms; dataset: updated Lane and Milesi-Ferretti (2007) EWN.
- Output per worker, relative to top 3 economies: Ratio of PPP GDP to working age population relative to average of Germany, Japan, and U.S., demeaned.
- Population growth: Annual growth rate of total population.
- Old age dependency ratio: Population aged over 65 divided by population between 30 and 64 years old.
- 5-year growth forecast: IMF WEO 5-years ahead real GDP growth (proxy for potential output growth).
- Public health spending/GDP: OECD definition noted; data harmonization caveats with other sources (e.g., WDI).
- Global risk aversion proxy, VXO:
  - Index of implied U.S. stock market volatility (CBOE) based on S&P 100.
  - Available since 1986.
  - Annual average during the sample period is 0.2.
  - VXO is interacted with capital account openness; also interacted with the country's share of its own currency in world reserves.
- Own currency share in world reserves:
  - 2017 shares: US dollar 67 percent; euro 20 percent; yen 4.7 percent; sterling 4.4 percent.
  - Variable enters alone and interacted with VIX and capital account openness.
  - Baseline specification example: variable by itself is negative (-0.36) and interaction coefficient is positive (+0.83).
- Commodity terms of trade:
  - Constructed as ratio of geometric weighted-average prices of 43 commodity export categories to 43 import categories, each relative to manufactured goods prices in advanced economies; weights = commodity shares in exports/imports.
  - Index normalized using 2011 value of terms of trade.
- Capital controls index:
  - Quinn index scaled between 0 and 1.
  - 2017 mean across countries: 0.16; range between 0 and 0.75.
  - Interacted with VIX and real interest rates.
- Foreign exchange intervention (FXI, instrumented):
  - Measured as change in central bank foreign exchange reserves including off-balance sheet intervention during the year, scaled by nominal GDP in U.S. dollars.
  - Instrumented with: difference between M2/GDP and reserves/GDP, reserve accumulation and EMDE indicator, all interacted with capital controls index; first stage controls include independent regressors of the REER regression.
- Real interest rate:
  - Nominal short-term interest rate minus annual inflation rate.
  - Demeaned and interacted with capital controls.
- Private credit-to-GDP gap:
  - Credit-to-GDP ratio detrended using one-sided Hodrick-Prescott filter; total credit to non-financial private sector excluding non-bank cross-border flows from BIS.
- Institutional quality:
  - ICRG 12 sub-indicators normalized between 0 and 1 (higher = less risk).
- Trade openness: Average ratio of goods and services exports and imports to GDP.
- REER Levels:
  - (Log) REER Index rebased to year 2011; add log of PPP relative prices.
  - PPP relative price uses 2011 GDP expenditure based price level rescaled so US price level = 1.
- Capital stock per employed person: capital stock at constant 2005 national prices divided by total employed population.
- VAT revenue: VAT revenue as percent of GDP.
- Ratio of Traded/Non-Traded Sector Productivity:
  - Estimated using sectoral labor productivities at 2005 USD PPP from Mano and Castillo (2015).
  - Missing PPP data imputed via OLS fitted values of sectoral USD log(PPP) on market-rate productivity.
- Share of administered prices:
  - Relevant for a few transition economies; otherwise assigned zero.

### Unit root and cointegration diagnostics (selected results)
- Appendix Table 1 / Appendix Table 2 summary excerpts (tests reported as Fisher test 1/ and Hadri test 2/; hypotheses noted):
  - REER-Level: Fisher test Z-statistic -2.27**; Hadri test Z-statistic 26.31*** — reported inference: inconclusive.
  - Commodity terms of trade (log level, rel. TRD PTR): Fisher 3.68; Hadri 56.31*** — inference: yes (stationary).
  - VIX*capital account openness (lagged): Fisher -5.18***; Hadri 1.95** — inference: inconclusive.
  - VIX*capital account openness * reserve currency status (lagged): Fisher -4.17***; Hadri -3.64 — inference: no.
  - Reserve currency status: Fisher 0.57; Hadri 9.41*** — inference: yes.
  - Old age dependency ratio (rel. TRD PTR): Fisher 5.18; Hadri 44.62*** — inference: yes.
  - Population growth (rel. TRD PTR): Fisher 0.06; Hadri 44.44*** — inference: yes.
  - Output per worker (lagged, rel. top 3 economies): Fisher 4.24; Hadri 49.41*** — inference: yes.
  - Capital stock per employed person (lagged, rel. TRD PTR): Fisher 0.74; Hadri 41.87*** — inference: yes.
  - Traded/non-traded productivity (lagged, rel. TRD, PTR): Fisher -1.30*; Hadri 46.95*** — inference: inconclusive.
  - Share of administered prices: Fisher -3.22***; Hadri -1.37 — inference: no.
  - VAT revenue (% GDP, rel. TRD PTR): Fisher -7.25; Hadri 29.47*** — inference: yes.
  - Institutional quality (rel. TRD PTR): Fisher -4.62***; Hadri 28.71*** — inference: inconclusive.
  - Trade openness (lag, rel. TRD PTR): Fisher 2.17; Hadri 45.85*** — inference: yes.
  - Expected real GDP growth 5 years ahead (rel. TRD PTR): Fisher -5.30***; Hadri 27.58*** — inference: inconclusive.
  - Net Foreign Assets (NFA) position (lagged): Fisher 2.44; Hadri 44.35*** — inference: yes.
  - Real interest rate * capital account openness (rel. TRD PTR): Fisher -10.70***; Hadri 20.81*** — inference: inconclusive.
  - Health spending (lagged, rel. TRD PTR): Fisher -0.49; Hadri 38.79*** — inference: yes.
  - FXI*capital controls (instrumented, rel. TRD PTR): Fisher -11.65***; Hadri 6.64*** — inference: inconclusive.
  - Credit gap (rel. TRD PTR): Fisher 2.80; Hadri 29.55*** — inference: yes.
- REER-Level model residual diagnostics:
  - Fisher unit root on residuals: -4.10***.
  - Dickey-Fuller t-statistic: -3.52***.
  - Modified Dickey-Fuller (adjusted for serial autocorrelation): -3.33***.
  - Augmented Dickey-Fuller (1 lag, adjusted): -3.66***.
  - Note: Alternative hypothesis — all panels are cointegrated.

### Sequential variable introduction (Appendix Table 3) — between estimation (truncated at 8 variables)
- Reported coefficients (statistical significance p-values in parentheses); R-squared progression and fit:
  - Variables appearing sequentially (columns 1 to 8) with coefficients (standard p-values shown in table as parenthesis; stars denote significance: *** p<0.01, ** p<0.05, * p<0.1):
    - Lag Demeaned PPP GDP/Top3(PPP): 0.54*** (column 1), 0.53*** (2), 0.37*** (3), 0.28*** (4), 0.29*** (5), 0.27*** (6), 0.14 (7), 0.12 (8)
    - Share of administered prices in CPI: -3.75***, -3.48***, -3.27***, -3.00***, -2.76***, -2.81***, -3.03***
    - Lag of Public health exp. (rel to TRD PRT): 7.52***, 6.42***, 4.15*, 4.00*, 3.59*, 4.50**
    - ICRG-12 (rel to TRD PRT): 1.05**, 1.43***, 1.48***, 1.54***, 1.47***
    - Lag of Trade Openness (rel to TRD PRT): -0.32**, -0.34***, -0.33***, -0.35***
    - NFA/GDP: 0.12**, 0.13**, 0.11**
    - Lag Capital stock per employed person at current PPPs (2005US$) (rel to TRD PRT): 0.13*, 0.16**
    - Share of the country's currency held as FX reserve by central banks worldwide: -0.38**
  - Constant across columns: ranges 0.15*** to 0.20***.
  - Observations: 990 in each column.
  - R-squared progression: 0.79, 0.89, 0.91, 0.93, 0.94, 0.95, 0.95, 0.96.
  - Number of ifs_code: 39.
  - RMSE progression: 0.2012, 0.1515, 0.1349, 0.1265, 0.1165, 0.1104, 0.1064, 0.09985.

### Appendix figures — robustness and comparisons (descriptive)
- Appendix Figure 1 and Figure 3: Cross-country ranking comparisons assessing robustness to using GDP-deflator for REER time series and robustness to different level REERs in the base year and time-series.
- Appendix Figure 2 and Figure 4: Comparisons of change over time and appreciation/depreciation across alternative REER measures (examples span 1992–2016 and 1992–2014 periods).
- Visual notes from figures:
  - Appreciation (+) / Depreciation (-) across alternative level REER measures reported for between 1996-2016 and between 1996-2014 periods.
  - Sources for figures: IMF staff calculations based on INS-IMF, WEO-IMF, Penn World Table and ICP-WB.

*Source: Annex I, Annex II, Annex III, and Appendix tables/figures from the provided IMF content unit.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019192-print-pdf.pdf_