## External Shocks, Policies, and Tail-Shifts in Real Exchange Rates

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### Empirical approach and key parameters
- Baseline quantile regression specification models the 훼th quantile of y (change in log REER between t-1 and t+h) including:
  - country fixed effect 훾푖,훼ℎ and time fixed effect 훿훼ℎ;
  - external shock 푠ℎ표푐푘푖,푡 (VIX or U.S. monetary policy shock; robustness with IMF US financial conditions index);
  - control vector X푖,푡: lagged international reserves to M2, trade openness, CPI inflation, banking crisis dummy, exchange rate regime dummy (less flexible = 1), and U.S. inflation;
  - key coefficient 훽훼ℎ measures the percent change in REER from a one standard deviation shock to the VIX (or analogous for other shocks).
- Extended specifications:
  - Interaction with policy/state variable P푖,푡 (equation (4)): includes 휎훼ℎ ∗ shock ∗ P푖,푡 and 휗훼ℎ ∗ P푖,푡 to assess FX intervention (FXI) and capital flow management (CFM) effects.
  - Further extension (equation (5)) includes country-specific characteristic Z푖,푡 and triple interaction 휑훼ℎ ∗ shock ∗ Z푖,푡 ∗ FXI푖,푡.
- Policy measures and coding:
  - FXI measure: size of foreign exchange intervention in percent of GDP (U.S. dollars), averaged over the six months prior to the shock.
  - CFM measure: cumulative stock coding tightenings as +1, easings as -1, zero otherwise (includes inflow and outflow restrictions); robustness uses Chinn and Ito (2006) and Fernandez et al. (2016) indices.
- Sample and data:
  - Balanced panel from 2000M1 to 2020M12 for 28 mostly inflation targeting economies.
  - Of 28 countries, 24 are classified as inflation targeting in AREAER as of 2021.
  - REER normalized to 100 in M1-2000.
  - REER, VIX, U.S. monetary shocks, CPI inflation are monthly; quarterly series converted to monthly by spline (trade openness, reserves, real GDP).

### Effects of external shocks on REER distribution
- VIX (global uncertainty) shocks:
  - A one standard deviation increase in the VIX weakens currencies across the REER distribution (leftward shift).
  - Effect is stronger on the left side of the distribution (increased likelihood of extreme depreciations).
  - VIX increases also raise REER volatility (rightward shift of volatility distribution); VIX reductions largely not statistically significant.
- U.S. monetary policy shocks:
  - Tend to depreciate small open economies’ currencies across the REER distribution; timing varies.
  - On impact, U.S. tightening increases likelihood of large depreciations (left tail) but effect on left tail is short-lived; more persistent depreciation pressure appears at the median and right tail.
  - U.S. monetary easing is mostly not statistically significant.
- Asymmetry:
  - Adverse shocks (VIX increases, U.S. tightening) drive leftward shifts; favorable shocks generally leave REER distribution unchanged.
  - VIX is the only external shock among those studied that significantly affects REER volatility distribution.

### Role and effectiveness of policies: FXI and CFM
- Foreign exchange intervention (FXI):
  - Size matters: stronger FXI (above 75th percentile) mitigates real depreciation from VIX shocks more than weak FXI (below 25th percentile).
  - Mitigating effect is stronger and more durable for the 10th percentile and the median of the REER distribution.
  - Example cost: mitigating the depreciation of the 10th percentile of the REER by 10 percent after a one standard deviation VIX shock would require an intervention of 2.8 percent of GDP, which is roughly 15 percent of the median holding of reserves in the sample in 2019 and equivalent to the decline in reserves observed for the median country during the GFC.
  - Direction matters:
    - Selling reserves (negative FXI) is particularly effective in mitigating depreciation pressures around the median and left tail.
    - Purchases of reserves are effective in dampening appreciation pressures in the middle and right tail.
  - Frequency matters:
    - FXI is more effective when used sporadically; heavy users (average FXI above 75th percentile) reduce credibility and effectiveness.
- Capital flow management (CFM):
  - CFM is mostly ineffectual in mitigating external shocks on the REER in most specifications.
  - Little differentiation between heavy users of CFMs and other countries.
  - CFM can complement FXI in some cases and quantiles:
    - For VIX shocks, FXI effectiveness is larger when strong CFMs are in place (notably in the median, temporarily).
    - For U.S. monetary shocks, CFMs may reduce the mitigating effects of FXI (some significance at the median), possibly due to endogeneity.

### When is FXI most effective? Country characteristics
- FX market shallowness and inflation anchoring:
  - Economies with shallow FX markets or low inflation anchoring experience larger REER changes absent intervention.
  - FXI generally mitigates shocks regardless of FX depth or inflation anchoring, but FXI is mostly ineffectual in countries with high inflation anchoring.
  - FXI is most effective at containing depreciations in countries with low inflation anchoring or shallow FX markets—differences most notable at the 50th percentile and for the 10th percentile for inflation anchoring.
- Sovereign credit risk:
  - Countries with high EMBIG spreads experience sharper depreciations, especially at the 10th percentile and the median.
  - FXI is more effective in containing excessive depreciations in high credit risk countries, with larger differences immediately after shocks.
- Policy caveats:
  - Overuse of FXI can reduce its effectiveness over time and create moral hazard, weaken fundamentals, and impede market development.
  - FXI should not substitute for sound macro frameworks and deeper FX markets.

### Extensions and robustness
- REER volatility:
  - REER volatility measured as 6-month rolling standard deviation of the (log) REER.
  - VIX shocks significantly increase REER volatility, especially on the right tail; U.S. monetary policy changes exacerbate volatility but are mostly not statistically significant across deciles.
  - FXI marginally reduces median REER volatility after VIX shocks but does not prevent large increases (no significant effect on right tail of volatility distribution).
- Initial conditions:
  - Net foreign asset position matters: net creditor countries experience more moderate REER movements after VIX shocks.
  - Capital account openness results are mixed and sensitive to the openness index used and whether openness reflects inflow or outflow measures.
- Potential contamination by subsequent policy changes:
  - Including FXI in month t+h in the specification yields quantitative differences but does not qualitatively change main FXI results.
- Additional robustness:
  - Bilateral local-currency US-dollar real exchange rate dynamics resemble REER dynamics.
  - REER dynamics after US FCI shocks closely follow VIX shocks (VIX salient in the US FCI).

### Descriptive statistics (sample of 28 countries, months included)
- ln (REER): average 4.56; st. dev. 0.14; min 3.99; max 5.11
- ln (ToT): average 4.60; st. dev. 0.04; min 4.36; max 4.75
- VIX: average 19.09; st. dev. 8.10; min 9.51; max 59.89
- US Monetary policy shocks: average -0.003; st. dev. 0.03; min -0.17; max 0.12
- Inflation, in percent: average 4.07; st. dev. 3.35; min -2.10; max 32.93
- Monetary policy rate (6 month rolling average, in percent): average 5.49; st. dev. 4.33; min 0.00; max 37.07
- Reserves over M2 (6 month rolling average, in percent): average 19.88; st. dev. 15.61; min 2.61; max 93.88
- Exports+Imports over GDP (annual, in percent): average 88.99; st. dev. 66.61; min 22.11; max 437.33
- US inflation (month-over-month, in percent): average 0.17; st. dev. 0.30; min -1.79; max 1.37
- FXI over GDP, in percent: average 0.09; st. dev. 0.82; min -8.53; max 7.44
- Cummulative CFM: average 0.22; st. dev. 2.18; min -9.00; max 13.00

### Main conclusions and policy implications
- External shocks (VIX and U.S. monetary policy) impact REER levels and volatility distributions, primarily through adverse shocks (VIX increases, U.S. tightening).
- VIX is unique in also shifting REER volatility distribution to the right (higher volatility), driven by the right tail.
- FXI can partially offset external shocks but:
  - Requires sizeable interventions to materially affect tail outcomes (e.g., 2.8 percent of GDP to offset a 10 percent depreciation at the 10th percentile after a VIX shock).
  - Is more effective when used infrequently and where FX markets are shallow, central bank credibility is low, or sovereign credit risk is high.
- CFM is largely ineffective alone, but can complement FXI under certain conditions.
- Policy recommendations:
  - Deepen FX markets, strengthen central bank credibility, and improve macro fundamentals to reduce reliance on frequent FXI.
  - Consider distributional (quantile) effects rather than average effects when designing counter-cyclical and tail-event policies.

*IMF Working Paper, "External Shocks, Policies, and Tail-Shifts in Real Exchange Rates."*

### references therein.

### External Shocks, Policies, and Tail-Shifts in Real Exchange Rates

### Empirical approach and key parameters
- Baseline quantile regression specification (equation (3)) models the 훼th quantile of y (change in log REER between t-1 and t+h) as a function of:
  - country fixed effect 훾푖,훼ℎ and time fixed effect 훿훼ℎ;
  - external shock 푠ℎ표푐푘푖,푡 (VIX or U.S. monetary policy shock; robustness with IMF US financial conditions index);
  - control vector X푖,푡: lagged international reserves to M2, trade openness, CPI inflation, banking crisis dummy, exchange rate regime dummy (less flexible = 1), and U.S. inflation;
  - key coefficient of interest 훽훼ℎ measures the percent change in REER from a one standard deviation shock to the VIX (or analogous for other shocks).
- Extended specifications:
  - Interaction with policy/state variable P푖,푡 (equation (4)) to assess FX intervention (FXI) and capital flow management (CFM) effects: includes 휎훼ℎ ∗ shock ∗ P푖,푡 and 휗훼ℎ ∗ P푖,푡.
  - Further extension (equation (5)) includes country-specific characteristic Z푖,푡 and triple interaction 휑훼ℎ ∗ shock ∗ Z푖,푡 ∗ FXI푖,푡 to examine when FXI is most effective.
- FXI measure: size of foreign exchange intervention in percent of GDP (U.S. dollars), averaged over the six months prior to the shock.
- CFM measure: cumulative stock coding tightenings as +1, easings as -1, zero otherwise (includes inflow and outflow restrictions); robustness uses Chinn and Ito (2006) and Fernandez et al. (2016) indices.
- Sample and data:
  - Balanced panel from 2000M1 to 2020M12 for 28 mostly inflation targeting economies.
  - Of 28 countries, 24 are classified as inflation targeting in AREAER as of 2021.
  - REER normalized to 100 in M1-2000.
  - REER, VIX, U.S. monetary shocks, CPI inflation are monthly; quarterly series converted to monthly by spline (trade openness, reserves, real GDP).

### Effects of external shocks on REER distribution
- VIX (global uncertainty) shocks:
  - A one standard deviation increase in the VIX weakens currencies across the REER distribution (leftward shift).
  - Effect is stronger on the left side of the distribution (increased likelihood of extreme depreciations).
  - VIX increases also raise REER volatility (rightward shift of volatility distribution); VIX reductions largely not statistically significant.
- U.S. monetary policy shocks:
  - Tend to depreciate small open economies’ currencies across the REER distribution; timing varies.
  - On impact, U.S. tightening increases likelihood of large depreciations (left tail) but effect on left tail is short-lived; more persistent depreciation pressure appears at the median and right tail.
  - U.S. monetary easing is mostly not statistically significant.
- Asymmetry:
  - Adverse shocks (VIX increases, U.S. tightening) drive leftward shifts; favorable shocks generally leave REER distribution unchanged.
  - VIX is the only external shock among those studied that significantly affects REER volatility distribution.

### Role and effectiveness of policies: FXI and CFM
- Foreign exchange intervention (FXI):
  - Size matters: stronger FXI (above 75th percentile) mitigates real depreciation from VIX shocks more than weak FXI (below 25th percentile).
  - Mitigating effect is stronger and more durable for the 10th percentile and the median of the REER distribution.
  - Example cost: mitigating the depreciation of the 10th percentile of the REER by 10 percent after a one standard deviation VIX shock would require an intervention of 2.8 percent of GDP, which is roughly 15 percent of the median holding of reserves in the sample in 2019 and equivalent to the decline in reserves observed for the median country during the GFC.
  - Direction matters:
    - Selling reserves (negative FXI) is particularly effective in mitigating depreciation pressures around the median and left tail.
    - Purchases of reserves are effective in dampening appreciation pressures in the middle and right tail.
  - Frequency matters:
    - FXI is more effective when used sporadically; heavy users (average FXI above 75th percentile) reduce credibility and effectiveness.
- Capital flow management (CFM):
  - CFM is mostly ineffectual in mitigating external shocks on the REER in most specifications.
  - Little differentiation between heavy users of CFMs and other countries.
  - CFM can complement FXI in some cases and quantiles:
    - For VIX shocks, FXI effectiveness is larger when strong CFMs are in place (notably in the median, temporarily).
    - For U.S. monetary shocks, CFMs may reduce the mitigating effects of FXI (some significance at the median), possibly due to endogeneity.

### When is FXI most effective? Country characteristics
- FX market shallowness and inflation anchoring:
  - Economies with shallow FX markets or low inflation anchoring experience larger REER changes absent intervention.
  - FXI generally mitigates shocks regardless of FX depth or inflation anchoring, but FXI is mostly ineffectual in countries with high inflation anchoring.
  - FXI is most effective at containing depreciations in countries with low inflation anchoring or shallow FX markets—differences most notable at the 50th percentile and for the 10th percentile for inflation anchoring.
- Sovereign credit risk:
  - Countries with high EMBIG spreads experience sharper depreciations, especially at the 10th percentile and the median.
  - FXI is more effective in containing excessive depreciations in high credit risk countries, with larger differences immediately after shocks.
- Policy caveats:
  - Overuse of FXI can reduce its effectiveness over time and create moral hazard, weaken fundamentals, and impede market development.
  - FXI should not substitute for sound macro frameworks and deeper FX markets.

### Extensions and robustness
- REER volatility:
  - VIX shocks significantly increase REER volatility, especially on the right tail; U.S. monetary policy changes exacerbate volatility but are mostly not statistically significant across deciles.
  - FXI marginally reduces median REER volatility after VIX shocks but does not prevent large increases (no significant effect on right tail of volatility distribution).
- Initial conditions:
  - Net foreign asset position matters: net creditor countries experience more moderate REER movements after VIX shocks.
  - Capital account openness results are mixed and sensitive to the openness index used and whether openness reflects inflow or outflow measures.
- Potential contamination by subsequent policy changes:
  - Including FXI in month t+h in the specification yields quantitative differences but does not qualitatively change main FXI results.
- Additional robustness:
  - Bilateral local-currency US-dollar real exchange rate dynamics resemble REER dynamics.
  - REER dynamics after US FCI shocks closely follow VIX shocks (VIX salient in the US FCI).

### Main conclusions and policy implications
- External shocks (VIX and U.S. monetary policy) impact REER levels and volatility distributions, primarily through adverse shocks (VIX increases, U.S. tightening).
- VIX is unique in also shifting REER volatility distribution to the right (higher volatility), driven by the right tail.
- FXI can partially offset external shocks but:
  - Requires sizeable interventions to materially affect tail outcomes (e.g., 2.8 percent of GDP to offset a 10 percent depreciation at the 10th percentile after a VIX shock).
  - Is more effective when used infrequently and where FX markets are shallow, central bank credibility is low, or sovereign credit risk is high.
- CFM is largely ineffective alone, but can complement FXI under certain conditions.
- Policy recommendation emphasis:
  - Deepen FX markets, strengthen central bank credibility, and improve macro fundamentals to reduce reliance on frequent FXI.
  - Consider distributional (quantile) effects rather than average effects when designing counter-cyclical and tail-event policies.

*IMF Working Paper, "External Shocks, Policies, and Tail-Shifts in Real Exchange Rates."*

### References

### References

### Foreign exchange intervention, capital controls, and reserves
- Adler, G., Chang, K. S., Mano, R., and Shao, Y. (2021) “Foreign exchange intervention: A dataset of public data and proxies,” IMF Working Paper 21/47 (International Monetary Fund: Washington, DC).
- Adler, G., R. Lama, and J.P. Medina (2019), “Foreign exchange intervention and inflation targeting: The role of credibility,” Journal of Economic Dynamics and Control, Volume 106, September 2019.
- Adler, G., N. Lisack, and R. Mano (2019), “Unveiling  the Effects  of Foreign Exchange Intervention:  A Panel Approach,” Emerging Markets Review, Volume 40, September 2019.
- Adler,  G. and  R.  Mano  (2021), “The  Cost  of  Foreign  Exchange  Intervention:  Concepts  and  Measurement,” Journal of Macroeconomics, Volume 67 (2021).
- Blanchard, O., Adler, G., de Carvalho Filho, I. (2015), “Can Foreign Exchange Intervention Stem Exchange Rate Pressures from Global Capital Flow Shocks?” NBER Working Paper 21427.
- Cavallino,  P.  (2019),  “Capital  Flows  and  Foreign  Exchange  Intervention”, American  Economic  Journal: Macroeconomics 2019, 11(2): 127–170.
- Chamon, M., D. Hofman, N. Magud, and A. Werner (2019), “Foreign Exchange Intervention in Latin American Inflation Targeting Countries,” (International Monetary Fund: Washington D.C.).
- Daude, C., E. Levy Yeyati, and A. Nagengast (2016), “On the Effectiveness of Exchange Rate Interventions in Emerging Markets.” Journal of International Money and Finance 64: 239–61.
- Dominguez,  K.,  and  J.  Frankel,  (1993), “Does Foreign-Exchange  Intervention  Matter? The Portfolio Effect.” American Economic Review 83 (5): 1356–69.
- Fratzscher, M., O. Gloede, L. Menkhoff, L. Sarno, and To. Stohr (2019), “When Is Foreign Exchange Intervention Effective? Evidence from 33 Countries.” American Economic Journal: Macroeconomics, 11(1), 132-156.
- Filardo, A., G. Gelos, and T. McGregor, (2022), “Exchange-Rate Swings and Foreign Policy Intervention,” IMF Working Paper WP/22/158.
- Levy Yeyati, E., and J. F. Gómez (forthcoming), “Leaning-Against-the-Wind Intervention and the “Carry-Trade” View of the Cost of Reserves,” Open Economies Review.
- Kim, M., R. Manu, and M. Mrkaic (2020) “Do FX Interventions Lead to Higher FX Debt? Evidence from Firm-Level Data,” IMF Working Paper WP/20/197.
- Laeven, L., and F. Valencia (2020), “Systemic Banking Crises Database II,” IMF Economic Review 68, 307–361.
- Bianchi, J. and G. Lorenzoni (2022), “The Prudential Use of Capital Controls and Foreign Currency Reserves,” forthcoming, V Handbook on International Economics.
- Magud, N. E., Reinhart, C. M., and Rogoff, K. S. (2018), “Capital controls: Myth and Reality,” Annals of Economics and Finance, 19(1):1–47.
- Magud, N. and others cited in related entries above.

### Capital flows, capital controls, and policy responses
- Acosta-Henao, M., L. Alfaro, and A. Fernandez (2021), “Sticky Capital Controls,” NBER Working Paper 26997, September.
- Alfaro, L., A. Chari, and F. Kanczuk (2017), “The real effects of capital controls: Firm-level Evidence from a Policy Experiment,” Journal of International Economics, 108:191–210.
- Andreasen, Eugenia, Sofia Bauducco, Evangelina Dardati, and Enrique Mendoza (2021), “Welfare  Effects  of Capital Controls,” mimeo.
- De Gregorio, J., Edwards, S., and Valdes, R. O. (2000), “Controls on Capital Inflows: Do they Work,?” Journal of Development Economics, 63(1):59–83.
- Fernández, A., A. Rebucci, and M. Uribe (2015), “Are capital controls countercyclical?,” Journal  of  Monetary Economics, Volume 76, November 2015, Pages 1-14.
- Fernández, A., M.  Klein,  M.  Schindler,  A.  Rebucci  and  M.  Uribe  (2016), “Capital Control Measures: A New Dataset,” IMF Economic Review, Vol. 64 (3): 548-574.
- Chinn,  M. D. and H. Ito (2006), “What Matters for Financial Development? Capital Controls, Institutions, and Interactions,” Journal of Development Economics, Vol. 81 (1): 163-192 (October).
- Farhi, E. and Werning, I.  (2014), “Dilemma not Trilemma? Capital Controls and Exchange Rates with Volatile Capital Flows,” IMF Economic Review, 62(4):569–605.
- Fernández,  A.,  A.  González,  and  D.  Rodríguez  (2018), “Sharing  a Ride  on  the Commodities Roller Coaster: Common Factors in Business Cycles of Emerging Economies,” Journal of International Economics, vol. 111(C), pages 99-121.
- Gelos, G., L. Gornicka, R. Koepke, R. Sahay, and S. Sgherri (2022), “Capital Flows at Risk: Taming the Ebbs and Flows, Journal of International Economics 134.

### Terms-of-trade, real exchange rates, and external adjustment
- Adler, G., N. Magud, and A. Werner (2018), “Terms-of-Trade Cycles and External Adjustment,” International Review of Economics and Finance, Vol. 54, pp. 103-122.
- Adler, G. and N. Magud (2015), “Four Decades of Terms-of-Trade Booms: Saving-Investment Patterns and a New Metric of Income Windfall,” Journal of International Money and Finance, Volume 55, July 2015, Pages 162-192.
- Carrierè-Swallow, Y., N. Magud, and J. Yepez (2021), “Exchange Rate Flexibility, the Real Exchange Rate, and Adjustment to Terms of Trade Shocks,” Review of International Economics, 29(2): 439-83.
- Mendoza, E. (1995), “The Terms of Trade, the Real Exchange Rate, and Economic Fluctuations,” International Economic Review, vol. 36, issue 1, 101-37.
- Fernández, A., S. Schmitt-Grohé, and M. Uribe (2017), “World Shocks, World Prices, And Business Cycles: An Empirical Investigation” Journal of International Economics, Vol. 108, May 2017, S2-S14.

### Global shocks, macro policy transmission, and growth-at-risk
- Adrian, T., N. Boyarchenko, and D. Giannone (2019), “Vulnerable Growth,” American Economic Review 109(4): 1263-1289.
- Adrian, T., F. Grinberg, N. Liang, S. Malik, and E. Yu (2022), “The Term Structure of Growth-at-Risk,” American Economic Journal: Macroeconomics, Vol. 14(3): 283-323.
- Das,  M.,  G. Gopinath,  and  S. Kalemli-Ozcan (2021), “Preemptive Policies and Risk-Off Shocks  in  Emerging Markets,” NBER Working Paper No. 29615.
- Rey, H. (2015), “Dilemma not Trilemma: The Global Financial Cycle and Monetary Policy Independence”, NBER Working Paper No 21162.
- Ilzetzki, E. and K. Jin (2021), “The puzzling change in the international transmission  of  U.S.  macroeconomic policy shocks,” Journal of International Economics 130 (May 2021) 103444.
- International Monetary Fund (IMF) (2017), Getting the Policy Mix Right, Global Financial Stability Report (April), International Monetary Fund, Washington, DC.
- Mano, R., and S. Sgherri (2020), “One Shock, Many Policy Responses,” IMF Working Paper WP/20/10.
- Basu,  S.,  E.  Boz,  G.  Gopinath,  F.  Roch, and F. Unsal (2020), “A Conceptual Model for the Integrated Policy Framework,” IMF Working Paper 2020/121.
- Adrian, T., C. Erceg, M. Kolasa, J. Linde, and P. Zabczyk (2021), “A Quantitative Microfounded Model for the Integrated Policy Framework,” IMF Working Paper 2021/292.

### Empirical methods, estimation techniques, and theoretical foundations
- Jordà, Ò. (2005),  “Estimation and inference of impulse responses by local projections. American  Economic Review, 95(1):161–182.
- Koenker, R. and J. Bassett (1978), “Regression Quantiles,” Econometrica 46(1): 33-50.
- Machado, J. and J.M.C. Silva (2019) “Quantiles via Moments,” Journal of Econometrics 213, 145-173.
- Kouri, P. (1976), “The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach.” Scandinavian Journal of Economics 78 (2): 280–304.
- Mussa, M. (1982), “A Model of Exchange Rate Dynamics,” Journal of Political Economy, Vol. 90, No. 1 (Feb., 1982), pp. 74-104.
- Obstfeld, M., and K. Rogoff (1998), “Risk and Exchange Rates.” NBER Working Paper Working Paper No 6694.
- Fanelli, S. and L. Straub (2017), “A Theory of Foreign Exchange Interventions,” The Review of Economic Studies, Volume 88, Issue 6, November 2021, Pages 2857–2885.
- Evans, M. and R. Lyons (2002), “Order Flow and Exchange Rate Dynamics,” Journal of Political Economy, Vol. 110, No. 1 (February 2002), pp. 170-180.
- Gertler, M.  and  P. Karadi (2015), “Monetary policy surprises, credit costs, and economic activity,” American Economic Journal: Macroeconomics, vol. 7 (1): 44-76.
- Calvo, G. and C. Reinhart (2002), “Fear of Floating,” The Quarterly Journal of Economics, Vol. 117, No. 2 (May, 2002), pp. 379-408.
- Calvo, G., C. Reinhart, and L. Leiderman (1993), “Capital Inflows and Real Exchange Rate Appreciation in Latin America: The Role of External Factors,” IMF Staff Papers, Vol. 40, No. 1 (Mar., 1993), pp. 108-151.
- Samuelson, P. A. (1964), “Theoretical Notes on Trade Problems,” Review of Economics and Statistics, 46 (2): 145–154.
- Balassa, B. (1964), “The Purchasing Power Parity Doctrine: A Reappraisal,” Journal of Political Economy, 72 (6): 584–596.

*References list from wpiea2023129-print-pdf - References*

### Annex 1. Figures and Tables

### Annex 1. Figures and Tables

### List of countries in analysis
- Countries grouped according to IMF regions.
- Countries included (as listed): Western Hemisphere, Europe, Asia, Africa, Brazil, Czech Republic, India, South Africa, Canada, Iceland, Indonesia, Chile, Israel, Kazakhstan, Colombia, Hungary, Republic of Korea, Costa Rica, Norway, Malaysia, Mexico, Poland, Philippines, Peru, Romania, Singapore, Russia, Thailand, Sweden, Vietnam, Switzerland, Türkiye.

### Descriptive statistics (Table 2)
- Note: Descriptive statistics are for the 28 countries and months included in the econometric analysis.
- ln (REER): average 4.56; st. dev. 0.14; min 3.99; max 5.11
- ln (ToT): average 4.60; st. dev. 0.04; min 4.36; max 4.75
- VIX: average 19.09; st. dev. 8.10; min 9.51; max 59.89
- US Monetary policy shocks: average -0.003; st. dev. 0.03; min -0.17; max 0.12
- Inflation, in percent: average 4.07; st. dev. 3.35; min -2.10; max 32.93
- Monetary policy rate (6 month rolling average, in percent): average 5.49; st. dev. 4.33; min 0.00; max 37.07
- Reserves over M2 (6 month rolling average, in percent): average 19.88; st. dev. 15.61; min 2.61; max 93.88
- Exports+Imports over GDP (annual, in percent): average 88.99; st. dev. 66.61; min 22.11; max 437.33
- US inflation (month-over-month, in percent): average 0.17; st. dev. 0.30; min -1.79; max 1.37
- FXI over GDP, in percent: average 0.09; st. dev. 0.82; min -8.53; max 7.44
- Cummulative CFM: average 0.22; st. dev. 2.18; min -9.00; max 13.00

### Main empirical findings (figures and notes)
- The estimated impact of changes in the VIX on the distribution of the change in the (log) REER is heterogeneous across quantiles; estimates are obtained using a panel quantile regression approach and compared with a fixed effects panel regression (Figure 1).
- Figure 2: Responses of the 10th, 50th, and 90th percentiles of the (log) REER change distribution to a one standard deviation change in the VIX are shown separately.
- Figure 3: Responses of the 10th, 50th, and 90th percentiles of the (log) REER change distribution to a one standard deviation change in US monetary policy shocks are shown separately.
- Directional asymmetries are examined:
  - Figure 4: Impact of VIX shocks by direction (positive vs. negative shocks) on REER deciles.
  - Figure 5: Impact of US monetary policy shocks by direction on REER deciles.

### Role of foreign exchange intervention (FXI)
- FXI conditions the impact of shocks on REER distribution:
  - Figure 6: Impact of VIX shocks on REER conditional on level of FXI (low FXI evaluated at zero; high FXI evaluated at the 75th percentile of the (absolute) FXI distribution). Panels for 10th, 50th, and 90th percentiles and high vs. low FXI comparisons are provided.
  - Figure 7: Analogous results for US monetary policy shocks.
  - Figures 8 and 9: Role of FXI by direction of intervention for VIX shocks and US monetary policy shocks respectively.
- Use and frequency of FXI:
  - Figure 10, Panel A: VIX shocks — REER responses at the 10th, 50th, and 90th percentiles conditional on level of FXI and frequency of intervention (low FXI evaluated at zero; high FXI at 75th percentile).
  - Figure 10, Panel B: US monetary policy shocks — analogous setup.

### Role of capital flow management measures (CFM)
- CFMs condition shock impacts:
  - Figure 11: Impact of VIX shocks on REER conditional on use of CFM (low CFM evaluated at zero; high CFM evaluated at 1). Panels for 10th, 50th, and 90th percentiles and strong vs. weak CFM responses.
  - Figure 12: Impact on REER by use of CFM and frequency of intervention; heavy CFM users defined as countries that, on average, have at least one CFM measure throughout the sample.
- Interactions between FXI and CFM:
  - Figure 13: Interaction effects (FXI-CFM) for VIX shocks at the 10th and 50th percentiles; difference between high FXI, high CFM and high FXI, low CFM shown.

### Heterogeneity by country characteristics, market conditions, and policy frameworks
- Inflation anchoring:
  - Figure 14: Effectiveness of FXI by inflation anchoring (low vs. high); panels for VIX shocks at 10th, 50th, 90th percentiles and high-low FXI difference by anchoring.
- Market liquidity (ask-bid spreads):
  - Figure 15: Effectiveness of FXI by ask-bid spread (low vs. high); panels for VIX shocks at 10th, 50th, 90th percentiles and high-low FXI difference by spread.
- Sovereign risk (EMBIG spread):
  - Figure 16: VIX changes on REER by EMBIG (high EMBIG defined as country-months when EMBIG exceeds the mean for the sample; countries with no EMBIG classified as low EMBIG). Panels for 10th, 50th, 90th percentiles.
  - Figure 17: Effectiveness of FXI by EMBIG spread; panels for VIX shocks at 10th, 50th, 90th percentiles and high-low FXI differences by EMBIG spread.
- State variables:
  - Figure 21: Impact of VIX shocks on REER conditional on Capital Account Openness (Chinn-Ito split by median) and Net Investment Position (split by NIIP<0 vs. NIIP>=0). Panels for 10th, 50th, 90th percentiles.
  - Figure 22: Impact of VIX shocks on REER by Fernandez and others (2016) capital account openness indices: overall KA, inflows index (KAI), outflows index (KAO). Higher KA, KAO, KAI indicate more restrictions (less openness); samples split by median; panels for 10th, 50th, 90th percentiles.

### REER volatility and shock dynamics
- REER volatility measure: 6-month rolling standard deviation of the (log) REER.
- Figure 18: Impact of shocks on REER volatility (VIX and U.S. MON POL shocks) across 10th, 50th, 90th percentiles of REER volatility distribution.
- Figure 19: VIX shocks on REER volatility by direction of shock (conditional on shock>0 vs. shock<0).
- Figures 20: Role of FXI in shaping REER volatility responses to VIX shocks (panels for 10th, 50th, 90th percentiles; high FXI evaluated at 75th percentile; low FXI at zero).
- Figure 23: VIX shocks and FXI — robustness controlling for contemporaneous interventions vs. controlling for future interventions (panels for 10th, 50th, 90th percentiles), with high FXI evaluated at the 75th percentile and low FXI at zero.

### Additional robustness and alternative measures
- Bilateral real exchange rate responses:
  - Figure 24: Impact of VIX shocks and U.S. MON POL shocks on the distribution of the change in the (log) LCUS (bilateral real exchange rate) across 10th, 50th, 90th percentiles.
- US Financial Conditions Index (IMF 2017):
  - Figure 25: Responses of the 10th, 50th, and 90th percentiles of the change in the (log) REER to a one standard deviation change in the US financial condition index.

*IMF Working Paper — Annex 1. Figures and Tables*

### Annex 2. Terms of Trade

### Annex 2. Terms of Trade

### Main finding
- Terms-of-trade (ToT) shocks have only a limited effect on the REER.  
- This finding is consistent with Fernandez, Schmitt-Grohé and Uribe (2017).

### Methodology summary
- Responses are measured with respect to a one standard deviation change in the gap between (log) ToT levels and its medium-term (HP) trend.
- Responses are shown for specific deciles of the (log) REER distribution (10th, 50th, 90th percentiles).
- Time horizon in reported figures: Months since shock from -1 to 12.

### Figure A1 — Impact of ToT shocks (overall deciles)
- Panels: 10th Percentile, 50th Percentile, 90th Percentile.
- Vertical effect scales shown in the panels:
  - Panel A and C scales: -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03, 0.04.
  - Panel B scale: -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03, 0.04.
- Months shown on horizontal axis: -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
- Confidence interval shown: 90 pct. CI.

### Figure A2 — Impact of ToT shocks, by direction of shock
- Panels: 10th Percentile, 50th Percentile, 90th Percentile.
- Effects conditional on shock direction (shock>0 vs. shock<0) with 90 pct. CI for each.
- Vertical effect scales in panels: -0.05, -0.03, -0.01, 0.01, 0.03, 0.05.
- Horizontal months since shock: -1 to 12.
- Confidence interval shown: 90 pct. CI.

### Figure A3 — Impact of ToT shocks on REER — the role of FXI
- Panels: for each decile (10th, 50th, 90th) there is a main panel and a "Strong vs. Weak FXI response" comparison.
- FXI conditioning:
  - Low FXI: estimated coefficient evaluated at zero.
  - High FXI: estimated coefficient evaluated at the 75th percentile of the (absolute) FXI distribution.
- Example vertical effect scales appearing in panels:
  - Panel A/C/E scales include: -0.015, -0.005, 0.005, 0.015, 0.025, 0.035.
  - Other panels show scales such as: -0.01, -0.005, 0, 0.005, 0.01 and -0.006, -0.004, -0.002, 0, 0.002, 0.004 and -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03 and -0.01, -0.005, 0, 0.005, 0.01.
- Horizontal months since shock in panels: -1 to 8 (some panels), and -1 to 8 in comparison panels.
- Plotted elements: Effect, high FXI; 90 pct. CI, high FXI; Effect, low FXI; High-low diff.; 90 pct. CI, high-low diff.

### Figure A4 — Impact of ToT shocks on REER — the role of FXI, by direction of intervention
- Panels: For each decile (10th, 50th, 90th) results are shown separately for positive and negative interventions.
- FXI conditioning:
  - Low FXI: estimated coefficient evaluated at zero.
  - High FXI: estimated coefficient evaluated at the 75th percentile of the (absolute) FXI distribution.
- Example vertical effect scales in panels: -0.02, 0, 0.02, 0.04, 0.06 and -0.04, -0.02, 0, 0.02, 0.04, 0.06.
- Horizontal months since shock in panels: -1 to 12.
- Plotted elements: Effect, high FXI; 90 pct. CI, high FXI; Effect, low FXI.

*External Shocks, Policies, and the Distribution of Real Exchange Rate Movements — Working Paper No. WP/23/129*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023129-print-pdf.pdf_