## _wp1689 - 0.6 percent of GDP for the median country in the sample, while at least 10 percent of the countries ## Source details **Canonical URL:** [_wp1689 - 0.6 percent of GDP for the median country in the sample, while at least 10 percent of the countries](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1689.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1689.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1689.pdf.json) --- ### Ex-post costs: observed outcomes and cross-country patterns - Ex-post total (roll-over) costs for the median country in the sample: 0.6 percent of GDP (average for the period). - At least 10 percent of the countries incurred costs in excess of 1 percent of GDP on average. - Countries with high ex-post marginal costs (e.g., Brazil and Turkey) do not necessarily appear among the highest total costs because of relatively lower holdings of FX during the period. - China and Singapore stand out at the top of the distribution of total opportunity costs despite being below the median in the distribution of marginal costs, reflecting their much larger FX position during the period. - Ex-post costs increased after 2008/09, reflecting low returns on foreign assets (very loose U.S. monetary policy) and appreciation pressures from capital inflows. - For most countries, total costs of rolling over FX positions increased significantly during the period of analysis, primarily due to increased positions. ### Ex-ante costs: definition, estimation approaches, and interpretation - Ex-ante (expected) marginal cost of FX intervention is the conditional expectation of the log marginal cost (equation (5) in source). - Expected total cost of rolling over an existing FX position is given by an exponential approximation involving the expected marginal cost and known NFA position (equation (6) in source). - The key unknown in ex-ante estimation is the expected exchange rate change (expected excess return on the currency, or currency risk premium). - Three primary approaches used to estimate expected exchange rate changes / marginal costs: - Nominal random walk: assume best predictor of future exchange rate is current rate → expected change = 0; ex-ante marginal cost equals the interest rate differential. - Survey-based exchange rate expectations: use Consensus Forecast (CF) 1-month ahead (or implied from 3- or 12-month ahead) log expectations; sample coverage restricted to 54 countries, data mostly from 2002 onwards. - Model-based risk premia: follow Hassan and Mano (2014) decomposition of risk premia into static (currency-specific), dollar (common time-series), and dynamic (idiosyncratic) components; estimate via regressions (equations (8)-(10)), and extend to multivariate regressions with additional factors (equations (12)-(14)). - Factors considered beyond interest differentials: broad money growth differential; actual real GDP growth differential; expected real GDP growth differential (from CF); expected inflation (from CF); real effective exchange rate gap (HP-filter deviation). - Pre-sample of four years used to estimate expected average interest rate differentials for each currency; specification with 2003 cut-off emphasized. ### Empirical findings on ex-ante vs ex-post costs and distributions - Different ex-ante marginal cost measures deliver medians in the range of 2.5-3.7 percent (percentage points), with differences in dispersion across methods. - The range of ex-ante cost estimates is significantly smaller than that of ex-post costs. - Median ex-ante marginal cost: about 3 percent. - Median ex-post marginal cost reached 6.3 percent during the sample period, reflecting widespread unexpected appreciation of EMEs' currencies. - For the median country, ex-ante total costs lie in the inter-quartile range of 0.3-0.5 percent of GDP per year (depending on the method); ex-post total costs: 0.6 percent of GDP. - Ex-post total costs and variance larger since the 2008-09 crisis; ex-ante measures display less evidence of structural break, except the broad time-varying version. - Time-varying variables (e.g., expected GDP growth differential) were key temporary drivers of expected excess returns in the post-crisis period. - Across sample: for 9 out of 73 countries, total costs averaged more than 1 percent of GDP per year over the sample period. - The range of ex-ante marginal and total cost estimates is wide for some countries, especially those with higher average estimates; ranking of countries is fairly stable across measures. - The dynamic component of risk premia is small in size and not robust to alternative sample cut-offs; inclusion does not materially change point estimates of risk premia. ### Exchange rate management, intervention intensity, and cost implications - Degree of exchange rate management constructed as ρj = σ(NFAj/GDP) / (σ(NFAj/GDP) + σ(exchange rate)), where ρj varies between 0 (pure floating) and 1 (peg). - Sample split into light and heavy interveners depending on whether ρj is below or above the cross-section median. - Heavy exchange rate management associated with: - Less dispersion and lower average ex-post marginal costs. - No clear statistical link to ex-ante measures: suggests either FXI is immaterial on risk premia, or FXI is undertaken where risk premia would be higher absent FXI. - Meaningfully larger total costs: heavy interveners inter-quartile range of 0.3-1.2 percent of GDP per year; light interveners inter-quartile range of 0.2-0.7 percent of GDP per year (due to larger balance sheets of heavy interveners). ### Other conditional determinants of cost: EMEs vs AMEs and global risk appetite - Emerging market economies (EMEs) vs advanced market economies (AMEs): - No significant difference in ex-post deviations from UIP between EMEs and AMEs. - Risk premia are higher and more dispersed in EMEs. - Implication: benefits of a stronger portfolio balance channel in EMEs (higher effectiveness of FXI) must be weighed against higher fiscal costs. - Global risk appetite: - Cross-section of estimated risk premia compared at January 2007 (VIX record low) and October 2008 (VIX peak). - Median risk premia and dispersion were significantly higher (twice as high median) in October 2008 relative to January 2007. - Extreme global financial conditions (tail events) may have important effects on cost of FXI; suggests, from a fiscal perspective, reducing FX positions during times of high uncertainty and increasing during times of low uncertainty. - VIX index itself was insignificant in estimation, indicating only tail events may meaningfully impact risk premia. ### Policy-relevant magnitudes and implications - Ex-post costs have been relatively large due to sizeable deviations from UIP and rapid growth of central bank FX positions. - From ex-ante perspective: - Marginal costs for median EME in inter-quartile range: 2-5.5 percent per year. - Ex-ante total costs of sustaining FX positions: 0.3-0.9 percent of GDP per year. - Heavy interveners: total costs inter-quartile range of 0.3-1.2 percent of GDP per year versus 0.2-0.7 percent for light interveners. - Fiscal costs of sustained FX intervention are a relevant dimension when conducting exchange rate policy. - There may be valid reasons for transitory FX intervention when benefits outweigh costs; the study focuses on measuring quasi-fiscal costs rather than on optimality of interventions. ### Annex — formal derivation and analytical insights (marginal cost and FXI interpretation) - Central bank balance sheet identity (equation (16)): - ttt SNFA NDA M K + = + (notation as in source: tSNFA denotes the net foreign asset position expressed in local currency; tNDA stands for the net domestic asset position; tM is the monetary base; and tK is the net worth or capital). - Inter-temporal budget constraint (equation (17)): incorporates foreign and domestic interest rates ( *t i and t i respectively) and transfers to the central government G t Ω . - Law of motion of central bank capital (equation (18)): - 11 (1) G tttttttt KiKSNFAmciM  = +  +  Ω (notation: t mc denotes the marginal cost of rolling over the foreign exchange position). - Definition of the marginal cost of rolling over the foreign exchange position (equation (19)): - t mc = *1 (1)(1) ttt t S mcii S  = +   + (as presented in the source). - Present discounted value of transfers and the central bank value (equation (20)): PV definitions used to relate central bank value to SNFA, NDA, M, K, mc and interest rates. - Definition of sterilized FX intervention (FXI) (equations (21) and (22)): - dFXI t S dNFA t = (sterilized FXI satisfies t dFXI = t dNFA) - 0 0 ttt t S dNFA dNDA dM + = = = (conditions for sterilization as given). - Decomposition of the effect of FXI on the present value of central bank transfers (equations (23) and (24)): - Three components identified: - Valuation gain on impact associated with the impact of FXI on the exchange rate (via the net FX position). - Expected present value of the cost of increasing the NFA position (given the ex-ante marginal cost). - Impact of FXI on the net present value of the cost of rolling over the FX position due to an increase in the risk premium. - Equation (24) explicitly links dm c, dS, and dFXI terms showing how these channels combine. - Special case: FXI causes an immediate depreciation φ and follows an AR(1) with coefficient ρ (equation (25)): - dS if j = 0 : φ ; if j ≠ 0 : ρ φ j (notation preserved as in source). - Under constant policy rates assumption ( *t i = 0 for simplicity), combination of effects yields (equation (26) and simplification to (27)): - The expected cost of FXI in terms of the impact on the net present value of the central bank equals the net present value of the ex-ante marginal cost: - { }1 t tt S t dEPV Emc dFXI i = − (equation (27) as presented). - The corresponding 1-period cost is { } tt Emc . - Key analytical insight: - The valuation gain on impact and the raise of the risk premium due to FXI offset each other when the currency depreciates on impact and is expected to appreciate thereafter; as a result, the expected present value cost of sterilized FXI reduces to the net present value of the ex-ante marginal cost, and the 1-period cost equals the expected marginal cost. *Source: _wp1689 - References (PDF).* ### 0.6 percent of GDP for the median country in the sample, while at least 10 percent of the countries ### _wp1689 - 0.6 percent of GDP for the median country in the sample, while at least 10 percent of the countries ### Ex-post costs: observed outcomes and cross-country patterns - Ex-post total (roll-over) costs for the median country in the sample: 0.6 percent of GDP (average for the period). - At least 10 percent of the countries incurred costs in excess of 1 percent of GDP on average. - Countries with high ex-post marginal costs (e.g., Brazil and Turkey) do not necessarily appear among the highest total costs because of relatively lower holdings of FX during the period. - China and Singapore stand out at the top of the distribution of total opportunity costs despite being below the median in the distribution of marginal costs, reflecting their much larger FX position during the period. - Ex-post costs increased after 2008/09, reflecting low returns on foreign assets (very loose U.S. monetary policy) and appreciation pressures from capital inflows. - For most countries, total costs of rolling over FX positions increased significantly during the period of analysis, primarily due to increased positions. ### Ex-ante costs: definition, estimation approaches, and interpretation - Ex-ante (expected) marginal cost of FX intervention is the conditional expectation of the log marginal cost (equation (5) in source). - Expected total cost of rolling over an existing FX position is given by an exponential approximation involving the expected marginal cost and known NFA position (equation (6) in source). - The key unknown in ex-ante estimation is the expected exchange rate change (expected excess return on the currency, or currency risk premium). - Three primary approaches used to estimate expected exchange rate changes / marginal costs: 1. Nominal random walk: assume best predictor of future exchange rate is current rate → expected change = 0; ex-ante marginal cost equals the interest rate differential. 2. Survey-based exchange rate expectations: use Consensus Forecast (CF) 1-month ahead (or implied from 3- or 12-month ahead) log expectations; sample coverage restricted to 54 countries, data mostly from 2002 onwards. 3. Model-based risk premia: follow Hassan and Mano (2014) decomposition of risk premia into static (currency-specific), dollar (common time-series), and dynamic (idiosyncratic) components; estimate via regressions (equations (8)-(10)), and extend to multivariate regressions with additional factors (equations (12)-(14)). - Factors considered beyond interest differentials: broad money growth differential; actual real GDP growth differential; expected real GDP growth differential (from CF); expected inflation (from CF); real effective exchange rate gap (HP-filter deviation). - Pre-sample of four years used to estimate expected average interest rate differentials for each currency; specification with 2003 cut-off emphasized. ### Empirical findings on ex-ante vs ex-post costs and distributions - Different ex-ante marginal cost measures deliver medians in the range of 2.5-3.7 percent (percentage points), with differences in dispersion across methods. - The range of ex-ante cost estimates is significantly smaller than that of ex-post costs. - Median ex-ante marginal cost: about 3 percent. - Median ex-post marginal cost reached 6.3 percent during the sample period, reflecting widespread unexpected appreciation of EMEs' currencies. - For the median country, ex-ante total costs lie in the inter-quartile range of 0.3-0.5 percent of GDP per year (depending on the method); ex-post total costs: 0.6 percent of GDP. - Ex-post total costs and variance larger since the 2008-09 crisis; ex-ante measures display less evidence of structural break, except the broad time-varying version. - Time-varying variables (e.g., expected GDP growth differential) were key temporary drivers of expected excess returns in the post-crisis period. - Across sample: for 9 out of 73 countries, total costs averaged more than 1 percent of GDP per year over the sample period. - The range of ex-ante marginal and total cost estimates is wide for some countries, especially those with higher average estimates; ranking of countries is fairly stable across measures. - The dynamic component of risk premia is small in size and not robust to alternative sample cut-offs; inclusion does not materially change point estimates of risk premia. ### Exchange rate management, intervention intensity, and cost implications - Degree of exchange rate management constructed as ρj = σ(NFAj/GDP) / (σ(NFAj/GDP) + σ(exchange rate)), where ρj varies between 0 (pure floating) and 1 (peg). - Sample split into light and heavy interveners depending on whether ρj is below or above the cross-section median. - Heavy exchange rate management associated with: - Less dispersion and lower average ex-post marginal costs. - No clear statistical link to ex-ante measures: suggests either FXI is immaterial on risk premia, or FXI is undertaken where risk premia would be higher absent FXI. - Meaningfully larger total costs: heavy interveners inter-quartile range of 0.3-1.2 percent of GDP per year; light interveners inter-quartile range of 0.2-0.7 percent of GDP per year (due to larger balance sheets of heavy interveners). ### Other conditional determinants of cost: EMEs vs AMEs and global risk appetite - Emerging market economies (EMEs) vs advanced market economies (AMEs): - No significant difference in ex-post deviations from UIP between EMEs and AMEs. - Risk premia are higher and more dispersed in EMEs. - Implication: benefits of a stronger portfolio balance channel in EMEs (higher effectiveness of FXI) must be weighed against higher fiscal costs. - Global risk appetite: - Cross-section of estimated risk premia compared at January 2007 (VIX record low) and October 2008 (VIX peak). - Median risk premia and dispersion were significantly higher (twice as high median) in October 2008 relative to January 2007. - Extreme global financial conditions (tail events) may have important effects on cost of FXI; suggests, from a fiscal perspective, reducing FX positions during times of high uncertainty and increasing during times of low uncertainty. - VIX index itself was insignificant in estimation, indicating only tail events may meaningfully impact risk premia. ### Policy-relevant magnitudes and implications - Ex-post costs have been relatively large due to sizeable deviations from UIP and rapid growth of central bank FX positions. - From ex-ante perspective: - Marginal costs for median EME in inter-quartile range: 2-5.5 percent per year. - Ex-ante total costs of sustaining FX positions: 0.3-0.9 percent of GDP per year. - Heavy interveners: total costs inter-quartile range of 0.3-1.2 percent of GDP per year versus 0.2-0.7 percent for light interveners. - Fiscal costs of sustained FX intervention are a relevant dimension when conducting exchange rate policy. - There may be valid reasons for transitory FX intervention when benefits outweigh costs; the study focuses on measuring quasi-fiscal costs rather than on optimality of interventions. *Source: IMF International Financial Statistics; and authors’ calculations.* ### References ### References ### Appendix — Tables and Figures inventory and scope - Tables reported in the appendix: - Table A1. Currency Risk Premia Estimation 1/ — includes panels "a. Interest rates only" and "b. Other factors"; methodology: Follows the methodology in Hassan and Mano (2014). Columns 2001, 2003 and 2005 correspond to the cut-off years for the beginning of the estimation period. Standard errors reported in parenthesis. *p<0.10, **p<0.05, ***p<0.01. - Table A2. Currency Risk Premia Estimation—Static Component 1/ — Follows the methodology in Hassan and Mano (2014). Standard errors reported in parenthesis. *p<0.10, **p<0.05, ***p<0.01. - Table A3. Currency Risk Premia Estimation—Dynamic Component 1/ — Follows the methodology in Hassan and Mano (2014). Standard errors reported in parenthesis. *p<0.10, **p<0.05, ***p<0.01. - Table A4. Currency Risk Premia Estimation—Common Component 1/ — Follows the methodology in Hassan and Mano (2014). Standard errors reported in parenthesis. *p<0.10, **p<0.05, ***p<0.01. - Table A5. Marginal cost of FXI, by country, 2002-13 1/ — Averages for the period 2002-13. Source: authors’ estimations. - Table A6. Total Cost of FXI, by country, 2002-13 1/ — Averages for the period 2002-13. Source: authors’ estimations. - Figures reported in the appendix: - Appendix Figure A1. FXI Marginal Cost in EMEs and AMEs, 2002-13 (percentage points, distribution based on annual averages). Sources: IMF International Financial Statistics; and authors’ calculations. - Appendix Figure A2. FXI Total Cost in EMEs and AMEs, 2002-13 (percentage points, distribution based on annual averages). Sources: IMF International Financial Statistics; and authors’ calculations. - Appendix Figure A3. Global Risk Appetite and Marginal Cost of FXI (percentage points, average for the period). Sources: IMF International Financial Statistics; and authors’ calculations. ### Annex 1 — Formal derivation of the marginal cost of FXI and interpretation - Central bank balance sheet identity (equation (16)): - ttt SNFA NDA M K + = + (notation as in source: tSNFA denotes the net foreign asset position expressed in local currency; tNDA stands for the net domestic asset position; tM is the monetary base; and tK is the net worth or capital). - Inter-temporal budget constraint (equation (17)): - Incorporates foreign and domestic interest rates ( *t i and t i respectively) and transfers to the central government G t Ω . - Law of motion of central bank capital (equation (18)): - 11 (1) G tttttttt KiKSNFAmciM  = +  +  Ω (notation: t mc denotes the marginal cost of rolling over the foreign exchange position). - Definition of the marginal cost of rolling over the foreign exchange position (equation (19)): - t mc = *1 (1)(1) ttt t S mcii S  = +   + (as presented in the source). - Present discounted value of transfers and the central bank value (equation (20)): - PV definitions used to relate central bank value to SNFA, NDA, M, K, mc and interest rates. - Definition of sterilized FX intervention (FXI) (equations (21) and (22)): - dFXI t S dNFA t = (sterilized FXI satisfies t dFXI = t dNFA) - 0 0 ttt t S dNFA dNDA dM + = = = (conditions for sterilization as given). - Decomposition of the effect of FXI on the present value of central bank transfers (equations (23) and (24)): - Three components identified: - Valuation gain on impact associated with the impact of FXI on the exchange rate (via the net FX position). - Expected present value of the cost of increasing the NFA position (given the ex-ante marginal cost). - Impact of FXI on the net present value of the cost of rolling over the FX position due to an increase in the risk premium. - Equation (24) in the source explicitly links dm c, dS, and dFXI terms showing how these channels combine. - Special case: FXI causes an immediate depreciation φ and follows an AR(1) with coefficient ρ (equation (25)): - dS if j = 0 : φ ; if j ≠ 0 : ρ φ j (notation preserved as in source). - Under constant policy rates assumption ( *t i = 0 for simplicity), combination of effects yields (equation (26) and simplification to (27)): - The expected cost of FXI in terms of the impact on the net present value of the central bank equals the net present value of the ex-ante marginal cost: - { }1 t tt S t dEPV Emc dFXI i = − (equation (27) as presented). - The corresponding 1-period cost is { } tt Emc . - Key analytical insight (directly from the derivation in the source): - The valuation gain on impact and the raise of the risk premium due to FXI offset each other when the currency depreciates on impact and is expected to appreciate thereafter; as a result, the expected present value cost of sterilized FXI reduces to the net present value of the ex-ante marginal cost, and the 1-period cost equals the expected marginal cost. *Source: _wp1689 - References (PDF)._ --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1689.pdf_