## 1. Derivation of Euler Equation and Regression

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---

### Overview
- Objective: investigate the impact of international reserves on (i) the likelihood of currency and banking crisis; and (ii) the frequency of liquidity dry-up episodes in FX markets.
- Definitions and sample:
  - Currency crises defined as in Gourinchas and Obstfeld (2011).
  - Banking crises defined as in Leaven and Valencia (2012).
  - FX market “liquidity dry-up” episodes: daily z-score of bid-ask spreads larger than 99 percentile of 34 AMs and 49 EMs.
  - Sample of liquidity events: January 1, 1999 to June 30, 2013. Episodes aggregated to annual counts per country.
- Models estimated separately for Advanced Markets (AMs) and Emerging Markets (EMs).

### Models and specification
- Currency crisis probability model:
  - Probit; sample period 1975–2012.
  - Right-hand-side variables: (i) net foreign assets/GDP, (ii) net external debt assets/GDP, (iii) net external portfolio equity/GDP, (iv) net FDI position/GDP, (v) FX reserves/GDP, (vi) relative per capita income (against USA, PPP per capita), (vii) current account/GDP (2-year moving average), (viii) REER gap (relative to the 5-year moving average), (ix) VIX, and (x) fiscal gap (relative to 5-year moving average).
- Banking crisis probability model:
  - Probit; similar specification with banking crisis dummy as dependent variable.
- FX liquidity episodes:
  - Tobit model (truncation point at 0) to account for heavy skew and many zeros in annual counts.
  - Tobit RHS includes the cost of variation of gross capital inflows/GDP (5-year window) in addition to variables used for currency crisis model.

### Key quantitative results — currency and banking crisis probabilities; liquidity
- Currency crisis probability (EMs):
  - "A one standard deviation increase in international reserve/GDP (13 percentage points) would reduce the probability of a currency crisis by about 8 percent."
  - Estimated coefficients broadly in line with economic intuition; net debt assets not significant; current account and REER gap at most marginally significant.
- Currency crisis probability (AMs):
  - Model performs poorly for AMs; most regressors neither have the correct sign nor statistical significance.
  - International reserve sometimes significant but effect becomes negligible once current account is added.
- Banking crisis probability (AMs):
  - "One standard deviation increase in international reserves in percent of GDP (19 percentage points) reduces the probability of a banking crisis by about 6 percent."
  - Other indicators of external vulnerabilities insignificant in these regressions.
- Banking crisis probability (EMs):
  - Evidence that reserves limit banking crisis risk is less robust. Impact of reserve buffers becomes insignificant once global stress (VIX) is controlled for.
- FX liquidity drying-up episodes (EMs and AMs):
  - Nonlinearity matters: Tobit coefficients larger than linear (fixed-effect) models and broadly correct signs.
  - "For EMs, a one standard deviation increase in international reserves (14 percentage points of GDP) would reduce the number of liquidity dry-up episodes by about 1.4 (around half the average of number of liquidity episodes in EMs of 3, with standard deviation is 9.7)."
  - Tobit regression for AMs does not work well.

### Model diagnostics and sample notes
- Data sources used: WEO, IFS, IIP, Milesi-Ferretti and Lane database, INS, Laeven and Valencia (2012), Bloomberg, and IMF staff estimates.
- Tobit truncation at 0 to account for mass of zeros in liquidity episodes.
- Significance notation in tables: *** p<0.01, ** p<0.05, * p<0.1.
- Tables report observations, Log likelihood and Pseudo R-squared for probit models; R-squared, Adjusted/Pseudo R-squared, Chi-squared, Log-Likelihood for Tobit and OLS (fixed-effect) drying-up models.

### Implications for intervention from currency-crisis models
- Literature summarized in three generations:
  - First generation — inconsistent policies: peg vs. unsustainable fiscal/monetary policy; reserves cannot avert crisis when parity unsustainable.
  - Second generation — temptation of inconsistent policies: self-fulfilling speculative attacks possible; probability depends on fundamentals and political cost of abandoning the peg; prolonged/intense intervention can in some circumstances increase attack probability; intervention may guide expectations and limit risk.
  - Third generation — financial fragility: crises driven by realization of implicit contingent liabilities from financial intermediaries; reserves may provide foreign currency liquidity to solvent financial institutions.
- Practical implication: role and timing of intervention depend on underlying crisis mechanism; reserves matter especially where they can be used to provide FX liquidity support or to influence expectations when fundamentals are not fully inconsistent with the peg.

### Examining determinants of FX selling intervention and impact on FX depreciation (EMs)
- Bottom line: "FX selling intervention can affect pace of depreciation while quantitatively negligible impact on depreciation."
- Empirical exercise (49 EMs, January 2004 onward):
  - Calculation of FX intervention:
    - Monthly reserve data from IFS.
    - Impact of the two 2009 SDR allocations removed.
    - Estimated valuation and income effects removed assuming COFER portfolio shares and using market exchange rates and bond yields.
    - Negative numbers indicate sale of FX; positive indicate purchase.
    - Filtered (3-month) implied intervention used for regressions when large fluctuations relative to official intervention are present.
  - First-stage regression (country-by-country; allows heterogeneity):
    - Dependent variable: estimated FX intervention (percent of GDP).
    - RHS variables: lagged change in exchange rate (first difference of natural logarithm; large number indicates depreciating exchange rate), REER misalignment (CGER or EBA), 3-month speed of exchange rate change, intra-month exchange rate volatility, and international reserves (percent of GDP).
    - Asymmetry: regressions estimated separately for episodes of central bank purchases and sales of FX.
  - Second-stage regression on exchange rate:
    - Given implied FX intervention from first stage, estimate fixed-effects exchange rate equations separately for purchases and for sales.
    - Three dependent-variable specifications:
      (i) level of bilateral exchange rate against the US$ (natural logarithm);
      (ii) appreciation/depreciation defined as first log-difference;
      (iii) pace of appreciation/depreciation defined as second difference.
    - RHS controls: interest rate differentials (short-term interest rates), EMBI spreads, commodity prices (metal, energy and food prices), VIX, and extent of FX intervention.
- First-stage regression summary statistics:
  - Scatter/fit from figure: y = -0.4846x -0.0143, R² = 0.1753.
  - Median coefficients of International Reserves (based on 1st stage regressions across 49 EMs):
    - Total: -0.013
    - Free floating & floating: -0.006
    - Other managed arrangement: -0.012
    - Non-floating & other managed: -0.027
  - Interpretation: in non-peg or more managed regimes, reserves enter the FX-selling reaction function more strongly (more negative coefficient), signaling a trade-off between addressing REER misalignment and preserving reserve levels.

### First-stage regression: reserves, FX regime, and trade-offs
- Estimated coefficients for international reserves with FX selling intervention:
  - Have negative sign and larger negative value for countries with less flexible FX regime.
- Policy-objective trade-off for central banks when selling FX:
  - A larger positive coefficient for exchange rate misalignment suggests central bank places more weight on addressing misalignment.
  - A larger positive coefficient for international reserves indicates greater emphasis on maintaining/building international reserves.
  - Under flexible exchange rate regime (based on AREAER) without capital controls, central banks face a negative trade-off between the level of FX misalignment and international reserves.
  - Estimated coefficients are consistent with flexible FX regime countries facing a negative trade-off as a group.

### Second-stage regression output—impact of FX selling intervention
- Depreciation:
  - The size of intervention has a negative (statistically marginally significant) coefficient, implying depreciation coincides with massive FX selling by central banks.
  - Possible explanations:
    - Measurement errors in the estimated FX intervention sample based on 49 countries.
    - Influence of very large shocks (e.g., the Lehman shock) to the capital account that could not be absorbed by intervention in the sample period.
  - Re-estimation using official intervention data for five countries (Chile, Colombia, Mexico, Peru and Turkey):
    - With the official intervention data, the impact on depreciation declines to the level which is quantitatively negligible.
    - Estimated regressions imply that FX selling intervention does not quantitatively affect exchange rate depreciation.
    - Findings similar to Adler and Tovar (2011) on FX intervention and appreciation.
- Pace of depreciation:
  - The estimated coefficient is positive and statistically significant, suggesting FX selling intervention does affect the pace of depreciation.
  - Consistent with Adler and Tovar (2011) finding that purchasing intervention can slow the pace of appreciation.
- Regression sample and statistics:
  - FX selling intervention, based on implied intervention: # of observations = 465; R-square entries in table: 0.344 0.077 0.155 0.007 (table shows R-square entries adjacent to models).
  - FX selling intervention, based on actual intervention data (5 countries): # of observations = 1,300; R-square shown as 0.007 in table alignment.
  - Note: *** p<0.01, ** p<0.05, * p<0.1.

### USD liquidity swap lines during the global financial crisis (design and chronology)
- Purpose: provide “foreign central banks with the capacity to deliver U.S. dollar funding to institutions in their jurisdictions during times of market stress,” and “prevent the spread of strains to other markets and financial centers.”
- Key events and terms (entries preserved exactly):
  - 2007 Dec 12 — Euro, Switzerland — Size: 55, 12 — Duration: O/N-3M — Lending rate: Fixed (OIS+100bp) or Variable
  - 2008 Sep 18 — Japan, UK, Canada — Size: 60, 40, 10 (size expanded) — ECB, Switzerland — 110, 27
  - 2008 Sep 24 — Australia, Sweden, Norway, Denmark — Size: 10, 10, 5, 5
  - 2008 Sep 29 — (size expanded) — Euro, Switzerland, Japan, UK, Canada, Australia, Sweden, Norway, Denmark — Size: 240, 60, 120, 80, 30, 30, 30, 15, 15
  - 2008 Oct 13-14 — (size expanded) — Euro, Japan, UK, Switzerland — No fixed limit — Lending rate: Fixed (OIS+100bp)
  - 2008 Oct 28 — New Zealand — Size: 15
  - 2008 Oct 29 — Brazil, Mexico, Korea, Singapore — Size: 30 each
  - 2010 Feb 1 — Termination
  - 2010 May 9 — Euro, Japan, UK, Switzerland, Canada — No fixed limit (CAN: 30) — Duration: 1W-3M — Lending rate: Fixed (OIS+100bp)
  - 2011 Nov 30 — Euro, Japan, UK, Switzerland, Canada — Duration: 1W-3M — Lending rate: Fixed (OIS+50bp)
  - 2013 Oct 31 — Euro, Japan, UK, Switzerland, Canada — Bilateral liquidity swap arrangements were converted to standing arrangements.
  - Note 1/ For details see http://www.federalreserve.gov/newsevents/press/monetary/20131031a.htm
- Operational responses and adjustments:
  - After Lehman Shock (September 15), the Federal Reserve expanded USD swap lines to broaden access to US dollars as the global US dollar funding market froze.
  - Swap lines expanded to BOJ, BOE, and BOC, then to Nordic, Pacific Asian, and Latin American central banks.
  - For most AMs, the size of swap lines more than doubled in less than 2 weeks before removal of caps for ECB, SNB, BOJ, and BOE.
  - Lending rate amended to fixed rate only; expiration date extended three times.
  - USD swap lines terminated on 2010 Feb 1 but reactivated in May 2010; premium on lending rate reduced by 50bps in November 2011 to improve usage, increasing bids; several swap lines extended.
- Non-USD swap lines (entries preserved exactly):
  - 2009 Apr 6 — Between US and Euro/Japan/UK/Switzerland — Size: €80bil, ¥10tri, £30bil, CHF40bil — Duration: TBD by Fed
  - 2010 Feb 1 — Termination
  - 2011 Nov 30 — Among US, Euro, Japan, UK, Canada, Switzerland — Size: No fixed limit — Duration: Max. 3M — Lending rate: TBD by CBs
  - 2013 Oct 31 — US, Euro, Japan, UK, Canada, Switzerland — Bilateral liquidity swap arrangements were converted to standing arrangements.
  - Note 1/ For details see http://www.federalreserve.gov/newsevents/press/monetary/20131031a.htm

### Measuring market dysfunction in the FX swap market
- Definition and detection:
  - Dysfunction occurs when liquidity suddenly tightens and transactions freeze; covered interest parity (CIP) tends not to hold.
  - FX market dysfunction episodes defined as extreme multi-day deviations from CIP where implied US dollar FX swap spreads exceed their 99th percentile value (for the 3 month tenor).
  - Normal market conditions are assumed restored when the differential returns to below the threshold level for 5 consecutive trading days.
- Sample and episodes:
  - Currencies included: Australian dollar, British pound sterling, Canadian dollar, Swiss franc, Danish kroner, euro, Hong Kong dollar, Icelandic krona, Japanese yen, Norwegian krone, New Zealand dollar, Swedish krona, and Singapore dollar.
  - Czech koruna, Israeli shekel, and Korean won excluded as they were considered EM currencies until recently.
  - From January 1989 to August 2013, 85 episodes of market dysfunction identified across the 13 currency pairs.

### Can international reserve level affect consumption growth volatility? (empirical study)
- Theoretical motivation:
  - Under consumption-smoothing with a floor on international reserves, when the reserve constraint does not bind consumption follows a standard Euler equation.
  - Implications:
    - A negative correlation between volatility of consumption growth and international reserve level.
    - A non-linear relationship due to a “smooth pasting” feature and declining marginal benefit of reserve level.
- Empirical strategy:
  - Reduced-form model: dependent variable is consumption growth volatility.
  - RHS variables: terms of trade (ToT); FX regime (AREAER); international reserves (alternate reserve adequacy metrics, natural logarithm used); current account balance.
  - Cross-country data: 44 EMs. Consumption volatility measured during 2008-12; explanatory variables in 2007 or current account averaged 2002-07 to reduce endogeneity.
- Main empirical findings:
  - Most variables have appropriate sign, but the natural logarithm of reserve adequacy metrics are not generally statistically significant.
  - A term combining the natural logarithm of ARA EM Metric with current account balance is statistically significant: widened deficit with low international reserves would result in bigger consumption growth volatility.
  - Other traditional metrics do not have statistically significant coefficients, individually or when interacted with current account.

### Comparison of reserve adequacy metrics and EMP/crisis prediction
- Logit regressions relating probability of exchange market pressure (EMP) events to reserve adequacy metrics (1990-2012) indicate:
  - The proposed metric outperforms traditional metrics: higher reserves coverage against this metric significantly reduces the probability of EMP event.
- Robustness:
  - Logit regression against extreme crisis-related events (Laeven and Valencia (2012)) and the 2009 Crisis Program Review also shows that low reserves coverage against the metric significantly explains crisis events.
- Selected coefficient estimates from Table 9 (examples preserved exactly):
  - Reserves/Metric 1 (RAM1): -2.191*** (std. err. 0.588) … -2.817*** (0.998) across specifications.
  - Reserves/Metric 2 (RAM2): values include -2.088*** (0.552), -2.651*** (0.784), -2.700*** (0.887), -2.584*** (0.776), -2.651*** (0.784), -2.784*** (0.775), -3.998*** (1.157), -2.523*** (0.680), -3.744** (1.491).
  - Cyclically Adjusted Primary Balance/GDP: e.g., -0.161* (0.0915), -0.156* (0.0921), -0.158* (0.0914).
  - Primary Balance Gap: -0.0250* (0.0145), -0.0266* (0.0146), -0.0270* (0.0140).
  - Other metrics examples: Reserves in months of imports: 0.359** (0.153); Reserves/Broad Money: 0.000000336 (0.00000180).
  - Number of observations by specification: 333, 295, 232, 323, 287, 228, 287, 287, 278, 287, 287, 218.
- Notes: All independent variables use previous year's data. Standard errors in parentheses. ***, **, * denote significance at 1, 5, and 10 percent levels.

### The sterilization cost of reserves and determinants of bond spreads
- Context:
  - Central banks in EMs increasingly sterilize reserve accumulation by issuing domestic public debt; quasi-fiscal sterilization cost estimated as the spread between yields on reserves and interest paid on domestic government bonds/bills.
- Methodology:
  - Annual panel fixed effects OLS regression of long-term government bond yield spreads (domestic LT yield minus US LT yield) for 1990-2013.
  - Controls: domestic public debt to GDP and its square, cyclically adjusted primary fiscal balance to GDP, short-term interest rates, inflation, potential real growth, change in financial development.
  - Country fixed effects capture time-invariant heterogeneity; year fixed effects account for global shocks. When VIX used as global factor, year effects omitted.
  - Non-linear relationship between domestic public debt and yields modeled via debt and debt^2.
- Regression results — baseline OLS (selected coefficients preserved exactly):
  - Domestic Public Debt/GDP: -0.234***, -0.231***, -0.259***, -0.235***.
  - Domestic Public Debt/GDP^2: 0.00367**, 0.00351**, 0.00377**, 0.0040***.
  - Potential GDP growth: -0.479*, -0.595*, -0.622**, -0.601*.
  - Short-term interest rate: 0.472***, 0.408***, 0.404***, 0.334**.
  - Reserves to metric: -0.009*, -0.010* where included.
  - Change in financial openness: -0.055*, -0.055.
  - VIX index: 0.042, 0.015, 0.138*** (in specifications where used).
  - Observations: 256, 178, 229, 167. Countries: 21, 18, 21, 17. R-squared: 0.47, 0.62, 0.44, 0.65.
  - Implied Domestic Debt to GDP thresholds: 31.2%, 32.9%, 34.4%, 29.4%. Sample EMs above threshold: 64, 38 (as reported).
- Robustness checks (Table 11):
  - Models with 1-year lags of fiscal variables, OLS in differences, and 2SLS with lags as instruments yield similar qualitative findings.
  - Example robustness coefficients:
    - Domestic Public Debt/GDP: -0.098*, -0.133***, -0.192***.
    - Domestic Public Debt/GDP^2: 0.00123**, 0.00308**, 0.00235***.
  - Observations: 253, 235, 247. Countries: 21. R-squared: 0.33, 0.32, 0.24.
  - Implied Domestic Debt to GDP thresholds: 40.1%, 21.6%, 40.9%.

### Survey responses and use of reserve metrics (membership survey and LIC teams)
- Membership survey:
  - Total of 40 responses, almost half from advanced economies.
  - Functions of reserves cited: precautionary liquidity needs, protection against income/commodity price shocks, savings for future generations, management of exchange rate level, smoothing FX volatility, bank recapitalization costs.
  - Institutions involved in liquidity needs: central bank, ministry of finance, financial sector regulator, national debt office/manager.
  - Metrics used to assess reserve adequacy: ratios to imports, ratios to short-term debt at remaining maturity, ratios to monetary aggregates, IMF Reserves Adequacy Metric, others.
  - Costs of holding reserves noted: spreads on external debt, cost of maturity mismatch, sterilization costs, exchange rate valuation losses, opportunity cost of consumption/investment.
  - Instruments considered similar to reserves: central bank swap lines, precautionary credit lines from IMF/other IFIs, precautionary credit lines from commercial banks, commodity price hedging, sovereign wealth fund (SWF) assets.
- Survey of LIC country teams on usage of the 2011 LIC metric:
  - About half of LIC country teams have used the metric in recent discussions with country authorities (total respondents: 58).
  - Regional heterogeneity: three-quarters of AFR LIC teams used the metric; about two-fifths of WHD and one-third of MCD LIC teams used it.
  - LIC metric tends to be used as a complement to other approaches; most common approach remains 3-month import coverage.
  - About 8 LICs supplemented their reserve adequacy analysis with the EM metric.
  - LIC metric tends to imply higher adequate reserve levels than other approaches:
    - In AFR LICs, median adequate level using LIC metric ≈ 6 months (with large margins); traditional metrics median ≈ 4 months.
    - AFR country teams using LIC metric tended to have median actual reserves > 4 months of imports; teams using import coverage had median actual reserves ≈ 3 months of imports.
- Feedback and suggested improvements on LIC metric:
  - Need guidance in estimating marginal cost of holding reserves; lack of data and sensitivity of adequate level to cost assumptions.
  - Refine parameters in marginal benefit regressions to reflect country heterogeneity: small states, resource-rich economies (RRs), monetary unions, dollarized economies.
  - Propose structured adjustments (e.g., fiscal balance in RRs) and new parameters (e.g., remittances in small islands, oil prices).
  - Call for cross-country calibration of unconditional probability of shocks accounting for LIC heterogeneity.
  - Request for more operational guidance, a simple template, and a PowerPoint to guide discussions with authorities.
- Country team practice examples:
  - Nigeria adjusted fiscal balance parameter for oil price sensitivity; Cape Verde estimated marginal benefit regression using country-specific data.
  - Common benchmark for cost of holding reserves: opportunity cost of holding reserves (marginal cost often assumed < 5 percent).
  - Methods: marginal product of capital, external/domestic funding cost, or judgment.

*Source: ASSESSING RESERVE ADEQUACY – SUPPLEMENTARY INFORMATION, INTERNATIONAL MONETARY FUND*

### 1. Derivation of Euler Equation and Regression _______________________________________________________ 16

### 1. Derivation of Euler Equation and Regression

### Overview
- Objective: investigate the impact of international reserves on (i) the likelihood of currency and banking crisis; and (ii) the frequency of liquidity dry-up episodes in FX markets.
- Currency crises defined as in Gourinchas and Obstfeld (2011). Banking crises defined as in Leaven and Valencia (2012).
- FX market “liquidity dry-up” episodes: daily z-score of bid-ask spreads larger than 99 percentile of 34 AMs and 49 EMs. Sample of liquidity events: January 1, 1999 to June 30, 2013. Episodes aggregated to annual counts per country.
- Models estimated separately for Advanced Markets (AMs) and Emerging Markets (EMs).

### Models and specification
- Currency crisis probability model: probit; sample period 1975–2012.
  - Right-hand-side variables: (i) net foreign assets/GDP, (ii) net external debt assets/GDP, (iii) net external portfolio equity/GDP, (iv) net FDI position/GDP, (v) FX reserves/GDP, (vi) relative per capita income (against USA, PPP per capita), (vii) current account/GDP (2-year moving average), (viii) REER gap (relative to the 5-year moving average), (ix) VIX, and (x) fiscal gap (relative to 5-year moving average).
- Banking crisis probability model: probit; similar to currency model but with banking crisis dummy on left-hand side.
- FX liquidity episodes: Tobit model (truncation point at 0) to account for heavy skew and many zeros in annual counts.
  - Tobit RHS includes the cost of variation of gross capital inflows/GDP (5-year window) in addition to variables used for currency crisis probability model.

### Key quantitative results (currency and banking crisis probabilities; liquidity)
- Currency crisis probability (EMs):
  - "A one standard deviation increase in international reserve/GDP (13 percentage points) would reduce the probability of a currency crisis by about 8 percent."
  - Estimated coefficients broadly in line with economic intuition; net debt assets not significant; current account and REER gap at most marginally significant.
- Currency crisis probability (AMs):
  - Model performs poorly for AMs; most regressors neither have the correct sign nor statistical significance. International reserve sometimes significant but effect becomes negligible once current account is added.
- Banking crisis probability (AMs):
  - "One standard deviation increase in international reserves in percent of GDP (19 percentage points) reduces the probability of a banking crisis by about 6 percent."
  - Other indicators of external vulnerabilities insignificant in these regressions.
- Banking crisis probability (EMs):
  - Evidence that reserves limit banking crisis risk is less robust. Impact of reserve buffers becomes insignificant once global stress (VIX) is controlled for.
- FX liquidity drying-up episodes (EMs and AMs):
  - Nonlinearity matters: Tobit coefficients larger than linear (fixed-effect) models and broadly correct signs.
  - "For EMs, a one standard deviation increase in international reserves (14 percentage points of GDP) would reduce the number of liquidity dry-up episodes by about 1.4 (around half the average of number of liquidity episodes in EMs of 3, with standard deviation is 9.7)."
  - Tobit regression for AMs does not work well.

### Model diagnostics and sample notes
- Probit and Tobit regressions use data sources: WEO, IFS, IIP, Milesi-Ferretti and Lane database, INS, Laeven and Valencia (2012), Bloomberg, and IMF staff estimates.
- Note thresholds and tests:
  - Tobit truncation at 0 to account for mass of zeros in liquidity episodes.
  - Significance notation in tables: *** p<0.01, ** p<0.05, * p<0.1.
- Observations and fit statistics reported in tables (examples in text): Number of observations (AMs and EMs vary by specification), Log likelihood and Pseudo R-squared reported for probit models; Tobit and OLS (fixed-effect) reported with R-squared, Adjusted/Pseudo R-squared, Chi-squared, Log-Likelihood for drying-up models.

### Implications for intervention from currency-crisis models
- Literature summarized in three generations:
  - First generation — inconsistent policies: peg vs. unsustainable fiscal/monetary policy; reserves cannot avert crisis when parity unsustainable.
  - Second generation — temptation of inconsistent policies: self-fulfilling speculative attacks possible; probability depends on fundamentals and political cost of abandoning the peg; prolonged/intense intervention can in some circumstances increase attack probability; intervention may guide expectations and limit risk.
  - Third generation — financial fragility: crises driven by realization of implicit contingent liabilities from financial intermediaries; reserves may provide foreign currency liquidity to solvent financial institutions.
- Practical implication: role and timing of intervention depend on underlying crisis mechanism; reserves matter especially where they can be used to provide FX liquidity support or to influence expectations when fundamentals are not fully inconsistent with the peg.

### Examining determinants of FX selling intervention and impact on FX depreciation (EMs)
- Bottom line: "FX selling intervention can affect pace of depreciation while quantitatively negligible impact on depreciation."
- Literature context:
  - Sarno and Taylor (2001) — official intervention can be effective, especially if publicly announced, concerted, and consistent with monetary/fiscal stance; 1990s studies more supportive than 1980s.
  - Ostry et al. (2012) — effectiveness of sterilized intervention in EMs mixed but generally more favorable than in advanced economies.
  - Adler and Tovar (2011) — FX purchasing interventions slow appreciation and are more effective when the exchange rate is already overvalued.
- Empirical exercise (49 EMs, January 2004 onward):
  - Calculation of FX intervention:
    - Monthly reserve data from IFS.
    - Impact of the two 2009 SDR allocations removed.
    - Estimated valuation and income effects removed assuming COFER portfolio shares and using market exchange rates and bond yields.
    - Negative numbers indicate sale of FX; positive indicate purchase.
    - Filtered (3-month) implied intervention used for regressions when large fluctuations relative to official intervention are present.
  - First-stage regression (country-by-country; allows heterogeneity):
    - Dependent variable: estimated FX intervention (percent of GDP).
    - RHS variables: lagged change in exchange rate (first difference of natural logarithm; large number indicates depreciating exchange rate), REER misalignment (CGER or EBA), 3-month speed of exchange rate change, intra-month exchange rate volatility, and international reserves (percent of GDP).
    - Asymmetry: regressions estimated separately for episodes of central bank purchases and sales of FX.
  - Second-stage regression on exchange rate:
    - Given implied FX intervention from first stage, estimate a simple fixed-effects exchange rate equation separately for cases where FX is purchased and where it is sold.
    - Three dependent-variable specifications estimated:
      (i) level of bilateral exchange rate against the US$ (natural logarithm);
      (ii) appreciation/depreciation defined as first log-difference;
      (iii) pace of appreciation/depreciation defined as second difference.
    - RHS controls: interest rate differentials (short-term interest rates), EMBI spreads, commodity prices (metal, energy and food prices), VIX, and extent of FX intervention.
- First-stage regression results (selected summary statistics from figures and text):
  - Scatter/fit from figure: y = -0.4846x -0.0143, R² = 0.1753.
  - Median coefficients of International Reserves (based on 1st stage regressions across 49 EMs):
    - Total: -0.013
    - Free floating & floating: -0.006
    - Other managed arrangement: -0.012
    - Non-floating & other managed: -0.027
  - Interpretation: cross-country median coefficients indicate that in non-peg or more managed regimes, reserves enter the FX-selling reaction function more strongly (more negative coefficient), signaling a trade-off between addressing REER misalignment and preserving reserve levels.

*Source: ASSESSING RESERVE ADEQUACY – SUPPLEMENTARY INFORMATION, INTERNATIONAL MONETARY FUND*

### 7.      The summary statistics of the estimated coefficients for international reserves with FX

### 7.      The summary statistics of the estimated coefficients for international reserves with FX selling intervention

### First-stage regression: reserves, FX regime, and trade-offs
- Estimated coefficients for international reserves with FX selling intervention:
  - Have negative sign and larger negative value for countries with less flexible FX regime.
  - Implications:
    - Building up reserves would be important for countries with less flexible FX regime in order to keep intervention effective.
    - Central banks with less flexible exchange rate regimes would intervene more to pressures in foreign markets when they have sufficient international reserves.
- Policy-objective trade-off for central banks when selling FX:
  - A larger positive coefficient for exchange rate misalignment suggests central bank places more weight on addressing misalignment.
  - A larger positive coefficient for international reserves indicates greater emphasis on maintaining/building international reserves.
  - Under flexible exchange rate regime (based on AREAER) without capital controls, central banks cannot freely choose both the level of FX misalignment and international reserves; they face a negative trade-off.
  - Estimated coefficients are consistent with this intuition: flexible FX regime countries face a negative trade-off as a group.

### Second-stage regression output—impact of FX selling intervention
- Depreciation:
  - The size of intervention has a negative (statistically marginally significant) coefficient, which is counterintuitive because it implies depreciation coincides with massive FX selling by central banks.
  - Possible explanations noted:
    - Measurement errors in the estimated FX intervention sample based on 49 countries.
    - Influence of very large shocks (e.g., the Lehman shock) to the capital account that could not be absorbed by intervention in the sample period.
  - Re-estimation using official intervention data for five countries (Chile, Colombia, Mexico, Peru and Turkey):
    - With the official intervention data, the impact on depreciation declines to the level which is quantitatively negligible.
    - Estimated regressions imply that FX selling intervention does not quantitatively affect exchange rate depreciation.
    - These findings are qualitatively similar to Adler and Tovar (2011) on FX intervention and appreciation.
- Pace of depreciation:
  - The estimated coefficient is positive and statistically significant, suggesting FX selling intervention does affect the pace of depreciation.
  - Consistent with Adler and Tovar (2011) finding that purchasing intervention can slow the pace of appreciation.
- Regression sample and statistics (as presented):
  - Depreciation / Pace of depreciation regressions:
    - FX selling intervention, based on implied intervention: # of observations = 465; R-square = 0.344 0.077 0.155 0.007 (table shows R-square entries adjacent to models)
    - FX selling intervention, based on actual intervention data (5 countries): # of observations = 1,300; R-square = 0.007? (table formatting indicates 1,300 observations and R-square 0.007 in column alignment)
  - Note: *** p<0.01, ** p<0.05, * p<0.1
  - (Table 4 reported various coefficient estimates for controls such as Interest rate differentials, Sovereign spreads, Metal prices, Energy prices, Food prices, VIX, and Constant; exact coefficient cells are shown in the source table image.)

### USD liquidity swap lines during the global financial crisis (design and chronology)
- Purpose of USD swap lines:
  - Provide “foreign central banks with the capacity to deliver U.S. dollar funding to institutions in their jurisdictions during times of market stress,” and “prevent the spread of strains to other markets and financial centers.”
- Key events and terms (Table 5, entries preserved exactly):
  - 2007 Dec 12 — Euro, Switzerland — Size: 55, 12 — Duration: O/N-3M — Lending rate: Fixed (OIS+100bp) or Variable
  - 2008 Sep 18 — Japan, UK, Canada — Size: 60, 40, 10 (size expanded) — ECB, Switzerland — 110, 27
  - 2008 Sep 24 — Australia, Sweden, Norway, Denmark — Size: 10, 10, 5, 5
  - 2008 Sep 29 — (size expanded) — Euro, Switzerland, Japan, UK, Canada, Australia, Sweden, Norway, Denmark — Size: 240, 60, 120, 80, 30, 30, 30, 15, 15
  - 2008 Oct 13-14 — (size expanded) — Euro, Japan, UK, Switzerland — No fixed limit — Lending rate: Fixed (OIS+100bp)
  - 2008 Oct 28 — New Zealand — Size: 15
  - 2008 Oct 29 — Brazil, Mexico, Korea, Singapore — Size: 30 each
  - 2010 Feb 1 — Termination
  - 2010 May 9 — Euro, Japan, UK, Switzerland, Canada — No fixed limit (CAN: 30) — Duration: 1W-3M — Lending rate: Fixed (OIS+100bp)
  - 2011 Nov 30 — Euro, Japan, UK, Switzerland, Canada — Duration: 1W-3M — Lending rate: Fixed (OIS+50bp)
  - 2013 Oct 31 — Euro, Japan, UK, Switzerland, Canada — Bilateral liquidity swap arrangements were converted to standing arrangements.
  - Note 1/ For details see http://www.federalreserve.gov/newsevents/press/monetary/20131031a.htm
- Operational responses and adjustments:
  - Immediately after Lehman Shock (September 15), the Federal Reserve promptly expanded USD swap lines to broaden access to US dollars as the global US dollar funding market froze.
  - The swap lines were expanded first to include BOJ, BOE, and BOC, and then to Nordic, Pacific Asian, and Latin American central banks.
  - For most AMs, the size of swap lines more than doubled in less than 2 weeks before removal of caps for ECB, SNB, BOJ, and BOE.
  - Lending rate under USD operations was amended to fixed rate only; expiration date was extended three times to allow borrowing at a transparent fixed rate for longer periods with appropriate collateral.
  - USD swap lines were terminated on 2010 Feb 1 but quickly reactivated in May 2010; borrowing terms initially inherited from previous lines.
  - In late 2011, premium on lending rate was reduced by 50bps (November 2011) to improve usage, which resulted in a substantial increase in bids; several USD swap lines were also extended.
- Non-USD swap lines (Table 6, entries preserved exactly):
  - 2009 Apr 6 — Between US and Euro/Japan/UK/Switzerland — Size: €80bil, ¥10tri, £30bil, CHF40bil — Duration: TBD by Fed
  - 2010 Feb 1 — Termination
  - 2011 Nov 30 — Among US, Euro, Japan, UK, Canada, Switzerland — Size: No fixed limit — Duration: Max. 3M — Lending rate: TBD by CBs
  - 2013 Oct 31 — US, Euro, Japan, UK, Canada, Switzerland — Bilateral liquidity swap arrangements were converted to standing arrangements.
  - Note 1/ For details see http://www.federalreserve.gov/newsevents/press/monetary/20131031a.htm

### Measuring market dysfunction in the FX swap market
- Definition and detection:
  - Dysfunction occurs when liquidity suddenly tightens and transactions freeze; covered interest parity (CIP) tends not to hold.
  - CIP condition (textual presentation preserved): where spot and forward exchange rates, and uncollateralized foreign and domestic interest rates are referenced; large deviations from CIP signal stress.
  - FX market dysfunction episodes defined as extreme multi-day deviations from CIP where implied US dollar FX swap spreads exceed their 99th percentile value (for the 3 month tenor).
  - Normal market conditions are assumed restored when the differential returns to below the threshold level for 5 consecutive trading days.
- Sample, exclusions, and episodes:
  - Currencies included: Australian dollar, British pound sterling, Canadian dollar, Swiss franc, Danish kroner, euro, Hong Kong dollar, Icelandic krona, Japanese yen, Norwegian krone, New Zealand dollar, Swedish krona, and Singapore dollar.
  - Czech koruna, Israeli shekel, and Korean won excluded as they were considered EM currencies until recently.
  - From January 1989 to August 2013, 85 episodes of market dysfunction identified across the 13 currency pairs included in the sample.

### Can international reserve level affect consumption growth volatility? (empirical study)
- Theoretical motivation and expected relationships:
  - Under consumption-smoothing with a floor on international reserves, when the reserve constraint does not bind consumption follows a standard Euler equation.
  - The solution suggests:
    - A negative correlation between volatility of consumption growth and international reserve level, reflecting that low international reserves increase the possibility of a binding constraint.
    - A non-linear relationship between international reserves and consumption growth volatility due to a “smooth pasting” feature and declining marginal benefit of reserve level.
- Empirical strategy:
  - Reduced-form model: dependent variable is consumption growth volatility.
  - Right-hand-side variables: terms of trade (ToT) as proxy for external demand shocks; FX regime (from AREAER) as proxy for economic flexibility; international reserves (alternate reserve adequacy metrics, natural logarithm used to reflect non-linearity); current account balance as proxy for existing imbalances.
  - Cross-country data set includes 44 EMs.
  - Macroeconomic data from WEO; reserve adequacy metrics from WEO and IFS; FX regime from AREAER.
  - To avoid endogeneity:
    - Consumption volatility measured during 2008-12.
    - All dependent variables are either values in 2007 or, for the current account balance, averaged over 2002-07.
- Main empirical findings:
  - Estimated parameters (Table 7) suggest most variables have appropriate sign, but the natural logarithm of reserve adequacy metrics are not generally statistically significant.
  - A term combining the natural logarithm of ARA EM Metric with current account balance is statistically significant:
    - Suggests widened deficit with low international reserves would result in bigger consumption growth volatility.
  - Other traditional metrics do not have statistically significant coefficients, either individually or when interacted with the current account balance, suggesting less explanatory power of reserves in smoothing consumption growth (Table 8 results summarized).
- Additional notes:
  - Analytical solution is difficult when the reserve constraint binds (corner solution); hence reduced-form approach used.
  - Regression time choices: consumption volatility 2008-12; explanatory variables in 2007 or averaged 2002-07 for current account balance.

*Source: Assessing Reserve Adequacy – Supplementary Information (excerpts provided).*

### 18.      The proposed metric seems predict periods of exchange market pressure (EMP) and

### 18.      The proposed metric seems predict periods of exchange market pressure (EMP) and 

### Comparison of reserve adequacy metrics and EMP/crisis prediction
- A series of logit regressions relating the probability of exchange market pressure (EMP) events to various reserve adequacy metrics were estimated (Table 9).
- Regressions included additional explanatory variables: cyclically adjusted primary balance, and primary balance gap.
- Main finding:
  - The proposed metric outperforms all the traditional metrics: higher reserves coverage against this metric significantly reduces the probability of EMP event.
- Robustness:
  - A logit regression run against a sample of extreme crisis-related events (Laeven and Valencia (2012)) and the 2009 Crisis Program Review also shows that low reserves coverage against the metric significantly explains crisis events.
- Selected coefficient estimates from Table 9 (logit regressions, 1990-2012):
  - Reserves/Metric 1 (RAM1): -2.191*** (std. err. 0.588) … -2.817*** (0.998) across specifications.
  - Reserves/Metric 2 (RAM2): values include -2.088*** (0.552), -2.651*** (0.784), -2.700*** (0.887), -2.584*** (0.776), -2.651*** (0.784), -2.784*** (0.775), -3.998*** (1.157), -2.523*** (0.680), -3.744** (1.491).
  - Cyclically Adjusted Primary Balance/GDP: coefficients reported include -0.161* (0.0915), -0.156* (0.0921), -0.158* (0.0914), -0.156* (0.0920), -0.129 (0.0930), -0.0902 (0.0913), -0.155* (0.0895), -0.416*** (0.155).
  - Primary Balance Gap: -0.0250* (0.0145), -0.0266* (0.0146), -0.0270* (0.0140).
  - Other metrics and coefficients (examples): Reserves in months of imports: 0.359** (0.153); Reserves/Broad Money: 0.000000336 (0.00000180).
  - Constants across specifications: e.g., -1.944*** (0.519), -1.343** (0.652), -1.858** (0.752), -1.979*** (0.506), etc.
  - Number of observations by specification: 333, 295, 232, 323, 287, 228, 287, 287, 278, 287, 287, 218.
- Notes: All independent variables use previous year's data. Standard errors in parentheses. ***, **, * denote significance at 1, 5, and 10 percent levels.

### The sterilization cost of reserves and determinants of bond spreads
- Central banks in EMs increasingly sterilize reserve accumulation by issuing domestic public debt; the chapter estimates the quasi-fiscal sterilization cost as the spread between yields on reserves and interest paid on domestic government bonds/bills.
- Methodology:
  - Annual panel (country and year) fixed effects OLS regression of long-term government bond yield spreads (domestic LT yield minus US LT yield) for 1990-2013.
  - Controls: domestic public debt to GDP and its square, cyclically adjusted primary fiscal balance to GDP, short-term interest rates, inflation, potential real growth, change in financial development (change in ratio of credit to private sector to GDP).
  - Country fixed effects used to capture time-invariant heterogeneity; year fixed effects used to account for global shocks. When using VIX index as global factor, year effects omitted to quantify global risk aversion effects.
- Premise: non-linear relationship between domestic public debt and yields — beyond a threshold, higher debt is associated with rising yields at an increasing rate; debt and its square included to capture this.

### Regression results: Spreads and Public Debt (Table 10 and robustness in Table 11)
- Baseline OLS (columns reported):
  - Domestic Public Debt/GDP: -0.234***, -0.231***, -0.259***, -0.235*** (across columns; significance at 1 percent).
  - Domestic Public Debt/GDP^2: 0.00367**, 0.00351**, 0.00377**, 0.0040***.
  - Primary balance to GDP: 0.105, 0.106, 0.016, -0.012 (not uniformly significant).
  - Potential GDP growth: -0.479*, -0.595*, -0.622**, -0.601*.
  - Inflation: 0.050, 0.032, 0.044, 0.004.
  - Short-term interest rate: 0.472***, 0.408***, 0.404***, 0.334**.
  - Reserves to metric: -0.009*, -0.010* (where included).
  - Change in financial openness: -0.055*, -0.055.
  - VIX index: 0.042, 0.015, 0.138*** (in specifications where used).
  - Country fixed effects: YES; Year fixed effects: YES for most baseline columns, NO when VIX included.
  - Observations: 256, 178, 229, 167.
  - Countries: 21, 18, 21, 17.
  - R-squared: 0.47, 0.62, 0.44, 0.65.
  - Implied Domestic Debt to GDP threshold: 31.2%, 32.9%, 34.4%, 29.4%.
  - Sample EMs above threshold: 64, 38 (as reported).
- Robustness (Table 11: OLS with 1-year lags of fiscal variables; OLS in differences; 2SLS with lags as instruments):
  - Examples of coefficients:
    - Domestic Public Debt/GDP: -0.098*, -0.133***, -0.192***.
    - Domestic Public Debt/GDP^2: 0.00123**, 0.00308**, 0.00235***.
    - Primary balance to GDP: 0.015, 0.140, -0.312**.
    - Potential GDP growth: -0.481*, -0.394, -0.399***.
    - Inflation and short-term interest rates remain relevant controls.
  - Observations: 253, 235, 247.
  - Countries: 21, 21, 21.
  - R-squared: 0.33, 0.32, 0.24.
  - Implied Domestic Debt to GDP thresholds: 40.1%, 21.6%, 40.9%.
  - Sample EMs above threshold: 21, 02 (as reported),  (numbers as shown).
- Robustness checks:
  - Results robust to using lags of dependent fiscal variables, re-estimating with 2SLS using lags as instruments, running regressions in differences to address non-stationarity.
  - Unit root findings: dependent variables are stationary; primary balance, inflation, potential growth stationary; domestic debt to GDP and its square non-stationary.

### Survey responses and use of reserve metrics (membership survey and LIC teams)
- Membership survey:
  - Total of 40 responses, almost half from advanced economies.
  - Survey covered motives and use of reserves, analytical frameworks for precautionary reserve adequacy, approach to intervention.
- Survey findings and themes:
  - Functions of reserves: precautionary liquidity needs, protection against income/commodity price shocks, savings for future generations, management of exchange rate level, smoothing FX volatility, bank recapitalization costs.
  - Liquidity needs and institutions involved: central bank, ministry of finance, financial sector regulator, national debt office/manager.
  - Metrics used to assess reserve adequacy: ratios to imports, ratios to short-term debt at remaining maturity, ratios to monetary aggregates, IMF Reserves Adequacy Metric, others.
  - Cost of holding reserves: spreads on external debt, cost of maturity mismatch, sterilization costs, exchange rate valuation losses, opportunity cost of consumption/investment.
  - Instruments considered similar to reserves: central bank swap lines, precautionary credit lines from IMF/other IFIs, precautionary credit lines from commercial banks, commodity price hedging, sovereign wealth fund (SWF) assets.
- Survey of LIC country teams on usage of the 2011 LIC metric:
  - About half of LIC country teams have used the metric in recent discussions with country authorities (Figure 1; total respondents: 58).
  - Regional heterogeneity: three-quarters of AFR LIC teams used the metric; about two-fifths of WHD and one-third of MCD LIC teams used it.
  - The LIC metric tends to be used as a complement to other approaches; the most common approach in policy discussions remains the 3-month import coverage.
  - About 8 LICs supplemented their reserve adequacy analysis with the EM metric.
  - LIC metric tends to imply higher adequate reserve levels than other approaches:
    - In AFR LICs, median adequate level using LIC metric ≈ 6 months (with large margins); traditional metrics median ≈ 4 months.
    - AFR country teams that used LIC metric tended to have median actual reserves > 4 months of imports; teams using import coverage had median actual reserves ≈ 3 months of imports.
- Feedback and suggested improvements on LIC metric:
  - Need guidance in estimating marginal cost of holding reserves; lack of data and sensitivity of adequate level to cost assumptions.
  - Refine parameters in marginal benefit regressions to reflect country heterogeneity: small states, resource-rich economies (RRs), monetary unions, dollarized economies.
  - Propose structured adjustments to existing parameters (e.g., fiscal balance in RRs) and inclusion of new parameters (e.g., remittances in small islands, oil prices).
  - Propose cross-country approach to calibrate unconditional probability of shocks accounting for LIC heterogeneity.
  - Call for more operational guidance, a simple template, and a PowerPoint presentation to guide discussions with authorities.
- Country team practice:
  - Teams applied judgment and modified parameters to reflect heterogeneity (examples: Nigeria adjusted fiscal balance parameter for oil price sensitivity; Cape Verde estimated marginal benefit regression using country-specific data).
  - Approaches to estimate cost of holding reserves:
    - Most common benchmark: opportunity cost of holding reserves (marginal cost often assumed < 5 percent).
    - Methods: marginal product of capital, external/domestic funding cost, or judgment.
    - Reasons for chosen approaches: capture return differences, reference values from staff reports, data availability, proxies from literature, opportunity cost of foregone riskless investment.
  - LIC teams’ most common approach to estimate cost of holding reserves (survey of authorities): cost of foregone consumption or investment (based on 5 LICs responding).

*Source: Staff estimates and survey results as presented in the chapter.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/np/pp/eng/2013/_111313e.pdf_