## _wp16108 — Global Financial Conditions and Monetary Policy Autonomy (Section 1–6)

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### Abstract and research question
- WP/16/108; June 2016.
- Research question: Is the Mundell-Fleming trilemma alive and well? International co-movement of asset prices and synchronized business cycles complicate identification of financial spillovers and assessments of monetary policy autonomy.
- Benchmark null hypothesis: central banks respond only to the outlook for domestic inflation and output.
- Main findings:
  - Common approaches to estimate interest rate spillovers tend to understate the degree of monetary autonomy enjoyed by small open economies with flexible exchange rates.
  - Proposed empirical strategy partials out spillovers associated with impaired monetary autonomy.
  - Using this approach, evidence that flexible exchange rates deliver monetary autonomy is more compelling than prior work has suggested.
- JEL Classification Numbers: C13, C15, E32, E43, E47, E52, E58, F44.
- Keywords: Monetary policy; monetary conditions; autonomy; global financial cycle.

### Conceptual framing: spillovers, pass-through, and autonomy
- Stylized fact: Domestic financial conditions in small open economies tend to move in tandem with those prevailing abroad; strong co-movement in interest rates across countries, particularly at short maturities.
- Distinction between:
  - Interest rate interdependence / pass-through: correlation due to common shocks and synchronized cycles.
  - Monetary policy spillovers: movements in domestic interest rates triggered by foreign monetary policy.
- Definition: autonomy-impairing spillovers are the subset of domestic rate responses to foreign shocks that are above and beyond what can be explained by pursuit of domestic objectives.
- Two empirical challenges:
  1. Simultaneity of international asset prices complicates identification of foreign interest rate shocks.
  2. Endogenous domestic response of macroeconomic outlook following foreign interest rate changes.
- Normative guidance for conditioning variables X_t: ground X_t in central bank objectives—domestic inflation (π_t) and economic activity/output (y_t). Empirical literature has generally followed this view.

### Monte Carlo design and baseline parameterization
- Simulation setup:
  - Two-economy structure: a ‘base’ economy and a ‘small’ open economy; shocks to base macro conditions (ܺ௧∗) can affect small-economy macro conditions (ܺ௧) but not vice versa.
  - Central banks follow inward-looking policy rules; small economy central bank reacts exclusively to domestic deviations when ߚ = 0 by construction (no autonomy-impairing spillovers in the DGP).
  - Monetary policy in the simulation does not feed back to macro conditions.
- Simulation particulars:
  - Using the baseline parameterization in Table 1, the authors simulate 5,000 replications of ܺ௧∗, ܺ௧, ݅௧∗ and ݅௧, each containing 200 observations.
- Baseline parameterization (exactly as in Table 1):
  - ߩ: 0.5 / 0.5
  - ߬: 0.5 / 0.5
  - ߪ: 1 / 1
  - ߠ: 0 / 0
  - ߙ: 1.25 / 1.75
  - ߜ: 0.5 / 0.5
  - ߛ: - / 1
  - ߚ: - / 0
- Key simulated correlations (from Table 2):
  - Corr(݅௧, ݅௧) = 1.00
  - Corr(݅௧, ݅௧∗) = 0.46
  - Corr(݅௧, ܺ௧) = 0.98
  - Corr(݅௧, ܺ௧∗) = 0.47
  - Corr(݅௧∗, ݅௧∗) = 1.00
  - Corr(݅௧∗, ܺ௧) = 0.50
  - Corr(݅௧∗, ܺ௧∗) = 0.97
  - Corr(ܺ௧, ܺ௧) = 1.00
  - Corr(ܺ௧, ܺ௧∗) = 0.51
  - Corr(ܺ௧∗, ܺ௧∗) = 1.00

### Empirical identification methods and their performance in Monte Carlo
- Common methods and limitations:
  - Method I (simple pass-through regressions): regress changes in domestic policy rate on changes in foreign policy rate; yields large and statistically significant estimated pass-through coefficient ߚመ even when ߚ = 0 in the DGP due to synchronized cycles.
  - Method II (include domestic macro controls X_t): choice of X_t is critical; under baseline parameterization estimated ߚመ = 0.36 with the lower bound of its 95% confidence interval at 0.25—leading to rejection of the null of full autonomy despite DGP having full autonomy.
  - Sensitivity: if no inertia in Taylor rules (scenarios 2 and 3), ߚመ is indistinguishable from zero at 5% significance; larger base-country policy noise (scenario 1) can reduce bias; large foreign macro shocks relative to domestic shocks can push ߚመ above 0.75.
  - Method IV (reduced-form VAR of Δ݅∗ and Δ݅ with block exogeneity): impulse responses of Δ݅ to orthogonalized shock to Δ݅∗ can be identified if base-country block exogeneity imposed, but timing assumptions remain fragile when variables are endogenous.
- Table 3 interpretation:
  - Table 3 reports cumulative spillover response from ݅∗ to ݅ after 12 periods following an increase of 100-basis points in ݅∗. “*” denotes significance at a 5% confidence level.
  - Under many parameter variants, single-equation and structural VAR estimates often indicate statistically significant spillovers even when true ߚ = 0.

### Proposed conservative two-stage approach (Method VI)
- Rationale: reverse the problem by starting from the domestic monetary policy reaction function to partial out systematic policy responses to domestic macroeconomic conditions.
- Step 1: estimate a dynamic inward-looking Taylor-type rule for the domestic policy rate and obtain reduced-form innovations (݁̂ ௜) that capture deviations from the fitted policy rule.
  - Ordinary least squares on the policy rule ensures reduced-form innovations are orthogonal to lagged values of controls.
- Step 2: purge monetary policy innovations of contemporaneous correlation with domestic macro innovations by regressing ݁̂ ௜ on reduced-form innovations to domestic economic conditions (ࢋොࢄ) and retaining residuals (ݑො ௧ ௜) as deviations from the historical policy reaction function.
  - Residuals ݑො ௧ ௜ are orthogonal to reduced-form innovations in domestic conditions under the timing restriction that expectations about the domestic outlook are predetermined with respect to monetary policy.
- Step 3: estimate a VAR(p) for Δ݅∗ and ݑො ௧ ௜, impose block exogeneity of Δ݅∗, and identify autonomy-impairing spillovers as the response of ݑො ௧ ௜ to an orthogonalized shock to Δ݅∗ (Cholesky timing restriction).
- Advantages documented in Monte Carlo:
  - Method VI yields estimated responses of domestic interest rates to base-country rate shocks that are statistically indistinguishable from zero under the DGP with ߚ = 0 across baseline and alternative parameterizations.
  - Two-stage single-equation (Method III) reduces bias relative to Method II (two-stage estimate for ߚመ about 40% smaller than Method II) but lacks the richer dynamics of Method VI.

### Empirical application — six small open economies (country-level results)
- Sample: Australia, Canada, New Zealand, South Korea, Sweden, United Kingdom.
  - Monthly data January 1998 to June 2009 (to avoid ZLB period).
  - Focus: spillovers from changes in the U.S. federal funds rate to domestic short-term interest rates (Treasury bills maturity between 3 and 6 months).
  - Responses rescaled so base-country interest rate response after 12 months = 100 basis points.
- Choice of domestic macro controls: 12-month-ahead Consensus Economics mean forecasts for consumer price inflation and industrial production (as proxy for output), linearly interpolated.
- Main country-level empirical findings:
  - Method V (VAR including domestic controls) — after 12 months:
    - Estimated spillovers significantly larger than zero for all six countries, magnitudes range from 30 to 60 basis points (central banks appear to respond about one-for-two to U.S. shocks under Method V).
  - Method VI (multi-stage VAR using residuals from inward-looking policy rule):
    - Autonomy-impairing spillovers substantially smaller than overall spillovers.
    - After 12 months, autonomy-impairing spillover ~10 basis points for most countries and indistinguishable from zero at a 5% confidence level in Australia, South Korea, and Sweden.
    - Canada and New Zealand: autonomy-impairing spillovers around 25 basis points after 12 months, roughly half the size of overall spillovers from Method V.
  - Rolling-window (Method VI (RW), 60-month windows):
    - Allowing policy-rule parameters to vary over time matters for some countries.
    - For New Zealand, Sweden, United Kingdom: Method VI and Method VI (RW) are indistinguishable.
    - For Canada and South Korea: Method VI and Method VI (RW) differ substantially, indicating time-variation in reaction-function parameters matters.
- Using identified U.S. monetary policy surprises (Gertler and Karadi 2015):
  - Method V generates much larger spillover estimates when using identified surprises than when using realized rate changes; in New Zealand, South Korea, and United Kingdom the magnitude more than doubles.
  - Method VI applied to identified surprises: impacts are substantially smaller and in all cases indistinguishable from zero at a 5% confidence level.
  - Canada: identified shocks produce about one-to-one spillovers under Method V (similar to Rey 2014); after removing endogenous domestic responses under Method VI the spillover is about half as large and the null of full monetary autonomy cannot be rejected at a 5% significance level.

### Panel evidence and implications for the trilemma
- Panel setup:
  - First stage: estimate inward-looking policy rules for each country using Consensus Economics forecasts for domestic inflation and output.
  - Second stage: PVAR with forward-mean differencing (Helmert) and system GMM to assess how deviations from historical policy rules respond to base-country interest rate changes.
  - Monthly sample January 2000 through October 2015 for 40 emerging and advanced economies (euro-area countries excluded); sample restricted to open and mid-open capital accounts.
  - Subsamples: floating exchange rates (2,178 observations) and pegged or soft-pegged exchange rates (3,616 observations).
  - Responses rescaled to a 100-basis-point increase in base-country rate after one year.
- Panel results:
  - Floating exchange rates: autonomy-impairing spillover response = 6 basis points after six months, indistinguishable from zero at a 10% confidence level.
  - Soft or hard peg: cumulative response after six months ≈ 38 basis points, with 90% confidence band from 24 to 53 basis points.
- Conclusion: Findings are consistent with the trilemma—autonomy-impairing spillovers significantly larger for pegged exchange rates; no evidence of autonomy-impairing spillovers among countries with floating exchange rates.

### Estimation, inference, and robustness
- Inference:
  - Draws of coefficient matrices used to re-calculate impulse-responses are generated using estimated coefficients and their variance-covariance matrix; repeated 2,000 times to obtain 5th and 95th percentiles for confidence bands.
  - Figures report cumulative spillover responses to a 100-basis-point increase in the base country policy rate with 90 percent confidence bands.
- Robustness checks:
  - Alternative base-country classification (Shambaugh (2004) mapping): euro area used for Sweden and United Kingdom in robustness exercise; results broadly consistent—no significant autonomy-impairing spillovers detected for United Kingdom; for Sweden larger spillovers from the euro area under Method V but Method VI indicates no additional response beyond time-varying inward-looking policy function.
  - Use of identified monetary policy surprises versus realized changes: identified surprises generate larger gross spillovers under methods that do not purge endogenous domestic responses, but the two-stage approach (Method VI) again yields substantially smaller and statistically insignificant autonomy-impairing spillovers.

### Data: country series coverage and forecast inputs
- Country short-term interest rate series constructed with interpolation and splicing where necessary; sample windows and specific series preserved as in the source (examples):
  - Argentina: March 2002 – June 2015: BCRA 6-month Treasury auction yields in new pesos (GFD). Interpolated using BCRA 1-year treasury auction yields in new pesos (GFD) and 2-year treasury auction yields in new pesos (GFD).
  - Australia: January 1998 – October 2015: 13-week treasury bills (IFS line 19360C..ZF...). Interpolated and spliced using 3-month generic government bond yield (Bloomberg ticker GACGB3M) and 1-year generic government bond yield (Bloomberg ticker GACGB1).
  - Canada: January 1998 – October 2015: Treasury bill rate (IFS line 15660C..ZF...). Interpolated using 6-month government bond yield (Bloomberg GCAN6M). Spliced using 3-month government bond yield (Bloomberg GCAN3M).
  - New Zealand: January 1998 – October 2015: 3-month treasury bill new issue rate (IFS line 19660C..ZF...). Interpolated using 6-month treasury bill yield (Bloomberg ticker NDTB6M).
  - United Kingdom: January 1998 – October 2015: Treasury bill rate (IFS line 11260C..ZF...).
  - (Full list and interpolation/splicing rules preserved in source.)
- Domestic macroeconomic controls:
  - For all countries: January 1998 – October 2015: mean forecast for consumer price inflation and real GDP growth provided by Consensus Economics at monthly frequency.
  - Fixed-point forecasts for current and following year linearly interpolated to form a fixed horizon forecast at a horizon of 12 months.

### Policy-relevant implications and concluding points
- Empirical approaches that do not explicitly purge domestic policy responses to domestic inflation and output outlooks tend to overstate autonomy-impairing spillovers.
- A conservative two-stage approach that:
  1. isolates residual movements in domestic policy rates orthogonal to domestic inflation and output outlooks, and
  2. then assesses the extent to which those residuals are driven by foreign financial conditions,
  produces substantially smaller estimated autonomy-impairing spillovers.
- Results:
  - For the six small open economies studied, estimated autonomy-impairing spillovers are typically small (about 10 basis points after 12 months for most countries) and often statistically indistinguishable from zero.
  - Panel evidence: floating exchange rate regimes exhibit negligible autonomy-impairing spillovers (6 basis points after six months, not significant at 10%); pegged regimes show sizable spillovers (≈38 basis points after six months).
- Interpretation: Findings are consistent with the trilemma—exchange rate flexibility is associated with greater monetary policy autonomy in the face of base-country monetary shocks.

*Source: IMF Working Paper WP/16/108, "Global Financial Conditions and Monetary Policy Autonomy" (Sections 1–6).*

### Section 1

### Global Financial Conditions and Monetary Policy Autonomy

### Abstract
- WP/16/108; June 2016.
- Research question: Is the Mundell-Fleming trilemma alive and well? International co-movement of asset prices and synchronized business cycles complicate identification of financial spillovers and assessments of monetary policy autonomy.
- Benchmark null hypothesis: central banks respond only to the outlook for domestic inflation and output.
- Main findings:
  - Common approaches to estimate interest rate spillovers tend to understate the degree of monetary autonomy enjoyed by small open economies with flexible exchange rates.
  - Proposed empirical strategy partials out spillovers associated with impaired monetary autonomy.
  - Using this approach, evidence that flexible exchange rates deliver monetary autonomy is more compelling than prior work has suggested.
- JEL Classification Numbers: C13, C15, E32, E43, E47, E52, E58, F44.
- Keywords: Monetary policy; monetary conditions; autonomy; global financial cycle.

### I. INTRODUCTION
- Stylized fact: Domestic financial conditions in small open economies tend to move in tandem with those prevailing abroad; strong co-movement in interest rates across countries, particularly at short maturities.
- Two possible interpretations of interest-rate co-movement:
  - Limited monetary autonomy (spillovers).
  - Fully independent central banks reacting to synchronized and interdependent economic cycles.
- Challenge highlighted (Bernanke, 2015): establish a benchmark degree of co-movement beyond which a small open economy lacks monetary autonomy.
- Key conceptual distinction:
  - Interest rate interdependence / pass-through: correlation due to common shocks and synchronized cycles.
  - Monetary policy spillovers: movements in domestic interest rates triggered by foreign monetary policy.
- Two empirical challenges in assessing autonomy via spillovers:
  1. Simultaneity of international asset prices complicates identification of foreign interest rate shocks.
  2. Endogenous response of domestic macroeconomic outlook following foreign interest rate changes, which may legitimately call for domestic policy responses.
- Definition: autonomy-impairing spillovers are the subset of domestic rate responses to foreign shocks that are above and beyond what can be explained by pursuit of domestic objectives.
- Empirical strategy overview:
  - Reverse the problem by starting from the domestic monetary policy reaction function.
  - Two-stage estimation of VAR models:
    - Stage 1: impose benchmark null that central bank exclusively pursues domestic output and price stabilization.
    - Stage 2: estimate impact of foreign interest rate movements on deviations of domestic rates from fitted values.
  - Comparison with alternative methods using simulated and actual data.
- Monte Carlo exercise:
  - Artificially generate macroeconomic and interest-rate series for ‘base’ and ‘small’ stylized economies.
  - Both central banks follow inward-looking policy rules (react exclusively to domestic conditions); by construction no autonomy-impairing spillovers.
  - Finding: methods used in the literature often reject full autonomy; the authors’ method does not reject null of full autonomy across wide parameterizations.
- Empirical coverage:
  - Country-by-country estimates for advanced small open economies with highly flexible exchange rates: Australia, Canada, New Zealand, South Korea, Sweden, United Kingdom.
    - Result: large and significant spillovers in levels, but autonomy-impairing spillovers much smaller and do not lead to rejection of monetary autonomy for several economies.
  - Panel VAR for 40 advanced and emerging economies:
    - Finding: autonomy greater in countries with floating exchange rates than with fixed exchange rates.
    - Autonomy-impairing spillovers are indistinguishable from zero in countries implementing floating exchange rate regimes.
- Scope limitation: focus on autonomy to set short-term interest rates (short end of yield curve); recognizes that transmission to longer rates, credit, and real activity may differ and are beyond this paper’s scope.

### II. THE ELUSIVE CONCEPTS OF MONETARY SPILLOVERS AND AUTONOMY
- Common empirical approach (Method I):
  - Regress changes in domestic policy rate on changes in foreign (base country) policy rate:
    - An estimated coefficient significantly different from zero has been interpreted as evidence of lack of monetary policy autonomy.
  - Caution: high co-movement can arise from synchronized business cycles (common shocks to oil prices, climate, global demand), so a nonzero coefficient ߚ̂ does not necessarily imply impaired autonomy.
- Augmented approach (Method II):
  - Include vector of controls X_t to isolate monetary policy spillovers:
    - Choice of X_t is critical because ߚ̂ is measured relative to the benchmark captured by X_t.
    - In principle, a sufficiently large X_t that fully characterizes movements in the domestic policy rate will imply complete autonomy.
- Normative guidance for X_t:
  - Ground choice in central bank’s stated objectives: inflation (π_t) and economic activity/output (y_t).
  - Literature foundation: optimal monetary policy in open economies (Svensson; Clarida, Galí, and Gertler) implies policy targeting a linear combination of inflation and the output gap.
- Theoretical debate on including external variables:
  - Woodford (2007) and related work: globalization need not affect the ability of a Taylor rule on inflation and output gap to control domestic inflation; no need for international policy coordination in many settings.
  - Caveats where external variables may matter:
    - de Paoli (2009): terms-of-trade externalities can imply central bank loss function includes real exchange rate.
    - Engel (2011): local-currency pricing can make addressing exchange rate misalignment welfare-enhancing, though resulting instrument rules may still be simple functions of domestic prices.
    - Fujiwara et al. (2013): similar conclusions in global liquidity trap context.
  - General conclusion: even where theory suggests additional objectives, the weight on them is typically found to be small.
- Empirical literature consensus: variables included in X_t have generally followed the view that domestic inflation and output are the central policy-relevant controls.

*Source: IMF Working Paper WP/16/108, "Global Financial Conditions and Monetary Policy Autonomy" (Section 1).*

### Section 2

### _wp16108 - Section 2

### Literature and conceptual framing
- Early and recent empirical approaches:
  - Clarida, Galí, and Gertler (1998) include expected inflation and industrial production in ࢄ௧ when estimating monetary policy reaction functions allowing for spillovers from foreign interest rates.
  - Klein and Shambaugh (2015), Obstfeld (2015), Hofmann and Takáts (2015), Aizenman, Chinn, and Ito (2015), and Edwards (2015) extend this literature by controlling for domestic inflation and output (or industrial production) when assessing monetary independence and the sensitivity of short-term interest rates to foreign rates.
- Conceptual definitions:
  - Spillovers ݏ௧ from global financial conditions are movements in domestic rates attributable to changes in global financial conditions: ݏ௧ = ߲݅௧߲݅௧∗.
  - Autonomy-impairing spillovers ݏ̅௧ are the subset of ݏ௧ not associated with domestic objectives—driven by shifts in ݃(݅௧∗) but not through impacts on ߨ or ݕ: ݏ̅௧ = ߲[݅௧|ߨ௧ݕ,௧]߲݅௧∗ = ߲݅௧߲݃·߲߲݃݅௧∗.
  - Presence of ݏ̅௧ (ݏ̅௧ ≠ 0) implies costly trade-offs for the central bank and evidence of limited monetary autonomy.

### Measuring autonomy-impairing spillovers: Monte Carlo design
- Simulation setup:
  - Two-economy structure: a ‘base’ economy and a ‘small’ open economy; shocks to base macro conditions (ܺ௧∗) can affect small-economy macro conditions (ܺ௧) but not vice versa.
  - Macro conditions in base and small economy follow autoregressive processes ((1) and (2) in the source).
  - Central banks follow inward-looking policy rules (equations (3) and (4)); small economy central bank reacts exclusively to domestic deviations when ߚ = 0.
  - No feedback from policy rates to macro conditions (monetary policy does not affect real activity or inflation in the simulation).
- Simulation particulars:
  - Using the baseline parameterization in Table 1 (parameters listed exactly in Table 1), the authors simulate 5,000 replications of ܺ௧∗, ܺ௧, ݅௧∗ and ݅௧, each containing 200 observations.

### Baseline parameterization (as in Table 1)
- Base country / Small open economy parameter values (exactly as in Table 1):
  - ߩ: 0.5 / 0.5
  - ߬: 0.5 / 0.5
  - ߪ: 1 / 1
  - ߠ: 0 / 0
  - ߙ: 1.25 / 1.75
  - ߜ: 0.5 / 0.5
  - ߛ: - / 1
  - ߚ: - / 0

### Key simulation statistics (from Table 2)
- Average correlations between simulated time series using baseline parameter values:
  - Corr(݅௧, ݅௧) = 1.00
  - Corr(݅௧, ݅௧∗) = 0.46
  - Corr(݅௧, ܺ௧) = 0.98
  - Corr(݅௧, ܺ௧∗) = 0.47
  - Corr(݅௧∗, ݅௧∗) = 1.00
  - Corr(݅௧∗, ܺ௧) = 0.50
  - Corr(݅௧∗, ܺ௧∗) = 0.97
  - Corr(ܺ௧, ܺ௧) = 1.00
  - Corr(ܺ௧, ܺ௧∗) = 0.51
  - Corr(ܺ௧∗, ܺ௧∗) = 1.00

### Empirical estimation approaches and results
- Method I (simple pass-through regressions):
  - Yields large and statistically significant estimated pass-through coefficient ߚመ, driven by high correlations between economies’ cycles even when ߚ = 0 in the DGP.
  - Historical literature (e.g., Shambaugh (2004), Obstfeld, Shambaugh, and Taylor (2005)) used similar methods and found large ߚመ for pegged and sometimes non-pegged countries (about 0.3, rising above 0.5 when sample restricted to countries with no capital controls).
- Method II (including domestic macroeconomic conditions as regressors):
  - Under baseline parameterization, estimated ߚመ = 0.36; the lower bound of its 95% confidence interval is 0.25.
  - Conclusion under baseline: estimation leads to rejection of the null of no autonomy-impairing spillovers despite the DGP being designed with complete monetary autonomy (ߚ = 0).
  - Sensitivity to parameterization:
    - If there is no inertia in Taylor rules (scenarios 2 and 3), ߚመ is indistinguishable from zero at a 5% confidence level.
    - Larger noise in the base-country policy rule (larger ߠ∗, scenario 1) reduces bias but ߚመ can remain significantly different from zero.
    - If foreign macro shocks are large relative to domestic shocks, ߚመ can exceed 0.75 and be highly significant.
  - These results help explain wide empirical heterogeneity in the literature (e.g., Klein and Shambaugh (2015), Obstfeld (2015), Hofmann and Takáts (2015), Edwards (2015)).

### Monte Carlo spillover estimation table highlights (structure and interpretation)
- Table 3 reports cumulative spillover response from ݅∗ to ݅ after 12 periods following an increase of 100-basis points in ݅∗. “*” denotes significance at a 5% confidence level.
- Main points illustrated by Table 3:
  - Under the baseline scenario and many parameter variants, simple single-equation and structural VAR estimates often indicate statistically significant spillovers, even when the true DGP has ߚ = 0.
  - The magnitude and significance of estimated spillovers vary substantially across scenarios that change persistence, shock variances, and linkage parameter ߛ.

### Implications for empirical work and alternative approach
- Identification and endogeneity concerns:
  - Estimating ߚመ is complicated by endogeneity between ݅௧ and regressors ࢄ௧ and ݅௧∗ (e.g., unobserved common shocks) and by dynamic relationships with lags.
  - These issues make it difficult to partial out the systemic domestic response to domestic macro conditions.
- Recommendation and alternative modeling:
  - Modeling the domestic policy rule explicitly—using VAR models that accommodate rich dynamics—can help address endogeneity and identification concerns.
  - The authors adopt a reduced-form VAR(p) representation (Method IV) for Δ݅∗ and Δ݅, with parsimonious lag structure (݌ = 2 given the DGP).
  - If the domestic economy is sufficiently small, coefficient matrices can be restricted to enforce block exogeneity of Δ݅∗ (base rates not affected by small-country rates), and identification of monetary policy shocks can be obtained via timing restrictions on innovations (assuming policy affects the real economy with a lag).
  - Spillovers are then measured by impulse responses of Δ݅ following an orthogonalized shock to Δ݅∗.

*Source: _wp16108 - Section 2, https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16108.pdf*

### Section 3

### _wp16108 - Section 3

### Identification challenges in VAR estimation of spillovers
- Timing assumptions to identify structural shocks to ݅Δ∗ are not credible when financial variables (e.g., interest rates) are endogenous and respond simultaneously to excluded information.
- A shock to global demand may affect monetary policy in both the large and the small economy within the period it occurs, creating simultaneity.
- Standard VAR approaches do not permit estimation of the partial effect of a shock from ݅∗ on ݅ that excludes the endogenous response of ࢄ.
- Using high-frequency market-price identification captures unanticipated monetary decisions but:
  - May not yield shocks orthogonal to global economic conditions; simultaneity can remain.
  - Identified shocks may be highly correlated across countries, capturing real and financial interlinkages as well as policy decisions.
- Monetary policy shocks in the base country likely affect expected economic conditions in the small economy; to assess monetary autonomy based on interest rate spillovers one must exclude the endogenous response of ݅ to ࢄ.

### Proposed solution: reverse problem and two-stage VAR (Method VI)
- Strategy: model the domestic monetary policy reaction function to partial out systematic policy responses to domestic macroeconomic conditions.
- Step 1 — Estimate a Taylor-type rule for dynamic relationship between domestic interest rates and domestic macroeconomic conditions:
  - Equation: ቂ ࢄ∆ ݅Δ ቃ ௧ ࡭ = ଴ ൅ ∑ ࡭ ௝ ௣ ௝ୀଵ ቂ ࢄ∆ ݅Δ ቃ ௧ି௝ ൅൤ ࢋ ࢄ ݁ ௜ ൨ ௧ .
  - Ordinary least squares ensures reduced-form innovations ࢋොࢄ and ݁̂ ௜ are orthogonal to lagged values of ࢄ∆ and ݅Δ, though contemporaneous correlation may persist.
- Step 2 — Purge monetary policy innovations of contemporaneous correlation:
  - Regress ݁̂ ௜ on ࢋොࢄ: ݁̂ ௜ =ߙ൅ࢼ ᇱ ࢋොࢄ ݑ൅ ௧ ௜ .
  - Residuals ݑො ௧ ௜ are orthogonal to reduced-form innovations to domestic economic conditions (timing restriction: expectations about the domestic outlook are predetermined with respect to monetary policy).
  - Interpret ݑො ௧ ௜ as deviations from the central bank’s historical policy reaction function (deviations from pursuit of price and output stabilization).
- Step 3 — Quantify extent residual movements in domestic interest rates are driven by foreign interest rates:
  - Estimate a VAR(p): ൤ ݅Δ∗ ݑො ௧ ௜ ൨ ௧ ࡮ = ଴ ൅ ∑ ࡮ ௝ ௣ ௝ୀଵ ൤ ݅Δ∗ ݑො ௧ ௜ ൨ ௧ି௝ ൅൤ ݒ ௜ ∗ ݒ ௜ ൨ ௧ .
  - Impose block exogeneity of ݅Δ∗ via restrictions on ࡮ ௝ and identify autonomy-impairing spillovers as the response of ݑො ௧ ௜ to a shock to ݅Δ∗ using Cholesky timing restriction.

### Alternative methods and their limitations
- Method IV (single-equation pass-through): estimates large, significant spillovers driven by correlation in macro conditions; under baseline parameterization the 95 percent confidence interval for the spillover estimate lies above 15 basis points (about ¼ of the increase in interest rates in the base country).
- Method V (VAR including ࢄ): inclusion of ࢄ does not reduce the magnitude of the response of domestic to foreign interest rates because estimated impact allows for endogenous response through ࢄ; may lead to erroneous conclusion that monetary autonomy is limited.
- Two-stage single-equation (Method III):
  - Stage 1: regress domestic interest rates on domestic macro conditions: ݅∆ ௧ ܺ∆ߩ൅ߙൌ ௧ ݑ .
  - Stage 2: regress residuals ݑො ௧ on foreign interest rates ݅∆∗: ݑො ௧ ݅∆ߚ൅ߙൌ ௧ ∗ ݒ .
  - Method III can reduce bias compared with Method II: the two-stage estimate for ߚመ is always closer to zero (the true value ሻߚ) and is about 40% smaller than under method II.
  - Nevertheless, the proxy for lack of monetary autonomy remains positive and statistically significant, highlighting the need for richer dynamics in modeling.

### Monte Carlo simulation results (summary)
- Figure 1 (Monte Carlo): cumulative responses following an orthogonalized shock to base country interest rates.
  - Panel A: response of ݅Δ∗ rises approximately 65 basis points after one year.
  - Panel B (Method IV): cumulative impulse response of ݅∆௧ large and similar to Method I estimates; 95 percent confidence interval above 15 basis points under baseline parameterization.
  - Panel C (Method V): inclusion of ࢄ does not reduce estimated spillover; impact allows endogenous response through ࢄ.
  - Panel D (Method VI): estimated response of domestic interest rates to changes in base economy rates is statistically indistinguishable from zero; no evidence of autonomy-impairing spillovers under data-generating assumptions.
- Method VI result (no autonomy-impairing spillovers) holds across alternative parameterizations reported in Table 3.

### Empirical application: assessing monetary autonomy in six small open economies
- Sample and focus:
  - Countries: Australia, Canada, New Zealand, South Korea, Sweden, United Kingdom.
  - Monthly data from January 1998 to June 2009 (to avoid period with U.S. policy rates at zero lower bound).
  - Focus: spillovers from changes in the U.S. federal funds rate to domestic short-term interest rates (Treasury bills maturity between 3 and 6 months).
  - Responses rescaled so response of base-country interest rate after 12 months is 100 basis points.
- Choice of domestic macro controls:
  - Theory suggests inflation and output sufficient for optimal policy reaction function.
  - At monthly frequency: consumer price inflation and industrial production as proxy for output.
  - Monetary authorities react to changes in economic outlook; therefore use expectations of private forecasters (Consensus Economics) to construct fixed horizon forecasts for expected evolution over the following 12 months.
- Figure 2 results (impulse responses to a shock generating a 100-basis-point increase in U.S. federal funds rate over 12 months):
  - Using Method V:
    - Estimated spillover significantly larger than zero after 12 months for all six countries.
    - Magnitudes range from 30 to 60 basis points.
    - Interpreted as central banks responding about one-for-two to U.S. monetary policy shocks.
  - Methods I and II (pass-through and single-equation):
    - For Australia, South Korea, United Kingdom: cumulative VAR responses similar after 12 months to single-equation spillovers.
    - For Canada, New Zealand, Sweden: structural VAR generates considerably larger spillover estimates than single-equation methods.
  - Method VI (multi-stage VAR using residuals from inward-looking policy rule):
    - Grey lines show autonomy-impairing spillovers using Method VI; substantially smaller than overall spillovers.
  - Method VI (RW) — rolling-window parameters in policy rule:
    - Allowing parameters to vary over time (rolling window estimations) can matter.
    - For New Zealand, Sweden, United Kingdom: Method VI and Method VI (RW) results are indistinguishable.
    - For Canada and South Korea: Method VI and Method VI (RW) differ substantially, suggesting parameter variation in central bank reaction functions over estimation period.
- Key empirical takeaway:
  - Autonomy-impairing spillovers estimated using the multi-stage VAR from Method VI tend to be substantially smaller than overall spillovers, especially when allowing the parameters of the policy rule to vary over time.

*Source: _wp16108 - Section 3*

### Section 4

### _wp16108 - Section 4

### Estimates of autonomy-impairing spillovers (methods V and VI)
- After 12 months, the response (autonomy-impairing spillover) is about 10 basis points for most countries, and is indistinguishable from zero at a 5% confidence level in Australia, South Korea, and Sweden.
- In Canada and New Zealand, autonomy-impairing spillovers are around 25 basis points after 12 months, but are roughly half the size of the overall spillovers estimated using method V.
- Method VI uses a multi-stage VAR; standard errors for IRFs are computed analytically with shaded regions indicating 95 percent confidence intervals. Because one endogenous variable is estimated in a previous step, standard errors would need a bootstrap procedure, likely widening the confidence intervals further.
- The first and second stages of method VI are estimated in a rolling window of 60 months.
- Interpretation: Unlike method V, method VI results suggest monetary policy in these open economies is not substantially influenced by U.S. monetary policy beyond what can be attributed to a standard inward-looking policy function. The estimations do not allow rejection of the null hypothesis that these central banks are following an autonomous policy rule that ignores global financial conditions Δ∗.

### Robustness: alternative base-country classification and results
- Robustness check: responses of local policy rates are estimated to changes in the monetary policy rate of their closest base country as classified by Shambaugh (2004): the euro area for Sweden and the United Kingdom, and the United States for others.
- United Kingdom: estimates broadly in line with earlier results; no significant autonomy-impairing spillovers detected.
- Sweden: method V suggests much larger spillover responses from the euro area, consistent with high business cycle synchronization between Sweden and the euro area. However, estimates indicate Swedish monetary policy displays no additional response to ECB monetary policy beyond what a time-varying inward-looking policy function accounts for—suggesting a high degree of autonomy aligned with exchange rate flexibility.
- Note: Deutsche Bundesbank rate is used before January 1999 for euro-area shocks; Shambaugh (2004) classifies Australia as core for New Zealand but the exercise does not consider Australian monetary policy spillovers for New Zealand here.

### Identification of monetary policy shocks and timing issues
- Realized changes in U.S. monetary policy rates may be anticipated by markets and lead to asset price changes ahead of rate changes; this can invalidate timing assumptions and lead to underestimation of spillovers.
- Identified monetary policy surprises (Kuttner 2001; Hanson and Stein 2015; Gertler and Karadi 2015; Gilchrist, López-Salido and Zakrajsek 2015) use changes in asset prices in tight windows around FOMC announcements; by construction, these surprises are orthogonal to market expectations at announcement time.
- Limitations of identified surprises:
  - If domestic central banks adjust rates in response to foreign-driven changes in domestic inflation/output, such adjustments are endogenous and do not constitute autonomy-impairing spillovers; using identified shocks without properly accounting for domestic conditions can bias autonomy assessments.
  - Identified shocks may not be fully orthogonal to global economic conditions because Federal Reserve surprises may reflect U.S. or global cyclical information; simultaneity between cycles can remain, potentially exacerbated if the Fed acts on private information. Evidence suggests deviations between Greenbook forecasts and private forecasts are correlated with identified shocks, though explaining a small share of variation.

### Results using U.S. monetary policy surprises (Gertler and Karadi 2015)
- Using surprises in futures contracts for short-term rates around FOMC announcements (Gertler and Karadi 2015):
  - Method V generally generates much larger spillover estimates than when using all realized movements in the Federal Funds rate—i.e., unanticipated rate movements produce substantially larger spillovers to foreign short-term rates.
  - In New Zealand, South Korea, and the United Kingdom, the magnitude of estimated spillovers more than doubles when using identified surprises.
  - Method VI (multi-stage VAR removing endogenous responses to domestic macro conditions) shows that impacts of U.S. monetary surprises are substantially smaller and in all cases indistinguishable from zero at a 5% confidence level.
  - Canada: spillover estimate is about one-to-one using identified shocks (similar to Rey 2014), but after removing the endogenous response to domestic macro conditions the spillover estimate is only half as large; still unable to reject the null hypothesis of full monetary autonomy at a 5% confidence level.

### Revisiting the trilemma with panel evidence
- The trilemma: exchange rate flexibility and capital account openness determine monetary policy autonomy; to target domestic objectives with open capital accounts, exchange rates must float or capital controls must be imposed.
- Literature overview: mixed empirical results; some studies find floating countries still follow base country rates, others find floating regimes consistent with autonomy.
- Methodology used:
  - First stage: estimate inward-looking policy rules for each country as a function of private forecasts for domestic inflation and output.
  - Second stage: use a panel vector autoregressive (PVAR) model to assess how much deviations of domestic rates from historical policy rules are attributable to base country interest rate changes. The specified first-order process includes country fixed effects and employs forward-mean differencing (the Helmert procedure) to preserve orthogonality and enable system GMM estimation.
  - Monthly data constructed from January 2000 through October 2015 for 40 emerging and advanced economies (euro-area countries excluded). Selection and classification largely follow Klein and Shambaugh (2015), Shambaugh (2004), and Chinn and Ito (2006). Base-country choices follow Reinhart and Rogoff (2004) adjustments for New Zealand and Singapore.
  - Sample restricted to observations with open and mid-open capital accounts. Subsamples: floating exchange rates (2,178 observations) and pegged or soft-pegged exchange rates (3,616 observations). Cumulative Cholesky-orthogonalized impulse response functions computed with base-country rates ordered as most exogenous.
- Panel results (following a 100-basis-point increase in the base country interest rate after one year):
  - Floating exchange rates: autonomy-impairing spillover response of domestic rates is 6 basis points after six months, indistinguishable from zero at a 10% confidence level.
  - Soft or hard peg: cumulative response after six months is about 38 basis points, with the 90% confidence band ranging from 24 to 53 basis points.
- Conclusion: Findings are consistent with the trilemma—autonomy-impairing spillovers from base country to domestic interest rates are significantly larger for pegged exchange rates, and the null hypothesis of full monetary autonomy cannot be rejected among countries with floating exchange rates.

*Source: _wp16108 - Section 4*

### Section 5

### _wp16108 - Section 5

### Estimation and inference procedures
- A draw of coefficient matrices ࡮଴ and ࡮ଵ in equation (5) is randomly generated using the estimated coefficients and their variance-covariance matrix and used to re-calculate impulse-responses.
- The process is repeated 2,000 times to generate 5th and 95th percentiles of this distribution, which are used as confidence bands for the impulse-responses.
- Figures report cumulative spillover response of domestic short-term interest rates to a 100-basis-points increase in the base country policy rate.
- Figures show a 90 percent confidence band around the estimated impulse responses.

### Country sample for the panel VAR estimation (Table 4)
- Advanced economies:
  - Australia
  - Canada
  - Czech Republic
  - Denmark
  - Hong Kong
  - Japan
  - Latvia
  - New Zealand
  - Norway
  - Singapore
  - South Korea
  - Sweden
  - Switzerland
  - United Kingdom
- Emerging and developing economies:
  - Argentina
  - BoliviaBrazil
  - Bulgaria
  - Chile
  - China
  - Colombia
  - Costa Rica
  - Croatia
  - EgyptHungary
  - India
  - IndonesiaIsrael
  - Mexico
  - Malaysia
  - Peru
  - Philippines
  - Poland
  - Romania
  - Russia
  - Saudi Arabia
  - South Africa
  - Thailand
  - Turkey
  - Vietnam

### Key conceptual points and challenges
- International asset prices are highly correlated across countries and asset classes; extensive literature documents pass-through of U.S. monetary policy to domestic interest rates in other countries.
- A benchmark for assessing monetary autonomy: policy rates are set exclusively as a function of the outlook for domestic inflation and outlook.
- Spillovers that reflect impaired monetary autonomy correspond to responses to global financial conditions that cannot be accounted for by this endogenous domestic relationship.
- In the presence of business cycle synchronization, identifying spillovers that reflect lack of monetary autonomy is challenging because the endogenous relationship between foreign interest rates, foreign macroeconomic conditions, and local macroeconomic conditions makes it difficult to identify the monetary spillover channel.
- Using a Monte Carlo simulation on artificial data, the paper shows that empirical approaches commonly employed in the literature tend to understate the extent of monetary autonomy under common parameterizations.

### Proposed two-stage (conservative) approach to assess monetary autonomy
- Stage 1: Model monetary policy in the small open economy to identify movements in domestic interest rates that are orthogonal to the outlook for domestic output and inflation.
  - Implementation in the paper: estimate a domestic system where monetary policy rates are dynamically determined by local macroeconomic conditions according to an inward-looking policy rule.
  - Residuals from this domestic policy rule capture movements in the policy rate not explained by domestic output and inflation outlook.
- Stage 2: Estimate spillovers in a separate model where foreign financial variables are allowed to explain the residuals from the domestic policy rule.
  - Significant spillover estimates in this second stage are interpreted as evidence that monetary autonomy is limited.

### Empirical findings (selected)
- Sample of six small open economies examined in detail: Australia, Canada, New Zealand, South Korea, Sweden, and the United Kingdom.
  - Using the two-stage approach, estimated spillovers are substantially smaller than spillovers estimated using methods employed in the literature.
  - In several cases, the null hypothesis that monetary policy is fully autonomous cannot be rejected.
  - Differences remain important when considering U.S. monetary policy surprises measured using high-frequency event windows.
- Panel estimates across a broad sample of advanced and emerging economies:
  - Responses of domestic interest rates to base country monetary policy shocks are much larger in countries with fixed exchange rate regimes.
  - No evidence of autonomy-impairing spillovers among countries with floating exchange rates, providing strong evidence for the predictions of the trilemma.

### Conclusion (summary)
- Empirical literature documents global pass-through of U.S. policy to other countries’ interest rates, but co-movement is not necessarily excessive relative to a benchmark where policy rates respond only to domestic outlook.
- Common empirical methods may understate monetary autonomy because endogenous international macro links obscure the spillover channel.
- A conservative two-stage approach that first isolates domestic-policy-rule residuals and then assesses foreign financial influences on those residuals produces smaller estimated spillovers and, for floating exchange rate regimes, finds no evidence of autonomy-impairing spillovers.
- Results are consistent with trilemma predictions: fixed exchange rate regimes are associated with much larger responses of domestic rates to base country monetary shocks; floating regimes show limited autonomy-impairing spillovers.

### Data appendix (selected series and sample windows)
- Short-term government bond yield in local currency series and their sample windows are constructed and documented for each country.
- Example entries (format preserved as in the source):
  - Argentina: March 2002 – June 2015: BCRA 6-month Treasury auction yields in new pesos (GFD). Interpolated using BCRA 1-year treasury auction yields in new pesos (GFD) and 2-year treasury auction yields in new pesos (GFD).
  - Australia: January 1998 – October 2015: 13-week treasury bills (IFS line 19360C..ZF...). Interpolated and spliced using 3-month generic government bond yield (Bloomberg ticker GACGB3M) and 1-year generic government bond yield (Bloomberg ticker GACGB1).
  - Brazil: January 2000 – November 2015: Treasury bill rate (IFS line 22360C..ZF...). Interpolated using Anbima 6-month government bond fixed (Bloomberg ticker BZAD6M) and 6-month generic government bond yield (Bloomberg ticker GEBR06M). Spliced using Anbima 3-month government bond fixed (Bloomberg ticker BZAF3M).
  - Canada: January 1998 – October 2015: Treasury bill rate (IFS line 15660C..ZF...). Interpolated using 6-month government bond yield (Bloomberg GCAN6M). Spliced using 3-month government bond yield (Bloomberg GCAN3M).
  - China: January 2000 – October 2015: 3-month treasury bond trading rate proxy (OECD MEI series 924.IR3TIB01.ST). Spliced using 3-month repo on treasury bills in renminbi (GFD) and prime lending rate (People’s Bank of China via Haver Analytics).
  - Japan: January 2000 – November 2015: 6-month treasury discount bill yield (Bloomberg ticker GJTB6MO). Interpolated using 3-month treasury discount bill yield (Bloomberg ticker GJTB3MO). Spliced using Financing bill rate (IFS line 15860C..ZF...).
  - New Zealand: January 1998 – October 2015: 3-month treasury bill new issue rate (IFS line 19660C..ZF...). Interpolated using 6-month treasury bill yield (Bloomberg ticker NDTB6M).
  - Norway: January 2000 – November 2015: 6-month government treasury bill yield (Bloomberg ticker GNGT6M).
  - Peru: January 2000 – November 2015: 6-month generic government bond yield (Bloomberg ticker GRPE6M). Interpolated using 3-month zero coupon bond yield (Bloomberg ticker I36103M). Spliced using central bank discount rate in new sol (GFD).
  - Philippines: January 2000 – October 2015: 91-day treasury bill rate (IFS line 56660C..ZF...).

*Source: _wp16108 - Section 5*

### Section 6

### _wp16108 - Section 6

### Country-level short-term interest rate series: data coverage, interpolation, and splicing
- Interpolated using PDEX PDST-F Fixing 3-months (Bloomberg ticker PDSF3MO).
- Poland:
  - January 2000 – November 2015: Treasury bill rate (IFS line 96460C..ZF...).
  - Interpolated using 1-year government note yield in new zloty (GFD) and 1-year government note yield (Bloomberg ticker POGB1YR).
- Romania:
  - January 2000 – September 2015: 91-day treasury bill rate (IFS line 96860C..ZF...).
  - Spliced using 3-month treasury bill yield in new leu (GFD).
- Russia:
  - January 2000 – October 2015: 3-month treasury bill yield in ruble (GFD).
  - Interpolated using 1-year government bond yield in ruble (GFD) and 6-month government bond yield in ruble (GFD).
  - Spliced using 1-week repo OMO auction rate (Haver Analytics).
- Saudi Arabia:
  - January 2000 – October 2015: 13-week treasury bill rate (Saudi Arabian Monetary Authority via Haver Analytics).
  - Spliced using 12-month treasury bill yield in riyal (GFD), 26-week treasury bill rate (IMF MBTS line 45660CC.ZN...), and reverse repo rate (IMF MBTS).
- Singapore:
  - January 2000 – November 2015: 3-month treasury bill yield (IFS line 57660C..ZF...).
  - Interpolated using Monetary Authority of Singapore paper 3-month yield (Bloomberg ticker MASB3M) and 6-month yield (Bloomberg ticker MASB6M).
- South Africa:
  - January 2000 – November 2015: 91-day treasury bill tender rate (South African Reserve Bank via Haver Analytics).
  - Interpolated using same concept from alternative sources (MBRF2 line 19960C..ZI... and OECD MEI series 199.IR3TIB01.ST).
  - Spliced using 2-year government bond yield (Bloomberg ticker GSAB2YR).
- South Korea:
  - January 1998 – October 2015: KCMP treasury bond yield (Bloomberg ticker GVSK3MON).
  - Spliced using 3-year government bond yield in won (GFD).
- Sweden:
  - January 1998 – October 2015: 3-month treasury bill yield (Sveriges Riksbank via Haver Analytics).
  - Interpolated using 6-month treasury bill yield (Bloomberg ticker GSGT6M) and 3-month treasury bill yield (Bloomberg ticker GSGT3M).
- Switzerland:
  - January 2000 – November 2015: Treasury bill rate (IFS line 14660C..ZF...).
  - Interpolated using 1-year government bond yield (Bloomberg ticker GSWISS03) and 1-year government bond yield (Bloomberg ticker GSWISS01).
- Thailand:
  - January 2000 – November 2015: Government bill yields (IFS line 57860C..ZF...).
  - Interpolated using Thai bond dealing center 1-month rate (Bloomberg ticker TBDC1M) 6-month rate (Bloomberg ticker TBDC6M).
- Turkey:
  - January 2000 – November 2015: 3-month treasury bill rate (MBRF2 line 18660C..YI...).
  - Interpolated using 6-month government bond yield (Bloomberg tickers IESM6M and IECM6M).
- United Kingdom:
  - January 1998 – October 2015: Treasury bill rate (IFS line 11260C..ZF...).

### Domestic macroeconomic conditions: forecast inputs and construction
- All countries:
  - January 1998 – October 2015: Mean forecast for consumer price inflation and real GDP growth provided by Consensus Economics at monthly frequency.
  - Fixed-point forecasts for current and following year linearly interpolated to form a fixed horizon forecast at a horizon of 12 months.

*Source: _wp16108 - Section 6*

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