## wp17204 — Sections 1–4

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### Introduction: context, motivation, and headline findings
- Context and policy actions:
  - Following the 2008-09 financial crisis, U.S. policymakers deployed sizeable fiscal and monetary policy stimuli.
  - Monetary policy rates were sharply lowered, rapidly reaching the zero lower bound (ZLB), followed by quantitative easing (QE) in different phases:
    - QE1 (Nov2008-Mar2009): purchases of $600 billion of agency and mortgage-backed securities (MBS);
    - QE1 extended (Mar2009-Mar-2010): purchases of $750 billion of MBS;
    - QE2 (Nov2010-Jun2011): purchases of $600 billion of long-term treasury bonds;
    - Operation twist (Sep2011-Jun2012): purchases of $400 billion of treasury bonds of long maturities (72-360 months) and equivalent sale of short-term maturities (3-36 months);
    - QE3 (Sep 2012-Oct2014): Purchases of $40 billion per month.
  - Expansionary fiscal policy was deployed “beyond automatic stabilizers,” evident in the near 8-percentage points of GDP weakening of the fiscal balance between 2007 and 2009.
- Research question and approach:
  - Assess trade spillovers of the post-crisis U.S. policy mix by evaluating the joint impact of monetary and fiscal policy on the trade balance.
  - Motivation: prior literature focused heavily on monetary policy, often omitting fiscal policy and risking omitted-variable (attenuation) bias.
- Headline empirical findings:
  - Extraordinary monetary and fiscal policy measures following the 2008-09 financial crisis had a sizable impact on the trade balance.
  - Unprecedented monetary policy stimulus contributed to the strengthening of the U.S. trade balance (demand-diverting effects).
  - Overall policy mix led to a weakening of the U.S. external position in the immediate aftermath of the crisis because fiscal stimulus more than offset loose monetary policy.
  - Aggregate trade effects varied over time with timing differences between fiscal and monetary stimuli; overall positive spillovers in the immediate aftermath.
  - Trade spillovers differed by trading-partner exchange rate regimes:
    - De facto rigid regimes vis-à-vis the U.S. dollar benefited significantly from the overall policy stimulus.
    - Economies with flexible exchange rates experienced demand-diverting effects (opposite result).
  - Effects of policy shocks on the trade balance are significantly larger when monetary and fiscal policies are estimated jointly rather than individually.
- Policy implication:
  - Assess spillovers from the overall policy mix rather than focusing on individual policies to avoid attenuation bias.
  - With the U.S. economy approaching full employment, fiscal loosening coupled with monetary tightening is likely to lead to significant deterioration of the U.S. external position and—other things equal—overall positive trade spillovers to the rest of the world.

### Empirical approach: data, model, identification
- Data and sample:
  - Monthly data covering 1992m1-2016m9.
  - Monthly GDP series from Macroeconomic Advisors; trend obtained by applying a standard HP filter.
- Endogenous variable vector:
  - Yt = [ TB E S F R Y ]'
- Variable definitions and measurement:
  - Rt: 10 year U.S. treasury bond yield (long-term interest rate); baseline uses nominal yields; alternative specification uses real yields as robustness.
  - Ft: seasonally-adjusted federal government budget balance (U.S. Treasury), expressed in percent of trend GDP; seasonality adjusted by TRAMO/SEATS.
  - St: S&P 500 composite index (log).
  - Et: nominal effective exchange rate (NEER) from IFS (log).
  - TBt: seasonally-adjusted trade balance (net exports) from the Census Bureau, expressed in percent of trend GDP.
- Econometric model:
  - Structural VAR estimated; reduced-form VAR:
    - Yt = sum_{k=1}^{2} B_k Y_{t-k} + ε_t
  - Variables are cointegrated; VAR estimated in levels to incorporate cointegrating relationships.
  - Impulse responses examined for return to steady-state.
- Identification strategy:
  - Contemporaneous sign restrictions with orthogonality constraint using randomly drawn orthonormal matrices Q.
  - Identification assumptions:
    - Positive cyclical shock increases stock prices, bond yields, and the fiscal balance, and leads to an appreciation of the U.S. dollar.
    - Monetary shock increases bond yields, reduces stock prices, and leads to domestic currency appreciation.
    - Discretionary fiscal tightening leads to lower stock prices.
    - Identified fiscal shocks interpreted as implementation surprises (actual changes in fiscal balance leading to asset price movements).
  - Orthogonality: shocks required to be orthogonal following Mountford and Uhlig (2009).
- Additional notes:
  - Identification aims to avoid capturing inflation-expectation shocks as monetary policy shocks by relying on the sign pattern (yields up, stocks down).
  - Alternative lags and robustness checks (including real yields) explored.

### Identification approach and impulse response estimation
- Computational procedure:
  - Random draws of Q generated until 1,000 parameterizations satisfying sign restrictions are obtained.
  - Model is set-identified; impulse response functions are bounded due to a group of models satisfying sign restrictions.
  - Model selection follows Fry and Pagan (2010): select model with impulse responses closest to the median of admissible responses.
  - Confidence bands computed using the standard deviation across admissible responses.
- Rationale:
  - Avoid imposing restrictions without clear theoretical support; let data speak. Alternative identifying restrictions tested as robustness and yield similar results.

### Baseline results — monetary and fiscal impulses
- Monetary loosening (negative monetary policy shock; 1 percentage point fall in the 10-year yield):
  - Leads to a nearly 10 percent depreciation of the nominal exchange rate within 4-6 months.
  - Leads to a 1 percent of GDP strengthening of the trade balance within 4-6 months, with gradual fading.
  - Interpretation: short-run demand-diverting effect from dollar depreciation dominates any short-run demand-augmenting effect.
  - Note: 1pp shock equals 4 standard deviations of the monthly changes (illustrative, rather large).
- Fiscal tightening (1 percentage point of GDP drop in the fiscal balance):
  - No meaningful effects on the nominal exchange rate.
  - Entails a nearly 0.2 percent of GDP weakening of the trade balance within a year, dissipating gradually.
  - Interpretation: consistent with ‘twin deficits’; demand-reducing effect of fiscal tightening dominates any demand-diverting real appreciation effect.
- Estimation presentation:
  - Impulse responses plotted with months on horizontal axis and one standard deviation confidence bands.
  - Fiscal policy shock series reported as 6-month moving average.

### Results for EMDEs and decomposition of policy variables
- EMDE-focused specification:
  - Trade balance vis-à-vis EMDEs reveals larger and statistically more significant effects than baseline (all trading partners).
- Decomposition of fiscal balance (1992-2016):
  - Sharp deterioration of nearly 8 percentage point of GDP from 2007 to 2012 largely endogenous to the cycle, but with a meaningful exogenous component—especially immediately after the crisis.
- Decomposition of 10-year yield (1992-2016):
  - Much of monetary loosening post-crisis consistent with normal cyclical response; also significant extraordinary loosening before and immediately after the crisis.

### Contribution of policy shocks to the trade balance (1992-2016)
- Individual and joint contributions:
  - Both monetary and fiscal policy shocks had large effects on the trade balance after the 2008-09 crisis—larger and more sustained than in prior periods.
  - Monetary loosening contributed to strengthening of the trade balance with lasting effects.
  - Fiscal stimulus contributed to weakening of the trade balance in immediate aftermath; as fiscal stimulus was withdrawn, its weakening effect dissipated and reversed, contributing to positive impact from monetary policy.
- Quantified post-GFC contributions (Table 3 summary):
  - During 2009-12: policy mix entailed a weakening of the US trade balance of nearly -0.5 percent of GDP — fiscal stimulus contribution: -0.8 percent of GDP; monetary easing contribution: 0.3 percent of GDP.
  - During 2013-16: with withdrawal of fiscal support, monetary policy strengthening contribution: 0.4 percent of GDP.
  - For the whole post-crisis period, the policy-mix effect on the trade balance estimated to be broadly neutral.

### Robustness checks
- Summary of robustness exercises (Table 4):
  - Relax assumption that positive monetary shocks lead to nominal exchange rate appreciation.
  - Introduce VIX as a measure of risk appetite; assume risk-off reduces stock prices and bond yields and leads to U.S. dollar appreciation.
  - Use REER instead of NEER to link positive fiscal shock to REER appreciation (cost: monetary shock impact on REER less clear).
  - Alternative specification linking fiscal shocks to the 10-year rate (premise: fiscal tightening reduces the 10-year rate via improved debt sustainability).
  - Results: baseline conclusions confirmed across specifications with varying statistical significance.
  - Model results hold with a 3-lag structure as well.

### Extensions: policy mix, price vs quantity effects, and exchange-rate-regime spillovers
- A. Policy mix versus single policies:
  - Joint identification of monetary and fiscal shocks yields much larger effects than estimating one policy at a time.
  - Fiscal impulse responses can change sign when estimated jointly with monetary policy—monetary shocks tend to dominate fiscal effects.
  - Controlling for the other policy tool is key to uncovering full effects; omission causes attenuation bias.
  - EMDE trade-balance focus minimizes problems from uncontrolled trading-partner policies.
- B. Price versus quantity effects:
  - Baseline trade-value specification captures price and quantity effects; trade-volume specification isolates quantity effects.
  - Finding: policy impacts on trade balance operate primarily through quantities; price effects offset partly.
  - Price effect important for monetary shocks due to nominal exchange rate appreciation.
- C. Spillovers and exchange rate regimes:
  - Spillovers depend on trading partners’ de facto exchange rate regime vis-à-vis the U.S.
  - NEER indexes for subgroups constructed as:
    - NEER_T = sum_j (e_ij * X_ij) / sum_j (X_ij)
    - where e_ij denotes indexed exchange rate vis-à-vis country j; X_ij (exports) and X_ij (imports) used as weights.
  - Data limitations: some specifications use only trade in goods due to services data constraints.

### Regime classification, trade-balance spillovers, and output effects
- Regime classification and data:
  - Trade balance series: real dollar basis (chained 2009 dollars) from US Census Bureau.
  - Regime grouping: countries classified by regime during 2007-10. Classification threshold: category at or above 10 (below 10) corresponds to de facto crawling peg with band narrower than ±5 percent — used to define de facto flexible (fixed) regimes. Countries pegged to currencies other than the U.S. dollar (e.g., Euro area members) classified as flexible.
- Trade-balance spillovers — key findings:
  - Monetary policy spillovers vary sharply by exchange rate regime:
    - De facto pegs (fixed regimes): US monetary and fiscal loosening generate unambiguously positive spillovers for trading partners (increased demand for partners; weakening of US trade balance).
    - Flexible regimes: monetary loosening tends to have dominant demand-diverting effect; net effect ambiguous and depends on relative magnitudes of monetary and fiscal shocks.
  - Fiscal spillovers:
    - Sizable for partners with rigid exchange rate regimes.
    - Muted for partners with flexible exchange rates.
  - Empirical confirmation: estimated contributions indicate fixed-rate economies benefited from overall US policy stimulus after the crisis — especially from fiscal loosening; flexible-rate partners were adversely impacted.
- Spillovers on output:
  - Output measure: de-trended industrial production (monthly).
  - Monetary loosening:
    - Leads to output contraction in flexible-regime trading partners (demand-diverting effect).
    - Expansionary in de facto peg economies (demand-augmenting effect).
  - Fiscal shocks:
    - Effects on output weaker and no meaningful statistical difference between fixed and flexible groups—possibly because fiscal shocks affect specific sectors while monetary shocks have broader effects.
- Interpretation and implications:
  - Extraordinary US monetary and fiscal measures had sizable influence on trading partners’ external balances.
  - Monetary stimulus strengthened the US trade balance; but overall policy mix initially weakened it because fiscal stimulus dominated.
  - Heterogeneity: fixed-rate partners largely benefited; flexible-rate partners were generally adversely affected.
  - Methodological implication: jointly estimating fiscal and monetary shocks is important to avoid attenuation bias.
  - Policy caveat: spillovers via trade are not an argument against using monetary or fiscal instruments; recipient economies can deploy their own policies to offset undesirable spillovers and help stimulate global demand.

### Appendix insight: volume and price effects decomposition
- Trade balance identity:
  - TB = X − M with X = P_X Q_X and M = P_M Q_M; Y is trend nominal GDP (mostly invariant to current policy shocks).
- Decomposition separates:
  - Volume changes (demand augmentation and diversion).
  - Price effects (direct impact on trade prices).
- Price-effect decomposition:
  - Trade prices decomposed into foreign-currency prices and exchange-rate (E = US$/FC) effects.
  - Price effect = exchange rate price effect + foreign currency price effect.
- Monetary tightening example:
  - Monetary tightening produces an overall negative impact on the trade balance with a volume effect of larger absolute magnitude, implying the price effect goes in the opposite direction.
  - Monetary tightening leads to US dollar appreciation (∂E/∂(policy) < 0). Given the US trade deficit, this generates a positive exchange rate price effect.
  - Overall price effect positive; foreign currency price effect small (positive or negative but small).

### Unit root and cointegration tests
- Dickey-Fuller unit root tests (Table A.III.1. Dickey-Fuller test for unit root):
  - bond yield: -1.02 — no
  - stock price index (logs): -1.367 — no
  - reer (logs): -1.273 — no
  - net trade (% trend GDP): -2.043 — no
  - fiscal balance (% trend GDP): -8.259 — yes
  - Critical values:
    - 1% critical value: -3.456
    - 5% critical value: -2.878
    - 10% critical value: -2.57
- Johansen cointegration tests (Table A.III.2. Johansen tests for cointegration):
  - Trend: constant
  - Number of obs =     29
  - Sample:  1992m3 - 2016m9
  - Lags  = 2
  - Test table lines (preserved verbatim as in source):
    - Maxmum rankparmsLLeigenvalue trace statistic5% criticalvalue
    - 0
    - 30
    - 878.73664.118.287468.52
    - 1
    - 39
    - 917.108360.2290641.5440*47.21
    - 2
    - 46
    - 929.671740.0816516.417229.68
    - 3
    - 51
    - 934.420860.031686.91915.41
    - 4
    - 54
    - 937.490190.020590.78033.76
    - 5
    - 55
    - 937.880350.00264

*Source: WP/17/204 — Policy Mix and the US Trade Balance, Sections 1–4*

### Section 1

### wp17204 - Section 1

### Introduction: context, motivation, and headline findings
- Context and policy actions:
  - Following the 2008-09 financial crisis, U.S. policymakers deployed sizeable fiscal and monetary policy stimuli.
  - Monetary policy rates were sharply lowered, rapidly reaching the zero lower bound (ZLB), followed by the implementation of quantitative easing (QE) in its different phases:
    - QE1 (Nov2008-Mar2009): purchases of $600 billion of agency and mortgage-backed securities (MBS);
    - QE1 extended (Mar2009-Mar-2010): purchases of $750 billion of MBS;
    - QE2 (Nov2010-Jun2011): purchases of $600 billion of long-term treasury bonds;
    - Operation twist (Sep2011-Jun2012): purchases of $400 billion of treasury bonds of long maturities (72-360 months) and equivalent sale of short-term maturities (3-36 months);
    - QE3 (Sep 2012-Oct2014): Purchases of $40 billion per month.
  - Expansionary fiscal policy was deployed “beyond automatic stabilizers,” as apparent in the near 8-percentage points of GDP weakening of the fiscal balance between 2007 and 2009.
- Research question and approach:
  - Study the trade spillovers of the post-crisis U.S. policy mix by assessing the joint impact of monetary and fiscal policy on the trade balance.
  - Motivation: prior literature focused heavily on monetary policy, often omitting fiscal policy and potentially incurring omitted-variable (attenuation) bias.
- Key empirical findings (summary from Section I):
  - Extraordinary monetary and fiscal policy measures following the 2008-09 financial crisis had a sizable impact on the trade balance.
  - Unprecedented monetary policy stimulus contributed to the strengthening of the U.S. trade balance, consistent with demand-diverting effects.
  - Contrary to a monetary-only interpretation, the overall policy mix led to a weakening of the U.S. external position in the immediate aftermath of the crisis, reflecting a sizable fiscal stimulus that more than offset the impact of loose monetary policy.
  - Aggregate trade effects varied over time, reflecting different timing of fiscal and monetary stimuli, with overall positive spillovers in the immediate aftermath of the crisis.
  - Trade spillovers differed markedly across trading partners depending on exchange rate regimes:
    - Trading partners with de facto rigid regimes (vis-à-vis the U.S. dollar) benefited significantly from the overall policy stimulus in the aftermath of the crisis, with both fiscal and monetary stimuli working in their favor.
    - Economies with flexible exchange rates experienced strong demand-diverting effects (the opposite result).
  - Effects of policy shocks on the trade balance are significantly larger when monetary and fiscal policies are estimated jointly rather than individually.
- Policy implication highlighted:
  - Assess spillovers from the overall policy mix rather than focusing on individual policies to avoid attenuation bias from omitting other policy variables.
  - With the U.S. economy approaching full employment, a policy mix of fiscal loosening coupled with monetary tightening is likely to lead to a significant deterioration of the U.S. external position, and—other things equal—overall positive trade spillovers to the rest of the world.

### Empirical approach: data, model, identification
- Data and sample:
  - Monthly data covering 1992m1-2016m9.
  - Monthly GDP series from Macroeconomic Advisors; trend obtained by applying a standard HP filter.
- Endogenous variable vector (as specified in the text):
  - Yt = [ TB E S F R Y ]'  (notation as presented in the source)
- Variable definitions and measurement:
  - Rt: the long-term interest rate (10 year U.S. treasury bond yield); baseline uses nominal yields, with an alternative specification using real yields as a robustness check.
    - Focus on long-term yields to capture monetary policy affecting the yield curve (conventional, QE, forward guidance).
  - Ft: the fiscal policy instrument — the seasonally-adjusted federal government budget balance, as reported by the U.S. Treasury, and expressed in percent of trend GDP.
    - Monthly U.S. Treasury figures were adjusted for seasonality by applying TRAMO/SEATS to receipts and outlays separately; balance computed on seasonally-adjusted subcomponents.
  - St: the S&P 500 composite index of stock prices, expressed in logarithm, as a proxy for cyclical conditions.
  - Et: the nominal effective exchange rate (NEER) from IMF International Financial Statistics, expressed in logarithms.
  - TBt: the seasonally-adjusted trade balance (net exports) from the Census Bureau, expressed in percent of trend GDP.
- Econometric model:
  - Estimate a structural vector autoregressive (SVAR) model; reduced-form VAR written as:
    - Yt = sum_{k=1}^{2} B_k Y_{t-k} + ε_t  (equation as presented)
  - Variables are cointegrated; VAR estimated in levels to incorporate cointegrating relationships without specifying a VECM.
  - Examination of impulse response functions reveals responses returning to steady-state values.
- Identification strategy:
  - Policy shocks identified via contemporaneous sign restrictions following Rubio-Ramirez and others (2005), Mountford and Uhlig (2009), Ehrmann and others (2011), and Matheson and Stavrev (2014).
  - Identification assumptions (summarized in text and Table 2):
    - A positive cyclical shock increases stock prices, bond yields, and the fiscal balance, and leads to an appreciation of the U.S. dollar.
    - A monetary shock is assumed to increase bond yields and reduce stock prices, and to lead to an appreciation of the domestic currency.
    - A discretionary fiscal tightening is assumed to lead to lower stock prices.
    - Identified fiscal policy shocks should be interpreted as implementation surprises (focus on actual changes in the fiscal balance that lead to movements in asset prices).
  - Orthogonality constraint:
    - Following Mountford and Uhlig (2009), shocks are required to be orthogonal; identification is based on randomly drawn orthonormal matrices Q (in equation 3 as presented).
- Additional methodological notes:
  - Long-term nominal yields may be affected by inflation expectations, but the identification strategy for monetary policy shocks (positive impact on yields and negative impact on stock prices) is designed so that inflation expectation shocks would not be captured as monetary policy shocks.
  - Alternative lag structures and robustness checks (including relaxing some identifying assumptions and using real yields) are discussed in later sections (referenced in the source).

*Source: WP/17/204 — Policy Mix and the US Trade Balance, Section 1*

### Section 2

### wp17204 - Section 2

### Identification approach and impulse response estimation
- Random draws of Q are generated until 1,000 parameterizations satisfying the sign restrictions are obtained.
- The econometric model is set-identified; this procedure can only bound the impulse response functions because there is a group of models that satisfy the sign restrictions.
- Model selection: follow Fry and Pagan (2010) to select the model with impulse responses closest to the median of the responses generated by the parameterizations that satisfy the sign restrictions.
- Confidence bands are computed using the standard deviation across these responses.
- Rationale: avoids imposing restrictions without clear theoretical support (e.g., effect of fiscal tightening on bond yields and the exchange rate) and lets the data speak; alternative identifying restrictions are explored as robustness checks and deliver very similar results.

### Baseline results — monetary and fiscal impulses
- Monetary loosening (negative monetary policy shock; 1 percentage point fall in the 10-year yield):
  - Leads to a nearly 10 percent depreciation of the nominal exchange rate within 4-6 months.
  - Leads to a 1 percent of GDP strengthening of the trade balance within 4-6 months, with a gradual fading especially of the latter effect.
  - Interpretation: in the short run, the demand diverting effect (from depreciation of the US dollar) dominates any short-run demand-augmenting effect (from lower interest rates on domestic demand).
  - Note: The choice of a 1pp shock to the 10-year yield is convenient for illustrative purposes, although is rather large—equivalent to 4 standard deviations of the monthly changes.
- Fiscal tightening (fiscal policy shock; 1 percent point of GDP drop in the fiscal balance):
  - Do not appear to have meaningful effects on the nominal exchange rate.
  - Entail sizable effects on the trade balance: a nearly 0.2 percent of GDP weakening of the trade balance within a year, with the effect dissipating only gradually.
  - Interpretation: consistent with the ‘twin deficits’ literature; any demand-diverting real appreciation effect is more than offset by the demand-reducing effect of fiscal tightening on aggregate demand.

- Estimation details shown in figures:
  - Impulse responses to a structural shock. Months are reported in the horizontal axis. Confidence bands correspond to one standard deviation.
  - Fiscal policy shock series reported as 6-month moving average.

### Results for emerging and developing market economies (EMDEs)
- Concern: baseline estimates (overall trade balance vis-à-vis all trading partners) may underestimate true effects due to uncontrolled-for policies in other economies, notably advanced economy trading partners whose policies are highly synchronous with the US.
- Alternative specification using trade balance vis-à-vis EMDEs reveals larger, and statistically more significant, effects (Figure 4).

### Decomposition of policy variables into endogenous and exogenous components
- Fiscal balance (1992-2016): the sharp deterioration of nearly 8 percentage point of GDP from 2007 to 2012 appears largely an endogenous response to the cycle, but with an economically meaningful exogenous component indicating fiscal response went beyond normal cyclical response, especially immediately after the crisis.
- 10-year yield (1992-2016): much of the sizable monetary loosening following the financial crisis was consistent with a normal response to cyclical conditions, although there was also significant extraordinary monetary loosening in the months preceding the financial crisis and in the immediate aftermath.

### Contribution of policy shocks to the trade balance (1992-2016)
- Both monetary and fiscal policy shocks individually entailed large effects on the trade balance in the aftermath of the 2008-09 financial crisis, with significantly larger and more sustained effects than in any previous period.
- Monetary loosening after the crisis contributed to a strengthening of the trade balance with lasting effects.
- Sizable fiscal policy stimulus contributed to a weakening of the trade balance in the immediate aftermath of the crisis; as fiscal stimulus was withdrawn, its weakening effect dissipated and eventually reverted, adding to the positive impact from monetary policy.
- Quantified post-GFC (2009-12 and 2013-16) contributions (Table 3 summary):
  - During 2009-12: policy mix entailed a significant weakening of the US trade balance—of nearly -0.5 percent of GDP—as the effect of the fiscal stimulus (-0.8 percent of GDP) more than offset the impact of monetary easing (0.3 percent of GDP).
  - During 2013-16: with gradual withdrawal of fiscal support, monetary policy strengthening (0.4 percent of GDP) dominated.
  - For the whole post-crisis period, the effect of the policy mix on the trade balance is estimated to have been broadly neutral.

### Robustness checks
- Summary of checks (Table 4) includes:
  - Relaxing the assumption that positive monetary policy shocks (rise in interest rate) lead to an appreciation of the nominal exchange rate (Table 4, column 2).
  - Introducing a measure of risk appetite (VIX) to control for effects of changes in risk aversion on bond and equity prices (Table 4, column 3):
    - Assumed that a risk-off shock reduces stock prices and bond yields (treasury bonds see prices increase and yields decrease), and that the U.S. dollar appreciates as investors shift toward U.S. investments.
  - Introducing an identifying assumption linking a positive fiscal shock to an appreciation of the real exchange rate (REER rather than NEER for identifying both fiscal and monetary shocks).
    - Note: shift from nominal to real exchange rate comes at a cost—impact of monetary shock on the real exchange rate is less clear than on the nominal exchange rate.
  - Alternative specification linking fiscal policy shocks to the 10-year rate (premise: fiscal tightening reduces the 10-year rate by improving debt sustainability).
- Results: in all cases, with varying degrees of statistical significance, the conclusions of the baseline model are confirmed.
- Additional note: model results also hold for a 3-lag structure.

### Extensions
- A. Policy mix versus single policies
  - Joint identification of monetary and fiscal shocks (jointly estimated model) versus models estimating one policy at a time:
    - Joint estimation unveils much larger effects (with expected signs) than when policies are estimated individually.
    - For fiscal shocks, impulse response can change sign when estimating jointly with monetary policy, indicating monetary policy shocks tend to dominate fiscal policy effects.
    - Controlling for the other policy tool—even without fully identifying its structural shock—is key to uncovering the full effect of individual policy shocks.
    - Implication: monetary and fiscal policy shocks are correlated; lack of control for one or the other is likely to lead to attenuation (omitted variable) bias in individually estimated effects.
  - Empirical focus: trade balance vis-à-vis EMDEs to minimize problems with lack of control for trading partner policies.

- B. Price versus quantity effects
  - Baseline specification based on trade values captures both price and quantity effects; alternative model based on trade volumes isolates quantity effects.
  - Finding: impact of policies on the trade balance operates primarily through quantities, with some offsetting effects via prices.
  - The price effect is especially important for a (positive) monetary policy shock, indicating price channel arises primarily from appreciation of the nominal exchange rate.

- C. Spillovers and exchange rate regimes
  - Spillovers on trading partners likely depend on their de facto exchange rate regime vis-à-vis the US, as this determines the extent of demand-diverting effects from movements in bilateral exchange rates.
  - Sample is divided according to de facto exchange rate regime (classification by Ilzetzki, Reinhart and Rogoff (2017)); separate models estimated for these groups, focusing on the partial trade balance with them and corresponding NEER.
  - NEER indexes against subgroups of trading partners constructed as:
    - NEER_T = sum_j (e_ij * X_ij) / sum_j (X_ij)  (notation from source: ܴܧܧܰ
ݐ
ܬ
ൌ
∑
ܵ
ݐ
݆
൬
ܺ
ݐ
݆
ܯ൅
ݐ
݆
∑
൫
ܺ
ݐ
݆
ܯ൅
ݐ
݆
൯
ܬ∈݆
൰
ܬ∈݆)
    - where ܵ
ݐ
݆ denotes the indexed exchange rate vis-à-vis country j; and ܺ
ݐ
݆ (ܯ
ݐ
݆) denote exports (imports) vis-à-vis the same country.
  - Data limitations: only trade in goods is reported in some specifications due to services volumes limitations.

_Authors' estimations._

### Section 3

### wp17204 - Section 3

### Regime classification and data
- Trade balance series: real dollar basis (chained 2009 dollars) from the US Census Bureau.
- Regime grouping rule: countries are grouped according to their regime classification during 2007-10. Trading partner countries classified with a category at or above 10 (below 10)—which corresponds to de facto crawling peg with a band narrower than ±5 percent—for more than half of the period are considered a de facto flexible (fixed) exchange rate regime.
- Note: Countries that maintain de facto pegs vis-a-vis currencies other than the US dollar (e.g., members of the Euro area) are classified as holding flexible regimes.

### Trade-balance spillovers: key findings
- Monetary policy spillovers differ sharply by exchange rate regime:
  - For de facto pegs (fixed regimes): spillovers from US monetary and fiscal loosening are unambiguously positive for trading partners (i.e., increased demand for trading partners; weakening of the US trade balance).
  - For flexible regimes: monetary loosening tends to have a dominant demand-diverting effect, producing opposite-sign effects relative to fiscal policy; the net effect is ambiguous and depends on the magnitude of monetary and fiscal shocks.
- Fiscal spillovers are:
  - Sizable for trading partners with rigid exchange rate regimes.
  - Somewhat muted for those with flexible exchange rates.
- Empirical confirmation:
  - Estimated contributions of policy shocks to variations in the trade balance (Figure 10) indicate that economies with fixed exchange rates benefited from the overall US policy stimulus in the aftermath of the financial crisis, with especially larger effects from fiscal loosening.
  - Trading partners with flexible rates were adversely impacted by such policies; the adverse net effects of the initial monetary loosening were only partially offset by initial fiscal loosening, while the later monetary tightening effects were more than offset by tighter fiscal policy.

### Spillovers on output
- Output measure: de-trended industrial production (monthly frequency, across large set of countries).
- Monetary shocks:
  - A US monetary loosening leads to an output contraction in trading partners with flexible exchange rate regimes — consistent with a dominating demand-diverting effect (reduced competitiveness due to US dollar depreciation / appreciation of partner currencies).
  - In economies with currencies tied to the US dollar (de facto pegs), a US monetary loosening is expansionary — consistent with a dominating demand-augmenting effect.
- Fiscal shocks:
  - Estimated effects on output are weaker and show no meaningful statistical difference between fixed and flexible regime groups.
  - Possible reason: fiscal shocks may affect only certain sectors, whereas monetary shocks have broader effects (demand and exchange rates).

### Interpretation and implications
- Overall assessment of 2008-09 policy mix:
  - Extraordinary US monetary and fiscal policy measures had sizable influence on trading partners as reflected in external balances.
  - The unprecedented US monetary stimulus contributed to a strengthening of the US trade balance (arguably to the detriment of trading partners).
  - However, the overall policy mix initially led to a weakening of the US external position in the immediate aftermath of the crisis because a strong fiscal stimulus more than offset the impact of extraordinarily loose monetary policy.
  - As the policy mix shifted with gradual withdrawal of fiscal support, the effect on the trade balance shifted as well.
- Heterogeneity across partners:
  - For the most part, economies with fixed exchange rates benefited from the overall US policy stimulus after the financial crisis.
  - Trading partners with flexible rates were adversely impacted by such policies.
- Methodological implication:
  - Importance of jointly estimating fiscal and monetary policy shocks to avoid attenuation bias from omitted variables and to identify effects more accurately.
- Policy caveat:
  - Presence of spillovers through trade is not an argument against using monetary or fiscal instruments. Their use can lead to desirable outcomes both for individual economies and globally, provided spillover-recipient economies can deploy their own policy instruments to partially offset undesirable spillovers and help stimulate global demand.

### Appendix insight: volume and price effects decomposition
- Trade balance TB = X − M, with X = P_X Q_X and M = P_M Q_M; Y is trend nominal GDP (mostly invariant to current policy shocks).
- Decomposition of policy shock i effect on trade balance (share of trend GDP) separates:
  - Volume changes (effects through demand augmentation and diversion).
  - Price effects (direct impact on trade prices).
- Price-effect decomposition:
  - Trade prices can be written as prices in foreign currency and the exchange rate (E = US$/FC).
  - Price effect = exchange rate price effect + foreign currency price effect.
- Monetary tightening example:
  - Empirical impulse responses show a monetary tightening entails an overall negative impact on the trade balance and a similar volume effect but of larger absolute magnitude, implying the price effect goes in the opposite direction.
  - A monetary tightening unequivocally leads to an appreciation of the US dollar (i.e., ∂E/∂(policy) < 0 as shown in the baseline results). Given the US trade deficit throughout the sample, this generates a positive exchange rate price effect.
  - Because the overall price effect is positive, the effect on foreign currency prices is either positive or negative but small.

*Source: authors' estimations, wp17204 - Section 3.*

### Section 4

### Unit root and cointegration tests

### Dickey-Fuller unit root tests
- Test statistic and unit root hypothesis rejection:
  - bond yield: -1.02 — no
  - stock price index (logs): -1.367 — no
  - reer (logs): -1.273 — no
  - net trade (% trend GDP): -2.043 — no
  - fiscal balance (% trend GDP): -8.259 — yes
- Critical values:
  - 1% critical value: -3.456
  - 5% critical value: -2.878
  - 10% critical value: -2.57

- Table heading: Table A.III.1. Dickey-Fuller test for unit root

### Johansen cointegration tests
- Test setup and sample information:
  - Trend: constant
  - Number of obs =     29
  - Sample:  1992m3 - 2016m9
  - Lags  = 2
- Test table lines (preserved verbatim as in source):
  - Maxmum rankparmsLLeigenvalue trace statistic5% criticalvalue
  - 0
  - 30
  - 878.73664.118.287468.52
  - 1
  - 39
  - 917.108360.2290641.5440*47.21
  - 2
  - 46
  - 929.671740.0816516.417229.68
  - 3
  - 51
  - 934.420860.031686.91915.41
  - 4
  - 54
  - 937.490190.020590.78033.76
  - 5
  - 55
  - 937.880350.00264

- Table heading: Table A.III.2. Johansen tests for cointegration

*Source: wp17204 - Section 4*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17204.pdf_