## wp1781 - Section 3 reports empirical investigation.  Section 4 lays out a standard open economy

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### Data and REER construction
- Sample:
  - balanced panel of 35 economies covering period from 2000Q1 to 2014Q4.
  - an annual sample dating back to 1995 used for robustness checks.
- REER definition and weights:
  - REERi = Πj≠i (Pi Sij / Pj)^λij where λij represents the weight of j in trade with i and Sij is the bilateral nominal exchange rate between i and j.  An increase in REER corresponds to appreciation in home currency.
  - Overall weight: λij = αM λMij + αC λCij + αT λTij (three trade categories: commodities, manufacture goods and service (tourism)).
- Deflators / REER measures:
  - REER-CPI, REER-GDP, and REER-ULC (unit labor cost index).
- Variance decomposition of ln(REER):
  - V ar(lnREER) = V ar(lnNEER) + Cov(lnNEER,lnP/P*) + V ar(lnP/P*) + Cov(lnNEER,lnP/P*)
  - Relative prices can account for around 10-20 percent of variation in annual growth in REER and substantially larger portions of quarterly growth in REER.
- Visual inspection:
  - REER measures move in tandem but with noticeable differences in magnitude; REER-ULC often most volatile.
  - Fluctuations in current account balance appear most closely mirrored by REER-ULC for multiple countries (including southern euro area, China, Korea, and the U.S.).
- Stationarity and cointegration:
  - Unit root tests: mixed results; most tests tend to reject "all panels contain a unit root" for at least one variable, while Hadri test (null: panels stationary) strongly rejects stationarity for all variables. Authors take conservative stance that all panels contain a unit root.
  - Cointegration tests: p-values strongly suggest REER measures are cointegrated with current account-to-GDP ratio.

### Empirical specification and identification
- Baseline econometric model (single-equation ECM):
  - ∆Yit = η (Y − β lnREER − β1 lnGDP − β2 lnGDP*)it−1 + γ ∆ lnREERit + γ1 ∆ lnGDPit + γ2 ∆ lnGDP*it + αi + εit
  - Y denotes external balance (current account balance or trade balance in percent of GDP).
  - GDP and GDP* denote home real GDP and weighted rest-of-world real GDP (same weights as REER).
- Estimators:
  - Baseline: dynamic fixed effects (DFE) assuming coefficient homogeneity with country fixed effects.
  - Alternatives: pooled mean-group (PMG) and mean-group (MG).
- Endogeneity concern:
  - Reverse causality from external balance to REER (improvement → appreciation) noted; may bias estimates upward.

### Baseline results (quarterly) — core empirical findings
- Short-run REER coefficient (SR_REER):
  - REER-ULC: SR_REER estimated negative and statistically significant (evidence consistent with expenditure-switching: REER depreciation → current account improvement).
  - REER-CPI: SR_REER negative and insignificant (but with some lagged effects).
  - REER-GDP: SR_REER negative and insignificant or positive and insignificant.
- Estimator robustness:
  - PMG and MG produce results very similar to DFE: REER-ULC consistently yields negative and statistically significant SR_REER; REER-CPI and REER-GDP coefficients not statistically significant.
  - Hausman test p-values indicate DFE preferred to PMG/MG for efficiency.
- Dynamics and lags:
  - REER-ULC: contemporaneous coefficient negative and statistically significant; lagged terms insignificant.
  - REER-CPI: negative and statistically significant coefficient estimates found in two-period lagged terms (delayed transmission).
  - REER-GDP: contemporaneous and lagged coefficients statistically insignificant.

### Robustness checks (section 3.3)
- Annual sample (3.3.1):
  - Quarterly results replicated at annual frequency.
  - SR_REER: REER-ULC negative and statistically significant; REER-CPI and REER-GDP positive and insignificant.
  - PMG and MG similar to DFE; Hausman tests favor DFE.
  - Time FE, pre-GFC sample, euro vs non-euro subsamples all preserve main finding.
- Additional controls (3.3.2):
  - Commodity terms of trade (IMF EBA dataset) included: coefficient on REER-ULC becomes larger negative; REER-CPI and REER-GDP become larger positive.
  - Control for capital cost (using Karabarbounis and Neiman (2014) data): negative correlation between REER-ULC and external balance hardly affected.
  - Endogeneity: reverse causality via nominal exchange rate affects all REER measures similarly; no obvious mechanism inducing relatively more severe upward bias for CPI- or GDP-deflators than ULC-deflators.
- Tradable versus nontradable composition (3.3.3):
  - REER measures constructed using tradable-sector ULC and GDP deflator.
  - Tradable-sector ULC REER: statistically significant and negative short-run relationship with external balance.
  - Tradable-sector GDP-deflator REER: no significant short-run relationship.
  - Conclusion: composition differences alone cannot explain the pattern; REER-ULC relationship persists in tradable sector.
- Dominant currency (3.3.4):
  - RERs measured against the United States: only ULC-based RER negatively related to external balance in the short-run.
  - Conclusion: USD invoicing/dominant currency paradigm not a relevant explanation for the disconnect across REER measures.
- Alternative external-balance and demand measures (3.3.5):
  - Using trade-balance-to-gross-trade ratio (Alessandria and Choi (2016) decomposition): only REER-ULC negatively and significantly correlated with external balance.
  - Replacing GDP with total consumption and investment (domestic absorption proxy): results unchanged.
- Alternative REER sources (3.3.6):
  - European Commission REER dataset (37 countries, 1994–2015): short-run coefficients for REER-ULC around -0.05 (close to quarterly benchmark -0.048); REER-CPI and REER-GDP not significant.
- Overall robustness conclusion:
  - The main finding—that only REER deflated by ULC is consistent with the expenditure-switching mechanism—is extremely robust across estimators, frequency, controls, sectoral composition, dominant currency tests, alternative external-balance/demand measures, and alternative REER data sources.

### Key reported statistics (selected exact figures)
- Table 1 (Quarterly sample, obs = 2100):
  - lnRER CPI: mean 4.71, sd 0.19, min 4.14, max 5.57.
  - lnRER ULC: mean 4.74, sd 0.26, min 3.90, max 6.13.
  - lnNER: mean 4.64, sd 0.15, min 3.87, max 5.06.
  - current account / GDP: mean 0.00, sd 0.06, min -0.31, max 0.20.
- Variance decomposition (Table 2):
  - Quarterly REER-ULC: NEER 66%, P/P* 34%.
  - Quarterly REER-CPI: NEER 93%, P/P* 7%.
  - Quarterly REER-GDP: NEER 60%, P/P* 40%.
  - Annual REER-ULC: NEER 79%, P/P* 21%.
  - Annual REER-CPI: NEER 83%, P/P* 17%.
  - Annual REER-GDP: NEER 87%, P/P* 13%.
- Core ECM baseline (Table 5, quarterly, obs = 2065):
  - SR REER: -0.048*** (REER-ULC), -0.005 (REER-CPI), 0.016 (REER-GDP).
  - SR SRec: -0.149***, -0.152***, -0.148*** (selected columns).
  - Long-run FD coefficients reported up to 0.222**, 0.200** in some columns.

### Model (Section 4.2) — labor union and intermediate-good producer
- Production and agents:
  - Final production: Ỹt = At Lt, where Lt = (∫0 1 Lit^(ζ−1)/ζ di)^(ζ/(ζ−1)); ζ is elasticity across labor types.
  - Labor union: monopoly supplier; W̃t = ζ/(ζ−1) Wt.
  - Intermediate goods pricing (perfect competition): P̃t = W̃t / At.
- Final-good firms price setting:
  - Pjt = θ/(θ−1) Et−1[MCjt · Ct^(1−ρ)] / Et−1[Ct^(1−ρ)]
  - Cjt = (Pjt / Pt)^(−θ) Ct
- Aggregation and marginal cost:
  - CES with home bias α ∈ (0.5,1); producer-currency pricing yields
    - MCjt = [ α (W̃t At)^(1−η) + (1−α) (W̃∗t A∗t St)^(1−η) ]^(1/(1−η))
- Core equilibrium conditions (preserved exact expressions):
  1. Wt / Pt = Et−1(Lt^ν) / Et−1(Lt Ct^(−ρ))
  2. Pt = θ/(θ−1) Et−1[MCt · Ct^(1−ρ)] / Et−1[Ct^(1−ρ)]
  3. W̃t = ζ/(ζ−1) Wt
  4. At Lt = α (W̃t / At MCt)^(−η) Ct + (1−α) (W̃t / At · St MC∗t)^(−η) C∗t
  5. MCt = [ α (W̃t At)^(1−η) + (1−α) (W̃∗t A∗t St)^(1−η) ]^(1/(1−η))
  6. Pt Ct = Mt
  7. Pt Ct^ρ = P∗t C∗t^ρ / St
  8. ln At = ρA ln At−1 + εAt
  9. ln Mt = ρM ln Mt−1 + εMt
- Monetary policy closure:
  - Pt Ct = Mt (domestic absorption stabilization CP = M).
- Mapping of RERs (preserved exact expressions):
  - RER-ULC = (Wt / At) / (W∗t / A∗t) · St
  - RER-CPI = Pt / P∗t · St
  - RER-GDP = (Pt Ct + TradeBalancet / At Lt) / (P∗t C∗t + TradeBalance∗t / A∗t L∗t) · St
- Trade Balance and current account:
  - Trade Balance = (1−α) [ MC∗t C∗t St − MCt Ct ]
  - Current Accountt = NFA t − NFA t−1; also Current Accountt = Trade Balancet + Bt

### Parametrization and shocks (preserved values)
- Parameters:
  - product elasticity and labor elasticity: 6 (implying a markup of twenty percent).
  - elasticity of substitution between imports and domestic goods: 1.6.
  - risk aversion level: 2.
  - Frisch elasticity: 1.
  - home bias: 0.75.
  - time discount factor: β = 0.99 (corresponding to annual interest rate four percent).
- Shock magnitudes for simulations:
  - Monetary shock: 20 basis point (represented via σM).
  - Productivity shock magnitude: 0.0015 (σA).
  - εAt ∼ N(0, σA^2), σA = 0.0015.
  - εMt ∼ N(0, σM^2), σM = 0.0020.

### Model impulse responses and simulated correlations
- Productivity shock (positive):
  - External balance: home country runs a surplus.
  - RER responses:
    - RER-ULC: significant depreciation.
    - RER-CPI: no contemporaneous response.
    - RER-GDP: milder depreciation than RER-ULC.
  - Mechanism: wage rigidity → full pass-through to ULC; price rigidity → CPI does not respond contemporaneously.
- Expansionary monetary policy shock:
  - All RERs: contemporaneous depreciation and gradual appreciation.
  - External balance: immediate deficit due to consumption jump and borrowing; partial recovery later.
  - Mechanism: preset prices cause consumption to jump with money supply shock, triggering nominal depreciation via risk sharing.
- Simulation moments (4000 periods, first half burn-in; moment computed Cov(RER, CA/Y) / Var(RER)):
  - RER-ULC: significant and negative contemporaneous correlation with external balance.
  - RER-CPI: point estimate positive contemporaneously.
  - RER-GDP: contemporaneous correlation insignificant.
  - Lagged (one-period) moments: RER-CPI and RER-GDP show significant negative correlation at lag one due to price resets; RER-ULC negative correlation persists beyond contemporaneous period.

### Policy and interpretive implications
- Choice of price deflator matters when assessing relationship between RER and external balance.
- Absence of negative correlation between RER (measured by CPI or GDP deflator) and external balances should not be taken as evidence against the expenditure-switching mechanism.
- Findings inform the international elasticity puzzle and warrant caution in interpreting observed empirical patterns based on CPI- or GDP-deflator–based RER measures.

*Source: wp1781 - Section 3 reports empirical investigation.  Section 4 lays out a standard open economy*

### Section 3 reports empirical investigation.  Section 4 lays out a standard open economy

### wp1781 - Section 3 reports empirical investigation.  Section 4 lays out a standard open economy

### Data
- Sample: balanced panel of 35 economies covering period from 2000Q1 to 2014Q4.  An annual sample dating back to 1995 is also used for robustness checks.
- REER construction:
  - REERi = Πj≠i (Pi Sij / Pj)^λij where λij represents the weight of j in trade with i and Sij is the bilateral nominal exchange rate between i and j.  An increase in REER corresponds to appreciation in home currency.
  - Weights calculated using Global System with three trade categories: commodities, manufacture goods and service (tourism). Overall weight: λij = αM λMij + αC λCij + αT λTij.
- Deflators used to produce three REER measures: REER-CPI, REER-GDP, and REER-ULC (unit labor cost index).
- Variance decomposition of ln(REER) using changes (levels non-stationary) shows:
  - V ar(lnREER) = V ar(lnNEER) + Cov(lnNEER,lnP/P*) + V ar(lnP/P*) + Cov(lnNEER,lnP/P*)
  - Relative prices can account for around 10-20 percent of variation in annual growth in REER and substantially larger portions of quarterly growth in REER.
- Visual inspection (Figure 1) for selected countries:
  - REER measures move in tandem but with noticeable differences in magnitude; REER-ULC often most volatile.
  - Fluctuations in current account balance appear most closely mirrored by REER-ULC for multiple countries (including southern euro area, China, Korea, and the U.S.).
- Stationarity and cointegration tests:
  - Unit root tests: mixed results; most tests tend to reject "all panels contain a unit root" for at least one variable, while Hadri test (null: panels stationary) strongly rejects stationarity for all variables. Authors take conservative stance that all panels contain a unit root.
  - Cointegration tests (Table 4): p-values strongly suggest REER measures are cointegrated with current account-to-GDP ratio. Interpretation: presence of cointegrating relationship between non-stationary REER and external balance measures.

### Empirical Evidence — Econometric specification
- Baseline model: single-equation error correction model (ECM) estimated to capture short-run relationship given non-stationarity and cointegration:
  - ∆Yit = η (Y − β lnREER − β1 lnGDP − β2 lnGDP*)it−1 + γ ∆ lnREERit + γ1 ∆ lnGDPit + γ2 ∆ lnGDP*it + αi + εit
  - Y denotes external balance (current account balance or trade balance in percent of GDP).
  - GDP and GDP* denote home real GDP and weighted rest-of-world real GDP (same weights as REER), capturing domestic and foreign demand effects.
- Model choices and estimators:
  - Baseline: dynamic fixed effects (DFE) assuming coefficient homogeneity across countries with country fixed effects.
  - Alternatives: pooled mean-group (PMG) allowing heterogeneous short-run dynamics but common long-run relationship; mean-group (MG) allowing heterogeneity in both short- and long-run relationships.
- Endogeneity concern:
  - Reverse causality from external balance to REER (improvement → appreciation) may bias estimates upward. Authors note this and consider implications when discussing results.

### Empirical Evidence — Baseline results and robustness
- Estimation frequency: quarterly data; Tables 5–9 summarize results across REER-ULC, REER-CPI, REER-GDP.
- Long-run and short-run coefficient reporting:
  - Top panel of reported tables: long-run coefficient estimates.
  - Bottom panel: short-run coefficient estimates including error-correction term (speed of adjustment).
- Key finding on short-run REER coefficient (SR_REER):
  - REER-ULC: SR_REER estimated negative and statistically significant.
  - REER-CPI: SR_REER negative and insignificant (but with some lagged effects; see below).
  - REER-GDP: SR_REER negative and insignificant or positive and insignificant.
  - Immediate interpretation: only ULC-based REER measure is consistent with expenditure-switching mechanism (REER depreciation → current account improvement).
  - Contrast across deflators is stark mainly for short-run REER coefficient; other short-run and long-run coefficients show much smaller differences.
- Estimator robustness:
  - PMG and MG estimators produce results very similar to DFE: REER-ULC consistently yields negative and statistically significant short-run REER coefficients; REER-CPI and REER-GDP coefficients not statistically significant (many positively signed).
  - Hausman test p-values (Table 6) indicate DFE preferred to PMG/MG for efficiency; subsequent tables report DFE results.
- Time-period robustness (Table 7):
  - Results hold when including time fixed effects and when restricting sample to pre-global financial crisis (pre-GFC) period.
- Eurozone vs non-eurozone (Table 8):
  - Patterns qualitatively identical for non-euro and euro countries: REER-ULC result holds in both subsamples.
- Dynamics and lags (Table 9):
  - Allowing additional lags of short-run REER:
    - REER-ULC: contemporaneous coefficient negative and statistically significant; lagged terms insignificant.
    - REER-GDP: contemporaneous and lagged coefficients statistically insignificant.
    - REER-CPI: negative and statistically significant coefficient estimates found in two-period lagged terms, suggesting delayed transmission from REER-CPI to external balance adjustments.
  - Interpretation: REER-CPI delayed effect may reflect relative stickiness of CPI compared to ULC rather than conventional J-curve timing for trade volumes/import prices.

*Source: wp1781 - Section 3 reports empirical investigation.  Section 4 lays out a standard open economy*

### 3.3    Robustness Checks

### 3.3 Robustness Checks

### 3.3.1 Annual Sample
- Purpose:
  - Repeat ECM estimation procedures applied to quarterly data using annual frequency data to enable longer time-series and broader set of robustness checks.
- Estimation setup:
  - Baseline ECM dynamic fixed effects estimation results reported in Table 10; top three rows summarize long-run coefficient estimates, bottom panel shows short-run coefficient estimates including the error-correction term.
  - Columns 1–3 correspond to regressions using REER constructed with ULC, CPI, and GDP deflator, respectively.
- Key findings:
  - The short-run REER coefficient (SR_REER) shows similar results to quarterly data:
    - REER-ULC: negative and statistically significant short-run coefficient.
    - REER-CPI: positive and insignificant short-run coefficient.
    - REER-GDP: positive and insignificant short-run coefficient.
  - The stark contrast across REER measures is concentrated in the short-run REER coefficient and mostly absent in other short-run and long-run coefficients.
- Alternative estimators:
  - PMG and MG ECM estimators applied (Table 11) allowing heterogeneity in coefficients:
    - PMG and MG results are similar to DFE estimator.
    - Qualitative pattern holds: REER-ULC yields negative and statistically significant short-run coefficients; REER-CPI and REER-GDP do not.
  - Hausman test p-values at bottom of Table 11 indicate dynamic fixed effects estimator preferred in terms of efficiencies; subsequent reporting focuses on dynamic fixed effects.
- Additional robustness checks (Tables 12–14):
  - Controlling for year fixed effects or restricting sample to pre-GFC period (Table 12) does not alter main finding: only REER-ULC yields negative and statistically significant short-run coefficient.
  - Subsamples by currency area (Table 13):
    - Non-euro and euro country samples each confirm the pattern.
  - Including additional lags of short-run REER (Table 14):
    - REER-ULC: contemporaneous REER negative and statistically significant; most lagged terms insignificant.
    - REER-GDP: contemporaneous and lagged coefficients statistically insignificant.
    - REER-CPI: negative and statistically significant coefficient estimates appear in two-period lagged terms, suggesting possible delays in transmission from REER-CPI to external balance adjustments.

### 3.3.2 Additional Controls
- Endogeneity and reverse causality concerns:
  - Argument: reverse causality via nominal exchange rate affects all REER measures similarly; no obvious mechanism that would induce a relatively more severe upward bias for CPI- or GDP-deflators than ULC-deflators.
  - If any upward bias exists, it is more likely muted for REER-CPI and more severe for REER-ULC to the extent exchange rate pass-through is higher in CPI than ULC.
- Omitted variable: commodity terms of trade
  - Intuition: commodity price collapse affects prices and external balance differently for commodity importers vs exporters and may bias short-run REER coefficients upward if omitted.
  - Table 15: controlling for commodity terms of trade (annual frequency data from IMF’s EBA dataset) does not drive main finding:
    - Coefficient on REER-ULC becomes larger negative.
    - Coefficients on REER-CPI and REER-GDP become larger positive.
    - Interpretation: any upward bias is more severe for REER-ULC, which would work against finding the observed pattern; results strengthen main claim.
- Omitted variable: other production costs (capital cost, intermediate input cost)
  - Under Cobb-Douglas assumption, ULC equals total production cost up to a constant wedge and they share dynamics after log-transformation; however, Cobb-Douglas may be a poor approximation in reality (labor share decline documented by Karabarbounis and Neiman (2014)).
  - Addressing capital cost:
    - Use Karabarbounis and Neiman (2014) data covering labor and capital share to output (back to 1970s where available).
    - Construct ratio (capital share + labor share) / labor share and add as control in baseline regression with REER-ULC.
    - Table 15 last column: negative correlation between REER-ULC and external balance is hardly affected, easing concerns about omitting other production cost types.

### 3.3.3 Tradable Price versus Nontradable Price
- Concern:
  - Composition differences across deflators (domestic vs imported goods, final vs intermediate goods, tradable vs nontradable) might drive empirical patterns.
  - CPI and GDP deflator include imported goods (negatively); ULC covers domestically produced goods. Intermediate goods and tradable-sector prices may be better captured in ULC than CPI or GDP deflator.
- Tests:
  - Construct REER measures using sector-level ULC and GDP deflator aggregated for tradable sectors only (Mano (2016) for details).
  - Table 16 results:
    - Tradable-sector GDP-deflator REER: no significant short-run relationship with external balance (column (3)).
    - Tradable-sector ULC REER: statistically significant and negative short-run relationship (column (1)).
    - Columns (2) and (4): alternative comparisons controlling for relative prices in tradable and nontradable sectors yield the same conclusion.
- Conclusion:
  - Composition of goods alone cannot explain empirical patterns; REER-ULC continues to exhibit a close negative relationship with external balance even when constrained to tradable sector.

### 3.3.4 Dominant Currency and Real Exchange Rate
- Context:
  - Casas et al. (2016): expenditure switching may depend on how a country’s currency fares against the USD (dominant currency paradigm).
- Test:
  - Consider real exchange rate movements against the United States specifically.
  - Table 17:
    - Only ULC-based RER is negatively related to external balance in the short-run.
- Conclusion:
  - Dominant currency paradigm (USD invoicing) is not a relevant consideration for the disconnect between REER measures and external balance found here.

### 3.3.5 Alternative Measures of External Balance and Demand
- Alternative external-balance measure:
  - Alessandria and Choi (2016) decomposition links external-balance-to-GDP ratio to a demand system: split trade-to-GDP into trade-balance-to-gross-trade ratio and gross-trade-to-GDP ratio; trade-balance-to-gross-trade can be linked to demand via first-order Taylor expansion.
  - Table 18:
    - Using trade-balance-to-gross-trade ratio as external balance measure yields similar empirical pattern:
      - Only REER-ULC is negatively and significantly correlated with external balance.
      - REER-CPI and REER-GDP remain disconnected.
- Alternative aggregate demand proxy:
  - Replace home and rest-of-world GDP with total consumption and investment (domestic absorption proxy).
  - Table 19:
    - Results unchanged: alternative measure of aggregate demand does not overturn findings; negative relationship between REER-ULC and external balance remains robust.

### 3.3.6 Alternative Sources of REER
- Motivation:
  - Cross-check results using REER data from other sources (European Commission dataset selected).
- Data:
  - European Commission dataset contains REERs based on ULC of total economy, ULC of manufactures, Harmonized Index of Consumer Price, and GDP deflator.
  - Coverage: mainly EU countries plus Australia, Japan, Mexico, New Zealand and the U.S.; 37 countries in total; 1994 to 2015.
- Results:
  - Baseline ECM estimation on European Commission data summarized in Table 20:
    - Short-run coefficients for REER-ULC around -0.05, very close to quarterly benchmark -0.048.
    - REER-CPI and REER-GDP yield no significant coefficient estimates.
- Overall conclusion from robustness checks:
  - The main finding—that only REER deflated by ULC is consistent with the expenditure-switching mechanism—is extremely robust across estimators, frequency (annual vs quarterly), additional controls (commodity terms of trade, capital cost), sectoral composition (tradable sectors), dominant currency consideration, alternative external-balance and demand measures, and alternative REER data sources.
  - Composition differences across price indices are insufficient to explain the empirical pattern; there must be additional factors that cause REER-ULC to move differently and better reflect relative prices relevant for external balance adjustments.
- Next step indicated in text:
  - Introduce and analyze a two-country open economy model (variant of Obstfeld (2001) and Devereux and Engel (2007)) that can generate qualitatively identical patterns to the empirical evidence.

*Source: wp1781 - 3.3 Robustness Checks*

### 4.2    Labor Union and Intermediate-Good Producer

### 4.2    Labor Union and Intermediate-Good Producer

### Labor union and intermediate-good production
- Production structure:
  - Final production uses a composite of differentiated labor:
    - Ỹt = At Lt, where Lt = (∫0 1 Lit^(ζ−1)/ζ di)^(ζ/(ζ−1))
    - ζ is the elasticity across different types of labor.
- Labor union behavior:
  - Labor union is a monopoly of labor supply, hires differentiated labor from households and supplies it to the intermediate-good producer.
  - Labor union charges manufacturers a markup and rebates profit to households.
  - Labor union wage relation:
    - W̃t = ζ/(ζ−1) Wt
- Intermediate goods pricing (perfect competition):
  - Price of intermediate goods equals marginal cost:
    - P̃t = W̃t / At

### Final-good producer and pricing
- Final-good manufacturers (continuum of firms) maximize expected profit with household subjective discounting:
  - max Pjt Et−1[((Pjt − MCjt) Cjt) Ct^(−ρ) Pt]
  - subject to Cjt = (Pjt / Pt)^(−θ) Ct
- First-order condition (price setting):
  - Pjt = θ/(θ−1) Et−1[MCjt · Ct^(1−ρ)] / Et−1[Ct^(1−ρ)]
- Aggregation of intermediate inputs and marginal cost:
  - Final goods use foreign and domestic intermediate goods with home bias α ∈ (0.5,1).
  - Producer-currency pricing implies domestic price of foreign intermediate good is W̃∗t A∗t St.
  - CES aggregation:
    - Yjt = (α^(1/η) Ỹt^(η−1)/η + (1−α)^(1/η) Ỹ∗t^(η−1)/η)^(η/(η−1))
    - ⇒ MCjt = [ α (W̃t At)^(1−η) + (1−α) (W̃∗t A∗t St)^(1−η) ]^(1/(1−η))

### Equilibrium closure and key conditions
- Monetary policy specification for floating or peg regimes: domestic absorption stabilization CP = M
- Equilibrium set:
  - {P, W, W̃, MC, L, C, P∗, W∗, W̃∗, MC∗, L∗, C∗; S} satisfying conditions (1) to (6) for both home and foreign countries and risk-sharing condition (7), given exogenous processes (8) to (9).
- Core equilibrium conditions (preserved exact expressions):
  1. labor supply:
     - Wt / Pt = Et−1(Lt^ν) / Et−1(Lt Ct^(−ρ))
  2. final good supply:
     - Pt = θ/(θ−1) Et−1[MCt · Ct^(1−ρ)] / Et−1[Ct^(1−ρ)]
  3. labor union wage:
     - W̃t = ζ/(ζ−1) Wt
  4. intermediate goods market clear:
     - At Lt = α (W̃t / At MCt)^(−η) Ct + (1−α) (W̃t / At · St MC∗t)^(−η) C∗t
  5. marginal cost:
     - MCt = [ α (W̃t At)^(1−η) + (1−α) (W̃∗t A∗t St)^(1−η) ]^(1/(1−η))
  6. monetary policy:
     - Pt Ct = Mt
  7. risk sharing:
     - Pt Ct^ρ = P∗t C∗t^ρ / St
  8. productivity shock:
     - ln At = ρA ln At−1 + εAt
  9. monetary policy shock:
     - ln Mt = ρM ln Mt−1 + εMt
- Combination of risk-sharing and monetary policy (implication for exchange rate):
  - Mt Ct^(ρ−1) = M∗t C∗t^(ρ−1) / St
  - Expansionary monetary policy or any shock leading to home consumption boom generates exchange rate depreciation.

### Mapping different real exchange rates (RERs) and trade measures
- RER definitions preserved exactly:
  - RER-ULC = (Wt / At) / (W∗t / A∗t) · St
  - RER-CPI = Pt / P∗t · St
  - RER-GDP = (Pt Ct + TradeBalancet / At Lt) / (P∗t C∗t + TradeBalance∗t / A∗t L∗t) · St
- Trade Balance:
  - Trade Balance = (1−α) [ MC∗t C∗t St − MCt Ct ]
- Trade share:
  - tby = 1 − Pt Ct / (Pt Ct + TradeBalance t)
- Current account:
  - Current Accountt = NFA t − NFA t−1, where NFA t = Et[β Uc,t+1 / Uc,t Pt / Pt+1 Bt+1]
  - Also Current Accountt = Trade Balancet + Bt

### Parametrization (preserved exact parameter values)
- Product elasticity and labor elasticity: 6 (implying a markup of twenty percent)
- Elasticity of substitution between imports and domestic goods: 1.6
- Risk aversion level: 2
- Frisch elasticity: 1
- Home bias: 0.75
- Time discount factor: β = 0.99 (corresponding to annual interest rate four percent)
- Shock magnitudes for simulations:
  - Monetary shock: 20 basis point (represented via σM)
  - Productivity shock magnitude: 0.0015 (σA)
  - εAt ∼ N(0, σA^2), σA = 0.0015
  - εMt ∼ N(0, σM^2), σM = 0.0020

### Impulse-response evidence (qualitative dynamics preserved)
- Productivity shock (positive):
  - External balance: home country runs a surplus.
  - RER responses:
    - RER-ULC: significant depreciation.
    - RER-CPI: no contemporaneous response.
    - RER-GDP: milder depreciation than RER-ULC.
  - Mechanism:
    - Wage rigidity ⇒ full pass-through of productivity shock to unit labor cost (Wt / At).
    - Price rigidity (preset final goods price) ⇒ CPI does not respond contemporaneously.
    - Nominal exchange rate: no contemporaneous spot response with fixed money supply and unchanged consumption, but depreciates at longer horizons to support higher home consumption as prices adjust.
    - Over time RER-CPI depreciates then appreciates back; wage increases and nominal exchange rate appreciation can lead RER-ULC to appreciate subsequently.
  - Key model prediction: complete pass-through of productivity shock to ULC and no pass-through to CPI once shock materializes; this drives negative contemporaneous correlation between external balance and RER-ULC and disconnect with RER-CPI.

- Expansionary monetary policy shock:
  - Common response across RERs: contemporaneous depreciation and gradual appreciation.
  - External balance: immediate deficit due to consumption jump and borrowing; later partial recovery as prices and wages reset.
  - Mechanism:
    - Preset prices cause consumption to jump one-to-one with money supply shock, lowering marginal utility in home country and triggering nominal depreciation via risk sharing.
    - Households consume more immediately despite smoothing motives to take advantage of temporarily low prices, borrowing internationally and running external deficit.
    - After one period, price/wage resets lead RERs to appreciate back toward steady state.
  - Monetary shock is a "generic" shock to nominal terms and affects RER-ULC, RER-CPI, and RER-GDP similarly, unlike productivity shocks that distinguish RERs.

### Correlation results from simulations
- Simulation setup:
  - 4000 periods with productivity and monetary policy shocks, first half burn-in.
  - Moment computed: Cov(RER, CA/Y) / Var(RER).
- Main simulated findings:
  - RER-ULC shows a significant and negative contemporaneous correlation with external balance.
  - RER-CPI and RER-GDP are not negatively correlated contemporaneously:
    - RER-CPI point estimate positive.
    - RER-GDP insignificant.
  - Lagged (one-period) moments:
    - RER-CPI and RER-GDP show significant negative correlation with external balance at lag one due to price setters resetting prices after one period of rigidity.
  - Negative correlation for RER-ULC extends beyond contemporaneous period; when RER-CPI and RER-GDP begin to show negative correlation, RER-ULC negative correlation persists.
- Model performance:
  - Parsimonious nominal rigidity and trade in intermediate goods replicate empirical features: negative contemporaneous correlation between RER-ULC and external balance, and absence of significant contemporaneous correlation for RER-CPI and RER-GDP.

### Policy and interpretive implications
- Choice of price deflators matters when assessing the relationship between RER and external balance.
- Absence of negative correlation between real exchange rates (measured by CPI or GDP deflator) and external balances should not be taken as evidence against the expenditure-switching mechanism.
- Findings have bearing on the international elasticity puzzle and warrant caution in interpreting observed empirical patterns.

*Source: "4.2    Labor Union and Intermediate-Good Producer", wp1781 — IMF Working Paper (chapter/section content).*

### References

### wp1781 - References

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### Appendix A.1 — Data sources (sample composition and data extraction)
- Sample includes 35 developed and emerging market economies: Australia, Austria, Belgium, Bulgaria, Canada, China, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Israel, Italy, Japan, Korea, Latvia, Lithuania, Netherlands, New Zealand, Norway, Poland, Portugal, Russia, Slovak Republic, Slovenia, South Africa, Spain, Sweden, Switzerland, United Kingdom, United States.
- Quarterly frequency data:
  - Bilateral nominal exchange rate: IMF Information Notice System (INS).
  - CPI and GDP deflator: International Financial Statistics (IFS).
  - ULC: OECD database for Hungary, Israel, Korea, New Zealand, Poland, and Slovenia; Haver for the rest of sample countries.
  - If seasonally adjusted series not available, X12 seasonal adjustment toolkit employed.
- Annual frequency data:
  - Bilateral nominal exchange rate and GDP deflator: WEO database.
  - CPI: INS.
  - ULC: OECD database for Israel, Korea, New Zealand; Haver for the rest.
- Quarterly and annual current account statistics: Haver and WEO, respectively.
- Export, import, and GDP series (quarterly and annual): WEO database.
- Commodity term of variable: External Balance Assessment (EBA) database at the IMF.
- Note: South Africa’s GDP deflator comes from the World Economic Outlook (WEO) database.

### Appendix A.2 — The role of home-bias (α) in simulations
- Parameter of interest: home bias, α, governs the extent to which exchange rate dynamics pass through to price indices and thereby shape evolution of RERs and their relationship with external balance.
- Impulse response experimentation:
  - No home bias (α = 0.5) to complete home bias (α = 1). Color lines in Figure 6 go from blue to green.
  - No home bias (α = 0.5): CPI-based RERs never respond to productivity shock because of same composition in indices between two countries; therefore no dynamics in external balance. ULC/GDP deflator-based RERs show significant depreciation in response to productivity increase due to nominal rigidity in wage level.
  - Complete home bias (α = 1): PPI- and ULC-based RERs perform similarly; GDP deflator-based RER resembles CPI-based RER.
- Parameterization used in simulations:
  - α takes the value of 0.75, described as "large enough to generate the dynamics in external balance and small enough to distinguish ULC-based RER from the rest."

### Key empirical findings and summary statistics (selected)
- Table 1 (Quarterly sample, obs = 2100):
  - lnRER CPI: mean 4.71, sd 0.19, min 4.14, max 5.57.
  - lnRER ULC: mean 4.74, sd 0.26, min 3.90, max 6.13.
  - lnNER: mean 4.64, sd 0.15, min 3.87, max 5.06.
  - current account / GDP: mean 0.00, sd 0.06, min -0.31, max 0.20.
  - trade balance / GDP: mean 0.01, sd 0.07, min -0.31, max 0.25.
  - export / GDP: mean 0.44, sd 0.24, min 0.09, max 2.06.
  - import / GDP: mean 0.43, sd 0.24, min 0.09, max 2.34.
  - lnGDP home (in billions $): mean -3.55, sd 3.01, min -10.84, max 2.79.
  - lnGDP row (in billions $): mean 0.62, sd 0.51, min -0.31, max 2.38.
- Table 1 (Annual sample, obs = 700/7004 depending on series):
  - lnRER CPI (annual): mean 4.69, sd 0.24, min 4.09, max 5.39.
  - lnRER ULC: mean 4.71, sd 0.27, min 3.84, max 5.71.
  - lnNER: mean 4.46, sd 0.59, min 1.43, max 5.22.
  - current account / GDP: mean 0.00, sd 0.06, min -0.24, max 0.18.
  - trade balance / GDP: mean 0.01, sd 0.06, min -0.21, max 0.21.
  - export / GDP: mean 0.35, sd 0.22, min 0.00, max 0.91.
  - lnGDP home (in billions $): mean 5.88, sd 1.61, min 2.28, max 9.69.
  - lnGDP row (in billions $): mean 11.00, sd 1.00, min 0.31, max 11.97.
- Table 2 — Variance decomposition of REER (contribution of NEER vs relative price):
  - Quarterly REER-ULC: NEER 66%, P/P* 34%.
  - Quarterly REER-CPI: NEER 93%, P/P* 7%.
  - Quarterly REER-GDP: NEER 60%, P/P* 40%.
  - Annual REER-ULC: NEER 79%, P/P* 21%.
  - Annual REER-CPI: NEER 83%, P/P* 17%.
  - Annual REER-GDP: NEER 87%, P/P* 13%.
- Panel unit root and cointegration (Tables 3 and 4) — p-values reported for multiple panel tests:
  - Quarterly: many unit-root test p-values reported (e.g., Levin-Lin-Chu for cagdp = 0.45; Hadri test H0: Stationary p-value 0.00).
  - Cointegration tests (Pedroni, Westerlund variants): p-values frequently reported as 0.00 for tests with cagdp and ln REER series (quarterly and annual panels).
- Error correction model core findings (Table 5, baseline ECM; quarterly panel unless otherwise stated):
  - Long-run coefficients (selected):
    - LR DD: coefficients range (columns reported) e.g., -0.061, -0.111**, -0.078* (standard errors in parentheses).
    - LR FD: 0.177**, 0.222**, 0.200**.
    - LR REER: 0.018, 0.139, 0.047.
  - Short-run coefficients (selected):
    - SR SRec: -0.149***, -0.152***, -0.148***.
    - SR REER: -0.048***, -0.005, 0.016.
  - Observations: 2065 (columns consistently report obs = 2065).
  - Significance notation: ***, **, * for 1%, 5% and 10%, respectively.
- Robustness checks and extensions (summarized across Tables 6–20):
  - Robustness to alternative long-run/short-run restrictions, different lag specifications, time/year fixed effects, pre-crisis subsamples, Euro vs non-Euro subsamples, alternative REER constructions (tradable-sector prices, REER against the U.S.), additional controls (commodity terms-of-trade, production cost measures), alternative external balance definitions (trade-balance-to-gross-trade ratio), and alternative data sources (European Commission).
  - Selected robustness highlights (exact reported coefficients and significance preserved in tables):
    - Table 6 (various longrun/shortrun restrictions): LR FD coefficients up to 0.495*** in some specifications; SR SRec strongly negative across specifications (e.g., -0.197***, -0.415***).
    - Table 7 (Time FE and pre-crisis): inclusion of time fixed effects and pre-crisis subsample still shows SR SRec = -0.158*** and SR REER = -0.047** in some specifications; obs reported as 1085 for pre-crisis.
    - Table 8 (Euro vs Noneuro): for Euro subsample (columns 4–6) LR DD coefficients include -0.173***, -0.287***, -0.244***; LR FD coefficients as high as 0.497***; SR SRec remains negative and significant.
    - Table 15 (Additional controls): D.commodity positive and significant (e.g., 0.489***, 0.460***, 0.414***), L.totalCost/laborCost negative and significant (-0.253**), D.totalCost/laborCost negative (-0.272***).
    - Table 16 (Tradable-sector-price deflated REER): SR ec ≈ -0.298*** to -0.322***; SRDD large negative and significant (≈ -0.328*** to -0.335***).
    - Table 17 (REER against the U.S.): baseline robustness holds with SR SRec ≈ -0.280*** and SR REER = -0.037** in one reported specification.
    - Table 19 (Total consumption and investment as proxy for total demand): LR REER negative in one specification (-0.160**); SR SRec ≈ -0.164***; SR DD strongly negative (e.g., -0.315***).
  - Across robustness checks, short-run cyclical demand deviations (SRec) frequently register large negative coefficients (statistically significant), indicating consistent short-run associations between cyclical demand components and external balance measures in the ECM framework.
  - Hausman tests reported in multiple tables produce p-values of 1.000 when comparing pooling mean group / mean group specifications versus dynamic fixed effect specification (reported in Tables 6 and 11).
- Figures (qualitative descriptions retained from source):
  - Figure 1: REERs and External Balance — country panels for Italy, Greece, Spain, China, Korea, United States with series NEER, REERcpi, REERulc, REERgdp and cagdp plotted (annual).
  - Figure 2: Flow Chart of the Model — agents: final producer, household, union, intermediate producer (and starred counterparts); note: agent shaded in blue is the one presetting price/wage.
  - Figure 3: Impulse Response to Labor Productivity Shock — plots for Exchange Rates (RERulc, RERcpi, RERgdp, NER) and External Balance (cay) across time.
  - Figure 4: Impulse Response to Monetary Policy Shock — analogous plots for exchange rates and external balance.
  - Figure 5: Contemporaneous and Lagged Correlations — lag plots for RERulc, RERcpi, RERgdp.
  - Figure 6: The Role of Home-Bias — impulse responses across α values (.5 to .95) for ULC-based RER, CPI-based RER, NER, GDP Deflator-based RER, TradeBalance/GDP Ratio, CurrentAccount/GDP Ratio.

### Key analytical takeaways (synthesis of presented empirical evidence)
- Real effective exchange rates (REERs) are driven substantially by nominal effective exchange rate (NEER) movements, but the relative contribution of NEER versus relative prices differs by REER measure:
  - REER-CPI shows the largest NEER contribution (e.g., 93% quarterly, 83% annual).
  - REER-ULC shows a smaller NEER share (66% quarterly, 79% annual) and larger relative-price share compared with CPI.
  - REER-GDP shows intermediate patterns (60% NEER quarterly; 87% NEER annual in reported decomposition).
- Error-correction model estimates consistently show:
  - Significant short-run negative associations between cyclical demand deviations (SRec) and external balance measures (large negative SR SRec coefficients, frequently significant at 1%).
  - Long-run relationships where domestic demand and foreign demand measures (LR DD, LR FD) and REER measures enter with varying signs and magnitudes depending on REER construction, but FD (foreign demand) often appears positively associated with the current account in long-run coefficients.
- Robustness checks across alternative samples, lag structures, REER constructions, and additional controls generally preserve the core short-run dynamics (SRec negative and significant) and maintain sensitivity of results to choice of REER measure and sample composition.
- The home-bias parameter α materially affects simulated RER responses to productivity shocks; the chosen α = 0.75 in the paper balances the ability to generate external balance dynamics while distinguishing ULC-based RER behavior from CPI- and GDP-deflator–based measures.

*Italic: Source — wp1781 - References (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1781.pdf_