## 3. Pricing Behavior of Domestic and Foreign Firms

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---

### I. Introduction
- Context:
  - Over the past two years (relative to the paper’s sample), the euro has appreciated by 30 percent against the dollar and by 20 percent in effective terms.
  - Key focus: the nature of exchange rate pass-through in the euro area and its role in external adjustment and “expenditure-switching.”
- Mechanisms generating incomplete pass-through:
  - Nominal rigidity and local currency pricing (LCP).
  - “Pricing to market” (PTM) via changing mark-ups in segmented markets.
  - Local distribution/trading costs that create international price discrimination.
- Methodology:
  - Two-part approach:
    - (1) empirical VAR analysis of the euro exchange rate and a system of euro area prices across the pricing chain;
    - (2) use VAR impulse-response functions (IRFs) to calibrate a NOEM-style open economy model to identify behavioral parameters (extent of LCP/PCP, nominal rigidity, local distribution costs).
  - Identification strategy: structural exchange rate shock obtained via Cholesky decomposition assuming high-frequency exchange rate innovations are driven by exogenous asset market disturbances.

### II. Empirical Estimates (data and main VAR findings)
- Data and variables (monthly, 1990–2002; all series in logarithms):
  - Exchange rate s: nominal effective series for ECB’s "narrow" partner group.
  - Factor prices/wages w: nominal compensation per employee (quarterly data extrapolated to monthly).
  - Trade prices pm (import) and px (export): unit values in extra-area manufacturing trade.
  - Producer prices py: producer price index for manufacturing, excluding construction and energy.
  - Consumer prices pc: core HICP (excluding energy and unprocessed foods).
- Stationarity/cointegration:
  - Levels nonstationary and first differences stationary (I(1)); residual-based cointegration tests do not find evidence of cointegration.
- VAR setup:
  - 6-variable VAR in first differences ordered: exchange rate, w, pm, px, py, pc.
  - Identification via Cholesky decomposition; exchange rate innovations assumed contemporaneously unaffected by price innovations.
- Impulse-response findings (accumulated responses to a unit structural exchange rate shock; horizon up to 18 months):
  - Short-run effects of a unit depreciation in the euro effective exchange rate on prices are very small; prices are initially sticky in local currency.
  - Pass-through generally rises over time; largest responses in trade prices, intermediate in wholesale/producer prices, smallest in wages and retail/consumer prices.
  - Export prices respond by almost one-half the response of import prices one year to 18 months after the shock, with import prices moving roughly in proportion to the unit exchange rate shock.
- Normalized pass-through elasticities (percent change in prices divided by percent change in exchange rate) from VAR IRFs:
  - Cpi: 0.00, 0.01, 0.02, 0.02
  - Ppi: 0.00, 0.04, 0.11, 0.17
  - Wage: -0.02, 0.04, 0.07, 0.05
  - Px: 0.02, 0.18, 0.31, 0.45
  - Pm: 0.03, 0.42, 0.81, 1.17
- Confidence and robustness:
  - Bootstrapped 90 percent confidence interval for import prices at 18 months: (0.6,1.4) (median 0.95).
  - Using headline rather than core inflation raises CPI pass-through to near 10 percent at 18 months; relative pass-through pattern unchanged.
  - Results robust to VAR reorderings and alternative specifications (though alternative specs can yield somewhat lower pass-through).

### III. Cross-Country Evidence (trade price pass-through comparisons)
- Import Prices (t = 1, t = 6, t = 12, t = 18):
  - Euro Area: 0.03, 0.42, 0.81, 1.17
  - United States: 0.06, 0.15, 0.18, 0.30
  - Japan: 0.61, 0.56, 0.57, 0.57
  - United Kingdom: 0.28, 0.58, 0.57, 0.60
  - Canada: 0.68, 0.54, 0.62, 0.68
- Export Prices (t = 1, t = 6, t = 12, t = 18):
  - Euro Area: 0.02, 0.18, 0.31, 0.45
  - United States: 0.00, 0.00, 0.06, 0.12
  - Japan: 0.62, 0.50, 0.48, 0.47
  - United Kingdom: 0.16, 0.47, 0.46, 0.50
  - Canada: 0.35, 0.19, 0.35, 0.44
- Cross-country patterns:
  - Pass-through is incomplete and typically small on impact.
  - Euro area: large rise in import price pass-through over time, near-unity by 18 months.
  - United States: smaller rise over time; US import/export pass-through remains low relative to euro area’s medium-term responses.
  - Japan and smaller open economies show higher immediate pass-through in trade prices.

### IV. Model of Incomplete Pass-Through (framework and parameters)
- Model structure:
  - Micro-founded NOEM-style model with imperfect competition, two differentiated goods (traded intermediate good and nontraded final good), and a domestic retail sector — yielding five price indices: pc, py, px, pm, w.
- Nominal rigidity:
  - Calvo-type price/wage updating with probability π of revision in a period; average duration between price changes = (1-π)/π.
- Currency pricing behaviors:
  - φ denotes share of domestic firms following producer currency pricing (PCP) for exports (φ = 1 → universal PCP; φ = 0 → universal LCP).
  - φ* denotes share of foreign firms following PCP in producing imports.
- Pricing to market via local distribution/trading costs:
  - Export sales require δ units of local labor services per unit sold; δ captures local distribution cost intensity and generates PTM behavior.
- Calibration benchmark:
  - Parameters generally follow Choudhri, Faruqee and Hakura (2002).
  - Monetary policy rule targets expected CPI inflation with interest rate smoothing (weights based on average non-U.S. G-7 estimates).
- Elasticities:
  - Elasticity of substitution σ between traded goods set at σ = 2.
  - Elasticity θ between varieties varied between θ = 4 to 10 in sensitivity checks.

### V. Matching Theory and Empirics (estimation of behavioral parameters)
- Identification and estimation:
  - Model shocked by an asset-market UIP shock ξ calibrated to match the VAR exchange rate IRF to a structural exchange rate shock sε.
  - Loss function minimized over structural parameters θ = {δ, π, φ, φ*} using least squares between model-simulated price IRFs and VAR price IRFs over an 18-month horizon.
- Empirical implications and patterns:
  - Asymmetric pricing behavior between domestic and foreign firms often outperforms symmetric mixtures of LCP and PCP.
  - Larger, more insular economies (United States and euro area) gravitate toward pricing in the domestic/dominant currency: LCP in imports and PCP in exports.
  - Smaller, more open economies and Japan gravitate toward pricing in foreign/destination currencies: LCP in exports and PCP in imports.
- Calibrated parameter ranges and country-specific minimum-distance estimates:
  - Implicit local distribution costs δ (percent of final goods price; broad ranges):
    - United States: 45-65
    - Euro Area: 55-65
    - Japan: 65-70
    - United Kingdom: 60-65
    - Canada: 50-65
  - Optimized behavioral parameter summary:
    - United States: φ = 1.00, φ* = 0.04, π = 0.05, δ = 0.65, R-squared = 0.61
    - Euro Area: φ = 0.94, φ* = 0.18, π = 0.10, δ = 0.60, R-squared = 0.91
    - Japan: φ = 0.24, φ* = 0.80, π = 0.05, δ = 0.65, R-squared = 0.98
    - United Kingdom: φ = 0.40, φ* = 0.68, π = 0.05, δ = 0.65, R-squared = 0.91
    - Canada: φ = 0.66, φ* = 0.78, π = 0.10, δ = 0.60, R-squared = 0.88
- Notes on identification:
  - π typically ranges from 5 percent to 10 percent in the optimized fits (average duration between price changes about 3–6 quarters).
  - Higher δ or lower π can both generate protracted incomplete pass-through; several combinations of (δ, π) yield similar model fits.
- Trade balance implications:
  - Even with LCP and PTM, expenditure-switching effects operate; an exchange rate depreciation improves the trade balance once volume and pass-through effects are included.
  - Because short-run trade elasticities can be small, achieving a moderate external adjustment solely through exchange rate moves may require substantial exchange rate changes absent other adjustments.

### VI. Conclusions (key takeaways)
- Short-run pass-through in the euro area is very low across a wide range of prices; immediate impact of an exchange rate shock on wages, trade prices, and wholesale/retail prices (excluding energy) is near zero.
- Pass-through rises over time in the euro area, but wage and consumer price pass-through remain comparatively small; import prices show the highest pass-through (near unity by 18 months).
- The wedge between import price pass-through and consumer price pass-through highlights the importance of local distribution and retail sectors in price determination.
- Pricing behavior is asymmetric across countries:
  - United States and euro area: firms tend to price in domestic/dominant currencies (LCP in imports, PCP in exports).
  - Japan and smaller open economies: firms tend to price in foreign/destination currencies.
- Policy implication:
  - Exchange rate movements can improve trade balances, but the magnitude of exchange rate adjustment required for moderate external rebalancing can be substantial given incomplete and persistent pass-through; other adjustment channels may be needed.

### Appendix — Selected test results (evidence supporting VAR approach)
- Unit root and stationarity tests (Euro Area monthly data, 1990–2002) — selected results (Phillips-Perron Zt and KPSS ητ; order of integration):
  - Neer: Phillips-Perron Zt = -2.34; KPSS ητ = 0.34**; Order I(1)
  - ∆ Neer: Zt = -8.46**; KPSS ητ = 0.07; Order I(0)
  - Cpi: Zt = -2.89; KPSS ητ = 0.74**; Order I(1)
  - ∆ Cpi: Zt = -10.87**; KPSS ητ = 0.36**; Order I(0) or I(1)
  - Ppi: Zt = -1.66; KPSS ητ = 0.32**; Order I(1)
  - ∆ Ppi: Zt = -5.86**; KPSS ητ = 0.09; Order I(0)
  - Px: Zt = -0.92; KPSS ητ = 0.27**; Order I(1)
  - ∆ Px: Zt = -3.29*; KPSS ητ = 0.10; Order I(0)
  - Pm: Zt = -2.38; KPSS ητ = 0.15**; Order I(1)
  - ∆ Pm: Zt = -2.61; KPSS ητ = 0.11; Order I(0) or I(1)
  - Wage: Zt = -2.46; KPSS ητ = 0.63**; Order I(1)
  - ∆ Wage: Zt = -6.56**; KPSS ητ = 0.07; Order I(0)
  - Note: An *(**) indicates significance at the 10 (5) percent level.
- Cointegration tests (Phillips-Ouliaris residual-based multivariate trace statistic; window size = 2):
  - No. of regressors n = 5: zPˆ Test (demeaned) = 115.10 (10 percent critical value = 225.23); zPˆ Test (demeaned & detrended) = 120.43 (284.01) — fail to reject null of no cointegration.
- Granger causality and block exogeneity tests:
  - Bivariate Granger causality p-values for H0: Exchange rate does not cause price measure (lags reported):
    - Cpi (lags 12): 0.66
    - Ppi (lags 14): 0.99
    - Px (lags 13): 0.06
    - Pm (lags 13): 0.00
    - Wage (lags 14): 0.54 (at one lag exchange rate Granger-causes wages with p = 0.04)
  - Block exogeneity (multivariate) with p = 7: H0: A2 = 0 → test statistic 32.42 (0.59); H0: B1 = 0 → 50.48 (0.04).

### Euro Area Pass-Through Elasticities Across VAR Reorderings (Table 9)
- Notes: Entries report percent change in price measure divided by percent change in exchange rate in response to unit exchange rate shock from Cholesky decomposition.
- Exchange Rate First in VAR:
  - Cpi — t = 1: 0.00; t = 6: 0.01; t = 12: 0.02; t = 18: 0.02
  - Ppi — t = 1: 0.00; t = 6: 0.04; t = 12: 0.11; t = 18: 0.17
  - Wage — t = 1: -0.02; t = 6: 0.04; t = 12: 0.07; t = 18: 0.05
  - Px — t = 1: 0.02; t = 6: 0.18; t = 12: 0.31; t = 18: 0.45
  - Pm — t = 1: 0.03; t = 6: 0.42; t = 12: 0.81; t = 18: 1.17
- Exchange Rate Last in VAR:
  - Cpi — t = 1: 0; t = 6: 0.02; t = 12: 0.02; t = 18: 0.03
  - Ppi — t = 1: 0; t = 6: 0.05; t = 12: 0.11; t = 18: 0.18
  - Wage — t = 1: 0; t = 6: 0.04; t = 12: 0.08; t = 18: 0.05
  - Px — t = 1: 0; t = 6: 0.10; t = 12: 0.20; t = 18: 0.30
  - Pm — t = 1: 0; t = 6: 0.30; t = 12: 0.63; t = 18: 0.97
- Appendix findings:
  - The implied pass-through elasticities from the two VAR reorderings are fairly similar.
  - On impact, euro area prices are essentially predetermined in response to the exchange rate shock.
  - For the euro area (and the United States) the restriction that prices are predetermined appears valid empirically; reordering makes little difference.
  - For other industrial countries, the restriction generally is not valid for trade prices and should not be imposed.

*Source: _wp0414 - 3. Pricing Behavior of Domestic and Foreign Firms (PDF chapter).*

### References..............................................................................................................

### _wp0414 - References.............................................................................................................................. 23

### Tables
- 1. Euro Area Pass-Through Elasticities ........................................................................... 9
- 2. Pass-Through Elasticities in Trade Prices: International Comparisons ..................... 11
- 3. Implicit Estimates of Local Distribution Costs.......................................................... 16
- 4.         Summary         of         Behavioral Parameter Estimates ........................................................... 17
- 5. Unit Root and Stationarity Tests................................................................................ 19
- 6.         Cointegration         Tests .................................................................................................... 19
- 7.         Bivariate         Granger         Causality Tests ............................................................................. 20
- 8. Block Exogeneity Tests ............................................................................................. 20
- 9. Euro Area Pass-Through Elasticities Across VAR Re-orderings.............................. 22

### Figures
- 1. Euro Area Nominal Exchange Rates ........................................................................... 3
- 2. Effects of an Exchange Rate Shock on Euro Area Prices............................................ 8

*Source: _wp0414 - References.............................................................................................................................. 23*

### 3. Pricing Behavior of Domestic and Foreign Firms ..................................................... 14

### _wp0414 - 3. Pricing Behavior of Domestic and Foreign Firms ..................................................... 14

### I. INTRODUCTION
- Over the past two years (relative to the paper’s sample), the euro has appreciated by 30 percent against the dollar and by 20 percent in effective terms.
- Key focus: the nature of exchange rate pass-through in the euro area and its role in external adjustment and “expenditure-switching.”
- Mechanisms generating incomplete pass-through discussed:
  - Nominal rigidity and local currency pricing (LCP).
  - “Pricing to market” (PTM) via changing mark-ups in segmented markets.
  - Local distribution/trading costs that create international price discrimination.
- Methodology overview:
  - Two-part approach: (1) empirical VAR analysis of the euro exchange rate and a system of euro area prices across the pricing chain; (2) use VAR impulse-response functions (IRFs) to calibrate a NOEM-style open economy model to identify behavioral parameters (extent of LCP/PCP, nominal rigidity, local distribution costs).
- Identification strategy: structural exchange rate shock obtained via Cholesky decomposition assuming high-frequency exchange rate innovations are driven by exogenous asset market disturbances.

### II. EMPIRICAL ESTIMATES (data and main VAR findings)
- Data:
  - Monthly frequency, 1990 through 2002; all series in logarithms.
  - Exchange rate s: nominal effective series for ECB’s "narrow" partner group.
  - Factor prices/wages w: nominal compensation per employee (quarterly data extrapolated to monthly).
  - Trade prices pm (import) and px (export): unit values in extra-area manufacturing trade.
  - Producer prices py: producer price index for manufacturing, excluding construction and energy.
  - Consumer prices pc: core HICP (excluding energy and unprocessed foods).
- Stationarity/cointegration:
  - Unit root and stationarity tests indicate levels are nonstationary and first differences stationary (I(1)); residual-based cointegration tests do not find evidence of cointegration.
- VAR setup:
  - 6-variable VAR in first differences with variables ordered: exchange rate first, then w, pm, px, py, pc (pricing-chain motivation).
  - Identification: Cholesky decomposition; exchange rate innovations assumed contemporaneously unaffected by price innovations.
- Impulse-response findings (accumulated responses to a unit structural exchange rate shock; horizon up to 18 months):
  - Short-run effects of a unit depreciation in the euro effective exchange rate on prices are very small; prices are initially sticky in local currency.
  - Pass-through generally rises over time; largest responses in trade prices, intermediate in wholesale producer prices, smallest in wages and retail consumer prices.
  - Export prices respond by almost one-half the response of import prices one year to 18 months after the shock, with import prices moving roughly in proportion to the unit exchange rate shock (suggesting near-full pass-through in imports over time).
- Normalized pass-through elasticities (Percent change in prices divided by percent change in exchange rate), based on VAR IRFs (time horizons T = 1, t = 6, t = 12, t = 18):
  - Cpi: 0.00, 0.01, 0.02, 0.02
  - Ppi: 0.00, 0.04, 0.11, 0.17
  - Wage: -0.02, 0.04, 0.07, 0.05
  - Px: 0.02, 0.18, 0.31, 0.45
  - Pm: 0.03, 0.42, 0.81, 1.17
- Confidence / robustness:
  - Bootstrapped 90 percent confidence interval for import prices at 18 months reported as (0.6,1.4) (median 0.95), indicating substantial standard errors but central estimate near or above unity.
  - Using headline rather than core inflation raises CPI pass-through to near 10 percent at 18 months; relative pass-through pattern unchanged.
  - Results robust to reorderings of the VAR and alternative specifications (though alternative specs can yield somewhat lower pass-through).

### III. CROSS-COUNTRY EVIDENCE (trade price pass-through comparisons)
- Pass-through elasticities in trade prices (Import and Export Prices) for t = 1, t = 6, t = 12, t = 18 (values drawn from VAR IRFs; based on monthly 1990–2002):
  - Import Prices
    - Euro Area: 0.03, 0.42, 0.81, 1.17
    - United States: 0.06, 0.15, 0.18, 0.30
    - Japan: 0.61, 0.56, 0.57, 0.57
    - United Kingdom: 0.28, 0.58, 0.57, 0.60
    - Canada: 0.68, 0.54, 0.62, 0.68
  - Export Prices
    - Euro Area: 0.02, 0.18, 0.31, 0.45
    - United States: 0.00, 0.00, 0.06, 0.12
    - Japan: 0.62, 0.50, 0.48, 0.47
    - United Kingdom: 0.16, 0.47, 0.46, 0.50
    - Canada: 0.35, 0.19, 0.35, 0.44
- Cross-country patterns:
  - Pass-through is incomplete and typically small on impact.
  - Euro area: large rise in import price pass-through over time, yielding near-unity pass-through by 18 months.
  - United States: much smaller rise over time; US import/export pass-through remains low relative to euro area’s medium-term responses.
  - Japan and smaller open economies show higher immediate pass-through in trade prices.

### IV. MODEL OF INCOMPLETE PASS-THROUGH (framework and parameters)
- The calibrated model: a micro-founded NOEM-style model with imperfect competition, two differentiated goods (traded intermediate good and nontraded final good), and a domestic retail sector — yielding five price indices: pc, py, px, pm, w.
- Nominal rigidity: Calvo-type price/wage updating with probability π of revision in a period; average duration between price changes = (1-π)/π.
- Currency pricing behaviors:
  - φ denotes share of domestic firms following producer currency pricing (PCP) for exports (φ = 1 → universal PCP; φ = 0 → universal LCP).
  - φ* denotes share of foreign firms following PCP in producing imports.
- Pricing to market via local distribution/trading costs:
  - Export sales require δ units of local labor services per unit sold; δ captures local distribution cost intensity and generates PTM behavior.
- Calibration benchmark: parameters generally follow Choudhri, Faruqee and Hakura (2002); monetary policy rule targets expected CPI inflation with interest rate smoothing (weights based on average non-U.S. G-7 estimates).
- Elasticities:
  - Elasticity of substitution σ between traded goods set at σ = 2 (minimizes distance between IRFs), elasticity θ between varieties varied between θ = 4 to 10 in sensitivity checks.

### V. MATCHING THEORY AND EMPIRICS (estimation of behavioral parameters)
- Identification approach:
  - Model shocked by an asset-market UIP shock ξ calibrated to match the VAR exchange rate IRF to a structural exchange rate shock sε.
  - Loss function minimized over structural parameters θ = {δ, π, φ, φ*} using least squares between model-simulated price IRFs and VAR price IRFs over an 18-month horizon.
- Optimal combinations and interpretation:
  - Figure 3 (described) maps optimal shares of PCP in exports (φ on horizontal axis) and PCP in imports (φ* on vertical axis) for major economies.
  - Empirical implication: asymmetric pricing behavior between domestic and foreign firms often outperforms symmetric mixtures of LCP and PCP.
    - Larger, more insular economies (United States and euro area) gravitate toward pricing in the domestic/dominant currency: LCP in imports and PCP in exports.
    - Smaller, more open economies and Japan gravitate toward pricing in foreign currencies: LCP in exports and PCP in imports.
  - Invoice-currency evidence (Bekx (1998) cited in text) aligns with these implied pricing patterns.
- Calibrated parameter ranges and country-specific estimates:
  - Implicit local distribution costs δ (expressed as percent of final goods price; broad ranges reflect parameter identification tradeoffs):
    - United States: 45-65
    - Euro Area: 55-65
    - Japan: 65-70
    - United Kingdom: 60-65
    - Canada: 50-65
  - Optimized behavioral parameter summary (minimum-distance estimates):
    - United States: φ = 1.00, φ* = 0.04, π = 0.05, δ = 0.65, R-squared = 0.61
    - Euro Area: φ = 0.94, φ* = 0.18, π = 0.10, δ = 0.60, R-squared = 0.91
    - Japan: φ = 0.24, φ* = 0.80, π = 0.05, δ = 0.65, R-squared = 0.98
    - United Kingdom: φ = 0.40, φ* = 0.68, π = 0.05, δ = 0.65, R-squared = 0.91
    - Canada: φ = 0.66, φ* = 0.78, π = 0.10, δ = 0.60, R-squared = 0.88
  - Notes on π and δ identification:
    - π typically ranges from 5 percent to 10 percent in the optimized fits (average duration between price changes about 3–6 quarters).
    - Higher δ or lower π can both generate protracted incomplete pass-through; several combinations of (δ, π) yield similar model fits.
- Trade balance implications from calibrated model:
  - Even with LCP and PTM, expenditure-switching effects operate; an exchange rate depreciation improves the trade balance once volume and pass-through effects are included.
  - Because short-run trade elasticities can be small, achieving a moderate external adjustment solely through exchange rate moves may require substantial exchange rate changes absent other adjustments.

### VI. CONCLUSIONS (key takeaways)
- Short-run pass-through in the euro area is very low across a wide range of prices; immediate impact of an exchange rate shock on wages, trade prices, and wholesale/retail prices (excluding energy) is near zero.
- Pass-through rises over time in the euro area, but wage and consumer price pass-through remain comparatively small; import prices show the highest pass-through (near unity by 18 months).
- The wedge between import price pass-through and consumer price pass-through highlights the importance of local distribution and retail sectors in price determination.
- Pricing behavior is asymmetric across countries:
  - United States and euro area: firms tend to price in domestic/dominant currencies (LCP in imports, PCP in exports).
  - Japan and smaller open economies: firms tend to price in foreign/destination currencies.
- Policy implication: exchange rate movements can improve trade balances, but the magnitude of exchange rate adjustment required for moderate external rebalancing can be substantial given incomplete and persistent pass-through; other adjustment channels may be needed.

### APPENDIX — Selected test results (evidence supporting VAR approach)
- Unit root and stationarity tests (Euro Area monthly data, 1990-2002) — summary of results (Phillips-Perron Zt and KPSS ητ tests; order of integration):
  - Neer: Phillips-Perron Zt = -2.34; KPSS ητ = 0.34**; Order I(1)
  - ∆ Neer: Zt = -8.46**; KPSS ητ = 0.07; Order I(0)
  - Cpi: Zt = -2.89; KPSS ητ = 0.74**; Order I(1)
  - ∆ Cpi: Zt = -10.87**; KPSS ητ = 0.36**; Order I(0) or I(1)
  - Ppi: Zt = -1.66; KPSS ητ = 0.32**; Order I(1)
  - ∆ Ppi: Zt = -5.86**; KPSS ητ = 0.09; Order I(0)
  - Px: Zt = -0.92; KPSS ητ = 0.27**; Order I(1)
  - ∆ Px: Zt = -3.29*; KPSS ητ = 0.10; Order I(0)
  - Pm: Zt = -2.38; KPSS ητ = 0.15**; Order I(1)
  - ∆ Pm: Zt = -2.61; KPSS ητ = 0.11; Order I(0) or I(1)
  - Wage: Zt = -2.46; KPSS ητ = 0.63**; Order I(1)
  - ∆ Wage: Zt = -6.56**; KPSS ητ = 0.07; Order I(0)
  - Note: An *(**) indicates significance at the 10 (5) percent level.
- Cointegration tests (Phillips-Ouliaris residual-based multivariate trace statistic; window size = 2):
  - No. of regressors n = 5: zPˆ Test (demeaned) = 115.10 (10 percent critical value in parentheses = 225.23); zPˆ Test (demeaned & detrended) = 120.43 (284.01) — fail to reject null of no cointegration.
- Granger causality and block exogeneity tests:
  - Bivariate Granger causality p-values for H0: Exchange rate does not cause price measure:
    - Cpi (lags 12): 0.66
    - Ppi (lags 14): 0.99
    - Px (lags 13): 0.06
    - Pm (lags 13): 0.00
    - Wage (lags 14): 0.54 (at one lag exchange rate Granger-causes wages with p = 0.04)
  - Block exogeneity (multivariate) with p = 7: H0: A2 = 0 → test statistic 32.42 (0.59); H0: B1 = 0 → 50.48 (0.04).

*Source: _wp0414 - 3. Pricing Behavior of Domestic and Foreign Firms (PDF chapter).*

### 0.2 with the notable exceptions of the exchange rate and trade prices and between trade

### _wp0414 - 0.2 with the notable exceptions of the exchange rate and trade prices and between trade

### Euro Area Pass-Through Elasticities Across VAR Reorderings (Table 9)
- Notes: Entries report percent change in price measure divided by percent change in exchange rate in response to unit exchange rate shock from Cholesky decomposition of innovations.
- (Exchange Rate First in VAR)
  - Cpi — t = 1: 0.00; t = 6: 0.01; t = 12: 0.02; t = 18: 0.02
  - Ppi — t = 1: 0.00; t = 6: 0.04; t = 12: 0.11; t = 18: 0.17
  - Wage — t = 1: -0.02; t = 6: 0.04; t = 12: 0.07; t = 18: 0.05
  - Px — t = 1: 0.02; t = 6: 0.18; t = 12: 0.31; t = 18: 0.45
  - Pm — t = 1: 0.03; t = 6: 0.42; t = 12: 0.81; t = 18: 1.17
- (Exchange Rate Last in VAR)
  - Cpi — t = 1: 0; t = 6: 0.02; t = 12: 0.02; t = 18: 0.03
  - Ppi — t = 1: 0; t = 6: 0.05; t = 12: 0.11; t = 18: 0.18
  - Wage — t = 1: 0; t = 6: 0.04; t = 12: 0.08; t = 18: 0.05
  - Px — t = 1: 0; t = 6: 0.10; t = 12: 0.20; t = 18: 0.30
  - Pm — t = 1: 0; t = 6: 0.30; t = 12: 0.63; t = 18: 0.97

### Findings from the Appendix discussion
- The implied pass-through elasticities from the two VAR reorderings are fairly similar.
- On impact, euro area prices are essentially predetermined in response to the exchange rate shock.
- In the VAR with exchange rate ordered last, the exchange rate shock has zero contemporaneous effect on prices (i.e., prices are fully predetermined) by construction based on the ordering of variables.
- For the euro area (and the United States) the restriction that prices are predetermined appears valid empirically; therefore, reordering makes little difference.
- For other industrial countries, the restriction generally is not valid for trade prices (as shown by Table 2 in the source) and should not be imposed.
- If the exchange rate appears before trade prices in the VAR for these other countries, alternative impulse-response functions will closely match those reported in the text.

### Enumeration and combinatorics noted in the Appendix
- The possible reorderings can be enumerated as follows: ∑ = 5 0x 5Cx = 32, where nCr denotes the “n choose r.”

*Source: Appendix (Table 9) and accompanying text, _wp0414*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0414.pdf_