## 1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010

## Source details

**Canonical URL:** [1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12226.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12226.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12226.pdf.json)

---

### Introduction and theoretical framing
- Central question: role of nominal rigidities and currency choice (producer currency pricing, PCP, versus local currency pricing, LCP) in determining exchange rate pass-through to import and export prices and implications for monetary policy.
- Baseline implications:
  - PCP → import pass-through = 1, export pass-through = 0 (baseline preset-price models).
  - LCP → reversed implications.
- Empirical regularities contradict baseline PCP/LCP predictions: import and export pass-through estimates typically lie between 0 and 1 and often near one-half.
- Alternate mechanisms in literature include markup adjustment; this paper focuses on a DSGE model with a mix of PCP and LCP firms and Calvo staggered price-setting with a constant markup (markup adjustment abstracted away).

### Empirical strategy and methodology
- Two empirical approaches:
  - Simple regression of log differences: Δp_t = a Δs_t (short-run pass-through = coefficient a); simple specification used to capture direct and indirect effects and avoid sensitivity to controls.
  - VAR approach: orthogonalized VAR (Δs_t ordered first) to estimate current-period elasticity of Δp_t to an innovation in Δs_t.
- Sample: quarterly import and export price indexes for countries with at least 52 quarters of data since 1979.
- Assumption: variables in logs are nonstationary and not cointegrated (unit root and cointegration tests support typical characterization).

### Key empirical findings (regression and VAR)
- Regression estimates (simple regression, no controls):
  - Advanced-country group (18 countries):
    - Import pass-through is, with one exception, between 0 and 1; significantly different from 0 for all countries, and significantly different from 1 for most.
    - Export pass-through is between 0 and 1 for all but one country; generally significantly different from both 0 and 1.
    - Import pass-through tends to be larger than export pass-through.
    - Average pass-through coefficients: export price = 0.39; import price = 0.67.
    - The average values for import and export pass-through are significantly different from each other.
  - Emerging-market group (16 countries):
    - Broadly similar pattern to advanced countries.
    - Two countries show negative pass-through coefficients.
    - In two countries, import pass-through is smaller than export pass-through.
    - Average pass-through coefficients: import price = 0.63; export price = 0.53.
- VAR estimates:
  - VAR-based pass-through estimates are close to simple-regression estimates.
  - Advanced countries (VAR):
    - Pass-through to both import and export price indexes is above 0 and below 1 for all countries.
    - Import pass-through exceeds export pass-through in 17 out of 18 countries; difference statistically significant (p-value ≤ 0.1) for 11 countries.
    - Average VAR-based pass-through for import price = 0.60.
- Subperiods (1985–1997 vs 1998–2010): estimates less precise, no clear systematic pattern across subperiods.

### DSGE model: structure, calibration, and key mechanisms
- Model features:
  - Open-economy DSGE with Calvo staggered price-setting.
  - Firms are a mix of PCP and LCP users; proportion of PCP (ψ, ψ*) varies between 0 and 1.
  - Constant markup (no explicit markup adjustment).
  - Both nominal and real shocks incorporated; shocks follow AR(1) processes with persistence parameters Xρ and Aρ (0 < Xρ < 1, 0 < Aρ < 1).
  - Central bank policy rule (simplified): Rt+1 = R + δ(πt+1 − Π), with δ > 0.
- Calibration choices (reported in text):
  - share of imports in income γ = 0.3 (median import share; sample average 0.32)
  - quarterly discount factor β = 0.99
  - coefficient of risk aversion χ = 2.0
  - elasticity of labor supply 1/ν = 0.5
  - elasticity of substitution between home and foreign goods η = 2.0
  - elasticity of substitution between varieties ε = 6.0
  - Aρ and *Aρ = 0.95
  - Av and *Av = 0.007
  - correlation of productivity disturbances = 0.25
  - Xv = 0.007; Xρ = 0.8 (baseline)
  - ψ = *ψ = 0.5; Wθ = θ = 0.75
  - δ = *δ = 0.5
  - transaction-cost parameter κ assumed very small (unique steady state SB*/P = 0)

### Log-linear relations and pass-through determinants
- Import-price log-linear relation highlights composition of PCP and LCP components and dependence on exchange rate log-differences and expected future values (equations summarized in text).
- Export-price linearized relations analogous.
- Linearized exchange rate equation: s depends on nominal and real shocks, inflation gaps, and interest-rate-response parameters (δ, δ*).
- Pass-through elasticities depend on:
  - shares of home and foreign firms using PCP (ψ, ψ*)
  - frequencies of price and wage change (θ, θW)
  - persistence of exchange rate shocks (ρx)
  - interest-rate responsiveness to inflation (δ, δ*)
  - nominal disturbances tend to have a stronger impact than real disturbances.

### Quantitative results: impulse responses and short-run elasticities
- Dynamic response horizon: 20 quarters; effects concentrated in first quarter.
- First-quarter effect of nominal shock is much larger than that of real shocks for exchange rate and trade prices.
- Short-run (current-period) pass-through elasticities to a one-standard-deviation nominal shock (baseline):
  - Import price pass-through elasticity: 0.57.
  - Export price pass-through elasticity: 0.40.
- Real-shock elasticities (examples):
  - Home productivity shock: export price elasticity = -0.22.
  - Foreign productivity shock: import price elasticity = -0.17.
- Composite (simultaneous one-standard-deviation increase in X, A, *A): elasticities similar to nominal-shock-only case (nominal shock dominates).

### Sensitivity experiments: PCP shares, wage-price stickiness, persistence, and monetary reaction
- Effect of foreign PCP share on import price pass-through (baseline home PCP = 0.5):
  - Import pass-through below 0.2 if foreign PCP share = 0.
  - Import pass-through increases with foreign PCP share and equals 1 when foreign PCP share = 1.
- Effect of home PCP share on export price pass-through (baseline foreign PCP = 0.5):
  - Export pass-through above 0.8 when home PCP share = 0.
  - Export pass-through decreases with home PCP share and falls below 0.1 when home PCP share = 1.
- Comparative implication: import pass-through would exceed export pass-through if both home and foreign PCP shares > a value just below 0.5.
- Wage-price stickiness experiment (Table 4):
  - Increase Wθ to 0.667 and θ to 0.5 (higher frequency of wage and price change):
    - import price pass-through increases from 0.57 to 0.73
    - export price pass-through decreases from 0.41 to 0.33
  - Interpretation: greater wage-price flexibility has an effect similar to increasing PCP shares.
- Persistence and monetary reaction experiments (vary Xρ from 0.6 to 0.95 and δ from 0.1 to 1.0): lower or higher persistence or less/more aggressive reaction to inflation do not have large effects on pass-through values.
- Conclusion: PCP shares and wage-price stickiness are the major sources of variation in short-run pass-through for import and export prices.

### Stochastic simulations and model variants: fit to data and role of nominal vs real shocks
- Simulation protocol: simulated series for 227 quarters; first 100 quarters dropped to match sample length of 127 quarters; variables used: Δs_t, Δp^M_t, Δp^X_t, Δp_t.
- Baseline model (selected statistics):
  - Standard Dev. Δs_t = 0.0329 ; Standard Dev. Δπ_t = 0.0075
  - OLS Import Price PT = 0.607 ; VAR Import Price PT = 0.614
  - OLS Export Price PT = 0.466 ; VAR Export Price PT = 0.463
- Data (Advanced countries) for comparison:
  - Standard Dev. Δs_t = 0.0245 ; Standard Dev. Δπ_t = 0.0086
  - OLS Import Price PT = 0.67 ; VAR Import Price PT = 0.60
  - OLS Export Price PT = 0.39 ; VAR Export Price PT = 0.39
- Variant 1 (better fit): Xv ↓ to 0.0025; Xρ ↑ to 0.95; ψ ↑ to 0.55; *ψ ↓ to 0.45
  - Standard Dev. Δs_t = 0.0233 ; Standard Dev. Δπ_t = 0.0083
  - OLS Import Price PT = 0.655 ; VAR Import Price PT = 0.611
  - OLS Export Price PT = 0.398 ; VAR Export Price PT = 0.405
- Variant 2 (only nominal shocks): result similar to Variant 1 (absence of real shocks does not much affect standard deviations or pass-through coefficients).
- Variant 3 (only real shocks): major differences
  - Standard Dev. Δs_t = 0.0040 ; Standard Dev. Δπ_t = 0.0015
  - OLS Import Price PT = 0.341 ; VAR Import Price PT = 0.072
  - OLS Export Price PT = 0.324 ; VAR Export Price PT = 0.050
  - Conclusion: nominal shocks are required to reproduce observed exchange rate and inflation variability and similarity of regression and VAR pass-through estimates.
- PCP-share variants:
  - Variant 4 (ψ = 0.8, *ψ = 0.2; U.S.-like): lowers both import and export pass-through coefficients (OLS Import PT = 0.437; OLS Export PT = 0.230).
  - Variant 5 (ψ = 0.2, *ψ = 0.8): both pass-through and variability measures increase (OLS Import PT = 0.883; OLS Export PT = 0.667).
  - Implication: cross-country differences in PCP shares can account for associations between inflation or exchange rate stability and low pass-through coefficients.

### Evidence on currency of invoicing and PCP shares
- Data (Kamps, 2006) for a subset of 15 countries used to construct invoicing-based measures of PCP shares.
- OLS regressions (Table 6) linking invoicing shares to VAR pass-through estimates:
  - Export price pass-through:
    - Constant = 0.615 (0.074)*
    - Exporter-currency share in exports coefficient = -0.005 (0.0016)* (negative and significant; consistent with model prediction that higher home PCP share reduces export pass-through)
  - Import price pass-through:
    - Constant = 0.461 (0.186)*
    - Exporter-currency share in imports coefficient = 0.002 (0.0027) (positive but insignificant; measure problematic due to inclusion of Euro invoicing)
    - US dollar share in imports coefficient = 0.008 (0.0035)* (positive and significant)
  - Observations: export model No. of Obs. = 15 ; import models No. of Obs. = 13
  - R-squared: export model = 0.440 ; import models = 0.053 and 0.287
- Empirical evidence from invoicing currency shares supports the model predictions on PCP shares' effects on import and export pass-through.

### Key tables and selected numeric summaries (selected exact figures)
- Table 1 — OLS (Advanced economies average): Import Price Pass-Through 0.67(0.03); Export Price Pass-Through 0.39(0.03).
- Table 2 — VAR (Advanced economies average): Import Price Response 0.60(0.03); Export Price Response 0.39(0.02).
- Table 3 — Pass-Through Elasticities for Different Shocks:
  - Nominal Shock: Import Price 0.572 ; Export Price 0.404
  - Home Productivity Shock: Import Price 0.346 ; Export Price -0.221
  - Foreign Productivity Shock: Import Price -0.167 ; Export Price 0.404
  - Composite Shock: Import Price 0.523 ; Export Price 0.381
- Table 4 — Wage-Price Stickiness (nominal shock elasticities):
  - Baseline: Import Price Pass-Through 0.572 ; Export Price Pass Through 0.419
  - Less stickiness (.5, .667 W θ θ  ): Import 0.727 ; Export 0.332
- Table 5 — Stochastic Simulations (selected rows shown above).
- Appendix subperiod averages (advanced economies):
  - 1985–1997: Import Price Response 0.550.036 ; Export Price Response 0.370.037
  - 1998–2010: Import Price Response 0.490.048 ; Export Price Response 0.460.044

### Policy-relevant conclusions and implications
- A hybrid model with a mix of PCP and LCP, even without markup adjustment, can reproduce:
  - pass-through elasticities in (0,1) for import and export prices;
  - systematic finding that import pass-through tends to exceed export pass-through;
  - similarity between simple-regression and VAR estimates (driven by dominance of nominal shocks and Calvo-style stickiness).
- Nominal shocks are essential to:
  - produce sufficient exchange rate and inflation variability;
  - account for similarity between regression and VAR pass-through estimates.
- Primary determinants of short-run pass-through: PCP shares (ψ, ψ*) and wage-price stickiness (θ, θW); monetary shock properties and Taylor-rule aggressiveness (δ) have smaller effects.
- Cross-country differences in home and foreign PCP shares can explain associations between exchange rate/inflation stability and low pass-through coefficients.
- Policy implication: exchange rate flexibility can facilitate relative price adjustment in transmission of shocks even when firms use a mix of PCP and LCP; benefits of flexibility are realized in the hybrid case.

* _wp12226 - 1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010 (excerpt from source PDF)._

### 1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010 ...........24

### 1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010

### Introduction and theoretical framing
- Central question: role of nominal rigidities and currency choice (producer currency pricing, PCP, versus local currency pricing, LCP) in determining exchange rate pass-through to import and export prices and implications for monetary policy.
- Baseline implications:
  - PCP (prices sticky in producer currency) → import pass-through = 1, export pass-through = 0 (in baseline preset-price models).
  - LCP (prices sticky in local consumer currency) → reversed implications.
- Empirical regularities contradict baseline PCP/LCP predictions:
  - Import price pass-through for OECD countries typically significantly different from 0 and 1 and on average close to one-half (Campa and Goldberg, 2005).
  - Export price pass-through estimates also do not support baseline PCP or LCP.
- Alternative mechanisms considered in literature:
  - Markup adjustment mechanisms (e.g., Corsetti and Dedola, 2005) can generate observed pass-through and exchange rate–terms-of-trade associations even with flexible prices.
  - This paper focuses on an alternative: a DSGE model with a mix of PCP and LCP firms and Calvo staggered price-setting, but with a constant markup (i.e., abstracting from explicit markup adjustment channels).

### Empirical strategy and methodology
- Two empirical approaches used:
  - Simple regression of log differences: Δp_t = a Δs_t + (controls omitted in the simple specification), where short-run (current quarter) pass-through is coefficient a. The paper uses the simple regression (without additional controls t_g) to incorporate direct and indirect effects and avoid sensitivity to choice/measurement of controls.
  - VAR approach: orthogonalized VAR (variables ordered with Δs_t first) to estimate current-period elasticity of Δp_t to an innovation in Δs_t (the exchange rate innovation is a composite of structural disturbances but isolates exogenous exchange rate shocks in this setup).
- Sample selection: quarterly import and export price indexes for countries with at least 52 quarters of data since 1979.
- Assumption for regression/VAR: variables in logs are nonstationary and not cointegrated (typical characterization supported by unit root and cointegration tests).

### Key empirical findings (regression and VAR)
- Regression estimates (simple regression, no controls):
  - Advanced-country group (18 countries):
    - For import prices: pass-through coefficient is, with one exception, between 0 and 1, significantly different from 0 for all countries, and significantly different from 1 for most countries.
    - For export prices: coefficient is between 0 and 1 for all but one country, generally significantly different from both 0 and 1.
    - Import pass-through tends to be larger than export pass-through.
    - Average pass-through coefficients: export price = 0.39; import price = 0.67.
    - The average values for import and export pass-through are significantly different from each other.
  - Emerging-market group (16 countries):
    - Pattern broadly similar to advanced countries.
    - Two countries show negative pass-through coefficients.
    - In two countries, import pass-through is smaller than export pass-through.
    - Average pass-through coefficients: import price = 0.63; export price = 0.53.
- VAR estimates:
  - VAR-based pass-through estimates are close to the simple-regression estimates (see Figure 1 referenced in source).
  - For advanced countries (VAR):
    - Pass-through to both import and export price indexes is above 0 and below 1 for all countries.
    - Estimates are significantly different from 0 and 1 for most countries (two-standard-deviation band lies in (0,1) for most).
    - Import pass-through exceeds export pass-through in 17 out of 18 countries.
    - The difference (import > export) is statistically significant (p-value ≤ 0.1) for 11 countries.
    - Average VAR-based pass-through for the import price is 0.60.

### DSGE model and quantitative analysis
- Model features:
  - Open-economy DSGE with Calvo staggered price-setting.
  - Firms in each economy are a mix of PCP and LCP users; proportion of PCP can vary between 0 and 1.
  - Constant markup (markup adjustment channels are abstracted away).
  - Both nominal and real shocks incorporated.
- Quantitative results and model fit:
  - A calibrated quantitative version shows that "reasonable values" of frequency of price adjustment and the proportion of PCP firms can reproduce:
    - Average pass-through elasticities for import and export price levels.
    - The observed difference between import and export pass-through.
    - Similarity between simple-regression and VAR estimates.
  - Cross-country variation:
    - Model predicts import price pass-through increases as the proportion of foreign varieties with PCP increases.
    - Model predicts export price pass-through decreases as the proportion of home varieties with PCP increases.
    - Empirical support found for these predictions for a subset of countries with available data on currency of invoicing.

### Implications and interpretation
- Mixed-pricing (mixture of PCP and LCP) combined with nominal rigidities (Calvo pricing) can account for:
  - Pass-through elasticities that lie in (0,1) for both import and export prices.
  - Systematic finding that import pass-through tends to exceed export pass-through.
  - Robustness of pass-through estimates to regression versus VAR methodologies.
- The evidence suggests markup-adjustment mechanisms are not the only way to generate intermediate pass-through; heterogeneity in invoicing currency and staggered nominal price setting are quantitatively important.
- The model’s predictions link observable invoicing-currency shares to pass-through magnitudes, offering a testable channel for cross-country differences.

*Italic source attribution: _wp12226 - 1. OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010 (excerpt from source PDF).*

### 0.39 for the export price. The results for emerging countries show similar tendencies, but as

### _wp12226 - 0.39 for the export price. The results for emerging countries show similar tendencies, but as

### Empirical findings on exchange rate pass-through to trade prices
- For a subset of countries the regression results show pass-through coefficients that are negative and instances where the import-price coefficient is smaller than the export-price coefficient.
- For this group, the average values of the pass-through are:
  - import price: 0.54
  - export price: 0.51
- Hypotheses explored in the literature for declining pass-through include:
  - inflation stabilization (Gagnon and Ihrig, 2004)
  - trade integration resulting from lower trade costs (Gust, Leduc, and Vigfusson, 2010)
- Sub-period analysis:
  - Estimates obtained for 1985-1997 and 1998-2010 (reported in Appendix Tables 1 and 2 for countries with sufficient data).
  - These subperiod estimates are less precise and show no clear systematic pattern: pass-through estimates are higher for some countries and lower for others in the second sub-period relative to the first.

### DSGE model purpose and scope
- Objective: develop a DSGE model to explain evidence on exchange rate pass-through to trade prices.
- Designed primarily for advanced countries whose financial markets and monetary policies can be modeled by:
  - an interest rate parity relation
  - a Taylor-type interest rate rule (here simplified to a rule that reacts only to inflation)
- Model is also relevant for emerging countries with similar financial markets and monetary policies.
- Model features and simplifications:
  - No nontraded goods or distribution services.
  - CES index for aggregating varieties.
  - Traded goods and labor services are differentiated.
  - Wages and prices adjust via Calvo-style staggered pricing.
  - Novel feature: Calvo price adjustment with a mix of producer currency pricing (PCP) and local currency pricing (LCP).
  - Excludes adjustment mechanisms such as markup variation or distribution-channel effects.

### Key model structure and conditions (high-level)
- Representative continuum of households indexed on [0,1] with preferences given in equation (3).
- Households hold one-period domestic and foreign bonds; foreign bond holdings subject to transaction cost shocks.
- Budget constraint and first-order conditions yield standard Euler-type and uncovered interest parity relations with a transaction-cost shock interpreted as a shock to interest parity.
- Central bank policy rule (simplified): the interest rate reacts only to inflation:
  - Rt+1 = R + δ(πt+1 − Π), with δ > 0 (as presented in equation (7)).
- Exchange rate expressed as a function of a composite nominal shock X (equation (8)).

### Goods, prices, and pricing currencies
- Aggregate consumption uses CES aggregators with home and foreign bundles; variety-level demands and price indexes defined (equations (9)–(17)).
- Firms supply to home and foreign markets; production function: Yjt = At Ljt (equation (18)).
- Marginal cost common across firms: MCt = Wt / At (equation (20)).
- Firms choose to set export prices in:
  - producer currency (PCP) for proportion ψ of firms
  - local/foreign currency (LCP) for proportion 1 − ψ of firms
- Frequencies of price change differ by currency in which price is set:
  - probability of price change for home-currency prices: 1 − θ
  - probability of price change for foreign-currency prices: 1 − θ*
- Optimal reset prices follow standard Calvo aggregations (equations (22)–(26)).
- Import price index (expressed in home currency) aggregates PCP and LCP components with foreign analogues and marginal-cost inputs (equations (27)–(29)).

### Wage setting and labor demand
- Labor demand affected by price dispersion under Calvo pricing; labor demand and wage-setting derived with staggered wage adjustments.
- Probability of a household changing wage in a period: 1 − θW.
- New-wage expression determined by maximizing household utility subject to budget and labor demand (equation (31)).
- Wage index expressed via Calvo aggregation (equation (32)).

### Shocks and stationarity
- Shocks follow autoregressive processes (equation (33)):
  - Xt and At follow AR(1) processes with persistence parameters Xρ and Aρ (0 < Xρ < 1, 0 < Aρ < 1).
  - White-noise disturbances: vtXt and vtAt.
  - Presence of the expression (SBt*/Pt)κ in the nominal shock process ensures convergence to a unique steady state with zero net foreign real assets (SB*/P = 0).

### Key linearized relations determining pass-through
- Log-linearized import-price relation (equation (34)):
  - pMt = ψ(1 − ·) pMP + (1 − ψ) pML + Δs terms, capturing PCP/LCP composition.
- Linearized expressions for PCP/LCP components and their dependence on expected future values (equations (35)–(37)).
- Final linearized import-price equation (equation (38)) highlights:
  - dependence on expected future export- and import-price components
  - dependence on exchange rate log-differences and real marginal cost indexes
  - coefficients are functions of PCP proportions (ψ, ψ*) and Calvo parameters (θ, θ*, β)
- Analogous linearized relations for export prices (equations (39)–(40)).
- Linearized exchange rate equation (equation (41)) indicates:
  - s depends on nominal and real shocks, inflation gaps, and interest-rate-response parameters (δ, δ*).
- Pass-through elasticities for import and export prices depend on:
  - impact of nominal and real disturbances (vXt, vAt, vAt*) on s through (41)
  - the propagation of s into pMt and pXt via (38) and (40)
  - presence of expected future values magnifies these impacts given shock persistence
  - nominal disturbances are suggested to have a stronger impact than real disturbances.

### Quantitative analysis: key determinants emphasized
- Model suggests pass-through to trade prices is influenced by:
  - shares of home and foreign firms using PCP (ψ and ψ*)
  - frequencies of price and wage change (θ and θW)
  - persistence of exchange rate shocks (ρx)
  - interest-rate responsiveness to inflation in home and foreign economies (δ and δ*)
- Calibration choices (reported in the text):
  - share of imports in income γ set equal to the median import share for advanced countries in sample: 0.3 (sample average is 0.32)
  - quarterly discount factor β = 0.99
  - coefficient of risk aversion χ = 2.0
  - elasticity of labor supply 1/ν = 0.5
  - elasticity of substitution between home and foreign goods η = 2.0

*Source: _wp12226 - 0.39 for the export price. The results for emerging countries show similar tendencies, but as (IMF working paper content provided).*

### 6.0 for the elasticity of substitution between varieties (

### _wp12226 - 6.0 for the elasticity of substitution between varieties (

### Model parameters and baseline calibration
- Elasticity of substitution between varieties: 6.0 (ε).
- Productivity shock AR coefficients: Aρ and *Aρ equal to 0.95.
- Productivity shock white-noise standard errors: Av and *Av equal to 0.007.
- Correlation coefficient for productivity disturbances: 0.25.
- Nominal shock initial white-noise standard error: Xv equal to 0.007.
- Nominal shock persistence (baseline): Xρ = 0.8.
- Baseline values for parameters that influence pass-through:
  - ψ = *ψ = 0.5 (baseline home and foreign PCP shares).
  - Wθ = θ = 0.75 (wage-price stickiness baseline).
  - δ = *δ = 0.5.
- Home economy assumed small; foreign real wage and inflation (*** /P and WΠ) treated as exogenous.
- Transactions cost parameter κ assumed very small (ensures unique steady state with zero net foreign assets; negligible dynamic effect).

### Impulse responses and shock dominance
- Dynamic response horizon: 20 quarters.
- Two key features of impulse responses to a one-standard-deviation increase in each shock (X, A, *A):
  - Effect of each shock is concentrated in the first quarter.
  - First-quarter effect of the nominal shock is much larger than that of real shocks for exchange rate and trade prices.
- Implication: Exchange rate innovations in the VAR would be dominated by the nominal shock; changes largely reflect current innovations so regression estimates resemble VAR estimates.

### Short-run (current-period) pass-through elasticities (one-standard-deviation shock, baseline)
- Nominal shock:
  - Import price pass-through elasticity: 0.57.
  - Export price pass-through elasticity: 0.40 (baseline case).
- Real shocks (examples; elasticities are negative):
  - Home productivity shock: export price elasticity = -0.22.
  - Foreign productivity shock: import price elasticity = -0.17.
- Composite (simultaneous one-standard-deviation increase in all three shocks): elasticities similar to nominal-shock-only case (nominal shock dominates).

### Sensitivity to PCP shares and wage-price stickiness
- Effect of foreign PCP share on import price pass-through (Figure 3(a), baseline home PCP = 0.5):
  - Import pass-through is below 0.2 if foreign PCP share = 0.
  - Import pass-through increases with foreign PCP share and equals 1 when foreign PCP share = 1.
- Effect of home PCP share on export price pass-through (Figure 3(b), baseline foreign PCP = 0.5):
  - Export pass-through is above 0.8 when home PCP share = 0.
  - Export pass-through decreases with home PCP share and falls below 0.1 when home PCP share = 1.
- Comparative implication: Import pass-through would exceed export pass-through if both home and foreign PCP shares are greater than a value just below 0.5.
- Wage-price stickiness experiment (Table 4):
  - Increase Wθ to 0.667 and θ to 0.5 (higher frequency of wage and price change as per US-based estimates).
  - Result: import price pass-through increases from 0.57 to 0.73; export price pass-through decreases from 0.41 to 0.33.
  - Interpretation: Greater wage-price flexibility has an effect similar to increasing PCP shares.
- Persistence and monetary reaction experiments:
  - Varied Xρ from 0.6 to 0.95 and δ from 0.1 to 1.0.
  - Result: Lower or higher persistence of the exchange rate shock or less/more aggressive reaction to inflation does not have a large effect on pass-through values.
- Conclusion: PCP shares and wage-price stickiness are the major sources of variation in short-run pass-through for import and export prices.

### Stochastic simulations, empirical fit, and model variants
- Simulation length: simulated series generated for 227 quarters; first 100 quarters dropped to match sample length of 127 quarters.
- Simulated variables: Δs_t, Δp^M_t, Δp^X_t, and Δp_t (trade prices and inflation measures) used to compute standard deviations and estimate pass-through via regression and VAR (VAR excludes *p_t because constant in model).
- Baseline model:
  - Yields pass-through coefficients not too different from average estimates for advanced countries.
  - Regression and VAR estimates derived from the model are very close to each other.
  - Baseline implies greater exchange rate variability and smaller inflation variability than in the data.
- Variant 1 (improves fit):
  - Decrease standard deviation of Xv from 0.007 to 0.0025.
  - Increase Xρ from 0.8 to 0.95.
  - Increase ψ from 0.5 to 0.55.
  - Decrease *ψ from 0.5 to 0.45.
  - Result: standard deviations and pass-through coefficients match data values very well.
- Variant 2 (only nominal shocks; Av and *Av set to zero; same as Variant 1 otherwise):
  - Absence of real shocks does not much affect standard deviations or pass-through coefficients.
- Variant 3 (only real shocks; Xv set to zero; other parameters as in Variant 1):
  - Absence of nominal shock leads to major differences:
    - Standard deviations for exchange rate appreciation and inflation decrease substantially.
    - VAR pass-through estimates are very small and much lower than regression estimates.
  - Conclusion: model requires nominal shocks to produce observed exchange rate and inflation variability and similarity of regression and VAR pass-through estimates.
- Variants for PCP share differences:
  - Variant 4: ψ = 0.8 and *ψ = 0.2 (high home PCP share, low foreign PCP share; U.S.-like):
    - Lowers both import and export pass-through coefficients.
    - Accompanied by a relatively small decrease in exchange rate and inflation variability.
  - Variant 5: ψ = 0.2 and *ψ = 0.8 (low home, high foreign PCP share):
    - Both pass-through and variability measures increase.
  - Implication: cross-country differences in PCP shares can account for associations between inflation or exchange rate stability and low pass-through coefficients.

### Currency of invoicing evidence on PCP shares and pass-through
- Data source: currency of invoicing data from Kamps (2006) for a subset of 15 countries (limited years and variable coverage).
- OLS regressions (Table 6) explain VAR estimates of import and export pass-through by indices of home or foreign PCP share based on invoicing-currency data:
  - Share of exporter-currency invoicing in exports (measure of home PCP share):
    - Negative and significant effect on export price pass-through (consistent with model).
  - Share of exporter-currency invoicing in imports (measure of foreign PCP share):
    - Positive effect on import price pass-through but insignificant; measure problematic because it includes invoicing in Euro (home currency for many sample countries).
  - Alternative measure: share of US dollar invoicing in imports (for US use one minus US dollar share):
    - US dollar measure has a positive and significant effect on import price pass-through.
- Empirical evidence from currency invoicing thus supports model predictions about PCP shares' effects on import and export pass-through.

### Key conclusions and policy-relevant findings
- A hybrid model with a mix of PCP and LCP, even with no markup adjustment, can fit data on pass-through elasticities and measures of exchange rate and inflation variability.
- The model accounts for why regression estimates of pass-through elasticities tend to be similar to VAR estimates: with significant wage-price stickiness, short-run changes are largely determined by current innovations.
- Presence of nominal shocks is essential to:
  - Produce sufficient exchange rate and inflation variability.
  - Account for similarity between regression and VAR pass-through estimates.
  - Explain the observed pattern of pass-through elasticities for imports and exports.
- PCP shares and wage-price stickiness are the primary determinants of short-run exchange rate pass-through; monetary shock properties and Taylor-rule aggressiveness have smaller effects.
- Cross-country differences in home and foreign PCP shares can produce the empirical association between exchange rate/inflation stability and low pass-through coefficients.
- Policy implication: exchange rate flexibility can yield appropriate relative price adjustment in transmission of shocks even when firms use a mix of PCP and LCP; benefits of flexibility are realized in the hybrid case.

*Source: _wp12226 - 6.0 for the elasticity of substitution between varieties (*

### References

### _wp12226 - References

### References cited
- Bacchetta, Philippe and Eric van Wincoop, 2005, “A Theory of the Currency Denomination of International Trade.” Journal of International Economics, 67(2), pp. 295-319.
- Betts, C. and Devereux M., 2000, "Exchange Rate Dynamics in a Model of Pricing to Market," Journal of International Economics 50, pp. 215-44.
- Bussière, Matthieu, and Tuomas Peltonen, 2008, "Exchange Rate Pass-Through in the Global Economy–The Role of Emerging Market Economies," Bank of Finland Discussion Paper No. 25.
- Calvo, Guillermo A., 1983, "Staggered Prices in a Utility-Maximizing Framework," Journal of Monetary Economics, pp. 383-98.
- Campa, Jose Manuel, and Linda S. Goldberg, 2005, “Exchange Rate Pass-Through to Import Prices,” Review of Economics and Statistics, 87(4), pp. 679-690.
- Choudhri, Ehsan U., Hamid Faruqee, and Dalia S. Hakura, 2005, “Explaining the Exchange Rate Pass-Through in Different Prices,” Journal of International Economics, 65 (March 2005), pp. 349-374.
- Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans, 2005, "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, 113(1), pp.1-45.
- Clarida, Richard, Jordi Gali, and Mark Gertler, 2002, “A Simple Framework for International Policy Analysis,” Journal of Monetary Economics 49, pp. 879-904.
- Corsetti, Giancarlo, and Luca Dedola, 2005, "A Macroeconomic Model of International Price Discrimination," Journal of International Economics 67, pp. 129-56.
- Corsetti, Giancarlo, Luca Dedola, and Sylvain Leduc, 2007, "Optimal Monetary Policy and the Sources of Local-Currency Price Stability," NBER Working Paper No. 13544.
- Corsetti, Giancarlo, Luca Dedola, and Sylvain Leduc, 2008, "High Exchange-Rate Volatility and Low Pass-Through in Business Cycle Models," Journal of Monetary Economics, 55, pp.1113-28.
- Corsetti, Giancarlo, and Paolo Pesenti, 2001, "Welfare and Macroeconomic Interdependence," Quarterly Journal of Economics 116, pp. 421-46.
- Corsetti, Giancarlo and Paolo Pesenti, 2005, "International dimension of optimal monetary policy," Journal of Monetary Economics 52, pp. 281-305.
- Devereux, Michael B., and Charles Engel, 2002, “Exchange Rate Pass-Through, Exchange Rate Volatility, and Exchange Rate Disconnect,” Journal of Monetary Economics, Vol. 49, pp. 913-940.
- Devereux, Michael B., and Charles Engel, 2003, "Monetary Policy in Open Economy Revisited: Price Setting and Exchange Rate Flexibility," Review of Economic Studies 70, pp. 765-83.
- Devereux, Michael, Charles Engel, and Peter Storegaard, 2004, “Endogenous Exchange Rate Pass-Through when Nominal Prices are set in Advance.” Journal of International Economics, 63(2), pp. 263-291.
- Gagnon, Joseph E., and Jane Ihrig, 2004, "Monetary Policy and Exchange Rate Pass-Through," International Journal of Finance and Economics, 9, pp. 315–338.
- Goldberg Linda S., and Cedric Tille, 2005, "Vehicle Currency Use in International Trade," NBER Working Paper No.11127.
- Gust, C., S. Leduc, and R. Vigfusson, 2010, "Trade integration, competition, and the decline in exchange rate pass-through," Journal of Monetary Economics 57, pp. 309–324.
- Kamps, Anette, 2006, "The Euro as Invoicing Currency in International Trade," ECB. Working Paper Series No. 665 (August).
- McCarthy J., 2000, "Pass-Through of Exchange Rates and Import Prices to Domestic Inflation in Some Industrialized Economies," Federal Reserve Bank of New York Staff Report No. 111.
- Obstfeld, Maurice, and Kenneth Rogoff, 1995, "Exchange Rate Dynamics Redux," Journal of Political Economy 102, pp. 624-60.
- Obstfeld, Maurice, and Kenneth Rogoff, 2000, "New Directions for Stochastic Open Economy Models," Journal of International Economics, 50, pp. 117-154.
- Smets, Frank R., and Raf Wouters, 2003, "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economics Association, 5, 1123-1175.
- Yun, Tack, 1996, "Nominal Price Rigidity, Money Supply Endogeneity, and Business Cycles," Journal of Monetary Economics 37, pp. 345-370.

### Table 1 — OLS Regressions: Impact of Exchange Rate Changes on Trade Prices, 1979-2010 (selected statistics)
- Advanced economies average: Import Price Pass-Through 0.67(0.03); Export Price Pass-Through 0.39(0.03).
- Example country coefficients (Import Price Pass-Through (standard error) No. of Obs. R-squared; Export Price Pass-Through (standard error) No. of Obs. R-squared):
  - United States: 0.387 (0.107)***### 1130.164 ; 0.152 (0.090)*### 1090.063
  - Japan: 0.982 (0.095)*** 1270.560 ; 0.528 (0.038)***###1270.653
  - Germany: 0.686 (0.117)***### 1270.247 ; 0.202 (0.036)***### 1270.210
- Emerging market economies average: Import Price Pass-Through 0.63(0.03); Export Price Pass-Through 0.53(0.04).
- Example emerging country entries:
  - Brazil: 0.997 (0.022)***1270.9118 ; 0.986 (0.027)***1270.8693
  - Argentina: 0.91 (0.046)***#640.8915 ; 0.879 (0.051)***##690.7057
  - Mexico: -0.021 (0.015)### 1260.028 ; -0.160 (0.073)** ###1260.072
- Notes: Trade prices sources and significance notation:
  - Trade prices for advanced economies: OECD's Monthly International Statistics database.
  - Trade prices for emerging market economies: IMF's International Financial Statistics database.
  - Nominal effective exchange rate data: IMF's Information Notice System.
  - * indicates coefficient significantly different from 0. # indicates coefficient significantly different from 1. ***, **, * denote 1, 5, 10 percent levels. ###, ##, # denote 1, 5, 10 percent levels for difference from 1. Robust standard errors in parentheses. Countries classified per IMF's World Economic Outlook publications. A constant included in OLS regressions.

### Table 2 — VAR: First Quarter Trade Price Response to a One Percent Change in the Exchange Rate, 1979–2010 (selected statistics)
- Advanced economies average: Import Price Response 0.60(0.03); Export Price Response 0.39(0.02).
- Emerging market economies average: Import Price Response 0.54(0.10); Export Price Response 0.51(0.11); p-value for t test of difference in trade price responses 0.84.
- Example country entries (Import Estimate (Std. error); Export Estimate (Std. error); p-value):
  - United States: 0.38(0.08) 0.17(0.05) 0.02
  - Japan: 0.90(0.09) 0.55(0.05) 0.00
  - Mexico: -0.01(0.01) -0.15(0.06) 0.02
  - Brazil: 0.86(0.08) 0.99(0.09) 0.28
- Data sources: OECD (advanced), IMF IFS (emerging), IMF Information Notice System (other variables).

### Table 3 — Pass-Through Elasticities for Different Shocks
- Nominal Shock: Import Price 0.572 ; Export Price 0.404
- Home Productivity Shock: Import Price 0.346 ; Export Price -0.221
- Foreign Productivity Shock: Import Price -0.167 ; Export Price 0.404
- Composite Shock: Import Price 0.523 ; Export Price 0.381
- Note: For nominal and home and foreign productivity shocks, elasticities are based on a one-standard-deviation increase in each shock. Composite shock elasticities represent simultaneous one-standard-deviation increases in all shocks.

### Table 4 — Wage-Price Stickiness, Exchange Rate Persistence, Inflation Reaction and the Pass-Through (nominal shock elasticities)
- Baseline values: Import Price Pass-Through 0.572 ; Export Price Pass Through 0.419
- Less stickiness (.5,.667 W θ θ  ): Import Price Pass-Through 0.727 ; Export Price Pass-Through 0.332
- Lower persistence ( 0.6 x ρ  ): Import Price Pass-Through 0.553 ; Export Price Pass-Through 0.438
- Higher persistence ( 0.95 x ρ  ): Import Price Pass-Through 0.599 ; Export Price Pass-Through 0.402
- Weaker reaction ( 0.1 δ  ): Import Price Pass-Through 0.564 ; Export Price Pass-Through 0.420
- Stronger reaction ( 1.0 δ  ): Import Price Pass-Through 0.583 ; Export Price Pass-Through 0.417
- Note: Pass-through values represent elasticities generated by the nominal shock.

### Table 5 — Stochastic Simulations (Advanced countries: selected rows)
- Data (Adv. Coun.): Standard Dev. Δs_t 0.0245 ; Standard Dev. Δπ_t 0.0086 ; OLS Import Price PT 0.67 ; VAR Import Price PT 0.60 ; OLS Export Price PT 0.39 ; VAR Export Price PT 0.39
- Model Baseline: Standard Dev. Δs_t 0.0329 ; Standard Dev. Δπ_t 0.0075 ; OLS Import Price PT 0.607 ; VAR Import Price PT 0.614 ; OLS Export Price PT 0.466 ; VAR Export Price PT 0.463
- Variant 1: Standard Dev. Δs_t 0.0233 ; Standard Dev. Δπ_t 0.0083 ; OLS Import Price PT 0.655 ; VAR Import Price PT 0.611 ; OLS Export Price PT 0.398 ; VAR Export Price PT 0.405
- Variant 2: Standard Dev. Δs_t 0.0238 ; Standard Dev. Δπ_t 0.0079 ; OLS Import Price PT 0.625 ; VAR Import Price PT 0.615 ; OLS Export Price PT 0.418 ; VAR Export Price PT 0.400
- Variant 3: Standard Dev. Δs_t 0.0040 ; Standard Dev. Δπ_t 0.0015 ; OLS Import Price PT 0.341 ; VAR Import Price PT 0.072 ; OLS Export Price PT 0.324 ; VAR Export Price PT 0.050
- Variant 4: Standard Dev. Δs_t 0.0227 ; Standard Dev. Δπ_t 0.0072 ; OLS Import Price PT 0.437 ; VAR Import Price PT 0.424 ; OLS Export Price PT 0.230 ; VAR Export Price PT 0.204
- Variant 5: Standard Dev. Δs_t 0.0263 ; Standard Dev. Δπ_t 0.0094 ; OLS Import Price PT 0.883 ; VAR Import Price PT 0.873 ; OLS Export Price PT 0.667 ; VAR Export Price PT 0.700
- Variant definitions (as given):
  - Variant 1: Adjusted nominal shock process and PCP shares ( (0.95,..() 0.0025 XX std dev v  = = , * 0.55,0.45 ψ ψ = = )
  - Variant 2: Only nominal shocks ( ..()0 A std dev v = , * ..()0 A std dev v = )
  - Variant 3: Only real shocks ( ..()0 X std dev v = )
  - Variant 4: Higher home and lower foreign PCP share ( * 0.8,0.2 ψ ψ = = )
  - Variant 5: Lower home and higher foreign PCP share ( * 0.2,0.8 ψ ψ = = )

### Table 6 — Invoicing Currency Shares and the Pass-Through (regression results)
- Export Price Pass-Through: Constant 0.615 (0.074)* ; Exp. curr. share in exports coefficient -0.005 (0.0016)*
- Import Price Pass-Through: Constant 0.461 (0.186)* ; Exp. curr. share in imports coefficient 0.002 (0.0027)
- US dollar share in imports: 0.008 (0.0035)*
- Observations: Export model No. of Obs. 15 ; Import models No. of Obs. 13 and 13
- R-squared: Export model 0.440 ; Import models 0.053 ; 0.287
- Standard errors in brackets. * Indicates significance at the 5% level or less.

### Figures (titles and focal relationships)
- Figure 1: Regression and VAR Estimates of the Pass-Through (visual comparison of regression vs VAR pass-through estimates).
- Figure 2: Impulse Response Functions — panels showing responses of Δs_t, Δp^M_t, Δp^X_t to Nominal shock, Home Productivity shock, Foreign Productivity shock (time horizon plotted to 20 periods).
- Figure 3: PCP Shares and the Pass-Through — panels:
  - (a) Foreign PCP Share and the Import Price Pass-Through (scatter showing relationship across 0–1 scale).
  - (b) Home PCP Share and the Export Price Pass-Through (scatter showing relationship across 0–1 scale).

### Appendix Tables — VAR: First Quarter Trade Price Response to a One Percent Change in the Exchange Rate
- Appendix Table 1 (1985–1997) average (advanced economies): Import Price Response 0.550.036 ; Export Price Response 0.370.037 ; p-value 0.00
- Appendix Table 2 (1998–2010) average (advanced economies): Import Price Response 0.490.048 ; Export Price Response 0.460.044 ; p-value 0.63
- Appendix Table 2 emerging markets average: Import Price Response 0.72(0.05) ; Export Price Response 0.60(0.05) ; p-value 0.09
- Selected country examples and statistics are presented in the appendix tables matching the structure of Table 2 for the subperiods 1985–1997 and 1998–2010.
- Data sources for appendix tables: OECD Monthly International Statistics (advanced), IMF International Financial Statistics (emerging), IMF Information Notice System (other variables).

*Source: _wp12226 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12226.pdf_