How Much Do Exchange Rates Move Trade Prices?
Exchange rates fluctuate daily, yet their impact on import and export prices remains one of the most debated questions in international economics. This lab guides you through the IV/2SLS methodology used to estimate causal pass-through, drawing on high-frequency monetary policy identification and the dominant currency paradigm.
Durée indicative : 40–50 min (10 min théorie, 10 min données, 15 min estimation IV, 10 min diagnostics, 5 min export).
The Exchange Rate Disconnect Puzzle
In 1983, Meese and Rogoff demonstrated that a random walk forecasts exchange rates as well as any structural model—a finding that still holds. Yet macroeconomic theory insists that exchange rate movements should feed through to trade prices. How much they actually do—the pass-through—has profound implications for monetary policy transmission and trade adjustment.
The Endogeneity Problem
A naive OLS regression of import price changes on exchange rate changes yields biased estimates. Why? Because exchange rates are endogenous: the same macroeconomic shocks that move exchange rates also directly affect trade prices. The demand shock that depreciates a currency simultaneously raises import demand and prices. This simultaneity biases OLS estimates toward zero (attenuation bias).
The IV Solution: High-Frequency Identification
Nakamura & Steinsson (2018, QJE) proposed using high-frequency monetary policy surprises as instruments. Within a narrow window around central bank announcements, the surprise component of policy decisions is plausibly exogenous—it affects trade prices only through its effect on the exchange rate (conditional on controls).
— Gopinath et al. (2020), “Dominant Currency Paradigm,” AER
The IV Framework
First Stage Δet = π0 + π1 · zt + vt
where ΔP = import price change, Δe = exchange rate change, z = monetary policy surprise instrument, X = controls (interest rate differential, lagged prices). β is the pass-through coefficient of interest.
Key IV Assumptions
1. Relevance: The instrument z must predict the endogenous regressor Δe. Tested via first-stage F-statistic (Stock & Yogo 2005: F > 10 rule of thumb).
2. Exclusion restriction: Monetary surprises affect import prices only through the exchange rate channel (conditional on controls). This is credible when the surprise window is narrow and controls absorb direct demand effects.
3. Independence: The instrument is uncorrelated with the structural error ε. High-frequency surprises within announcement windows are plausibly random.
Gopinath et al. (2020) show that most global trade is invoiced in US dollars, regardless of the trading partners. Goods invoiced in USD exhibit near-complete pass-through of the dollar exchange rate, while goods invoiced in the exporter's currency show near-zero pass-through. This asymmetry is invisible in aggregate regressions—we will test it in Phase 3.
Monthly Data: January 2010 – December 2024
Explore 15 years of exchange rates, trade prices, and monetary policy surprises. Toggle series on and off. Hover for exact values. Key episodes are marked: the taper tantrum (2013), COVID shock (2020), and the Fed hiking cycle (2022–23).
Monetary Policy Surprises
High-frequency surprises around FOMC meetings. Most months show zero (no meeting or no surprise). Positive values indicate unexpected tightening; negative values indicate unexpected easing.
Import prices tend to move inversely with EUR/USD (when the euro weakens, imports from the US become more expensive). But the correlation is imperfect—this is the endogeneity we need IV to address. Monetary surprises are sparse and small (typically ±0.25 pp), concentrated around FOMC dates.
From OLS Bias to Causal Identification
Naive OLS: Regressing Import Prices on Exchange Rate Changes
We start with the baseline that most practitioners would run: a simple OLS regression of monthly import price changes on exchange rate changes. The coefficient tells us how much a 1% depreciation of the euro translates into higher import prices from the US.
| Variable | Coefficient | Std. Error | t-stat | |
|---|---|---|---|---|
| Intercept | 0.002 | 0.003 | 0.67 | |
| Δe (EUR/USD) | 0.247*** | 0.058 | 4.26 | p < 0.001 |
N = 180 | R² = 0.094 | *** p<0.01, ** p<0.05, * p<0.1
The OLS coefficient of 0.247 suggests that a 10% euro depreciation raises import prices by only 2.5%. This is the “exchange rate disconnect” in action—but we suspect the true pass-through is higher. Endogeneity biases OLS toward zero because positive demand shocks that raise prices also appreciate the currency (negative correlation between ε and Δe).
First Stage: Does the Instrument Predict Exchange Rate Movements?
For IV to work, the monetary policy surprise must be a relevant predictor of exchange rate changes. An unexpected Fed tightening should appreciate the dollar (depreciate EUR/USD). We test this with the first-stage regression.
| Variable | Coefficient | Std. Error | t-stat | |
|---|---|---|---|---|
| Intercept | -0.001 | 0.002 | -0.50 | |
| z (Monetary surprise) | -3.842*** | 0.768 | -5.00 | p < 0.001 |
N = 180 | R² = 0.122 | Partial F-statistic = 25.04
F = 25.04 — STRONG
Stock & Yogo (2005) critical values for one instrument, one endogenous regressor:
| Max. Bias | Critical Value | Our F | Status |
|---|---|---|---|
| 10% | 16.38 | 25.04 | PASS |
| 15% | 8.96 | 25.04 | PASS |
| 20% | 6.66 | 25.04 | PASS |
A 1 pp unexpected tightening depreciates the EUR/USD by 3.84%. The F-statistic of 25.04 comfortably exceeds all Stock-Yogo critical values, so we can rule out weak instrument concerns. The negative sign is consistent with theory: unexpected US tightening strengthens the dollar.
Interactive: What If the Instrument Were Weaker?
Two-Stage Least Squares: The Causal Pass-Through
We now estimate the second stage using the predicted exchange rate changes from the first stage (fitted values from the regression of Δe on z). This isolates the exogenous variation in exchange rates driven by monetary surprises.
| Estimator | β (Pass-through) | Std. Error | 95% CI | |
|---|---|---|---|---|
| OLS | 0.247*** | 0.058 | [0.133, 0.361] | Biased downward |
| IV / 2SLS | 0.648*** | 0.142 | [0.370, 0.926] | Causal estimate |
Hausman test: χ² = 7.83, p = 0.005 — reject equality of OLS and IV
The IV estimate (0.648) is more than twice the OLS estimate (0.247). This is consistent with attenuation bias from simultaneity: positive demand shocks that raise import prices also tend to appreciate the domestic currency (strengthening the euro). This induces a negative correlation between the exchange rate change and the error term, biasing OLS toward zero. IV removes this contamination by isolating exchange rate movements driven only by exogenous monetary surprises.
Economic Significance
A pass-through of 0.65 means that a 10% depreciation of the euro against the dollar raises import prices by 6.5% within the month. This is incomplete pass-through (full pass-through = 1.0), but substantially higher than the OLS estimate suggested. The Hausman test confirms that OLS and IV estimates are statistically different—endogeneity is real.
Dominant Currency Test: USD-Invoiced vs. EUR-Invoiced Goods
Gopinath et al. (2020) predict that pass-through depends on the invoicing currency. We split the sample: goods whose contracts are denominated in USD versus goods invoiced in EUR. The results are striking.
| Subsample | βIV | Std. Error | 95% CI | Interpretation |
|---|---|---|---|---|
| Full sample | 0.648*** | 0.142 | [0.370, 0.926] | Average |
| USD-invoiced goods | 0.852*** | 0.118 | [0.621, 1.083] | Near-complete |
| EUR-invoiced goods | 0.147 | 0.095 | [-0.040, 0.334] | Near-zero |
USD-invoiced goods show pass-through of 0.85—nearly complete. When the euro depreciates 10% against the dollar, USD-invoiced import prices rise by 8.5%. But EUR-invoiced goods show pass-through of only 0.15, statistically indistinguishable from zero. Prices are sticky in the invoicing currency. This means the aggregate pass-through (0.65) is a weighted average that masks a dramatic asymmetry.
— Gopinath et al. (2020), AER
Testing the Instrument’s Validity
Instrument Relevance: First-Stage F-Statistic
The first-stage F-statistic tests whether the excluded instrument has explanatory power for the endogenous regressor. Stock & Yogo (2005) provide critical values for the null hypothesis that the instrument is weak (that 2SLS bias exceeds a specified fraction of OLS bias).
| Test | Statistic | Critical Value (5%) | Decision |
|---|---|---|---|
| Cragg-Donald F | 25.04 | 16.38 (10% max bias) | Reject weak IV |
| Kleibergen-Paap rk Wald F | 23.91 | 16.38 | Reject weak IV |
Weak-Instrument Robust Inference: Anderson-Rubin Test
Even though our F-statistic passes conventional thresholds, it is good practice to report weak-instrument robust confidence sets. The Anderson-Rubin (AR) test inverts a statistic that is valid regardless of instrument strength.
| Method | β estimate | 95% CI | Width |
|---|---|---|---|
| 2SLS (Wald) | 0.648 | [0.370, 0.926] | 0.556 |
| Anderson-Rubin | 0.648 | [0.298, 1.072] | 0.774 |
The AR confidence set is wider (0.774 vs. 0.556) but still excludes zero, confirming that pass-through is statistically significant even under weak-instrument asymptotics. The two intervals overlap substantially, which is reassuring.
Exclusion Restriction: Is It Credible?
The exclusion restriction requires that monetary surprises affect import prices only through the exchange rate, not directly. This is the untestable assumption at the heart of IV.
Arguments for validity:
- High-frequency surprises are measured within a 30-minute window around FOMC announcements, minimizing contamination from other news.
- We condition on lagged prices, interest rate differentials, and commodity price indices, absorbing direct demand channels.
- Import prices are measured monthly, so any direct effect of a surprise on daily demand is averaged out.
Potential threats:
- Nakamura & Steinsson (2018) document an “information effect”—monetary surprises may reveal the central bank’s private information about economic conditions, potentially violating exclusion.
- Large surprises may trigger portfolio rebalancing that affects commodity prices directly.
Over-Identification: Two Instruments (Fed + ECB Surprises)
If we add ECB monetary surprises as a second instrument, we can test the over-identifying restriction using the Sargan-Hansen J test. Under the null, all instruments are valid.
| Test | Statistic | df | p-value | Decision |
|---|---|---|---|---|
| Hansen J | 1.347 | 1 | 0.246 | Cannot reject validity |
The J-statistic of 1.347 with p = 0.246 means we cannot reject the null that both instruments are valid. The IV estimate with two instruments is 0.637 (SE = 0.121), consistent with the single-instrument estimate. Adding the ECB surprise modestly improves precision.
The J test has low power when instruments are correlated or when both are invalid in the same direction. It is a necessary but not sufficient condition for instrument validity.
Sensitivity: What If the Exclusion Restriction Is Partially Violated?
Conley, Hansen & Rossi (2012) propose a “plausibly exogenous” framework. Instead of assuming the direct effect of z on ΔP is exactly zero, we allow it to be δ, a bounded parameter. Use the slider to explore how the IV estimate changes when the exclusion restriction is partially relaxed.
Adjusted βIV: 0.648
95% CI: [0.370, 0.926]
Still significant? YES
The IV estimate remains statistically significant as long as the direct effect δ is below approximately 0.18. Beyond that, the confidence interval includes zero. This provides a quantitative bound on how much exclusion restriction violation the result can tolerate.
Summary of Findings
| Specification | β | SE | 95% CI | N | Method |
|---|---|---|---|---|---|
| OLS baseline | 0.247*** | 0.058 | [0.133, 0.361] | 180 | OLS |
| IV / 2SLS (Fed surprise) | 0.648*** | 0.142 | [0.370, 0.926] | 180 | 2SLS |
| IV (Fed + ECB surprises) | 0.637*** | 0.121 | [0.400, 0.874] | 180 | 2SLS |
| IV — USD-invoiced only | 0.852*** | 0.118 | [0.621, 1.083] | 95 | 2SLS |
| IV — EUR-invoiced only | 0.147 | 0.095 | [-0.040, 0.334] | 85 | 2SLS |
Key Takeaways
1. Exchange rate pass-through is incomplete but substantial. The causal IV estimate of 0.65 means that roughly two-thirds of exchange rate movements are transmitted to import prices within a month.
2. OLS understates true pass-through. The Hausman test confirms significant endogeneity bias. OLS picks up only a quarter of the actual price adjustment because demand shocks simultaneously move prices and exchange rates in offsetting directions.
3. Invoicing currency is the key determinant. The dramatic gap between USD-invoiced (0.85) and EUR-invoiced (0.15) goods validates Gopinath’s dominant currency paradigm. Trade prices are sticky in the currency of invoicing, not the currency of the exporter or importer.
Policy Implications
For central banks: Exchange rate channels of monetary transmission are stronger than OLS-based evidence suggests. A depreciation engineered through rate cuts will raise import prices meaningfully—but the effect depends on the share of USD-invoiced imports.
For trade policy: The dominant currency paradigm implies that bilateral exchange rate movements between non-dollar economies have limited effect on bilateral trade prices. This challenges the traditional expenditure-switching mechanism at the core of open-economy macro.
Nakamura, E. & Steinsson, J. (2018). “High-Frequency Identification of Monetary Non-Neutrality.” QJE, 133(3), 1283–1330.
Gopinath, G. et al. (2020). “Dominant Currency Paradigm.” AER, 110(3), 677–719.
Meese, R.A. & Rogoff, K. (1983). “Empirical Exchange Rate Models of the Seventies.” J. Int’l Econ., 14(1-2), 3–24.
Stock, J.H. & Yogo, M. (2005). “Testing for Weak Instruments.” In Andrews & Stock (Eds.), Identification and Inference.
Conley, T.G., Hansen, C.B. & Rossi, P.E. (2012). “Plausibly Exogenous.” Rev. Econ. Stat., 94(1), 260–272.