I. Introduction

The degree to which fluctuations in the nominal exchange rate affect the relative prices of real goods will in large part determine the effect of exchange rate policy on patterns of international trade. A large empirical literature in international macroeconomics estimates how quickly exchange rate changes translate into import prices (for example, Yang 1997; and Campa and Goldberg, 2005). This speed of adjustment is referred to as exchange rate pass-through. In this paper, we examine the speed of adjustment in the price of exports to the U.S. in response to changes in the value of the U.S. dollar. An innovation in our paper is an application of the modern sticky price theory that is embedded into the New Open Economy Macroeconomics literature (see Obstfeld and Rogoff, 1995) to create a statistical model in which exchange rate pass-through can be represented as a structural parameter immune to the Lucas critique. We then apply some of the techniques that have been developed to understand the dynamics of domestic inflation (referred to as the New Keynesian Phillips curve literature) to estimate our model and consistently identify the structural parameter which we refer to as exchange rate pass-through.

The idea that the prices of imports would incorporate exchange rate changes only slowly has a long heritage. Many theoretical models were developed to explain this particular failure of the Law of One Price. In particular, price stickiness implies that the Law of One Price fails to hold at any time, and exchange rate pass-through is imperfect.² In the context of sticky price models, Betts and Devereux (1996, 2000) develop the theory of local currency pricing (LCP) to explain violations of purchasing power parity. In contrast, when monopolistic producers set sticky prices in their own currency, which is the case of producer currency pricing (PCP), exchange rate changes are reflected one-for-one in foreign currency prices (perfect pass-through).

To generate richer dynamics, many sticky price models have adopted a (time-dependent) model of pricing developed by Calvo (1983) and incorporated it into the dynamic general equilibrium modeling structure (Yun, 1996). In this type of models, inflation is forward-looking and can be written as a discounted sum of future marginal costs. When real marginal costs are high or expected to be high in the future, firms have an incentive to raise prices inducing inflation. The recursive form of an inflation equation in which inflation is written as a function of current marginal cost plus expected future inflation (as a proxy for future marginal costs) has been represented as a modern alternative to the Phillips curve. Galí and Gertler (1999) and Sbordone (2002, 2005) show that this forward-looking representation of inflation can be estimated with general methods of moments (GMM) using lag variables as valid instruments. This literature can be used to estimate the rate at which sticky prices change.

There exists an exact parallel to the New Keynesian Phillips curve in the LCP literature. Import price inflation will be high when the real U.S. dollar marginal cost of foreign production is high or expected to be high. We can decompose the real U.S. dollar marginal cost of foreign production into two parts, the real marginal cost of production in the exporting country and the gap between import prices in the U.S. and the PCP price (that is, the exchange-rate-adjusted price of goods in the foreign country). Finding a consistent measure of marginal costs in the foreign country may be difficult. However, the theory of the New Keynesian Phillips curve implies that the measure of real marginal costs can be inferred from inflation since real marginal costs drive inflation. Therefore, the estimation of a recursive, forward-looking representation of the LCP Euler equation governing import price inflation enables us to provide a consistent estimate of the frequency with which foreign firms change their U.S. prices in response to changes in U.S. dollar marginal costs. We can interpret this structural parameter as the New Keynesian rate of exchange rate pass-through because one of the determinants of these U.S. dollar marginal costs is the exchange rate. As a byproduct of this procedure, we are able to estimate the rate at which foreign producers adjust their own home price levels without ever constructing a measure of marginal cost.

This paper offers several findings on exchange rate pass-through effects on U.S. import prices. First, we find strong evidence of price stickiness in U.S. import prices; consistent with a structural model in which prices change every 5 quarters on average. Second, a model in which some firms adopt LCP and others adopt PCP pricing fits the data most coherently. The estimated fraction of PCP price setters is small: 10 percent or less. Third, we find only weak evidence that rates of price change have slowed over time. Fourth, the degree of import price stickiness is similar to that of the domestic price stickiness of U.S. trading partners. Lastly, as in the New Keynesian Phillips curve, there is a substantial forward-looking element to the adjustment of import prices which is consistent with the idea that many firms are adjusting in an optimal manner. Also, like that literature, only a smaller fraction of firms are backward-looking.

II. The Model

We consider a model in which all firms exporting to the U.S. adjust their U.S. dollar prices infrequently and optimally according to the local currency pricing (LCP) pass-through theory. A producing firm that changes prices in the home market chooses a price to maximize the discounted sum of expected profits over the time. The firm must set producer prices in advance using the information set available at time t-1 (see Rotemberg and Woodford, 1997). Discounted expected profits in the domestically oriented sector can be written as:

Where β is the discount factor of the firm’s managers, κ is the probability of adjusting the producer price in each period, ppi is the firm’s producer price, PPI is the aggregate producer price index, Q is output, and MC is nominal marginal cost in terms of home currency. The optimal producer price ${\mathit{\text{ppi}}}_t^{*}$ that maximizes the expected profits is given by

Linearizing the first order conditions as in Galí and Gertler (1999),

where mc_t = log(MC_t/PPI_t), and ${\pi }_t^{\mathit{\text{PPI}}}$ is the inflation rate in foreign prices.

Similarly, when importing firms choose their prices for imports into the U.S., they maximize their profits from the U.S. market:

where ipi is the firm’s import price measured in U.S. dollars, IPI is the aggregate import price index, IM is the volume of imports, S_t is the spot exchange rate with the U.S. dollar, and ν is the probability of adjusting the import price in each period. The optimal import price ${\mathit{\text{ipi}}}_t^{*}$ that maximizes the expected profits is given by

We can extend the Galí and Gertler (1999) and Sbordone (2002) technique to the case of import prices and write

where μ_t is the logarithm of $M_t\equiv \frac{{\mathit{\text{IPI}}}_t}{{\mathit{\text{PPI}}}_t/S_t}$, the mark-up of U.S. imports over their (U.S. dollar) domestic prices (that is, μ = ln M).

Combining equations (1) and (2) to eliminate mc_t, we have

Equation (3) will form the statistical model that we can use to measure structural pass-through. This equation reflects an error-correction mechanism, where μ (= ln M) is a cointegrating vector for U.S. import prices, the foreign producer price level, and the exchange rate because the ratio M converges in expectation to a steady state when firms are fully able to adjust prices.

The theory constrains the dynamics of equation (3) in a number of ways. First, in this optimal price setting equation, all corrections come through changes in foreign or import prices, and the exchange rate only appears as part of the error-correction term. This is in contrast with the standard literature which essentially regresses import price inflation (or CPI inflation) on changes in the exchange rate. Second, the prices adjust geometrically so we can include only a single lead of each kind of inflation in the dynamic equation. The reduced-form exchange rate pass-through literature typically focuses on backward-looking dynamics and does not use theory to constrain the number of lags in the model. Third, the price setting firms operate under rational expectations, so the error term is uncorrelated with all variables in the information set available for price-setters at time t-1. This produces a natural set of identification conditions and allows consistent estimation with GMM. Fourth, the pass-through of real foreign marginal cost into import prices occurs at the same speed as exchange rate pass-through as implied by equation (2). Finally, the long-term pass-through is 100 percent.

III. The Data

To estimate the pass-through effect model given by equation (3), we need data on domestic import price inflation, foreign producer price inflation, and the relative price of imports to foreign price levels. Detailed descriptions about data are provided in the appendix.

We also need trade weights to aggregate foreign prices over U.S. trading partners. We calculate trade weights for 40 trading partners of the U.S. (Appendix C).³ Country j’s share in U.S. imports of manufactured goods at quarter t, $w_t^j$, is calculated as imports of manufactured goods from country j divided by the sum of imports of manufactured goods from all countries in the list of trading partners.

We measure the markup of import prices over the PCP price, M_t, using geometric weights to aggregate time series of the markup for each of the trading partners, as in Thomas and Marquez (2006). The markup for country j is defined as $m_t^j\equiv \frac{S_t^j·{\mathit{\text{IPI}}}_t}{{\mathit{\text{PPI}}}_t^j}\frac{1}{{\mathit{\text{PPP}}}_{1995}}$, where $S_t^j$ is the number of currency units in country j needed to buy 1 U.S. dollar in spot markets relative to the exchange rate in 1995 (Source: IFS), and ${\mathit{\text{PPI}}}_t^j$ is the producer price index of manufactured goods for country j relative to the index in the base year 1995.⁴ The import price index for the U.S. is from a database of OECD manufactured goods import price indices that spans the period 1975–2002. The data is extended forward in time using an index of non-petroleum import prices from BLS.⁵ The variable ${\mathit{\text{PPP}}}_{1995}^j$ is the purchasing power parity ratio from the Penn World Tables (Heston, Summers, and Aten, 2006) in the base year, 1995.

We create an aggregate measure of the relative prices of goods produced in the U.S. relative to its trading partners using geometric trade weights, ${\stackrel{⌢}{w}}_{t-k}^j$:

where ${\stackrel{⌢}{w}}_{t-k}^j$ are averaged over n quarters and lagged by k quarters to eliminate endogeneity issues.

The markup does not contain any discernable secular drifts although it exhibits somewhat persistent swings over the period 1980:Q1–2005:Q4, as shown in Figure 1. The markup is measured by the logarithm of the trade-weighted index of the relative prices: that is, μ_t = ln(M_t). An augmented Dickey-Fuller test with an intercept and four lags rejects the hypothesis of a unit root in the series at the 5 percent level. The standard deviation of this series is about 4.1 percent. Wide swings in this figure roughly correspond to fluctuations in the dollar. When the dollar is strong in the early 1980s and near the turn of the millennium, this markup is also high. This indicates that import prices are not as low as might be expected given the strong value of the dollar. In the mid-1980s and in recent periods, the markup has been low, indicating that import prices have not risen to the same degree that the dollar has fallen.

The Trade-Weighted Index of the Relative Prices

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure depicts the logarithm of the trade-weighted index of the relative prices (µ_t) for the period 1980:Q1–2005:Q4.0

• Download Figure
• Download figure as PowerPoint slide

View Full Size

The Trade-Weighted Index of the Relative Prices

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure depicts the logarithm of the trade-weighted index of the relative prices (µ_t) for the period 1980:Q1–2005:Q4.0

• Download Figure
• Download figure as PowerPoint slide

The Trade-Weighted Index of the Relative Prices

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure depicts the logarithm of the trade-weighted index of the relative prices (µ_t) for the period 1980:Q1–2005:Q4.0

• Download Figure
• Download figure as PowerPoint slide

We construct aggregate measures of foreign inflation as weighted averages of the country-by-country inflation. The import-weighted average of foreign inflation is given by ${\pi }_t^{\mathit{\text{PPI}}}={\displaystyle \sum _{j=1}^{40}}\left[{\stackrel{⌢}{w}}_{t-k}^j·\Delta \ln ({\mathit{\text{PPI}}}_t^j)\right]$. Figure 2 shows the behavior of U.S. import price inflation (measured in U.S. dollars) and the (weighted) inflation of domestic production of U.S. trading partners (measured in foreign currency). Both were relatively high in the late 1980s and fell during the 1990s. During relatively long periods of the early and late 1980s and the 1990s, U.S. import price inflation was consistently below foreign domestic inflation.

U.S. Import Price Inflation and Foreign PPI Inflation

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure compares inflation in the U.S. import price for manufactured goods with trade weighted foreign producer price inflation for the period 1980:Q1–2005:Q4.

• Download Figure
• Download figure as PowerPoint slide

View Full Size

U.S. Import Price Inflation and Foreign PPI Inflation

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure compares inflation in the U.S. import price for manufactured goods with trade weighted foreign producer price inflation for the period 1980:Q1–2005:Q4.

• Download Figure
• Download figure as PowerPoint slide

U.S. Import Price Inflation and Foreign PPI Inflation

Citation: IMF Working Papers 2008, 213; 10.5089/9781451870718.001.A001

Notes: This figure compares inflation in the U.S. import price for manufactured goods with trade weighted foreign producer price inflation for the period 1980:Q1–2005:Q4.

• Download Figure
• Download figure as PowerPoint slide

Similarly, we construct aggregate measures of foreign interest rates and exchange rate depreciation as weighted averages of the country-by-country variables. The import-weighted exchange rate appreciation of the U.S. dollar ${\mathit{\text{ds}}}_t={\displaystyle \sum _{j=1}^{40}}\left[{\stackrel{⌢}{w}}_{t-k}^j·\Delta \ln (S_t^j)\right]$; and import-weighted foreign interest rates are $i_t^{*}={\displaystyle \sum _{j=1}^{40}}\left[{\stackrel{⌢}{w}}_{t-k}^j·i_t^j\right]$ (see Appendix D for details on foreign interest rates).

IV. The Estimated Results

B. Specification and Benchmark Regressions

The theory implies a rational expectations model of the form:

$\begin{array}{ccc}{\pi }_t^{\mathit{\text{IPI}}}={\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2{\pi }_{t+1}^{\mathit{\text{IPI}}}+{\alpha }_3{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2{\alpha }_3{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]& & (4)\end{array}$

Where coefficients α₁, α₂, α₃ > 0 are functions of the subjective discount factor and the structural parameters of price setting. Specifically, ${\alpha }_1=\frac{(1-\nu )(1-\beta \nu )}{\nu }$, α₂=β, and ${\alpha }_3=\frac{(1-\nu )(1-\beta \nu )}{\nu }·\frac{\kappa }{(1-\kappa )(1-\beta \kappa )}$. Coefficient α₁ represents the effect of exchange rate pass-through. The smaller is α₁, the slower is exchange rate pass-through: that is, an increase in the producer price relative to the import price lead to a smaller current increase in import inflation as α₁ declines. Also, a measure of α₃ < 1 indicates that exchange rate pass-through is slower than foreign countries’ domestic price adjustment.

We estimate the above model with the GMM method. Our “benchmark” instrument set includes contemporaneous import inflation, ${\pi }_t^{\mathit{\text{IPI}}}$; contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. This instrument list exploits the fact that the predetermined price level is “known” by price setters and is thus in the information set at time t-1. We use a one-step Newey-West estimator of the covariance matrix constructed with pre-whitened residuals.

The estimated results of regression (4) are reported in Table 1. The coefficients on μ_t and ${\pi }_{t+1}^{\mathit{\text{IPI}}}$ (α₁ and α₂) are positive and significant at the 1 percent level. This allows us to construct estimates of the structural parameters v and β. The estimate of the subjective discount factor, β = 1.114, is within a standard deviation of its standard estimate (say, β = 0.99) at a quarterly frequency. The estimate of the probability of no import price adjustment, ν = 0.754, is consistent with price changes of imports occurring on average once per year. This is similar to estimates of Galí and Gertler (1999), as to the adjustment of domestic prices in the U.S. However, the estimate of α₃ is negative and insignificant which makes it impossible to develop a parameter estimate of foreign price stickiness, κ. The insignificance of α₃ suggests no evidence of pass-through of foreign marginal cost into U.S. import prices. The Hansen’s J-statistic test of the overidentification conditions of the model, which are not rejected at the 10 percent level, suggests that our instruments are valid.

Table 1.

Estimation Results of the Pass-Through Effect Model

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4 using different sets of instruments. The benchmark instrument set includes contemporaneous import inflation, ${\pi }_t^{\mathit{\text{IPI}}}$; contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. We are able to calculate a real estimate of κ only in the case where the estimate of α₃ > 0 (that is, panel C). Adjustments were made to the benchmark instrument set for panels B–E as indicated above. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets) which is only valid for optimal GMM. The Wald test is a parameter restriction test for the null hypothesis that α₄ = −α₂ ×α₃ (with p-values in square brackets). Standard errors are reported in parentheses. In panel F, the benchmark instrument set is used, and Newey-West corrected standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

Table 1.

Estimation Results of the Pass-Through Effect Model

A. Benchmark
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.069*** (0.024)	1.114*** (0.104)	–0.033 (0.138)	0.754*** (0.019)	––	1.114*** (0.104)	18.15 [0.513]
Wald Test: α4 = –α2 × α3		0.198 [0.657]
B. No Current Information: drop contemporaneous ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.078*** (0.027)	0.988*** (0.120)	–0.099*** (0.178)	0.785*** (0.018)	––	0.988*** (0.120)	18.06 [0.385]
Wald Test: α4 = –α2 × α3			1.295 [0.255]
C. Full Current Information: add contemporaneous μt, dst$i_t^{*}$, and $i_t^{\mathit{\text{FF}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.050*** (0.018)	0.555*** (0.082)	0.213*** (0.065)	0.915*** (0.015)	0.763*** (0.055)	0.555*** (0.082)	20.87 [0.589]
Wald Test: α4 = –α2 ×α3			10.368 [0.017]
D. Only Included Instruments: drop all lags of μt, dst,$i_t^{*}$, and $i_t^{\mathit{\text{FF}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.059* (0.035)	1.339*** (0.182)	–0.321 (0.367)	0.682*** (0.057)	––	1.339*** (0.182)	9.33 [0.968]
Wald Test: α4 = – α2 ×α3			0.004 [0.949]
E. Short List Instruments: include only two lags of all instruments
Parameters	α1	α2	α3	ν	κ	β	J-Test
	0.072*** (0.036)	1.172*** (0.129)	–0.139 (0.287)	0.731*** (0.034)	––	1.172*** (0.129)	13.49* [0.061]
Wald Test: α4 =– α2 ×α3			0.635 [0.425]
F. Two-Stage Least Squares Method
Parameters	α1	α2	α3	ν	κ	β
	0.076* (0.042)	1.060*** (0.208)	–0.049 (0.342)	0.765*** (0.040)	––	1.060*** (0.208)
Wald Test: α4 =– α2× α3			0.427 [0.513]

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4 using different sets of instruments. The benchmark instrument set includes contemporaneous import inflation, ${\pi }_t^{\mathit{\text{IPI}}}$; contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. We are able to calculate a real estimate of κ only in the case where the estimate of α₃ > 0 (that is, panel C). Adjustments were made to the benchmark instrument set for panels B–E as indicated above. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets) which is only valid for optimal GMM. The Wald test is a parameter restriction test for the null hypothesis that α₄ = −α₂ ×α₃ (with p-values in square brackets). Standard errors are reported in parentheses. In panel F, the benchmark instrument set is used, and Newey-West corrected standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

View Table

Table 1.

Estimation Results of the Pass-Through Effect Model

A. Benchmark
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.069*** (0.024)	1.114*** (0.104)	–0.033 (0.138)	0.754*** (0.019)	––	1.114*** (0.104)	18.15 [0.513]
Wald Test: α4 = –α2 × α3		0.198 [0.657]
B. No Current Information: drop contemporaneous ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.078*** (0.027)	0.988*** (0.120)	–0.099*** (0.178)	0.785*** (0.018)	––	0.988*** (0.120)	18.06 [0.385]
Wald Test: α4 = –α2 × α3			1.295 [0.255]
C. Full Current Information: add contemporaneous μt, dst$i_t^{*}$, and $i_t^{\mathit{\text{FF}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.050*** (0.018)	0.555*** (0.082)	0.213*** (0.065)	0.915*** (0.015)	0.763*** (0.055)	0.555*** (0.082)	20.87 [0.589]
Wald Test: α4 = –α2 ×α3			10.368 [0.017]
D. Only Included Instruments: drop all lags of μt, dst,$i_t^{*}$, and $i_t^{\mathit{\text{FF}}}$
Parameters	α1	α2	α3	v	κ	β	J-Test
	0.059* (0.035)	1.339*** (0.182)	–0.321 (0.367)	0.682*** (0.057)	––	1.339*** (0.182)	9.33 [0.968]
Wald Test: α4 = – α2 ×α3			0.004 [0.949]
E. Short List Instruments: include only two lags of all instruments
Parameters	α1	α2	α3	ν	κ	β	J-Test
	0.072*** (0.036)	1.172*** (0.129)	–0.139 (0.287)	0.731*** (0.034)	––	1.172*** (0.129)	13.49* [0.061]
Wald Test: α4 =– α2 ×α3			0.635 [0.425]
F. Two-Stage Least Squares Method
Parameters	α1	α2	α3	ν	κ	β
	0.076* (0.042)	1.060*** (0.208)	–0.049 (0.342)	0.765*** (0.040)	––	1.060*** (0.208)
Wald Test: α4 =– α2× α3			0.427 [0.513]

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4 using different sets of instruments. The benchmark instrument set includes contemporaneous import inflation, ${\pi }_t^{\mathit{\text{IPI}}}$; contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. We are able to calculate a real estimate of κ only in the case where the estimate of α₃ > 0 (that is, panel C). Adjustments were made to the benchmark instrument set for panels B–E as indicated above. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets) which is only valid for optimal GMM. The Wald test is a parameter restriction test for the null hypothesis that α₄ = −α₂ ×α₃ (with p-values in square brackets). Standard errors are reported in parentheses. In panel F, the benchmark instrument set is used, and Newey-West corrected standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

This equation is analogous to a hybrid New Keynesian Phillips curve à la Galí, Gertler, and Lopez-Salido (2005), which nests the pure forward-looking model as a special case. As shown in panel C, we find no evidence that the lagged variable enters significantly. The inclusion changes neither the basic result that α₁ and α₂ are both positive and statistically significant nor the estimate of the frequency of import price changes.

To assess whether our results are biased by the lack of significance of the foreign producer price inflation term, we re-estimate the model after calibrating the term $\frac{\kappa }{(1-\kappa )(1-\beta \kappa )}=12$, which woud be consistent with κ =0.75 and β =1. The regression will then be of the form:

$\begin{array}{ccc}{\pi }_t^{\mathit{\text{IPI}}}={\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2{\pi }_{t+1}^{\mathit{\text{IPI}}}+{\alpha }_1·12·{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_1·12·{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]& & (8)\end{array}$

We report the results in panel D. The estimate of ν is close to the benchmark level with a fairly narrow standard error. However, the coefficient α₁ is very small and only marginally significant. This model, by imposing the constraint that foreign producer price inflation passes through into import price inflation proportionately to the markup of import prices over the PCP price, results in a very low level of exchange rate pass-through. Further, we can reject the hypothesis that β =0.99 at the 5 percent level.

Panel E reports the results from a specification that relaxes the assumption that foreign producer price inflation passes through into import price inflation at the same rate as exchange rates. We estimate the specification

$\begin{array}{ccc}{\pi }_t^{\mathit{\text{IPI}}}={\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2{\pi }_{t+1}^{\mathit{\text{IPI}}}+{\alpha }_8·12·{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_8·12·{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]& & (9)\end{array}$

Not surprisingly, after dropping the proportional assumption we return to our benchmark results in terms of α₁ and α₂ but find a negative estimate of α₈. The hypothesis that α₁ =α₈ was easily rejected at the 5 percent level, suggesting that the impact on domestic import inflation of foreign price inflation appears to be quite different from that of the nominal exchange rate.

We view the negative estimate of the coefficient on foreign inflation in LCP models (Tables 1 and 2) as a result of ignoring the role of PCP firms. In the following subsections, the coefficient estimates on foreign inflation become positive (and often significant) in the mix of LCP and PCP models, which enables us to report significant estimates of structural parameters.

Table 2.

Estimating the Pass-through Effect Model: Alternative Specifications

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4. In all panels, the instrument set includes contemporaneous import inflation,${\pi }_t^{\mathit{\text{IPI}}}$ contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of π ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. The J-stat is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

Table 2.

Estimating the Pass-through Effect Model: Alternative Specifications

A. Equation (5): unrestricted coefficient on ${\pi }_{t+1}^{\mathit{\text{PPI}}}$
Parameters	α1	α2		α3	α4	J-Test
	0.069*** (0.024)	1.087*** (0.108)		–0.032 (0.141)	–0.064 (0.183)	18.65 [0.412]
B. Equation (6): with a lagged PPI inflation, ${\pi }_{t-1}^{\mathit{\text{PPI}}}$
Parameters	α1	α2		α3	α5	J-Test
	0.072*** (0.023)	1.086*** (0.105)		–0.056 (0.145)	0.024 (0.057)	17.72 [0.474]
C. Equation (7): with a backward-looking term, ${\pi }_{t-1}^{\mathit{\text{IPI}}}$
Parameters	α1	α2		α3	α6	J-Test
	0.072*** (0.022)	1.015*** (0.111)		–0.076 (0.125)	0.075 (0.060)	18.39 [0.430]
D. Equation (8): imposing κ[ (1– κ)(1–βκ)] –1 = 12
Parameters	α1		α2			J-Test
	0.015 (0.010)	1.219*** (0.061)				18.21 [0.573]
E. Equation (9): imposing κ[ (1– κ)(1–βκ)] –1 = 12;α1 ≠ α8
Parameters	α1	α2		α8		J-Test
	0.069*** (0.024)	1.114*** (0.104)		–0.003 (0.011)		18.15 [0.513]

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4. In all panels, the instrument set includes contemporaneous import inflation,${\pi }_t^{\mathit{\text{IPI}}}$ contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of π ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. The J-stat is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

View Table

Table 2.

Estimating the Pass-through Effect Model: Alternative Specifications

A. Equation (5): unrestricted coefficient on ${\pi }_{t+1}^{\mathit{\text{PPI}}}$
Parameters	α1	α2		α3	α4	J-Test
	0.069*** (0.024)	1.087*** (0.108)		–0.032 (0.141)	–0.064 (0.183)	18.65 [0.412]
B. Equation (6): with a lagged PPI inflation, ${\pi }_{t-1}^{\mathit{\text{PPI}}}$
Parameters	α1	α2		α3	α5	J-Test
	0.072*** (0.023)	1.086*** (0.105)		–0.056 (0.145)	0.024 (0.057)	17.72 [0.474]
C. Equation (7): with a backward-looking term, ${\pi }_{t-1}^{\mathit{\text{IPI}}}$
Parameters	α1	α2		α3	α6	J-Test
	0.072*** (0.022)	1.015*** (0.111)		–0.076 (0.125)	0.075 (0.060)	18.39 [0.430]
D. Equation (8): imposing κ[ (1– κ)(1–βκ)] –1 = 12
Parameters	α1		α2			J-Test
	0.015 (0.010)	1.219*** (0.061)				18.21 [0.573]
E. Equation (9): imposing κ[ (1– κ)(1–βκ)] –1 = 12;α1 ≠ α8
Parameters	α1	α2		α8		J-Test
	0.069*** (0.024)	1.114*** (0.104)		–0.003 (0.011)		18.15 [0.513]

Notes: This table shows the GMM estimation results of a structural model given by equation (4) for 1980:Q1– 2005:Q4. In all panels, the instrument set includes contemporaneous import inflation,${\pi }_t^{\mathit{\text{IPI}}}$ contemporaneous foreign producer price inflation, ${\pi }_t^{\mathit{\text{PPI}}}$; along with 4 lags of π ${\pi }_t^{\mathit{\text{IPI}}}$, ${\pi }_t^{\mathit{\text{PPI}}}$, the markup (μ_t), the appreciation rate of the U.S. dollar (ds_t), the foreign interest rate $(i_t^{*})$, and the U.S. Federal funds rate. The J-stat is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

E. Pass-through Effect Model with A Mix of LCP and PCP

The above models assume that all firms exporting to the U.S. adjust their U.S. dollar prices infrequently and optimally according to the local currency pricing (LCP) pass-through theory. We relax this assumption by modeling a world in which some fraction of firms (that is, PCP firms) price their goods in their home currency based on changes in aggregate prices.

In producer currency pricing (PCP), firms have sticky prices in their own currency while their invoice prices in U.S. dollar adjust automatically as exchange rates change. We assume that a fraction, λ, of firms set prices in their home currency and pass on the prices into import goods with a one-period lag.

${\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}={\pi }_{t-1}^{\mathit{\text{PPI}}}-{\mathit{\text{ds}}}_{t-1}$

We assume that these firms are randomly distributed and their home prices adjust the same as other firms. For the LCP firms, we model the inflation in the standard way

$\begin{array}{ccc}{\pi }_t^{\mathit{\text{IPI}},\mathit{\text{LCP}}}={\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2{\pi }_{t+1}^{\mathit{\text{IPI}},\mathit{\text{LCP}}}+{\alpha }_3{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_3{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]& & (10)\end{array}$

Total import price inflation can be written as ${\pi }_t^{\mathit{\text{IPI}}}=\lambda ·{\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}+(1-\lambda )·{\pi }_t^{\mathit{\text{IPI}},\mathit{\text{LCP}}}$

$\begin{array}{l}{\pi }_t^{\mathit{\text{IPI}}}=\lambda {\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}+(1-\lambda )·\left\{{\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2{\pi }_{t+1}^{\mathit{\text{IPI}},\mathit{\text{LCP}}}+{\alpha }_3{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_3{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]\right\}\\ =\lambda {\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}+(1-\lambda )·\left\{{\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_2\frac{{\pi }_{t+1}^{\mathit{\text{IPI}}}-\lambda {\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}}{(1-\lambda )}+{\alpha }_3{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_3{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]\right\}\\ =\lambda {\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}+{\alpha }_2{E}_{t-1}\left[{\pi }_{t+1}^{\mathit{\text{IPI}}}-\lambda {\pi }_{t+1}^{\mathit{\text{IPI}},\mathit{\text{PCP}}}\right]+(1-\lambda )·\left\{{\alpha }_0+E_{t-1}\left[-{\alpha }_1{\mu }_t+{\alpha }_3{\pi }_t^{\mathit{\text{PPI}}}-{\alpha }_2·{\alpha }_3{\pi }_{t+1}^{\mathit{\text{PPI}}}\right]\right\}& & (11)\end{array}$

where${\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}={\pi }_t^{\mathit{\text{PPI}}}-{\mathit{\text{ds}}}_{t-1}$. We estimate equation (11) with GMM using the benchmark set of instruments and report the results in Table 3.

Table 3.

Estimating the Pass-through Effect Model: A Mix of LCP and PCP

Notes: This table reports the GMM estimation results of a pass-through model with a mix of local currency pricing (LCP) and producer currency pricing (PCP), structural equation (11) for different sample periods. For the full sample, the benchmark instrument set is used. For the sub-sample regressions (panels B and C), we use contemporaneous measures of ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$ and only two lags (rather than four lags) of each of the variables included in the benchmark instrument list. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

Table 3.

Estimating the Pass-through Effect Model: A Mix of LCP and PCP

A. Full Sample 1980:Q1–2005:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.067*** (0.023)	1.032*** (0.119)	0.036 (0.127)	16.40 [0.565]
Structural Parameters	ν	κ	β	λ
	0.784*** (0.023)	0.420 (0.432)	1.032*** (0.119)	0.066*** (0.018)
B. Sub-Sample 1980:Q1–1991:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.080* (0.049)	0.945*** (0.277)	0.609 (0.415)	9.65 [0.140]
Structural Parameters	ν	κ	β	λ
	0.796*** (0.052)	0.749*** (0.060)	0.945*** (0.277)	0.029 (0.050)
C. Sub-Sample 1992:Q1–2005:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.024 (0.018)	1.069*** (0.104)	0.534*** (0.134)	10.67 [0.099]
Structural Parameters	ν	κ	β	λ
	0.839*** (0.047)	0.802*** (0.053)	1.069*** (0.104)	0.135*** (0.018)

Notes: This table reports the GMM estimation results of a pass-through model with a mix of local currency pricing (LCP) and producer currency pricing (PCP), structural equation (11) for different sample periods. For the full sample, the benchmark instrument set is used. For the sub-sample regressions (panels B and C), we use contemporaneous measures of ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$ and only two lags (rather than four lags) of each of the variables included in the benchmark instrument list. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

View Table

Table 3.

Estimating the Pass-through Effect Model: A Mix of LCP and PCP

A. Full Sample 1980:Q1–2005:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.067*** (0.023)	1.032*** (0.119)	0.036 (0.127)	16.40 [0.565]
Structural Parameters	ν	κ	β	λ
	0.784*** (0.023)	0.420 (0.432)	1.032*** (0.119)	0.066*** (0.018)
B. Sub-Sample 1980:Q1–1991:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.080* (0.049)	0.945*** (0.277)	0.609 (0.415)	9.65 [0.140]
Structural Parameters	ν	κ	β	λ
	0.796*** (0.052)	0.749*** (0.060)	0.945*** (0.277)	0.029 (0.050)
C. Sub-Sample 1992:Q1–2005:Q4
Coefficient Estimates	α1	α2	α3	J-test
	0.024 (0.018)	1.069*** (0.104)	0.534*** (0.134)	10.67 [0.099]
Structural Parameters	ν	κ	β	λ
	0.839*** (0.047)	0.802*** (0.053)	1.069*** (0.104)	0.135*** (0.018)

Notes: This table reports the GMM estimation results of a pass-through model with a mix of local currency pricing (LCP) and producer currency pricing (PCP), structural equation (11) for different sample periods. For the full sample, the benchmark instrument set is used. For the sub-sample regressions (panels B and C), we use contemporaneous measures of ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$ and only two lags (rather than four lags) of each of the variables included in the benchmark instrument list. The J-test is Hansen’s overidentification test for all instruments (with p-values in square brackets). Standard errors are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

The fraction of firms that operate as PCP firms is estimated as very small as indicated by the λ estimate, which is about 6 percent and significant at the 1 percent level. The inclusion of the ${\pi }_t^{\mathit{\text{IPI}},\mathit{\text{PCP}}}$ and ${\pi }_{t+1}^{\mathit{\text{IPI}},\mathit{\text{PCP}}}$ terms has little effect on the estimates of α₁ and α₂, which are still consistent with an economically reasonable subjective discount factor and import price changes with a frequency between 4 and 5 quarters. The coefficient on foreign price inflation, α₃, is positive but not significant. We are able to estimate a parameter of probability of foreign producer price stickiness of κ ≈0.4 although its standard errors are so large that it is not statistically different from 0 or 1.

We split the sample in two parts, one running through 1991 and the other from 1992 to 2005, for two reasons. The first reason concerns data quality. To construct our measure of foreign producer price inflation, we had to make compromises with data quality in order to extend our measure back through 1980 (see the appendix). The data after 1992 should be more accurate. The second reason pertains to a recent literature on structural change in import price pass-through. Marazzi et al. (2006) argue that import price pass-through has declined significantly over time, partly attributable to a change in pricing strategy after the 1997–98 East Asian crises. Our structural model estimations help us identify the reasons for changes in reduced form regressions. We estimate the sub-sample regressions by GMM with contemporaneous measures of ${\pi }_t^{\mathit{\text{IPI}}}$ and ${\pi }_t^{\mathit{\text{PPI}}}$ and only two lags of each of the instruments owing to the shortness of the sample period.

In both sub-samples, we find considerably more evidence for the pass-through of foreign prices into U.S. import inflation as shown by positive estimates of α₃. Panel B shows the parameters from the regression for 1980–1991. The estimates of α₁ and α₂ are both positive and of a size consistent with the benchmark regressions. The estimated frequency of import price changes is on average once per 5 quarters. The average frequency of foreign producer price changes is estimated at around once per 4 quarters. Interestingly, in this period, the fraction of PCP firms is near zero (λ =0.029), and we cannot statistically reject the hypothesis that λ =0 at the 10 percent level.

In the 1992–2005 period (panel C), we find a much larger fraction of PCP firms, as suggested by the λ estimate of 13.5 percent. In this sample period, we estimate a frequency of import price change that is slightly slower than that during the earlier sample period: price changes occurring on average about once per 6 quarters. However, the increase in the stickiness of import prices is neither sizable nor significant. In both sub-samples, the estimate of the subjective discount factor is within a standard error of an economically reasonable number. It should be noted that the model restricts the data along a number of dimensions, and in the latter sample period the overidentifying restrictions are marginally rejected at the 10 percent level.