A new approach to tests of pricing-to-market

Journal of International Money and Finance 32 (2013) 654–667

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Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf

A new approach to tests of pricing-to-market Joseph P. Byrne*, Ekaterina Kortava, Ronald MacDonald Adam Smith Business School (Economics), University of Glasgow, Glasgow G12 8QQ, UK

a b s t r a c t JEL classification: F1 F3 Keywords: Exchange rate Forecasting Parameter instability Pricing-to-market

This study proposes a new approach to tests of pricing-to-market, which defines the responsiveness of export prices to currency movements. Pricing-to-market parameters may be susceptible to time variation, and we account for this in a novel theoretical and empirical contribution to the literature. We extend the benchmark model of pricing-to-market to account for instability in the relationship between export prices and exchange rates. Moreover, using an empirical methodology robust to parameter instability, we examine the forecasting performance of a pricing-to-market model. In doing so we apply a selection of model misspecification tests robust to varying degrees of parameter evolution to recent aggregate and disaggregate UK export data. Our estimation results provide strong evidence of pricing-to-market and the instability in the response of export prices to exchange rate fluctuations. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction The concept of pricing-to-market was first introduced to explain the failure of US prices of imported European luxury automobiles to fall as the dollar appreciated against European currencies (see Krugman, 1986). The unresponsiveness of import prices to exchange rate fluctuations was justified with “pricing-to-market”, which implies price discrimination across export destinations by exporting firms. Thus, in markets with an appreciating currency, exporters may increase export prices to stabilize import prices and prevent their fall. Similarly, in countries whose currency is weakening, exporters may decrease export prices to offset an increase in import prices caused by a depreciation. Both policies lead to the stabilization of the domestic price level.

* Corresponding author. Tel.: þ44 (0) 141 330 4617. E-mail address: [email protected] (J.P. Byrne). 0261-5606/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jimonfin.2012.06.001

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The definition of pricing-to-market was subsequently systematized in the open economy macro literature using the distinction between local-currency pricing and producer-currency pricing (see Betts and Devereux, 1996; Devereux and Engel, 2003; Obstfeld, 2006). Specifically, in the context of a general equilibrium framework, the term pricing-to-market refers to the local-currency pricing whereby prices are preset in the buyer’s currency. In contrast, producer-currency pricing implies that prices are set in the exporter’s currency (Smets and Wouters, 2002). The assumption of local-currency pricing has become popular in open macroeconomic models as it facilitates the explanation of a number of macro ‘puzzles’. For example, Chari et al. (2002) employ price-discriminating firms to justify volatility and persistence in real exchange rates. Furthermore, since local-currency pricing implies import price stability, the assumption ensures consistency with widespread evidence on the rigidity of nominal prices (see Eichenbaum et al., 2011) and local currency price stability (see Frankel et al., 2012). The first comprehensive estimation of pricing-to-market was undertaken by Knetter (1989). This study of price discrimination by US and German exporters employed a fixed-effects regression framework to test for the responsiveness of a product’s export price to the destination-specific exchange rate change. While Knetter (1989) examines the export price dynamics, Campa and Goldberg (2002) analyse the response of import prices to nominal exchange rate fluctuations by estimating a log-linear OLS regression. Knetter (1989) and Campa and Goldberg (2002) assume their estimated relationships are stable over time, although Campa and Goldberg (2002) perform structural break tests to complement their main conclusions. However, Stock and Watson (1994) document that the majority of economic time series relationships exhibit coefficient instability. Parameter instability significantly affects the validity of estimation results, since it leads to fundamental changes in the null hypothesis on the parameter vector (Rossi, 2006). Namely, in an unstable coefficient environment, a researcher is faced with a joint hypothesis specifying that a given coefficient equals some constant and that this constant is zero. Only tests robust to coefficient instability are appropriate for testing this joint hypothesis. Out-of-sample forecast tests are robust to parameter instability, since they update parameters as new information becomes available. Gervais and Larue (2009) were among the first to explicitly allow coefficient variation within a tworegime threshold model of export price determination estimated with sequential least squares. Nogueira and Leon-Ledesma (2011) employ a logistic smooth transition model to test for non-linearity in the relationship between exchange rates and consumer prices. Our study generalizes the approach followed in Gervais and Larue (2009) by allowing varying degrees of parameter instability, namely more than two regimes. Hence, we seek to make three contributions to the literature. First, within the context of a stylized theoretical model of pricing-tomarket, we show that the response of export prices to exchange rates may be unstable over time. Second, we use a time-varying parameter framework to test for pricing-to-market by examining the responsiveness of UK export prices to exchange rate movements. Finally, we use a recently developed forecast encompassing test (see Clark and McCracken, 2001) to formally compare the forecasting performance of nested models of export price. Although Diebold and Mariano (1995) also propose a methodology to compare predictive accuracy of models, we adopt the forecast encompassing test by Clark and McCracken (2001), since it was specifically designed for nested models. We are not aware of any other paper which applies forecasting models to test for pricing-to-market. The study is organized as follows. Section 2 presents our extension of the benchmark model of pricing-to-market outlined in Gagnon and Knetter (1995) and Knetter (1995). We argue that exchange rate volatility leads to the instability in the relationship between export price and exchange rate. Section 3 describes the out-of-sample tests that we employ to test for pricing-to-market and Section 4 outlines data selection. Section 5 discusses the results of estimation and robustness check. Section 6 concludes the study. 2. Model The main purpose of this section is to propose a model that explains parameter instability in the dynamics of export prices. We extend the approach followed in Gagnon and Knetter (1995) and Knetter (1995) to design a partial equilibrium model in which the volatility of import prices induces an instability into the relationship between export prices and exchange rates. The effect of price volatility

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on consumer demand has previously been mentioned in Krugman (1986). Rationalizing the stickiness of imported goods’ prices, he suggested that consumers follow a two-stage purchase process. In the first stage, consumers decide whether it is reasonable to enter the market. Entering the market implies embarking upon product analysis, which may be costly for goods possessing complex characteristics that require a commitment to research various options available in the market. For instance, customers may need to go to venues displaying cars and test-drive a particular model. Krugman (1986) argues that only if import prices fluctuate within a stable range will the consumer enter the market and proceed to the second stage, which involves an actual purchase. If import prices are unstable, customers will be unable to match their budget resources with an affordable product to determine whether the benefits of the price offer outweigh the costs of market research. As a result, they will either refrain from entering the market or switch to a supplier with a more credible pricing policy. Consequently, we attempt to apply the hypothesis proposed by Krugman (1986) to analysing the parameter instability in export price models. 2.1. Producers A representative profit-maximizing firm produces a differentiated export good using both domestic and foreign inputs. Its profits, Pt , depend on the export price, Pt, the quantity demanded, Qt, and the marginal cost of production, MCt, which varies in response to the spot exchange rate, St, as a result of foreign input usage.1 Specifically, since the exchange rate, St, is defined as the number of units of the importer’s currency required to purchase one unit of the exporter’s currency, an increase in St indicates an appreciation of the exporter’s currency. Consequently, a rise in St reduces the firm’s foreign input costs, since less units of the exporter’s currency are required to buy one unit of the importer’s currency. The profit function in algebraic form is as follows:

Pt ¼ Pt Qt  MCt Qt

(1)

2.2. Consumers The quantity demanded is assumed to be a function of the good’s import price, PtSt, and the average annual volatility of the import price, st:

Qt ¼ Q ðPt St ; st Þ

(2)

Since Krugman (1986) argued that import price volatility affects consumer purchase decisions, we augment the benchmark demand function from Knetter (1989) with a measure of price instability, st. The variable st denotes the import price volatility observed over the period spanning t  1 through t  12.2

st ¼ sðPt1 St1 ; Pt2 St2 ; .; Pt12 St12 Þ

(3)

We assume a negative relationship between the import price volatility and demand: vQ =vst < 0. Since consumers are assumed to have a preference for price stability, an increase in the import price volatility discourages them from entering the market and making purchases. Thus, demand falls in response to import price variability. 2.3. Optimal export price Firms maximize their profits (1) subject to the demand in the destination market (2). The following expression for the profit-maximizing export price represents the solution to this optimization problem:

1 We adopt a constant marginal cost function for computational simplicity. Marginal cost constancy is a conventional assumption in pricing-to-market models (see Gross and Schmitt, 2000). 2 The choice of time span does not affect the main results of the analysis. Annual volatility may be replaced with quarterly or monthly volatility, although the annual measure has the advantage of a greater span.

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Pt ¼ MCt 

Qt ; vQ =vPt

657

(4)

where vQ =vPt ¼ St ½vQ =vðPt St Þ þ ðvQ =vst Þðvst =vðPt St ÞÞ: The optimal price (4) can be rearranged and expressed as a mark-up, mt, over marginal cost:

Pt ¼ mt MCt

(5)

The mark-up, mt, is a function of the demand elasticity, qt:

mt ¼

qt

; ðqt  1Þ

(6)

where qt > 1. Equation (5) is a conventional way of specifying the optimal price set by monopolistic competitors (see Knetter, 1989). Consequently, export price is falling in the elasticity of demand and increasing in the mark-up and marginal cost. 2.4. Pricing-to-market The existence of a mark-up over marginal cost implies that the firm has the market power to stabilize the import price by manipulating its mark-up. For instance, if the importer’s currency depreciates (St increases), the exporter can prevent the resulting rise in the import price, PtSt, by reducing its mark-up. Thus, an exporter is implementing pricing-to-market by reducing the export price Pt in response to a rise in the exchange rate St. The aim of pricing-to-market is to protect the exporter’s market share in the importer’s country. The extent of pricing-to-market is computed as the derivative of export price (4) with respect to exchange rate:

vPt vMCt vQ vPt Qt v2 Q ¼  þ vSt vSt vSt vQ ðvQ =vPt Þ2 vPt vSt

(7)

The exporter’s marginal costs fall with the appreciation of his currency, since the imported inputs become relatively cheap ðvMCt =vSt < 0Þ. Similarly, the demand falls with the depreciation of the importer’s currency, since a weaker currency implies a higher import price ðvQ =vSt < 0Þ. Assuming a conventional downward-sloping demand schedule, the relationship between the export price and the quantity demanded is negative ðvQ =vPt < 0Þ. Thus, the sign of the expression (7) depends on the value of the derivative v2 Q =vPt vSt . If the latter is negative (or positive and small), the depreciation of the importer’s currency will induce a fall in the export price ðvPt =vSt < 0Þ. Intuitively, the firm decreases its mark-up over the marginal cost to offset at least a portion of the import price increase generated by the currency movement. Hence, the firm wishes to benefit from its market power to reduce the negative demand consequences of the currency movement. If the term v2 Q =vPt vSt is positive and large, the depreciation of the importer’s currency will cause an increase in the export price ðvPt =vSt > 0Þ. Thus, the exporter exacerbates the currency effect by increasing its export price despite the rise in the import price following the depreciation. Empirical observations on such counterintuitive responses of the export price to currency movements inspired the first attempts to qualify and quantify the phenomenon of pricing-to-market (Krugman, 1986). 2.5. Instability in pricing-to-market The pricing-to-market Equation (7) provides insight into the instability of the relationship between export price and the exchange rate. Krugman (1986) argued that import price volatility may have a significant impact on exporters’ price-setting behaviour, since price instability affects demand by discouraging consumers from entering the firm’s market. Based on this assumption on the negative effect of price volatility on demand, we argue that pricing-to-market is time-varying. For instance,

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since during periods of high exchange rate instability the volatility of import price, PtSt, increases, the exporter facing an appreciation of his currency should cut the export price sharply to reduce the import price and mitigate its fluctuations. However, when exchange rate volatility is low, the exporter may not need to decrease its export price dramatically, since the frequency of import price fluctuations is not high enough to encourage consumers to leave the firm’s market. Thus, in periods of a higher exchange rate volatility we will observe a stronger export price adjustment, but in a stable environment the pricing-to-market relationship will weaken. In order to demonstrate the instability in pricing-to-market, the response of export price to the exchange rate (7) is differentiated with respect to the volatility st:

v2 Pt vðvPt =vSt Þ vQ v2 Q 1 ¼ ¼ s0 vst vst vPt vSt ðvQ =vPt Þ2 vSt vst

(8)

For computational simplicity, we assume that Q is a linear function of st. Equation (8) suggests that swings in import price volatility induce non-linearity into the relationship between export price and the exchange rate. Since the derivative of pricing-to-market with respect to volatility, st, is different from zero, changes in volatility are transmitted to the extent of pricing-to-market. As empirical studies indicate that exchange rate volatility is not constant (see Diebold and Nerlove, 1989), the term vst denoting a change in the volatility of import price will vary over time. Consequently, the degree of pricing-to-market, vPt/vSt, will not be constant. It is worth noting that the functional form of demand is crucial. If the demand function is not sensitive to the volatility, st, the channel forcing a structural break in the link between export price and exchange rate disappears, since the derivative in (8) equals zero. To summarize, we have extended the benchmark model of pricing-to-market (see Gagnon and Knetter, 1995 and Knetter, 1995) to justify empirical tests of the pricing-to-market instability by building a framework that predicts structural breaks in the relationship between export prices and exchange rates. Next we outline a series of tests aimed at detecting pricing-to-market in the situation of parameter instability. 3. Forecasting framework This section discusses the proposed empirical methodology for testing for time-varying pricing-tomarket. Our approach is based on the out-of-sample tests of Granger causality derived in Ashley et al. (1980), who propose using out-of-sample forecasting performance to test hypotheses about causation between advertising and consumption in a time series context. More generally, in order to determine whether the series Xt causes the series Yt, Ashley et al. (1980) suggest comparing two forecasts of the variable of interest, Ynþ1, made at time n. The first forecast uses all available information excluding data on the past and present observations Xnj, j  0. The second forecast is based on all available data including the observations Xnj. The superiority of the second forecast to the first serves as evidence of the causation running from Xt to Yt. Thus, out-of-sample forecast tests represent an effective tool to test for pricing-to-market, since the hypothesis of pricing-to-market implies that the exchange rate causes export prices. Using the terminology employed in the forecasting literature, the exchange rate should have predictive power for export prices of the goods that are subject to pricing-to-market. However, testing the presence of the pricing-to-market effect is not the only rationale behind using the out-of-sample forecast tests. One of the most appealing features of the out-of-sample forecasting is its robustness to coefficient inconstancy. The robustness to parameter instability is necessary for the validity of inference in the presence of parameter instability hypothesized in our theoretic model, since coefficient inconstancy leads to fundamental changes in the null hypothesis designed to compare nested models. Instead of a zero coefficient restriction on the exchange rate, we should consider a joint null hypothesis. The first part of this joint hypothesis implies that the exchange rate coefficient is stable and equals some constant, while the second part equates this constant value to zero. This joint hypothesis can only be tested through an out-of-sample forecasting technique that utilises coefficient updating schemes.

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An additional advantage of the forecasting framework lies in its ability to detect pricing-to-market in situations where fixed parameter regression models fail to do so. A researcher is less likely to reject the significance of the variable of interest if parameter instability is accommodated (Rossi, 2006). If the researcher fails to find the predictive content of the forecasting relation over the full sample, there may still be some subsample containing the predictive content (Stock and Watson, 1994). The parameter updating schemes incorporated in the out-of-sample forecasting framework enable examining forecasting relationships over individual subsamples. We apply a recently developed framework for comparing the forecasting performance of nested models by re-estimating coefficients over time (see Clark and McCracken, 2001; Rossi, 2006; Stock and Watson, 1994). This forecasting methodology enables us to detect both the presence of pricing-tomarket and the instability in pricing-to-market. The remainder of this section outlines the estimation steps involved in testing these two phenomena. 3.1. Testing the existence of pricing-to-market The test of pricing-to-market will be carried out by comparing the forecasting performance of the restricted (10) and unrestricted (9) logarithmic specifications of export price. The unrestricted model represents the restricted equation augmented with the variables with putative predictive content, i.e. the exchange rates lnStk :

lnPt ¼ dt þ

m X

akt lnPtk þ

k¼1

lnPt ¼ dt þ

m X k¼1

m X k¼1

akt lnPtk þ

m X

bkt lnMCtk þ

m X

gkt lnStk þ εt

(9)

k¼1

bkt lnMCtk þ εt

(10)

k¼1

The Equation (9) states that export price is a function of the previous values of export price as well as lagged marginal costs and nominal exchange rates. There are two main differences between the price Equation (9) and the price definition (4) derived in Section 2. First, in order to apply a recently developed framework for testing forecasting performance and parameter instability (see Clark and McCracken, 2001; Rossi, 2006; Stock and Watson, 1994), we model export price as an m-order autoregression augmented with m lagged exogenous regressors. An additional motivation for this transformation comes from the price stickiness underpinning the modern open macroeconomic theory (Benigno and Faia, 2010), which assumes that some firms in the industry are unable to re-set their prices frequently. As a result, the current industry price level is affected by the past price indices and their determinants, since some firms charge prices set in previous periods. The gradual adjustment of prices to exchange rates and costs has already been highlighted in the empirical literature. For instance, Campa and Goldberg (2002) regress import prices on lagged exchange rate and cost terms. Second, (9) and (10) exclude a measure of the import price volatility, st, since Section 2 showed that the volatility induces an instability in the relationship between export price and the exchange rate. Therefore, the test of parameter instability will pick up the volatility effect. Moreover, the inclusion of st in (9) and (10) is not desirable due to multicollinearity issues. Since st is a function of Pt1 and Pt2, we risk introducing multicollinearity into the model through the correlation among its regressors. The exclusion of the volatility term does not impact the results of our test for pricing-to-market, because the presence of pricing-to-market is indicated by the effect of the exchange rate terms on reducing the forecasting error of the model. If we add the volatility measure to both unrestricted (9) and restricted (10) equations, we will change the size of each model’s forecasting error, but the difference between these two errors should not be affected. We pursue the following algorithm for testing pricing-to-market. We compare out-of-sample forecasts delivered by the Equations (9) and (10) using a selection of techniques that differ in the degree of parameter evolution, such as fixed (also known as linear), rolling, recursive and random walk coefficient time-varying parameter (RW-TVP) models. A superior forecasting performance of the

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unrestricted model (9) suggests that the hypothesis restricting the coefficients on the exchange rate terms, gkt, to equal zero can be rejected. Therefore, the forecasting superiority of the unrestricted model serves as evidence of pricing-to-market, since the predictive power of exchange rates is confirmed. Similarly, the dominant predictive power of the restricted model (10) indicates the absence of pricing-to-market, as exchange rates fail to exhibit any predictive content for the dependent variable. The next subsection contains the description of our tests of pricing-to-market. 3.2. Econometric methodology 3.2.1. Out-of-sample tests This study employs various out-of-sample tests, which are an appropriate method to choose between nested models when the parameter constancy is questioned (Rossi, 2006). The robustness to parameter instability is achieved through a recursive estimation of coefficients. Out-of-sample tests represent a handy tool for detecting a superior forecasting model. These tests are performed in three steps. First, a portion of the sample is used to obtain the in-sample OLS estimates of coefficients. In the second step, the obtained estimates are used in constructing one-step-ahead forecasts of the dependent variable for the remainder of the sample. Finally, Root Mean Squared Forecast Errors (RMSFE) are computed for each model to find the set-up that minimizes the out-of-sample average squared errors. In the first step, R in-sample observations on the explanatory variables are used to obtain P onestep-ahead forecasts of the dependent variable. The first step varies depending on the type of the u r out-of-sample test, since these tests differ in the method for obtaining bt and bt denoting the in-sample u r estimates of the coefficients in (9) and (10), respectively: bt ¼ ½akt ; bkt ; gkt  and bt ¼ ½akt ; bkt . The u r subscript t in bt and bt implies that the estimates are obtained based on data from 1 to t. Recursive, rolling and fixed (linear) schemes represent three prevalent methods for computing the in-sample coefficient estimates (McCracken, 2007). Due to the differences in obtaining the in-sample estimates, these three tests vary in adaptivity. In linear tests, the parameters are estimated on a fixed portion of the sample and used to predict the dependent variable in all subsequent periods. The parameters are not updated with the availability of new data. Recursive tests add new data to the sample used for estimating coefficients as forecasting advances through time. Rolling tests use only a fixed window of most recent observations in obtaining the in-sample estimates for subsequent forecasting. Unlike the linear tests, the recursive and rolling regressions exploit a possible time variation in parameters, since coefficients are re-estimated over time. Therefore, only rolling and recursive tests are consistent with our hypothesis that the relationship between exchange rates and export prices is unstable. The second and third steps are invariant to the type of test. Denoting the vectors of observations on u r explanatory variables for the unrestricted and restricted regressions as X and X , respectively, the oneu0

u

r0

r

step-ahead forecasts of the export price in (9) and (10) can be represented as bt Xtþ1 and bt Xtþ1 , respectively. The RMSFE delivered by the unrestricted model is computed as follows:

RMSFEu ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP  2 u0 u u t t lnPtþ1  bt Xtþ1

(11)

P u0

u

r0

r

The RMSFE for the restricted model is obtained by replacing bt Xtþ1 with bt Xtþ1 in (11). The specification delivering the lowest out-of-sample RMSFE offers the best description of data. However, the crucial question is whether RMSFE are significantly different across competing models (see Diebold and Mariano, 1995). The next subsection presents a recently developed forecast encompassing test for determining the significance of the difference in the RMSFE delivered by nested models. 3.2.2. Forecast encompassing test (ENC-NEW) Although the best forecasting model may be determined by comparing out-of-sample mean squared forecast errors (Stock and Watson, 1994), recent contributions proposed a more formal methodology to detect the superior forecasting model. Clark and McCracken (2001) show that the new

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encompassing test ENC-NEW is the most powerful out-of-sample forecast statistic for small samples. In contrast to the out-of-sample test proposed by Diebold and Mariano (1995), the ENC-NEW test by Clark and McCracken (2001) is suitable for testing nested models. ENC-NEW is a function of one-step-ahead squared forecast errors delivered by competing nested models using OLS:

P ENC  NEW ¼ P

t

u2r;tþ1  ur;tþ1 uu;tþ1 P 2 uu;tþ1

 (12)

t

ur,tþ1 and uu,tþ1 denote the forecast errors for the restricted and unrestricted models, respectively, and P is the number of one-step-ahead forecasts. The inference suggested by Clark and McCracken (2001) implies comparing the statistics computed in (12) to the appropriate critical value from the table of numerically generated asymptotic critical values. If the test statistic value fails to exceed the critical value, the null hypothesis that the excess terms In Stk have no predictive power cannot be rejected. Thus, the rejection of the null hypothesis serves as evidence of pricing-to-market, since the export price responds to exchange rate movements. 3.2.3. Random walk time-varying parameter estimation Similar to the out-of-sample tests discussed previously, the random walk coefficient time-varying parameter (RW-TVP) model allows varying magnitudes of coefficient evolution. The instability in relationships is explicitly built into the RW-TVP methodology, since the parameters are estimated by recursive least squares. Following the RW-TVP specification used in Rossi (2006), we may express the unrestricted model as follows:

  u0 u lnPt ¼ bt Xt þ xt s:t: xt wN 0; s2x u

u



(13) 

u

  u0 1

bt ¼ bt1 þ ht s:t: ht wi:i:d: 0; l2 s2x E Xt Xt

u The restricted model may be represented by replacing bt u r

(14) r u and Xt with bt

r

and Xt , respectively, in (14). The model parameters bt and bt are assumed to follow a random walk process with zero drift. The degree of coefficient evolution is governed by the value of the parameter l. We consider a range of possible values for l to accommodate various degrees of adaptivity.3 The value for l and the number of lags l is chosen recursively to minimize the RMSFE of the model. The difference between the RW-TVP model and the out-of-sample tests discussed previously lies in the methodology for obtaining the coefficient estimates that are subsequently used in computing onestep-ahead forecasts. Coefficient estimation is performed in three steps. First, all past observations are used to obtain the estimated coefficient vectors for the unrestricted u r and restricted models: Eðbt jlnP1 ; lnP2 ; .; lnPt1 Þ and Eðbt jlnP1 ; lnP2 ; .; lnPt1 Þ. Second, these estimates are used to compute one-step-ahead predictions of the dependent variable: u r u r Xt Eðbt jlnP1 ; lnP2 ; .; lnPt1 Þ and Xt Eðbt jlnP1 ; lnP2 ; .; lnPt1 Þ. In the third step, the coefficient estimates are corrected with a Kalman filter, Kt, by adding the information delivered by the observation In Pt. The corrected estimates are labelled filtered estimates (see Garbade, 1977; Lütkepohl, 2005). This three-step algorithm is performed for each subsequent period. Equation (15) presents the unrestricted filtered estimate. Replacing the superscript u with r yields the restricted filtered estimate:

 u   u  E bt lnP1 ; .; lnPt ¼ E bt lnP1 ; .; lnPt1 þ Kt ðlnPt  EðlnPt jlnP1 ; .; lnPt1 ÞÞ

3

Adaptivity implies the robustness to parameter evolution.

(15)

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Following the formula in (11), we use the filtered estimates to compute the RMSFE from the restricted and unrestricted models. As in the linear, recursive and rolling tests, a smaller RMSFE reflects a superior forecasting performance. 3.3. Testing pricing-to-market instability Stock and Watson (1994) argue that forecasting tests may be applied to detect the presence of parameter instability in the data. They suggest estimating the model with a selection of methods to allow varying degrees of adaptivity. According to their three-group classification of forecasting methods, fixed parameter models fall into the non-adaptive category. The group of models with moderate adaptivity contains recursive tests, rolling regressions and the RW-TVP models with small coefficient evolution. RW-TVP models with large coefficient evolution are classified as models with high adaptivity. The algorithm proposed in Stock and Watson (1994) implies comparing average forecasting errors across various groups of tests. If the RMSFE generated by relatively adaptive models are lower than the average forecasting errors from non-adaptive tests, we may reject the parameter constancy hypothesis. Similarly, the forecasting superiority of non-adaptive models may be interpreted as an indication of parameter stability. Thus, estimating the unrestricted model (9) with fixed, rolling, recursive, and RWTVP regressions enables detecting the inconstancy of the pricing-to-market coefficients, gkt. 4. Data This study of pricing-to-market employs monthly figures for the export price indices of the UK trade in manufactures with the EU. The data was retrieved from the Monthly Review of External Trade Statistics released by the Office for National Statistics, which provides detailed time series data (not seasonally adjusted) disaggregated by commodity group according to the Standard International Trade Classification. We chose the Manufactures category, since producers of differentiated goods are more likely to implement pricing-to-market due to a considerable market power. Moreover, the assumption of the two-stage purchasing process underpinning our theoretic model is more applicable to manufactured goods, since differentiated product characteristics generate high costs of choosing among varieties. Observations span the period from January 1999 to April 2010, giving 136 monthly observations. Empirical evidence suggests that the extent of pricing-to-market varies across commodities (see Campa and Goldberg, 2002; Goldberg and Knetter, 1997). Thus, this study examines the disaggregated export price and PPI data for 10 product categories to ensure a sufficient variation in the degree of product differentiation. The following selection of industries is considered: Food, Wood and Cork Manufactures, Chemicals, Machinery, Electrical Machinery, Clothing, Paper and Paperboard, Miscellaneous Metal Manufactures, Tobacco, and Road Vehicles. We obtained the figures for the Broad Sterling Effective Exchange Rate Index proposed by the Bank of England (Lynch and Whitaker, 2004) from the Financial Statistics Freestanding release by the Office for National Statistics. This index summarizes the value of sterling vis-à-vis the basket of the currencies of the UK’s main trading partners by assigning a time-varying trade weight to each partner. Since Europe receives the heaviest weight, a measurement consistency between the dependent variable, ln Pt, and the regressors, ln Stk, is ensured. Specifically, we regress the export price indices of UK trade with the EU on the Effective Exchange Rate Index driven by the bilateral exchange rates between the pound sterling and individual European currencies. Preference was given to the Broad Sterling Effective Exchange Rate Index due to its ability to reflect changes in the UK’s international competitiveness. The dynamics of competitiveness makes an important contribution to export price movements. For instance, as the competition in the importer’s market intensifies, British exporters must stabilize import prices to protect their vulnerable market shares from currency fluctuations. Therefore, measuring exchange rate fluctuations with the Effective Exchange Rate Index is likely to increase the predictive power of exchange rates in forecasting export prices. As in Vigfusson et al. (2007), marginal costs of production are approximated by the PPI series. Data on the PPI for the output of manufactured products was obtained from the PPI First Release 2005 ¼ 100 provided by the Office for National Statistics.

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5. Empirical results 5.1. Forecasting export prices This section presents the results from running the unrestricted (9) and restricted (10) models with linear, rolling, recursive and RW-TVP tests. Table 1 reports the unrestricted model RMSFE. The Table highlights in bold and with an asterisk the models with the lowest errors. The rolling and recursive models consistently have the lowest RMSFE. This result suggests that introducing a moderate degree of adaptivity improves the forecasting performance of the model, compared to the linear and RW-TVP approaches. We illustrate the implied parameter inconstancy in Fig. 1, which plots g1t and g2t denoting the exchange rate coefficients from (9) estimated with rolling and recursive regressions. A clear variation over the forecast period supports our contention that a time-varying parameter model is more appropriate for testing the pricing-to-market. Having highlighted the importance of parameter inconstancy in the pricing-to-market model (9), we may assess whether it outperforms the non-pricing-to-market model (10) in predicting export prices. Table 2 presents the actual differences between the average squared errors delivered by the restricted and unrestricted models: (RMSFEr  RMSFEu). Moreover, it provides evidence of whether there is a statistically significant difference between these two errors, based upon Clark and McCracken (2001). The significance of the difference in respective RMSFE serves as a tool for comparing the predictive ability of nested models and hence detecting pricing-to-market. The symbols c, b, and a denote the significance of the ENC-NEW statistic at the 1%, 5%, and 10% levels, respectively. Asymptotic critical values are generated by conducting 5000 simulated draws from the statistic’s limiting distribution (Clark and McCracken, 2001). Overall, our findings in Table 2 strongly support the pricing-to-market hypothesis, since they confirm the importance of exchange rates in predicting export prices. The results of the rolling, recursive and linear tests run on aggregate series reflect the predictive superiority of the unrestricted model, since the ENC-NEW statistic suggests that the RMSFE of the unrestricted equation are significantly lower than the restricted model’s RMSFE. Therefore, the pricing-to-market model delivers significantly lower forecasting errors. The RW-TVP method also supports the dominant predictive power of the unrestricted model, but the significance of this finding cannot be verified due to the unavailability of critical values for the ENC-NEW test run with the RW-TVP procedure. The significance of the predictive content of exchange rates for aggregate export prices indicates the existence of pricing-to-market. Combining aggregate evidence from Tables 1 and 2 provides evidence of a timevarying pricing-to-market behaviour in the aggregate UK export price data, since an adaptive unrestricted model displays dominant predictive power. Evidence of pricing-to-market is also found at a disaggregated level of product classification. Applying 4 forecasting tests to 10 product price series yields 40 comparison cases. In 23 cases out of 40, Table 1 Pricing-to-market forecast errors. Series

Rolling

Recursive

Linear

RW-TVP

Aggregate series Food Chemicals Machinery Electric machinery Clothing Road vehicles Paper and paperboard Misc. metal manufactures Wood and cork manufactures Textile fabrics

0.00586* 0.00630 0.00586* 0.00699* 0.00912* 0.00890* 0.00555* 0.00727 0.00627 0.00649* 0.00612*

0.00605 0.00611* 0.00597 0.00711 0.00950 0.00938 0.00558 0.00709* 0.00622* 0.00650 0.00620

0.00839 0.00677 0.01468 0.02810 0.01432 0.01446 0.00979 0.01033 0.00983 0.00751 0.01509

0.01047 0.01085 0.01113 0.01066 0.01273 0.01621 0.00748 0.01296 0.01130 0.01015 0.01102

Notes: This table contains Root Mean Squared Forecast Errors (RMSFE) delivered by the four unrestricted pricing-to-market models (see (9)): Rolling, Recursive, Linear, and Random Walk TVP (RW-TVP). Bold type and asterisk (*) indicate the lowest RMSFE across the four tests of the unrestricted model. Sample period is January 1999–April 2010. To summarize the results, rolling and recursive pricing-to-market models consistently provided lowest RMSFE.

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-0.1

roll

-0.15

rec

-0.2 -0.25 -0.3 -0.35 -0.4

2005

2006

2007

2008

2009

2010

0.2 0.15 0.1 0.05

roll

0

rec 2005

2006

2007

2008

2009

2010

Fig. 1. Time-varying aggregate pricing-to-market coefficients. Notes: This figure contains the estimated exchange rate parameters from rolling and recursive regressions of Equation (9) on aggregate export price data. The top panel shows the first autoregressive coefficient (g1t) for rolling (roll) and recursive (rec) estimation. The bottom panel contains the second autoregressive coefficient (g2t). This figure clearly demonstrates the time-variation of the parameters in the pricing-to-market Equation (9).

the unrestricted model delivers lower RMSFE. Moreover, according to the ENC-NEW test, the predictive content of the exchange rate is statistically significant in 15 cases out of 23. This finding confirms the pricing-to-market hypothesis for individual products. For each level of industry disaggregation, at least one test supports the dominant predictive ability of the unrestricted model. Failure of the four tests to yield the same conclusion on the predictive power Table 2 Forecast error differential. Series

Rolling

Recursive

Linear

RW-TVP

Aggregate series Food Chemicals Machinery Electric machinery Clothing Road vehicles Paper and paperboard Misc. metal manufactures Wood and cork manufactures Textile fabrics

0.00056c 0.00016 0.00007 0.00009c 0.00010 0.00004c 0.00015 0.00028 0.00024c 0.00007 0.00031c

0.00025c 0.00015 0.00012a 0.00001c 0.00021 0.00019 0.00010 0.00007 0.00023c 0.00014c 0.00027c

0.00104c 0.00093c 0.00050c 0.00083 0.00230c 0.00053 0.00089c 0.00046 0.00170 0.00507c 0.00016c

0.00007 0.00002 0.00014 0.00011 0.00004 0.00034 0.00049 0.00031 0.00016 0.00048 0.00013

Notes: This table displays the Root Mean Squared Forecast Errors (RMSFE) delivered by the restricted model (10) minus the RMSFE from the unrestricted model (9) using the Rolling, Recursive, Linear, and Random Walk TVP (RW-TVP) methods. Bold type indicates the rejection of the null hypothesis that the two error terms are equal using the ENC-NEW test statistic. The symbols c, b, and a denote the significance of the ENC-NEW statistic at the 1, 5, and 10%, respectively. A positive and significant differential in RMSFE is indicative of pricing-to-market. Asymptotic critical values are generated by conducting 5000 simulated draws from the statistic’s limiting distribution (Clark and McCracken, 2001). Sample period is January 1999–April 2010.

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of exchange rates may be explained by the differences in parameter updating techniques, which induce a divergence in forecasting errors. For instance, methods allowing an excessively rapid or slow coefficient evolution may accumulate large forecasting errors that undermine the ability of the test to accurately compare nested models. In contrast, methods with moderate adaptivity may minimize prediction errors and enable a more reliable comparison. Thus, these forecasting tests are not equally successful in detecting the predictive content of the exchange rate. Stock and Watson (1994) report that models with small degrees of adaptivity show a superior forecasting performance over both linear and adaptive RW-TVP tests. Our results are consistent with their finding. Models with moderate degrees of adaptivity, such as recursive least squares and rolling regressions, show the best forecasting performance by delivering the lowest prediction errors among all methods. However, the RW-TVP and linear tests exhibit a weaker prediction accuracy. The forecasting errors from the RW-TVP estimation exceed those delivered by the rolling and recursive tests for all product categories. Linear regression models display the worst predictive ability among all tests, since its RMSFE overshoot all errors from the rolling and recursive tests and half of the RW-TVP forecasting errors. The inferior forecasting performance of the RW-TVP regressions, compared to moderately adaptive methods, can be explained with a trade-off between the forecast accuracy and the parameter instability. A frequent parameter updating limits the number of observations used to estimate parameters. Consequently, high adaptivity may jeopardize the precision of estimates and accumulate large forecasting errors. In contrast, less adaptive tests benefit from a larger information set, which enables lowering the size of forecasting errors by identifying the parameters with a higher degree of accuracy. Our findings are highly indicative of a substantial degree of the pricing-to-market instability. The superior performance of adaptive forecasting methods suggests that the exchange rate coefficients, gkt, in (9) are characterized by a time-varying structure that cannot be captured by fixed parameter regressions. The observed parameter instability serves as an additional justification for adopting the proposed estimation methodology. 5.2. Robustness In this subsection we examine the robustness of our results to seasonality in monthly data. Export prices may reach abnormally high or low levels in particular months due to seasonal swings in product demand. In order to alleviate the seasonal effects on export prices, monthly indices, Pt, are transformed into annualized inflation rates, Dp12 t :

Dp12 t ¼ 100ðlnPt  lnPt12 Þ

(16)

Table 3 Pricing-to-market forecast errors: seasonally adjusted data. Series

Rolling

Recursive

Linear

RW-TVP

Aggregate series Food Chemicals Machinery Electric machinery Clothing Road vehicles Paper and paperboard Misc. metal manufactures Wood and cork manufactures Textile fabrics

0.64794 0.68169 0.65695 0.76343* 1.11108* 0.93871 0.56131 0.83980 0.90351 0.71312* 0.74716

0.62840* 0.65089* 0.63529 0.80002 1.12171 0.91567* 0.52296* 0.82557* 0.88094* 0.72475 0.73787*

0.68950 0.81381 0.61388* 0.87787 1.22780 0.92493 0.58028 0.83583 1.11436 0.81465 0.94613

1.07293 1.19944 1.22343 1.11280 1.36299 1.82023 0.84167 1.60385 1.48680 1.16943 1.41389

Notes: This table contains Root Mean Squared Forecast Errors (RMSFE) delivered by the four unrestricted pricing-to-market models (see (9)): Rolling, Recursive, Linear, and Random Walk TVP (RW-TVP). Bold type and asterisk (*) indicate the lowest RMSFE across the four tests of the unrestricted model. Sample period is January 1999–April 2010. Rolling and recursive models typically provided lowest RMSFE.

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Table 4 Forecast error differential: seasonally adjusted data. Series

Rolling

Recursive

Linear

RW-TVP

Aggregate series Food Chemicals Machinery Electric machinery Clothing Road vehicles Paper and paperboard Misc. metal manufactures Wood and cork manufactures Textile fabrics

0.04676c 0.02013 L0.00539b 0.02452c 0.03598 0.02106 0.02838 0.01330 0.02249 0.05190c 0.03577c

0.03549a 0.00747 L0.00122b 0.01680 0.00241 L0.00680b 0.02176 0.00766 L0.01450b 0.03909b 0.02263c

0.01879 0.13059c 0.01600c 0.28760c 0.12609c L0.00691c 0.05196 0.04371c 0.16653 0.05799c 0.12467

0.00195 0.00690 0.00514 0.00403 0.01338 0.00279 0.00940 0.04832 0.00340 0.03665 0.01640

Notes: This table displays the Root Mean Squared Forecast Errors (RMSFE) delivered by the restricted model (10) minus the RMSFE from the unrestricted model (9) using the Rolling, Recursive, Linear and Random Walk TVP (RW-TVP) methods. Bold type indicates the rejection of the null hypothesis that the two error terms are equal using the ENC-NEW test statistic. The symbols c, b, and a denote the significance of the ENC-NEW statistic at the 1, 5, and 10%, respectively. A positive and significant differential in RMSFE is indicative of pricing-to-market. Asymptotic critical values are generated by conducting 5000 simulated draws from the statistic’s limiting distribution (Clark and McCracken, 2001). Sample period is January 1999–April 2010.

In addition to its power to alleviate seasonality, differencing the data has the ability to remove potential non-stationarity. We transform each index using the formula in (16) and repeat all estimation steps by running linear, rolling, recursive and RW-TVP regressions on seasonally adjusted figures for export price indices, PPI and Broad Sterling Effective Exchange Rate Index. Table 3 displays the unrestricted RMSFE across four forecast models. Table 4 displays the differences in the RMSFE generated by the unrestricted (9) and restricted (10) regressions using seasonally adjusted data. Our results are similar to our previous conclusions. Although our RMSFE are larger with seasonally adjusted data, Table 3 indicates that introducing a mild degree of adaptivity to our parameters reduces forecast errors. Moreover, in Table 4, exchange rates have a significant predictive content for all but one export price series. However, the predictive power of exchange rates is not consistent across all forecasting methods due to the aforementioned differences in their parameter updating algorithms. As with unadjusted series, recursive and rolling regressions deliver the lowest errors among the four techniques. The overall rise in the RMSFE may be explained by the increase in the number of forecasted variables, since the prediction of Dp12 tþ1 essentially implies forecasting both In Ptþ1 and In Pt11 (see Equation (16)). However, the increase in the absolute value of RMSFE does not undermine the pricingto-market theory, as evidenced by the significant predictive content of the exchange rate for the export price. 6. Conclusion This study has extended the benchmark model of export price behaviour (see Gagnon and Knetter, 1995; Knetter, 1995) to develop a robust tool for testing pricing-to-market. Following Krugman (1986), we assumed that price instability affects consumer demand. This assumption enabled us to design a partial equilibrium framework in which the relationship between export price and the exchange rate is unstable. Since parameter inconstancy necessitates a methodology that is robust to coefficient instability, we employ recently developed forecasting techniques (see Clark and McCracken, 2001; Rossi, 2006; Stock and Watson, 1994) to build a robust test of the pricing-to-market by UK exporters. First, our empirical findings demonstrate that nearly all product categories considered in this study are subject to pricing-to-market, as evidenced by the significant predictive content of exchange rates for these export price series. Second, in accordance with Stock and Watson (1994), models with moderate degrees of adaptivity deliver a superior forecasting performance over more adaptive tests. Finally, our results suggest that pricing-to-market has a time-varying pattern. Overall, our findings imply that a plausible general equilibrium macroeconomic model should incorporate a pricing mechanism with a time-varying mark-up over marginal cost (see Ravn et al., 2006).

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