Can inaction account for the incomplete exchange rate pass-through? Evidence from threshold ARDL model

ABSTRACT Numerous empirical studies suggest that the responses of prices to exchange rate movements are muted, i.e. the exchange rate pass-through is incomplete. In this study we investigate whether this result can be explained by inaction to small changes in the exchange rate, in which case the incompleteness would constitute merely an artefact introduced by the linear specification of the pass-through equation. The results obtained for Polish industry show significant sign- and size-dependence in the sensitivity of export prices to exchange rate movements, but only in a few cases they fully account for the incompleteness of the pass-through. The tendency for inaction is to a large extent determined by industry’s characteristics, with sectors more technologically advanced and more involved in international activities, more willing or able to absorb exchange rate movements in their markups, thereby stabilizing their prices in the destination markets.


Introduction
The exchange rate pass-through (ERPT), i.e. the sensitivity of prices to exchange rate (ER) movements, is one of the classical topics in international macroeconomics. Due to its implications for the conduct of monetary and exchange rate policy, as well as for its relevance in evaluating the impact of ER fluctuations on the real economy, the degree of ERPT has been extensively studied for three decades now, beginning with seminal contributions by Dornbusch (1987) and Krugman (1987).
The degree of ERPT depends on the way exporters set their prices. Theoretically, if prices are set in their own currency, the pass-through to destination prices (i.e. prices expressed in importers' currency) is full (destination prices move one-to-one with the ER). In such circumstances, exchange rate movements generate expenditure-switching effects between home and foreign goods and, consequently, have implications for the real economy: depreciations boost international competitiveness and, thus, tend to increase net exports, while appreciations tend to hamper it. Therefore, under producer pass-through variability, mainly inflation environment in the destination market (Choudhri & Hakura, 2006;Gagnon & Ihrig, 2004;Taylor, 2000), volatility of the exchange rate (Campa & Goldberg, 2002;Devereux & Yetman, 2010;Ozkan & Erden, 2015) or position in the business cycle (Ben Cheikh & Rault, 2016;Ben Cheikh, Ben Zaied, Bouzgarrou, & Nguyen, 2018;Chew, Ouliaris, & Tan, 2011;Nogueira Jr & Leon-Ledesma, 2011). Another form of state-dependence is suggested in Forbes (2016), Forbes, Hjortsoe, & Nenova (2017), Comunale & Kunovac (2017) and Forbes, Hjortsoe, & Nenova (2018). These contributions indicate that the ERPT fluctuates over time more quickly than can be explained by slow-moving structural changes (such as market structure or inflation environment) and suggest that the reason for this is different reaction of prices to exchange rate depending on what kind of shock caused its movement, i.e. that the pass-through is shockdependent.
Another strand of the literature concentrates on the role of the direction of ER changes in the pass-through determination. On the one hand, exporters should be more motivated to absorb ER appreciations than depreciations, since their failing in doing so translates into losses in their competitiveness and, ultimately, their market share, while passing through exchange rate depreciations can help to expand their position in the destination market. On the other hand, however, if quantities of exported goods are rigid upwards (due to export quotas or capacity constraints) and prices are rigid downwards (due to nominal rigidities), exporters may be unable to realize their gain in price competitiveness. In such a case they would rather increase their markups, thereby compensating for previous or building a buffer for future markup squeezes caused by currency strengthening. Both lines of reasoning point to possible asymmetry (albeit opposite in direction) in the relation between the ER and destination prices that has been studied and confirmed in several empirical studies thus far (e.g. Brun-Aguerre et al. 2012;Brun-Aguerre, Fuertes, & Greenwood-Nimmo, 2017;Delatte & López-Villavicencio, 2012;Knetter, 1994;Pollard & Coughlin, 2004;Przystupa & Wróbel, 2011).
The literature provides also theoretical arguments for possible size-dependence in the sensitivity of export prices to exchange rate movements. Firstly, it may arise from the limited ability of exporters to absorb ER movements in their markups, as beyond a certain point it would imply negative profit margins. This is additionally amplified by changes in the market structure caused by currency fluctuations. Due to the existence of irreversible entry and exit costs (Baldwin, 1988;Dixit, 1989) exporting activity is marked by a certain degree of hysteresis, i.e. only after a sufficiently large ER appreciation (depreciation), market exits (entries) are triggered, thereby changing competitive pressure in the destination market. Therefore, when a 'pain threshold' of exchange rate appreciation is exceeded and the ensuing losses exceed exit costs, forcing firms to leave the foreign market, a higher pass-through is expected. However, the empirical evidence on size-dependence in the ERPT is scarce and shows little consistency across countries (Bussière, 2013;Larue, Gervais, & Rancourt, 2010) and sectors (Pollard & Coughlin, 2004).
Against this background, the present study aims to contribute to the literature by combining asymmetry and size-dependence in the pass-through equation and, thereby, testing for the existence of a 'band of inaction', 2 within which the ERPT is relatively weak and beyond which stronger reactionsat least in the case of ER apperceptionsare triggered. For this purpose we develop a threshold ARDL model as an extension to non-linear modelling framework proposed by Shin, Yu, & Greenwood-Nimmo (2014).
Polish industry serves as an application example. We also test whether inaction can explain the partiality of ERPT that is observed under the linear specification of the pass-through equation. Namely, if the 'band-of-inaction' hypothesis is true, the degree of passthrough obtained assuming linearity of the DGP constitutes a weighted average of lower ('within-the-band') and higher ('beyond-the-band') degrees, possibly rendering the incompleteness an artefact introduced by the linearity conjecture. In such case, the ERPT parameter obtained within a linear model would underestimate (overestimate) the degree of pass-through of 'large' ('small') ER changes, giving misleading implications for the conduct of exchange rate policy. Introducing threshold-type non-linearities can, therefore, provide a new insight into ERPT variability over time as well as serve as a useful guidance to policy-makers.
The paper is organized as follows. Section 2 discusses the econometric methodology employed in the study as well as specifies the empirical framework and data upon which the estimates are based. Section 3 brings and discusses the empirical results. The last section concludes.

Methodology
In the presence of nominal rigidities it takes many periods for exchange rate changes to be transmitted to prices, rendering the ERPT a dynamic phenomenon. Therefore, for the purpose of its modelling we use cointegration analysis. Specifically, we utilize and extend cointegration analysis within the non-linear ARDL model proposed by Shin et al. (2014), building upon a linear framework developed by Pesaran and Shin (1999) and Pesaran, Shin, & Smith (2001).
In Shin et al. (2014) the non-linearity in the cointegration equation takes the form of asymmetry: min(Dy i , 0) constitute partial sums of positive and negative changes in y t so that y t = y 0 + y + t + y − t . Since y t is decomposed into y + t and y − t around the threshold zero, parameter d + 1 captures the longrun response of x t to the increase in y t , whereas d − 1 the response to a decrease. The framework can be generalized by imposing a different threshold or by determining its value endogenously (e.g. via a grid search).
In order to test for the existence of a 'band of inaction' in the exchange rate passthrough, we propose to extend this framework by incorporating threshold-type non-linearities into the cointegration equation: where In line with the 'band-of-inaction' hypothesis we additionally restrict the threshold values so that t 1 , 0 and t 2 . 0.
Following Pesaran and Shin (1999), the estimation of short-and long-run elasticises as well as testing for the existence of a cointegration relationship is performed within the ARDL(p,q) model. Its threshold version takes the following form: After reparametrisation the model is estimated in the unrestricted error correction form: In order to recover the long-run parameters from the estimated ECM, its restricted version can be derived: are the estimated long-run elasticities,d + 1 ,d 0 1 andd − 1 respectively, andĝ is the error correction coefficient.
The existence of a long-run relationship is established using bounds-testing approach proposed by Pesaran & Shin (1999). It consists in testing the null hypothesis of The framework is applicable for both I(1) and I(0) regressors. Therefore, there are two asymptotic critical values: one under the assumption that all regressors are I(1) and the other assuming their stationarity. If the test statistics falls outside the critical value bounds, the null of no level relationship can be rejected. If it falls within the bounds, the inference is inconclusive. The relevant critical values are tabulated in Pesaran et al. (2001).
Thresholds t 1 and t 2 are estimated by means of a grid search so as to minimize the sum of squared residuals Q: in the error correction model (Equation 4). The domain D is set by trimming extreme observations (at the 15th and 85th percentile, Hansen, 1999). Due to the fact that thresholds t 1 and t 2 are unknown and, consequently, have to be estimated, the Wald statistics used for the purpose of testing long-run linearity (d + 1 = d 0 1 = d − 1 ) follows a nonstandard asymptotic distribution (the Davies problem, 1977). For this reason the approximate critical values are obtained by means of a bootstrap procedure proposed in Hansen (1996Hansen ( , 2000.

The model and data
The degree of ERPT is estimated within a variant of a standard pass-through equation that has been employed throughout the literature following Knetter (1989): where the transmission of the exchange rate (e t ) changes to destination prices (p exp * t ) is estimated controlling for the marginal costs borne by exporting firms (c t ) as well as the demand in the destination market (y * t ). The equation incorporating the threshold-type relationship between the exchange rate and destination prices, allowing to test for the 'band-of-inaction' hypothesis, takes the following form: where: As in most empirical studies in this field, we employ a single-equation model of the pass-through. The estimates obtained on its basis are, however, subject to simultaneity bias should the variables be endogenously determined, which is especially likely in the case of exchange rates and prices. In such a case system approach should be followed, e.g. by estimating a VAR model (e.g. Ca'Zorzi et al., 2007;Choudhri, Faruqee, & Hakura, 2005;Comunale & Kunovac, 2017;Faruqee, 2006;Hahn, 2003;Ito & Sato, 2008;McCarthy, 2007). In our case, however, the sectoral structure of the data allows to unambiguously determine the direction of causality (sectoral pricesunlike the overall price leveldo not cause exchange rate movements), which justifies the utilization of a univariate framework.
All the data used in the analysis come from Eurostat and are expressed in natural logarithms. The sectoral coverage includes 22 divisions of NACE rev. 2 section C (manufacturing). For basic characteristics of the sectors see Table 1. Data are of monthly frequency and cover years 2006 through 2018 (till September).
Destination prices are export prices denominated in importers' currency. Two measures of prices can be used in this respect: unit values and production prices. Unit value index can be derived from international trade statistics as a FOB value of traded goods over their harmonized quantity. Its advantage over available price indices is that, using customs data, it can be calculated separately for every trading partner. The index has been, however, criticized in the literature for its biasedness in the face of compositional changes in quantities and in quality of what is exported or imported (Silver, 2010). Price indices, on the other hand, measure the evolution of prices of representative goods and, thus, are superior in the face of product differentiation (Marczewski, 2014;United Nations, 1979, 1981. Additionally, price indices are aggregated according to economic activity (NACE) rather than (or along to) product (e.g. SITC) classification, which ensures compatibility of prices and costs (which are available only by activity) in the pass-through equation. For these reasons we use non-domestic production price index as a proxy for export prices. The series are derived from short-term business statistics (STS) database and show the average price developments (expressed in the national currency) of all goods and services sold outside of the domestic market. Destination prices are computed as a product of nondomestic production price index and the exchange rate.
The employment of price indices for geographically aggregated exports necessitates the use of effective exchange rate in the pass-through equation that was approximated by nominal effective exchange rate (NEER) vis-à-vis the currencies of 42 main trading partners. It should be, however, borne in mind that the series were computed using weights for the overall exports, which could be a source of bias if the sectoral weights substantially differ from the overall pattern. The rate is defined as the number of foreign currency units for one unit of domestic currency (direct quotation), implying that its increase indicates appreciation of the home currency. Costs incurred by the exporters are approximated in the literature either by wages (or unit labour costs), or by prices of domestic production. Due to possible variation (e.g. over the business cycle) in the cost pass-through, we decided, along e.g. Vigfusson, Sheets, and Gagnon (2009), on the latter proxy. For lack of a better alternative, demand in the destination market is surrogated by sectoral volumes of production (by NACE sectors) in the main Polish trading partner, i.e. the EU. Nonetheless, a high share (ca. 81% as of 2016) of the EU in Polish manufacturing exports ensures measurement consistency with other variables in the pass-through equation.

Empirical findings
Cointegration analysis within the ARDL model as proposed by Pesaran & Shin (1999) and Pesaran et al. (2001) can be used for a mixture of I(0) and I(1) series but not for variables of higher degree of integration. For this reason the I(2)-ness of the series has to be excluded. The results of unit root tests indicate integration of order 1 with some weak signs of stationarity (the non-stationarity null rejected at the 10% significance level) in a few cases (see Table 2), allowing for the application of the ARDL methodology.
First, a linear specification of the pass-through equation (Equation 7) was estimated (see Table 3). In most industries the null hypothesis of the cointegration test is rejected, pointing to the existence of a long-run relationship between variables. However, in several sectors the relation is degenerate, with the long-run pass-through parameter non-significantly different from zero. Therefore, there seems to be no linear relationship between the exchange rate and destination prices in almost a third of industries, most of which are high or medium-high technology sectors according to the UNIDO classification. 3 The average estimated degree of the long-run pass-through (d 1 ) is approximately 40% 4 (38% and 43% in trade-weighted and non-weighted case, respectively), indicating that a 10% appreciation (depreciation) of PLN translates on average into 4% rise (fall) in destination prices. However, the estimates vary substantially across sectors. Corroborating the results of previous studies (e.g. Campa & Goldberg, 2002;Gaulier, Lahrèche-Rèvil, & Mejean, 2008), the highest pass-through estimates were obtained for industries manufacturing low-technology goods (beverages, coke and refined petroleum products, wood, rubber and plastic, textiles, basic metals), in some of which the null hypothesis of complete pass-through cannot be rejected. The pattern is, however, far from being clear, since relatively small sensitivity of prices to ER movements was estimated in the case of food industry (40%) which constitute a large portion of low-technology exports. Nevertheless, the sensitivity of destination prices to exchange rate movements seems to be decreasing with technologyintensity, with the unweighted average long-run pass-through parameters for low-, medium-and high-technology sectors equal to 0.66, 0.51 and 0.12, respectively. Interestingly, this difference is much less pronounced in the case of short-run parameters (b 0 ) averaging at 0.55, 0.49 and 0.50, respectively. In low-and medium-technology sectors, Notes: Cointegration test verifies H 0 : g = b 1 = 0. One, two and three asterisks indicate statistical significance at the level of 10%, 5% and 1%, respectively. B-G stands for the Breusch-Godfrey test. P stands for the number of lags of p exp * t , q -for the number of lags of e t . The lag structure is established based on the Schwarz information criterion and controlling for serial correlation of residuals.
the degree of pass-through in the long-run is mostly similar (or higher) than in the shortrun. However, in the technologically advanced sectors the on-impact elasticities by far surpass the long-run ones, implying that the initial changes in destination prices caused by exchange rate movements tend to be subsequently absorbed in the exporters' markups.
Next, in order to investigate possible sign-and size-dependence in the sensitivity of export prices to exchange rate movements, we turned to a threshold specification (Equation 8). For all sectors the estimated threshold values are below one standard deviation of the exchange rate distribution (1.7%), whichtogether with relative symmetry of this distributionensures that in all three regimes ('large' depreciations, 'small' ER changes, 'large' appreciations) there are enough observations to efficiently estimate the parameters. 5 In all cases the no-cointegration null is strongly rejected and in most of them (except for manufacturing of electrical equipment) the relation is non-degenerate (at least one of the long-run elasticities is significantly different from zero), implying the existence of a meaningful long-run relationship between the exchange rate and prices (see Table 4). Moreover, the long-run linearity hypothesis (i.e. d + is also rejected in virtually all sectors, pointing to the existence of a threshold-type relationship. In most industries the long-run response of destination prices differs significantly depending not only on the size of exchange rate fluctuations, but also on their sign, since the symmetry null (i.e. d + 1 = d − 1 ) is rejected. However, in most cases the short-run responses show no sign of threshold behaviour (see Table 5), i.e. the on-impact reactions of destination prices are equal, irrespective of the sign or size of the exchange rate changes triggering them. It seems, therefore, that the estimated short-run elasticities roughly reflect the extent of producer currency pricing in a given sector, i.e. the percentage of goods with prices fixed in producers' currency for which the instantaneous pass-through isby constructionfull. Only in a couple of industries (manufacturing of beverages, clothes, paper, metal products and electrical equipment) some patterns indicating on-impact adjustment emerge, albeit they are less pronounced than in the long run.
The long-run elasticities estimated within the threshold equation (see Table 6) give a puzzling insight into the nature of exchange rate pass-through in Polish industry. In most sectors the 'band-of-inaction' hypothesis seems to be supported by the data, i.e. the 'within-the-band' elasticity (d 0 1 ) is significantly lower than the 'beyond-the-band' ones (d − 1 and d + 1 )in some cases even significantly negativesuggesting that the exporters tend to neglect minor changes in the exchange rates until some pain threshold is passed. However, a few sectors (manufacturing of food, beverages, wood, coke and rubber) exhibit the opposite pattern with prices reacting to a greater extent to 'smaller' exchange rate fluctuations than to 'larger' ones. In all of those cases the degree of passthrough within the band is full, or even significantly surpasses 100%, whereas beyond the band it is smaller, especially in the case of 'large' appreciations. There is also no clear-cut pattern regarding the asymmetry of the exchange rate pass-through. In most sectors 'beyond-the-band' reactions of destination prices seem fairly symmetrical or are slightly stronger in the case of appreciations, whereas in some cases (mostly less technologically-advanced industries) prices are significantly more responsive to 'large' depreciations.
In approximately half of the industries the partiality of traditionally-estimated ERPT seems to result from the linear, and apparently inadequate, specification of the pass-through equation. The strictly defined 'band-of-inaction' hypothesis, i.e. the pass-through that is complete 'beyond-the-band' and significantly lower (preferably insignificant) 'within-the-band', seems to be true in three cases: manufacturing of chemicals, metals and computers. In three additional cases (manufacturing of leather, paper and metal products) the hypothesis is partially true, since beyond a threshold point appreciations are fully transmitted to destination prices, while in the case of 'large' depreciations the response is still muted. In the case of manufacturing of food, beverages, wood, coke and rubber the opposite pattern ('band-of-action') seems to prevail, since 'small' One, two and three asterisks indicate statistical significance at the level of 10%, 5% and 1%, respectively. B-G stands for the Breusch-Godfrey test. P stands for the number of lags of p exp * t , qfor the number of lags of e t . The lag structure is established based on the Schwarz information criterion and controlling for serial correlation of residuals. changes in the ER are fully passed to prices (even with some overshooting), while larger changes (especially appreciations) tend to be absorbed.
In order to shed some light on the factors behind the observed heterogeneity in ER transmission patterns, we tabulated each industry's estimated pass-through parameters against its characteristics: technologic intensity, export penetration and import intensity of production (see Figure 1). As mentioned before, the degree of pass-through estimated within a linear model seems to be higher for low-technology sectors than for more advanced ones. However, this seems to pertain only to the reactions to 'small' ER changes, as in the case of relatively large depreciations and appreciations the behaviour of destination prices does not depend on industry's technologic intensity. A similar pattern can be observed in the case of export penetration (a ratio of non-domestic sales to total sales). There seems to be some negative relation (Pearson's correlation coefficient equal to −0.37 and significant at 0.1 level) between the share of non-domestic sales and the estimated linear pass-through parameter, suggesting that the more reliant the industry on foreign markets, the bigger its incentive to price-to-market. However, again this result hinges upon the reactions of destination prices to 'small' exchange rate movements that are more muted (mostly insignificant, or even negative) for industries with higher export penetration (correlation coefficient equal to −0.72 and highly significant). On the other hand, in transmitting larger depreciations and appreciations exports-reliance plays no role whatsoever. Import intensity of production is often found in the literature to be one of the most important factors explaining ERPT variability, with import-intensive firms or sectors having lower pass-through to their export prices (e.g. Amiti, Itskhoki, & Konings, 2014). Our results seem to contradict previous findings, since none of the estimated elasticities is significantly correlated with the share of imported inputs in intermediate One, two and three asterisks indicate statistical significance at the level of 10%, 5% and 1%, respectively. consumption, and in the case of 'large' depreciations the relation appears to be even slightly positive. However, the obtained results are highly influenced by just one sector: manufacturing of coke and refined petroleum products. Despite almost 60% share of imports in its intermediate consumption, the sector is characterized by the highest degree of pass-through. Its exclusion from the sample renders the elasticity from the linear model negatively correlated with import intensity of production (significant of 0.1 level). However, this correlation stems again from the behaviour of destination prices in response to 'small' exchange rate changes thatwith correlation coefficient equal to −0.67seem to be strongly influenced by the offsetting effects of imported inputs on industry's costs and, consequently, profit margins. Again, even after the exclusion of the outlying sector, the pass-through of 'large' appreciations and depreciations is independent of industry's import-reliance. It seems, therefore, that sectoral characteristics (technologic intensity, export-and import-reliance) explain Notes: Technologic intensity is assigned according to UNIDO classification, where L stands for low technology, M for medium technology and H for medium-high or high technology. Corr stands for Pearson's correlation coefficient.
not so much the degree of pass-through as the industry's tendency for inaction (up to some point) to exchange rate movements, with exporters from sectors that are more technologically advanced and more involved in international activities, more willing or able to stabilize their prices in destination markets. As for the width and symmetry of the band given by the threshold values, no clear-cut patterns emerge when tabulated against sectoral characteristics (see Figure 2). The upper threshold seems to be slightly higher in the case of industries with higher import intensity of production (suggesting that the offsetting impact of imports on costs gives the industry more scope for inaction) and the band is slightly narrower in the case of more technicallyadvanced industries, but the correlation coefficients are too low to ensure significance at conventional levels, given the number of observations in the sample. On the other hand, the estimated speed of adjustment to the long-run equilibrium is significantly correlated with both import-intensity and technological advancement (see Figure 3). It seems that the sectors less reliant on imports for their production and producing goods of lower technology adjust their export prices quicker. Notes: Technologic intensity is assigned according to UNIDO classification, where L stands for low technology, M for medium technology and H for medium-high or high technology. Corr stands for Pearson's correlation coefficient. Blue dots represent the lower threshold (t 1 ), while the orange onesthe upper threshold (t 1 ). Figure 3. Estimated speed of adjustment to the long-run equilibrium against sectoral characteristics.
Notes: Technologic intensity is assigned according to UNIDO classification, where L stands for low technology, M for medium technology and H for medium-high or high technology. Corr stands for Pearson's correlation coefficient.