Asymmetric Exchange Rate Pass-Through in the Euro Area: New Evidence from Smooth Transition Models

This paper examines the presence of asymmetric behavior in exchange rate pass-through (ERPT) to CPI inflation in 12 euro area (EA) countries. Using a class of nonlinear smooth transition models, we test for asymmetry with respect to the direction and the magnitude of exchange rate changes. On one hand, we find only 5 out 12 EA countries showing asymmetric pass-through to exchange rate appreciations and depreciations. Results are somewhat mixed with no clear evidence about the direction of asymmetry. On the other hand, we report strong evidence that ERPT responds asymmetrically to the size of exchange rate changes as a result of presence of menu costs. The degree of ERPT is found to be higher for large exchange rate changes than for small ones in 9 out of 12 EA countries.


Introduction
The issue of asymmetries and nonlinearities is one of the burgeoning topics in the literature of Exchange Rate Pass-Through (ERPT). 1 There are various circumstances that could generate asymmetric adjustment of prices to exchange rate changes which can't be modeled within a simple linear framework. Some spectacular exchange rate movements like those experienced by the US dollar in the 1980s seems to be a good illustration of the existence of an asymmetric behavior in ERPT. At that time, the appreciation of the dollar against the Deutsch mark amounted to 70% between 1980-1985 and the subsequent depreciation amounted to 80% by the end of 1987. 2 Similarly, since the creation of the euro area (EA), there has been a large depreciation of the European currency against the US dollar from 1999 till the last of 2001. After that date, the euro started appreciating to become a strong and well established currency. It is expected that these dramatic exchange rate developments may affect asymmetrically domestic prices, raising the question of the presence of a nonlinear dynamic in ERPT mechanism (see Bussière (2007)).
Nonetheless, the empirical literature has paid little attention to the issue of asymmetries and nonlinearities in ERPT in spite of its strong policy relevance. The number of studies which have investigating for nonlinearities in this context is to date relatively scarce, and most of papers assume linearity rather than testing it. The sparse empirical evidence on this area of research has put forth the role of exchange rate movements in generating nonlinearities. According to this literature, mainly, there are two potential sources of pass-through asymmetry. 3 On one hand, asymmetry can arise from the direction of exchange rate changes i.e., in response to currency depreciations and appreciations. On the other hand, the extent of pass-through may also respond asymmetrically to the magnitude of exchange rate movements, i.e. depending on whether exchange rate changes are large or small. However, as pointed by Marazzi et al. (2005), previous studies provide mixed results with no clear support for the existence of important asymmetries or nonlinearities. If the existing literature is not conclusive, an important caveat should be noted in this regard which is related to the econometric specification. Several empirical studies on asymmetries in ERPT experiment a standard linear model augmented with interactive dummy variables. These added interactive terms would account for appreciation or depreciation episodes as well as for some specific events such as unusual exchange rate developments (See Yang (2007)). For example, in order to capture possible asymmetries in ERPT, Coughlin and Pollard (2004) use threshold dummy variables to distinguish between large and small exchange rate changes. The authors choose an arbitrary threshold value for all US industries equal to 3%. A large exchange rate change is defined as being 3% and above, while a small change is below 3%. However, for more accuracy, the threshold level must be estimated from the data instead of using an arbitrary value. So, a relevant econometric method is required. An alternative methodology is to estimate a nonlinear regime-switching model where a grid search is used to select the appropriate threshold. Amongst this class of models, two popular nonlinear models can be mentioned. First, the so-called threshold regression model where the transition across regimes is abrupt. 4 Second, the smooth transition regression (STR) model with the transition between states is rather smooth. 5 In our paper, we propose to use the second type of regime-switching model, namely a class of smooth transition regression models, in order to investigate for the presence of an asymmetric mechanism in the ERPT.
To our knowledge, there are very few studies testing for asymmetries and nonlinearities in ERPT using a smooth nonlinear regression. Shintani et al. (2009) estimated the ERPT to US domestic prices with respect to inflation regime. They found that periods of low ERPT would be associated with low inflation levels. In a similar vein, Ben Cheikh (2012) has investigated for the presence of nonlinear mechanism in pass-through within logistic STR framework. The author found a strong evidence of nonlinearities with respect to inflation environment in 8 out of 12 EA members, that is, when inflation rate surpasses some threshold, the transmission of exchange rate becomes higher in some European countries. In a more complete study , Nogueira Jr. and Leon-Ledesma (2008) examine the possibility of nonlinear pass-through for a set of inflation target countries. They found that ERPT respond nonlinearly to several macroeconomic factors, including inflation rate, the size of exchange rate changes, macroeconomic instability and output growth. 6 Therefore, our paper aims at contributing to fill the gap in empirical evidence on the nonlinearities in ERPT. We focus on "consumer-price pass-through", i.e. the sensitivity of consumer prices to exchange rate changes. Our study is close to Nogueira Jr. and Leon-Ledesma (2008) who examined the role of the size of the exchange rate movements in generating asymmetry by implementing an exponential STR model. However, in our work, we aim to explore the two possible sources of asymmetries in ERPT, i.e. with respect to both direction and size of exchange rate changes. Also, as in Ben Cheikh (2012), we are interested in the EA case since we expect that the different exchange rate arrangements experienced by the monetary union members would generate a nonlinear mechanism in ERPT. However, as mentioned above, Ben Cheikh (2012) has tested for nonlinearity stemming from inflation environment, while our study deals with another kind of nonlinearities, i.e. relative to the direction and the magnitude of exchange rate changes. To the best of our knowledge, there is no other study has applied a nonlinear STR estimation approach in this context.
The remainder of the paper is organized as follows. Section 2 gives some arguments that justify the existence of asymmetric pass-through and discusses the analytical framework that underlies this dynamic behavior. In section 3, the empirical specification is presented. Section 4 gives the main empirical results and Section 6 concludes.

ERPT and nonlinearities
2.1 Why ERPT would be asymmetric?
From a theoretical point of view, the assumption that ERPT is linear and symmetric is not realistic. In fact, there are various circumstances that could generate asymmetry in the pass-through mechanisms. Despite its policy relevance, studies dealing with this issue are still relatively scarce. The sparse empirical evidence on this area of research has put forth the role of exchange rate movements in generating nonlinearities. On one hand, asymmetric behavior can arise from the direction of exchange rate changes i.e., in response to currency depreciations and appreciations (see e.g. Gil-Pareja (2000)). On the other hand, the extent of pass-through may also respond asymmetrically to the magnitude of exchange rate movements, since there is a differential effect of large versus small exchange rate changes (see e.g. Coughlin and Pollard (2004)). There are some theoretical (microeconomic) arguments behind the potential asymmetric relationship between the exchange rate and prices. Mainly, we mention three major explanations of a possible ERPT asymmetry: -Market share objective: faced with a depreciation of the domestic currency, foreign firms can follow pricing-to-market (PTM) strategy by adjusting their markups to maintain market. However, with an appreciation, they maintain their markups and allow the import price to fall in the currency of destination market. Consequently, the extent of ERPT would be different with respect to exchange rate changes direction. If foreign producers attempt to keep competitiveness and maintain market share, then an appreciation of the domestic currency might cause higher pass-through than a depreciation.
-Capacity constraints: quantities may be rigid upwards in the short run. Faced with an appreciation of the importing country's currency, foreign exporters would gain in price competitiveness by passing this exchange rate change into their prices. But, if foreign firms have already reached full capacity, the ability of increasing sales in destination market is limited, and they may be tempted to increase their markup instead of lowering prices in the currency of the importing country. 7 As argued by Knetter (1994), if exporting firms are subject to binding quantity constraints, then an appreciation of the currency of the importing country might cause lower pass-through than a depreciation.
It is important to note that arguments cited above have a clear implication for possible asymmetric mechanism in ERPT, but in the same time they give rise to opposite interpretations of asymmetry. According to market share explanation, pass-through will be higher when the importer's currency is appreciating than when it is depreciating. While, the quantity constraint hypothesis suggest the opposite result, and ERPT would be highest when exchange rate is depreciating. Empirically, previous studies provide no clear evidence on the direction of asymmetry. In some cases the pass-through associated with depreciations exceeded appreciations; however, in other cases, this result is rather the opposite. Gil-Pareja (2000) analyzed the differences in pass-through in a set of industries across a sample of European countries. He found that the direction of asymmetry varied across industries and countries. According to Coughlin and Pollard (2004), the contrasting direction of the asymmetry highlights the importance of analyzing pass-through at the industry level. If the direction of asymmetry varies across industries then aggregation may obscure asymmetry that is present at the industry level.
Finally, the third potential source of nonlinearities is relative to menu costs.
-Menu Costs: because of the costs associated with changing prices, foreign exporters may leave their price in importer's currency unchanged if exchange rate changes are small. However, when exchange rate changes exceed some threshold i.e., with large magnitude, exporters do change their prices. Thus, according to menu costs hypothesis, ERPT may be asymmetric with respect to the size of the exchange rate shocks, since price adjustment is more frequent with large exchange rate changes than with small ones.
This latter asymmetric dynamic behavior has been put forth empirically by Coughlin and Pollard (2004). In their study on U.S. import prices of 30 industries, they found that most firms respond asymmetrically to large and small changes in the exchange rate with ERPT positively related to the size of the change. It is noteworthy that Coughlin and Pollard (2004) use threshold dummy variables to distinguish between large and small exchange rate changes, in order to capture a possible asymmetric behavior in pass-through mechanism. The authors choose an arbitrary threshold value for 30 US industries to distinguish between small and large exchange rate changes. A large currency movement is defined as a change greater than 3%. In our paper, unlike Coughlin and Pollard (2004), we propose to estimate a nonlinear smooth transition model where a grid search is used to select the appropriate threshold level instead of using an arbitrary threshold value.
Moreover, imported goods have to go through production or distribution processes before they reach consumers in domestic country. Thus, given the different pricing strategies along the distribution channel, this would affect substantially the transmission of exchange rate changes and, thereby, would account for asymmetric ERPT to consumer prices. As discussed in Bacchetta and van Wincoop (2002), the weakness of CPI inflation reaction to exchange rate changes is due, in part, to differences in the optimal pricing strategies of foreign producers and domestic wholesalers/retailers. Due to competitive pressure in the domestic market, domestic wholesalers import goods priced in foreign currency (PCP) and resell them in domestic currency (LCP). This would entail much lower ERPT to CPI inflation than expected. Also, substitution effect can occur following changes in relative prices. For example, if home currency is depreciating, domestic firms or wholesalers may reduce sourcing foreign products (since their price becomes higher), shifting towards substitute domestically produced goods. That way, consumer prices would be more insulated from exchange rate movements. Clearly then, the direction and the size of exchange changes would also affect pricing strategy of domestic wholesalers/retailers, and would account for possible asymmetric pass-through.
Finally, it should be noted that dramatic exchange rate fluctuations, like those experienced by the European currencies in the 1980s, would provide an illustration of what seems to constitute an asymmetric pattern. The French Franc had depreciated by roughly 30 percent vis-a-vis major currencies (on a trade-weighted basis) between 1980-1985, followed by an appreciation of roughly the same magnitude by the end of 1990 (see Figure 1). Similarly, at the launch of the EA, there has been a large depreciation of the Euro against the US dollar from 1999 till the last of 2001. After that date, the euro started appreciating to become a strong and well established currency. Thus, it is expected that these spectacular exchange rate developments may affect asymmetrically domestic prices, raising the question of the presence of a nonlinear dynamic in ERPT mechanism. 8 conomics Discussion Paper

Analytical framework
Let us consider a foreign firm that exports its product i to an importing country. Under monopolistic competition, the first-order conditions for exporter profit maximization, with price, P i , set in importing country currency, yield the following expression: Where E is the exchange rate measured in units of the importer currency per unit of the foreign currency, µ i is the markup of price over marginal cost W * i of foreign producer. The markup is defined as where η i is the price elasticity of demand for the good i in the importing country. As in Bailliu and Fujii (2004), µ i is assumed to depend essentially on demand pressures in the destination market: µ i = µ(Y ), with Y is the income (expenditures) level in the importing country.
The log-linear form of equation (1) gives the standard ERPT regression traditionally tested throughout the exchange rate pass-through literature (see Goldberg and Knetter (1997)): 9 From equation (2), the ERPT coefficient is given by β and is expected to be bounded between 0 and 1. If β = 1, exporter markup will not respond to fluctuations of the exchange rate, price is set in foreign country currency (producercurrency pricing, PCP) and then the pass-through is complete. If β = 0, the ERPT is zero, since foreign firm decide not to vary the prices in the destination country currency and absorb the fluctuations within the markup. This is a purely local-currency pricing (LCP).
In fact, pricing strategies of firms depend not solely on demand conditions in the market. We suggest that foreign firm would adjust prices with respect to the magnitude or the direction of exchange rate movements. As mentioned above, exporters may leave their price unchanged if exchange rate changes are small due to the presence of menu costs. They change their prices only when the exchange rate change is above a given threshold. Thus, there will be differential effect of large versus small exchange rate changes on ERPT. Similarly, if firms attempt to keep competitiveness, faced with a depreciation of the importer currency, they tend to adjust markups to maintain market. Then an appreciation of the importing country's currency might cause higher pass-through than a depreciation. We have seen above that this latter result may be reversed when foreign firms are subject to capacity constraints in the short run, then an appreciation of the currency of the importing country might cause lower pass-through than a depreciation.
Consequently, we assume that pricing strategy of foreign firms to depend on the magnitude and the direction of exchange rate changes in a nonlinear framework. We consider κ(∆e) as a function that captures the size or the direction of exchange rate changes. This can be seen as a firms' strategic decision on how much to adjust price in importer's currency given the size or the direction of exchange rate movements. Taking into account this factor, we can rewrite foreign firm markup as follow: We can capture the arguments of equations (1) and (3) through a log-linear regression specification as follows: According to the function κ(∆e), there is an indirect channel of pass-through which depends on the extent of currency movements which is assumed to affect firm's markup in a nonlinear way. We consequently consider that there is some exchange rate changes threshold level ∆e * which provides two extreme regimes: According to (4) and (5), the degree of pass-through would be different and depends on whether the exchange rate changes is above or below a threshold level.
Here the extent of ERPT would be different with respect to the size of exchange rate change, i.e. to large and small exchange rate changes. If the importer's currency changes are below some threshold (∆e ≤ ∆e * ), then ERPT would be equal to β . While for large exchange rate movements (∆e > ∆e * ), then ERPT becomes (β + θ ). Similarly, when the threshold level is close to zero (∆e * 0), this pattern (equation (4) and (5)) can describe asymmetric ERPT with respect to the direction of exchange rate. Therefore, when exchange rate is appreciating (∆e < 0), the degree of pass-through would be equal to β , and when is depreciating (∆e > 0), ERPT corresponds to (β + θ ). The advantage of equation (4) is to describe this changing behavior in pass-through in a nonlinear fashion. Then, we expect that price responsiveness to be different with respect to the size and the direction of exchange rate changes. Finally, it should be noted that the transition from one regime to the other is assumed to be smooth.

Empirical approach 3.1 Smooth transition regression models
To capture nonlinearity in the exchange rate transmission, we use the family of smooth transition regression (STR) models as a tool. A STR model is defined as follows: is an ((m + 1) × 1) vector of explanatory variables with w t = (y t−1 , ..., y t−d ) and x t = (x 1t , ..., x kt ) . β = (β 0 , β 1 , ..., β m ) and φ = (φ 0 , φ 1 , ..., φ m ) are the parameter vectors of the linear and the nonlinear part, respectively. G(s t ; γ, c) is the transition function bounded between 0 and 1, and depends upon the transition variable s t , the slope parameter γ and the location parameter c. 10 The transition variable s t is an element of z t , and then is assumed to be a lagged endogenous variable (s t = y t−d ) or an exogenous variable (s t = x kt ).
There are two popular choices for the transition function: -Exponential Function Equations (6) and (7) jointly define the logistic STR (LSTR) model and the pattern formed jointly by (6) and (8) is called the exponential STR (ESTR) model. In Both models, the parameter c can be interpreted as the threshold between two extremes regimes G(s t ; γ, c) = 0 and G(s t ; γ, c) = 1. For the LSTR model, the nonlinear coefficients would take different values depending on whether the transition variable is below or above the threshold. So, the parameters β + φ G(s t ; γ, c) changes monotonically as a function of s t from β to (β + φ ). In this sense, as (s t − c) → −∞, G(s t ; γ, c) → 0 and coefficients correspond to β ; if (s t − c) → +∞, then G(s t ; γ, c) → 1 and coefficients become (β + φ ) ; and if s t = c, then G(s t ; γ, c) = 1/2 and coefficients will be (β + φ /2).
Concerning ESTR model, this specification is appropriate in situations in which the dynamic behavior is different for large and small values of s t ; what matters is the magnitude of shocks, if they are large or small. In other words, the coefficients change depending on whether s t is near or far away from the threshold, regardless of whether this difference (s t −c) is positive or negative. Therefore, the exponential transition function G(s t ; γ, c) → 1 as (s t − c) → ±∞, and then coefficients of the model will be equal (β + φ ). If s t = c, then G(s t ; γ, c) = 0 and coefficients becomes β .
The implied nonlinear dynamics under logistic and exponential functions are drastically different. LSTR model is pertinent in describing asymmetric dynamic behavior between negative or positive deviations of the transition variable s t from the threshold level c. As mentioned in the STR literature (van Dijk et al. (2002)), when modeling business cycle, LSTR can describe processes whose dynamic properties are different in expansions from what they are in recessions. For example, if the transition variable s t is a business cycle indicator (such as output growth), and if c 0, the model distinguishes between periods of positive and negative growth, that is, between expansions and contractions. Regarding the empirical ERPT literature, Ben Cheikh (2012) has explored the existence of nonlinearities with respect to inflation environment within LSTR framework. Using quarterly data spanning from 1975 to 2010, the author found that the transmission of exchange rate is higher when inflation rate surpasses some threshold for 8 out of 12 EA countries. The result were supportive to the view of Taylor (2000), that is, pass-through is decreasing in a lower and more stable inflation environment. On the other hand, an ESTR allow for symmetric dynamics with respect to negative or positive deviations of s t from the threshold level. The function rather depends on whether the transition variable is close or far away from the threshold c. Exponential specification was popularly employed in analyzing the nonlinear adjustment of real exchange rates (see e.g. Taylor et al. (2001)).
Since LSTR and ESTR models would allow for different nonlinear behavior, we must be careful in our implementation of these specifications in our ERPT analysis. When we consider exchange rate as transition variable, LSTR model can account for asymmetric ERPT during currency appreciations and depreciations, i.e. with respect to the direction of exchange rate changes. 11 For ESTR model, the interpretation is different, and what matters is the magnitude of exchange rate changes, i.e. whether exchange rate changes are large or small. According to ERPT literature, firms are willing to absorb small changes in exchange rate rather than larger ones due to the presence of menu costs. Thus, the costs of changing prices may result in asymmetric pass-through for large and small exchange rate shocks. ESTR specification would be more appropriate in describing this kind of behavior as argued by Nogueira Jr. and Leon-Ledesma (2008). It is important to note that choosing the relevant transition function can be conducted together with nonlinearity specification tests in addition to the economic intuition (more details in section 4).

Model specification and data
In our empirical analysis, we define a STR pass-through that enables us to test the presence of an asymmetric ERPT mechanism in the EA countries. As a matter of fact, the theoretical model (4) is designed to test the ERPT to import prices, i.e. the so-called "first step pass-through", while our paper instead deals with the responsiveness of consumer prices. Thus, as recommended by Bailliu and Fujii (2004), typical pass-through equations (such as equation (4)) could be adjusted in order to have all the elements of a backward-looking Phillips curve. Mainly, there are two issues which we consider here: first, the inertial behavior of inflation. This could be accomplished by including lags of inflation (π t− j ) as explanatory variables in the empirical specification (backward-looking inflation). Second, a proxy for changes in domestic demand conditions should enter the pass-through equation. We use the changes in real GDP (∆y t ) to capture this effect. 12 Once these two elements have been considered, our LSTR pass-through equation can be described as a nonlinear backward-looking Phillips curve as follows: Where π t is the CPI inflation rate, ∆e t is the rate of depreciation of the nominal effective exchange rate, ∆y t is the output growth and ∆w * t is the changes in foreign producer cost. G(s t ; γ, c) is the logistic transition function driving the nonlinear dynamic. We consider the lagged exchange rate depreciation as transition variable s t = ∆e t− j . According to (9), the degree of ERPT is given by the following time-varying coefficients: For the LSTR model, ERPT coefficient would take different values depending on whether the transition variable is below or above the threshold. 13 If (∆e t − c) → −∞, pass-through elasticity corresponds to: ERPT= β 0 . If (∆e t − c) → +∞, pass-through coefficient becomes: ERPT= β 0 + φ 0 . In the case of the ESTR model, pass-through elasticities change depending on whether ∆e t is near or far away from the threshold c, regardless of whether the difference (∆e t − c) is positive or negative. Therefore, if (∆e t − c) → ±∞, ERPT is equal to β 0 + φ 0 ; and if ∆e t = c, pass-through elasticity becomes = β 0 .
The STR pass-through equation (9) is estimated for 12 EA countries (Austria, Belgium, Germany, Spain, Finland, France, Greece, Ireland, Italy, Luxembourg, Netherlands and Portugal), using quarterly data spanning the period 1975:1 to 2010:4. All the data we use are taken from the OECD's Economic Outlook database, except for exchange rate series which are obtained from International Financial Statistics (IFS) of the International Monetary Fund (IMF). Inflation rates series represents the quarterly change in consumer prices index (CPI). Output growth is constructed using the rate of growth of the real GDP. The nominal exchange rate is defined as domestic currency units per unit of foreign currencies, which implies that an increase represents a depreciation for home country. Finally, 13 We can define the long-run ERPT as follows: ∑ N j=0 β j + ∑ N j=0 φ j G(s t ; γ, c) 1 − ∑ N j=1 λ j . This definition of long-run pass-through was criticized by de Bandt et al. (2008). The authors point out that this measure is very sensitive to the number of lags introduced in the model, leading to inaccurate long-run effect. Hence, in our paper we focus solely on the short-run ERPT as given by equation (10). to capture changes in foreign costs, we construct a typical export partners cost proxy (W * t ) that used throughout the ERPT literature (see Bailliu and Fujii (2004) and Campa and Goldberg (2005) where Q t is the unit labor cost based real effective exchange rate, W it is the domestic unit labor cost and E t is the nominal effective exchange rate. Taking the logarithm we obtain the following expression: w * it = q t + w t − e t . Since the nominal and real effective exchange rate series are trade weighted, we obtain a measure of foreign firms' costs with each partner weighted by its importance in the domestic country's trade. 14 To determine the lag length of the variables, we follow van Dijk et al. (2002) by adopting a general-to-specific approach to select the final specification. We start with a model with maximum lag length of N = 4, and then dropping sequentially the lagged variables for which the t-statistic of the corresponding parameter is less than 1.0 in absolute value.

Main Empirical Results
In this section we investigate the presence of asymmetric behavior in ERPT mechanism for 12 EA countries. As discussed above, there are two types of asymmetries that can be modeled using nonlinear STR models. On one hand, pass-through asymmetries may arise with respect to exchange rate change direction i.e., in response to currency depreciations and appreciations. On the other hand, there is a second type of asymmetry which is related to the size of exchange rate movements, since pass-through could be greater when exchange rate changes are large than when they are small. Consequently, the rate of exchange rate depreciation (∆e t−i ) is considered as the driving factor of the nonlinearity in STR models.
We begin by choosing the relevant transition variable by means of linearity tests as reported in Table 3 in Appendix A. The linearity tests are conducted for each lagged rate of depreciation ∆e t− j with j = 1, 2, 3, 4. Also, no remaining nonlinearity tests are conducted after estimation in our choice of transition variable. We select the transition variables that provided the strongest rejection of both the null of linearity of the baseline linear model, and of no additive nonlinearity after estimation of the nonlinear model. According to Table 3, there is an evidence of presence of nonlinearity in all EA countries expect for Austria. Once linearity has been rejected, we employ the sequence of null hypotheses for selecting the relevant transition function, i.e. logistic or exponential (see Appendix A for details). As 14 We have checked the possibility of cointegrating relationship among our variables in ERPT equation (4). Individual series in level are non-stationary but do not appear to be cointegrated according to Engle-Granger tests. As a result, log differences of the variables are used in the estimation the STR pass-through equation as shown in equation (9). Augmented Dickey Fuller (ADF) tests suggest that variables in differences are appropriately described as stationary series. discussed in van Dijk et al. (2002), recent increases in computational power have made the decision rule, based on testing a sequence of nested null hypotheses, less important in practice. The authors argued that is easy to estimate a number of both LSTAR and ESTAR models and choose between them at the evaluation stage by misspecification tests. In addition, economic intuition must be considered in selecting the adequate transition function. In their study , Nogueira Jr. and Leon-Ledesma (2008) examined the role of the size of the exchange rate movements in generating asymmetry by implementing an ESTR specification. However, in our work, we aim to explore the two possible sources of nonlinearities in ERPT, i.e. with respect to both direction and magnitude of exchange rate changes. Therefore, we follow van Dijk et al. (2002) approach by estimating a number of both LSTAR and ESTAR models for each country. This is a sensible way to check what kind of asymmetry that really drives the nonlinear mechanism in ERPT. As explained in section 3, LSTR specification is appropriate to capture asymmetry arising from the direction of exchange rate changes, while ESTR specification is more suitable for asymmetric behavior with respect to the size of exchange rate movements.

Results from LSTR model
The NLS estimates of LSTR pass-through equation are summarized in Table 1. We report pass-through coefficient for the two extremes regimes (G(s t ; γ, c) = 0 and G(s t ; γ, c) = 1) as defined in equation (10). Full results from all STR models are presented in Table 4 in Appendix C. We compute sum of squared residuals ratio (SSR ratio ) between LSTR model and the linear specification which suggests a better fit for the nonlinear model. We also check the quality of the estimated LSTR models by conducting several misspecification tests. In most of cases, the selected LSTR models pass the main diagnostic tests, i.e. no error autocorrelation, no conditional heteroscedasticity, parameters constancy and non remaining nonlinearity. In Table 1, we give only results for countries with significant nonlinear mechanisms. We note that there are only 5 out of 12 EA countries showing a significant response of CPI inflation to exchange rate movements in a nonlinear way. The threshold levels are quite similar for Italy, Luxembourg and Portugal (around 4%), but differ greatly in comparison to Belgium and Greece. We have plotted both the estimated transition functions and the ERPT as a function of the lagged transition variable (s t = ∆e t−i ) in Figure 2 in Appendix B. It is clear that the transition between both extreme regimes (G = 0 and G = 1), is smooth in most of cases, except for Belgium where γ is very high indicating a rather abrupt transition. 15 Concerning ERPT estimates, our results are to some extent mixed. For Italy, Luxembourg and Portugal, when exchange rate is depreciating above some threshold level, the degree of pass-through becomes higher. For example, ERPT coefficient rise from 0.07% to 0.27% in Portugal once the rate of currency depreciation is exceeding 4.5%. We can say that exchange rate transmission is higher for large rate of depreciation, but it becomes lower for small depreciation and when currency is appreciating. These results seem to be consistent with the so-called capacity constraints hypothesis. This latter stipulates that a depreciation of the importer's currency would cause higher pass-through than an appreciation. Since quantities may be rigid upwards in the short run, exporters may not be able to increase sales when importing country currency is appreciating. So, they are willing to raise markup leaving quantity and price unchanged in importing country. In this case, pass-through would be greater when the importer's currency is depreciating than when it is appreciating. However, results are quite different for Belgium and Greece. The response of CPI inflation to exchange rate is negatively correlated with the rate of depreciation (See Figure 2 in Appendix B). For Belgium, ERPT decreases significantly from 0.1% to 0.04% as the exchange rate is depreciating. Since the threshold level is close to zero (c = 0.004), we can say that the extent of pass-through is smaller during the depreciation than in appreciation episodes. This is in line with the thesis of Market share objective. Faced with a depreciation of the importing country's currency, foreign firms can follow pricing-to-market strategy by adjusting their markups to maintain market. But in the case of an appreciation, they maintain their markups and allow the import price to fall in the currency of destination market.
Consequently, an appreciation of the importing country's currency might cause larger pass-through than depreciation.
In all, our results are somewhat mixed since there is no clear direction of asymmetry. For 3 out of 5 EA countries (Italy, Luxembourg and Portugal), ERPT is greater when exchange rate is depreciating, while for Belgium and Greece, pass-through is lower when importer's currency is depreciating. Nevertheless, our findings corroborate with previous empirical studies which provide also no clear evidence on the direction of asymmetry in ERPT. For a set of European industries, Gil-Pareja (2000) found that the direction of the asymmetry varied across industries and countries. Coughlin and Pollard (2004) confirm the same results in their study on 30 U.S. industries.

Results from ESTR model
The second potential source of nonlinearity is related to the magnitude of exchange rate change. In other words, what matters is if exchange rate movements are large or small. As discussed above, an ESTR specification would be more appropriate to capture this kind of asymmetry since dynamic must be different whether ∆e t−i is close or far away from a certain threshold. As we can see in Table 2, most of EA countries (except Austria and Portugal) exhibit a significant nonlinear dynamic behavior with respect to the size of exchange rate changes. 16 Our results provide an evidence of positive correlation between pass-through and the magnitude of currency changes for 9 EA countries. 17 For instance, the ERPT coefficient in Spain is not significantly different from zero when exchange rate variation is small, i.e. ∆e t−i is close to the threshold of c = 0.006. But for large currency movements, when ∆e t−i is far away from the threshold level, the Spanish passthrough corresponds to 0.12%. Figure 3 in appendix B gives a supportive evidence of the presence of asymmetries arising from the size of exchange rate shocks. That is, large exchange rate changes elicit greater ERPT. This result is consistent with the menu costs assumption. If foreign firms perceive that price changes are costly, a small currency change can be accommodated within the markup. But, if exchange rate changes exceed some threshold, firms are tempted to change their prices in the currency of importing country. Empirically, Nogueira Jr. and Leon-Ledesma (2008) has put forth the role of menu costs in explaining nonlinearities in ERPT. To the best of our knowledge, it is the only work using ESTR model in this context. The results of Nogueira Jr. and Leon-Ledesma (2008) suggest that only two out of six countries (Mexico and UK) provide an evidence of nonlinear ERPT with respect to the size of exchange rate changes.
To give further insight on the relationship between pass-through and the magnitude of exchange rate changes, we plot the time-varying ERPT coefficients over the period 1975-2010 (see Figure 4 in Appendix B). We also report lagged exchange rate depreciation and the threshold value on the same graph. An interesting result concerns the period of launching the euro area. It is well-known that EA countries -except Greece that joined the monetary union in 2001 -have experienced an ongoing depreciation of the euro between the end of 1998 until the last quarter of 2001. 18 , while since the mid-2002 the euro has started a steady appreciation until the end of 2004.
As argued by Bussière (2007), such dramatic changes in the value of European currency may give rise to asymmetric pass-through. Thereby, it is clear from the visualization of Figure 4 that ERPT was higher following the introduction of the euro for most of our EA countries. According to our results, the dramatic change of the European currency during the first three years of the euro has elicited a higher rate of pass-through. When the depreciation of the euro surpassed some limit, those countries have experienced a higher response of CPI inflation which can be interpreted as a proof of nonlinear mechanisms of pass-through.
Also, another prominent result is relative to the European Monetary System (EMS) crisis (1992)(1993). During this episode, the extent of pass-through was higher for most of EA countries. It is known that for members of EMS, currencies were allowed to fluctuate within pre-specified bands (a system known as the Exchange Rate Mechanism (ERM)). During the crisis period, a wave of devaluations has occurred for major EMS countries, especially for Italy that was forced to withdraw the ERM in September 1992. 19 Consequently, due to the excessive variability of the European currencies (conjugated with confidence crisis), it is expected that foreign firms tend to modify pricing strategy, shifting from importer's currency pricing (LCP strategy) to exporter's currency invoicing (PCP strategy). As a result, the degree of pass-through is found to be higher during this episode. Similarly, one might say that the EMS crisis could be an illustration of asymmetric mechanisms of ERPT with respect to the magnitude of exchange rate change. When exchange rate changes surpass some limit, the exchange rate transmission becomes larger.
conomics Discussion Paper  Table reports elasticities of exchange rate pass-through into CPI inflation from ESTR models. Numbers in parentheses are p-values of estimates. R 2 denotes the coefficient of determination and SSR ratio is the ratio of sum of squared residuals between ESTR model and the linear specification. The following rows corresponds to the misspecification tests: pJB is the p-values of Jarque-Bera normality test, pLM AR(4) is the p-values of the LM test of no error autocorrelation up to forth order, pLM ARCH(4) is the p-values of the LM test of no ARCH effects up to forth order, pLM C is the p-values of the LM test of parameter constancy and pLM RNL is the p-values of the LM test of no remaining nonlinearity. www.economics-ejournal.org

Conclusion
In this study, we investigate for possible nonlinear mechanisms in the ERPT to consumer prices for 12 EA countries. This exercise is conducted using the family of smooth transition regression models as a tool. Using quarterly data spanning from 1975 to 2010, we explore the existence of nonlinearities with respect to the direction and the size of exchange rate changes. First, we provide a support of asymmetrical ERPT to appreciations and depreciations, but there is no clear-cut about the direction of asymmetry. In other words, for some countries pass-through is found to be greater when exchange rate is depreciating than when it is appreciating. This finding is consistent with the so-called quantity constraint theory. Nevertheless, we find the opposite result for the rest of EA countries, i.e. ERPT is higher during importer's currency appreciation than during a period of depreciation. This latter result is line with the market share explanation. It is important to note that similar mixed result was pointed out by a number of empirical studies (Gil-Pareja (2000) and Coughlin and Pollard (2004)). Next, we check the asymmetry of pass-through with respect exchange rate magnitude. CPI inflation reaction is found to be higher for large exchange rate changes than for small ones. This can be interpreted as an evidence of the presence of menu costs, where large currency movements are promptly transmitted to prices. A careful inspection of time-varying pass-through elasticities reveals that CPI inflation responsiveness to exchange rate variation was relatively higher during the EMS Crisis and at the launch of the euro.