Market Entries and Exits and the Nonlinear Behaviour of the Exchange Rate Pass-Through into Import Prices

Abstract

This paper develops an empirical framework giving rise to a nonlinear behaviour of the exchange rate pass-through (ERPT). Rather than shifts between low and high inflation, the nonlinearity arises when large swings in the exchange rate trigger market entries and exits of foreign firms. Switching regressions are used to distinguish between low and high pass-through regimes of the exchange rate into import prices. For the case of Switzerland, the corresponding results suggest that, though inflation has been low and stable, the ERPT still doubles in value in times of a rapid appreciation of the Swiss Franc.

1 Introduction

The pass-through coefficient in the phase where the number of foreign firms is constant is quite small, perhaps close to zero, whilst its values in the phases with entry or exit are much larger, perhaps close to one. Dixit (1989, p.227)

In several areas of economic policy, the exchange rate pass-through (ERPT)—that is the impact of price changes of foreign currency upon import prices measured in terms of an elasticity—is a closely watched variable. For example, for monetary policy, the value of the ERPT connects the developments on the foreign exchange market with inflation whilst, for antitrust policy, the ERPT indicates in how far import competition prevents local producers from charging excessively high prices. It is therefore not surprising that a large body of empirical research has been devoted to estimating the pass-through effect. Campa and Goldberg (2005), Ihrig et al. (2006), Frankel et al. (2012), and An and Wang (2012) provide some recent examples reporting estimates for several countries. Numerous other studies have dealt with the conditions of individual countries and industries. Probably the most important stylised fact arising from this plethora of research is that, even in the long-term, import prices adjust incompletely to exchange rates. Elasticities of around -0.5 are commonly found (Goldberg and Knetter 1997).

Market frictions are essential to explain why import prices react partially to changes in currency prices. Such frictions include price rigidities, which are a key ingredient in open economy models of the ERPT (see Taylor 2000; Choudhri and Hakura 2006; Devereux and Yetman 2010), or Pang and Tang 2014). Though it has long been recognised that, with sticky prices, different levels of inflation can give rise to differences in the ERPT between countries (e.g. Taylor (2000); Gagnon and Ihrig 2004; Campa and Goldberg 2005; Choudhri and Hakura 2006; Frankel et al. 2012), only recently, Al-Abri and Goodwin (2009) as well as Shintani et al. (2013) have suggested that this might warrant nonlinear models to estimate the nexus between import prices and exchange rates. Arguably, when menu cost create a threshold delineating when an adjustment of import prices is worthwhile, the ERPT of a given country could vary between periods with low and high inflation.

This paper endeavours to contribute to the empirical literature measuring the ERPT by considering that nonlinearities can also arise from changes in competition when importing firms start to enter or exit a given market. Imperfect competition has provided a second explanation for why foreign firms only partially adjust their import prices to changes in the exchange rate. Dornbusch (1987) has pioneered the literature embedding the ERPT into models of industrial organisation. A strand of the literature tying the incomplete ERPT with oligopolistic market structures and product differentiation has allowed for the possibility that market entries and exits by foreign firms alter the degree of import competition. Though they pursue slightly different theoretical approaches, the seminal contributions of Baldwin (1989) and Dixit (1989) both emphasise the combined role of irreversible entry and exit cost and exchange rate uncertainty in guiding the decision of foreign firms to, respectively, start or terminate supplying goods to a given market. As illustrated by the quote at the outset, a key result of this literature is that exchange rates can impact upon prices in a nonlinear manner. In particular, during periods with relatively stable exchange rates, even modest sunk cost could discourage foreign firms from changing the status quo. With a fixed market structure, competition is limited to the setting of prices and the ERPT might be relatively low. Conversely, sufficiently large swings in the foreign exchange market affect the profits of foreign firms to a degree where they will want to incur the irreversible cost to enter or exit a market. The resulting adjustment in the share of imported goods gives rise to an additional channel forcing foreign firms to adapt their prices according to the conditions on the foreign exchange market. Though the role of openness to international trade has received attention in the empirical ERPT literature (McCarthy 2000; Gust and Leduc 2010; An and Wang 2011), the nonlinearities arising in the theoretical work of Baldwin (1989) and Dixit (1989) from changes in the market structure have hitherto been ignored.

To fill this gap, this paper develops a stylised model where the ERPT has the widely found elasticity of around -0.5 when the market structure is fixed, but higher values when large shifts in the foreign exchange market induce foreign firms to enter or exit the market. Consistent with Baldwin (1989) and Dixit (1989), the theoretical framework gives rise to a low and high pass-through regime. Empirically, these regimes can be represented by switching regressions. The possibility of a regime change is illustrated for the case of Switzerland, which has been chosen due to its low and stable level of inflation during the last decades. Nevertheless, an unobserved regime switching regression suggests that the effect of the exchange rate is not constant, but doubles in value in times of marked appreciations of the Swiss Franc, when inflation was in general low and, hence, a menu cost explanation is unlikely to apply.

The paper is organised as follows. Section 2 derives the model distinguishing different regimes of the ERPR depending on whether or not firms enter or exit the market. Section 3 connects this theoretical framework with a regime switching regression. Section 4 presents an empirical application with data from Switzerland. Section 5 summarises and concludes.

2 Market Entry and Exchange Rate Pass-Through

This section develops a stylised model where the market entry and exit of foreign firms gives rise to nonlinear transmission effects of the exchange rate onto import prices. Rather than providing an in depth discussion about this topic, which has appeared in the seminal work on the hysteresis effects of the exchange rate (Baldwin 1989; Dixit 1989; Baldwin and Krugman 1989), the aim is merely to develop a framework underpinning the empirical analysis of Sections 3 and 4.

Consider a model where the domestic market of a given country is served by a number of identical foreign firms, whose weight equals ω _t , whilst (1−ω _t ) of the market is covered by identical domestic producers. Furthermore, during period t, the foreign and local sector charge prices denoted by, respectively, $p^{*}_{t}$ and p _t .

The demand conditions are modeled with the transcendental logarithmic (or translog) expenditure function. Translog-preferences have the distinctive property that the market share between, say, locally produced and foreign goods is not constant, but depends on the differences between the corresponding prices $p^{*}_{t}$ and p _t (see Bergin and Feenstra 2000, 2001). This is maybe a crucial ingredient when considering the effect of a changing market structure, where foreign firms can enter or exit the market. As derived in Herger (2012), for a scenario of representative domestic and foreign firms, the expenditure E _t at time t with a translog function is given by

$$\begin{array}{@{}rcl@{}} \ln E_{t}(\overline{U}, p_{t}^{*}, p_{t}) & = & \omega_{0} + \ln \overline{U} +\omega_{t}\ln p_{t}^{*}+(1-\omega_{t})\ln p_{t} \\ \!\!\! & - & \!\!\! \frac{1}{2} \gamma^{*} \ln p_{t}^{*} \ln p_{t}^{*}+ \frac{1}{2}\gamma^{*}\ln p_{t}^{*} \ln p_{t} + \frac{1}{2}\gamma\ln p_{t}\ln p_{t}^{*} - \frac{1}{2} \gamma\ln p_{t} \ln p_{t} \end{array} $$

where ω ₀ is a constant and $\overline {U}$ the utility level to be reached with expenditure E at prevailing prices $p^{*}_{t}$ and p _t . Furthermore, γ and γ ^∗ reflect in how far prices p _t and $p^{*}_{t}$ set by, respectively, local and foreign firms affect the level of expenditure E. Shephard’s Lemma¹ implies that the expenditure share $s_{t}^{*}$ on imports is given by

$$ s_{t}^{*}(p_{t}^{*}, p_{t}) = \frac{\partial \ln E_{t}}{\partial \ln p_{t}^{*}} = \omega_{t} - \gamma^{*}\ln p_{t}^{*} + \underbrace{\frac{\gamma+\gamma^{*}}{2}}_{=\gamma^{*}{\Gamma}}\ln p_{t}. $$

(1)

Unlike in Bergin and Feenstra (2000), the symmetry assumption γ ^∗=γ is here not introduced. This implies that the reaction measured by γ and γ ^∗ of the expenditure to the same price change can differ between, respectively, domestic and foreign goods. Following Herger (2012, p.385), the degree of asymmetry between the (countervailing) effects of foreign and domestic producer prices on the share of imports is summarised by γ ^∗Γ=(γ+γ ^∗)/2 with Γ=1 reflecting symmetric conditions whilst Γ>1 and 0<Γ<1 indicate, respectively, a relatively high and low sensitivity of $s_{t}^{*}$ to domestic producer prices. As mentioned above, even with a constant weight ω _t of foreign firms, the expenditure share $s_{t}^{*}$ is not fixed but depends on the price difference between locally produced and imported goods. The price sensitivity of goods that have been produced at home or abroad depends on the degree of substitutability embodied in γ and γ ^∗ with the limit value of 0 reflecting the CES-case with perfect complements.

For a foreign firm, the price $p_{t}^{*}$ of selling a product abroad and the production cost are denominated in different currencies. With the nominal exchange rate e _t —expressed here as the ratio between the foreign and the domestic currency—the profit (denominated in domestic currency) that foreign firms obtain from selling goods on the domestic market at price p ^∗ (denominated in domestic currency) equals

$$ \pi_{t}^{*}=p^{*}_{t}-(1/e_{t}), $$

(2)

where, for the sake of simplicity, the quantity of imports and foreign production costs have been normalised to 1. Equation (2) shows that an increase in e _t , which is an appreciation of the domestic currency, reduces the cost of foreign production relative to the import price $p^{*}_{t}$. From this, as derived in Appendix A, the optimal price setting rule is given by

$$ p_{t}^{*} =\left[1+\frac{s_{t}^{*}} {(1-\nu{\Gamma})\gamma^{*}}\right]\frac{1}{e_{t}}, $$

(3)

where $\nu = \frac {\partial p_{t}}{\partial p_{t}^{*}}\frac {p_{t}^{*}}{p_{t}}$ is the conjectural elasticity reflecting the percentage change of domestic prices that foreign firms expect when they change their price by one percent. As discussed in Bernhofen and Xu (2000), the conjectural elasticity provides a concise way to account for the impact of various degrees of price competition upon the ERPT. In particular, we have that $-\infty <\nu <1$ with higher values reflecting less competition in the sense that a foreign firm can push prices $p_{t}^{*}$ further above the marginal cost 1/e _t . The special case of Cournot-Nash behaviour implies that ν=0 by assumption. Taking logarithms of Eq. 3 and using the first order Taylor approximation yields $\ln p_{t}^{*} \approx \frac {s_{t}^{*}}{(1-\nu {\Gamma })\gamma ^{*}} - \ln e_{t}$. Inserting (1) for $s_{t}^{*}$, and solving for import prices, yields the optimal pricing equation

$$ \ln p_{t}^{*} \approx \frac{1}{(2-\nu{\Gamma})} \ln p_{t} - \frac{1-\nu{\Gamma}}{2-\nu{\Gamma}}\ln e_{t} - \frac{1}{(2-\nu{\Gamma})\gamma^{*}}\omega_{t}. $$

(4)

Reflecting the seminal result of Dornbusch (1987), in Eq. 4, the ERPT given by (1−νΓ)/(2−νΓ) depends on degree of price competition. In particular, perfect competition with $\nu =-\infty$ implies that (1−νΓ)/(2−νΓ)=1 and the adjustment of import prices to exchange rate movements is instantaneous and complete. Conversely, under a scenario with perfectly matched price setting across domestic and foreign firms with ν=1 and Γ=1, there is no effect of the exchange rate upon import prices. Note that Cournot-Nash behaviour with ν=0 and symmetric reactions with Γ=1 give rise to a pass-through effect of 1/2. Implicitly, this parametrisation appears in Bergin and Feenstra (2000, pp.662-663) and is also close to the values that are widely found in empirical work (Goldberg and Knetter 1997).

Competition might not only depend on the extend with which foreign firms react to the price setting of existing rivals, but also on the prospect that profits and losses can trigger market entries and exits. The pass-through effect discussed in the previous paragraph has neglected the effect of the exchange rate on the weight ω _t of the foreign firms. However, as discussed at the outset, it has been argued that market entries and exits occur predominantly in times of large swings in the foreign exchange market, since episodes of marked depreciations or appreciations can have profound effects on the earnings of foreign firms. Inserting the optimal price of Eq. 3 into Eq. 2 implies that the profit function (expressed in domestic currency units) equals $\widetilde {\pi }_{t}^{*}=(s_{t}^{*}/(\gamma ^{*}(1-\nu {\Gamma }))(1/e_{t})$. As shown in Appendix A.1, inserting (1) for $s_{t}^{*}$ yields approximately

$$ \ln \widetilde{\pi}_{t}^{*} \approx \frac{1}{(1-\nu{\Gamma})\gamma^{*}}\omega_{t}-1 - \frac{1}{1-\nu{\Gamma}} \ln p_{t}^{*} + \frac{\Gamma}{1-\nu{\Gamma}}\ln p_{t} - \ln e_{t}. $$

(5)

Equation (5) reflects how the profits of foreign firms depend on their market share (ω), the exchange rate (e _t ), and prices $(p_{t}, p_{t}^{*})$. What is important as regards the ERPT, is that (5) implies that prices and exchange rates are tied together in a relationship that depends on the conduct parameters ν and Γ. A useful benchmark arises under the Cournot-Nash ν=0 and symmetry assumption Γ=1, where—at a given optimal profit $(\pi _{t}^{*})$ and market share (ω _t )—(5) gives rise to a direct proportional relationship between exchange rates and prices, which resembles the purchasing power parity condition (PPP). However, empirically this is perhaps of limited use since observed profits are often highly incomplete.² A more useful interpretation is that profits are directly related with exchange rate misalignments, defined here with u _t . In particular, positive profits by foreign firms, that is $\widetilde {\pi }_{t}^{*}>0$, encapsulate a scenario where the domestic currency is overvalued, which is here defined by u _t >0. Conversely, losses with $\widetilde {\pi }_{t}^{*}< 0$ are associated with a domestic currency that is undervalued, defined here by u _t <0.

Adjustments in the weight ω _t of importing firms occur when the profit and losses of Eq. 5 outweight the cost accruing, respectively, to entering and exiting the local market. Assume, for the sake of simplicity, that the cost of a foreign firm that wants to switch its status between serving and exiting a market equals f (an extension with different entry and exit cost would be straightforward). Since profits are connected with exchange rate misalignments, as long as $|\widetilde {\pi }_{t}^{*}|=|u_{t}|\leq f$, no firms enter or exit and ω _t is constant. Yet, large swings in the foreign exchange market could give rise to sufficiently high profits or losses to trigger an adjustment of the market structure until $|\widetilde {\pi }_{t}^{*}|=|u_{t}|=f$. Solving (5) for the corresponding import share yields $\omega _{t} = \gamma ^{*} \ln p_{t}^{*} - \gamma ^{*}{\Gamma }\ln p_{t} + (1-\nu {\Gamma })\gamma ^{*}\ln e_{t}+c$ where c is a constant. Taken together, depending on $|\widetilde {\pi }_{t}^{*}|=|u_{t}| \lessgtr f$, we have that

$$ \omega_{t}= \left\{\begin{array}{lll} \omega_{t} & \text{if} \quad |u_{t}| \leq f & \textrm{No Entries/Exits}\\ \gamma^{*} \ln p_{t}^{*} - \gamma^{*}{\Gamma}\ln p_{t} + (1-\nu{\Gamma})\gamma^{*}\ln e_{t}+c & \text{if} \quad |u_{t}| > f & \textrm{Enties/Exits.} \end{array} \right. $$

(6)

Since the import share ω _t adjusts as function of e _t , the ERPT exhibits a nonlinear behaviour around the points where entries and exits occur. In particular, as derived in Appendix A.2, substituting (6) into (4) and rearranging yields

$$\ln p_{t}^{*} \! \approx \! \left\{\begin{array}{llll} \left[1/(2-\nu{\Gamma})\right]\ln p_{t}&\!\!- \left[(1-\nu{\Gamma})/(2-\nu{\Gamma})\right]\ln e_{t}& \!\!\!\! - \! \left[1/((2-\nu{\Gamma})\gamma^{*})\right]\omega_{t} & \!\! \text{if} \ |u_{t}|\leq f \\ \left[(2{\Gamma})/(3-\nu{\Gamma})\right] \ln p_{t}&\!\! - \left[(2-2\nu{\Gamma})/(3-\nu{\Gamma})\right]\ln e_{t} & & \!\! \text{if} \ |u_{t}|>f. \end{array}\right. $$

Subtracting lagged terms from both sides transforms this into log differences, which are denoted by ${\Delta } p_{t}^{*}= \ln p_{t}^{*}-\ln p^{*}_{t-1}$, ${\Delta } p_{t}= \ln p_{t}-\ln p_{t-1}$, and ${\Delta } e_{t}= \ln e_{t}-\ln e_{t-1}$, that is

$$ {\Delta} p_{t}^{*} \approx \left\{\begin{array}{lll} \left[1/(2-\nu{\Gamma})\right] {\Delta} p_{t} &- [(1-\nu{\Gamma})/(2-\nu{\Gamma})]{\Delta} e_{t} & \text{if} \ |u_{t}| \leq f \\ \left[(2{\Gamma})/(3-\nu{\Gamma})\right] {\Delta} p_{t} &- [(2-2\nu{\Gamma})/(3-\nu{\Gamma})]{\Delta} e_{t} & \text{if} \ |u_{t}|>f. \end{array}\right. $$

(7)

The first line of Eq. 7 refers to a scenario where prices and exchange rates are close to their equilibrium and hence only price competition from established rivals forces foreign firms to adjust their import prices to exchange rates (note that Δω _t =0). This reflects the scenario discussed above after (4). However, sufficiently large swings in the foreign exchange rate result in profits and losses that end up changing the market structure. Then, the weight ω _t of the importing sector becomes an endogenous variable. The second line of Eq. 7 accounts for this channel, which fosters the ERPT since a sufficiently large mis-valuation of a currency can give rise to market entries and exits which, in turn, increase the competitive pressure to adjust the import prices to changes in the exchange rate. It is maybe again instructive to consider the case of Cournot-Nash behaviour with ν=0 and symmetry Γ=1 which, in the second line of Eq. 7, gives rise to a pass-through elasticity of 2/3.

The merit of Eq. 7 is to tie with Baldwin (1989) and Dixit (1989) who have emphasised the role of nonlinearities in the relationship between exchange rates and import prices. In sum, there might be two regimes in the ERPT with relatively larger effects arising in times of pronounced shifts in the value of the exchange rate. This possibility has been neglected in the empirical literature on the ERPT. The following sections will turn to this issue.

3 Econometric Strategy

This section develops an econometric framework that encapsulates the nonlinear effects of the ERPT discussed in Section 2. In particular, the switching regression³ lends itself to tracing the distinction between a low pass-through regime where price competition and the high pass-through regime where also market entries and exits force foreign firms to adjust their prices according to the conditions on the foreign exchange market. The econometric equation reflecting the structure of Eq. 7 is given by

$$ {\Delta} p_{t}^{*} = {\beta^{e}_{m}}{\Delta} e_{t} +{\beta^{p}_{m}}{\Delta} p_{t} +\epsilon_{t}(\sigma_{m}), $$

(8)

where ${\beta ^{e}_{m}}$ and ${\beta ^{p}_{m}}$ are coefficients to be estimated. The variables enter in logarithmic differences that is ${\Delta } p_{t}^{*}= \ln p_{t}^{*}-\ln p_{t-1}^{*}$, ${\Delta } e_{t}= \ln e_{t}-\ln e_{t-1}$, and ${\Delta } p_{t}= \ln p_{t}-\ln p_{t-1}$. The main difference between a standard regression equation and (8) is that the value of the coefficients can differ across regimes m where m=0 denotes the low pass-through and m=1 the high pass-through regime. Hence, the theoretical expectation is that ${\beta ^{e}_{0}}<{\beta ^{e}_{1}}$. Finally, 𝜖 _t (σ _m ) is a stochastic error term whose standard deviation σ _m can be regime dependent.

In practice, the postulated ERPT-regimes m∈0,1 are not directly observable. However, the theoretical framework of the previous section resulting in Eq. 7 indicates that the probability P[m _t =i] of observing regime i=0,1 during period t depends on the exchange rate misalignments u _t−1. Regime switching models differ with respect to the definition of this probability. In a simple case, the probabilities P[m _t =i] are independent of each other and depend on u _t−1 according to a multinomial logit distribution, that is

$$ P_{i}[m_{t}=i|u_{t-1}, \delta_{i}]=\frac{\exp(\delta_{i}u_{t-1})}{1+\exp(\delta_{i} u_{t-1})} $$

(9)

with δ _i denoting a regime specific coefficient with normalisation δ ₀=0. The special case where u _t−1=1 ∀ t yields a constant regime probability. A more popular specification assumes that regimes follow each other according to a Markov-chain with P(m _t =i|m _t−1=j) with j=0,1. Under this scenario, a matrix of transition probabilities arises that contains all four contingencies of moving between a low and high pass-through regime (P[m _t =0|m _t−1=0],P[m _t =0|m _t−1=1],P[m _t =1|m _t−1=0],P[m _t =1|m _t−1=1]). Similar to the discussion above, the transition probability can depend on observable variables according to a multinomial logit distribution, that is

$$ P_{i}(m_{t}=i|m_{t-1}=j, u_{t-1},\delta_{ij})=\frac{\exp(\delta_{ij}u_{t-1})}{1+\exp(\delta_{ij} u_{t-1})} $$

(10)

which involves four coefficients δ _{i j} as well as the normalisation δ ₀₁=δ ₁₁=0.

Assuming that the stochastic error term follows a normal distribution, that is 𝜖 _t ∼N(0,σ _m ), the likelihood contribution of an observation at time t equals $L_{t}=\sigma _{m}^{-1}({\Delta } p_{t}^{*} - {\beta ^{e}_{0}}{\Delta } e_{t} -{\beta ^{p}_{0}}{\Delta } p_{t})P[m_{t}=0]+\sigma ^{-1}_{m}({\Delta } p_{t}^{*} - {\beta ^{e}_{1}}{\Delta } e_{t} -{\beta ^{p}_{1}}{\Delta } p_{t})P[m_{t}=1]$. The log-likelihood function, from which the coefficients β can be estimated, equals then

$$ \ln L = \sum\limits_{t=1}^{T}\ln \left\{\phi\bigg(\!\frac{\Delta p_{t}^{*} - {\beta^{e}_{0}}{\Delta} e_{t} -{\beta^{p}_{0}}{\Delta} p_{t}}{\sigma_{0}}\!\bigg)P[m_{t}=0] +\phi\bigg(\!\frac{\Delta p_{t}^{*}-{\beta^{e}_{1}}{\Delta} e_{t} -{\beta^{p}_{1}}{\Delta} p_{t}}{\sigma_{1}}\!\bigg)P[m_{t}=1]\right\} $$

(11)

with ϕ denoting the probability density function of the standard normal distribution. An exact specification of Eq. 11 arises when Eqs. 9 or 10 define the probability P[m _t =i]. However, (11) depends on the one-step ahead probability P[m _t =i|u _t−1], wherefore the maximisation occurs via a recursive evaluation.⁴

Finally, since u _t−1 is not directly observable, it needs estimating from the data. It is well known from the cointegration literature that equilibrium relationships that tie variables together, such as the one postulated by Eq. 5, can be uncovered by regressing the level of e.g. the import prices $\ln p_{t}^{*}$ onto the level of the exchange rate $\ln e_{t}$ and the domestic producer prices $\ln p_{t}$, that is

$$ \ln p_{t}^{*} = \alpha_{0}+\alpha^{e}\ln e_{t} +\alpha^{p} \ln p_{t}+\alpha^{\omega} \omega_{t} + u_{t}, $$

(12)

where ω _t can empirically be measured by the share of imports relative to GDP and u _t is the usual error term. Equation (12) contains the ”error-correction term” u _t that should be stationary according to the Engle-Granger test. However, the current approach differs from the error-correction model of Frankel et al. (2012) or Ceglowski (2010) to calculate the ERPT in the sense that u _t−1 will not enter as an additional variable in a second stage equation such as ${\Delta } p_{t}^{*} = \beta ^{e}{\Delta } e_{t} +\beta ^{p}{\Delta } p_{t} +\lambda u_{t-1} +\epsilon _{t}$, where λ is an adjustment speed, but rather determines the probability (9) and (10) of being in a low or high pass-through regime.

4 Empirical Illustration: Exchange Rate Pass-Through in Switzerland

This section provides an example of a regime dependent ERPT by focusing on the case of Switzerland. There are several reasons why Switzerland might lend itself to illustrating the pass-through model of Section 2. Firstly, since the collapse of the Bretton Woods System in the 1970s, the monetary policy conditions have been relatively stable in Switzerland. As depicted in the top left panel of Fig. 1, with averages of the quarter-to-quarter change of the GDP Deflator of 0.4 per cent and a maximum value of 2.3 per cent since the beginning of the 1980s, this has lead to a high degree of price stability. This is important since Shintani et al. (2013) have shown that, rather than swings in the exchange rate, a time-varying ERPT can also be an artefact of changing levels of inflation. Secondly, as a small economy that is open to international trade, imports account for around 1/3 of Swiss GDP implying that an exchange rate induced shift in the volume of imports could have noticeable price effects. Conversely, Switzerland is too small to affect the world economy, whose condition can therefore be considered as exogenous. Thirdly, though studies dedicated to Switzerland such as Stulz (2007) or Herger (2012) have found a highly incomplete ERPT with typical values between -0.2 and -0.5, the possibility that this value could be higher in times of dramatic shifts in the exchange rate has not been considered. Such events can indeed be recurrently observed for the Swiss Franc. In particular, as depicted in the top right panel of Fig. 1 by means of a nominal exchange rate index, the Swiss Franc has followed an upward trend against most other currencies. However, due to a safe haven effect, a much steeper appreciation tends to occur in times of international political or financial crises. The most spectacular episode has occurred in the aftermath of the global financial and the Euro crisis when the Swiss Franc appreciated by around 30 per cent within 3 years prompting the Swiss National Bank to set a lower floor of 1.20 against the Euro in September 2011. Owing to this extraordinary effect, in the regression analysis below, a dummy variable will be introduced to account for the possible structural break after the third quarter of 2011. Other episodes where the Swiss Franc appreciated sharply, that are marked by the grey shaded areas, are associated with the bursting of the Dotcom bubble in 2000 and the 9/11 terrorist attacks in 2001, the turbulences in the European Exchange Rate Mechanism in the middle of the 1990s, or the weakening of the US Dollar during the second half of the 1980s.

Fig. 1

Exchange Rates, Prices, and Regime Probabilities

To connect the results with the widely cited work of Campa and Goldberg (2005), $p_{t}^{*}$ is measured by an import price index, e _t by a nominal effective exchange rate index, and p _t by a proxy for domestic production cost calculated from the product between a producer price index and the ratio between the nominal and real effective exchange rate index. For the case of Switzerland, the top right panel of Fig. 1 depicts these variables for the period between the first quarter of 1980 up to the first quarter of 2013. A detailed description of the data and their sources is relegated to the appendix. Campa and Goldberg (2005, p.682) have conducted extensive tests suggesting that these price and exchange rate variables are integrated of order one, that is their (logarithmically) transformed values are non-stationary whilst stationarity arises after a transformation into logarithmic differences, that is ${\Delta } p_{t}^{*}$, Δe _t , and Δp _t .⁵

To prepare the field, Table 1 embeds the current sample with some of the previous studies calculating the ERPT. The first column estimates (4) to uncover the short-term pass-through effect. The results concur with the theoretical expectation that an increase in the exchange rate index, which reflects an appreciation of the Swiss Franc, tends to reduce import prices. With an elasticity of -0.48, the magnitude of the coefficient is consistent with the previous findings discussed above. Remarkably, this coefficient estimate is almost identical to the value of 1/2 that would according to Eq. 4 occur under the Cournot-Nash and symmetry assumption (ν=0 and Γ=1). Column 2 extends the specification to the distributed lag model of Campa and Goldberg (2005), where the past four observations, which are supposed to account for the inertia in the ERPT, and ΔG D P enter as additional variables. This hardly changes the instantaneous pass-through effect to −0.46 whilst the long-term impact reflected by the sum of coefficients of the past changes in the exchange rate cumulates to -0.12. Hence, even in the long term, the ERPT remains incomplete. Choudhri and Hakura (2006) have included a lagged dependent variable and a time trend. Again, adopting this specification in column 3 barely affects the value of the instantaneous ERPT.

Table 1 Different specifications of the ERPT onto import prices in Switzerland

Ceglowski (2010) and Frankel et al. (2012) have employed the error-correction model to disentangle the short and long-term effects of the exchange rate on import prices. Following (12) and using the single equation approach of error-correction modelling, Column 4 of Table 1 reports the results of the first stage regressing the levels of import prices ($\ln p_{t}^{*}$) onto the levels of producer prices ($\ln p_{t}$), the nominal exchange rate index ($\ln e_{t}$), and the import share of GDP (ω _t ). The pass-through effect increases to -0.66 but, similar to the long-term effect of the distributed lag model of Column 2, remains statistically different from a compete pass-through. Our measure for the over- or undervaluation of the Swiss Franc, that is according to Eq. 12 given by the residual—here reported relative to its standard deviation—of the regression of Column 4, is depicted in the bottom right panel of Fig. 1. It is maybe not surprising that periods of overvaluation often overlap with the safe haven episodes marked again by grey shaded areas. Furthermore, with a test statistic of -3.7, the Augmented Dickey Fuller test statistic (ADF) suggests that at the 10 per cent level of rejection, the disequilibrium term is stationary, which permits to include it as an error-correction term in the second stage regression of Column 5.⁶ Then again, this does not alter the general picture as regards the value of the short-term pass-through effect. In sum, all specifications of Table 1 give rise to an incomplete pass-through effect in the short term of about −1/2. Furthermore, the information criteria favour the use of the most parsimonious model of column 1, which will therefore serve as baseline to investigate the possible time varying nature of the (short-term) ERPT.

Table 1 ignores the different regimes of Eq. 7 where the short-term ERPT is temporarily higher in times of marked swings in the foreign exchange market. To allow for low and high pass-through regimes, Table 3 reports the results of switching regressions. Further to the discussion of Section 3, the various specifications of the switching regressions differ as regards the definition of the transition probability P[m _t =i]. In the simplest case, this probability is defined according to Eq. 9 and is fixed in terms of depending only on a constant. The corresponding results, reported in column 1, uncover substantial differences in the impact of the exchange rate upon import prices. Specifically, the elasticity almost doubles between the low and high pass-through regime from -0.34 to -0.66. Remarkably, the latter value coincides with the ERPT of the second line of Eq. 7 when ν=0 and Γ=1. The constant pertaining to the regime switching regression equals -0.07. This implies that the probability to be in the high or low pass-through regime equals, respectively, 0.48 and 0.52 meaning that an observation has a close to fifty-fifty chance to fall into either of the two regimes. Of course, this carries over when reexpressing the results in terms of a (constant) expected duration to stay in a given regime, which equal, respectively, 1/0.48=2.08 and 1/0.52=1.92 that is around two quarters. To account for the possibility that the high and low pass-through regimes are connected across time, column 2 employs the Markov-chain of Eq. 10 to define the transition probability, which depends in the simplest case again only on a constant. Compared with the results of column 1, the coefficients pertaining to the ERPT change barely. However, in this case, two coefficients arise with respect to the transition between the low and high pass-through regimes to represent the matrix with four transition probabilities whose estimated values appear in Table 2.

Table 2 Constant transition probabilities of markov-switching model

Several observations arise from Table 2. As indicated by the probabilities of 0.77 and 0.95, there is a substantial degree of inertia in the sense that, respectively, the low and high pass-through regimes have a marked tendency to follow each other. Conversely, with probabilities of 0.23 and 0.05, it much less likely, and hence rarer,to move from a regime with, respectively, a low into one with a high ERPT and vice versa.

Hitherto, the transition probabilities are by construction constant across time. However, as discussed in Section 2, if entry competition is responsible for the differential effect of exchange rates on import prices, it is plausible that the transition probability P[m _t =i|u _t−1] depends on the exchange rate misalignment u _t−1. Using the standardised residual of the bottom right panel of Fig. 1, and employing again (9) and (10) to calculate the transition probability, the estimated coefficients are reported, respectively, in columns 3 and 4 of Table 3. Again, a differential effect arises between the low and high pass-through regime with similar coefficients to the case with a constant probability. Maybe, the specifications of columns 3 and 4 of Table 3 are incomplete in the sense that the transition probability cannot react differently to over- and undervaluations. This could indeed by an important aspect when the entry and exit cost differ and, hence, foreign firms react differently to the over- and undervaluation of a currency (see also Section 2). Furthermore, making this distinction could be important for the case of Switzerland since extraordinary effects in the pass-through are mainly associated with the safe haven effect where the Swiss Franc appreciates rapidly. To account for this, for both the simple and Markov switching probability, columns 5 and 6 consider only the impact of an undervalued Swiss Franc u _t−1<0 and columns 7 and 8 of an overvalued Swiss Franc u _t−1>0. Then again, the separate inclusion of these effects does not give rise to entirely satisfactory results as regards the transition probabilities. In particular, with a value of -41.83, the coefficient estimate for δ ₀₀ in column 6 suggests that the probability P[m _t =0|m _t−1=0] of remaining in the low-pass regime is essentially equal to 1 when considering the effect of and undervalued currency (where u _t−1<0). This might reflect the observation above that dramatic changes in the Swiss Franc exchange rate are mainly associated with appreciations. Hence, the results of column 6 should be interpreted with caution. Furthermore, most of the coefficients pertaining to the transition probabilities for the case of an overvalued Swiss Franc in columns 7 and 8 are insignificant. Therefore, columns 9 and 10 add both effects together in terms of using separate variables for u _t−1<0 and u _t−1>0 to calculate the regime transitionprobability.

Table 3 Regime switching regressions of the ERPT onto import prices in Switzerland

It is however remarkable that the short-term pass-through effects remain virtually unchanged across all specifications with an elasticity of around −1/3 in the low and around −2/3 in the high pass-through regime. Based on a t-test with $t=({\beta _{0}^{e}}-{\beta _{1}^{e}})/({\sigma _{0}^{e}}+{\sigma _{1}^{e}})$, aside from the specifications of constant regime switching probabilities in columns 1 and 2, the difference in the ERPT is statistically significant at the 5 per cent level of rejection.

Based on the comprehensive specification of column 10 of Table 3, Table 4 reports the average transition probabilities of moving between the low and high pass-through regimes contingent on the conditions during the previous quarter. The results are broadly similar to those of Table 2. The main difference is that the average transition probabilities disguise that they fluctuate depending on the degree of the over- and undervaluation of the Swiss Franc. For example, an overvaluation of 2 as measured by the standardised value u _t−1, which according to the bottom right panel of Table 5 reflects e.g. the conditions at the end of 2010, increases the probability to move from the low into the high-pass regime to 0.34. Similarly, an undervaluation of the Swiss Franc of -2, which reflects e.g the conditions in the second quarter the of 2003, increases the probability to move from the high into the low pass-through regime to 0.71.

Table 4 Average transition probabilities of Markov-switching model

To trace the changes in the transition probabilities more precisely, the bottom left panel of Fig. 1 depicts the development of the (filtered) probability of being in the high pass-through regime. Concurring with the discussion above, the distinction between the low and high pass-through regime follows, by and large, periods during which the Swiss Franc was, respectively, depreciating and appreciating against the major foreign currencies. This result is maybe not surprising since the safe haven effect implies that episodes of a Swiss Franc appreciation arise often amid fundamental shifts in the global economy compared with episodes of a depreciation that tend to occur when the international financial system is relativelystable.The results of Table 3 have been subject to several robustness checks. In particular, as discussed above, the period after the third quarter of 2011 has witnessed the extraordinary event of the introduction of an exchange rate floor of 1.20 Swiss Francs against the Euro. Likewise, the time after the third quarter of 2008 was marked by the global financial and the Euro crisis with extraordinary circumstances such as interest rates that were close to zero over a long period of time. However, recalculating the results of Table 3 dropping the corresponding observations did not change the essence of the findings. For the sake of brevity, these results are not reported here, but are available on request. Secondly, (Shintani et al. 2013) have suggested that differences in the ERPT are an artefact of varying levels of inflation. However, the GDP deflator depicted in the top left panel of Fig. 1 did not significantly affect the regime switching probability whilst the coefficient estimates for the ERPT remained by and large unchanged.

In sum, the results of Table 3 provide some support for theoretical models where market entries and exits give rise to two regimes with the ERPT being low when fluctuations on the foreign exchange market are modest whilst large values can arise in times of dramatic swings in the foreign exchange market. Econometric models considering only average effects ignore such differences.

5 Summary and Conclusion

The plethora of empirical studies that have been devoted to measuring the exchange rate pass-through (ERPT) find overwhelming evidence that exchange rates impact less than proportional upon import prices. Price inertia arising from menu cost provide one explanation for this incomplete pass-through effect. Al-Abri and Goodwin (2009) and Shintani et al. (2013) have recently argued, and confirmed with empirical evidence, that this should introduce nonlinearities in the pass-through with respect to the level of inflation.

Drawing on theoretical work by Baldwin (1989) and Dixit (1989), this paper suggests that nonlinearities in the ERPT can also arise from changes in the market structure. In particular, sufficiently large shifts in foreign exchange rates could trigger market entries or exits which increase the competitive pressure on foreign firms to align their prices with currency prices. Hence the hypothesis that ”the pass-through coefficient in the phase where the number of foreign firms is constant is quite small [...] whilst its values in the phases with entry or exit are much larger” Dixit(1989, p.227). Regime switching regressions, where the transition between a low and high pass-through regime is a function the exchange rate misalignment, lend themselves to account for such periodical shifts in the ERPT.

The implication of estimating the ERPT within a regime switching regression is that, even for low inflation countries, temporary increases in the ERPT can occur. This possibility has been confirmed for the case of Switzerland where, despite the generally low level of inflation, spikes in the ERPT seem to occur in times of a dramatic appreciation of the Swiss Franc.

Appendices

Appendix A: Derivations

1.1 A.1 Derivation of the Optimal Pricing Rule

Multiplying (2) with $E_{t}/p^{*}_{t}$ and rearranging yields $\pi _{t}^{*}E_{t}/(p_{t}^{*})=[1-1/p_{t}^{*}e_{t}]E_{t}$. Since quantities are normalised to 1, we have from footnote 1 that $E_{t}/(p_{t}^{*})= 1/s_{t}^{*}$ wherefore profits expressed in market share form are given by

$$\pi_{t}^{*}=\left[1-\frac{1}{e_{t}p_{t}^{*}}\right]s_{t}^{*} (p_{t}^{*}, p_{t})E_{t}. $$

Differentiating this with respect to import prices yields

$$ \frac{\partial \pi_{t}^{*}}{\partial p_{t}^{*}}= \frac{1}{e_{t}(p_{t}^{*})^{2}}s_{t}^{*}E_{t}+\left(1-\frac{1}{e_{t}p_{t}^{*}}\right) \left[\frac{\partial s_{t}^{*}}{\partial p_{t}^{*}}+\frac{\partial s_{t}^{*}}{\partial p_{t}}\frac{\partial p_{t}}{\partial p_{t}^{*}}\right]E_{t}=0. $$

Since (1) defines the import share $s_{t}^{*}$, we have that

$$\left(1-\frac{1}{e_{t}p_{t}^{*}}\right) \left[-\frac{\gamma^{*}}{p_{t}^{*}}+\frac{\gamma^{*}{\Gamma}}{p_{t}}\frac{\partial p_{t}}{\partial p_{t}^{*}}\right]= -\frac{1}{e_{t}(p_{t}^{*})^{2}}s_{t}^{*}. $$

Multiplying this with $(p_{t}^{*})^{2}$ yields

$$(p_{t}^{*}-1/e_{t}) [-\gamma^{*}+ \gamma^{*}\nu{\Gamma}]= -s_{t}^{*}/e_{t} $$

where $\nu = \frac {\partial p_{t}}{\partial p_{t}^{*}}\frac {p_{t}^{*}}{p_{t}}$ is the conjectural elasticity. Solving for the import price yields

$$ p_{t}^{*}= \left[1 + \frac{s_{t}^{*}}{(1-\nu{\Gamma})\gamma^{*}}\right]\frac{1}{e_{t}}. $$

1.2 A.2 Derivation of the Profit Function

Inserting (1) into $\widetilde {\pi }_{t}=(s^{*}_{t}/(\gamma ^{*}(1-\nu {\Gamma }))(1/e_{t})$ yields

$$\widetilde{\pi}_{t}^{*}=\left[\frac{1}{(1-\nu{\Gamma})\gamma^{*}}\omega_{t}-\frac{1}{1-\nu{\Gamma}}\ln p_{t}^{*}+\frac{\Gamma}{1-\nu{\Gamma}}\ln p_{t}\right](1/e_{t}). $$

Taking logarithms and using the first order Taylor approximation⁷ yields

$$\ln \widetilde{\pi}_{t}^{*} \approx \frac{1}{(1-\nu{\Gamma})\gamma^{*}}\omega_{t}-1-\frac{1}{1-\nu{\Gamma}}\ln p_{t}^{*}+\frac{\Gamma}{1-\nu{\Gamma}} - \ln e_{t}. $$

1.3 A.3 Derivation of High Pass-Through Regime

Inserting $\omega _{t} = \gamma ^{*} \ln p_{t}^{*} - \gamma ^{*}{\Gamma }\ln p_{t} + (1-\nu {\Gamma })\gamma ^{*}\ln e_{t}+c$ of the first line of Eq. (6) into (4) yields

$$\begin{array}{@{}rcl@{}} \ln p_{t}^{*} &\approx& \frac{\Gamma}{(2-{\Gamma}\nu)} \ln p_{t} - \frac{1-\nu{\Gamma}}{2-\nu{\Gamma}}\ln e_{t} -\frac{1}{1-{\Gamma}\nu}\\ \ln p_{t}^{*}&+&\frac{\Gamma}{2-\nu{\Gamma}}\ln p_{t}-\frac{1-\nu{\Gamma}}{(2-\nu{\Gamma})}\ln e_{t} +constant \end{array} $$

Ignoring the constant and solving this for $\ln _{t}p_{t}^{*}$ yields.

$${\Delta} p_{t}^{*} \approx \left[(2{\Gamma})/(3-\nu{\Gamma})\right] \ln p_{t} - \left[(2-2\nu{\Gamma})/(3-\nu{\Gamma})\right]\ln e_{t} $$

B Data Appendix

Table 5 Description of the data set