The impact of exchange rate volatility on Eurozone-United States bilateral exports

(1)

The impact of exchange rate volatility on

Eurozone-United States bilateral exports

Master Thesis, Academic year 2015-2016 Faculty of Economics and Business University of Amsterdam

Jordy van Aalst, 6124534

Supervisor: Dhr. Prof. Dr. Franc Klaassen Second corrector: Dr. Ward Romp This version: 6-3-2016

Number of words: 14983

Abstract: There is in both the theoretical and empirical models no clear consensus about the effect of exchange rate volatility on trade. The lack of a clear consensus in the empirical literature is mostly due to the sensitivity of the choice of the proxy for exchange rate volatility. This paper therefore uses three different proxies for exchange rate volatility and checks whether the results are robust. The relationship between exchange rate volatility and exports is investigated using data on bilateral aggregate Euro Area exports to the United States. The results of this paper indicate that the volatility measure used in an export regression must take into account that the decision how much to export is based upon a forward looking prediction of the expected volatility.

(2)

Statement of originality

This document is written by Student Jordy van Aalst who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

1. Introduction

In the aftermath of the credit crisis of 2008, which most affected the United States and the Eurozone, central banks all over the world used unconventional monetary policies in order to try to stimulate their economies. These policies resulted in increased exchange rate volatility on the markets following a long period in which currency markets have been relatively calm. The increase in exchange rate volatility has been triggered by a divide between the Federal Reserve, the Bank of Japan and the European Central Bank. Where the Federal Reserve has stopped its quantitative easing programme, the Bank of Japan and the ECB are still pursuing their unconventional monetary policies. The current turmoil on the currency markets makes the discussion about the effect of exchange rate volatility on export an important topic (Buttonwood, 2015).

The effect of exchange rate volatility on export flows already has been the subject of a large number of theoretical and empirical papers which all find no consensus about how exchange rate volatility affects trade. The theoretical effect of exchange rate volatility on trade differs based on the assumptions made in the models. For example, Clark (1973) finds that exchange rate volatility has a negative effect on exports. This view is been contradicted by De Grauwe (1987) who finds that exchange rate volatility positively affects the level of trade. These different conclusions have been supported by the empirical literature. Some researchers, like Bini-Smaghi (1991) and Klaassen (2004) have tried to find an answer to why there is no clear consensus about the effect of exchange rate volatility on trade.

This paper aims to find how exchange rate volatility affects the bilateral export flows between Europe and the United States. This will be investigated, using three different measures of exchange rate volatility, according to the following research question:

What is the effect of exchange rate volatility on bilateral export flows between the Eurozone and the United States?

It adds to the literature in various ways. First of all, there are not very much empirical studies which focus on the bilateral exports flows between the Eurozone and the United States. Second, this paper will make use of a method which takes into account data sample properties as unit roots and cointegration: the autoregressive distributed lag (ARDL) bounds testing approach (Pesaran, Shin, & Smith, 2001). In addition, we will try to implement the results of Klaassen (2004) to capture most of the effect of the foreign GDP, the real exchange rate and the real exchange rate volatility into our regression model. Finally, one of the three measures of exchange rate volatility will be a new approach as recently proposed by Serenis & Tsounis (2014).

(5)

The paper is organized as follows: in section 2, the existing theoretical and empirical will be presented; in section 3, the theoretical model of Hooper & Kohlhagen (1978) will be explained in order to give a motivation for the variables used in the regression model. Section 4 will present our ARDL representation of the economic model. In section 5, the results of the regression model will be presented as well as our explanation of how exchange rate volatility should be measured. In section 6, the main conclusions will be provided.

(6)

2. The links between exchange rate volatility and trade

A lot of theoretical and empirical studies have been trying to find a relationship from exchange rate volatility to trade. This section shows that for both the theoretical and the empirical studies there are different ranges of results. As suggested by the theoretical models, the most important view is that an increase in exchange rate volatility increases the uncertainty of profits on contracts denominated in a foreign currency. Regarding the empirical studies, the effect of exchange rate volatility on trade depends mainly on the proxy of exchange rate volatility. In this section a theoretical and empirical foundation will been given to justify the methods used in this paper. 2.1 Theory

In the theoretical models there are several main assumptions which play an important role in the outcome of the model. The most important assumptions are about the level of risk aversion of the firm, the nature of the trader and the capital markets (McKenzie, 1999). We will focus on the level of risk aversion of the firm. In this section we will discuss the partial equilibrium models of Clark (1973), De Grauwe (1987) and Demers (1991) as well as the more recently developed general

equilibrium models of Obstfeld & Rogoff (1998), Bacchetta & van Wincoop (2000) and Bergin & Tchakarov (2003). These models will be used to show that the theoretical models are contradictory regarding the effect of exchange rate volatility on trade.

The hypothesis that exchange rate volatility has a negative impact on trade found support in the theoretical model from Clark (1973). His analysis was based on the assumption that a firm’s willingness to engage in international trade depends on the expected profits made with international trade in the long-run. His model considers a risk averse firm with a constant output in a perfectly competitive market which produces and exports one homogeneous product. The model assumes that there is a forward market for only one maturity; ninety days. Thus the domestic currency value of the exports is known with certainty only ninety days in advance. The long-run planning horizon of the exporting firm is assumed to be considerably longer than the ninety day forward contract so there is a variable and unpredictable stream in domestic currency between the date of the export decision and ninety days before the importer makes his payment. The firm must take into account the uncertainty of future receipts when deciding how much to export. The paper concludes that in case of a risk averse firm the marginal revenue must exceed the marginal cost. The reasoning behind this is that the price of the exported product not only has to cover the costs of production,

represented by the marginal costs, but also has to compensate the firm for the exchange rate risk. So if the firm is risk averse, its production is lower at the same market price compared to a firm which is

(7)

indifferent to risk. In order to produce the same amount of output, the risk averse firm wants to receive a risk premium that increases the supply price of the exports.

In contrast with Clarks’ conclusion that there is a negative relation between exchange rate volatility and the level of trade, De Grauwe (1987) demonstrates that an increase in exchange rate volatility can lead to a higher level of trade. His model considers a risk averse individual producer who has to choose whether to produce for the foreign or for the domestic market and does not incorporate the possibility of hedging the exchange rate risk. Both markets are assumed to be perfectly competitive. Similar to the model of Clark, the only source of risk is the price which is obtained for the output sold in the foreign market, and this risk is due to exchange rate volatility. His analysis shows that if an increase in the volatility of the exchange rate increases the expected marginal utility of income from exports, then this will lead to more export activity. Whether an increase in exchange rate volatility increases or decreases the expected marginal utility depends on the shape of the utility function. If the utility function is convex, i.e. the individual producer is risk averse, an increase in exchange rate volatility raises the expected marginal utility of export income and so induces him to increase his export activity. The intuition behind this is that when the producer is risk averse, he will worry a lot about the possible income loss. In response to this possibility, the producer will choose to export more. Vice versa, when the utility function is concave, i.e. the

individual producer is a risk lover, a higher exchange rate risk reduces the expected marginal utility of export income and it thus induces him to decrease his export activity. When the producer is a risk lover, he is less concerned about a possible income loss. As a result, they view the return on export activity less attractive given the increase in risk and choose to reduce export (De Grauwe, 1987).

Although these models give insight in the relationship between exchange rate volatility and the level of trade, the models are not useful as they are built on several simple and unrealistic assumptions. First, Clark assumes that there are no imported inputs used in the production process. Omitting the possibility of importing inputs from abroad will remove the firm’s possibility to offset the decline in revenue by lower input costs. A depreciating currency of a foreign country has a negative effect on the domestic currency value of the profit of the exporting firm. The decline in profits can be offset by lower input costs, if this exporting firm imports intermediate inputs from a country whose currency is depreciating. So when this assumption is relaxed, the impact of variations in the exchange rate on the variance of the exporting firm’s profits will be reduced. Therefore, the impact of exchange rate volatility on export will be smaller. Another weakness of the models of Clark and De Grauwe is that they both assume a minimal role for the forward exchange market in hedging the exchange rate risk. De Grauwe assumes that there is no forward exchange market at all whereas Clark assumes that there is only a forward exchange market for one maturity. Regarding the model of

(8)

Clark, this assumption not only does rule out the possibility of hedging the exchange rate risk by borrowing in foreign currency, also just one type of transaction can be hedged. For developing countries this assumption may be reasonable, as forward markets for their currencies does not always exist. However, for advanced economies there are well developed forward markets where exchange rate risk can be easily hedged for any type of transaction (Clark, Tamirisa, & Wei, 2004). As argued by Makin (1978) the forward exchange market plays an important role in hedging exchange rate risk. According to his portfolio theory framework, which incorporates variances and covariances of exchange rate changes along with the expected level of such changes to determine an overall hedging strategy, there are many possibilities for a multinational corporation to hedge foreign currency risks. Omission of the forward exchange market therefore increases the effect of exchange rate volatility on trade. However, even when there is a forward exchange market with more than one maturity there are still limitations and costs. One of those limitations is the size of contracts. The average forward contract is large, averaging more than one million dollar. Other limitations are the requirement that customers must often maintain minimum deposit balances and maturities are commonly in multiples of 30 days. Using the forward market can be hard for trading firms as it is often difficult to plan the magnitude and timing of all their international transactions (Caporale & Doroodian, 1994).

The models of Clark and De Grauwe both assume that risk aversion is important for getting a positive or negative impact of exchange rate volatility on trade. Yet, Demers (1991) showed how the assumption of risk aversion is not necessary to find a negative relationship. This paper considers a risk neutral competitive firm which was uncertain about the state of demand due to price

uncertainty caused by exchange rate risk. It is shown how the irreversibility of investment in physical capital and uncertainty about the state of demand together with the anticipation of receiving informative signals in the future and of eventually learning the unknown state, lead to cautious investment behavior and, hence, to lower investment levels than otherwise since the firm cannot disinvest if market conditions turn out to be less favorable than currently anticipated. The lower investment levels lead to reduced production levels and so lower trade volume over time.

Although the models mentioned before give some insight about how exchange rate volatility can affect the level of trade, the results are derived from a partial equilibrium framework and therefore weak. A partial equilibrium framework is a framework wherein the only changing variable is the some measure of the volatility of the exchange rate, and all other factors that may have an influence on the level of trade are assumed to remain unchanged. However, exchange rate volatility is likely to affect other aspects of the macroeconomy as well which will in turn have an effect on trade. For this reason, several authors build a general equilibrium framework. In this framework

(9)

there is an interaction between all the major macroeconomic variables, therefore a more complete picture of the relationship between exchange rate volatility and trade will be obtained (Clark, Tamirisa, & Wei, 2004).

Such a general equilibrium model has been presented by Bacchetta & van Wincoop (2000). Their framework studies the main mechanisms through which exchange rate stability affects trade and welfare. Their model is a simple one period model where capital accumulation is not allowed, there is no international trade in assets (no hedging) and money is introduced through a simple cash-in-advance constraint. The main finding of their paper is that exchange rate stability is not necessarily associated with more trade. Trade is higher under a fixed exchange rate regime when consumption and leisure are substitutes, but it is lower when they are complements. It is important to note that these results still hold when international trade in assets is introduced, for any asset market structure.

Obstfeld & Rogoff (1998) also analyze the welfare tradeoff between different exchange rate regimes. They develop a sticky-price monetary model with two countries in which risk has an impact not only on assets prices and short-term interest rates, but also on the price-setting decisions of individual producers, and thus on expected output and international trade flows. The most important conclusion of their paper is that pegging the exchange rate, thus reducing the variance of the

exchange rate to zero, could result in a welfare gain of one percent of GDP. Regarding the effect of exchange rate volatility on trade Obstfeld & Rogoff found that for relatively small countries a greater volatility will raise the terms of trade for that country. The mechanism behind this result is that for a small country exchange rate volatility has a bigger effect on the home than on the foreign demand curves, making world demand for home good relatively more variable. This in turn leads to a higher expected disutility of effort in the home country which raises the terms of trade and so reduce trade. For bigger countries exchange rate volatility does not affect the ex-ante terms of trade.

More recently, Bergin & Tchakarov (2003) provided an extension of the model of Obstfeld & Rogoff. Their model explains the welfare effects of exchange rate volatility for more realistic

situations involving incomplete asset markets and investment by firms. In addition, Bergin & Tchakarov used a second order approximation to solve their model numerically. This stands in contrast to the standard method relying upon log-linear approximations, which would miss many of the implications of risk. The results regarding the impact of exchange rate volatility on trade indicate that there is a positive relationship, although the effects are small. This effect is larger when the asymmetric assets markets are taken into account, which is in line with the reasoning that the omission of the forward exchange market increases the effect of exchange rate volatility on trade.

(10)

Bergin & Tchakarov argue that when there is an international market for bonds in the currency of only one of the two countries, this country will tend to save more and have a higher welfare in the stochastic steady state and therefore the impact on trade volume is higher. The higher welfare comes at the direct expense of the other country, which saves less and has lower welfare in the steady state. This asymmetry exists because saving in the international bond is a better hedge against exchange rate risk for a country that can save in terms of its own currency. This results indicates that countries that host a reserve currency, like the United States or the Eurozone have substantial benefits.

The aforementioned theoretical models show that there is no clear consensus about the effect of exchange rate volatility on trade. The impact of exchange rate volatility seems to depend heavily on the assumptions made in the models. Take for example the model of De Grauwe, where he showed that the impact of exchange rate volatility on trade could be either positive or negative depending on the level of risk aversion of the firm. There can be a negative effect as risk averse agents respond to the increase in uncertainty by increasing the supply price of exports or by redirecting their activity to the lower risk home market. Exchange rate volatility can also have a positive effect on trade when firms are sufficiently risk averse making them worried about the possible income loss and therefore they choose to export more. Alternatively, some researchers have suggested that it is possible to offset potential exchange rate volatility by investing at the forward market causing producers to be unaffected by movements of the exchange rate. However, investing in the forward markets has its limitations and costs. In addition, it is argued that when some of these assumptions were relaxed the impact of exchange rate volatility is weaker.

2.2 Volatility measurement: Theory

Just as in the theoretical models, the empirical literature finds no clear consensus about the link between exchange rate volatility and trade. The lack of a clear consensus in the empirical literature is due to the sensitivity of the choices of sample period, model specification, different proxies for exchange rate volatility and countries considered (developed versus developing) (Baum & Caglayan, 2008). Foremost amongst these choices is the proxy for exchange rate volatility. This problem stems from the fact that there is no generally accepted technique by which one may quantify such volatility, while economists generally agree that it is uncertainty in the exchange rate which constitutes the exchange rate risk. Most papers report insignificant estimates, therefore there is a consensus among researchers to believe that exchange rate volatility has no, or at least a small, effect on trade (Klaassen, 2004). Accurate measurement and good forecasts of the exchange rate volatility is important for trading and hedging strategies. For exports, the exchange rate volatility has

(11)

to refer to the unpredictable factor, the variation of risk over time, which matters for goods traders and thus affects exports (Serenis & Tsounis, 2014). So, the measure which is best able to capture the variation of risk over time is the best suitable measure of exchange rate risk. In addition, researchers also need to consider whether it is real or nominal exchange rate which is relevant for the decision making process of firms. In the next subparagraphs, we will briefly present the theoretical

background behind two measures which are most used to specify exchange rate volatility. We will then, use the theory in the next paragraph to assess the quality of the measures.

2.2.1 (Moving) standard deviation

The (moving) standard deviation is one of the most popular measures in the empirical literature to gauge exchange rate volatility. It measures how widely the exchange rate at time t is dispersed from the exchange rate at time t-1. The formula for forecasting the one-period-ahead exchange rate volatility is given by:

𝑉𝑡−1{𝑆𝑡} = √ 1 𝑚∑(𝑆𝑡−𝑖− 𝑆𝑡−𝑖−1) 2 𝑚 𝑖=1

(Note that the formula for the standard deviation is the same except for the fact that it is not smoothed by taking the average.) This measure can be interpreted as first approximating the volatility in month m and then smoothing by taking the average over m months. In the empirical literature the window width is often about two years (m=24). The main characteristic of the (moving) standard deviation is that it implies a high persistence of real exchange rate shocks and thus suggests a high serial correlation in risk (Klaassen, 2004). As mentioned before, exchange rate volatility has to refer to the unpredictable factor. The calculation of the (moving) standard deviation suggests however that this measure is backward looking which means that there is no unpredictable factor. This is a first indication that the (moving) standard deviation is not a good measure to calculate exchange rate risk, we will discuss this in more detail in section 4.2.

2.2.2 Generalized Autoregressive conditional heteroscedasticity (GARCH)

The GARCH model originally devised by Engle & Bollerslev (1986) is widely used by both academics and practitioners to model the conditional variance. The GARCH model was proposed as a better measure to capture the conditional variance n-steps into the future because it is able to capture the available information set and therefore changes over time. In its simple GARCH (1,1) form, the GARCH model basically states that the conditional variance of assets returns in any given period depends upon a constant, the previous period’s squared random component of the return

(12)

and the previous period’s variance. In other words, if we denote the conditional variance of the return at time t by𝑉𝑡−1{𝑆𝑡} and the squared random component of the return in the previous period by (𝑆𝑡−1− 𝑆𝑡−2)2, for a standard GARCH (1,1) process, we have:

𝑉𝑡−1{𝑆𝑡} = 𝜔 + 𝛼(𝑆𝑡−1− 𝑆𝑡−2)2+ 𝛽𝑉𝑡−2{𝑆𝑡−1}

This equation yields immediately the one step ahead volatility forecast (𝑙 = 1). For 𝑙 > 1 one can compute 𝑉𝑡−𝑙{𝑆𝑡} recursively from 𝑉𝑡−𝑙{𝑆𝑡−𝑙+1} (Klaassen, 2004).

An important application of the GARCH model is to measure and forecast the time-varying volatility of returns on financial assets, particularly assets observed at high sampling frequencies such as the daily exchange rate returns (Dunis & Huang, 2001).

2.3 Empirical research

In this section we will discuss the empirical studies. A summary of the results, the methods used, population and time period is given in Table 1 of the appendix. Most empirical studies gauge exchange rate volatility using the (moving) standard deviation of the level or the change of the exchange rate. Another method which is often used to estimate the exchange rate volatility is a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model.

In an attempt to explain the effect of exchange rate volatility on trade, De Grauwe & Verfaille (1988) used the standard deviation of the rate of change of the exchange rate. Using the standard deviation as a measure of risk has the advantage of capturing higher frequency movements of the exchange rate (Bini-Smaghi, 1991). The authors conclude that the exchange rate variability has a significant negative effect on exports. Hasan Vergil (2002) comes to another conclusion as he

empirically investigates the impact of real exchange rate volatility on the export flows of Turkey to its major trading partners. The empirical results of the paper suggest that exchange rate volatility has, in most cases, a statistically significant negative impact on trade. In contrast to Vergil, Rahutami (2013) concludes that exchange rate volatility had no significant positive impact on exports while no significant negative impact was found for imports. Several other authors used the moving standard deviation (MSD) of the growth rate of the exchange rate. This measure captures the temporal variation in the absolute magnitude of changes in real exchange rates, and therefore exchange rate risk over time (Chowdhury, 1993). Chowdhury researches the impact of exchange rate volatility on the trade flows of the G7 countries over the sample period 1973-1990. The results of this research indicates that there is a significant negative relationship between exchange rate volatility and the volume of exports in each of the G7 countries. In a different study Klein (1990) analyzes the effects of real exchange rate volatility on the bilateral exports of nine different categories of goods from the

(13)

United States to major industrial countries. He finds that in six out of nine categories the volatility of the real exchange rate significantly affects the value of exports, while in five of these categories the effects are positive. More recently, Huchet-Bourdon & Korinek (2011) examines the impact of

exchange rates and their volatility on trade flows in China, the Euro area and the United States in two broadly defined sectors, agriculture and manufacturing and mining. In this paper the volatility

variable is constructed using two different measures, a five-year MSD and a GARCH model. Using an ARDL model they find that trade in both the agricultural and the manufacturing and mining sector is affected by the level of the exchange rate over the time period 1999-2009. In contrast to the level of the exchange rate, the impact of exchange rate volatility on trade was minimal at the sectoral level (Huchet-Bourdon & Korinek, 2011).

Despite the fact that the (moving) standard deviation is one of the most popular measures for exchange rate volatility, its use has been criticized. A problem with the use (moving) standard deviation is that they potentially ignore information on the stochastic process by which exchange rates are generated. Speculative price series, in this case exchange rates, have common

characteristics like fat tails or volatility clustering which violate the assumptions underlying the standard regression analysis (McKenzie & Brooks,1997). In this paper, we will make use of monthly data and therefore the data will not clearly show the characteristics of speculative price series. Thus these characteristics will not cause many problems. The MSD also suffers from a variant of the error-in-variable problem given that risk should be measured as a function of the conditional moments of a distribution, and produce an underestimation of the effect of risk (Pagan & Ullah, 1988). Stated differently, using the MSD as a proxy for risk will make the errors in the independent variable much larger than those for the dependent variable. Where it is usually assumed that all errors are in the dependent variable, and that the independent variables are known perfectly. This will lead to much difference to the fit of the regression. Finally, according to Serenis & Tsounis, the main criticism for the application of the of the MSD is that it fails to capture the potential effects of high and low peak values of the exchange rate. According to some economic models, these high and low values refer to the unpredictable factor and as mentioned before, it is the unpredictable factor which matter for goods traders and thus affects exports (Serenis & Tsounis, 2014).

Other papers rely on volatility measures based on the autoregressive conditional

heteroscedasticity (ARCH) model and its extension, the generalized ARCH (GARCH) model. These papers are summarized in Table 2 of the appendix. These models take into account that the exchange rates are characterized by skewed distributions and volatility clustering (Sauer & Bohara, 2001). In addition, the GARCH procedure is able to capture the time-varying conditional variance as a parameter generated from a time-series model of the conditional mean and variance of the

(14)

exchange rate (Caporale & Doroodian, 1994). Caporale & Doroodian (1994) use GARCH as a measure to assess exchange rate volatility in order to test if real exchange rate volatility has an adverse effect on the value of U.S. imports from Canada over the period January 1974 to December 1992. The authors conclude that exchange rate uncertainty has a negative and significant effect on trade flows. In a comparable study by McKenzie & Brooks (1997), where the effect of exchange rate volatility on Germany-US bilateral trade flows for April 1973 to September 1992 is analyzed, the results indicate that there is a significant positive relationship between exchange rate volatility and trade flows. One year later, McKenzie (1998) found the same result when he investigated the impact of exchange rate volatility on Australian trade flows over the period 1969-1995. A negative relationship between exchange rate volatility and exports was found by Verheyen (2011). This study uses data on the bilateral exports from the Eurozone countries to the United States over the period February 1996 – October 2010. Verheyen (2011) investigates the effects of exchange rate volatility by using the ARDL bounds testing approach for cointegration. The ARDL bounds testing approach is a very promising research method because it does not require a precise pretesting for unit roots of the time series under consideration. This approach is suitable because the time series approximating exchange rate volatility might be stationary, while other variables like exports or price levels may be integrated of order one meaning that they have a stochastic trend. This same bounds testing approach was used by Mohd Sidek et al. (2010). Their paper attempts to estimate the impact of exchange rate risk on Malaysian exports. The main findings of the paper are that both exchange rate misalignment and volatility have a significant negative impact on exports. Specifically, the impact of exchange rate misalignment on exports is greater than the impact of volatility on exports in the long run.

Although GARCH is used for volatility forecasting, its ability to accurately predict volatility over the long run is weak. This can be seen from figure 1. Figure 1 displays the GARCH (1,1) one month volatility forecasts for the USD/GBP exchange rate both in- and sample. The out-of-sample forecasts range from April 1999 to May 2000, where the start of the out-of-out-of-sample forecasts is indicated by the red line. The figure also shows the realized volatility. The realized volatility is computed by summing the observed squared returns. It thus measures what actually happened in the past.

(15)

Figure 1: Forecasts using GARCH (Dunis & Huang, 2001)

As can be seen from the figure, overall, the GARCH model fits the realized volatility rather well during the in-sample period. However, during the out-of-sample period, the GARCH forecasts are quite disappointing. The reason for this, as mentioned by Engle & Bollerslev (1986), is that when GARCH is used for long term forecasts the dependence on the available information becomes negligible and the GARCH volatility measure will therefore show up as a constant. This has been supported by Klaassen (2004) who found that squared real exchange rate changes exhibit no autocorrelation at the monthly frequencies. This suggests that the parameters 𝛼 and 𝛽 in the equation for GARCH are equal to zero, and this results in the lack of persistence of shocks in the monthly GARCH risk measures. Stated differently, GARCH estimations show low or zero time variation of estimated volatility over long horizons which are relevant to goods traders. Another problem which will arise when there is no persistence of shocks, is that the measure for volatility will appear in the regression model as a constant and so the model suffers from perfect multicollinearity. In response to GARCH, Klaassen (2004) proposed another method to capture the variation of risk over time, the second order autoregressive (AR(2)) risk measure. This measure was developed in order to capture, in a better way, the autocorrelation in exchange rate risk. His alternative measure is found to have the highest explanatory power, among the MSD and GARCH, for future volatility. Although, this AR risk measure still shows that shocks do not persist very long in risk and that the time variation of the volatility is small so it may not affect the choices of goods traders very much. It may be therefore no surprise that the results of his paper indicate that the effect of exchange rate volatility on United States exports to the other G7 countries is found to have no significant effect.

(16)

A new way to measure exchange rate volatility is the dummy variable approach as

recommended by Serenis & Tsounis. In their 2014 paper they examine the effect of exchange rate volatility for two small countries, Croatia and Cyprus, on aggregate exports during the period of the first quarter of 1990 to the first quarter of 2012. They make use of a recently developed method to find a relationship between exchange rate volatility and trade: the ARDL bounds test approach. As mentioned before, Serenis & Tsounis criticized the MSD as a measure of exchange rate volatility because it is not able the capture the potential effects of high and low peak values of the exchange rate. To solve this problem a new approach was developed in which they construct a dummy variable to capture only the high and low values of the exchange rate. These high and low values refer to the unpredictable factor which, according to some economic models, affect exports. Whether or not this a good way of measuring exchange rate volatility will be discussed in section 4.2. Their analysis uses both the standard deviation of the log effective exchange rate and the dummy approach. The results indicate that exchange rate volatility has, mostly positive, significant effects for both exports of Croatia and Cyprus. Only for Croatia there was a negative effect when the standard deviation was used as a measure of exchange rate volatility (Serenis & Tsounis, 2014). The results of this paper indicate that the standard deviation was more significant than the proposed dummy approach.

The aforementioned empirical studies show that the effect of exchange rate volatility on trade in generally conflicting and inconclusive. In the beginning of this section it was mentioned that the lack of a clear consensus in the empirical literature is due to the sensitivity of the choices of sample period, model specification, different proxies for exchange rate volatility and countries considered (developed versus developing) where the choice of the proxy for exchange rate volatility is the most important. A lot of economists therefore proposed and applied several new measures for exchange rate volatility however ambiguity of the estimated relationship continues to dominate the empirical literature. This paper is intended to examine the relationship between exchange rate volatility and Eurozone-United States exports in light of the empirical developments regarding the measurement of exchange rate volatility. Because there is no generally accepted technique of how to measure exchange rate volatility, we will use in this paper several measures for exchange rate volatility and check whether the results are robust.

(17)

3. Methodology

In this section, the regression model will be specified. The first paragraph presents the export equation underlying the regression model. This export equation will be the starting point for the regression model. In addition, we will present our data.

3.1 The export supply model

Before the regression model underlying the empirical analysis can be specified, we will present the theoretical two-period model of Hooper & Kohlhagen (1978) to give a motivation for the variables used in the regression. Hooper & Kohlhagen developed a model in which both the import demand and export supply sides of the market are specified. The demand and supply functions are derived for individual firms and are then aggregated to derive market demand and supply in order to obtain the reduced form equations for the market quantity. An important feature of the model is that the firm receives orders for its domestic output and places order for its imported inputs at time t=1, while at time t=2 the firm receives and pays for the imported input and is paid for its own output. This assumption is important because it implies that unexpected variations of the spot exchange rate affect the unhedged profit stream of the firms because of the time lag between the contract and the payment date. It is further assumed that traders have a relatively short term planning horizon, so that all variables except next period’s exchange rate are known with certainty. For simplicity it is assumed that the costs of hedging in the forward market do not vary with the exchange rate risk and that the contracts are invoiced only in the currencies of the exporter and the importer. Since the focus of this paper is on exports we will denote the variables of the importer, who is the foreigner to the exporter, with an asterisk.

Import demand

The model starts with an importer who is a price taker and is assumed to buy intermediate goods from the exporter. The importer faces a domestic demand for its output (𝑄∗) which is

increasing in the domestic money income (𝑌∗) and the prices of other good in the domestic economy (𝑃𝐷∗). Furthermore, it is a decreasing function of the price (𝑃∗) and the non-price rationing (𝐶𝑈∗) of its own output. The non-price rationing variable behaves just as the price: as demand pressure and capacity utilization increase during cyclical upswing, available supply is rationed through longer order-delivery lags and tighter customer credit conditions, thereby depressing quantity demanded. The domestic demand for its output, 𝑄∗, is thus a function of:

(18)

The importer and exporter are assumed to maximize their utility, where the utility depends positively on the expected value of profits (π) and negatively on the standard deviation (V) of these profits.

max 𝑈 = 𝐸(𝜋

∗_{) − 𝛾√𝑉(𝜋}∗_),

where E(.) is representing the expectation term and 𝛾 is the measure of relative risk aversion. The profits of the importer, assuming constant input-output coefficients, are explained by:

𝜋∗ = 𝑄∗𝑃∗(𝑄∗_{) − 𝑈𝐶}∗_𝑄∗_{− 𝐻}∗_𝑃𝑖𝑄∗_,

where 𝑈𝐶∗ is the unit cost of production, P is the price of the exporter, 𝑖 is the fixed ratio of imports to total output, so 𝑖𝑄∗ represents the quantity of imports needed to produce 𝑄∗, and 𝐻∗ is the cost of foreign exchange to the importer.

The importer faces uncertainty over these profits when part of the contract is invoiced in the exporter’s currency and when not all of the importer’s foreign currency obligation is covered

forward. It is assumed that some proportion β of the contract is denominated in the exporter’s currency, while (1-β) is denominated in the importer’s currency. Of the proportion denominated in foreign currency, the importer is assumed to hedge some proportion, α, in the forward exchange market. All variables, except for the spot rate (S), are assumed to be known with certainty on the date of the contract. In addition, the covariance between the spot rate and the price is assumed to be zero. Thus, the variance of the importer’s profits can be given by:

𝑉∗(𝜋) = (𝑃𝑖𝑄𝛽(1 − 𝛼))2𝑉(𝑆)

where V(S) is the variance of the spot rate and the spot rate, S, is the importer’s currency per unit of the exporter’s currency.

The import demand function of the importer can then be determined from the utility maximizing output 𝑄∗. This leads to an import demand, M, which is a function of:

(19)

Export supply

The exporter in this model faces a downward sloping market demand curve for his exports which is equal to the aggregated import demand functions of n identical competitive firms. The exporter is assumed to sell some proportion, β, of his total output 𝑄 at 𝑃, and some proportion (1-β) at SP in the importer’s currency.

Just as the importer, the exporter is assumed to maximize his utility. This utility function is analogous to the utility function of the importer, except that 𝜋∗ is changed in 𝜋. The exporter’s profit function is somewhat different, because it is not using imported inputs in production. The profit function is therefore given by:

𝜋 = 𝑄𝑃𝐻 − 𝑄𝑈𝐶

Where UC is the exporter’s domestic unit cost of production and 𝐻 the cost of foreign exchange to the exporter. 𝐻 represents the adjustment to the exporter’s own-currency receipts due to the effect on his uncovered position of changes in the spot exchange rate during the contract period, and the cost of hedging.

The exporter is assumed to hedge a constant proportion 𝛼∗ of his foreign exchange exposure by selling forward at a rate F. The remaining, 1-𝛼∗, must be converted to local currency at the spot rate S’ (inverse of spot rate of the importer). Again all variables except S’ are known with certainty on the contract date. The variance of the exporter’s profits is thus:

𝑉(𝜋∗) = (𝑃∗_𝑄∗_{(1 − 𝛽)(1 − 𝛼}∗_)𝑆′₎2_𝑉(𝑆′₎

The export supply function can then be derived from the utility maximizing output Q: 𝑋 = 𝐹(𝑈𝐶, 𝐸𝐻, 𝑃, 𝑉(𝑆′))

The model shows that the resulting import demand and export supply functions can be used to obtain a reduced form function for the equilibrium quantity of exports:

𝑋 = 𝐹(𝑌∗, 𝐶𝑈∗, 𝑈𝐶∗, 𝑈𝐶, 𝑃𝐷∗, 𝐸𝐻∗, 𝐸𝐻, 𝑉(𝑆′)), Where:

X = the quantity of exports,

Y*_{= GDP from the importing country,} CU*_{= importer’s non-price rationing,}

UC*_{, UC = importer’s and exporter’s unit cost,} PD*_{= importer’s domestic price level,}

(20)

EH*_{, EH = expected cost of foreign exchange for the importer and exporter,} 𝑉(𝑆′) = standard deviation of the future spot rate.

The equilibrium quantity of exports is an increasing function of the GDP from the importing country and the importer’s domestic price level. It is negatively affected by the importer’s non-price

rationing, the importer’s and exporter’s unit cost, the expected cost of foreign exchange for the importer and exporter, and the standard deviation of the future spot rate. The standard deviation of the future spot rate reduces export supply at a given price.

The export supply equation derived by Hooper & Kohlhagen will be the starting point for the economic model used in this paper. We will proxy the non-price rationing variable of the importer by using the capacity utilization rate (Cushman, 1983). In addition, we will use the real exchange rate instead of the nominal exchange rate. The reason for this is that the real exchange rate seeks to measure the value of a country’s goods against those of another country at the prevailing nominal exchange rate. It is therefore more relevant when investigating real exports (Catão, 2007). The real exchange rate will be calculated using: 𝑅𝐸𝑅 = 𝑆 ∙ (𝑃∗

𝑃) where we use the total producer prices (PPI) of the manufacturing sector instead of the consumer prices. The total PPI is used because it covers goods and services delivered to all domestic and foreign markets so it’s relevant for export. Also, we restrict the PPI to the manufacturing sector as it is more representative for tradable goods and therefore this way of calculating the real exchange rate would seem to be most relevant for competitiveness (Lafrance, Osakwe, & St-Amant, 1998). The CPI will be removed from our model since it is likely that it is correlated with the PPI. For simplicity, we remove from this model the expected cost of foreign exchange for the importer and exporter as both variables are hard to measure.

In the model, all variables are known with certainty except for the next period’s real

exchange rate. To account for the uncertainty of the exchange rate at time 𝑡 − 𝑚, it is assumed that the past real exchange rates are sufficient to capture the effects of exchange rates on export

demand. The conditional mean of the exchange rate is denoted by 𝐸𝑡−𝑚(𝑅𝐸𝑅𝑡). Instead of using the variance of the future spot rate, the variance of the real exchange rate will be included in the model. The variance of the real exchange rate is denoted by 𝑉𝑡−𝑚(𝑅𝐸𝑅𝑡). The fact that the conditional mean and variance are included in the export supply equation originates from the assumption that the firm receives orders for its domestic output and places order for its imported inputs at time t=1, while at time t=2 the firm receives and pays for the imported input and is paid for its own output. In addition, this time lag is very important because it makes the traders forward-looking and motivates the relevance of real exchange rate risk as a possible determinant of trade. Another important

(21)

determinant of export demand is based on the order that the foreign importer expect for his customers between the contract date 𝑡 − 𝑚 and the date of the delivery t. This order flow is represented by a single order at time k, which is assumed to be smaller than the time lag m. The order quantity is determined by 𝑌∗𝑡−𝑘 which thus captures the effect of income on foreign demand.

Using the aforementioned variables, the economic model which will be used in this paper is specified as:

𝑋 = 𝐹(𝑌∗

𝑡−𝑘, 𝐶𝑈∗, 𝐸𝑡−𝑚(𝑅𝐸𝑅𝑡), 𝑉𝑡−𝑚(𝑅𝐸𝑅𝑡)).

This economic model can be summarized by the following regression model: 𝑋𝑡 = 𝛽0+ 𝛽1𝑌∗𝑡−𝑘+𝛽2𝐶𝑈𝑡∗+ 𝛽3𝐸𝑡−𝑚(𝑅𝐸𝑅𝑡) +𝛽4𝑉𝑡−𝑚(𝑅𝐸𝑅𝑡) +𝜀𝑡

where 𝑋𝑡 is the natural logarithm (ln) of real exports, 𝑌∗𝑡−𝑘 is the ln of foreign income, 𝐶𝑈𝑡 is the foreign capacity utilization rate, 𝐸𝑡−𝑚(𝑅𝐸𝑅𝑡) is the conditional mean of the real exchange rate (𝑅𝐸𝑅𝑡 is the ln of the real exchange rate (home per foreign)) and 𝑉𝑡−𝑚 is a measure for exchange rate volatility.

According to the theory we expect exports to be an increasing function of foreign income and the real exchange rate. We expect the foreign capacity utilization rate to have a negative impact on exports to the foreign country. For the exchange rate volatility we expect it to have a negative impact as we assume that the agents are on average risk averse.

3.2 Data

In this paper, data over the period January 1986 – November 2014 is used. This gives us 347 monthly observations. The data range is starting from 1986 because there was no data available for the PPI of both countries for the period before 1986. We use monthly observations for the variables because there are more exchange rate fluctuations on a monthly basis when compared to the quarterly basis. It is thus better to use monthly observations so that we can capture more exchange rate fluctuations. The export data is taken from the US bureau of the census. We took the sum of US bilateral imports of all the 19 Euro Area countries to derive the aggregate bilateral exports to the US and then converted the aggregate bilateral exports using the nominal exchange rate in order to have total exports denoted in euros. For Cyprus, Estonia, Latvia, Lithuania, Luxembourg, Slovenia and Malta this data is only available from 1992 onwards, while for Slovakia we only have data from 1993 onwards. It is chosen to leave these countries in our dataset since their share in total exports (1993-2014) is low (see figure 2) and we want the dataset to represent the whole Euro Area.

(22)

Figure 2: Share of total exports

The data for the monthly US GDP (Y) is only available at a quarterly frequency. In order to get monthly GDP data, a proxy is used; the U.S. industrial production (IP). This data is available at Datastream. The US capacity utilization rate (CU) is also available at Datastream.

As mentioned before, the real exchange rate is constructed by using the total PPI for the manufacturing sector. The PPI for the US is available at the website of the Federal Reserve Bank of St. Louis. Due to a lack of data availability, the PPI for the Euro Area is somewhat different. This PPI is not only covers the manufacturing sector but also the sectors: mining and quarrying, energy supply and water supply. In addition, for the Euro Area, the domestic price index is used instead of the total price index. The difference between these is that the former measures the average price change of all covered goods and services delivered to the domestic market only while the latter covers goods and services delivered to all domestic and foreign markets (OECD, 2015). Data for the Euro Area PPI is downloaded from the Eurostat database. The nominal exchange rate is also available at the Eurostat database. The data is presented in figures 3-6.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Cyprus Latvia Malta Estonia Luxembourg Slovenia Lithuania Greece Slovakia Portugal Finland Austria Spain Belgium Netherlands Ireland Italy France Germany

(23)

Figure 3: Real exports Figure 4: Industrial production (United States)

(24)

4. Regression model

In this section, we will specify our ARDL regression model. First, it will be briefly described how the various exchange rate measures are calculated since the theoretical background of some of the exchange rate measures is already presented in section 2.2. The order of integration of the variables will be tested to make sure that neither of the variables are integrated of order two because otherwise the ARDL model will produce spurious results. After the cointegration test, our ARDL representation of the economic model can be given. Lastly, we have to make sure that our ARDL model has serially independent error terms.

4.1 Specification of the expectation of the real exchange rate

Before we specify our ARDL model, it is useful to present a specification for the expected real exchange rate. As mentioned before the regression model used in this paper accounts for the uncertainty of the real exchange rate. Therefore we need to define the expectation of the real exchange. We follow the approach of Klaassen (2004) and model the expectation as follows:

𝐸𝒕−𝒍{𝑅𝐸𝑅𝑡} = 𝑅𝐸𝑅𝒕−𝒍.

where 𝑙 denotes the 𝑙 periods ahead forecast. The abovementioned forecasting rule gives a reliable forecast for the real exchange rate at horizons of 3-12 months (Mark & Choi, 1997). In section 4.3 we will explain which value is chosen for 𝑙 and why it is reasonable that those horizons are relevant for goods traders.

4.2. Specification of the real exchange rate volatility

4.2.1 Moving variance

The first measure for exchange rate volatility used in our regression model will be the moving variance of past real exchange rate changes. The window width of the moving variance used in our regression will be 12 months. The moving variance for 𝑙 = 1 will be calculated by the following formula: 𝑉𝑡−1{𝑅𝐸𝑅𝑡} = 1 12∑(𝑅𝐸𝑅𝑡−𝑖− 𝑅𝐸𝑅𝑡−𝑖−1) 2 12 𝑖=1

For longer horizons (𝑙 > 1) the moving variance is given by: 𝑉𝑡−𝑙{𝑅𝐸𝑅𝑡} = 𝑙 ∙ 𝑉𝑡−𝑙{𝑅𝐸𝑅𝑡−𝑙+1}. This measure can be interpreted as first approximating the volatility in month t by (𝑅𝐸𝑅𝑡− 𝑅𝐸𝑅𝑡−1)2 and then smoothing it by taking the average over 12 months (Klaassen, 2004). The graph of the moving variance is shown in figure 7.

(25)

The moving variance as a measure of exchange rate volatility is criticized for several reasons as mentioned in section 2.3. We would like to add another argument against the use of the moving variance as a measure of exchange rate volatility. The reason for this is that the moving variance pretends that the past volatilities over last 12 months are a good indication for the future exchange rate volatility; the moving variance is backward looking. However, it is not reasonable that future volatility behaves the same as past volatility and therefore its explanatory power for the future volatility is very low. Although this measure is the most used proxy for exchange rate volatility, it is not likely that goods traders use this measure in order to estimate future volatility when making export decisions.

Figure 7: The moving variance 4.2.2 Dummy variable approach

As mentioned before this paper will make use of the dummy variable approach as developed by Serenis & Tsounis (2014) as a measure of exchange rate volatility. This measure was intended to capture only the high and low values of the exchange rate. This dummy variable is constructed in the following way:

1) First, the average exchange rate over the time period January 1986 – November 2014 is computed. It was found that the average real exchange rate over this period was equal to approximate 1.35. 0 .0 0 2 .0 0 4 .0 0 6 MVAR 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 time

(26)

2) Next, we identify the high and low values of the exchange rate. Since it is not known which values will be perceived as a high or a low value, Serenis & Tsounis (2014) used several fluctuations and then checked which result was the most significant. This is beyond the scope of this paper so we will therefore use a >5% deviation around the average value calculated in step (1) to identify the high and low values. Based on this we found a lower bound equal to 1.28 and an upper bound of 1.42.

3) Once we found the upper and lower bound of the interval, we can construct the dummy variables. This is done by putting (1) for the cases where the average real exchange rate is either 𝑅𝐸𝑅𝑡 < 1.28 or 𝑅𝐸𝑅𝑡 > 1.42. When the average real exchange rate is 1.28 ≥ 𝑅𝐸𝑅𝑡 ≤ 1.42, we denote (0). By doing so, we are able to capture only the (unpredictable) high and low values which affect exports. In figure 8 it is visible for which periods we included a (1) and for which periods a (0).

Although we agree with Serenis & Tsounis that the high and low values of the real exchange rate refer to the unpredictable factor which has an effect on exports, using the dummy variable approach is not justified for the same reason the moving variance is not suitable as a measure of exchange rate volatility; it is backward looking and therefore it has low explanatory power for future volatility. The dummy variable approach pretends that the volatility in a given month explains the future volatility which can never be the case.

Figure 8: The dummy variable approach

0 .2 .4 .6 .8 1 DV 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 time

(27)

4.2.3 AR(2) risk measure

This idea starts with the obtaining of the monthly volatility calculated by taking the sum of the squared daily exchange rate changes over all days in the month. The squared daily returns are used because Andersen & Bollerslev (1998) argue that the squared monthly returns are a noisy indicator for the latent volatility in that period. The original idea from Andersen & Bollerslev focuses on the intraday squared returns to calculate the daily exchange rate volatility, however there is no intradaily data on the exchange rate so we will use daily exchange rate data. Calculating the monthly volatility as the sum of the squared daily returns, ensures that the estimated measure is reasonably precise because there are many return observations.

𝑉𝑡 = ∑ (𝑅𝐸𝑅𝑑− 𝑅𝐸𝑅𝑑−1)2 𝑑∈𝐷𝑡

If we use that the expected exchange rate is: 𝐸𝑡−𝑙{𝑅𝐸𝑅} = 𝑅𝐸𝑅𝑡−𝑙. Then this measure for the one-period ahead forecast is thus:

𝑉𝑡−1{𝑅𝐸𝑅𝑡} = 𝐸𝑡−1{ ∑ (𝑅𝐸𝑅𝑑− 𝑅𝐸𝑅𝑑−1)2 𝑑∈𝐷𝑡

} = 𝐸𝑡−1{𝑉𝑡}

Using the equation for the monthly volatility, we can estimate an AR(2) model to measure the exchange rate risk indicated by 𝑉𝑡:

𝑉𝑡 = 𝜇𝑣+ 𝛼1(𝑉𝑡−1− 𝜇𝑣) + 𝛼2(𝑉𝑡−2− 𝜇𝑣) + 𝜖𝑡,

where the error term 𝜖𝑡 is uncorrelated with the error term in our regression model and is

distributed with mean zero and a constant variance. This measure can be defined by: 𝑉𝑡−1{𝑅𝐸𝑅𝑡} = 𝐸𝑡−1{𝑉𝑡} for the one-period ahead risk. For longer horizons 𝑉𝑡−𝑙{𝑅𝐸𝑅𝑡} = 𝐸𝑡−𝑙{𝑉𝑡−𝑙+1} + ⋯ + 𝐸𝑡−𝑙{𝑉𝑡−𝑙}, where each expectation is a multi-period ahead forecast based on the AR(2) model (Klaassen, 2004). The graph of the AR(2) risk measure is shown in figure 9.

The AR(2) risk measure is, in contrast to the moving variance and the dummy variable approach, forward looking. Suppose the forecast horizon in the abovementioned formula is equal to 12 months (𝑙 = 12). In this case the goods trader uses all the information about past real exchange rate

fluctuations and uses this information to proxy the exchange rate volatility in the next 12 months. By calculating the volatility, the AR(2) risk measure thus takes into account that traders make a forecast about the future volatility instead of assuming that the past volatility can be used to explain the future volatility. It therefore has more explanatory power than the moving variance or the dummy variable approach.

(28)

Figure 9: The AR(2) risk measure

4.3 Cointegration test

In this paper we will make use of the ARDL approach (Pesaran, Shin, & Smith, 2001). The regression will be executed by using EViews 9. The most important feature of the ARDL approach is that the existence of a long run relationship can be tested without knowing in advance whether the variables are integrated of order zero (I(0)) or order one (I(1)). However, if the variables are

integrated of a higher order, the ARDL model would produce spurious results (Oteng-Abayie & Frimpong, 2006). Therefore we will test for the order of integration using the augmented Dickey-Fuller (ADF) test for a unit (autoregressive) root. Prior to testing for unit root, the number of lags have to be determined. The number of lags can be determined by using the Bayes Information Criterion (BIC) or the Akaike Information Criterion (AIC). These two measures almost identically calculate the number of lags to include in the model, however the AIC suggests to include more lags in the model. This study will therefore make use of the AIC, because studies of the ADF statistic suggest that it is better to have too many lags than too few, so it is recommended to use the AIC instead of the BIC (Stock & Watson, 2012). Inspection of the graphs of the variables (figures 3-9) included in our model suggests that only the real exports and the proxy for US GDP, US industrial production, contain a (positive) trend. Therefore we include, a drift term, when performing the ADF test. Applying the ADF test to the variables, the results show that real exports, US industrial

.0 1 5 .0 2 .0 2 5 .0 3 .0 3 5 .0 4 AR 2 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 time

(29)

production, and the real exchange rate all have p-values greater than 0.05, so the null hypothesis that the variables have unit root is not rejected. When the test is applied to the first differences of those variables, all the p-values are equal to 0.00 indicating that neither of the variables is integrated of order two so that the ARDL model can be applied. Note that a unit root for the real exchange rate means that the purchasing power parity (PPP) is violated. It is however, still reasonable to use a unit root analysis as an approximation because empirical studies generally fail to find support for long-run PPP, especially during the recent floating exchange rate period. In fact, the empirical consensus is that PPP does not hold over this period (Dueker & Serletis, 2000).

4.4 The ARDL representation of the economic model

After establishing that all the variables are either I(0) or I(1), we are able to specify our ARDL regression model. The formulation of our model is based on the paper of Pesaran et al. (2001) and uses the lag order as specified by AIC. For the real exchange rate, the real exchange rate volatility and the US industrial production the lag order is different. The reason for this is that Klaassen (2004) investigated in his paper, using Poisson lags, at which lags of the real exchange rate, real exchange rate volatility and foreign industrial production the maximal effect on exports occurs. This is important especially for the real exchange rate risk as the real exchange rate risk horizon that is relevant for goods traders is very important for the conclusion of our paper. Klaassen (2004) found in his paper that the effect of the aforementioned variables on exports is the biggest when, for both the real exchange rate and real exchange rate volatility, the lags 11 to 13 are included in the regression model. For US industrial production (foreign income), lag three must be included in the model (see figure 10). Although Klaassen (2004) pointed out that the lag structure depends on the data, his result is based on the panel data for the biggest economies in the world and therefore we will assume that the lag structure for our data will be the same. To make sure that we will capture the effect on exports and only have one value for the long-run effect (discussed below) we will only include lag 12 for the real exchange rate and real exchange rate volatility and lag 3 for foreign industrial production.

(30)

Figure 10: Distribution of total effect β of regressors on exports over time

After taking into account the lags for the foreign income, real exchange rate and the volatility the ARDL model, can be written as:

∆𝑋𝑡= 𝛽0+ 𝜃1𝑋𝑡−1+ 𝜃2𝑌∗𝑡−3+ 𝜃3𝐶𝑈𝑅∗𝑡−1+ 𝜃4𝑅𝐸𝑅𝑡−12+ 𝜃5𝑉𝑡−12+ ∑ 𝛼𝑗∆ 𝑋𝑡−𝑗+ 𝑝 𝑗=1 ∑ 𝛽1𝑗∆𝐶𝑈𝑅∗𝑡−𝑗+ 𝑝 𝑗=0 𝜀𝑡

where ∆ is the first-difference operator, p is the number of lags and 𝜀𝑡 is a white noise error term which is normally distributed with mean zero and a constant variance 𝜎2. We also included eleven monthly dummy variables to allow for seasonal differences. Important to note is that we initially also included the first differences on the foreign income, the real exchange rate and the volatility into the regression model. However, the parameters on these variables were found to be all insignificant. Therefore we decided to leave them out of the model to prevent the model for being

over-parametrized. It is true that some of the first differences on real exports and the capacity utilization rate are also insignificant. Those first differences are however automatically included by EViews 9 when included as dynamic regressors. For the variables foreign income, the real exchange rate and the volatility this is not the case since they are all included as fixed regressors in order to take into account the findings of Klaassen (2004).

This equation will be used to estimate the long-run relationship between the explanatory variables and the dependent variable. The long-run equilibrium (steady state) requires that all the differenced terms equal zero, so that the long run coefficients are found by calculating the ratio of the level coefficients by using the following expression:

𝛾̂ = − 𝑖 𝜃̂𝑖 𝜃̂1,

(31)

where 𝑖 = 2,3,4 or 5 (Bardsen, 1989). This measure is automatically calculated using EViews 9. 4.5 Diagnostic checking

As mentioned before, one of the key assumptions of the ARDL Bounds Testing approach of Pesaran et al. (2001) is that the error term of the regression model must be serially independent. It is therefore important that the lag order of our regression model is selected appropriately. On the one hand, we must choose the lag order sufficiently large to mitigate the residual serial correlation problem, and on the other hand, it must be sufficiently small so that our regression model is not over-parametrized (Pesaran, Shin, & Smith, 2001). The lag order was determined using the AIC. Using this information criterion, the ARDL models in tables 4 and 5 are selected. To test the hypothesis of no residual serial correlation against the alternative hypothesis, we follow the same approach as Pesaran et al. and use the Lagrange multiplier (LM) statistics. The results of the LM test for the ARDL models which included respectively the moving average standard deviation, the AR risk measure or the dummy variable are in each case bigger than 0.05 indicating that the null hypothesis of no residual serial correlation cannot be rejected.

5. Empirical results

In this chapter, we present the results of our ARDL regression and check whether the results are robust to a varying sample period. In the last paragraph, we will give an explanation for those results. 5.1 Estimation results

We mentioned earlier that the most important feature of the ARDL approach is that the existence of a long-run relationship can be tested without knowing in advance whether the variables are integrated of order zero or order one. In order to test for a long-run relationship Pesaran & Shin (2001) supplied the bounds on the critical values for the distribution of the F-statistic for an arbitrary mix of I(0) and I(1) variables. For various number of variables (k), they give the lower and upper bounds on the critical values. The lower bound indicates that all of the variables are I(0), while the upper bound indicates that all of the variables are I(1). If the computed F-statistic falls below the lower bounds this means that the variables are I(0), so no cointegration is possible. If the F-statistic exceeds the upper bounds, we conclude that we have cointegration. Finally, if the F-statistic falls in between the bounds, the test is inconclusive (Giles, 2013). Table 3A indicates that for each of the models used here there is a long-run relationship between the dependent and the independent variables.

Table 4 in the appendix presents the full model of the empirical results for the estimated export supply model using the three alternative measures for exchange rate volatility. In this section we will only discuss the long-run effects, a summary of the most important long-run coefficients

(32)

derived from our regression model is given in table 4A. We will only briefly discuss the results here, an in depth analysis of which volatility measure is best suitable for measuring exchange rate volatility will be presented in the discussion in paragraph 5.3.

Table 4A: Long run coefficients

Moving variance Second order AR Dummy variable

US income(-3) 2.134*** 2.080*** 2.137***

(0.062) (0.077) (0.081)

US capacity utilization rate(-1) 0.000 0.000 0.001

(0.003) (0.004) (0.004)

Real exchange rate(-12) -0.564*** -0.544*** -0.392*

(0.156) (0.176) (0.194)

Volatility(-12) 59.367** 18.684** 0.003

(23.739) (8.305) (0.056)

R-squared 0.769 0.769 0.769

Adjusted R-squared 0.750 0.751 0.750

Standard errors in parentheses, *** significant at 1% level, ** significant at 5% level, * significant at 10% level

The coefficient of the proxy for foreign income is in all of the three models statistically significant at a one percent significance level. The results indicate that a one percent increase in foreign income leads, in all models, to an increase in real exports by approximate 2.1% in the long-run. This positive effect is consistent with what we expected based on the theory. The capacity utilization rate of the United States has a negligible effect on real exports, and is in neither of the three models significant. This effect is so small that a 100% increase in this rate only leads to a maximum increase of 0.1%. It can thus be argued that the capacity utilization rate has almost no effect on real exports in the long-run. Since the capacity utilization rate is, in theory, depressing the domestic demand for goods of the importer, the positive effect of this rate in our models may not be justified. The real exchange rate is found to have a negative influence on real exports. This result is in two out of three model specifications significant at a 5% significance level. The long-run coefficient ranges from -0.564 to -0.392, which indicates that in the long-run, a one percent increase in the real exchange rate decreases real exports by a maximum of 0.564%. This is not in line with our

expectations since we expected that there was a positive effect between the real exchange rate and real exports. As shown by Berthou (2008) the effect of the real exchange rate on exports is reduced when the destination country has a low quality of institutions, the country is more distant and when the efficiency of customs is low in both the importing and exporting countries. These results are consistent with the existence of a hysteresis effect of real exchange rate movements on trade, as suggested by Baldwin & Krugman (1989). This paper looks at trade between the Euro Area and the United States, therefore it is not likely that the negative effect of the real exchange rate can be explained by either a low quality of institutions or low efficiency of customs. The large distance

The impact of exchange rate volatility on Eurozone-United States bilateral exports