The Effects of Yuan Appreciations on the Eurozone-China Trade Balance
An assessment of the Yuan exchange rate elasticities of the trade balance of the Eurozone with China
Author: Supervisor:
Philip F.P. van de Linde Drs. Naomi J. Leefmans
5656478 Second reader:
philip.vandelinde@gmail.com Dr. Dirk Veestraeten
Table of Contents
1. Introduction ... 3
2. Literature Review ... 7
2.1 The Marshall-Lerner Condition ... 7
2.1.1 Reduced Form Equation Methods ... 8
2.1.2 Cointegration Analysis ... 9
3. Description of the Variables and Data ... 17
3.1 Dependent Variable ... 17
3.2 Independent Variables ... 17
4. Model and Methodology ... 21
4.1 Empirical Model ... 21
4.2 Introducing the ARDL-ECM ... 23
4.3 Step I: The Bounds Test Approach to Cointegration ... 26
4.3.2 Unit Root Test ... 28
4.3.3 Bounds Test ... 28
4.4 Step II: Short-Run Dynamics ... 30
4.4.1 Constructing the Conventional ARDL-ECM ... 30
4.4.2 Short-Run Elasticities ... 31
4.5 Diagnostic and Stability Tests... 32
5.1 Unit Root Test ... 32
5.2 Long-Run Cointegration Relationship ... 33
5.2.1 Bounds Test Approach for Cointegration ... 34
5.2.2 Long-Run Elasticities ... 35
5.3 Short Run Dynamics ... 36
5.3.2. Short Run Elasticities ... 37
5.4 Stability and Diagnostics Tests ... 38
5.4.1 Stability Tests ... 38
5.4.2 Diagnostic Tests ... 39
6. Conclusion ... 42
7. References ... 44
1. Introduction
Within the field of international economics the growing trade deficit between the United States and China has been subject of debate for several years. Since China pegged the Yuan to the US Dollar, the foreign exchange reserves of China have increased dramatically. This huge accumulation of US Dollar reserves by China has put enormous downward pressure on the Yuan and the Chinese fixed exchange rate regime. The USA, who blames China of an unfair competitive advantage because of the peg, pressures China to change to a more flexible exchange rate regime. The USA expects this to lead to an appreciation of the Yuan and a decrease of their own trade deficit. Although there is no consensus on the exact rate of undervaluation of the Yuan, it is argued that the Yuan is undervalued to the order of 35 to 40 percent towards the US Dollar. The US trade deficit with China amounted to 231 billion Euro in 2012 (You and Sarantis, 2012).
Since the debate on these global imbalances was primarily focused on the bilateral trade relations between China and the USA, at first Europe was rather indifferent about the issue. However, imbalances between the Eurozone and China have also been growing sizeably since the early 2000s as China has become the second trading partner of the Eurozone, measured by total imports and exports, and the Eurozone’s main source of imports. Figure 1 shows the net trade imbalances of different regions, it illustrates the development of the total trade deficit of the Eurozone and the total trade surplus of China.
Figure 1. Global trade imbalances as percentage of world GDP
Source: IMF World Economic Outlook
The yearly trade deficit of the Eurozone with China, henceforth the Eurozone-China trade balance, has increased from 32 billion Euro in 2000 to a peak of 118 billion Euro in 2008 and fell to 93 billion Euro in 2012. According to Eurostat (2013), sectors like office and telecommunication equipment, shoes and textiles, iron and steel, are the main drivers causing
this trade deficit. Figure 2 shows the development of the monthly trade balance between the Eurozone and China over the period 1999 to 2013.
Figure 2. Monthly bilateral Eurozone-China trade balance (billion Euros)
Datasource: Eurostat (Graph constructed by author)
The increasing Eurozone trade deficit with China led to political pressures on China from European nations and international organizations, such as the WTO and OECD, to adjust its exchange rate regime. Because of these increasing political pressures China finally de-pegged its currency in 2005 which led to an immediate appreciation of the Yuan. In July 2005, the Chinese authorities revalued the Yuan from 8.27 to 8.11 per US Dollar. This small revaluation was accompanied by an official revision of the Chinese exchange rate regime (Goujon and Guérineau, 2005). From then on, the People’s Bank of China would set the value of the Yuan relative to a currency basket comprising of the US Dollar, Euro, Korean Won, and Japanese Yen; further details regarding the weight of each currency in the basket were not provided however.
In 2010 the People’s Bank of China announced that it would increase the flexibility of the Yuan again and that China would change to a managed float of their currency. The exchange rate of the Yuan has appreciated from 8.27 Yuan per US dollar in 2005 to a record high of 6.213 Yuan per US Dollar in March 2013. The Euro-Yuan exchange rate follows a comparable pattern. Figure 3 shows the development of the nominal exchange rate of the Yuan to the Euro and US Dollar, and shows the nominal appreciation of the Yuan to both currencies from 2005 onwards.
Although a lot of literature is available on the effects and linkages between the Chinese exchange rate and the trade deficit of the USA, literature on the effects of the
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Chinese exchange rate on the Eurozone trade balance is scarce. Moreover, the results in the empirical literature on the impact of changes in exchange rates on trade and more specifically on the effects of Chinese exchange rate changes on trade with China’s main trading partners, strongly differ. A more incisive analysis of the impact of the Chinese exchange rate on bilateral trade between the Eurozone and China is of particular relevance in the context of global imbalances and international trade. These notions motivated the study in this thesis.
Figure 3. Monthly nominal Euro and Dollar to Yuan exchange rates
Datasource: ECB and Federal Reserve of St. Louis (Graph constructed by author)
The goal of this thesis is to study the effect of Yuan appreciations on the Eurozone trade balance. To conduct this study the following research question is formulated: “What are the
effects of changes in the Euro-Yuan exchange rate on the bilateral trade balance of the Eurozone with China?” I intend to focus my research on the long-run and short-run
elasticities of the Eurozone bilateral trade balance with China to fluctuations in the exchange rate of the Yuan.
Traditional theory on bilateral trade flows uses gravity models with demand and price competitiveness as explanatory variables for the analysis of trade flows (Wang & Ji, 2006). However, based on the study by Bahmani-Oskooee and Brooks (1999), who investigated a J-curve between the US and her trading partners, I will construct an Autoregressive Distributed Lag - Error Correction Model (ARDL-ECM) as developed by Pesaran et al. (2001) to estimate a regression equation for the Eurozone trade balance with China. An ARDL-ECM, in contrast to a gravity model, allows for the estimation of both short and long run effects of changes in the Euro-Yuan exchange rate on the trade balance and hence enables the analysis of the complete post appreciation dynamics of the Eurozone trade balance after a Yuan
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appreciation. In addition, when using an ARDL-ECM to test for cointegration stationary series, non-stationary series or a combination of both can be used. Finally, the error correction model allows for analysing the convergence of the trade balance towards equilibrium after a shock in the exchange rate. Hence, the ARDL-ECM approach by Pesaran et al. (2001) as used in the study by Bahmani-Oskooee and Brooks (1999) has several advantages over traditional gravity models that fit this study perfectly, this allows to understand the implications of changes in the Euro-Yuan exchange rate on China-Eurozone trade and whether political claims are justified.
Using the ARDL-ECM, a time series analysis will be conducted on the bilateral trade balance between the Eurozone and China. Monthly data will be used for the period 1999:12 to 2013:04 on the Eurozone-China trade balance, Eurozone and Chinese national income, the real Euro-Yuan exchange rate and its volatility.
I expect to find that the sensitivity of Eurozone trade will not be very high, mainly because of low labour costs in China. I expect that even when Chinese wages will increase in Euro terms after a depreciation of the Euro to the Yuan, the low Chinese labour costs remain another structural factor of China’s competitiveness.
While some authors have tried to estimate the effect of Yuan appreciations on several of China’s trading partners, to my knowledge, no paper has done an analysis on the specific case of estimating the Eurozone exchange rate sensitivity of bilateral trade between China and the Eurozone. Therefore, to my knowledge this is the first study to investigate the effect of changes in the Yuan exchange rate on the Eurozone. By doing so I hope to contribute to the existing literature and expand on the existing methodology by including exchange rate volatility as an additional explanatory variable. A more profound knowledge of the effect of the exchange rate on trade between the Eurozone and China is of particular interest in the context of global imbalances.
The thesis is structured as follows, chapter 2 consists of a literature review. The literature review aims to clarify the effects of exchange rate changes on the trade balance by studying both the theoretical and empirical literature on the Marshall-Lerner condition and J-curve phenomenon. Chapter 3 describes the variables and data used in the empirical analysis. Chapter 4 will present the model and methodology used in this thesis. Chapter 5 contains the empirical results and their analysis. Finally chapter 6 will provide a conclusion.
2. Literature Review
The purpose of this chapter is to provide a literature review on the theoretical and empirical background of this study. It aims to clarify how changes in the exchange rate level are related to the trade balance. Furthermore, the literature review will provide insights on the development of trade theories and on the methodologies used in the existing empirical literature in order to form the base for the model and methodology used in this thesis.
2.1 The Marshall-Lerner Condition
Numerous studies have been conducted on the effect of exchange rate changes on trade. Economic theories and empirical evidence are inconsistent however on the exact impact of exchange rate changes on trade. The theoretical starting point for analysing the effects of an appreciation or depreciation on trade flows are the twin concepts of the Marshall-Lerner condition and the J-curve phenomenon. This literature review will therefore start with an analysis on the existing literature on the Marshall Lerner condition. Next, the literature on the J-curve phenomenon will be reviewed.
Economic theory states that a currency devaluation or depreciation does not lead to an improvement of the trade balance in every case. The Marshall-Lerner condition, hereafter the M-L condition, named after Alfred Marshall and Abba Lerner, provides the conditions under which a devaluation or depreciation leads to an improvement of a country’s trade balance. Since a country’s trade balance consists of the value of its exports (𝑋𝑋) minus the value of its imports (𝑀𝑀) and both are calculated as a price times its quantity, 𝑇𝑇𝑇𝑇 = (𝑋𝑋 ∙ 𝑃𝑃𝑋𝑋) − (𝑀𝑀 ∙ 𝑃𝑃𝑀𝑀) , the M-L condition states that when a country’s currency depreciates, the prices of
exports will decrease while the prices of imports will increase and this will lead to an increase in the quantity of exports and a decrease in the quantity of imports. This implies that the trade balance can only improve after the depreciation if the export or import quantities respond sufficiently to compensate for the change in price. Hence export quantities must increase or import quantities must decrease adequately. The M-L condition states that the sum of the absolute values of the elasticities of import and export demand must be greater than one in order for a depreciation or devaluation to lead to an improvement of the trade balance (Bahmani et al., 2013) .
Because of this seemingly necessary condition it became vital to be able to accurately measure trade elasticities with regard to currency devaluations and international trade policy. This section will describe the main findings in the existing empirical literature on the M-L
condition and the methodologies used to estimate the effect of a depreciation on a country’s trade balance.
2.1.1 Reduced Form Equation Methods
The earliest empirical studies on the M-L condition and trade elasticities were simple reduced form equations and did not take the exchange rate into account in their studies, albeit the key point of the M-L condition is to study the effect of exchange rate changes on trade volume. Instead of the exchange rate as price ratio these studies merely used export and import prices in their estimations as a ratio of a world price index of the same goods. Assuming that purchasing power parity holds, this price ratio would equal the long-run exchange rate (Bahmani et al., 2013). Houthakker and Magee (1969) were the first in estimating trade elasticities to use simple reduced-form equations where each equation has the endogenous variable on the left side and the exogenous variables on the right side. These reduced form equations were later also used by Goldstein and Kahn (1985) and Wilson and Takacs (1979). These equations became the basis for studies on this topic in the modern literature.
Houthakker and Magee (1969) set up log-log regression equations for both imports and exports using national and world income and the above-mentioned price ratios as explanatory variables. Using OLS the authors study both the price and income elasticities of import and export for 26 countries from 1951 to 1966. Houthakker and Magee find relatively small price elasticities for aggregate trade compared to the income elasticities, suggesting a relatively small effect of changes in relative prices on trade volumes.
Goldstein and Kahn (1985) further developed and elaborated on the reduced-form equations used by Houthakker and Magee (1969) to what has become one of the most used specifications in international trade literature. Houthakker and Magee’s specifications only took long-run conditions into account, however in order to be able to study the dynamic short-run adjustments of the trade balance, Goldstein and Kahn included lagged variables for the first time. Goldstein and Kahn use an import price index over a wholesale price index and an export price index over an index of partners’ import prices as price ratios.
Wilson and Takacs (1979) were the first to include the nominal exchange rate as explanatory variable in their reduced form equations for their study on the price and exchange rate response of trade. They estimate their equations for six different countries using OLS for the period 1955-1971. They find different estimates of the response of trade volumes to changes in the nominal exchange rate with weak significance. In fact, just like the previous
studies, they do not formally test the M-L condition though, since they do not include a relative price such as the real exchange rate, in their equations.
2.1.2 Cointegration Analysis
Most recent studies on the M-L condition apply cointegration analysis to test for a long run relationship between the trade balance and the exchange rate. Engle and Granger (1987) were the first to introduce cointegration analysis in time-series econometrics. The principle is, since many time series are non-stationary, that when you regress these series you might get a false result as the variables might only seem correlated because they are all growing over time. This might lead to a spurious relationship.
When two variables are nonstationary and integrated of order one I(1) it is possible that a linear combination of the two variables exist that is stationary and I(0). This linear combination represents a long-run cointegrated relationship between the variables, a stationary equilibrium relationship.Cointegration analysis tests for such a relationship.
The first studies to use cointegration analysis within the analysis of exchange rate changes on trade were Rose (1991) and Andersen (1993). They estimate an equation for both import and export volume and besides foreign and home income do include a relative price. This relative price is usually a price ratio of domestic export prices over world export prices and import prices over domestic prices, whereas in other studies the real exchange rate is used. The studies on the M-L condition that use cointegration analysis then estimate some variant of the following reduced form equations:
𝑙𝑙𝑙𝑙𝑙𝑙𝑋𝑋 = 𝛼𝛼 + 𝛽𝛽𝑙𝑙𝑙𝑙𝑌𝑌𝑓𝑓+ 𝛾𝛾𝑙𝑙𝑙𝑙𝛾𝛾𝑃𝑃 + 𝜖𝜖
𝑙𝑙𝑙𝑙𝑙𝑙𝑀𝑀 = 𝛿𝛿 + 𝜀𝜀𝑙𝑙𝑙𝑙𝑌𝑌ℎ+ 𝜃𝜃𝑙𝑙𝑙𝑙𝛾𝛾𝑃𝑃 + 𝜖𝜖
, where 𝑙𝑙𝑋𝑋 is the quantity of exports, 𝑙𝑙𝑀𝑀 the quantity of imports, 𝑌𝑌𝑓𝑓 is foreign income, 𝑌𝑌ℎ is home income and 𝛾𝛾𝑃𝑃 is a relative price. The coefficients of interest here are 𝛾𝛾 and 𝜃𝜃 that estimate the export and import elasticities.
Using cointegration analysis, several of the earlier studies found a lack of evidence to support the M-L condition. Rose (1991) analyses the empirical relationship between the real effective exchange rate and the real aggregate trade balance for five OECD countries and finds a lack of evidence for cointegration to support the M-L condition. Andersen (1993) studies 16 different countries and finds either insignificant coefficients or coefficients with a sign that contradicts the existing economic theory.
2.1.3 Single Equation Methods
An alternative method to test the ML-condition and to estimate the effect of a change in the exchange rate on trade is to use the trade balance as only endogenous variable instead of using two separate regression equations for both import and export quantities. Although this method consequently does not test the separate import and export elasticities needed to formally test the M-L condition, Arize (1996) states that this method is an ‘acceptable substitute for testing the M-L condition’. Such studies use some variant of the following equation to analyse the effect of an exchange rate change on a country’s trade balance:
𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡= 𝛼𝛼 + 𝛽𝛽𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡𝑓𝑓+ 𝛾𝛾𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡ℎ+ 𝛿𝛿𝑙𝑙𝑙𝑙𝛾𝛾𝑃𝑃𝑡𝑡+ 𝜖𝜖
The trade balance (𝑇𝑇𝑇𝑇) is constructed using both exports and imports and is set up as either the difference between them (𝑋𝑋 − 𝑀𝑀) or as a ratio of exports over imports (𝑋𝑋/𝑀𝑀). Since both exports and imports are implicitly included in the equation, also home and foreign income need to be included (𝑌𝑌ℎ and 𝑌𝑌𝑓𝑓). The coefficient for the relative price is 𝛿𝛿. If 𝛿𝛿 is positive, this implies that a depreciation of the home currency leads to an increase in the trade balance.
The empirical literature shows mixed evidence for the M-L condition when using single equation methods. Applying a dynamic single-equation model and performing an OLS regression, Prawoto (2007) tests the M-L condition for four Asian countries. For only two of the four countries the study finds the M-L condition to be met. Razafimahefa and Hamori (2005) focus on the trade balance of Mauritius and Madagascar, using a single equation method they find only significant price elasticities for Mauritius that meet the M-L condition. Sinha (2001) uses a single equation and investigates the M-L condition for five Asian countries. The price elasticities Sinha finds indicate that the M-L condition holds for all countries except for Sri Lanka.
These studies do not formally test the M-L condition however. The M-L condition states that the import and export elasticities must be greater than one in order for a depreciation to lead to an improvement of the trade balance. Since the single-equation method, instead of estimating one import and one export equation, use only one equation for the trade balance, the separate export and import elasticities cannot be obtained. Most of these studies hence fall under the J-curve phenomenon literature and will be reviewed extensively in the next section.
From the literature review on the M-L condition it can be concluded that the existing studies on the M-L condition are inconclusive on the effect of exchange rate changes on trade and do not provide enough evidence for the M-L condition. Studies on the M-L condition test whether the sum of the absolute value of both elasticities exceeds one and whether at this point the trade balance improved. It seems that the M-L condition does not need to hold in order for a depreciation of a country’s currency to have a positive effect on its trade balance. Cases where the trade balance improved while the M-L condition was not satisfied were encountered as well. (Bahmani-Oskooee, 1985).
Although the M-L condition is one theory on the effect of exchange rate changes on the trade balance and therefore helps to understand the possible effect of a change in the Euro-Yuan exchange rate on the Eurozone-China trade balance it is not the main purpose of this thesis to test whether the M-L condition holds or not. This thesis aims to study whether there is a long run relationship between the exchange rate and the trade balance and to investigate the complete post depreciation dynamics of the Eurozone trade balance after a change in the Euro-Yuan exchange rate.
For this reason in the next section the focus will change towards the analysis of the short-run dynamics that influence the trade balance, i.e. the J-curve phenomenon, jointly constituted by a negative short-run effect and positive long-run effect of a change in the exchange rate on the trade balance (Bahmani-Oskooee and Ratha, 2004). This allows for a more extensive analysis of the complete post-depreciation dynamics of a country’s trade balance, both in the short and the long run. The next section provides a review of the economic theory and the results in the empirical literature onthe J-curve phenomenon.
2.2 The J-Curve Phenomenon
Magee (1973), who first introduced the J-curve phenomenon, states that a depreciation of the home currency leads to a short run deterioration of the trade balance but a long run improvement. He argues that instantaneously after a depreciation of the home country, the imports by the home country become more expensive while the exports by the home country become cheaper. In the short run, the trade balance is therefore subject to a price effect because of a lag in the adjustment of volumes to changes in these relative prices. Since the short-run demand curve is inelastic, the price effect because of the depreciation of the home currency, increases the domestic value of imports, decreases the value of exports, and thus worsens the trade balance. Quantity adjustments take longer than price adjustments, for example because of contracts, so only in the long run the demand elasticities increase. With a
sufficient increase, a volume effect dominates the price effect and causes an increase in exports and a decrease in imports by the home country, leading to an improvement of the trade balance. The initial worsening and the subsequent improvement of the trade balance represents the letter J, therefore the term J-curve phenomenon.
There are two main definitions of the J-curve phenomenon when short- and long-run coefficients are included within a trade balance regression equation. Traditionally only short-run results have been used, the J-curve was then defined as a negative exchange-rate coefficient for the short-run lags and positive ones for longer lags. Afterwards, Rose and Yellen (1989) defined the J-curve phenomenon as negative short-run coefficients combined with a positive long-run real exchange rate coefficient. Although there are reasons to assume the J-curve phenomenon describes the short-run dynamics of the trade balance, there are also several reasons why it may not. The evidence on the existence of the J-curve phenomenon from empirical studies is miscellaneous and indecisive.
Figure 4. The J-curve Phenomenon
Source: Krugman and Obstfeld, 2008
The main difference between the methodology in studies on the J-curve phenomenon and those on the M-L condition is that in the former there are no separate estimates needed for both import and export elasticity, only a coefficient for the real exchange rate elasticity of the trade balance is needed for every period after a depreciation of the home currency. This results in only one regression-equation for the trade balance, instead of one for export and one for import quantities. In general, regarding J-curve studies, the same variables are used as
in M-L condition studies, only the model specification is different. Mostly this leads to equations of the following form:
𝑇𝑇𝑇𝑇 = ƒ(𝑌𝑌ℎ, 𝑌𝑌𝑓𝑓, 𝑃𝑃𝛾𝛾)
Where 𝑇𝑇𝑇𝑇 is the trade balance, 𝑌𝑌ℎ is home country income, 𝑌𝑌𝑓𝑓 is foreign country income and 𝑃𝑃𝛾𝛾 is a price ratio.
2.2.1 Aggregate Trade Data Analysis
Most of the earlier papers on the J-curve phenomenon used the total trade data of one country with all its trading partners in analysing a J-curve for a specific country, these studies, from now on aggregate trade data studies, will be discussed first. Subsequently the more recent papers that make use of bilateral trade data will be discussed, these studies investigate the trade balance of a country with one specific partner, from now on bilateral trade data studies.
Himarios (1985) shows in his study that in the long run, like predicted by the traditional economic theory, a devaluation does affect the trade balance positively while in the short-run the trade balance is affected negatively. He points out that it is the real exchange rate rather than the nominal exchange rate that affects trade flows and that the lagged value of these exchange rates must also be included in the analysis as they play an important role in studying the trade balance dynamics.
Haynes and Stone (1982) are the first to define the trade balance as the ratio of a country’s imports over its exports. This way the trade balance is expressed in unit free terms. Using data for 41 countries over a period of 19 years they find mixed evidence for a J-curve effect.
Bahmani-Oskooee and Malixi (1992) apply a model where a lag structure is applied on the real effective exchange rate variable. They use trade data for the period 1973-1985 for 13 less developed countries. Although they find a positive long term effect on the trade balance in most cases, the short term effects do not seem to follow a standard pattern. Besides a J-curve they also find shapes such as N-, M-, and I-curves. These results differ from those of Himarios (1985) with regard to the short-run effects. Both studies however show that in the long run a devaluation leads to a favourable effect on the trade balance.
According to Bahmani-Oskooee and Ratha (2004) the short-run effect on the trade balance from a currency depreciation is country specific. They conclude that the type of
model or data (aggregate or bilateral) used does not indicate an exclusive pattern of the trade balance directly after a depreciation. Nevertheless, regarding the long run effects of a currency depreciation, Bahmani-Oskooee and Ratha argue that models using bilateral trade data are better in explaining the long-run effect of a depreciation on the trade balance than studies using aggregate data.
2.2.2 Bilateral Trade Data Analysis
The previously discussed papers all make use of aggregate trade data in their analyses. This poses a particular threat when analysing the J-curve phenomenon. When aggregate data is used it is possible that the trade balance improves against one country while at the same time worsens against another country. The same situation is possible regarding real exchange rates. These effects might cancel each other out and suppress the actual movements at bilateral levels, this is called aggregation bias (Bahmani-Oskooee and Brooks, 1999). More recent studies therefore use bilateral trade data. This section hence examines the existing literature on the effect of a depreciation on the trade balance using bilateral trade data.
Rose and Yellen (1989) study a possible J-Curve at bilateral level for the United States in the period 1963–1988. Rose and Yellen have several reasons to choose a bilateral approach. First of all they state that a bilateral analysis does not need a proxy for the rest of the world income variable, but most importantly it reduces aggregation bias. Rose and Yellen (1989) estimate a log-linear equation where the trade balance is explained by the logarithm of home and foreign income and the bilateral real exchange rate. The trade balance is defined as the difference between the value of exports and imports. Rose and Yellen find a unit root for all variables; in order to realize stationarity they first-difference these variables. They find no evidence of cointegration amongst the used variables. Next, Rose and Yellen try different lag structures for the explanatory variables but find no evidence of a J-curve and no significant effect of the exchange rate on the trade balance for any lag length.
Bahmani-Oskooee and Brooks (1999) attribute the negative findings of Rose and Yellen (1989) to the following insufficiencies. First, because Rose and Yellen define the trade balance as the difference between exports and imports measured in current US dollars their results are sensitive to the units of measurement. Second, after finding a lack of evidence of cointegration only an autoregressive analysis is used but no error-correction model, which can be used as an alternative to test for cointegration. Within an error correction model the error correction term represents the gap between the dependent and independent variable in the long run. When all variables are adjusting toward their long-run
equilibrium this gap must decrease, this is measured by the coefficient of the error correction term. Therefore when a negative and significant coefficient for the error correction term is found this does not only imply adjustment toward equilibrium but it is also an alternative way of supporting cointegration among variables (Bahmani and Ardalani, 2006). Furthermore, the lag structures used by Rose and Yellen are not based on any objective measure, such as the Akaike Information Criterion.
Shirvani and Wilbratte (1997) use monthly bilateral trade data for the United States and its main trading partners in order to analyse the relationship between the real exchange rate and the United States trade balance. They focus on the period 1973-1990. The authors use the logarithm of all variables in order to obtain elasticities. They estimate the following equation:
𝐿𝐿𝑙𝑙𝑇𝑇𝑡𝑡= 𝛼𝛼 + 𝛽𝛽𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡+ 𝛾𝛾𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡∗+ 𝛿𝛿𝑙𝑙𝑙𝑙𝛾𝛾𝑅𝑅𝑋𝑋𝑡𝑡+ 𝜖𝜖
Here 𝑇𝑇, the trade balance, is defined as exports/imports, creating a unit free trade balance variable. The explanatory variables; 𝑌𝑌 is domestic real income, 𝑌𝑌∗ is foreign real income and 𝛾𝛾𝑅𝑅𝑋𝑋 is the real exchange rate constructed as 𝑃𝑃/𝑅𝑅𝑃𝑃∗, where 𝑅𝑅 is the number of domestic
currency per unit of foreign currency, and 𝑃𝑃 and 𝑃𝑃 ∗ are domestic and foreign price indices. Given the economic theory 𝛿𝛿 is expected to be positive. Shirvani and Wilbratte find that, except for Italy, there is a statistically significant positive effect of the real exchange rate on the trade balance. Additionally, they find that the real exchange rate does not affect the trade balance in the very short run (1 to 6 months), though over the longer period (1 to 24 months), it does positively. This would indicate a horizontally reversed L-curve effect.
Correcting for imperfections of previous studies using bilateral trade data, Bahmani-Oskooee and Brooks (1999) expand the existing literature. They use a model similar to Rose and Yellen but they define the trade balance, like Shirvani and Wilbratte (1997), as the ratio of imports over exports by the country, this way they do not only create a unit free measure but it also reflects the changes of the trade balance in both real and nominal terms. They estimate:
𝐿𝐿𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡𝑗𝑗 = 𝛼𝛼 + 𝛽𝛽𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡𝑈𝑈𝑈𝑈 + 𝛾𝛾𝑙𝑙𝑙𝑙𝑌𝑌𝑡𝑡𝑗𝑗+ 𝛿𝛿𝑙𝑙𝑙𝑙𝛾𝛾𝑅𝑅𝑋𝑋𝑡𝑡𝑗𝑗+ 𝜖𝜖
Where 𝑇𝑇𝑇𝑇𝑗𝑗 is the US trade balance with trading partner 𝑗𝑗, 𝑌𝑌𝑈𝑈𝑈𝑈 is US real income, 𝑌𝑌𝑗𝑗 is country 𝑗𝑗’s GDP, and 𝛾𝛾𝑅𝑅𝑋𝑋𝑗𝑗 is the bilateral real exchange rate between US Dollar and 𝑗𝑗’s currency, such that a decrease implies a real depreciation of the Dollar against the currency of
trading partner 𝑗𝑗 . Next, Bahmani-Oskooee and Brooks use the two step ARDL-ECM approach by Pesaran et al. (2001). This approach allows for estimating both short- and long-run effects simultaneously. In the first step the Pesaran et al. (2001) bounds-testing approach is used to investigate a long run cointegration relationship. Lags of each variable are included separately in the model and an F-test is performed on the joint significance of these lags. Next, an autoregressive distributed lag model where an error correction term is included is used to estimate both the short- and long-run elasticities. This method is effective for both stationary and non-stationary variables, and is performed by including lags of each variable separately into the ARDL-ECM. The error correction term, as explained earlier, furthermore allows to assess the convergence of the trade balance towards its long run equilibrium after a shock in the exchange rate.
The authors use bilateral trade data for the period 1973-1996 and conclude that their study doesn’t support any short run pattern that implies the J-curve phenomenon. The run results however support the economic theory that a real depreciation has a positive long-run effect on the US trade balance.
The two step ARDL-ECM approach by Pesaran et al. (2001) as used by Bahmani-Oskooee and Brooks (1999) has several advantages:
(1) It allows to analyse a long-run cointegration relationship and the short-run dynamics simultaneously.
(2) Variables can be either I(0), I(1) or a combination of both.
(3) The error correction term allows for analysing the convergence towards equilibrium after a shock.
Given the objective of this thesis, analysing the overall effect of a change in the Chinese exchange rate on the Eurozone trade balance with China, the coefficient of interest is that of the real exchange rate in both the short- and long-run. Additionally the variables used in this thesis will most likely not be integrated to the same order. Therefore the two-step ARDL-ECM approach by Pesaran et al. (2001) as used in the study by Bahmani-Oskooee and Brooks (1999) suits this study best and hence forms the preferred base for this thesis’ model and methodology. The model of Bahmani-Oskooee and Brooks (1999) will be extended however by adding exchange rate volatility as control variable to increase the explanatory power of the model. The empirical model and methodology used in this thesis will be explained further in chapter 4.
3. Description of the Variables and Data
This chapter describes the variables and data used in the empirical analysis in this study. The analysis covers the period from 1999 to 2013 and employs monthly data from December 1999 to April 2013. The total number of observations therefore amounts to 160. The start date of the sample period was dictated by the introduction of the Euro in 1999 and the availability of Chinese indices, such as the Industrial Production Index, which is used as an indicator of Chinese national income and was only published from 1999 onward.
3.1 Dependent Variable
Trade Balance: The variable of interest is the bilateral trade balance of the Eurozone with
China. This variable is constructed as a ratio of Eurozone exports to China over Eurozone imports from China in order to create a unit free measure, this is measure the most common in the empirical international trade literature. Data on the exports and imports between the Eurozone and China were provided by Eurostat. Figure 5 shows an increase of the Eurozone-China trade balance from 2005 onward, when Eurozone-China allowed the appreciation of the Yuan.
Figure 5. Eurozone-China Trade Balance (X/M)
Datasource: Eurostat (Graph constructed by author)
3.2 Independent Variables
Eurozone National Income: Eurozone national income is represented by the Eurozone
Industrial Production Index (IPI) since GDP is not available on a monthly frequency. The industrial production refers to the volume of output generated by production in the industrial sectors. The IPI is commonly used as a proxy for income, especially when the observations
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Ja n. 19 99 Se p. 1 999 M ay . 200 0 Ja n. 20 01 Se p. 2 001 M ay . 200 2 Ja n. 20 03 Se p. 2 003 M ay . 200 4 Ja n. 20 05 Se p. 2 005 M ay . 200 6 Ja n. 20 07 Se p. 2 007 M ay . 200 8 Ja n. 20 09 Se p. 2 009 M ay . 201 0 Ja n. 20 11 Se p. 2 011 M ay . 201 2 Ja n. 20 13 EA-CH TB
are monthly. The Eurozone real industrial production index is collected from the European Central Bank (Figure 6).
Figure 6: Eurozone Industrial Production Index
Datasource: European Central Bank (Graph constructed by author)
China National Income: Chinese national income is represented by the Chinese Industrial
Production Index (IPI). The Chinese real industrial production index is collected from the OECD Database Library (Figure 7).
Figure 7. China Industrial Production Index
Datasource: OECD (Graph constructed by author)
Real Exchange Rate: The real exchange rate is defined as: 𝛾𝛾𝑅𝑅𝑋𝑋 = 𝐸𝐸𝐸𝐸 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶
𝐶𝐶𝐶𝐶𝐶𝐶𝐸𝐸𝐸𝐸 , where 𝑅𝑅𝛾𝛾 is the
nominal Euro-Yuan exchange rate and 𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶and 𝐶𝐶𝑃𝑃𝐶𝐶𝐸𝐸𝐸𝐸are the consumer price indices for China and the Eurozone respectively. The nominal exchange rate is defined as number of
80,00 85,00 90,00 95,00 100,00 105,00 110,00 115,00 120,00 Ja n. 19 99 Se p. 1 999 M ay . 200 0 Ja n. 20 01 Se p. 2 001 M ay . 200 2 Ja n. 20 03 Se p. 2 003 M ay . 200 4 Ja n. 20 05 Se p. 2 005 M ay . 200 6 Ja n. 20 07 Se p. 2 007 M ay . 200 8 Ja n. 20 09 Se p. 2 009 M ay . 201 0 Ja n. 20 11 Se p. 2 011 M ay . 201 2 Ja n. 20 13 IPIEA 95,00 100,00 105,00 110,00 115,00 120,00 125,00 Ja n. 19 99 Se p. 1 999 M ay . 200 0 Ja n. 20 01 Se p. 2 001 M ay . 200 2 Ja n. 20 03 Se p. 2 003 M ay . 200 4 Ja n. 20 05 Se p. 2 005 M ay . 200 6 Ja n. 20 07 Se p. 2 007 M ay . 200 8 Ja n. 20 09 Se p. 2 009 M ay . 201 0 Ja n. 20 11 Se p. 2 011 M ay . 201 2 Ja n. 20 13 IPICH
Euro’s per Yuan, hence an increase of the nominal exchange rate indicates an appreciation of the Chinese Yuan and a depreciation of the Euro. The monthly bilateral exchange rate is collected from the European Central Bank. Data on both Eurozone and Chinese CPI is provided by the Federal Reserve Bank of St. Louis. Figure 8 shows an increasing trend of the real exchange rate from 2005 onwards, which indicates a real depreciation of the Euro.
Figure 8. Euro-Yuan Real Exchange Rate
Datasource: ECB and Federal Reserve of St. Louis (Graph constructed by author)
Exchange Rate Volatility: According to McKenzie (1999) exchange rate volatility is
important in explaining changes in trade flows and hence might influence the trade balance as well. As a result exchange rate volatility will be included as independent control variable in the model. Bahmani and Brooks (1999) did not include such a variable for exchange rate risk in their study, so this is an addition compared to their study.
Since the trade balance is the value of exports (𝑋𝑋) minus the value imports (𝑀𝑀), or in this thesis 𝑋𝑋/𝑀𝑀, volatility can only influence the trade balance if the effect of exchange rate volatility is different for exports than for imports. There is no consensus in the existing literature on the direction of the effect of exchange rate risk on exports and imports, neither is there one measure of exchange rate volatility that dominates the literature.
Regarding the effect of exchange rate volatility on imports and exports the empirical literature differs. Concerning the effect on exports the main finding is that volatility effects exports negatively, see for example Doganlar (2002), Vergil (2002) and Baak (2004). The findings on the effect of volatility on imports differ more strongly, Hwang and Lee (2005) find a positive effect while Dickson (2012) finds that the effect can either be positive or negative. The level of risk aversion to exchange rate uncertainty of Eurozone and Chinese
0,0750 0,0850 0,0950 0,1050 0,1150 0,1250 0,1350 0,1450 Ja n. 19 99 Se p. 1 999 M ay . 200 0 Ja n. 20 01 Se p. 2 001 M ay . 200 2 Ja n. 20 03 Se p. 2 003 M ay . 200 4 Ja n. 20 05 Se p. 2 005 M ay . 200 6 Ja n. 20 07 Se p. 2 007 M ay . 200 8 Ja n. 20 09 Se p. 2 009 M ay . 201 0 Ja n. 20 11 Se p. 2 011 M ay . 201 2 Ja n. 20 13 REXEURMB
importers and exporters will hence determine the effect of the exchange rate volatility on the trade balance.
In order to include exchange rate volatility in the empirical model, a proxy for exchange rate risk needs to be constructed. Besides the effect of exchange rate volatility on trade, there is no agreement in the theoretical literature on what is the best measure for exchange rate volatility. The first point of discussion is whether to use the nominal or real exchange rate. Qian and Varangis (1994) state that it does not make a substantial difference whether nominal or real exchange rate measures are used. Although the nominal exchange rate might be better at capturing the risk that determines the uncertainty faced by exporters, others find that the real exchange rate is a more suitable measure, mostly since it has an impact on trade through price competitiveness (Bini-Smaghi, 1991), therefore real exchange rate volatility is used in this thesis.
Next, a measure of exchange rate volatility has to be chosen. Several measures of volatility have been used as a proxy for uncertainty in the existing literature, there is no agreement about the most suitable measure however. Most often it is a measure of variance that is used. Exchange rate volatility can then be constructed as the standard deviation of the exchange rate variable or as a moving standard deviation of the exchange rate over a certain period.
Figure 9. Real Exchange Rate Volatility
Datasource: ECB and Federal Reserve of St. Louis (Graph constructed by author)
Regarding the moving standard deviation there are two measures that are commonly used in the existing literature. Firstly, as a short run measure of exchange rate volatility a 12-month moving standard deviation can be used. In this case each month’s exchange rate volatility is
0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 0,018 Ja n. 19 99 Se p. 1 999 M ay . 200 0 Ja n. 20 01 Se p. 2 001 M ay . 200 2 Ja n. 20 03 Se p. 2 003 M ay . 200 4 Ja n. 20 05 Se p. 2 005 M ay . 200 6 Ja n. 20 07 Se p. 2 007 M ay . 200 8 Ja n. 20 09 Se p. 2 009 M ay . 201 0 Ja n. 20 11 Se p. 2 011 M ay . 201 2 Ja n. 20 13 VOL (12m) VOL (5y)
based on the standard deviation of the exchange rate of the previous 12 months ending that particular month. The 12 month moving standard deviation is commonly used in international trade studies. Secondly, a similar moving standard deviation over a 5 year period can be used to acquire the long run exchange rate volatility (Huchet-Bourdon and Korinek, 2011). However, since the Euro was only introduced in 1999, using a 5 year moving window of the standard deviation would mean that the volatility measure can only be constructed from 2004 onward. This would very much decrease the period of study in this thesis, see figure 9. Using a 12 month moving window would only decrease the number of observations by one year. Therefore within this thesis, the 12 month moving window of the standard deviation is used as a proxy for the real exchange rate volatility.
4. Model and Methodology
This chapter provides the regression model and methodology used in this study to empirically test the effect of changes in the Euro-Yuan exchange rate on the bilateral Eurozone trade balance with China. The chapter explains the two-step autoregressive distributed lag - error correction model (ARDL-ECM) approach by Pesaran et al. (2001). The first step of this approach consists of a bounds-test to investigate a long-run cointegration relationship, this will be explained in section 4.3. In the second step the long-run and short-run elasticities are estimated through an error correction model, this is described in section 4.4. But first, in section 4.1 and 4.2, the empirical model will be presented and the ARDL-ECM approach will be introduced.
4.1 Empirical Model
The focus of this study is on the effect of the Euro-Yuan exchange rate on the Eurozone trade balance with China, therefore the following equation is specified:
𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡 = 𝛼𝛼 + 𝛽𝛽ln𝑌𝑌𝐸𝐸𝑈𝑈𝐸𝐸𝑡𝑡 + 𝛾𝛾ln𝑌𝑌𝐶𝐶𝐶𝐶𝑡𝑡 + 𝛿𝛿ln VOL𝑡𝑡 + 𝜀𝜀lnREX𝑡𝑡 + 𝜖𝜖𝑡𝑡 (1)
The dependent variable 𝑇𝑇𝑇𝑇 is the value of the Eurozone-China trade balance. Besides the real bilateral exchange rate between the Eurozone and China (𝛾𝛾𝑅𝑅𝑋𝑋), which is the variable of interest in this thesis, Eurozone real income (𝑌𝑌𝐸𝐸𝑈𝑈𝐸𝐸), China real income (𝑌𝑌𝐶𝐶𝐶𝐶) and the bilateral exchange rate volatility between the Eurozone and China (𝑉𝑉𝑉𝑉𝐿𝐿) are included as control variables. All the variables are taken as logarithms to allow for the estimation of elasticities. Based on economic theory the sign of the coefficient on Eurozone income is expected to be negative. As the income of the Eurozone rises, the Eurozone will import more and this
will cause the trade balance to decrease. Along the same line of reasoning the coefficient of the national income of China is expected to be positive, as an increase in Chinese national income will probably lead to more imports from the Eurozone which increases the Eurozone trade balance. Since a real depreciation of the Euro, i.e. an increase of the real exchange rate, is expected to encourage the Eurozone exports and discourage its imports from China, the coefficient of this variable is expected to be positive. Finally, the economic theory predicts that the effect of an increase in the volatility of the Euro-Yuan exchange rate on the Eurozone trade balance depends on the difference in the degree of risk aversion between exporters and importers and is therefore unclear. Equation (1) augmented with its short-run dynamics forms the basis of the empirical analysis.
A reduced-form model such as equation (1), where no lagged variables are included, is referred to as a static model and shows the immediate and full adjustment of 𝑌𝑌 after a change in 𝑋𝑋 to the new “equilibrium value” within the same period and represents the effects over the long run (Stock and Watson, 2007). Since it is the aim of this thesis to study the complete post-depreciation dynamics of the Eurozone trade balance with China, both the long-run effects and the short-run effects, i.e. the J-curve, equation (1) needs to be modified to include these short-run dynamics. Typically this is done by formulating equation (1) in an error-correction format. An error-correction model has all the characteristics needed to analyse the dynamics of the trade balance to changes in the Euro-Yuan exchange rate.
Following the article of Bahmani-Oskooee and Brooks (1999) as described in the literature review, one such technique using an error correction model is especially appealing within international trade literature since it can yield the short-run and long-run effects simultaneously; this is the autoregressive distributed lag - error correction model (ARDL-ECM) by Pesaran et al. (2001). Additionally, within the ARDL-ECM a mixture of both I(0) and I(1) variables can be included. An error correction model (ECM) moreover allows for analyzing the convergence of the trade balance towards equilibrium after a shock. Given these characteristics the ARDL-ECM fits this study perfectly.
Pesaran et al. (2001) provide a two-step ARDL-ECM approach that first tests for a long-run cointegration relationship among the variables using the bounds-test approach and additionally investigates the short-run dynamics that allows to estimate both the long- and short-run exchange rate elasticities. Hence the ARDL-ECM allows for the estimation of a long-run relationship between the Euro-Yuan exchange rate and the trade balance and the analysis of a possible J-curve effect between China and the Eurozone. These two procedures and the ARDL-ECM will be explained further in the next section.
4.2 Introducing the ARDL-ECM
Before elaborating on the two step ARDL-ECM approach, the concepts of the Autoregressive Distributed Lag (ARDL) Model and the Error Correction Model (ECM) are explained first. This section will review the use of the traditional ARDL model and its adjustment to the ARDL-ECM which allows for the estimation of the short-run dynamics and long-run relationship when series are integrated of different orders.
To understand the effect of changes in the Euro-Yuan exchange rate on the Eurozone-China trade balance the analysis of a long run relationship between the variables is required. In the case of time series analysis, when the variables are considered stationary, the common approach to estimate the relationship of these series is to use the ARDL Model (Shittu et al., 2012), where ARDL stands for Autoregressive Distributed Lag. The word “autoregressive” refers to the fact that lags of the dependent variable are included in the model, representing that past values of the variable can determine its current value. The word “distributed” refers to lags of the independent variables which are included in addition to the contemporaneous value of the independent variable. These lags represent the fact that the dependent variable can be affected by the independent variables either instantly or postponed. This leads to the following specification of a basic ARDL(1,1):
𝑌𝑌𝑡𝑡 = 𝛽𝛽0+ 𝛽𝛽1𝑋𝑋𝑡𝑡+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1+ 𝛽𝛽3𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡
As an ARDL can have several numbers of lags, generally it can be formulated as follows: 𝑌𝑌𝑡𝑡 = 𝛽𝛽0 + ∑ 𝛽𝛽𝑖𝑖𝑋𝑋𝑡𝑡−𝑖𝑖 + ∑ 𝛾𝛾𝑖𝑖𝑌𝑌𝑡𝑡−𝑖𝑖 + 𝑢𝑢𝑡𝑡
Since the ARDL specification, through its lag structure, includes the different dynamics between the dependent and independent variable over time, it is called a dynamic model. The dynamic ARDL model shows the adjustment from one equilibrium state to another over more than one period, hence the coefficients on the lagged variables constitute the long run effects in the dynamic model. Because of these characteristics an ARDL model can be used to test for a long-run relationship between two time series. Within the ARDL model the error term is assumed to be stationary and independent of 𝑋𝑋 and 𝑌𝑌, in such a case the ARDL model can be consistently estimated by OLS. ARDL analysis becomes more difficult however when the variables are non-stationary, the variables cannot be analysed using the traditional ARDL model in such case.
alternative estimation procedure can be used; cointegration analysis. Cointegration analysis tests for a long run relationship between variables which are integrated to the same order. The principle is, since many time series are nonstationary, that when you regress these series you might get a false result as the variables might only seem correlated because they are all growing over time. This might lead to a spurious relationship.
When two variables 𝑋𝑋 and 𝑌𝑌 are nonstationary and integrated of order one, I(1), it is possible that a linear combination of the two variables, 𝑌𝑌𝑡𝑡− 𝜃𝜃1𝑋𝑋𝑡𝑡, exists where 𝜃𝜃1is chosen to eliminate the common trend. Hence 𝑌𝑌𝑡𝑡− 𝜃𝜃1𝑋𝑋𝑡𝑡 is stationary and I(0). This linear combination represents a long-run cointegrated relationship between the variables, a stationary equilibrium relationship, which allows to investigate the long run relation among the variables (Stock and Watson, 2007) .
The cointegration analysis also has a shortfall however since it cannot be used when the series are integrated to a different order, in such case a long run relationship between two variables cannot be estimated. The approach by Pesaran et al. (2001) who adjusted the ARDL model to an ARDL-ECM model has become the solution in recent literature to determine a long run relationship between time series integrated to different orders. In addition the ARDL-ECM can provide both the short-run dynamics and the long-run relationship simultaneously.
The next part shows how the ARDL model can be augmented with an error correction model to form the ARDL-ECM and to test for a long run relationship in the presence of both stationary and non-stationary time series.
In order to use the ARDL model, the included variables and the error term have to be stationary. In the case of time series integrated to different orders this condition is not met however. Therefore the model has to be transformed in order to obtain a stationary specification. Pesaran et al. (2001) showed that in the case of cointegration and time series integrated to different orders, by de-trending through differencing the variables and forming a stationary linear combination of the non-stationary variables, all the variables within the ARDL are transformed into an ARDL - Error Correction Model with stationary series only. Since between cointegrated time series a linear combination of the time series exists that is I(0) and stationary, by including this combination and differencing the variables the ARDL-ECM specification becomes stationary as well. This allows for the unbiased and consistent estimation of the long-run and short-run effects.
To understand the transformation and the dynamics within the ARDL-ECM, consider the following simple ARDL (1,1) specification:
(1) 𝑌𝑌𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋𝑡𝑡+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1+ 𝛽𝛽3𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 (Then, subtract 𝑌𝑌𝑡𝑡−1 from both sides) (2) 𝑌𝑌𝑡𝑡− 𝑌𝑌𝑡𝑡−1 = 𝛽𝛽0+ 𝛽𝛽1𝑋𝑋𝑡𝑡+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1+ 𝛽𝛽3𝑌𝑌𝑡𝑡−1− 𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 (rewrite)
(3) ∆𝑌𝑌𝑡𝑡= 𝛽𝛽0+ 𝛽𝛽1𝑋𝑋𝑡𝑡+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1− (1 − 𝛽𝛽3)𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 (subtract and add 𝛽𝛽1𝑋𝑋𝑡𝑡−1 to the RHS) (4) ∆𝑌𝑌𝑡𝑡 = 𝛽𝛽0+ 𝛽𝛽1𝑋𝑋𝑡𝑡− 𝛽𝛽1𝑋𝑋𝑡𝑡−1+ 𝛽𝛽1𝑋𝑋𝑡𝑡−1+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1− (1 − 𝛽𝛽3)𝑌𝑌𝑡𝑡−1+ (rewrite)
(5) ∆𝑌𝑌𝑡𝑡 = 𝛽𝛽0+ 𝛽𝛽1∆𝑋𝑋𝑡𝑡+ 𝛽𝛽1𝑋𝑋𝑡𝑡−1+ 𝛽𝛽2𝑋𝑋𝑡𝑡−1− (1 − 𝛽𝛽3)𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 (rewrite)
(6) ∆𝑌𝑌𝑡𝑡 = 𝛽𝛽0+ 𝛽𝛽1∆𝑋𝑋𝑡𝑡+ (𝛽𝛽1+𝛽𝛽2)𝑋𝑋𝑡𝑡−1− (1 − 𝛽𝛽3)𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 Next, Taking (1 − 𝛽𝛽3) = 𝛾𝛾 and (𝛽𝛽1+ 𝛽𝛽2 )= 𝜇𝜇 leads to: (7) ∆𝑌𝑌𝑡𝑡 = 𝛽𝛽0+ 𝛽𝛽1∆𝑋𝑋𝑡𝑡+ 𝜇𝜇𝑋𝑋𝑡𝑡−1− 𝛾𝛾𝑌𝑌𝑡𝑡−1+ 𝑢𝑢𝑡𝑡 (rewrite) (8) ∆𝑌𝑌𝑡𝑡 = 𝛽𝛽0′+ 𝛽𝛽1∆𝑋𝑋𝑡𝑡− 𝛾𝛾(𝑌𝑌𝑡𝑡−1− 𝜃𝜃0 − 𝜃𝜃1𝑋𝑋𝑡𝑡−1) + 𝑣𝑣𝑡𝑡 Where 𝛾𝛾 = (1 − 𝛽𝛽3), 𝜇𝜇 = (𝛽𝛽1+ 𝛽𝛽2 ), 𝜃𝜃0 = 𝛽𝛽0 1−𝛽𝛽3 and 𝜃𝜃1 = 𝜇𝜇 1−𝛽𝛽3
Equation (8) is the traditional ARDL-ECM where, through differencing, the variables are de-trended and stationary. The linear combination (𝑌𝑌𝑡𝑡−1− 𝜃𝜃0− 𝜃𝜃1𝑋𝑋𝑡𝑡−1) is only stationary however if the variables are cointegrated, in which case the combination corresponds to the cointegration relationship which is I(0) and stationary. Therefore only in the case of cointegration among the variables the ARDL-ECM is a stationary specification and can be used to perform unbiased estimation. The ARDL-ECM then allows to analyse the short-run and long-run relationship between the variables and circumvents the problems with the traditional ARDL or cointegration analyses.
The ARDL-ECM states that the current change in 𝑌𝑌 is the sum of two components: (1) The current change in 𝑌𝑌 is related to the current change in X. The coefficient 𝛽𝛽1 of the first difference of 𝑋𝑋, shows how 𝑌𝑌 responds to the current, short run change in 𝑋𝑋.
(2) The current change in 𝑌𝑌 is a partial correction for the degree to which the lag of 𝑌𝑌 deviates from its equilibrium value. This can be seen in the following way. Since (𝑌𝑌𝑡𝑡−1 = 𝜃𝜃0 − 𝜃𝜃1𝑋𝑋𝑡𝑡−1+ 𝑢𝑢𝑡𝑡−1), (𝑌𝑌𝑡𝑡−1− 𝜃𝜃0− 𝜃𝜃1𝑋𝑋𝑡𝑡−1= 𝑢𝑢𝑡𝑡−1). The linear combination (𝑌𝑌𝑡𝑡−1− 𝜃𝜃0 −
𝜃𝜃1𝑋𝑋𝑡𝑡−1) is called the error correction term in this case, as it corresponds to the residual or
error from the previous period. 𝛾𝛾 shows how 𝑌𝑌 responds to the degree of disequilibrium between the variables in the previous period. Within the error correction term 𝜃𝜃1 is the long run multiplier, the long-run effect on 𝑌𝑌 of a change in 𝑋𝑋.
The static long run equilibrium of 𝑌𝑌 is reached when 𝑌𝑌𝑡𝑡= 𝑌𝑌𝑡𝑡−1= 𝑌𝑌� and 𝑢𝑢𝑡𝑡 = 0, then 𝑌𝑌� = 𝜃𝜃0+ 𝜃𝜃1𝑋𝑋 and there is no change of either 𝑌𝑌 or 𝑋𝑋. When 𝑌𝑌𝑡𝑡−1 > 𝑌𝑌�, this indicates that the
value of 𝑌𝑌 in the previous period, exceeds its equilibrium value. In order to converge to its equilibrium value, 𝑌𝑌 has to increase and the change in 𝑌𝑌 has to be positive. Therefore if 𝛽𝛽3<1, 𝛾𝛾 is positive, 𝑌𝑌 will increase and 𝑌𝑌 will decrease when 𝑌𝑌𝑡𝑡−1 < 𝑌𝑌�. These dynamics will make
𝑌𝑌 converge towards its long run equilibrium. 𝛾𝛾 = (1 − 𝛽𝛽3) indicates the speed of adjustment
towards the long run equilibrium. The larger 𝛽𝛽3 is, the faster the adjustment towards the new equilibrium is because the error disappears faster.
4.3 Step I: The Bounds Test Approach to Cointegration
The ARDL-ECM leads to unbiased estimates when time series are integrated to different orders since the ARDL-ECM provides a stationary specification of the variables. One of the elements of the ARDL-ECM specification is the specification of the stationary linear combination of the variables, the error correction term, which is stationary in the case of cointegration. Henceforth a cointegration relationship among the variables is required in order to construct an error correction term and obtain a stationary ARDL-ECM specification. The first step of the ARDL-ECM approach by Pesaran et al. (2001), before being able to estimate the short- and the long-run elasticities, is therefore to analyse whether such a cointegration relationship exists. Following Bahmani-Oskooee and Brooks (1999) and Pesaran et al. (2001), a test for a cointegrating must be performed. For this purpose several tests can be used, most common are the Johansen test for cointegration (Johansen, 1988) or the two step Engle and Granger approach (Engle and Granger, 1987). These cointegration techniques have their limitations however.
To use the Johansen (1988) method all the variables have to be integrated of order one. When there are both stationary variables and non-stationary variables, statistical conclusions based on standard likelihood ratio tests are not valid, the Johansen method can lead to erroneous outcomes in such a case. The cointegration approach of Engle and Granger (1987) on the other hand is not applicable in the case of short samples or when there are structural breaks (Bahmani-Oskooee and Brooks, 1999).
Pesaran et al. (2001) developed a new approach to test for cointegration, the bounds test for cointegration, that can be used regardless of whether the included variables are integrated of order zero, one or a combination of both. Therefore the bounds testing approach overcomes the problems within the Johansen procedure in the presence of variables with different orders of integration. Hence it is a more suitable and relevant method than other
cointegration methods since in this thesis there can be both stationary (exchange rate (volatility)) and nonstationary (imports or exports) variables. The bounds testing approach is used within an (ARDL) model as will be explained in section 4.3.1.
4.3.1 Constructing the Unrestricted ARDL-ECM
In order to perform the bounds test for cointegration an unrestricted error correction term needs to be included in the ARDL model. The unrestricted error correction term is equivalent to the conventional (restricted) error correction term in section 4.2, as the same lagged levels are included as in the traditional ARDL-ECM, the only difference is that the coefficients are not restricted. This allows performing the bounds test for cointegration through an F-test on the coefficients of these lagged variables. In the conventional model the coefficients are restricted because there the error correction term is constructed by estimating the long run equilibrium and its coefficients by OLS first, this is explained further in section 4.4.1.
Following Pesaran et al. (2001) and Bahmani-Oskooee and Brooks (1999) the lagged levels of the variables are included to form the unrestricted error correction term. The additional step of first estimating an unrestricted ARDL-ECM solves the problem of using both I(0) and I(1) variables when testing for a cointegration relation, as is the case in this thesis. The bounds test for cointegration as developed by Pesaran et al. (2001) is conducted by performing an F-test on the joint significance of the coefficients of these lagged variables to test for a long run relationship.
Applying the bounds testing approach on the simple long run regression in equation (1) as a result leads to the following specification for the ARDL approach as an ‘unrestricted’ ARDL-ECM:
∆ 𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡 = 𝛼𝛼 + ∑ 𝛽𝛽∆𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡−𝑖𝑖 + ∑ γ∆𝑙𝑙𝑙𝑙𝑌𝑌𝐸𝐸𝑈𝑈𝐸𝐸𝑡𝑡−𝑗𝑗 + ∑ δ∆𝑙𝑙𝑙𝑙𝑌𝑌𝐶𝐶𝐶𝐶𝑡𝑡−𝑗𝑗 + ∑ ε∆𝑙𝑙𝑙𝑙𝛾𝛾𝑅𝑅𝑋𝑋𝑡𝑡−𝑗𝑗 +
∑ θ∆𝑙𝑙𝑙𝑙𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡−𝑗𝑗 + 𝜕𝜕0𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡−1 + 𝜕𝜕1𝑙𝑙𝑙𝑙𝑌𝑌𝐸𝐸𝑈𝑈𝐸𝐸𝑡𝑡−1 + 𝜕𝜕2𝑙𝑙𝑙𝑙𝑌𝑌𝐶𝐶𝐶𝐶𝑡𝑡−1 + 𝜕𝜕3𝑙𝑙𝑙𝑙𝛾𝛾𝑅𝑅𝑋𝑋𝑡𝑡−1 + 𝜕𝜕4𝑙𝑙𝑙𝑙𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡−1 + 𝜖𝜖
(2)
This specification of the model allows the first step of the procedure to be conducted and to test for a long run relationship among the variables. The coefficients 𝜕𝜕0 - 𝜕𝜕4, represent the long run multipliers and correspond to the long-run cointegration relationship in the conventional error correction model as explained in section 4.2. These are jointly tested for their significance to check for a cointegration relationship. The short-run coefficients are estimated by 𝛽𝛽,…,θ as the coefficients of the differenced variables only include the changes
between two periods and are therefore temporary. Henceforth these coefficients represent the short-run dynamics between the trade balance and the independent variables and will be analysed in the second-step of the procedure, when the conventional (restricted) ARDL-ECM is estimated.
4.3.2 Unit Root Test
Although the bounds test approach for cointegration can be used irrespective of whether the variables are either I(0), I(1) or a combination of both, the variables cannot be I(2) as this leads to spurious results. The F-statistics developed by Pesaran et al. (2001) cannot be interpreted properly in such a case (Pesaran et al., 2001).
Therefore, before applying the bounds test approach for cointegration, the order of integration of the variables has to be determined using a unit root test. For this purpose, the Augmented Dickey Fuller (ADF) test is used. The appropriate lag length for the ADF regression is determined using the Akaike Information Criterion (AIC). The AIC is a statistic that trades-off the goodness of fit and the complexity of a model. It shows how much information is lost for a given model specification. When comparing different lag structures within a model, the model with the lowest AIC is chosen as this is the model with the smallest loss of information.
4.3.3 Bounds Test
The bounds test for cointegration involves an F-test for joint significance of the lagged variables in equation (2), being ∂0, ∂1,…∂4, testing for their cointegration or long run
relationship. Therefore equation (2) has to be estimated through OLS first. Since the F-test result can be sensitive to the lag length however (Bahmani-Oskooee and Ardalani, 2006), the optimal amount of lags on each variable has to be determined in advance.
Since equation (2) is based on the assumption that the error term is serially independent, otherwise the estimation might lead to spurious results, it is necessary to choose enough lags to prevent the possible problem of serial correlation while at the same time choosing not too much lags to avoid over-parameterization of the model (Pesaran et al., 2001). The Akaike information Criterion (AIC) is used to determine the optimal amount of lags to be included within the ARDL-ECM.
As serial independency of the regression errors is a key assumption in the bounds testing approach, additionally the Breusch-Godfrey Lagrange Multiplier (LM) test is used to test for possible serial correlation. Serial correlation could originate either from omitted
variable bias, misspecification or measurement error. The LM test tests for autocorrelation in the errors of the regression model. Serial correlation can lead to inefficient OLS estimates and an overestimated R2.
After selecting the optimal lag structure, the coefficients of the lagged level variables are tested for their joint significance. This is done by performing an F-test on the null-hypothesis (H0: ∂1,… ∂4 = 0) against the alternative hypothesis (H1: ∂1,… ∂4 ≠ 0) of an
existing cointegration relation amongst the variables. As in conventional cointegration testing, like the Johansen or Engle-Granger method, the F-test tests for the absence of a long run relationship between the variables. Absence of such a relationship means zero coefficients for 𝑙𝑙𝑙𝑙𝑇𝑇𝑇𝑇𝑡𝑡−1, 𝑙𝑙𝑙𝑙𝑌𝑌𝐸𝐸𝑈𝑈𝐸𝐸𝑡𝑡−1, 𝑙𝑙𝑙𝑙𝑌𝑌𝐶𝐶𝐶𝐶𝑡𝑡−1, 𝑙𝑙𝑙𝑙𝛾𝛾𝑅𝑅𝑋𝑋𝑡𝑡−1 and 𝑙𝑙𝑙𝑙𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡−1 in equation (2). In the case of
rejecting the null hypothesis there is evidence of a long-run cointegration relationship between the variables.
The F-test used for the bounds testing approach has an asymptotic and non-standard distribution, the bound critical values developed by Pesaran et al. (2001) are used to analyse the computed F-statistic. The critical values for the upper bound can be determined by assuming all variables to be integrated of order one, the lower bound accordingly can be determined by assuming all variables to be integrated of order zero. The upper bound value can also be used if some of the variables are integrated of order one and some order zero, this is why pre-unit-root testing is not necessary (Pesaran at al., 2001).
When the computed F-statistic lies above the upper level bound value, the null-hypothesis is rejected which implies cointegration among the variables. When the F-statistic lies below the lower bound the null-hypothesis cannot be rejected and therefore implies that no cointegration relation among the variables exist. If the F-statistic falls within the band any conclusion regarding cointegration of the variables is inconclusive, in such a case an auxiliary test is needed. Additionally, following Bahmani-Oskooee and Brooks (1999) and Pesaran et al. (2001) the t-statistic of the lagged level of the explanatory variable of interest, the real exchange rate variable can be used as a supplementary test for a cointegration relation using the t-critical values developed by Pesaran et al. (2001). Once a cointegrating relationship is determined, it is possible to calculate the long-run and short-run elasticities.
In the case of evidence for a cointegration relationship, following Bahmani-Oskooee and Brooks (1999), based on evidence by Pesaran et al. (2001) the long-run effects can be extracted from the estimated coefficients in the unrestricted ARDL-ECM by normalizing them on the lagged trade balance variable. Looking back at equation (2), and knowing that in
