Do long-term changes in the real exchange rate impact the trade balance in the United States?

Bachelor’s Thesis

Statement of Originality

This document is written by Student Ioannis Gkalogiannis Koutsogiannis 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.

1. Introduction

1.1. Scope

This paper aims to shed light on whether a long run relationship exists between the trade balance and the real exchange rate. The analysis is focused on the United States and six major trade partners of the country. The six US trade partner countries under investigation are Canada, South Africa, the United Kingdom, South Korea and Mexico. In order to test such a relationship a cointegration technique has been implemented. In addition, statistical tests such as the Augmented Dickey-Fuller and Unit Root tests were used in this research.

1.2 Background

Following the breakdown of the Bretton-Wood system, participant countries have allowed their currencies to fluctuate, altering sometimes significantly the terms of trade. A change in the real exchange rate has potentially a debatable effect on the trade balance of a country. According to the elasticity approach and the Marshall-Lerner condition, a depreciation of the exchange rate is followed by an improvement of the current account of the home country in the long run (Keith Pilbeam, 2013). Justification behind this theory is that prices will adjust much quicker to economic changes than allocation of recourses. Therefore, the effect of changes in the real exchange rate on the trade balance has attracted a lot of researcher’s attention.

According to Machlup (1955), although the elasticity approach has been the most popular method to investigate the relationship between the trade balance and the real exchange rate so far, the technique comes with a few downsides. Increased exports favored by a lower currency lead to an increase in domestic income, which leads to an improvement of the balance of payments, something that is neglected by the elasticity approach, which assumes a constant level of income. An alternative to the elasticity approach is the income absorption approach. As described by Sidney Alexander’s paper (1952), the absorption approach states that the effect of a currency devaluation on the balance of payments will depend on three things. These are, the effects of devaluation on income, the effects of income on the absorption and the direct

effects of devaluation on the absorption. According to Machlup (1955), although the absorption approach takes income changes into account, it neglects relative prices between countries. In other words, factors such as inflation and monetary aspects cannot be considered under the absorption approach. Therefore, as shown by SC Tsiang (1961), the absorption approach should be considered as a complementary method to the elasticity approach rather as a substitute.

The cointegration approach is an alternative method to the elasticity and absorption approach that has been gaining popularity among researchers the last few years due to recent econometric advances. According to Granger (1986), the technique aims to establish a direct relationship between the trade balance and the real exchange rate. Finally, according to Bahmani-Oskooee (1991), cointegration analysis is considered to be a substitute to the elasticity approach as both methods search for the existence of a long run relationship. 1.3 Outline In the following section a literature review of related past research is discussed. In the third section a detailed analysis of the methodology pursued is provided, whilst the results of this research are demonstrated in section four. Finally, a conclusion is provided in the last section of this paper.

2. Literature review

As mentioned above the cointegration technique aims to establish a direct long-term relationship between the trade balance and the real exchange rate. According to Granger (1986), certain economic variables do not diverge from each other in the long run. That is, some divergence may occur in the short-run, however, paired variables seem to wander in the long term interdependently rather individually as one has the tendency to adjust for changes in the other. According to Granger (1986) and Engle and Granger (1987), a stationary time series, with no deterministic component has a mean that is crossing rather often over the years, thus it has a tendency to return and flactuate around it with short-term and rare stochastic excursions away from it. On the other hand, a nonstationary time series has a stochastic trend and no mean to return to. It will also wonder wildly and away from previous values. According to Granger (1986), in general when two time series 𝑥_!, 𝑦_!, have a similar stochastic trend over the years, there should be a linear relationship that the two variables almost entirely cancel each other out. If that is the case, the two time series will be cointegrated thus, have a special relationship in the long run. Examples of such economic variables can be inflation and wages, income and government expenditure or certain stock markets around the globe. In such cases, cointegration technique is often implemented to investigate a long-term relationship between the paired variables.

An alternative way to test for cointegration between time series was pioneered by Johansen (1988). Engle and Granger’s methodology to investigate existence of cointegration involves testing the stationarity of the residuals of a bivariate relationship described by a regression model. On the other hand, Johansen’s methodology involves a process where more relationships are taken into account and the parameters of the cointegration vectors are calculated by maximum likelihood estimation. According to Gonzalo and Lee’s comparison of the two cointegration techniques, although Engle and Granger’s method was found generally more robust, both methods were recommended in order to avoid pitfalls, such as spurious cointegration (Gonzalo and Lee’s, 1997). The present paper though is delimited to the first method of Engle and Granger.

2.1 Previous research with Cointegration analysis

Popularity of cointegration analysis has been growing the last few years due to recent econometric advances (Hakkio and Rush, 1991). As a result, an increasing amount of scientists have shown their approval and accommodated the technique to their research. Some indicative examples of the technique are briefly presented below. In Kanas’s paper (1998), research was conducted on potential linkages between the US stock markets and stock markets in several European countries. However, no pairwise cointegration was found between any of the investigated countries. In this paper Kanas has opted for the Johansen test instead of the Engle and Granger test to investigate cointegration as many variables were involved in his research. Lardic and Mignon (2008), having rightly suspected asymmetries in the links between oil prices and national income in the United States, have proceeded to identify asymmetric cointegration between the two variables. Their paper has used both methods for cointegration, however, the researchers have detected asymmetric cointegration between oil prices and income only with the Engle and Granger method, as the Johansen test has indicated no asymmetric cointegration. Finally, according to Ghali (1999), there is a long run relationship between price and wages, however, the exogenous factors of import prices and output gap have to enter the analysis in order for a long-term relationship to be established through multivariate cointegration.

2.2 Cointegration, Trade balance and Real interest rate

The pair of economic variables under consideration in this paper is the trade balance and the real exchange rate. Cointegration analysis has recently become an increasingly popular method among scientists looking to test the long run relationship of these two economic variables. A few indicative examples of studies using cointegration analysis to establish a relationship between the trade balance and the real exchange rate are briefly discussed below. According to Narayan (2006), the trade balance and the real exchange rate between China and

the United States are strongly cointegrated, as the two time series were found to have a relationship in the long run as well as in the short run. Findings in the paper have also shown that there was no J-curve adjustment in their relationship, as a real devaluation of the Chinese currency will improve China’s trade balance with the United States. According to Rahman et al. (1997), the long run relationship between the trade balance and the real exchange rate in the case of Japan and the United States was tested with cointegration analysis and an Engle-Granger Augmented Dickey Fuller test was performed to investigate existence of cointegration. According to the study’s results, there was no empirical evidence to conclude the two variables had a long run relationship. According to Ng, Har and Tan (2008), the US-Malaysian trade balance and the US-Malaysian real exchange rate show clear signs of cointegration and as a result, a long run relationship can be indicated. Furthermore, the researches have used two cointegration methods to investigate the relationship. Both the Engle-Granger Augmented Dickey Fuller and Johansen test have shown in their paper that cointegration exists between the two time series. Bahmani-Oskooee and Hegerty (2011) have generated empirical evidence by cointegration analysis that the trade balance of only 24 out of 102 industries has improved after a real long run depreciation of the exchange rate had occurred. Finally, Bahmani-Oskooee (1991) has shown in his research that a real long run depreciation will improve the trade balance of most least developed countries that he chose to investigate. In his analysis cointegration techniques and an Engle-Granger Augmented Dickey Fuller test were implemented.

When testing for cointegration to provide empirical evidence on linkages between the trade balance and the real exchange rate, it is important to select a long period of time or the research’s data. According to Hakkio and Rush (1991), cointegration is a long-run concept. Therefore, long run spans of data are necessary to make cointegration tests more powerful. Long-term time series capable of generating more observations on long run fluctuations are present in most of the studies searching for cointegration. Some of the studies that have been discussed above are mentioned again as illustrative examples for data

selection. Bahmani-Oskooee and Hagerty (2011) are using for their study on US-Mexico trade and the J-curve annual data from 1962 to 2004. Ng, Har and Tan (2008) have used annual data from 1955 to 2006 in their paper about Malaysia and the relationship between the trade balance and the real exchange rate. Finally, Narayan (2006) has used quarterly data from 1973 to 1993 and Rahman et al. (1997) monthly data from 1979 to 2002 in analogous studies involving cointegration analysis. Therefore, according to previous research, when dealing with cointegration analysis, a long time span of data should be preferred as it will generate sufficient number of observations to capture the long run fluctuations of the exchange rate and the trade balance.

3. Methodology

3.1 Countries, explanatory variables and period of data

In order to investigate the relationship between the real exchange rate and the trade balance six major trade partners of the United States have been selected to test this relationship. The six trade partners under consideration in this paper are Canada, South Africa, the United Kingdom, Australia, South Korea and Mexico. Furthermore, according to previous economic research (Hakkio and Rush, 1991), cointegration analysis investigates a long run relationship. Therefore, the longer the time span of data, the more sufficient the number of observations will be for such an analysis. As a result, a time span of three decades has been selected for each case for this research based on cointegration analysis.

To investigate for a potential relationship between the trade balance and the real exchange rate, historical data have been collected for the following economic variables, US Exports to the other countries, US Imports from the other countries, the price level of the home and foreign countries as well the nominal exchange rates for each pair of countries. These economic variables are explained in more detail below. 𝑇𝐵_! Trade balance between the United States and one of the six trade partners, _𝑇𝐵 != 𝐸𝑋!/𝐼𝑀! 𝐸𝑋! US exports to one of the six trade partners 𝐼𝑀_! US imports from one of the six trade partners 𝑅𝐸𝑅_! Real exchange rate between the United States and one of the six trade partners, _𝑅𝐸𝑅 != (𝑃 ∗ 𝐸!/𝑃) 𝐸_! Nominal exchange rate between the United states and one of the six trade _partners. 𝑃∗ _{Foreign price level measured by the consumer price index, CPI} 𝑃 Domestic price level measured by the consumer price index, CPI

Where t stands for the corresponding period and indicate variable is a time series. Also, It should be noted that home country in this analysis is assumed to be the United States and the nominal exchange rate is therefore defined as units of foreign currency per one unit of domestic currency (US dollar). In addition, the consumer price index, CPI, is in an index form with 2010 base year. As far as the trade balance is concerned, it is typically calculated by subtracting imports from exports. However, according to Bahmani-Oskooee (1991), when the trade balance is defined as the ratio between exports and imports, it will be insensitive to changes in the unit of measurement of exports and imports. Therefore, given United States is the home country, the ratio of home exports (EX) to home imports (IM) has been decided to be the trade balance instead of the difference between the two. Finally, according to Hakkio and Joines (1990), the trade balance depends on the relative demands of imports and exports that is, how domestic goods compete with foreign goods in relative prices. Therefore, changes in the nominal exchange rate can influence the trade balance only insofar as they change the real exchange rate. As a result, the real exchange rate is the appropriate variable for this analysis.

As mentioned above, data have been drawn approximately from a three-decade period apart from in Mexico’s case where the period was restricted to two decades due to data unavailability. In addition, frequency of data is monthly or quarterly. Table 1 shows in more detail the period and frequency of data for each US trade partnership.

Trade partnership Frequency Period

Canada – US Quarterly 1985 – 2014 S. Africa – US Quarterly 1985 – 2014 UK – US Monthly 1985 – 2015 Australia – US Quarterly 1985 – 2015 S. Korea – US Monthly 1985 – 2015 Mexico – US Monthly 1994 – 2015 Table 1: Frequency and period of data

It should be mentioned that data start from the first period of the first year and finish on the last period of the last year without any missing observations. This applies to all six cases.

3.2 Data sources

Data for US imports and exports have been procured by the Federal Reserve Bank of St. Louis (FRED), whereas consumer price index (CPI) data have been collected from the Organisation for Economic Co-operation and Development (OECD) for all seven countries including the United States. Finally, the data source for the nominal exchange rate between the United States and Canada, Australia and South Africa has been the U.S. Census Bureau, whereas data for the nominal exchange rate between the United States and Mexico, the United Kingdom and Korea have been obtained from the Federal Reserve Bank of St. Louis (FRED).

3.3 Test Procedure

According to Granger (1986) and Engle and Granger (1987), the stationarity condition for the trade balance and real interest rate should be investigated. That is, the two time series need to be differentiated, potentially more than once, until they reach a stationary condition. In general, if the trade balance, 𝑇𝐵_! and the real exchange rate, 𝑅𝐸𝑅! are integrated of the same order that is 𝑇𝐵!~𝐼(𝑑) and 𝑅𝐸𝑅_!~𝐼(𝑑), it holds that any linear combination of the two will be integrated of the same order d. However, if there is a number 𝜃, such that 𝑧_!= 𝑇𝐵_!− 𝜃𝑅𝐸𝑅_! is integrated of order zero that is 𝑧_!~𝐼(0), then the two time series will be cointegrated and the number 𝜃 will be called the cointegrating coefficient. If the error term 𝑧_! is in a stationary condition then the two time series should have some sort of association in the long run.

In case the level of integration differs, it is assumed that the time series have no sign of cointegration and thus, deemed unrelated. In order to identify the level of integration, a unite root test is performed for every case. For this purpose we rely on the Augmented Dickey Fuller test. According to Ng and Perron (2001), a modification of Akaike information criterion (AIK), the MAIC, is proven to be an improved criterion for lag selection. As a result, the choice of lag

length is based on MAIC criterion for all of the tests performed in this paper. For the trade balance (TB) and the real exchange rate (RER), the Augmented Dickey fuller test is formulated as follows. 𝛥𝑇𝐵! = 𝑎 + 𝑏𝑇𝐵!!!+ 𝑞! ! !!! 𝛥𝛵𝛣!!!+ 𝑒! 𝛥𝑅𝐸𝑅!= 𝑐 + 𝑑𝑅𝐸𝑅!!!+ 𝑠! ! !!! 𝛥𝑅𝐸𝑅!!!+ 𝑤! 𝛥𝑇𝐵! and 𝛥𝑅𝐸𝑅! in the two equations above are the first differences of the trade balance and the real exchange rate respectively. The first difference of each variable in the two equation is the change in the value of 𝑇𝐵_! or 𝑅𝐸𝑅_! between period t-1 and t. Furthermore, 𝑇𝐵!!! and 𝑅𝐸𝑅!!! are the first lagged variables for trade balance and real exchange rate respectively, while 𝑒_! and 𝑤_! are the corresponding error terms of the two equations. In addition, 𝑎 and 𝑐 are constants, while 𝑏 and 𝑑 are the coefficients of trade balance’s and real exchange rate’s first lagged variables. Also, q and s are coefficients of other lagged variables of the trade balance and the real exchange rate respectively. The test is performed for all pairs of countries and its purpose is to investigate whether the coefficients of the first lagged variables are equal to zero. Thus, when b or d is equal to zero, the trade balance or the real exchange rate is assumed to be a stationary variable. The corresponding null and alternative hypothesis of the test for the trade balance is as follows. 𝐻_!: 𝑏 = 0 𝐻_!: 𝑏 ≠ 0 That is, the coefficient of the first lagged variable is equal to zero under the null and different than zero under the alternative hypothesis. Accordingly, the null and alternative hypotheses for the real exchange rate are as follows.

𝐻_!: 𝑑 = 0 𝐻_!: 𝑑 ≠ 0

If the null hypothesis is not rejected for both tests and both coefficients, b and d are equal to zero, the two time series, 𝑇𝐵! and 𝑅𝐸𝑅! are said to be both integrated of order one, 𝑇𝐵_!~𝐼(1) and 𝑅𝐸𝑅_!~𝐼 1 . If the null hypothesis is not rejected in both cases and both coefficients, b and d, are different than zero, we conclude that the time series are not integrated of order one and thus, proceed by taking the second differences of the trade balance and the real exchange rate. Then, by following the same methodology we test for stationarity. We continue to differentiate the two time series and test their stationarity until we find their integration order. However, if the null hypothesis is accepted for one and rejected for the other, we conclude that the two time series will be integrated of a different order. If this is the case, we cannot proceed with our analysis any further.

As soon as we establish that both the trade balance and the real exchange rate are integrated of the same order, existing cointegration between the two time series can be investigated. For this purpose a two-step Engle Granger Augmented Dickey Fuller (EG-ADF) test has been chosen to determine whether cointegration exists between the two. The first step of the test is an Ordinary Least Square regression between the two variables (Stock & Watson, 2012). Specifically, the trade balance is regressed on the real exchange rate. From this regression the cointegrating coefficient as well ad the error term can be estimated. The regression equation is formulated as follows: 𝑇𝐵! = 𝛼 + 𝜃𝑅𝐸𝑅!+ 𝑧! where 𝜃 is the cointegrating coeeficient, 𝛼 is a constant and 𝑧_! is the error term of the equation. The second step of the Engle Granger Augmented Dickey Fuller test is to investigate whether or not the error term 𝑧_! is stationary that is integrated of

order zero. The order of integration is investigated once again with the Augmented Dickey Fuller test and a similar methodology to the one described above for the trade balance and the real exchange rate has been followed. If the error term 𝑧_! is stationary, then the two time series of the trade balance and the real exchange rate are said to be cointegrated. Therefore, cointegration implies the existence of a long run relationship as the two variables are following a similar path in the long-term. Stated otherwise, in case of cointegration, there is statistical evidence to believe a change in the real exchange rate will have an impact on the trade balance especially in the long run.

4. Results

In this paper six major trade partners of the United States have been under consideration. Specifically, Canada, South Africa, the United Kingdom, Australia, South Korea and Mexico have been selected to investigate whether changes in the real exchange rate affect their trade relationship with the United States. Canada, South Africa and the United Kingdom were the three countries to alter their trade balance with the United States following persistent changes in the real exchange rate. As far as the other three are concerned, there were not enough statistical evidence to claim presence of cointegration between their trade balance and real exchange rate, thus no relashionship was established between the two variables for these countries.

As mentioned in the methodology section above, we first had to make sure that both trade balance and real exchange rate for each country were integrated of the same order. In the cases of Canada and Australia, the trade balance and the real exchange rate had to be differentiated twice in order to reach stationarity. In the cases of South Africa, the United Kingdom and South Korea the first difference was enough to bring both variables to a stationary condition. However, in Mexico’s case, we could not proceed further with our cointegration analysis, as there were significant indications of differences in the order of integration between the trade balance and the real exchange rate. These findings are demonstrated in Table 2 below.

𝑇𝐵! 𝑅𝐸𝑅!

MAIC ADF Int. Order MAIC ADF Int. Order

Canada 8 -20.96 𝐼(2) 8 -14.57 𝐼(2) S. Africa 12 -3.67 𝐼(1) 10 -3.42 𝐼(1) UK 16 -5.29 𝐼(1) 16 -5.41 𝐼(1) Australia 8 -5.46 𝐼(2) 8 -5.03 𝐼(2) S. Korea 14 -5.01 𝐼(1) 8 -5.28 𝐼(1) Mexico 12 -3.16 𝐼(1) 1 -0.26* 𝐼 𝑑 > 𝐼(1)

Table 2: Augmented Dickey Fuller test statistics for TB!, RER! from their first or second

differences * Indication for (absolute) ADF test statistic lower than its 5% critical value (accept 𝐻!) According to the third column in Table 2, the trade balance and the real exchange rate for Canada and Australia are integrated of the same order two. Also, these two variables for South Africa, the United Kingdom and South Korea were all found to be integrated of order one. These two variables for Mexico though, had to be treated differently as they were found to have a different integration order. Specifically, as the table indicates for Mexico, the trade balance is integrated of order one, whilst there is not enough statistical evidence to support a stationary condition for the first difference of the real exchange rate, which implies that the real exchange rate is integrated of a higher order than one. Thus, we cannot proceed further with cointegration analysis and we assume that no relationship between the trade balance and the real exchange rate exists in Mexico’s case.

Once the countries with integrated variables of the same order had been distinguished, the analysis went further with the Engle-Granger Augmented Dickey Fuller test. During the first part of the test, which is the linear regression, the cointegrating coefficients had been estimated for each country except for Mexico. Furthermore, in this part of the test, the error terms z! were also estimated for the cases of Canada, South Africa, the United Kingdom, South Korea and Australia.

When the error terms z_! for the five countries had been estimated the analysis proceeded to the second step of the Engle-Granger Augmented Dickey Fuller test. During the second stage of the test, stationarity of the error terms had been checked. Therefore, an Augmented Dickey Fuller test was performed for each country in order to establish the order of integration and detect stationarity. The outcome of the five tests is demonstrated in Table 3 below.

𝑧_!

MAIC ADF Int. Order

Canada 3 -3,851 𝐼(0) S. Africa 3 -3,851 𝐼(0) UK 14 -2,855 𝐼(0) Australia 3 -1,970* 𝐼 𝑑 > 𝐼(0) S. Korea 12 -1,847* 𝐼 𝑑 > 𝐼(0) Mexico - - - Table 3: Augmented Dickey Fuller test statistics for z! * Indication for (absolute) ADF test statistic lower than its 5% critical value (accept 𝐻!) As indicated in the third column of Table 3, the error terms 𝑧_! for Canada, South Africa and the United Kingdom are all at 5% significant level integrated of order zero, therefore, they are assumed to be stationary. It is worth mentioning that in the case of the United Kingdom the error term actually failed the stationarity test by a very small margin. Specifically, it was found that the p-value for its statistic was 0.0508, which is slightly larger than the 5% significant level that it was conditioned upon. Nevertheless, we assume the error term passes the stationarity test, as the absolute value of its test statistic (2,855) is just marginally smaller than its corresponding critical value (2,876). The situation is quite different for Australia and South Korea. Both cases indicate errors of a higher integration order than zero at 5% significant level. Thus, the two errors for these two countries are assumed to be non-stationary.

These findings presented in Table 2, conclude our cointegration analysis and indicate that the trade balance and the real exchange rate in Canada, South Africa and the United Kingdom have a long run relationship as the corresponding errors are found to be stationary. On the other hand, there is no sign of a long run relationship between the trade balance and the real exchange rate in the cases of Australia and South Korea, as the corresponding errors of these countries appear to be non-stationary in our analysis. As a result, cointegration was found only in the first three cases.

According to these findings, Canada, South Africa and the United Kingdom are all assumed to have cointegrated time series of trade balance and real exchange rate. Furthermore, since cointegrating coefficients for these three countries are all positive and significant, it is inferred that a depreciation of the US Dollar, the home currency, or an increase in the real exchange rate will probably improve the trade balance of the United States with the other country in the long run. Thus, a more general approach to our findings so far implies that a devaluation of the home currency will improve the terms of trade for the home country in the long run. On the contrary, for Mexico, South Korea and Australia, the trade balance and the real exchange rate are assumed to be independent as no evidence of cointegration was found. However, failing to detect cointegration in these countries could be down to a short time span of data in Mexico’s case or other peculiarities such as fixed exchange rate regimes that might impede an investigation on the relationship between the two variables.

5. Conclusion

In this paper an attempt to establish the existence of a long run relationship between the trade balance and the real exchange rate was made. Cointegration analysis with a two-step Engle-Granger Augmented Dickey Fuller test has been the foundation of this research. In the end, empirical evidence was found in support of an existing long run relationship as well as against it. Specifically, cointegration was found in three out of the six cases under consideration. Cointegrated trade balance and real exchange rate time series in the cases of Canada, South Africa and the United Kingdom indicate that according

to this paper’s findings a depreciation of the US Dollar with respect to one of these three currencies will generally have a positive impact on the trade balance between the United States and that country in the long run. On the other hand, no cointegration thus, no relationship was found between the trade balance and the real exchange rate in the cases of Australia, South Korea and Mexico.

Although results have been robust in this paper and found to be significant, one should not be in rush to make any conclusions or judgments. As indicated previously, cointegration analysis with an Engle-Granger Augmented Dickey Fuller test is not the only option and sometimes, alternative techniques such as the Johansen test should be seen as more appropriate. According to previous research, when dealing with cointegration analysis, a multi-method approach will usually provide the most accurate results and thus, inferences closer to reality. However, it is believed that the methodology pursued is the most suitable to address the research question in this paper.

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