The determination of the Sterling Equilibrium Exchange Rate and the Impact of Brexit Scenarios.

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Faculty of Economics and Business

The determination of the Sterling Equilibrium Exchange Rate

and the Impact of Brexit Scenarios.

Master Thesis International Economics and Business

University of Groningen

Name: J.T. (Joost) de Haan Student number: S2522837

Student e-mail: j.t.de.haan.1@student.rug.nl Supervisor: dr. A.C. Steiner

Co-assessor: prof. dr. D. J. Bezemer Version: Resit Version

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Abstract

This paper aims to determine equilibrium real effective exchange rate of the sterling and the impact of Brexit scenarios. The methodology used is based on the co-integration approach. The variables used are the real effective exchange rate, the terms of trade, the non-tradable to tradable ratio, trade openness, money supply, a real interest rate differential and a risk premium. The sample consists of monthly data covering the period 1999M1-2017M2. Due to the three co-integration equations found, a vector error correction model is used to estimate a term relationship with the dependent variable to derive the long-run elasticities. These are used to determine the equilibrium real effective exchange rate of the UK. With the derived elasticities, shocks are applied to the real effective exchange rate to assess the impact on its equilibrium values. The results indicate that the expansionary monetary policy conducted by the BoE holds the real effective exchange rate of the sterling near long-term equilibrium values despite current political and economic uncertainty surrounding the Brexit. Furthermore, the shocks applied to the equilibrium real effective exchange rate show that the relative price competitiveness measure terms of trade has the biggest impact, causing a 0.03% increase in the equilibrium exchange rate. The outcome of the negotiations with the EU and its impact on the equilibrium exchange rate will highly depend on the terms of trade.

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1. Introduction

In June 2016, the citizens of the United Kingdom (UK) had to decide on whether or not to leave the European Union (EU), known as the Brexit referendum. Although it was by a tight margin (52%:48%), a majority voted in favor of a Brexit and the UK government had to start preparing the country for a political and economic break with their main trading partners. The EU constituted for 44% of UK’s total exported goods and services in 2015 and 53% of UK imports came from the EU (Office for National Statistics, 2016). The political magnitude and the uncertainty surrounding the economic implications caused financial markets to decline. Figure 1, shows the valuation of the sterling against the Euro during the entire referendum process and shows a sharp depreciation after the outcome. Comparing the nominal UK/US exchange rate, a decline of nearly 20% till January 2017 shows a similar depreciation after the Brexit outcome. Plakandaras et al. (2017) find that the uncertainty surrounding the Brexit, measured by Economic and Political Uncertainty (EPU) indices, explain deviations of the UK/US nominal exchange rate. This nominal depreciation of the sterling can temporarily boost UK exports as the depreciation increases foreign demand for UK goods and services. However, for UK policy makers and businesses the real effective exchange rate (REER) is a more appropriate indicator as it measures the trade weighted average value of the sterling against a basket of foreign currencies, adjusted for inflation. Misalignment is the overvaluation/undervaluation of the REER from its long-term equilibrium value and is an important indicator for monetary policy as this equalizes the current account (CA) balance. Additionally, the long-term value of the REER will depend on possible negotiation outcomes with the EU, starting March 2017. Switha and Sampson (2016) discussed four possible Brexit scenarios: (i) the European Economic Area (EEA), (ii) through bilateral trade agreements (BTA), (ii) Free Trade Agreements (FTA), and (iv) under World Trade Organization (WTO) guidelines and considered the EEA and WTO scenarios to be the most likely to occur.

This raises the following three research questions: First, what is the equilibrium real effective exchange rate of the sterling relative to seven main trading partners of the UK between 1999M1 till 2017M2? Secondly, is the sterling overvalued, undervalued or at equilibrium value? Lastly, what are the effects of shocks on the sterling equilibrium real effective exchange rate in a EEA and WTO Brexit scenario?

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To answer the first research question, the behavioral equilibrium exchange rate (BEER) approach of Clark and Macdonald (1998, 2004) is used. This model enables to make a distinction between short-term and long-term economic variables affecting the real exchange rate and can estimate whether the REER is of the UK. The countries chosen are Belgium, France, Germany, Italy, the Netherlands, Switzerland and the US. The countries are chosen based on their relative share of trade with the UK. Monthly time series data is used to conduct the research, ranging from January 1999 till February 2017. At the moment of writing, there is no research paper relating the Brexit and the real exchange rate. Although the outcome of the Brexit itself remains highly unsure, this paper attempts to add to the literature available on the possible economic impacts of the Brexit on the UK. The data covers the latest International Finance Statistics (IFS) data available at the moment of writing.

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Figure 1: Relevant events during Brexit referendum and the EURO-GBP nominal

exchange rate

Source: Armorsson and Zoega (2016).

2. Literature Review

2.1 History of sterling exchange rate development and

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Figure 2: Development of GBP/USD nominal exchange rate and REER 1980m1-2017m2.

The first empirical literature assessing the effects of a Brexit on the UK economy are starting to reveal. In more recent work by Switha et al. (2017) a distinction between the impact of a “soft Brexit” scenario (EEA), and a “hard Brexit” scenario (WTO). Estimates of trade elasticities derived from literature is used to measure the changes in UK trade flows and the effect on income levels in the UK. This paper follows a similar distinction of Brexit scenarios and the predicted changes in trade cost to analyze the effects on the REER. The incurred trade cost in the different scenarios are divided in tariff barriers, non-tariff barriers (NTB). In earlier work, Pavlidis et al. (2011) found that trade cost positively affects the dollar-sterling real exchange rate as it explained deviations from the long-term equilibrium. The assumptions for the different scenarios are listed Table 1. This research relates the impact of the Brexit scenarios in recent empirical research and the impact on the REER of the UK. Therefore, the assumptions of the different scenarios are taken as guidelines to assess the impact of the shocks on the REER. To gain further insight in the dependent variable, the concept of exchange rates is further explained in the next section. It will attempt to summarize the theory and the measurement of the real equilibrium exchange rate. GBP/USD=100 REER, Jan2005=100 50 10 0 15 0 20 0 25 0 An nu al a ve ra ge R ee r / a nn ua l a ve ra ge G BP U SD 1980 1985 1990 1995 2000 2005 2010 2015

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8 Table 1: Possible Brexit scenarios

2.2The equilibrium exchange rate

General economic theory states that the equilibrium exchange rate is a condition that equals the demand and supply of the same currency. However, the concept of equilibrium exchange rate can be measured using various definitions of relevant prices and can cover different time spans. As mentioned by Driver and Westaway (2004), all different equilibrium concepts are useful depending on the research question to be answered. It is therefore important to determine which definitions of exchange rates are applicable for the research question at hand.

The most known relative price measure is the nominal exchange rate, which is determined directly in financial markets and is defined as the price of domestic currency per unit of foreign currency. In a seminal paper by Cassel (1918), the Purchasing Power Parity (PPP) theory is derived from the “Law of One Price” (LOOP). It states that in an open economy with identical consumer preferences and no trade impediments, domestic and foreign Brexit

Scenario

Assumptions: Incurred Trade Cost

(i) EEA - There is single market access - Independent trade negotiations countries outside of the EU. - Implement Single Market policies - Not part of EU’s

customs union - Contribute to EU budget 5% (ii) WTO - Independent trade negotiations - Not required to adopt EU economic policies and regulations - No obligation to contribute to the EU budget

- Trade with EU subject to MFN tariffs and any non-tariff barriers that comply with WTO agreements.

- No freedom of movement of people with the EU. - No right of access to

EU markets for service providers.

- Goods exported to the EU must meet EU standards

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prices of goods should be equal in the long-term. However, the nominal exchange rates do not incorporate adjustments for differences in price levels of goods between countries. For an economy, it is more valuable to have a better understanding in the domestic price of a good in terms of another country’s goods price

The real exchange rate (RER) can be more formally written as:

𝑅𝐸𝑅 = 𝑒(

𝑃

∗

𝑃

)

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where e is the nominal exchange rate between two countries stated in units of domestic currency per unit of foreign currency and implies that an increase in the nominal exchange rate appreciates the domestic currency. 𝑃∗ is the average foreign value of a good, and 𝑃 is the average domestic value of a good. Holding prices equal to one, changes in the nominal exchange rate would cause a similar appreciation of the RER. If the relative domestic prices increase through inflation, the nominal exchange rate should increase to hold the RER in equilibrium since we assume that long-term prices converge.

The empirical validity of the PPP theory is highly debated. Testing for its validity, Kugler and Lenz (1993) use monthly data for the Deutsche Mark (DM) compared to 15 different currencies, including the sterling between 1973-1990. Using Johansen’s multivariate co-integration method, the authors find that relative PPP holds in the long-term. In more recent work, Huan and Yang (2015) compared relative prices in EU countries before and after the adoption of the euro as its currency. It is hypothesized that PPP is more likely to hold for the period 1999-2013. Surprisingly, the results show more evidence for the condition to hold in the time period before the adoption of the euro. For EU countries not using the euro, a strong support was found throughout the entire sample period (1957-2013). This can either be explained by the short sample period or due to the transition of all domestic currencies into the single Euro nominal exchange rate. In other work, Lothian (2016) used panel data covering up to 28 countries on three different time periods; the gold standard era, the interwar period and post-World War II till 1998. The results show that price levels react as theory would predict under the different monetary regimes. Under a flexible exchange rate regime, the exchange rate will adjust to hold PPP against the country with a higher level of expansive monetary policy. While Sarantis and Stewart (1993) find that the PPP does not hold in the long-term for the sterling relative to nine different bilateral exchange rates using co-integration techniques on quarterly data between 1970-1990. Next, the dependent variable for this researched is defined.

To determine the equilibrium REER of the UK, a real effective exchange rate (REER) is used as our dependent variable. The REER is a weighted average of bilateral RERs between a country and each of its trading partners, with countries weighted according to their relative importance as an export and import destination for country i.

𝑅𝐸𝐸𝑅 = ∏n (𝑅𝐸𝑅_𝑖𝑗𝑡)𝑤𝑖𝑗

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where 𝑅𝐸𝑅_𝑖𝑗𝑡 is the real exchange rate between country i and country j at time t as presented in equation (1), and 𝑊_𝑖𝑗 is the weight of country j in country i's effective exchange rate, according to Zanello and Desruelle (1997) calculated as:

𝑊_𝑖𝑗 = 𝜆_𝑖𝑀𝑀𝑊_𝑖𝑗 + 𝜆𝐵𝑋_𝑖 𝐵𝑋𝑊_𝑖𝑗+ 𝜆_𝑖𝑇𝑋𝑇𝑋𝑊_𝑖𝑗 (3) where 𝑀𝑊_𝑖𝑗 is country i’s weight in import competition, 𝐵𝑋𝑊_𝑖𝑗 its weight in bilateral export market competition, and 𝑇𝑋𝑊𝑖𝑗 its weight in third-market competition. The three

weights of competition, (𝜆), together add up to 1. This paper uses the sterling Exchange Rate Index (ERI) constructed by the Bank of England based on consumer price indices. It measures the change in price competitiveness of traded goods and services, with weights reflecting trade flows in manufactured goods and services. It takes into account UK domestic competition from imports abroad, competition between UK exports and domestic products in country j, and competition between the UK and country j in third-country markets. January 2005 is the base average monthly exchange rate (Jan2005=100). Exchange rates based on equation (2) are suitable to research the movement of the real exchange rates driven by changes or shocks in the tradable and non-tradable sectors (Siregar, 2011). Looking at Figure 2, we can see that the REER is relatively stable from the end of the 1990s up to the financial crisis in 2008. The base year 2005 can therefore be seen as a stable year in the UK economy with the financial crisis and Brexit referendum yet to unfold. These effects should be captured by the real effective exchange rate index. However, the ERI is determined by changes in prices of goods and services and does not take into account economic fundamentals that determine a country’s overall competitiveness. Literature on the model used the determine equilibrium REER of the sterling based on underlying economic fundamentals, will be explained in the next section.

2.3 The Behavioral Equilibrium Exchange Rate

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than through the supply of money. The equilibrium relationship can be described through a rise in the supply of money, which increases domestic prices causing the exchange rate to appreciate. Accordingly, as income levels rise, the demand for domestic currency increase and interest rates will rise. However, price levels don’t change instantly, as mentioned by Frankel (1979). He constructs a model where the prices would adjust gradually over time to an increase in demand and in line with the rate of inflation. In the monetary approach, the aggregate supply for domestic money is vertical and output can vary based on an increase in technological progress, capital accumulation, and an increase in the size of the labor force. The demand for money in the monetary model is based on the level of real income, where an increase in the real income leads to an appreciation of the domestic currency.

Williamson (1994) presented the fundamental equilibrium exchange rate (FEER) approach where changes in the capital account is included in determining the equilibrium exchange rate. The exchange rate is defined as a function of economic fundamental variables and is in equilibrium when both internal balance and external balance are achieved. Internal balance (savings – investment) holds the assumption of full employment, while external balance equalizes the balance of payments (CA = KA). The capital account is determined exogenously through net foreign assets. Thus, only changes in the net trade balance (NTB) will allow for external balance to be achieved and interest rates have to be in their long-term equilibrium levels (Bayoumi et al. 1994). Therefore, the equilibrium REER is determined through changes in trade flows. Using the alternative FEER approach, Giacomo et al. (2006) calculate the equilibrium exchange rate for six economies, using 20 years of quarterly data. Their results indicate that the FEER approach is an improvement over the PPP approach in explaining medium to long-run real exchange rate trends for the major industrialized countries, particularly for the UK, Germany, and Canada. A similar result is found by Saadaoui (2015) who uses panel data covering 26 industrialized countries between the period 1982-2010. He finds that there is a positive long-run relationship between the real equilibrium exchange rate and the estimated FEERs, thereby concluding that the FEER approach is a useful method to detect currency misalignments and stabilizing the current account. Church (1999) determines the equilibrium real exchange rate for the UK, and finds that the sterling is overvalued throughout most of the 1990s compared to the DM. He concluded that it would be costly for the UK to enter the single currency of the Euro-area as an adjustment through the nominal exchange rate would no longer be an option for the UK government. To achieve equilibrium, the output growth rate would have to lower and the unemployment rate of the UK would rise. One of the limitations of the model is that short-term deviations and cyclical factors in determining the equilibrium value are not included. The BEER approach used in this paper differs from the FEER approach as it relates the deviation of the actual exchange rate and the value given by the estimated equilibrium of the real effective exchange rate (Clark and Macdonald, 2004).

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instead uses the current values of economic fundamentals to determine the equilibrium path of the exchange rate, thereby relaxing the assumption of full employment made under the FEER approach. This allows the economic fundamentals to have a long-term effect on the exchange rate and makes the BEER approach more suitable in determining the equilibrium REER in the sample period. The BEER approach is based on an ordinary least squares (OLS) model, in which the dependent variable chosen is the real effective exchange rate. Clark and Macdonald (1998, 2000) estimate the BEER using the Johansen’s cointegration test to identify cointegration between the real effective exchange rate and the independent variables on the right-hand side of the OLS equation. In a study by Nikolaos and Minoas (2011) the nominal exchange rate of the euro converges to its equilibrium compared to the EU’s four main trading partners (i.e. US, UK, China, and Japan). They find that there is an equilibrium relationship between all the nominal exchange rates and the economic fundamentals. Using these results, the BEER approach finds that the euro/yuan, and euro/sterling currency pairs follow an equilibrium process. Clark and Macdonald (2004) find that the BEER estimates of equilibrium exchange rates differ considerably from those of the PPP approach. They find a single cointegrating vector for the sterling. The relative interest rate coefficient is much larger in the UK than for the other countries in this study (the United States and Canada) and they find no significance for the position of NFA in the case of the UK. The only long-term relationship found is with the real interest rate differential. To assess whether long-term relationships exist for the UK in this research, the following chapter will explain the estimation procedure under the BEER approach.

3. Methodology

3.1 Theoretical model

To determine the equilibrium REER of the sterling, this research follows the BEER approach of Clark and MacDonald (1999, 2004). The starting point of the approach is the uncovered interest parity (UIP) condition,

𝐸𝑡 𝛥𝑆𝑡+𝑘 = − (𝑖𝑡 – 𝑖𝑡∗) + 𝜋𝑡 (4)

Where St is the nominal exchange rate as defined in section 2.2, 𝑖_𝑡 is the domestic nominal interest rate, 𝑖_𝑡∗_{is the foreign nominal interest rate, 𝜋𝑡 = 𝜆𝑡}

𝑡+𝑘 the risk premium that has

a time-varying component, λt, and 𝐸𝑡 is the conditional expectations operator, and 𝑡 + 𝑘 is the maturity horizon of the bonds. The UIP condition implies that if nominal exchange rates are in equilibrium, the expected return on domestic and foreign assets should be equal if no risk premium for domestic assets exists.

By subtracting the expected inflation differential, 𝐸𝑡 (𝛥𝑝_𝑡+𝑘– 𝛥𝑝_𝑡+𝑘∗ ), from the exchange

rate and interest rate differential, we could convert equation (4) into a real relationship. After rearranging, we have:

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where 𝑟_𝑡 = 𝑖_𝑡 – 𝐸_𝑡(𝛥𝑝_𝑡+𝑘) describes the ex-ante real interest rate relation.

Equation (5) describes the equilibrium REER, 𝑞𝑡, as being determined by the expectation

of the equilibrium REER in period t + k, (𝐸_𝑡[𝑞_𝑡+𝑘]), the real interest differential (𝑟𝑡 – 𝑟∗𝑡), and the risk premium, 𝜋𝑡 . The UIP relationship is implemented as a

reduced-form expression of the BEER approach. The reduced reduced-form is as follows:

𝑞_𝑡= 𝛽′₁𝑍_1𝑡+ 𝜏′𝑇_𝑡+ 𝜀_𝑡 (6) where 𝑞𝑡, is affected by long-term economic fundamentals variables, 𝑍1𝑡, 𝜏′𝑇𝑡 affects the

REER in the short term and 𝜀_𝑡 is the error term. The assumption Clark and MacDonald (1999, 2004) make, is that the expected value of the equilibrium REER (𝑞′_{𝑡), is}

determined only by long-term economic fundamentals.

𝑞′𝑡 = 𝐸_𝑡[𝑞_𝑡+𝑘] = (𝐸_𝑡[𝛽′₁𝑍_1𝑡]) = 𝛽′₁𝑍_1𝑡. (7) The actual observed equilibrium REER, 𝑞𝑡, can deviate from the current equilibrium

REER based on long-term economic fundamental values, 𝑞_𝑡′.

By subtracting the current equilibrium REER from the actual observed value of the REER, the current misalignment of exchange rate can be calculated as follows:

𝑐𝑚 = (𝑞𝑡 − 𝑞′𝑡) = 𝑞𝑡 − 𝛽′₁𝑍1𝑡+ 𝛽′₂𝑍2𝑡 = 𝜏′𝑇𝑡+ 𝜀𝑡 (8)

the current misalignment is therefore the sum of the short-run variables and the error term. To answer the first research question, the same calculation as Nguyen and Sarantis (2008) is made to determine the misalignment percentage of the sterling exchange rate.

∆𝑚𝑖𝑠𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 =𝑅𝐸𝐸𝑅−𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑅𝐸𝐸𝑅

𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑅𝐸𝐸𝑅 ∗ 100% (9)

Clark and Macdonald (1998) assume the economic fundamentals used to calculate the BEER are at their sustainable long-term levels. To abstract short term random disturbances from the current misalignment, the Hodrick-Prescott (HP) filter is applied to determine total misalignment (tm). Total misalignment is defined as: “the difference between the

actual real rate and the real rate given by sustainable levels or the long-rum values of the economic fundamentals” (Clark and Macdonald 1998, pp.10). The total misalignment

consists of two components: (i) the current misalignment (𝜏′𝑇_𝑡+ 𝜀_𝑡), and (ii) the effect of departures of the current fundamentals from their sustainable values [𝛽′

1(𝑍1𝑡− 𝑍̅̅̅̅)]. 1𝑡

Combining the two components yields the following equation: 𝑡𝑚 = 𝜏′𝑇_𝑡+ 𝜀_𝑡+ [𝛽′

1(𝑍1𝑡− 𝑍̅̅̅̅)] 1𝑡 (10)

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The model based on the reduced-form equation for this research and the expected relationship (+/-), are as follows:

𝑅𝐸𝐸𝑅 = 𝛽₀ + (+) 𝛽1𝑇𝑂𝑇+ (+) 𝛽2𝑇𝑁𝑇+ (−) 𝛽3𝑀2+ (+) 𝛽4𝑂𝑃𝐸𝑁+ (+) 𝛽5𝑅𝐼𝐷+ (−) 𝛽6𝑅𝑃 (11)

In addition to the real interest rate differential and the risk premium from equation (5), which will be referred to as RID an RP in the above equation, the long-term economic variables in this study are informed by Farouquee (1995), Alberola et al. (1999), and Clark and MacDonald (1998, 2004). The variables used to describe the long-term economic relationship are Terms of trade (TOT), relative price of tradable to non-tradable goods (TNT), the M2 money supply (M2), and trade openness (OPEN) as a proxy for the amount of tradable goods relative within the economy. In the following section, the definition of the variables in equation (11) and the expected effect of the variables on the equilibrium REER will be described.

3.2. Construction of the variables and data sources

This section describes the variables as derived from the literature. All the variables in the regression equation are included as their natural logarithm, apart from RID that is included in its original form

- Equilibrium REER

The dependent variable of this research is the equilibrium value of the REER as constructed in equation (2). This research uses the ERI, which is deflated by the Consumer Price Index (CPI). It measures the monthly average change in the trade-weighted real exchange rate value of the sterling, where the weights reflect trade flows between the UK and 7 main trading partners. The base year of the index is 2005. If the value of UK goods increase, this implies an increase in the equilibrium REER. The data is sourced from the BoE database on interest and exchange rates.

- Terms of Trade (+ / -)

The terms of trade measures the UK’s export prices relative to the import prices, more formally;

ln

𝑇𝑂𝑇 =

𝐼𝑛𝑑𝑒𝑥 𝑜𝑓 𝐸𝑥𝑝𝑜𝑟𝑡 𝑃𝑟𝑖𝑐𝑒𝑠

𝐼𝑛𝑑𝑒𝑥 𝑜𝑓 𝐼𝑚𝑝𝑜𝑟𝑡 𝑃𝑟𝑖𝑐𝑒𝑠

∗ 100

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shock is of a permanent nature, the current account will be more determined by the investment rather than the savings effect. Thus, if the terms of trade are of a permanent nature it is expected to decrease the current account and the equilibrium REER, while temporarily a current account surplus and increase in the equilibrium REER is expected. Therefore, the relationship between the terms of trade and the dependent variable is difficult to predict. The monthly data is sourced from both the International Financial Statistics Database (IFS) database up to 2013, while the remaining monthly data is sourced from the BoE database and constructed into one index with (2013M1=100).

- Tradable to non-tradable ratio (+)

The variable TNT is included to capture the difference in price levels between tradable and non-tradable goods and services. It measures the “Balassa-Samuelson effect” (1964), which states that if the price of tradable goods is relatively high compared to non-tradable prices, real wages in the tradable goods sector increase. With free labor movement, the supply of labor will fall in the non-tradable sector. As a result, the prices of non-tradable goods will increase. If the ratio increases, the price of UK tradable goods rise relatively faster than the weighted average price of foreign tradable goods. This increases aggregate demand for the domestic currency and the equilibrium REER increases, creating a current account surplus. Olson (2007) tests the empirical validity of the Balassa-Samuelson hypothesis by examining the relationship of productivity and the real exchange rate in Japan, the US, Germany and the EU. The findings are in line with Clark and MacDonald (1998) and confirms the hypothesis as relative productivity shocks explain the greatest part of long-term variance in the real exchange rate when long-term equilibrium relationships are considered. In this research, the non-tradable goods are measured by the CPI, while tradable goods are measured by the domestic Producer Price Index (PPI) relative to the corresponding foreign ratio (wj). The variable is calculated using the equation below:

𝑇𝑁𝑇 = ln (

𝑃𝑃𝐼𝑢𝑘/𝐶𝑃𝐼𝑢𝑘

∏_𝑗(𝑃𝑃𝐼_𝑗/𝐶𝑃𝐼_𝑗)𝑤𝑗

)

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The data is sourced from the BoE database for the CPI and PPI indices of the UK and the IFS database is used for the UK’s main trading partners.

- M2 money supply (-)

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is predicted between the REER and M2 money supply. The monthly data is sourced from the BoE database and

- Trade openness (+)

Trade openness determines the amount of tradable goods within the economy. Following Iossifov and Loukoianova (2007) it is defined as the ratio of the sum of exports and imports of goods to GDP. Cameron (1978) finds that a more open economy is more prone to external shocks and risks and that trade openness can intensify this effect. In more recent work, Cavallo and Frankel (2008) find that countries with a larger supply of tradable goods, are less vulnerable to sudden stops in capital flows. Magud (2010) finds that a negative shock to an open economy with a flexible exchange rate regime, will cause a real depreciation of the exchange rate. The trade openness is therefore included to account for the vulnerability to sudden stops, as both the effect of the financial crisis and Brexit events are visible in the sample data. A positive relationship between trade openness and the equilibrium REER is expected. The data on the sum of exports and imports of goods and services is sourced from the IFS database, while the monthly GDP estimates are sourced from the Gross Domestic Product Real-Time Database of the BoE.

- Real Interest Rate Differential (RID)

The real interest rate differential is the difference between the domestic real interest rate (r) and the foreign real interest rate (r*).

𝑅𝐼𝐷 = 𝑟 − 𝑟∗ (14)

where the domestic real interest rate is the nominal long-term government bond yield minus the CPI percentage change of the same month of the year before. The foreign real interest rate is average weighted real interest rates, calculated similarly as the domestic rate. Hoffman and Macdonald (2000) test relationship between the real interest rate and bilateral US exchange rates. The find evidence that there is a significant relationship between the variables and that the real interest rate differential is a good indicator for expected long-term depreciation. When the UK real interest rate differential increases, the overall demand for UK assets will decrease and domestic currency flows out of the country. To balance the current account, the equilibrium real exchange rate must increase. Therefore, a positive relationship between the equilibrium REER and the RID is expected.

- Risk Premium

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increased risk will decrease demand in domestic assets and the equilibrium REER to balance the current account.

4. Results

4.1 The augmented Dickey-Fuller test

The ADF- test checks the time series data for stationarity. Stationarity of the data implies that the mean, variance and autocorrelation structure do not change over time. If this is not the case, regression with non-stationary variables could give spurious results. When the null hypothesis of non-stationarity is rejected, the variables are “integrated at order zero”, I(0). If the null hypothesis is not rejected, the variables need to be differenced to make it stationary, known as “integrated at order one”, I(1). Graphs of both the time series and the first differenced variables are used to determine which of the ADF- models is chosen to test for stationarity.1 The number of lags for this test can be chosen based on information criteria, such as the Akaike Information Criteria (AIC) and the Schwarz’s Bayesian Information Criteria (SBIC), or as a function based on the sample size (Tam, 2013). This research includes the number of lags recommended by the SBIC. The results of the test are depicted in Table 2.

The results indicate that all the variables are non-stationary at the 1% significance level. When the variables are differenced, they are all stationary at the 1% significance interval. Since the differenced variables are stationary, a Johansen co-integration test is used to determine if co-integration exists amongst the variables. The procedure will be explained in the following section.

Table 2: Augmented Dickey-Fuller test results 1999M1-2017M2

1_{See appendix for the ADF-test graphs}

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Note: C if constant is included, T if a trend is included and L represents the number of lags.

4.2 The Johansen co-integration test

Following MacDonald and Clark (2004), the Johansen co-integration test is performed on equation (12) to determine the presence of co-integration. Co-integration describes a long-run equilibrium relationship between the time series variables. If the current value of a time series variable depends on current values of other variables in the model, co-integration relationships are present. The concept was first introduced by Granger (1981) and allowed for a single co-integration relationship, if there exists a linear combination between the two variables. The Johansen co-integration test examines the amount of independent linear combinations (k) for an m amount of time series variables, allowing for more than one co-integration relationship to exist in the model. There are two different models of the test; (i) the trace test, and (ii) the maximum eigenvalue test. The former tests whether there is at least one linear combination for the variables, while the latter examines if the amount of linear combinations are not equal to the number of variables in equation (11). If so, the variables are stationary and co-integration is irrelevant. The results of both model (i) and (ii) are reported in Table 3. Looking at the trace statistic, that tests for 𝐻₀: 𝐾 = 0 of no linear combinations, against the alternative 𝐻₁: 𝐾 > 0 of one or more integration relationship amongst the variables, suggests there are at least three co-integration relationships in the chosen model. From the maximum eigenvalue test, we can conclude there are no equal amount of linear combinations at the 5% significance level.

Table 3: Johansen co-integration test results Maximum

Rank

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19 3 40 3378.74 0.15124 40.6816* 47.21 21.8382* 27.07 4 47 3389.6591 0.09574 18.8434 29.68 10.9965 20.97 5 52 3395.1573 0.04941 7.8469 15.41 4.0793 14.07 6 55 3397.1969 0.01862 3.7676 3.76 3.7676 3.76 7 56 3399.0807 0.01721

The trace-statistic indicates there are at least three co-integration relationships in the chosen model. Now that co-integration is determined in the model, to model both the short-term and the long-short-term equilibrium relationships a VECM will be used. Using equation (12), we can now capture the short-term price dynamics that affect the course of the real effective exchange back to equilibrium value. The number of lags chosen are informed by the information criteria described in the previous section, for the entire model 1 lag is chosen. The regression results are presented in Table 4. Where the 𝛽-parameter is a vector containing long-run effects of the estimates and the 𝛼-parameter is the error correction term and determines the adjustment speed back to equilibrium values.

Table 4: VECM regression results β parameters

Variable Coefficient P>|z| Coefficient P>|z|

lnREER 1,0000 . -0.214669 0.005* lnTOT -6.783365 0.001* -.0113683 0.075*** lnTNT -31.35403 0.000* -.0077862 0.520 lnM2 1.581862 0.015** -.0135558 0.229 lnOPEN -16.47033 0.000* .00035558 0.001* RID -.0379748 0.267** .0476116 0.001* lnRP 1.177904 0.000* .02445594 0.000* _cons 7,194642

Note: * 1% significance, ** 5% significance, *** 10% significance

After multiplying the 𝛽-parameter by -1, based on the table above the first co-integration equation in the reduced form can be calculated from the regression result as follows:

𝑙𝑛𝑅𝐸𝐸𝑅 = 𝐶 + 𝛼𝛽𝑙𝑛𝑇𝑂𝑇 + 𝛼𝛽𝑙𝑛𝑇𝑁𝑇 − 𝛼𝛽𝑙𝑛𝑀2 + 𝛼𝛽𝑙𝑛𝑂𝑃𝐸𝑁 + 𝛼𝛽𝑅𝐼𝐷 − 𝛼𝛽𝑙𝑛𝑅𝑃 This leads to the following co-integration equation:

𝑙𝑛𝑅𝐸𝐸𝑅 = −7.19 + 0,077𝑙𝑛𝑇𝑂𝑇 + 0,244𝑙𝑛𝑇𝑁𝑇 − 0,021𝑙𝑛𝑀2 + 0,005𝑙𝑛𝑂𝑃𝐸𝑁

+(0,002 ∗ 100)𝑅𝐼𝐷 − 0,028𝑙𝑛𝑅𝑃 (14)

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significant at the 1% level. We can accept the hypothesis that increased export prices leads to an increase in the equilibrium REER. A 1% increase in export prices of the UK, leads to a 0.77% increase in the equilibrium REER. The coefficient of the adjustment parameter is correctly signed and statistically significant at the 10% level.

The variable TNT has a positive long-term effect on the equilibrium REER and is statistically significant at 1% level. This confirms the Balassa-Samuelsson hypothesis that if the price of tradable goods increases relatively faster than the price of non-tradable goods, the REER should increase to balance the current account. A 1% increase in the TNT ratio, increases the equilibrium REER with 0.24%.

The long-term relationship between M2 money supply is as expected, an increase in the money supply decreases the equilibrium REER, although the estimate is significant only at the 90% confidence interval. It is in line with the hypothesis that expansionary monetary policy creates an excess supply of the domestic currency, resulting in a decrease of the equilibrium REER. A 1% increase of M2, decreases the equilibrium REER with -0.021%. Openness to trade has the expected positive long-term relationship and is statistically significant at 1% critical value. Considering the time periods of increased exchange rate volatility due to the financial crisis and Brexit in the sample data, the UK appears to be less vulnerable to sudden stops in capital flow. A 1% increase in the variable OPEN leads to a .005% increase in the equilibrium REER.

RID has the expected positive relationship with the equilibrium REER. An increase in the RID increases foreign demand in sterling denominated assets as return on these assets increase. The variable is statistically insignificant with a p-value of 0.267. An estimated 1% increase in RID would otherwise increase the equilibrium exchange rate by 0.02%. The coefficient is multiplied by 100 to determine its effect since RID is the only variable not represented in its natural logarithm form.

The RP is significant at the 1% critical value and has the expected negative sign. A 1% increase in the RP will decrease the equilibrium REER with -0.028%. This confirms that increased volatility of domestic assets decreases expected returns on these assets and the equilibrium REER decreases through a fall in aggregate foreign demand.

The model is checked for autocorrelation and overall stability2 According to the output of Table 5, found in the appendix, there are no signs for the presence of autocorrelation in the specified model. Table 6 reports the eigenvalue stability condition, where two variables are close to unity.

5. Sterling Equilibrium REER and Total Misalignment

5.1 Equilibrium REER and Current Misalignment

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By determining the co-integration equation (14) in the previous section, we can now calculate the estimated equilibrium REER (𝑞′_𝑡) as expressed in equation (7). The deviation of the actual observed REER from the estimated equilibrium REER is the current misalignment. The results are shown in Figure 3. In the left panel, the equilibrium REER is more volatile than the actual REER. Sharp upward and downward pressures are followed by a quick recovery to equilibrium of both exchange rates. The right panel shows the current misalignment in percentages as expressed in equation (9). The current misalignment ranges between and +7.66% in July 2007 and -7.29% in July 2016.

Initially, the sterling was overvalued until reaching near equilibrium values in July 2002 (-0.09%) after reaching an overvaluation of 7.2% in August 2000. An explanation for the initial overvaluation of the sterling can be the introduction of the Euro, that started to recover quickly in value afterwards, reaching a peak in 2004. Shortly before the start of the financial crisis, the sterling reached an overvaluation of 7.66% after which a sharp decrease till October 2008 can be seen. In 2009, the BoE announced to conduct further expansionary monetary policy and an increase from -1.44% undervaluation in December 2008 to 5.36% overvaluation in January 2009 can be seen and undervaluation in the aftermath of the crisis. This period is characterized by increased exchange rate volatility and overall decrease in trade flows and is clearly visible in an overall overvaluation, until the BoE intervened in October 2011. However, a month after the outcome of the Brexit referendum the real exchange rate was undervalued by 7.29% and shows the uncertainty surrounding its implications.

Figure 3: Equilibrium REER and current misalignment (%)

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22 5.2 Total misalignment

Following Clark and MacDonald (2004), the total misalignment is stated in equation (10). The equation states that total misalignment is the difference between the observed real exchange rate and the long-term economic fundamentals at full employment levels. The current misalignment based on the BEER approach measure the path of the REER back to equilibrium values, however the current misalignment still contains cyclical factors affecting the REER. Hodrick-Prescot (1997) filters out the cyclical factors and trend factors of the variables by solving a minimization problem. All the independent time series variables in equation (11) are divided into trend and cyclical factors. After which we use the variables in co-integration equation (15). The percentage change in the total misalignment is calculated using equation (9). Figure 4 shows the results for the total misalignment, Figure 5 shows the results of the current and total misalignment together. Figure 4: Total misalignment and total misalignment (%)

These findings are in line with Clark and Macdonald (2004) who use annual data from 1960- 1997 to determine the current misalignment and total misalignment of the UK. There is quite the difference between the current misalignment and the total misalignment, with the latter being less volatile ranging between -1.81% and + 4.06%. The total misalignment clarifies the extent to which a current misalignment is cyclical or transitory. The total misalignment appears to predict the real value of the sterling rather well and predicts the fall of the actual exchange rate before the financial crisis and the Brexit. This indicator is a more suitable explanation for the real value of the pound. Despite the increased uncertainty surrounding the Brexit, the total misalignment of the sterling compared to seven of its main trading partners shows a small undervaluation, -.67% respectively. However, one of the limitations of this research is that the specified VECM in this research imposes the standard normalization restrictions on the 𝛽-parameters of the variables in equation (14). This research could therefore be further expanded by posing restrictions on the variables derived from existing

-2 0 2 4 T o ta l Mi sa lig n me n t % 2000m1 2005m1 2010m1 2015m1 time 4 .3 4 .4 4 .5 4 .6 4 .7 2000m1 2005m1 2010m1 2015m1 time

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literature, to improve possible issues of endogeneity arising from demand -side factors. Another improvement would be to account for structural breaks in the data. With the financial crisis and Brexit effects visible in the REER, other factors than demand and supply can cause deviations from the equilibrium value.

Figure 5: REER, equilibrium REER and total misalignment

5.3 Impulse- Response functions

This section shows the impulse-response functions obtained from equation (14). Where the response variable is the equilibrium REER, and the response variables consist of the independent variables. In Figure 6, the shock can be interpreted as a 1 standard deviation change in the impulse variable, that will cause a (value Y/ Steps) % increase in the equilibrium REER. The outcome of the impulse- response function should be interpreted with caution, as the outcome of the Brexit is highly unpredictable and no exogenous factors are taken into account in determining the severity of the response. The results are shown in Figure 6. A positive shock to TOT causes the equilibrium REER to increase, in line with predicted theory. A standard deviation change in TOT, will cause the equilibrium REER to increase with 0.03% after 20 months, after which the increase diminishes. However, within the time span of 5 years the equilibrium REER does not decrease and TOT shock appears to be persistent. If the UK entered a WTO-scenario after the negotiations, this would increase the shock on TOT with 20% compared to the EEA-scenario. This result indicates the importance of negotiating favorable trade deals in the aftermath of Brexit.

A standard deviation change TNT, leads to an initial increase of the equilibrium REER of 0.05% per month over the first five months. Afterwards, the effect of TNT diminishes increasingly till it remains relatively stable after 3 years. One explanation of this trend is that the relative prices of non-tradable increase, as hypothesized by the Balassa-Samuelson effect.

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As expected, a positive shock of M2 money supply sharply decreases the equilibrium REER. In the first five months, an instant drop to -.5% can be seen and the equilibrium REER experiences a constant depreciation in the years after. The BoE thus has the ability to counteract on negative trade shocks using monetary policy. However, if the BoE decides to mitigate the effect of these negative Brexit shocks on the equilibrium REER, the BoE can no longer pursue an expansionary monetary policy. Seeing recent announcement of the BoE, this is not a viable option.

The equilibrium REER reacts positively to a positive shock in OPEN. There is not an initial sharp increase in the equilibrium REER as we would expect from theory. There seems to be no intensified effect of shocks on the equilibrium REER due to increased openness to trade. The impact is relatively small (0.006%) after two years and the increase diminishes to a constant rate after three years.

The equilibrium REER show no response to the RIR on the long-term and close to no response in the first months. As the discount rate for commercial banks on financial assets are set exogenously by the BoE to control liquidity levels within the economy. Any short-term differences in the RID should therefore be cleared by arbitrage conditions.

RP show a similar picture as the RID, although a slight decrease is seen initially. The RP is considered to have a transitory effect on the equilibrium REER and does not determine its value in the long-term. The small negative response in the beginning can be explained by the increased RP at the end our sample, having an effect on expected future return on assets Figure 6: Impulse- Response Functions

-.5 0 .5 -.5 0 .5 0 20 40 60 0 20 40 60 0 20 40 60

vec_eg, RIR, lnREER vec_eg, lnM2, lnREER vec_eg, lnOPEN, lnREER

vec_eg, lnRP, lnREER vec_eg, lnTNT, lnREER vec_eg, lnTOT, lnREER

step

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6. Conclusion

In this paper, the equilibrium real effective exchange rate of the sterling relative to seven main trading partners is determined. To do this, a behavioral equilibrium exchange rate approach is used as constructed by Clark and MacDonald (1998, 2004). We use the terms of trade, ratio of tradable goods to non-tradable goods, M2 money supply and openness to trade as measures of relative price levels and a real interest rate differential plus a time-varying risk premium to account for the relative fiscal position of the UK.

The following research questions are answered; (i) What is the equilibrium real effective exchange rate of the sterling relative to seven main trading partners of the UK between 1999M1 till 2017M2? (ii) Is the sterling currently overvalued, undervalued or at equilibrium value based on long-term economic fundamentals? And, (iii) What are the effects of shocks on the sterling equilibrium real effective exchange rate in a EEA and WTO Brexit scenario? For the first research question, the current misalignment is calculated and is based on transitory effects influencing the equilibrium REER and shows misalignment ranging between +7.66% in -7.29% in the sample period. The lower and upper bound values are reached slightly before the start of the financial crises. To calculate the equilibrium REER based on long-term economic fundamental, the total misalignment is derived by subtracting cyclical factors from the current misalignment. This shows a better indicator for the value of the sterling, as it is less volatile and shows a useful tool to predict a crisis. These findings are in line with literature on the equilibrium REER of the sterling as found by Clark and MacDonald (2004) The total misalignment ranges between -1.81% and + 4.06%, while the latest value shows a small undervaluation of -.67%. Overall, we can conclude that the total misalignment is a good indicator for UK policy makers to assess the real value of the sterling and that current expansionary monetary policy of the BoE helps the sterling to remain relatively close to equilibrium values.

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a Johansen co-integration test. With these result, the VECM model is chosen to separate long-term and short-long-term effects on the equilibrium REER. The result from the VECM regression all show the expected relationship with the dependent variable. The variables M2 and RP are negatively related to the equilibrium REER. With a 1% increase leading to a 0.021% and -0.028% decrease in the equilibrium REER respectively. The remaining variables increase the equilibrium REER for every 1% increase. TOT increases the equilibrium REER with 0.07%, TNT with 0.24%, OPEN with 0.005% and the RID with 0.02%. The RID is the only variable with an insignificant 𝛽-parameter, M2 is significant only at the 10% critical value, while the remaining values are all within the 95% confidence level.

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Appendix

The ADF-test considers three models; (i) time series with no trend and no constant, (ii) time series with a constant and no trend and (iii) time series with a constant and a trend. More formally written as; (i) ∆𝑌𝑡= ∅𝑌𝑡−1+ 𝛼1𝑡∆𝑦𝑡−1+𝛼𝑡, (ii) ∆𝑌𝑡 = 𝑎0+ ∅𝑌𝑡−1+ 𝛼1𝑡∆𝑦𝑡−1+

𝛼_𝑡, and (iii) ∆𝑌_𝑡= 𝑎₀+ ∅𝑌_𝑡−1+ 𝛾𝑡 + 𝛼_1𝑡∆𝑦_𝑡−1+𝛼_𝑡. The ADF test will be performed on the equation similar to the test graphs inserted below. The first column of the graph shows the level series of the time series data. None of the variables fluctuate around a zero mean and show an upward or downward trend throughout the period, apart from lnM2. Therefore, the ADF test will be performed on model (iii), and model (ii) for lnM2 respectively. For the second column, lnM2 and lnOPEN are the only variables fluctuating around a zero mean, despite several sharp increases or decreases that can be seen. The variables lnM2, lnOPEN and lnRP are tested on model (i), as no clear trend is visible. The remaining variables will be tested on model (i) .

Augmented Dickey-Fuller test graphs

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Table 5: Langrange multiplier test for autocorrelation

Lag Chi2 Df Prob > Chi2

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33 Table 6: Eigenvalue Stability Condition

-1 -. 5 0 .5 1 Ima g in a ry -1 -.5 0 .5 1 Real

The VECM specification imposes 5 unit moduli

The determination of the Sterling Equilibrium Exchange Rate and the Impact of Brexit Scenarios.

Faculty of Economics and Business