Exchange rates and political uncertainty: The Brexit case

Manasse, Paolo; Moramarco, Graziano; Trigilia, Giulio Working Paper Exchange rates and political uncertainty: The Brexit case Quaderni - Working Paper DSE, No. 1141 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Manasse, Paolo; Moramarco, Graziano; Trigilia, Giulio (2020) : Exchange rates and political uncertainty: The Brexit case, Quaderni - Working Paper DSE, No. 1141, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/6327 This Version is available at: https://hdl.handle.net/10419/245883 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ ISSN 2282-6483 Exchange Rates and Political Uncertainty: The Brexit Case Paolo Manasse Graziano Moramarco Giulio Trigilia Quaderni - Working Paper DSE N°1141 Exchange Rates and Political Uncertainty: The Brexit Case ∗ Paolo Manasse1, Graziano Moramarco2, and Giulio Trigilia3 1,2University of Bologna, Department of Economics 3University of Rochester, Simon Business School February 3, 2020 Abstract This paper studies the impact of political risk on exchange rates. We focus on the Brexit Referendum as it provides a natural experiment where both exchange rate expectations and a time-varying political risk factor can be measured directly. We build a simple portfolio model which predicts that an increase in the Leave probability triggers a depreciation of the British Pound, both on account of exchange rate expectations and of political risk. We estimate the model for multilateral and bilateral British Pound exchange rates. The results confirm the model’s main implications. When we extend the analysis to a portfolio model of multiple currencies, we find that the cross-currencies restrictions implied by the theory are not rejected by our system estimation. Moreover, the joint estimates of the multi-currency model in the presence of time-varying political risk premium are in many cases consistent with the Uncovered Interest Parity. Key words: Brexit, Exchange Rates, Political Risk, Time-Varying Risk Premium, Uncovered Interest Parity JEL classification: F31, F41, G11, G15. ∗All errors are our own. The most recent version of the paper is available here. 1 Non-technical Summary Politics has long been recognized as a major determinant of exchange rates. However, political risk is notoriously difficult to quantify. To overcome this hurdle, the recent literature has privileged breadth relative to depth, proposing indices of political uncertainty that aggregate over multiple sources of primary information, mainly from the press, and count the frequency by which a number of keywords, such as uncertainty, economy, deficit, tax policy, appear. This paper takes the opposite approach. We focus on a major recent political event—the Brexit Referendum in Great Britain—for which the response of currencies to political risk can be measured directly. The Brexit Referendum has shaken the European and international political scene in 2016: for the first time a European Union (EU) member country, the UK, voted for leaving the Union. Indeed, with the unexpected victory of the “Leave” camp, the British Pound (BP) depreciated overnight by about 7% against the Euro and other main currencies. What makes the Brexit Referendum an interesting “natural experiment” for economists is that political risk can be measured with precision, because the event has been preceded by an exceptionally liquid betting market. Bookmakers, such as Betfair and PredictIt, provided online platforms on which individuals could bet on the likely outcome of the Referendum in real time. From the bookmakers’ odds, we can extract a daily series of the probability of Brexit and derive the “correct” measure of the political uncertainty associated with the Referendum result. In the paper we ask a number of questions. The first is whether, and why, the evolution in the Leave probability is associated to movements in the price of currencies. To answer, we write down a simple model where risk-neutral investors form expectations about postReferendum exchange rates, and where these expectations depend of their assessment of the Leave/Remain probabilities. In our benchmark estimates, we find that markets expected a depreciation of the BP against a basket of major currencies of approximately 20% in case of a Leave victory. Our second question is whether there is evidence that currency markets price a political risk premium. We extend the model by allowing investors to be risk-averse, and from the Leave probabilities we derive a formula for the premium associated to political risk. The estimates suggest that when the political risk factor increases the BP tends to depreciate with respect to all the currencies considered, since investors reallocate their investments to less risky assets. Thus, as the probability of a Leave outcome increases, the BP depreciates due to two effects. The first operates via expectations: a more likely Leave outcome induces 2 investors to expect a future depreciation after the Referendum, so that the exchange rate weakens immediately. The second works trough the political risk premium: as the Leave probability gets closer to 50%, investing in BP becomes riskier and investors re-allocate their portfolios away from it. Relating time-varying political risk and exchange rates is especially important in the context of the so-called “Uncovered Interest Parity (UIP) anomaly”, which refers to the puzzle that the spread between the domestic and the foreign-currency denominated assets tends to be either weakly or negatively correlated to the depreciation rate of the domestic currency, particularly at short maturities and for low-inflation countries, and so borrowing in the the low-rate currency and investing in the high-rate one—the socalled carry trade—allows investors to realize possibly unbounded profits. Thus, our third question is whether measuring political risk directly helps to reconcile the exchange rate behavior with the UIP. In this case, the empirical results are more nuanced, but go in the direction of reconciling the data with the theory. Our last question is whether our portfolio framework can improve on the standard approach that considers exchange rates in isolation. Indeed, we find that the model’s restrictions are not rejected by the data and that they help reconciling the data with the UIP condition of arbitrage—especially for the EU and the US. 2 Introduction Politics has long been recognized as a major determinant of the international price of currencies. However, political risk is notoriously difficult to quantify. To overcome this hurdle, recent work has privileged breadth relative to depth, proposing indices of political uncertainty that aggregate over multiple sources of primary information to generate widely applicable and relatively long time series (e.g., Baker, Bloom and Davis (2016)). In order to complement this literature and to dig into the mechanism by which political risk is priced, this paper takes the opposite approach. It focuses on a major recent political event—the Brexit Referendum in Great Britain—for which the response of currencies to time-varying political risk can be measured directly. Our findings confirm that a time-varying political risk premium plays a crucial role in exchange rate determination. Moreover, our theory-based methodology identifies the premium from economic fundamentals, and can be applied to the analysis of other political events. The Brexit Referendum has shaken the European and international political scene in 2016: for the first time a European Union (EU) member country, the UK, voted for leaving the Union. The debate in the run-up to the Referendum focused mainly on in3 ternational issues, trade and immigration, which justifies our interest in the implications for exchange rates. With few exceptions, economists agreed that Brexit would have negative consequences on the British economy (e.g., Sampson et al. (2016)),1and expressed concerns that the City of London would lose its role as the main market for Euro denominated assets (e.g., Reuters, 2016). Indeed, with the unexpected victory of the “Leave” camp, the British Pound (BP) depreciated overnight by about 7% against the Euro and other main currencies. What makes the Brexit Referendum an interesting “natural experiment”, where political risk can be measured with some precision, is that the event has been preceded by an exceptionally liquid betting market.2Bookmakers, such as Betfair and PredictIt, provided online platforms on which individuals could bet on the likely outcome of the Referendum in real time. From the bookmakers’ odds, we can extract a daily series of the (risk neutral) probability of Brexit. With the benefit of hindsight the level of political odds has been criticized, as it failed to predict the outcome,3however we note that the informativeness of the odds-implied probabilities should not be measured by the accuracy of their levels, but rather by their ability to track changes through time, which is captured by our time-series regressions. Thus, our first question is whether, and why, the evolution in the odds-implied Leave probability before the Referendum is associated to movements in the price of the British Pound in terms of other currencies. To answer, we start by writing down a simple model where risk-neutral investors form expectations about post-Referendum exchange rates. In the absence of arbitrage opportunities, the Uncovered Interest Parity (UIP) should hold, and the interest rate on a domestic currency-denominated asset should exceed the foreign one when the domestic currency is expected to depreciate. We extend the UIP condition allowing the expected depreciation to depend on the (time-varying) probability of Leave. We then take this model to the data, and find that, consistent with the post-Referendum outcomes, market participants expected the British Pound to depreciate against all major currencies upon a victory of the Leave campaign. In particular, our benchmark estimates suggest that the markets expected a depreciation of the BP against a basket of major currencies of approximately 20% in case of a Leave victory, regardless of whether the basket is weighted 1For example, a study by H.M. Treasury (2016) concluded that “taking as a central assumption that the UK would seek a negotiated bilateral agreement, like Canada has, [...] our GDP would be 6.2% lower, families would be £4,300 worse off and our tax receipts would face an annual 36 billion black hole.” 2Mike Smithson, founder and editor of PoliticalBetting.com, defined Brexit as “the biggest political betting event of all time, anywhere”. According to a Guardian column (June 24, 2016), “More than £40m was gambled in the biggest political betting event in British history.” 3See for example the Guardian (June 24, 2016) and the Independent (June 24, 2016). A notable exception is the New York Times (June 24, 2016), which emphasized that the odds were close to 50%. 4 according to trade flows or international investment positions.4 While the odds-implied probability can be used to estimate the expected effect of Brexit on exchange rates (first moment), it also provides the basis to construct a timevarying political risk premium (second moment). Intuitively, the closer the odds-implied probability gets to one half, the closer the political risk faced by market participants gets to its peak, in a non-linear fashion. Thus, we can extend the model allowing the marginal investor in the currency market to be risk-averse, and derive a closed form solution for the time-varying risk premium, as a non-linear function of the Leave probability. Our second question is whether there is evidence that currency markets price our (modelbased) measure of political risk premium. The answer turns out to be clearly positive. Our political risk factor is positively and highly significantly associated to the BP price of a basket of other currencies and to bilateral exchange rates, with the exception of the BP-Japanese Yen, irrespective of the sample period considered and of the estimation method employed. Thus, as the probability of a Leave outcome increases, the BP depreciates due to two effects. The first operates via expectations: a more likely Leave outcome induces investors to expect a future depreciation after the Referendum, so that the exchange rate weakens immediately.5The second works trough the political risk premium: as the Leave probability gets closer to 50%, investing in the BP becomes riskier and investors re-allocate their portfolios away from it. The significance of our direct measure of the time-varying political risk factor complements the recent work that stresses the importance of political uncertainty by studying aggregate indices (e.g., Baker, Bloom and Davis (2016), Pastor and Veronesi (2012), Brogaard and Detzel (2015), Fernández-Villaverde, Guerrón-Quintana, Kuester and RubioRamírez (2015) and Kelly, Pástor and Veronesi (2016)), in a setting where the definition of political risk is derived from the theory and can be measured from the bookmakers’ odds—a market price that conveys the ‘wisdom of the crowd’. Other related work on the price of political uncertainty has either focused on tax policies (Sialm (2009), Croce, Nguyen and Schmid (2012)), or on equity premia (Santa-Clara and Valkanov (2003), Belo, Gala and Li (2013), Bittlingmayer (1998), Voth (2003), and Boutchkova, Doshi, Durnev and Molchanov (2012)). 4We focus on ten currencies, which are representative of the major British partners: Euro, US Dollar, Japanese Yen, Swiss Franc, Canadian Dollar, Danish Krone, Swedish Krone, Norwegian Krone, Australian Dollar, New Zealand Dollar. 5This has also been documented in recent papers that focus on exchange rate predictability and Brexit (e.g., Korus and Celebi (2018), Hanke, Poulsen and Weissensteiner (2018), Auld and Linton (2019) and Clark and Amen (2017)). None of these papers considers second moments—so their findings are unrelated to political uncertainty—or builds a model to interpret the result ‘structurally’. 5 In addition, our results relate to the vast literature on exchange rates. While recent work analyzed the pricing of macroeconomic uncertainty in currency markets (e.g., Rossi and Sekhposyan (2015)), the role of political uncertainty has been largely overlooked. To our knowledge, the only exception is Bachman (1992), who studies the impact of political news (elections) on the time-varying risk premium in foreign exchange markets. Before an election, there is uncertainty on whether the new government will implement a policy (a tax on domestic assets) which affects the domestic interest rate. This uncertainty is resolved after the elections. As a result, the parameters of an exchange rate equation should be unstable: those estimated in the sample before the elections should differ significantly from those in the post-election period. The author considers 13 election episodes in Canada, US, France and UK and finds evidence of parameter instability for about half of the episodes. Unlike Bachman (1992), we do not limit ourselves to testing for structural breaks, but we estimate the effects of time-varying political uncertainty on the exchange rate parameters. Relating time-varying political risk and exchange rates is especially important in the context of the so-called “UIP anomaly”, which refers to the puzzle that while the arbitrage condition predicts that the domestic interest rate should rise to compensate an expected depreciation of the domestic currency, the spread between the domestic and the foreigncurrency denominated assets is typically found to be either weakly or negatively correlated to the depreciation rate of the domestic currency, particularly at short maturities and for low-inflation countries (see Fama (1984), Hodrick (1987), Froot and Frankel (1989), Burnside et al. (2006), Chinn and Quayyum (2012), Engel (2014) and Ismailov and Rossi (2018)), and so borrowing in the the low-rate currency and investing in the high-rate one—the so-called carry trade—allows investors to realize possibly unbounded profits. The literature on exchange rates has tried to rationalize the puzzle either by positing a time-varying risk premium (e.g., Fama (1984), Verdelhan (2010), Lustig et al. (2011), Bansal and Shaliastovich (2013), Farhi and Gabaix (2015)), or deviating from standard, rational preferences and beliefs (e.,g., Gourinchas and Tornell (2004), Burnside et al. (2011), Ilut (2012)). In our paper, we do not make assumptions about the co-movement of exchange rate expectations and risk premia: we can measure it directly from bookmakers’ odds. Thus, our third question is whether measuring political risk directly helps to reconcile the exchange rate behavior with the UIP. Interestingly, the theoretical model implies that the “true” political risk-premium should co-move with the exchange rate exactly in the way required by Fama (1984) to explain the UIP puzzle. In this case, the empirical results are encouraging. On the one hand, both for the 6 basket of currencies and for the major trading partners of the UK (i.e., the US and the EU), we find that the spread between the domestic and the foreign-currency denominated assets tends to be positively correlated to the depreciation rate of the domestic currency, as the UIP requires. On the other, we often observe a higher coefficient than that predicted by the UIP, although the standard errors are too large to rule out that the coefficient is one (as required by the theory). Moreover, consistent with the previous literature, such coefficients seems to be quite unstable across samples and specifications, at least when we proceed estimating single equation models, currency by currency. Interestingly, the UIP performs much better when we take into account the cross-equation restrictions implied by the portfolio choice model and when we expand the sample period (see below). It has also been extensively argued that testing the UIP might fail for econometric reasons. This may be either because a random walk model for the exchange rate typically outperforms structural models in terms of out-of-sample forecasts (see Meese and Rogoff (1983a,b), Cheung, Chinn and Pascual (2005), Alquist and Chinn (2008)), or because of hard-to-predict rare catastrophic currency crashes (Brunnermeier, Nagel and Pedersen (2008), Farhi and Gabaix (2015)), or because of biases in the standard errors (Baillie and Bollerslev (2000), Rossi (2006)), or because of small sample biases (Chinn and Meredith (2005), Chinn and Quayyum (2012), and Chen and Tsang (2013)), or due to time-varying volatility (e.g., Clarida et al. (2009), Menkhoff et al. (2012)) This leads to our fourth question, which is whether it is possible to improve on the standard approach of estimating single-equation exchange rate models by considering a simultaneous, multi-currency setting. In this respect, one interesting property of our portfolio-choice approach is that it can easily be extended to a setting in which investors choose between more than two currencies. The model helps us to identify one cross-equation restriction that should hold and improve the efficiency of the estimates. This restriction derives from two considerations: first, the coefficient of risk-aversion of the marginal investor should not vary systematically across currency-pairs; second, the optimal share of every currency in the portfolio should depend on the entire co-variance structure of exchange rates. Indeed, when estimating a dynamic Seemingly-UnrelatedRegressions (SUR) system, we find that our restriction is not rejected by the data, while the coefficients on both odds and odds-volatility remain similar and statistically significant for most countries. Moreover, relative to the currency-pair regression in isolation, the SUR estimates are more often significant and the UIP parameter of the interest rate differential is much closer to the theoretical value—especially for the EU and the US. The paper unfolds as follows. Section 3presents the theoretical model. First, we assume risk neutrality. Then, we introduce risk-aversion and consider a simple mean7 where αj=E[e′ j|R], βj=E[e′ j|L]−E[e′ j|R],˜γ=r∑ j∑ k>j sjskβjβk, θ = 1,for j= 1, ..., N Expression (14) represents a system of Nnon-linear equations. This system is characterized by a cross-equation restriction on the parameters. The restriction comes from the fact that, unlike the intercept αjand the slope βjwhich are country-specific, the coefficient of the volatility term, ˜γ, depends on the expected “jumps” of all the exchange rates in the portfolio and on the risk-aversion parameter, and should therefore be identical across currencies. In this model, the coefficient of the political risk premium term, ˜γ, can in principle be negative, so that the BP would “appreciate” when political risk increases. This would apply if the British Pound, in case of Leave, were expected to appreciate relative to some currency jand to depreciate relative to some other currency k,βj<0, βk>0. In these (unlikely) circumstances, investing in BP may entail a diversification benefit which would reduce exposure to political risk. This extension suggests that imposing the restriction that the volatility coefficient should be the same across currencies and estimating a system of equations could improve the efficiency of the estimates. 4 The Data For the empirical analysis we collected daily data from May 27, 2015, to June 23, 2017 on exchange rates, interest rates, bookmakers odds, as well as other measures of political and economic uncertainty suggested by previous research. We study the behavior of the British Pound (BP) vis-à-vis the currencies of a number of major trading partners among advanced economies: the Euro (EUR), the US Dollar (USA), the Japanese Yen (JAP), the Swiss Franc (CHE), the Canadian Dollar (CAN), the Danish Krone (DAN), the Swedish Krone (SWE), the Norwegian Krone (NOR), the Australian Dollar (AUS) and the New Zealand Dollar (NZL). To this aim, we consider two specifications of a multilateral nominal exchange rate of the BP against a basket of these ten currencies, as well as each bilateral exchange rate. Our first multilateral exchange rate (and the corresponding interest rate differential) is constructed as a weighted average of the country-specific exchange rates (interest rates), using trade weights—based on international trade flows between the UK and the other countries. More specifically, each trade weight is calculated as the ratio of the bilateral trade (the sum of exports and imports) to the total value of UK trade with the ten 14 countries, measured in 2015. We also construct an alternative measure of multilateral exchange rate based on financial weights. Specifically, for a generic country i, the financial weight is given by the ratio of the financial position (the sum of assets and liabilities) of the UK towards country i, relative to the total financial position of the UK against all the other ten countries, measured as of December 2015. Table 1reports the two sets of weights in column 2 and 4, and the value of bilateral trade and of the bilateral financial position in 2015 in column 1 and 3, respectively. In both exchange rates the Euro and the USD play a dominant role. The trade-weights reflect the predominant share of the EU in UK trade (64.3 percent) with a relatively minor role for the USD (17 percent) and a non-negligible role for the Swiss Franc (6 percent), while financial weights are relatively more balanced, and assign to the Euro and the USD respectively 46 and 36 percent, and about 6 percent to Japan. The data source for the exchange rates and interest rates is Datastream. As in Ismailov and Rossi (2018), the interest rates considered here are 3-month euro LIBOR rates. The source for international financial positions is the IMF Coordinated Portfolio Investment Survey (CPIS). International trade data are from the IMF Direction of Trade Statistics (DOTS). Our Leave probability measure is constructed using real time data provided by two betting companies: Betfair and PredictIt. For either provider, we take the daily average probability of Leave derived from the corresponding odds. The probability variable π is the average of the two series. We chose to use these data as we consider that these prediction markets reflect the ‘wisdom of the crowd’. In particular, unlike survey data, they are immune from misreporting as investors “put their money where their mouth is”. In the words of Arrow et al. (2008), “because information is often widely dispersed among economic actors, it is highly desirable to find a mechanism to collect and aggregate that information. Free markets usually manage this process well because almost anyone can participate, and the potential for profit (and loss) creates strong incentives to search for better information”. Prediction markets are used to manage risks—such as flu outbreaks and environmental disasters—by public entities (e.g., U.S. Department of Defense) as well as firms (e.g., General Electric, Google, France Telecom, Hewlett-Packard, IBM, Intel, Microsoft, Siemens, Yahoo). Betfair is a British online gambling company headquartered in Hammersmith (West London) and Clonskeagh (Dublin). It claims to have over 4 million customers (1.1 million active customers) and a turnover in excess of £50 million a week. As of April 2013, the company employed 1,800 people. In its betting website, Betfair listed two Brexit-related contracts. The first paid out £1 in the event of a Leave victory, the other paid £1 in the event of Remain. Betfair supplied us with the odds implicit in the contract prices, 15 which are observed from 5/27/2015 to 6/24/2016 at different time-intervals (often of 1 second), each week day for a total of 143,290 observations. This data source was used in recent papers, e.g., Auld and Linton (2019). We complement this with a second source for betting odds, the New Zealand-based company PredictIt, which launched a market on the Brexit vote on November 3, 2014 and caters mainly US-based investors.9 Figure 1compares the two Leave probability series derived from the Betfair odds (solid blue line) and the PredictIt ones (dashed green line). The figure reveals that the Leave probability measures were quite noisy in 2015: until December 2015, the two series exhibit a negative correlation (-0.35) and the standard deviation of their difference is 9.30%. However, starting in January 2016 the odds appear to behave similarly: for the period January 1 - June 22 the standard deviation falls to 4.23% and the correlation coefficient rises to 0.51. Among a series of relevant political events which marked the run-up to the Referendum and the progress of UK-EU negotiations, two dates were pivotal, at least according to the briefing paper by the UK House of Commons Library on Brexit (Walker (2018)): the first is December 17, 2015—when the EU Referendum Act was promulgated—and the second is February 22, 2016—when Prime Minister David Cameron announced that the Referendum would take place on June 23, 2016. The Referendum Act was the act of the Parliament that made legal provision for a consultative referendum to be held in the United Kingdom and Gibraltar, on whether the UK should remain a member state of the European Union or leave it. Following the Royal Assent to the Act, although the Prime Minister did not indicate a precise date for the vote, the British media considered June 2016 as the most likely period well before David Cameron’s official announcement.10 A dashed vertical line in Figures 1-2identifies the date (December 17, 2015) on which the European Union Referendum Act received Royal Assent and was therefore promulgated. 9Investors in PredictIt buy assets whose price represents the probability of a certain outcome (e.g. a Leave victory) and can hold the asset until maturity (the Referendum day) or trade it before maturity, at the ongoing price. In order to comply with U.S. regulators, PredictIt caps the size of trading positions (see Wolfers and Zitzewitz (2018)). We do not have information on individual traders, however PredictIt described to us its investors as follows: “they are affluent (100-200k annual income), well-educated millennials, aged 22-35, living in metropolitan areas like NYC, DC, Philadelphia, Dallas, Chicago, and San Francisco. Most traders work in finance, law, politics, and technical fields, such as mathematics, statistics, and economics. They are politically diverse with Democrats, Republicans, libertarians, “unaffiliated” or “no party” affiliates all using the site. There are about 30-35k active traders on PredictIt (defined as someone with money in their account) at any given time, with people entering and exiting markets regularly. Nearly 180,000 people have opened an account at the time of writing.” 10See, e.g., the Telegraph (Dec. 18, 2015),the Independent (Dec. 18, 2015) and the Guardian (Jan. 24, 2016). 16 Figure 2plots the average of the two Leave probability series (solid blue line, left scale) along with the effective exchange rate of the BP against the basket of ten currencies (dashed yellow line, right scale), using financial weights. Interestingly, around the approval of the EU Referendum Act, the exchange rate exhibits an upward movement (a depreciation of the BP of approximately 10%), while the correlation between the two variables increases—it is 0.18 from May 27 to December 17, 2015, it rises to 0.57 in the subsequent period. The graphical evidence and the descriptive statistics suggest that from late 2015 the odds associated to the bets on the Referendum result may have played a stronger role in explaining the BP exchange rate movements, consistently with the implication of our model. The additional measures of political and economic uncertainty that we collected will be introduced in the robustness section, as they are not employed in our baseline estimation. Figure 3plots all (log) exchange rates considered in this paper, from 27 May 2015 to 23 June 2017. The financially-weighted basket and the trade-weighted basket are denoted by ROWFand ROWT, respectively (where “ROW” stands for “rest of the world”). The figure shows that, qualitatively, the BP exhibited similar patterns relative to the currencies considered in the paper, with a large depreciation occurring around the Referendum Act of mid December 2015. 5 Empirical Analysis In this section we estimate a version of the Uncovered Interest Parity relationship implied by the theoretical model, which emphasizes the role of market expectations and of the political risk premium that are embodied in the odds of Leave. For this purpose we focus on the long-run (cointegration) relationship between the exchange rates and its determinants. We do so for different currencies, sample periods and by employing different statistical estimators. Thus we leave aside short-run dynamics issues. Estimates of an Error Correction Model, available upon request, confirm the results presented here and show that the exchange rates converge over time to this long-run relationship. 5.1 Setup Based on equation (11), the impact effects of the Leave probability and of the political risk premium on the exchange rate of the BP may change as a result of a shift in market expectations on the future exchange rate. Equation (13) introduces the additional possibility that these effects may change as the result of a shift in q, the probability of 17 the Referendum being held.11 The approval of the Referendum Act, by removing the uncertainty over the Referendum, in our interpretation affects the parameter q. Although we do not directly observe this probability, since there were no betting markets on the possibility of a vote, we will assume that this parameter takes the value of one after the date of promulgation of the Act, τ. Therefore, our approach consists in estimating equation (13) under the assumption that a discrete upward shift in qoccurs at the date of the promulgation of the EU Referendum Act: qt=   q0if t≤τ 1if t > τ with q0<1. We first estimate equation (13) for the effective exchange rate of the BP vis-à-vis our two baskets of ten currencies (either with financial-weighting or with trade-weighting of the countries). Next, we proceed to the analysis of country-by-country equations for bilateral exchange rates. Finally, we consider the joint estimation of a multi-currency portfolio model, allowing for cross-currency shock correlation and cross-equation constraints. Our benchmark sample spans the period from 27 May 2015, which is the first day when the odds on the Referendum outcome are available, to 30 June 2016. We include a few days after the vote for identification purposes. We also estimate the equations on a longer sample ending in June 2017. Because the Leave probability never exceeds 50% before the vote, our volatility measure π(1 −π)is a monotonic transformation of πand the correlation between the two variables is close to 1. Collinearity would make their individual coefficients not identified and lead to inaccurate estimates.12 On 24 June 2016, the day after the vote, πjumps to 1 and π(1 −π)drops to 0, as the Leave camp prevails and uncertainty about the outcome of the Referendum is resolved. Accordingly, the inclusion of post-referendum observations helps us to identify βand γby exploiting the opposite movements of πand π(1 −π)following the vote. In the robustness section, we will make sure that our esti11Alternatively, qmay be interpreted as a measure of the attention paid by investors to the odds on the Referendum, thus capturing such factors as the expectations on the timing of the Referendum. 12This issue is reminiscent of the long-standing “peso problem” in the international macro literature, which refers to the measurement of exchange rate expectations (or, more generally, asset-price expectations) and risk premia in samples that do not include large infrequent events, such as devaluations (Engel (2014)). Similarly, if we limited the sample to the pre-Referendum period, we may not be able to disentangle the contributions of the expected exchange rate and of the risk premium to the exchange rate movements. 18 mated coefficients on πand π(1 −π)do not not simply capture a pre-post Referendum time effect. Before presenting the results, we test our variables for the presence of unit roots and cointegration. 5.2 Unit Roots and Cointegration Table 2shows the results of the augmented Dickey-Fuller (ADF) test for unit roots in e and i∗−i, both over our benchmark sample 5/27/2015-6/30/2016 (“short sample”), which covers a few days after the Referendum, and over a sample period 5/27/2015-6/23/2017 (“long sample”), in which about half of the observations lie before and half after the Referendum. We choose to test the (non-)stationarity of the interest spreads, rather than the individual interest rates, because we will impose the theoretical restriction that it is the difference of yields that enters the UIP condition. All exchange rates appear to be non-stationary at any conventional level of significance on both samples. For the interest rate differentials, the results are more heterogeneous across countries and samples. Both the average differential based on financial weights and the one based on trade weights are non-stationary over the long sample, while the test rejects the presence of a unit root for both over the short sample. The interest rate differential appears non-stationary on both samples for the Euro area, USA, Japan, Canada and Denmark at the 5% level of significance, while for the remaining countries the null cannot be rejected in one of the two samples. Table 3shows the results of the ADF test for π. In this case, the results are reported for the pre-Referendum sample 5/27/2015-6/22/2016 (for any sample ending after the Referendum, the test fails to reject the null due to the jump of πfollowing the vote). As suggested by Figure 2, the Leave probability is stationary before the Referendum. In addition, the table presents the results for qπ, using two values for q0–the perceived probability of the Referendum prior to the Referendum Act. We will discuss the issue of how to estimate this parameter in the next paragraphs. For the moment we assume that this prior can take two values, q0∈ {0.25,0.5}, which turn out to be plausible according to our estimates. In either case, the unit root hypothesis is not rejected for the interaction variable qπ. This is the result of the upward shift in qat the time of the promulgation of the Referendum Act. Given our specification (13), we test for cointegration between e,i∗−i,qπ and qπ(1 −π), using the Phillips-Ouliaris residual-based test for single equations. The null hypothesis is that the variables are not cointegrated. As before, we show results for 19 q0∈ {0.25,0.5}. The results for q0= 0.25 are reported in Table 4. At the 10% level of significance, the test unambiguously indicates cointegration in the case of the effective exchange rate, both financially-weighted and trade-weighted. Looking at individual currencies, the evidence is mixed, but on balance it appears mildly consistent with our hypothesis of cointegration: for all currencies except the Norwegian krone and the Australian dollar, the null of no cointegration is rejected at the 10% level of significance in at least one of the two samples. When we perform the cointegration test assuming q0= 0.5 (Table 5), it signals cointegration at the 10% level in most cases. The interaction of π and π(1 −π)with qis critical for establishing a cointegration relationship: when the test is conducted using the variables πand π(1 −π), cointegration is generally ruled out. 5.3 Estimation Results. This section presents our main results. We begin by considering ordinary least squares (OLS). The OLS estimator is known to be “superconsistent” (i.e., it converges in probability to the true parameter value at a speed of T, the sample size, rather than the usual T1/2) when the variables are non stationary but cointegrated. However, the estimator has an asymptotically biased and non-normal distribution, and does not allow for standard inference. Moreover, as noted by Banerjee et al. (1986), the OLS estimator can suffer from substantial finite sample bias, and cointegration relationships should be in general estimated through dynamic regressions rather than static regressions. Maddala and Kim (1998) review the finite sample evidence on estimators of cointegrating vectors provided in Monte Carlo studies and advice against estimating long-run parameters by static regressions. For these reasons, we turn to the dynamic ordinary least squares (DOLS) estimator, proposed by Saikkonen (1991) and Stock and Watson (1993). We also show results obtained using the fully-modified OLS (FMOLS) proposed by Phillips and Hansen (1990). Unlike the OLS, these estimators are asymptotically efficient in the presence of cointegration and allow for inference on the coefficients of I(1) variables, as their test statistics have conventional asymptotic distributions. As highlighted by Rossi (2013), cointegration vectors are typically estimated by DOLS in the literature on exchange rates. The DOLS estimator applies a parametric correction to the OLS in order to account for the correlation between residuals and regressors. In practice, the estimator is obtained by augmenting the cointegration regression with lags and leads of first-differenced 20 regressors. More specifically, in our case the benchmark DOLS regression is given by: et=θ(i∗ t−it) + α+βqtπt+γqtπt(1 −πt) + δqt+ h ∑ j=−l ϕ′ j∆Xt+j+εt(15) where Xt+j≡[i∗ t+j−it+j, qt+jπt+j, qt+jπt+j(1 −πt+j)]′, for every j,∆Xt+j=Xt+j− Xt+j−1,ϕjis a 3×1vector of parameters, for every j, and εtis an error term. We employ an automatic lag/lead selection based on the Bayesian information criterion. This indicates that only contemporaneous differences should be included in the regression, regardless of the value of q0. Nevertheless, we also include lags and leads of order 1 (i.e. l=h= 1) in order to capture more adequately the dynamics of our dependent variable. We also employ the FMOLS estimator, which applies a different correction to OLS. It controls for the correlation between the error term of the cointegrating regression and the innovations of the regressors using a non-parametric consistent estimate of the long-run covariance matrix. Table 6reports the estimates obtained in the shorter sample by OLS, DOLS, FMOLS for the financially-weighted effective exchange rate (ROWF) and the trade-weighted effective exchange rate (ROWT). In order to obtain estimates for q0, we actually make use of non-linear least squares.13 The table shows that the estimated coefficients of the Leave probability and the political risk premium, βand γrespectively, are both positive and highly significant across all estimation methods. In our interpretation, βmeasures the percent BP depreciation rate that the market prices in the Leave scenario, relative to the Remain scenario. The value of the BP conditional on Leave is estimated to be around 19%-22% lower than the value under the Remain scenario. Importantly, a positive coefficient for our measure of 13More specifically, we use the Gauss-Newton algorithm for the numerical minimization of the sum of squared residuals. In the case of DOLS and OLS, we optimize over all parameters simultaneously. To make sure that we detect a global minimum, we repeat the optimization 1000 times, each time using random draws from uniform(-10,+10) distributions as the starting values of the parameters. In the case of FMOLS, estimating q0and the other parameters simultaneously is unfeasible. Therefore, we follow a 2-step procedure in each iteration of the optimization algorithm: we first set a value for q0, then we estimate the remaining parameters using conventional (linear) FMOLS, conditional on q0. Thus, in this case we optimize numerically over q0only. For DOLS and OLS, the standard errors of the parameters are obtained using the Newey-West heteroskedasticity and autocorrelation (HAC) estimator. For FMOLS, the standard error of q0is calculated as bσlr(h/2)−1/2, where bσlr is the long-run standard error of FMOLS residuals and his the second derivative of the objective function (the sum of squared residuals) with respect to q0. This approach follows conventional methods for calculating standard errors of non-linear regressions from the Hessian matrix (Amemiya (1983)). For the other parameters, we calculate ordinary FMOLS standard errors, conditional on q0. 21 time-varying political risk premium, π(1 −π), means that higher Brexit uncertainty is associated with a BP depreciation. More generally, our approach allows to disentangle the two channels (first and second moments) by which the odds affect the exchange rate. For instance, let us consider what the model predicts should happen to the BP after the Leave victory, using the estimates in the first column of Table 6. Given the average value of π(0.3) and π(1−π)(0.21) before the Referendum, the model predict a BP depreciation of about 7 percent. This is the net effect of: (i) the surprise of the Referendum outcome, which accounts for a depreciation of 14.8% = (1 −0.3) ·0.2112; (ii) an appreciation effect due to the resolution of uncertainty: −8% = (0 −0.21) ·0.3834. The net result is a depreciation rate of ≃6.8%. Table 6presents another very interesting result. Unlike a large body of literature that found negative coefficients on interest rate differentials in the UIP relationship, we obtain the a-priori correct positive sign in our estimates for θ, although with high standard errors. The point estimates are generally higher than one, but they are not significantly different from 0. The model for the basket of currencies does not violate the UIP, as the hypothesis θ= 1 cannot be rejected. The DOLS estimates of q0are 0.26 and 0.2 for ROWFand ROWT, respectively, with large confidence intervals (at the 90%, the parameter lies between 0 and 0.6 approximately). The estimates are somewhat lower for FMOLS and OLS.14 Thus, as expected, the effects of the odds variables are much higher after the Referendum Act, which confirms the intuition that only when market participants perceive that the Referendum will take place for sure, they start placing more weight on the evolution of the odds.15 Also, the coefficient δon the variable q(non-interacted) is not significant, except for FMOLS estimates for ROWT. This is consistent with the assumption that market participants expected the same value for the exchange rate in the case of No Referendum and in the case of a Remain victory. If the non-interacted qvariable is omitted from the regression, the estimates of q0become larger and significant, but still remain below 0.5 (the DOLS point estimates are around 0.44 for ROWFand 0.43 for ROWT). In our interpretation, the term α+δq gives the expected (log) exchange rate conditional on a Remain vote. This implies that the multilateral (financially-weighted) 14Note that the standard errors of q0in Table 6are obtained without imposing that q0lies between 0 and 1. So, for instance, the 90% confidence interval of the DOLS estimate for ROWFhas a lower bound of -0.08 and an upper bound of 0.59 approximately. To impose 0< q0<1, we can use the logit transformation of q0, denoted by λq, i.e. we can replace q0with exp(λq)/(1 + exp(λq)) in the regression. In this case, while the point estimate of q0remains the same, the lower and upper bounds of the 90% interval are 0.06 and 0.66, respectively. 15The Wald test for the hypothesis q0π= 0 has a p-value of 14%, for q0π(1 −π) = 0 the p-value is 17%. 22 BP exchange rate after the Referendum Act (q= 1) should be approximately equal to exp(α+δq) = exp(−0.5046−0.0515) = 0.57, which is close but below the average rate prevailing before the Referendum Act (see Figure 2). Tables 8-10 report the DOLS estimates for each individual currency. Here we impose the a priori restriction that q0is the same for all countries, and equal to 0.25.16 The coefficient on the Leave probability qπ is positive and significant at the 1% level for all currencies, with point estimates ranging from 0.17 to 0.30. The coefficient on qπ(1 −π)is also positive for all countries and significant at the 1% for all countries except Japan (for which it is not significant), Norway (for which it is significant at the 10%) and New Zealand (for which it is significant at the 5%). The estimates for the interest rate spread coefficient θexhibit large cross-sectional variability. However, for all countries except Japan and Sweden, the point estimate is positive. Due to the large standard errors, the coefficient is not significantly different from 1 in the equations for the Euro, the Swiss franc, the Swedish krone, the Australian dollar and the New Zealand dollar. For the other currencies, the UIP is violated. As shown in Tables 9to 11, our main results remain valid when we extend the sample by including one year of post-Referendum observations. In all equations, the estimates of the Leave probability coefficient, β, are larger and those of the risk-premium coefficient, γ, are lower than over the short sample, but in general the estimates are very similar. Moreover, the estimates of the interest spread coefficient, θ, are now closer to the theoretical value of one both for the basket of currencies and for individual currencies, with the exceptions of the Swiss franc and the Australian dollar. Notably, the UIP is now not violated by the US dollar either. 5.4 Robustness Checks for Single Equation Estimation 5.4.1 Robustness to a Pre-Post Referendum Time Effect As a first check, we show that our Leave probability and risk-premium variables do not simply capture a pre-post Referendum time effect. We do this in two ways. 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Zitzewitz, “The” Standard Error” of Event Studies: Lessons from the 2016 Election,” in “AEA Papers and Proceedings,” Vol. 108 2018, pp. 584–89. 33 Table 1: Financial and trade weights of the UK’s economic partners in 2015 financial weights trade weights country billions US$ percent billions US$ percent EUR 2950.94 46.36% 472.46 64.30% USA 2297.17 36.09% 124.58 16.96% JAP 396.33 6.23% 15.99 2.18% CHE 172.98 2.72% 41.99 5.72% CAN 122.68 1.93% 19.14 2.61% DAN 51.40 0.81% 8.76 1.19% SWE 99.68 1.57% 17.15 2.33% NOR 120.09 1.89% 23.80 3.24% AUS 142.70 2.24% 8.64 1.18% NZL 11.51 0.18% 2.21 0.30% Notes: The table reports the weights used to construct the multilateral exchange rates of the British pound against the basket of ten currencies considered in the paper. For a generic country i, the financial weight is given by the ratio of the financial position (the sum of assets and liabilities) of the UK towards country i, relative to the total financial position of the UK against all the other ten countries, measured as of December 2015. The trade weight is calculated as the ratio of the bilateral trade (the sum of exports and imports) between the UK and country i, relative to the value of UK trade with the ten countries, measured in 2015. The source for international financial positions is the IMF Coordinated Portfolio Investment Survey (CPIS). The source for international trade data is the IMF Direction of Trade Statistics (DOTS). 34 Figure 1: Odds of Leave Notes: The figure shows the odds-derived probabilities of Leave provided by Betfair and PredictIt from 27 May, 2015 to 23 June, 2016. The data are daily and span the period from 27 May, 2015 to 23 June, 2016. The dashed red vertical line identifies the date (17 December, 2015) on which the Referendum Act received Royal Assent and thus came into force. Missing values are interpolated using previous-day values. The result of the vote became known in the early hours of 24 June, 2016 in UK time, corresponding to the late hours of 23 June in US time: this explains the divergence of the two series on 23 June. 35 Figure 2: Brexit odds and British pound (BP) Notes: The figure shows our Leave probability measure (left-hand scale), constructed as the average of the Betfair and PredictIt odds-derived probabilities of Leave, along with the effective exchange rate of the British pound vis-à-vis the basket of 10 currencies considered in the paper (right-hand scale). The basket is constructed as the weighted average of bilateral exchange rates using international financial positions as weights. The data are daily and span the period from 27 May, 2015 to 23 June, 2016. The dashed red vertical line identifies the date (17 December, 2015) on which the Referendum Act received Royal Assent. 36 Figure 3: Log exchange rates of the British pound Notes: The figure plots all log exchange rates used in the paper, from 27 May 2015 to 23 June 2017. An increase in any exchange rate means a depreciation of the British pound against the currency considered. The exchange rates are displayed for the financially-weighted basket (ROWF) and the trade-weighted basket (ROWT), as well as all ten individual currencies: the Euro (EUR), the US dollar (USA), the Japanese yen (JAP), the Swiss franc (CHE), the Canadian dollar (CAN), the Danish krone (DAN), the Swedish krone (SWE), the Norwegian krone (NOR), the Australian dollar (AUS) and the New Zealand dollar (NZL). The data are daily. 37 Table 2: Augmented Dickey-Fuller test: eand i∗−i short sample long sample variable currency t-stat. p-value t-stat. p-value eROWF0.0183 0.9586 -0.9794 0.7619 ROWT-0.1272 0.9440 -1.0056 0.7527 EUR -0.3935 0.9070 -1.1132 0.7121 USA -0.1350 0.9432 -1.0233 0.7463 JAP 1.1351 0.9977 -1.2306 0.6626 CHE -0.3678 0.9113 -0.8002 0.8178 CAN -0.0185 0.9552 -0.8369 0.8073 DAN -0.3316 0.9170 -1.0918 0.7205 SWE -0.3794 0.9094 -1.3243 0.6197 NOR -0.7616 0.8278 -0.8838 0.7932 AUS -0.2915 0.9230 -0.7816 0.8230 NZL 0.1610 0.9697 -0.4978 0.8888 i∗−iROWF-4.1646 0.0009 -1.4572 0.5547 ROWT-2.9065 0.0458 -2.0634 0.2599 EUR -2.1247 0.2352 -2.8261 0.0553 USA -1.3541 0.6047 -0.9823 0.7609 JAP -2.3054 0.1710 -2.5403 0.1065 CHE -3.2307 0.0193 -2.3211 0.1657 CAN -2.2905 0.1758 -1.3548 0.6051 DAN -2.6713 0.0803 -2.6722 0.0795 SWE -2.2909 0.1757 -3.1354 0.0246 NOR -3.1094 0.0270 -2.6175 0.0900 AUS -2.6572 0.0829 -3.8028 0.0031 NZL -2.8236 0.0562 -3.2074 0.0201 Notes: e: log exchange rate, i∗−i: difference between the foreign and the domestic (UK) interest rates. Under the null hypothesis, the series has a unit root. MacKinnon (1996) p-values are reported. The data are daily. Short sample: 27 May 2015 to 30 June 2016. Long sample: 27 May 2015 to 23 June 2017. The lag order used for all tests is 5. 38 Table 3: Augmented Dickey-Fuller test: πand qπ variable t-stat. p-value π-3.7481 0.0039 qπ (q= 0.25 before Ref. Act) -1.1760 0.6854 qπ (q= 0.5before Ref. Act) -1.3929 0.5863 Notes: πis our Leave probability variable, calculated as the average of the Betfair and PredictIt odds-derived probabilities, qdenotes the probability of the Referendum being held (after the EU Referendum Act, it is assumed to take value 1). The sample used for the tests is: 5/27/2015 - 6/22/2016. Under the null hypothesis, the series has a unit root. MacKinnon (1996) p-values are reported. The data are daily. The lag order used for all tests is 5. Table 4: Phillips-Ouliaris test of cointegration between e,i∗−i,qπ and qπ(1 −π), with q= 0.25 before the Referendum Act short sample long sample currency tau-stat. p-value tau-stat. p-value ROWF-4.2152 0.0408 -4.3286 0.0284 ROWT-3.8752 0.0925 -4.4056 0.0228 EUR -3.7424 0.1230 -4.4336 0.0210 USA -5.6049 0.0004 -3.7631 0.1146 JAP -3.5305 0.1858 -3.9798 0.0702 CHE -3.2195 0.3103 -4.1857 0.0418 CAN -4.3852 0.0259 -3.9736 0.0712 DAN -4.1354 0.0500 -4.6831 0.0098 SWE -3.3361 0.2593 -4.3752 0.0249 NOR -2.7482 0.5496 -3.4241 0.2209 AUS -2.6069 0.6230 -3.4449 0.2130 NZL -3.7467 0.1219 -4.3929 0.0237 Notes: e: log exchange rate, i∗−i: difference between the foreign and the domestic (UK) interest rates, π: Leave probability, q: probability of the Referendum being held. Under the null hypothesis, the series are not cointegrated. MacKinnon (1996) p-values are reported. q takes value 1 after the EU Referendum Act. The data are daily. Short sample = 27 May 2015 to 30 June 2016. Long sample = 27 May 2015 to 23 June 2017. 39 Table 10: DOLS estimates for bilateral exchange rates of the British pound, long sample (5/27/2015-6/23/2017) EUR USA JAP CHE CAN i∗−i2.7628 1.8932 -9.1891*** 4.2397** 12.6548*** (2.0052) (1.7048) (2.2928) (1.8117) (2.0046) qπ 0.2556*** 0.2276*** 0.3427*** 0.2812*** 0.2311*** (0.0424) (0.0224) (0.0854) (0.0313) (0.0594) qπ(1 −π)0.3762*** 0.1969*** 0.2436 0.4174*** 0.4276** (0.1333) (0.0667) (0.2739) (0.1043) (0.1872) const -0.333*** -0.4469*** -5.3488*** -0.3505*** -0.7139*** (0.0158) (0.0061) (0.0169) (0.0279) (0.0033) q-0.0527 -0.0289 0.015 -0.1093*** -0.0965 (0.0436) (0.0224) (0.087) (0.0327) (0.06) q00.25 0.25 0.25 0.25 0.25 Notes: The table reports DOLS estimates (and HAC standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Euro (EUR), the US dollar (USA), the Japanese yen (JAP), the Swiss franc (CHE) and the Canadian dollar (CAN). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the constrained value of q0. Significance levels: *** 1%, ** 5%, * 10%. 46 Table 11: DOLS estimates for bilateral exchange rates of the British pound, long sample (5/27/2015-6/23/2017) DAN SWE NOR AUS NZL i∗−i4.9617*** 0.9038 8.0821*** -1.9371 0.8259 (1.3013) (1.689) (2.5124) (2.4186) (2.1076) qπ 0.2539*** 0.2427*** 0.248*** 0.3693*** 0.3426*** (0.0461) (0.0466) (0.066) (0.0483) (0.0452) qπ(1 −π)0.386*** 0.4778*** 0.3226 0.4749*** 0.283* (0.1446) (0.1506) (0.2059) (0.1608) (0.1489) const -2.3069*** -2.5835*** -2.5984*** -0.7335*** -0.8918*** (0.0154) (0.0184) (0.0138) (0.0432) (0.0551) q-0.0627 -0.0652 -0.0683 -0.1241** -0.0447 (0.0471) (0.0473) (0.0676) (0.0494) (0.0438) q00.25 0.25 0.25 0.25 0.25 Notes: The table reports DOLS estimates (and HAC standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Danish krone (DAN), the Swedish krone (SWE), the Norwegian krone (NOR), the Australian dollar (AUS) and the New Zealand dollar (NZL). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the constrained value of q0. Significance levels: *** 1%, ** 5%, * 10%. 47 Table 12: Robustness to pre-post Referendum time effect (1) (2) i∗−i2.4226 1.7625 (2.6838) (2.6822) qπ 0.3875*** 0.3225*** (0.0728) (0.0651) const -0.5008*** -0.5015*** (0.0207) (0.0234) q-0.0274 -0.0108 (0.0306) (0.0345) dvote -0.1455*** (0.042) q00.2333 0.2106 (0.1587) (0.1986) sample end 6/22/2016 6/30/2016 Notes: The table reports DOLS estimates (and HAC standard errors in parentheses) for the (log) financially-weighted effective exchange rate of the British pound (ROWF). The first column shows the estimates of the model under risk neutrality (i.e., excluding the volatility variable) over the pre-Referendum sample (ending on 22 June, 2016). The second column reports the estimates of the model with risk neutrality over our benchmark sample (ending on 30 June, 2016), including a pre-post Referendum time dummy, dvote.i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the estimates of q0. Significance levels: *** 1%, ** 5%, * 10%. 48 Table 13: Robustness: unrestricted breaks in βand γ parameter ROWFROWT θ3.88614* 2.911352 (2.27855) (2.302994) βpre -0.05966 -0.150593 (0.212925) (0.259593) γpre 0.336357 0.484026 (0.380051) (0.455674) βpost 0.183298*** 0.192482*** (0.022474) (0.027325) γpost 0.325318*** 0.345194*** (0.077369) (0.0909) α-0.522409*** -0.486603*** (0.023154) (0.030174) break date 1/7/2016 1/7/2016 F-test βpre =γpre = 0 0.0496 0.1178 Notes: The table shows the DOLS estimates (and HAC standard errors in parentheses) of equation (11) with breaks in coefficients βand γat an unknown date. Results are reported for the effective exchange rates ROWFand ROWT.βpre and βpost denote the values of β(i.e., the coefficient of variable π) before and after the promulgation of the Referendum Act, respectively. γpre and γpost denote the values of γ(i.e., the coefficient of variable π(1 −π)) before and after the promulgation of the Referendum Act, respectively. θis the coefficient of the interest rate differential i∗−i,αis the constant. The bottom part of the table reports the estimated break date and the p-value of a F-test of joint non-significance of βpre and γpre. The sample goes from 27 May 2015 to 30 June 2016. Significance levels: *** 1%, ** 5%, * 10%. 49 Table 14: Robustness: other uncertainty measures, short sample (5/27/2015-6/30/2016) (1) (2) (3) (4) (5) i∗−i2.9421 2.0983 0.6452 1.0581 0.9303 (2.7322) (2.5196) (2.7719) (2.8055) (2.8122) qπ 0.1423*** 0.2046*** 0.1595*** 0.1945*** 0.0547 (0.0349) (0.034) (0.0173) (0.0206) (0.0378) qπ(1 −π)0.4724*** 0.3799*** 0.2298*** 0.2972*** 0.0339 (0.1077) (0.1076) (0.0681) (0.0701) (0.0939) const -0.5072*** -0.5128*** -0.5337*** -0.5097*** -0.6008*** (0.0151) (0.0158) (0.0184) (0.0155) (0.0226) q-0.0573* -0.0512 -0.0249 -0.0412* 0.0324 (0.0301) (0.0349) (0.0201) (0.0232) (0.0249) epuuk 0.0045** 0.0005 (0.0019) (0.0016) vftse 0.0005 0.0006 (0.0004) (0.0004) volfx 0.0034*** 0.0125*** (0.0009) (0.0028) riskrev 0.0039*** -0.0139*** (0.0015) (0.0045) q00.25 0.25 0.25 0.25 0.25 Notes: The table reports DOLS estimates (and HAC standard errors in parentheses). The dependent variable is the log financially-weighted effective exchange rates of the British pound against the basket of ten currencies considered in the paper. i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the constrained value of q0.epuuk is the Economic Policy Uncertainty index (Baker et al., 2016) for the UK, divided by 100, vftse is the VFTSE index, i.e. the option-implied 1-month-ahead volatility of the FSTE 100 stock market index, volfx is the index of option-implied 3-month-ahead volatility of the BP/USD exchange rate, riskrev is the risk reversal of the BP, i.e. the difference between the implied volatility of out-of-the-money put options and the implied volatility of symmetric out-of-the-money call options. Significance levels: *** 1%, ** 5%, * 10%. 50 Table 15: Robustness: other uncertainty measures, long sample (5/27/2015-6/23/2017) (1) (2) (3) (4) (5) i∗−i0.5935 1.3074 2.8892 1.6795 2.3109 (2.1909) (2.1376) (1.9552) (2.0345) (1.96) qπ 0.2513*** 0.2478*** 0.2031*** 0.2214*** 0.2113*** (0.0341) (0.0338) (0.0205) (0.0204) (0.031) qπ(1 −π)0.2843*** 0.2883*** 0.1392* 0.1673** 0.0828 (0.108) (0.1081) (0.0803) (0.0692) (0.0892) const -0.511*** -0.5109*** -0.5182*** -0.5064*** -0.5263*** (0.0117) (0.0138) (0.0131) (0.0112) (0.0172) q-0.0432 -0.0443 -0.0153 -0.0253 -0.0112 (0.0348) (0.0344) (0.0221) (0.0217) (0.0271) epuuk -0.0007 -0.0023** (0.001) (0.0011) vftse 0.0001 0.0008 (0.0004) (0.0005) volfx 0.0028*** 0.0022 (0.001) (0.0027) riskrev 0.0049*** 0.0035 (0.0015) (0.0049) q00.25 0.25 0.25 0.25 0.25 Notes: The table reports DOLS estimates (and HAC standard errors in parentheses). The dependent variable is the log financially-weighted effective exchange rates of the British pound against the basket of ten currencies considered in the paper. i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the constrained value of q0.epuuk is the Economic Policy Uncertainty index (Baker et al., 2016) for the UK, divided by 100, vftse is the VFTSE index, i.e. the option-implied 1-month-ahead volatility of the FSTE 100 stock market index, volfx is the index of option-implied 3-month-ahead volatility of the BP/USD exchange rate, riskrev is the risk reversal of the BP, i.e. the difference between the implied volatility of out-of-the-money put options and the implied volatility of symmetric out-of-the-money call options. Significance levels: *** 1%, ** 5%, * 10%. 51 Table 16: Dynamic SUR (DSUR) estimates with cross-equation restriction on γ, short sample (5/27/2015-6/30/2016) EUR USA JAP CHE CAN i∗−i2.7124*** 3.3844** -8.2819*** 1.2882 12.9645*** (0.7166) (1.4367) (1.7205) (1.1762) (1.1735) qπ 0.212*** 0.1944*** 0.3458*** 0.2348*** 0.212*** (0.038) (0.0275) (0.057) (0.0387) (0.0475) qπ(1 −π)0.3773*** 0.3773*** 0.3773*** 0.3773*** 0.3773*** (0.0751) (0.0751) (0.0751) (0.0751) (0.0751) const -0.3366*** -0.4444*** -5.3476*** -0.3987*** -0.716*** (0.0072) (0.0055) (0.0142) (0.0191) (0.0065) q-0.0366 -0.0593** -0.0063 -0.0812*** -0.0779*** (0.0251) (0.0231) (0.0304) (0.0252) (0.0274) q00.2726 0.2726 0.2726 0.2726 0.2726 Notes: The table reports DSUR estimates (and standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Euro (EUR), the US dollar (USA), the Japanese yen (JAP), the Swiss franc (CHE) and the Canadian dollar (CAN). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the estimate of q0. The value of q0 and the long-run error covariance matrix are estimated in the first step by DOLS, imposing the equality of q0across currencies. The long-run covariance matrix is estimated using a Bartlett kernel with Newey-West fixed bandwidth of 6. In the second step (estimated by GLS), the coefficient of qπ(1 −π), i.e. γ, is constrained to be the same across currencies. Significance levels: *** 1%, ** 5%, * 10%. 52 Table 17: Dynamic SUR (DSUR) estimates with cross-equation restriction on γ, short sample (5/27/2015-6/30/2016) DAN SWE NOR AUS NZL i∗−i3.1692*** 1.2978 10.3613*** 5.5535*** 4.4605*** (0.4608) (1.1661) (1.2082) (1.3204) (1.0968) qπ 0.2153*** 0.2004*** 0.2091*** 0.251*** 0.2916*** (0.0366) (0.0401) (0.0524) (0.0553) (0.0505) qπ(1 −π)0.3773*** 0.3773*** 0.3773*** 0.3773*** 0.3773*** (0.0751) (0.0751) (0.0751) (0.0751) (0.0751) const -2.3303*** -2.583*** -2.6129*** -0.8691*** -0.9948*** (0.0071) (0.0129) (0.0098) (0.0246) (0.0309) q-0.0452* -0.0268 -0.0599** -0.052* -0.0181 (0.0247) (0.0255) (0.0289) (0.0295) (0.029) q00.2726 0.2726 0.2726 0.2726 0.2726 Notes: The table reports DSUR estimates (and standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Danish krone (DAN), the Swedish krone (SWE), the Norwegian krone (NOR), the Australian dollar (AUS) and the New Zealand dollar (NZL). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the estimate of q0. The value of q0and the long-run error covariance matrix are estimated in the first step by DOLS, imposing the equality of q0across currencies. The long-run covariance matrix is estimated using a Bartlett kernel with Newey-West fixed bandwidth of 6. In the second step (estimated by GLS), the coefficient of qπ(1 −π), i.e. γ, is constrained to be the same across currencies. Significance levels: *** 1%, ** 5%, * 10%. 53 Table 18: Dynamic SUR (DSUR) estimates with cross-equation restriction on γ, long sample (5/27/2015-6/23/2017) EUR USA JAP CHE CAN i∗−i2.0337*** 1.5482 -8.2178*** 1.8582** 8.4545*** (0.5483) (0.9981) (1.6131) (0.7491) (1.2655) qπ 0.2677*** 0.2941*** 0.3883*** 0.2872*** 0.2555*** (0.0332) (0.0341) (0.0354) (0.0332) (0.0351) qπ(1 −π)0.4089*** 0.4089*** 0.4089*** 0.4089*** 0.4089*** (0.108) (0.108) (0.108) (0.108) (0.108) const -0.3439*** -0.452*** -5.3514*** -0.3912*** -0.7155*** (0.0067) (0.0069) (0.0146) (0.013) (0.0076) q-0.0598* -0.0885*** -0.0215 -0.103*** -0.0997*** (0.034) (0.0343) (0.0372) (0.034) (0.0353) q00.2908 0.2908 0.2908 0.2908 0.2908 Notes: The table reports DSUR estimates (and standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Euro (EUR), the US dollar (USA), the Japanese yen (JAP), the Swiss franc (CHE) and the Canadian dollar (CAN). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the estimate of q0. The value of q0 and the long-run error covariance matrix are estimated in the first step by DOLS, imposing the equality of q0across currencies. The long-run covariance matrix is estimated using a Bartlett kernel with Newey-West fixed bandwidth of 6. In the second step (estimated by GLS), the coefficient of qπ(1 −π), i.e. γ, is constrained to be the same across currencies. Significance levels: *** 1%, ** 5%, * 10%. 54 Table 19: Dynamic SUR (DSUR) estimates with cross-equation restriction on γ, long sample (5/27/2015-6/23/2017) DAN SWE NOR AUS NZL i∗−i2.2747*** 1.0526 8.2497*** 1.4313 2.507*** (0.3911) (0.9661) (0.988) (1.2742) (0.8589) qπ 0.2691*** 0.2216*** 0.2731*** 0.3462*** 0.3802*** (0.0331) (0.0332) (0.0347) (0.0342) (0.0339) qπ(1 −π)0.4089*** 0.4089*** 0.4089*** 0.4089*** 0.4089*** (0.108) (0.108) (0.108) (0.108) (0.108) const -2.3427*** -2.5882*** -2.6031*** -0.7982*** -0.9443*** (0.0069) (0.0111) (0.0097) (0.0241) (0.025) q-0.0655* -0.0378 -0.0898** -0.0924*** -0.0635* (0.0339) (0.034) (0.0359) (0.0356) (0.0358) q00.2908 0.2908 0.2908 0.2908 0.2908 Notes: The table reports DSUR estimates (and standard errors in parentheses) for the bilateral log exchange rates of the British pound against the Danish krone (DAN), the Swedish krone (SWE), the Norwegian krone (NOR), the Australian dollar (AUS) and the New Zealand dollar (NZL). i∗−iis the difference between the foreign and the domestic (UK) interest rates, πis the Leave probability, qis the probability of the Referendum being held. qtakes value q0before the Referendum Act and 1 afterwards. The bottom part of the table reports the estimate of q0. The value of q0and the long-run error covariance matrix are estimated in the first step by DOLS, imposing the equality of q0across currencies. The long-run covariance matrix is estimated using a Bartlett kernel with Newey-West fixed bandwidth of 6. In the second step (estimated by GLS), the coefficient of qπ(1 −π), i.e. γ, is constrained to be the same across currencies. Significance levels: *** 1%, ** 5%, * 10%. 55