Stock market information and the real exchange rate - real interest rate parity

Transcription

1 Stock market information and the real exchange rate - real interest rate parity Juha Junttila y Marko Korhonen January 26, 2010 Abstract The real exchange rate is one of the key fundamental macroeconomic variables that economists continuously analyze, and one of the most intuitively and theoretically appealing approaches to model the behavior of the real exchange rate stems from the so called real exchange rate - real interest rate (RERI) parity. The main hypothesis in the RERI parity is that the di erence between the domestic and foreign real interest rates should be negatively correlated with the real exchange rate. Even though the RERI hypothesis appears reasonable theoretically in most monetary and portfolio balance models of the exchange rate, its empirical validity has not proven strong in previous studies. In this paper we propose an augmentation of the traditional RERI relationship, based on introducing the stock market equilibrium condition as an additional longrun concept a ecting the RERI condition. In view of our theoretical arguments, the proposed new information variable is the relative dividend yield. Using cointegration analysis applied to monthly observations for the period of 1974:1-2008:9 from the U.K., Japan, Canada and for 1991:1-2008:9 for the Eurozone, all relative to the U.S., we nd that the introduction of stock market information is highly relevant for the functioning of the RERI hypothesis. The role of relative stock market performance is especially important in the short-term (3 month) horizon, where the augmented RERI representation is most stronlgy supported. Hence, according to our results the di erences in stock market performance of the analyzed countries should absolutely be taken into account when analyzing the relationship between real interest rates and real exchange rates in view of the famous RERI hypothesis. Key words: real exchange rate, real interest rates, stock markets, cointegration JEL classi cation: E44, F21, F31, F41 This study is part of the research program of the Oulu Macroeconomic Group (OMaG), and the nancial support from the Yrjö Jahnsson foundation and the OP-Pohjola research foundation for the launching of the OMaG is gratefully acknowledged. y Corresponding author, contact information tel.: , fax: , Juha.Junttila@oulu.. Contact information for Marko Korhonen tel.: , fax , mjkorho@utu.. Address for both authors: University of Oulu, Department of Economics, Po Box 4600, FIN UNIVERSITY OF OULU, Finland. 1

2 1 Introduction The real exchange rate is one of the key fundamental macroeconomic variables that economists continuously analyze. Its importance in macroeconomic analyses is based its role in re ecting the competitiveness of national real economies. One of the most intuitively and theoretically appealing approaches to model the behavior of the real exchange rate stems from the so called real exchange rate - real interest rate (RERI) parity. The original roots of this approach are in the sticky-price monetary models of Dornbusch (1976) and Frankel (1979), and especially in Meese and Rogo (1988). The main message from the RERI approach 1 is that the di erence between the domestic and foreign real interest rates should be negatively correlated with the real exchange rate, when the nominal exchange rate is measured in units of domestic currency per one unit of foreign currency. This indicates that as the di erence between the domestic and foreign real return on (interest yielding) assets increases, the value of the domestic currency appreciates 2. Even though the RERI hypothesis appears reasonable theoretically in most monetary and portfolio balance models of the exchange rate, its empirical validity seems questionable. Using quarterly data Baxter (1994) found some empirical evidence for the RERI relationship at trend and business-cycle frequencies during the oating-rate period of for France, Germany, Japan, Switzerland, and the U.K., all pairwise analyzed against the U.S. Furthermore, her results indicated that the real interest di erentials are related only to the temporary component of real exchange rates, and because most of the movement in real exchange rates seemed to be due to changes in the permanent component, the link was very weak. Other recent studies focusing on the RERI hypothesis (and modi cations of it) are the papers by Wu (1999), Edison and Melick (1999), Nakagawa (2002), Ho man and MacDonald (2003 and 2009), Coakley et al (2004), and Mark and Moh (2005). Wu (1999) utilized the Johansen cointegration procedure and extended the standard RERI hypothesis to allow for the e ects of cumulative current account (CCA) balance on the US-Germany and US-Japan exchange rates. His main nding was that the data contained long-run relationships among real exchange rates, real interest di erentials and cumulative current account di erentials, supporting the prediction of most monetary approaches to real exchange rate determination. Also Edison and Melick (1999) introduced the CCA to the analysis of RERI hypothesis as one of their three di erent approaches. They labeled their rst approach as the standard, i.e. assuming constant expected real exchange rate in the long run, whereas the second approach utilized the above mentioned CCA as the additional variable in the RERI equation, and the third approach was based on using the ex post values and forecast errors for the real exchange rate in the analysis. However, their empirical evidence remained somewhat limited, and only moderate support for cointegration between the relevant variables was found at long horizons, and the evidence was even more vague for short horizons. Nakagawa (2002) used a non-linear time series analytical approach to examine the RERI hypothesis, and found that only outside the so called band of inaction (based on a transaction cost-induced price adjustment), the real exchange rate behaves like a mean reverting variable and is associated to real interest di erentials. Other highly methodologically oriented papers have been provided by Ho man and MacDonald (2003 and 2009). In their 2003 paper the main emphasis was in strengthening the ndings of both Baxter (1994) and Edison and Pauls (1993), suggesting that the strongest link between real exchange rates and real interest di erentials is in the business cycle domain, and not in the low frequency domain. Ho man and MacDonald (2003) used the cointegration approach for 1 Theoretical details of the original, pure RERI hypothesis are given in the next section. 2 Like emphasized by Baxter (1994), it is important to di erentiate between the ex ante and ex post measures at this point. For example, in terms of ex ante values for the RERI, if the euro real exchange rate is above its long-run level against the U.S. dollar, the euro is expected to depreciate in real terms in the future, and to equate the ex ante real returns between the Euro area and the U.S., the ex ante real return on the euro-denominated securitites must exceed the corresponding return on the U.S. securities by the expected real devaluation of the euro over the term of the securities. Hence, there is a predicted link between the level of the real exchange rate and the ex ante relative real interest rate. 2

3 the period of for the G7 countries and indeed obtained ndings mainly consistent with Baxter and Edison and Pauls. However, in the more recent Ho man and MacDonald (2009) paper the main focus was somewhat di erent. Using an approach was based on the Campbell and Shiller (1987) present value model, they were able to provide robust evidence that the RERI link is actually strong and the real interest rate di erential strongly re ects the expected rate of currency depreciation over long horizons. The main idea was that if we assume that the real interest rate di erential is the sum of expected period-to-period changes in real exchange rates, the real interest rate di erential can be interpreted as the spread variable in a present-value model where the discount factor is known and close to one 3. This enables them to derive the projection for the change in the real exchange rate from a bivariate VAR for the change in the real exchange rate and the real interest rate di erential, and to correlate this projection with the real interest di erential. Based on the obtained results they suggested that the RERI relationship should be interpreted more broadly as a signi cant and positive relationship between expected real exchange rate changes and the real interest rate di erential in the data from the G7 countries for the period from 1978 to 2007, and a high fraction of the variability in interest rate di erentials is actually explained by changes in the rate of expected depreciation. Furthermore, for a larger country set, Coakley et al (2004) used a nonstationary panel regression framework and attempted to accommodate both permanent and temporary shocks to the RERI parity. They also found that there is a signi cant long-run relationship between exchange rates and both short-term and long-term interest rate di erentials in the data from 23 industrialized countries over the period. The approach adopted in our paper is partly based on the ideas given in Mark and Moh (2005), who also have proposed the pricing of the real exchange rate be based on real interest parity in a non-linear framework. They regressed the log real US dollar prices of the Canadian dollar, deutschemark, yen and pound on the fundamental values implied by some nonlinear models for the RERI, and found an important role for the nonlinearities especially for shorter horizons. However, because our approach is actually more directed towards including other, more explicit, variables in the RERI relationship, in the empirical analysis we stick to the linear approach, at least at this stage of our research. In fact, the origin for our suggestion to include the stock market information in the analysis of the RERI relationship is the famous paper by Solnik (1987). He was among the rst to introduce stock market data to exchange rate modelling. The main innovation in his paper was to realize and empirically formulate the role of exchange rates as nancial prices, which mimick the discounted value of all available information e.g. about the expected future real economic activity. Accordingly, he argued that if real economic activity is expected to improve in the near future, it should be immediately discounted in the exchange rate as well as in current stock prices. Furthermore, Solnik (1987) treated the changes in interest rates mainly as indicators of monetary shocks. Using monthly and quarterly observations for the period from 1973 to 1983 from Canada, France, Germany, Japan, the Netherlands, Switzerland, the U.K., and the U.S. he was able to nd some evidence that the real exchange rates were a ected by changes in the interest rate di erentials, but not prior to 1979 at all. More importantly, especially in the period after September 1979, a positive relation between real stock return di erentials and changes in the real exchange rate was evident. More recent papers examining the relationships between stock market information and exchange rates are the studies by Malliaropulos (1998), Hau and Rey (2006), Mercereau (2006), Andersen et al (2007), Pavlova and Rigobon (2007), Matsumoto et al (2008), and Engel and Matsumoto (2009). Malliaropulos (1998) analyzed the existence of permanent and temporary components both in real exchange rates and relative stock prices and found an observable relationship between expected stock return di erentials and expected changes in the real exchange rates for four OECD countries relative to the U.S. He also revealed that the long-horizon stock 3 See also Engel and West (2004) for the implications of the unitary discount factor in the monetary models of exchange rate. 3

4 returns of G5 countries relative to the US were negatively correlated with long-horizon deviations of dollar exchange rates from the purchasing power parity in these countries. Hau and Rey (2006) derived an elegant theoretical (equilibrium) model for exchange rates, stock prices and capital ows under incomplete foreign exchange risk hedging. Their theoretical analysis implied that increasing equity market di erentials in favor of the home market depreciate the home currency, and that net equity ows into the foreign market are positively connected to foreign currency appreciations. Their theoretical a priori hypotheses obtained support from their empirical analyses for the data from 17 OECD countries against U.S. data at daily, monthly and quarterly frequencies during the period , especially for the countries with high equity market capitalizations relative to GDP. Hence, they also found that the observed exchange rate dynamics are clearly related to equity market development. Another theoretical derivation has been provided by Mercereau (2006), who stressed the role of a country s nancial structure in a ecting its real exchange rate, as well as the volatility of it. He showed that countries whose nancial assets provide more risk-hedging bene ts to the world have an appreciated real exchange rate, and the more risk-hedging bene ts a country can derive from international nancial markets, the more its real exchange rate appreciates. Andersen et al (2007) is among the rst comprehensive studies to analyze all the relevant asset markets (i.e., stock, bond and foreign exchange) in a multi-country setting. They used a high-frequency (futures) dataset that clearly revealed the response of U.S., German, and British stock, bond, and foreign exchange markets to real-time (U.S.) macroeconomic news. They analyzed empirically the explicit role of fundamentals in the pricing processes of these assets, and the main result was that macro announcement surprises produced conditional mean jumps in the asset market returns. Hence, according to their results the high-frequency stock, bond and exchange rate market dynamics are linked to macro fundamentals in the data from 1992 (and from 1998 for a sub-sample) to Furthermore, in their generalized approach, taking into account simultaneous e ects for all the analyzed asset markets, they found signi cant contemporaneous cross-market and cross-country linkages, even after controlling for the macroeconomic announcement e ects. Pavlova and Rigobon (2007) have also analyzed the e ects of real economy shocks on the international propagation mechanisms in the asset markets. Their work theoretically generalized the many previous ideas in the extant literature regarding the comovements in stock, bond and foreign exchange rate markets in an international asset pricing model. The main implication from their theoretical model was that the introduction of trade in goods and demand shocks into an otherwise traditional international asset pricing model results in a representation where the worldwide nancial state prices and the equilibrium values of the terms of trade are strongly connected, enabling a full characterization of the transmission mechanism and the ensuing dynamic behavior of asset prices and exchange rates. Thus, they found that in a two-country setting, the stock, bond, and currency market prices are all characterized by a common set of fundamental factors in equilibrium. Their theoretical a priori hypotheses were supported to a degree by the empirical analyses of monthly and daily data from the U.S. and the U.K. Finally, among the most recent attempts to formalize the relationships between currency and other asset markets and the macroeconomy are the papers by Matsumoto et al (2008) and Engel and Matsumoto (2009). Both these highly innovative papers utilized the modern dynamic stochastic general equilibrium (DSGE) models to analyze the connections of both the currency and equity markets to the real economy. In Matsumoto et al (2008) the main emphasis was in deriving a model that enabled them to study the role of news about future productivity and monetary policy for equity price and exchange rate dynamics, especially focusing on volatility and comovement of the prices in these markets under alternative information assumptions and monetary policy reactions to productivity shocks. The model was an extension of Devereux and Engel (2006, 2007), and the two main theoretical hypotheses focused on i) the e ects of current and news shocks on macro fundamentals, and ii) the role of currency denomination of the equity returns and monetary policy. For the rst part, they identi ed the positive correlation between current and news shocks as 4

5 an indicator of the information content in the news shocks that generate higher volatility in exchange rates and equity prices. They showed that when news shocks are positively correlated with current shocks, asset prices are more volatile for a given volatility of the underlying stochastic processes. The basic intuition behind this was that asset prices are forward looking and respond both to information about future evolution and current values of their fundamentals. Second, they postulated that the comovement between exchange rate and equity return di erentials is dependent on the currency denomination of the equity returns and monetary policy. More speci cally, they claimed that if the monetary authority does not engage in systematic monetary policy, or if monetary policy does not respond to the output gap, equity return di erentials measured in investor currency are independent of the exchange rates and a ected only by current and news shocks to productivity. On the other hand, if the output gap plays a role in monetary policy actions, there is counterfactual correlation between equity return di erentials measured in investor currency and the exchange rate according to the model. For a set of 17 countries (calculating the asset returns relative to the US market), and based on quarterly observations, they were able to nd some empirical support for these main hypotheses. From a somewhat di erent point of view Engel and Matsumoto (2009) argued purely theoretically for the role of price stickiness of nominal goods markets as a potential factor a ecting the degree of equity market diversi cation in a two-country setting. They obtained two main outcomes from their model. First, they showed that when there is a high degree of nominal goods price stickiness, the availability of foreign-exchange hedges has a role to play in international risk sharing, if agents can trade equity shares and forward positions in foreign exchange. On the other hand, if agents can diversify against risk arising from nominal exchange rate uctuations, with su cient nominal price stickiness, diversi cation in the equity portfolio need be minimal. Their second main theoretical implication from the model was that transitory price stickiness can have a large impact on international asset choice, stressing again the role of goods market price behavior on asset market outcomes. Based on the given literature review it is obvious that both the theoretical and empirical approaches to the analysis of the behavior of real exchange rate vary a lot. However, the most recent theoretical and empirical advances seem to be connected to introducing the role of stock market information into the analysis in one way or another. This is the main innovation we aim to analyze in our paper. We present a novel, but very simple approach to the analysis of the RERI relationship, based on joining together some of the many ideas in the previous literature. The main emphasis in our analysis is in acknowledging that the behavior of real exchange rate is governed both by long-run goods and asset market equilibrium relationships, and the information contained in them should be jointly included in the analysis of the real exchange rate behavior. Hence, our basic idea is to augment the original, theoretically and intuitively highly appealing RERI relationship with additional information, where this additional information is based on the main long-run equilibrium relationships in the goods, asset, and currency markets. The introduction of these equilibrium conditions ultimately leads as to conclude, that the relative dividend yield is the additional simple information variable to be included in the RERI analysis. Moreover, because here we allways speak about long-run equilibrium relations in the analyzed markets, our empirical approach at this stage also utilizes only the highly familiar long-run method, i.e., cointegration analysis. Our paper proceeds in the following way. In section 2 we give the theoretical background for the part of the traditional real interest parity and our idea on the augmentation of it using stock market information. Section 3 contains the description of the data and methods for the empirical analysis of the proposed augmentation, and section 4 gives details of the empirical results. Finally, in section 5 we report the main implications from our empirical evidence for the proposed role of stock market information in the analysis of the RERI hypothesis, and also sketch something for the future research agenda on this theme. 5

6 2 Theoretical background 2.1 The traditional real interest rate parity Analogously to Meese and Rogo (1988) and Nakagawa (2002), we start our analysis from the sticky-price models of exchange rate determination, where deviations of the expected real exchange rate at time t + k (denoted E t q t+k ) from its long-run equilibrium value 4 in the future (q t+k ) are related to the current deviations of the real exchange rate from its current long-run equilibrium value, i.e., E t (q t+k q t+k ) = k (q t q t ); (1) where 0 < < 1 is the speed of adjustment. The above expression can equally well be written as E t q t+k q t = ( k 1)(q t q t ) + E t q t+k q t ; (2) where the term E t q t+k q t is zero when the ex ante purchasing power parity holds in the long run, i.e., there are no real shocks in the economy or all the real shocks follow a random walk. On the other hand, values other than zero for this term can be justi ed if expected in ation or productivity growth are di erent from zero. Furthermore, equation (2) may also be given as E t q t+k q t = ( k 1)(q t q t ) + constant. (3) Now, according to the uncovered interest parity condition, in equilibrium the expected changes in the nominal exchange rate (s t ; denoted as the value of domestic currency in relation to one unit of foreign currency) are related to the k period nominal interest rate di erences between the corresponding domestic (i) and foreign (i ) interest rate, i.e. E t s t+k s t = i t;k i t;k: (4) Taking both these equilibrium conditions into account, we may write the familiar Dornbusch (1976) and Frankel (1979) real interest rate parity condition as E t q t+k q t = E t r t;k E t r t;k; (5) where the ex ante value for the k period real interest rate for the domestic country is and correspondingly, for the foreign country E t r t+k = i t;k E t (p t+k p t ); (6) E t r t+k = i t;k E t (p t+k p t ); (7) where p and p are the logs of domestic and foreign country price indexes, respectively. Combining equation (3) with equation (5) we obtain q t = 1 Et k r t;k 1 E t rt;k + qt + constant. (8) Under the assumption 0 < < 1 we obtain the traditional Meese and Rogo (1988) null that the real exchange rate is negatively related to the expected real interest rate di erence. This is the basic form of the RERI parity that has been analyzed empirically in Nakagawa (2002) and Mark and Moh (2005). However, di erent from all of the previous studies, in this paper we augment the real interest rate parity with stock market information given in the form of dividend yields (from the aggregate stock markets of both the domestic and foreign countries), and the theoretical background for this augmentation of the standard real interest rate parity is given next. 4 This equilibrium value can be noted to re ect the exible price equilibrium value (see Meese and Rogo (1988) and Nakagawa (2002)). 6

7 2.2 Stock market information and the real exchange rate The starting point in our augmentation process for the real interest parity is the traditional Gordon (1962) growth model that gives the fundamental stock market pricing equation as D t Pt S = i t gt+1 e e ; (9) t+1 where the current (time t) value of equity (stock price) is denoted by P S t, and i t is the nominal (short-term) interest rate at time t, D t is the dividend realized at time t, and g e t+1 is the expectation of the growth rate of economy for the next period (formed at time t based on information at time t), re ecting also the growth possibilities of future real yields on stock investments, and correspondingly, e t+1 is the expected in ation rate for the next period at time t. Put simply, equation (9) states that in equilibrium the current stock price should be a discounted value of the expected future dividend conditional on the available information at time t. When compared to the more conventional text-book presentations of this fundamental pricing equation, we actually decompose the required rate of return k t in two time-varying parts, namely the expected growth in dividends captured by the combination of current (observed) dividend yield and the real growth rate of aggregate economy, g e t (mimicking the growth potential of future dividends), and the real required rate of return from alternative investment targets, proxied by the real ex ante short-term rate of interest, i t e t. 5 Note that because (9) actually involves expectations on more than one variable, it basically gives a dynamic relationship between the current stock price and the explicit, D t, and implicit, (i.e. the risks in g e t+1 and e t+1), fundamentals which have an e ect on it. At this point we do not want to formalize the model in terms of any certain expectations horizons (like daily, monthly or lower frequencies), but wish to keep the representation as general as possible. Equation (9) can equally well be written in terms of the dividend yield, d t = D t =P S t, that is, d t = i t g e t+1 e t+1: (10) Our representation at the moment involves two very frequently analyzed macroeconomic variables, namely the expected in ation and real growth of the economy. The role of stock and other nancial market information in forecasting these two variables has recently been high on the research agendas of many leading economists, like James Stock and Mark Watson. Hence, in the spirit of their 2003 study (see Stock and Watson (2003) and the references therein), we next introduce two very familiar macroeconomic equilibrium conditions regarding these variables to our analysis. These are the Fisher (1930) equation and the Euler equation 6 i t = r e t+1 + e t+1 (11) r e t+1 = + g e t+1: (12) We add these as behavioral long-run equilibrium conditions, not just accounting identities, to the model. In addition to the previously de ned variables, is the rate of time preference, and is the reciprocal of the intertemporal elasticity of substitution, both assumed to be constant over time. 5 A more thorough discussion and the backround for using explicitly this form of the Gordon valuation model are given (and available on request) in a working paper version of the authors recent study on using stock market information in forecasting macroeconomic variables other than the real exchange rate, too. 6 Put more precisely, our speci cation of the Euler equation follows the Romer (2006, p ) presentation for household behaviour, assuming that household consumption growth is strongly connected to the expectations of future aggregate economic activity (see also the introduction in Cochrane (2006)). 7

8 Moving towards an open economy extension of this single-country representation involves the use of some additional basic long-run equilibrium conditions. As in the previous subsection, using the simple two-country setting, we rst rewrite the Fisher equation given in (11) for each country in the form i t = rt+1 e + E t p t+1 (13) i t = rt+1 e + E t p t+1 where we use the expectations one period ahead only for notational convenience. Star (*) again indicates the foreign country variables. Equation (13) gives the nominal interest rate in each country as the sum of ex ante real interest rate and expected in ation. For example, for the home country e t+1 = E t p t+1 p t = E t p t+1 and here p t+1 and p t refer now to the log values of the domestic Consumer Price Index (CPI). The purchasing power parity (PPP) introduces a long-run goods market condition in the form of di erences in the country-speci c price levels to the model, yielding an equilibrium condition for the goods markets in the two countries. Using the log notations de ned in the previous subsection we have q t = p t + s t p t ; that is, s t = p t p t + q t : (14) After introducing both the nancial market equilibrium conditions (9-12) and the goods market condition (14) to the model, we need a connection between these two. This comes from adding again the uncovered interest parity (UIP) condition to the model, indicating that in an overall long-run equilibrium the current di erence between the nominal interest rates in the two countries should equal the expected change in the exchange rate, i.e., i t i t = E t s t+1 (15) Hence, the nal derivation of a testable equation for on open economy extension of the Gordon model would start from formulating the PPP relation in (14) for expected values, which gives E t s t+1 = E t p t+1 E t p t+1 + E t q t+1 ; and using the relative version of PPP, the previous equation can be written as E t s t+1 = E t p t+1 E t p t+1 + E t q t+1 : (16) Assuming an overall equilibrium in all the markets analyzed, we may replace the nominal interest rate di erence from UIP on the left hand side of (16), which gives us i t i t = E t p t+1 E t p t+1 + E t q t+1 : (17) From the Fisher equations for both countries we get E t p t+1 = i t r e t+1 and E t p t+1 = i t r e t+1 and placing the Fisher equations now in (17) gives us the equation that is, i t i t = E t p t+1 E t p t+1 + E t q t+1 : E t q t+1 = r e t+1 r e t+1; or written in terms of levels for the real exchange rate as q t = E t q t+1 (r e t+1 r e t+1): (18) The last equation is again the real interest rate parity, but now perhaps more familiar from studies like Malliaropulos (1998) in this form. The basic idea is that in the longrun equilibrium based on the PPP and UIP conditions the expected real exchange rate 8

9 can be expressed as the sum of the current real exchange rate and the real interest rate di erence. In other words, the current real exchange rate is the expected real exchange rate minus the di erence between the domestic and foreign (ex ante) real interest rates. Most of the literature on PPP (starting with Dornbusch (1976)), has stated that the real interest rate di erence and the current real exchange rate move in opposite directions, indicating a negative correlation between them. Many later empirical tests of this framework have assumed that expectations about the future real exchange rate are constant, but Meese and Rogo (1988) pointed out that this assumption is invalid; market fundamentals would seem to have strong e ects on the long run expectations of the real exchange rate, and they should actually be modeled as time-varying expectations. However, assume for now that the PPP as a long-run hypothesis holds, and hence, the expectations on the real exchange rate could be deemed constant (denoted by ). If we collect all the relevant equations for the equilibrium values of asset prices in our model together, we have for both countries a stock market fundamentals equation (i) that is based on the equilibrium conditions stated in equations (10) and (12) together and rearranging, and based on equations (11) and (12) a Taylor-rule type interest rate equation (ii), and nally, real interest parity condition (iii) for the real exchange rate in the two-country context, that is based on equation (18), and assumes that the PPP holds as a long-run equilibrium condition. Hence, the total system of equations is comprised of i) d t = (1 )g e t+1 ii) i t = + g e t+1 + e t+1 iii) q t = (r e t+1 r e t+1): We can see that the country-speci c Euler equation is the central building block for the rst two equations, and using Euler equations for both countries (namely, that rt+1 e = + gt+1 e and rt+1 e = + gt+1), e equation (iii) in the above system comes into form 7 q t = (g e t+1 g e t+1); (19) and solving for the expected values rst from equations (i) and (ii) yields gt+1 e = 1 e t+1 = i t 1 d t 1 d t 1 : Finally, by using the obtained real growth equilibrium equations, gt+1 e = 1 and gt+1 e = d t 1 1, and noting that the dividend yields in the di erent stock markets are allowed to deviate from each other, from equation (19) we get the third, and the most interesting nal equation for our system of equations linking the pure nancial market information to the development of the macro economy, and especially the real exchange rate. This is an equilibrium condition for the currency market in terms of di erences in the dividend yields between foreign and domestic markets, that is q t = d t d t 1 1 : (20) Equation (20) is among the key hallmarks for our empirical analysis, and hence, it requires a more detailed discussion regarding its theoretical a priori implications. First, if 7 Here we make use of an assumption on average investors behaviour that in both countries the rate of time preference and the intertemporal elasticity of substitution are the same and constant, so the di erences in the real rates of interest are here supposed to come basically from the di erences in the growth rates of real economies. d t 9

10 we relax the PPP as a long-run hypothesis (i.e. the rst term,, in equation (20) for the real exchange rate is not a constant), we would have the case where the expectations on real exchange rate are time-varying, and equation (20) actually comes into form d qt+1 e = q t + t d t 1 : (21) A somewhat similar representation has previously been analysed by Malliaropulos (1998), but not by using the same kind of stock market information we emphasize, i.e. the dividend yield data. For a more detailed discussion, note rst that the dividend yields d t and d t consist of both the current dividend streams, D t and Dt, and the current values of the stock prices Pt S and Pt S at domestic and foreign markets, respectively. If we assume that the dividend streams in both countries are fairly smooth, i.e., almost constant (but not similar), at least when compared to the stock prices, the interesting part about the discussion actually involves the di erences in the stock prices, and hence, expected returns in these two markets. In fact, for an intuitive example, in case of assuming that PPP holds, the analysis can be executed purely in terms of di erences in the current stock prices between the two markets. Suppose, for instance, the foreign stock market price index at time t has the value of Pt S = 5, whereas the domestic index is Pt S = 6, and for simplicity, assume that the aggregate market dividend paid in both countries is 0.2 per share, measured in common currency. Hence, the di erence in the dividend yields is now greater than zero (because (0.2/5) > (0.2/6)) implying a depreciating e ect on the current real exchange rate according to equation (20). However, when the PPP hypothesis is relaxed, i.e., when equation (21) is the appropriate equilibrium condition for the expected real exchange rate, we might think of the stock market variables in terms of current stock prices versus expected stock returns. This indicates analysis to be conducted in terms of proportional changes in dividend yields between the two countries. If for example Pt S would now be expected to decrease from 5 to 4 (that is, the foreign market would crash 20 %) and correspondingly, the domestic market price is expected to decrease from 6 to 5 (that is, the domestic crash is only 17 %), this would entail that, ceteris paribus, the proportional change is higher in Pt S than in Pt S in terms of expected returns. This gives us a novel hypothesis proposing that as the current Pt S goes down, the expected foreign stock market return (for given dividend streams in both countries) rises, and if the change in the foreign stock prices is proportionally higher than the change in domestic stock prices, that is R e t+1 > R e t+1; where Rt e and Rt e are the foreign and domestic expected total stock market returns (comprising of both the capital and dividend yields), we have a case, where the expected real exchange rate appreciates. So basically, when remembering that the higher the current stock price is in either of the markets the lower is the expected return on that market, we obtain here a null hypothesis that the real exchange rate is expected to appreciate, when (d t d t ) > 0; because the proportionally high current foreign stock price implies a low foreign dividend yield when compared to the domestic dividend yield. A dynamic relationship for the connection between the stock market information and real exchange rate based on equation (21) can be derived as follows. Referrring to (21) we de ne = 1, qe t = E t q t+1 and t = d t d t : Based on these notations we obtain from (21) a representation q t = t + E t q t+1 (22) Forwarding this equation one period ahead we have and inserting this in equation (22) gives q t+1 = t+1 + E t+1 q t+2 ; q t = t + E t ( t+1 + E t+1 q t+2 ) = t + E t ( t+1 ) + E t q t+2 : 10

11 By continuing this forward iteration for k periods (and using the law of iterated expectations, i.e. that E t (E t+1 (x t+2 ) = E t (x t+2 ) etc.) we get the representation q t = t + E t ( t+1 ) + E t ( t+2 ) + ::: + E t ( t+k ) + E t q t+k+1 : Assuming that in the long-run equilibrium E t q t+k+1 = q, i.e., that the expectations for the real exchange rate in the far distant future are constant 8, we get the nal representation for the dynamic relationship between the stock market information and the real exchange rate as kx q t = q + 4 E t t+j 5 kx = q + E t 4 (d t+j d t+j ) 5 ; (23) 1 j=0 implying that the values for the real exchange rate at time t are partly composed of the sum of future dividend yield spreads. Hence, we propose that taking into account this potential relationship might be useful in empirical analyses of real interest rate parity, and help to resolve the previously observed mismatch of the theoretical ideas and empirical ndings. 2.3 Joining the real interest rate parity and stock market information The derivation of the nal representation for the empirical analysis in this paper is based on combining the two above given equilibrium frameworks for the value of the real exchange rates. In section (2.1) we already observed that for the derivation of the original Dornbusch (1976) and Frankel (1979) real interest rate models the uncovered interest rate parity plays the nal key role. In view of this, and analogously to Mark and Moh (2005), we next use the UIP in the form E t (s t+1 s t ) = (i t i t ); (24) and we again de ne the log of the real exchange rate as q t = s t + p t p t ; where all the notations follow our work above (for the log of the real exchange rate, log of the nominal exchange rate (domestic currency per one unit of foreign currency), and logs of foreign and domestic price levels, respectively, star (*) denoting again the foreign values). However, de ne now the (expected) real interest rate di erential as E t t+1 E t (rt+1 r t+1 ) = (i t i t ) E t p t+1 p t (p t+1 p t ) : From this we get the real interest rate parity by subtracting the expected in ation di erential from both sides of (24), i.e., E t (s t+1 s t ) E t (pt+1 p t ) (p t+1 p t ) resulting in j=0 = (i t i t ) E t (pt+1 p t ) (p t+1 p t ) ; E t q t+1 q t = E t (r t+1 r t+1 ): Now, because E t (r t+1 r t+1 ) = E t t+1 ; the previous equation gives us E t q t+1 q t = E t t+1 ; and hence, q t = E t q t+1 + E t t+1 : Forward iteration of this representation one period ahead and using again the law of iterated expectations yields q t = E t q t+2 + E t t+1 + E t t+2 ; and for the k-period ahead case we get, correspondingly q t = E t q t+k + E t t+1 + E t t+2 + ::: + E t t+k : 8 This is analogous to the exible price equilibrium value referred to in connection to equation (1) in the previous subsection. 11

12 For the very long-run horizon we may again use the assumption that expectations of the real exchange rate are constant, i.e. E t q t+k = q: This gives us now the representation kx kx q t = q + E t 4 t+j 5 = q + E t 4 (rt+j r t+j ) 5 ; j=0 stating that the real exchange rate is comprised of a sum of future expected real interest rate di erentials. Combining this implication with our nding given in equation (23), stating that the values for real exchange rate at time t are at least partly comprised of the sum of future dividend yield spreads, gives us the nal equation for the empirical analysis of an augmented real interest rate parity in the form kx q t = constant + E t 4 (rt+j r t+j ) 5 Xk1 + E t 4 (d t+j d t+j ) 5 : (25) 1 j=0 Furthermore, based on our discussion after the equations (21) and (22) for the role of stock market information, and on the previous results in many empirical papers (see also the introduction) on the theoretical a priori assumptions for the original real interest parity, we impose the following a priori assumptions for the e ects of real interest rates and dividend t < 0; > 0; < 0; > t;k t;k In addition, an obvious restriction for the regression analyses regarding the model given in (25) is that 6= 1 for the coe cient on the dividend yield di erence to be well de ned, implying also that the intertemporal elasticity of substitution should not be equal to one. 3 Data and empirical methods We examine the empirical relationship between real exchange rates, relative real interest rates and relative dividend yields for four countries: the U.K., Japan, Canada and the Eurozone, and maintain the U.S. as the foreign counterpart for each country. The empirical analyses use monthly data and the sample period varies for each country depending on the availability of the data. For the UK, Japan and Canada the sample period is 1974:1-2008:9 and for the Eurozone the sample period is 1991:1-2008:9. The primary sources of data are the IMF s International Financial Statistics (IFS) and OECD Main Economic Indicators databases, but the dividend yield data are from Datastream 9. When measured in levels, we convert all data except interest rates and dividend yields to log values, so the growth rates of each of the analyzed variables are measured by log di erences. Price levels are measured by consumer price indices (CPI), and the in ation rates are annual in ation rates, measured as the 12-month log di erences of CPIs. Short-term nominal interest rates are the 3-month money market rates (or "call money rates"). Exchange rates are de ned against the U.S. dollar, and long-term interest rates are the 10 year long bond yields. The real exchange rate is calculated by taking log values of the expression based on multiplying nominal spot bilateral exchange rates by foreign (U.S.) prices, that are divided by domestic prices. The nominal exchange rates are de ned as units per dollar, so an increase in nominal exchange rate indicates depreciation of the domestic currency and appreciation np 9 P In Datastream the dividend yield is calculated based on the equation d t= 100[( D n tn t)=( Pt SNt), N=1 N=1 where d t is the aggregate dividend yield on day t (and we use the values for the last trading day in each month), D t is the dividend per share on day t, N t is the number of shares in issue on day t, Pt S is the unadjusted share price on day t, and n is the number of constituents in the index. The useful data on dividend yields for our purposes are calculated for the shares quoted only in the domestic market of each of the analyzed countries, and these series are available from Datastream. j=0 12

13 of the U.S. dollar. For the real interest rates and dividend yields we compute both ex ante and ex post values. For the ex post values we have assumed rational expectations, and subtracted annualized realized 3-month CPI in ation rate from the short-term nominal interest rate and 36-month CPI in ation rate from the nominal long-term interest rate. For the calculation of ex ante real interest rates we rst generated in ation expectations over a three month horizon for the short-term rates and over a three year horizon for the long-term rates. These procedures were based on running univariate rolling autoregressions for the CPI-in ation with appropriate lag structures in view of the Schwarz information criterion and the statistical signi cance of the AR-parameters in each case 10. To be exact, according to our theoretical model we need to calculate cumulative sums for relative real interest rates, P (r r); and relative dividend yields, P (d d); and these values are based on the cumulative sums for the short-term (3 month) and long-term (36 month) periods, both for the ex post and ex ante values. However, for comparison, we will also report the results based on point values of the explanatory variables in our main regression equation regarding the most relevant parts of our analysis. 4 Empirical results Table 1 presents a summary of descriptive and other statistics on the real exchange rates and ex ante and ex post measures of cumulative real interest rate and cumulative dividend yield di erentials. Based on these results it would seem that the data generating processes (DGP) of all the analyzed series are highly persistent and have very high rst order autocorrelation coe cients, which might indicate the presence of unit roots in the DGPs. The tests for unit roots were conducted without a deterministic trend, and the results indicated that the series mainly behave like unit root processes. However, in some cases the augmented Dickey-Fuller (1979)-test results based on the null of unit root were inconclusive with the Kwiatkowski-Phillips-Schmidt-Shinn (1992)-test results based on the null of stationarity. Especially for the real exchange rate series the test results were in favor of nonstationarity. The fact that the null of unit root could not be rejected for our main variable indicates that deviations from PPP may have lasted a long time in this data set. Notice that Baxter (1995) has strongly argued that the real exchange rate should be a stationary variable, and the existence of permanent components in its DGP does not imply that the real exchange rate follows a random walk, i.e. that it is non-stationary, because in the long run there might be temporary (mean-reverting) components in the data as well. Nevertheless, based on our results from the preliminary descriptive statistics we clearly are able to argue that real exchange rates are quite persistent, and we might be forced to conclude that they are nonstationary in our data set 11. [Table 1 here] On the other hand, regarding our new interesting variable in connection to the RERI analysis (the relative dividend yield) Ang and Bekaert (2007) present evidence that dividend yields and interest rates should also be stationary series. Based on these previous notes and discussions, in this paper we will proceed with our analysis by allowing for the possibility that all our variables may be either stationary or nonstationary in small samples, and examine all the relevant data both in levels and di erence forms when we empirically analyze our proposed model. Furthermore, because our cumulative procedures for calculating 10 The use of a 3-year period for the long-term (10 year) real rate calculations was based on the empirical nding that the expected values of in ation generated from the rolling AR-procedure did not change materially when moving from the 36-month horizon to the longer horizons, so the 10-year horizon values were very close to the 3-year horizon values. 11 For similar kinds of arguments on the inference from the unit root test results for real exchange rates, see Engel (2000). 13

14 the explanatory variables also involve overlapping mechanisms, especially for the long-run variables, the observed autocorrelation in some of our data series might be arti cially generated. To control for these arti cial persistence e ects we also report the results from the cointegration analysis using the future point values for the explanatory variables. When using the data in levels, we consider two di erent speci cations. The rst speci- cation in table 2 is based on analyzing our version of the traditional RERI representation, involving only the real exchange rate and real interest rate di erentials. The second speci - cation, based on equation (25) given in the previous section, augments the traditional RERI hypothesis, and introduces the relative dividend yield to the analysis. The results reported in table 2 are designed to give a priori judgement for the validation of these two di erent regressions for the modeling of real exchange rate 12. The column titled Traditional RERI reports the very simple OLS- regression results based on using only the relative real interest rate as the regressor. The column titled Augmented RERI gives the results from the model, where the relative dividend yield is an additional regressor. We report the regression coe cients and test results from the F-tests for the validity of including the additional relative dividend yield variable to the model. In addition, as a proxy for the explanatory power of each of the competing speci cations, and for the purposes of giving a quantitative measure for the observed validity of the models based on visual inspection in gure 1, we also report the cross correlation coe cient between the actual real exchange rates and the tted values of each of the analyzed models, respectively. From the F-test results we see that the relative dividend yield is a signi cant additional regressor in almost all of our cases at the 1% signi cance level. Furthermore, simply by testing the statistical signi cance of the additional variable we nd that the augmentation is useful in 13 cases out of 16 at the 5 % level. Hence, we obtain preliminary support for the use of an augmented model instead of the traditional RERI presentation for our further analyses. Also based on the cross correlation coe cients the explanatory power of the augmented model clearly improves compared to the traditional representation. [Figure 1 here] [Table 2 here] Based on our results in table 1 and in many previous papers (e.g. Meese and Rogo 1988 and Edison and Pauls 1993), we next proceed to the stage allowing for the presence of unit roots in the analyzed time series processes. We use the Johansen (1988) multivariate cointegration system approach to test for cointegration between the variables in our model. The estimation results are based on a vector autoregressive (VAR) model with a constant term. The optimal lag lengths were chosen using the likelihood ratio statistics, and the residuals from the chosen VAR speci cations were then checked for white noise characteristics implying the validity of the nal representations. Our cointegration analysis for the augmented RERI model is based on a three variable vector error correction model (VECM), given in its general form as: z t = z t 1 + px i=1 iz t i + t ; (26) where z t = q t ; P (r t+j r t+j ); P (d t+j d t+j ) ; = 0 ; and and are 3 1 vectors, whereas i is a 3 3 matrix of parameters associated with z t i in our application. Table 3a reports the results from the cointegration analysis using the cumulative values of the right-hand-side (RHS) variables in equation (25). Again, we give the results for the traditional RERI model and for the augmented version of it. In most (that is, 12) of the 16 possible cases (comprising of 4 countries, for short- and long-term horizons, and for ex post and ex ante values of the explanatory variables) we were able to nd one cointegrating 12 For this kind of preliminary regression based analysis of parity-type relationships see Ang and Bekaert (2007). 14