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Taylor Rules and Exchange Rate Predictability in Emerging Economies Jaqueson K. Galimberti Marcelo L. Moura Insper Working Paper WPE: 217/2010 Copyright Insper. Todos os direitos reservados. É proibida a reprodução parcial ou integral do conteúdo deste documento por qualquer meio de distribuição, digital ou impresso, sem a expressa autorização do Insper ou de seu autor. A reprodução para fins didáticos é permitida observando-sea citação completa do documento T AYLOR R ULES AND IN E XCHANGE R ATE P REDICTABILITY E MERGING E CONOMIES J A Q U E S O N K. G A L I M B E R T I UNIVERSIDADE FEDERAL DE SANTA CATARINA M A R C E L O L. M O U R A † INSPER – INSITUTE OF EDUCATION AND RESEARCH FEBRUARY, 2010 Abstract This study links exchange rate determination and endogenous monetary policy represented by Taylor rules. We fill a gap in the literature by focusing on a group of fifteen emerging economies that adopted free-floating exchange rate and inflation targeting beginning in the mid-1990s. Due to the limited time-series span, a common obstacle to studying emerging economies, we employ panel data regressions to produce more efficient estimates. Following the recent literature, we use a robust set of out-of-sample statistics using bootstrapped and asymptotic distributions for the Diebold-Mariano, Clark and West and Theil’s U ratio. By evaluating different specifications for the Taylor rule exchange rate model based on their out-of-sample performance, we find that the forward-looking specification shows strong evidence of exchange rate predictability. Key words: Taylor rule exchange rate model; forecasting; emerging economies; panel data; bootstrap. JEL: † F31, F37, F41, F47. Corresponding author: Rua Quatá 300, São Paulo-SP – Brazil – CEP:04546-042,Tel.: 4504-2435, [email protected] 1 1 - INTRODUCTION This study aims to investigate exchange rate predictability for a selected group of fifteen emerging economies (Brazil, Chile, Czech Republic, Colombia, Hungary, Israel, Mexico, Peru, Philippines, Poland, Romania, South Africa, South Korea, Thailand and Turkey) that share similar monetary policy regimes and have adopted free-floating exchange rate regimes. We contribute to the literature by joining two promising approaches. First, we use panel data regression to deal with limited time series and increase forecasting efficiency. Second, we investigate more realistic endogenous monetary models by testing a robust set exchange rate Taylor rule model. We also respond to Rogoff and Stavrakeva’s (2008) criticism of exchange rate models’ predictability regarding the misinterpretation and biased use of out-of-sample statistics. In particular, we construct appropriate bootstrapped confidence intervals for out-of-sample statistics from Diebold and Mariano (1995), Clark and West (2006, 2007) and Theil’s U ratio. Where does this study stand regarding the exchange rate predictability literature? First, let us say a few words about the literature itself. Testing exchange rate models became popular after the major industrialized economies adopted floating exchange rates with the abandonment of the Bretton Woods system in the early 1970s.1 The gathering of data on independently floating exchange rates allowed the proliferation of several empirical studies, as in Bilson (1978), Hodrick, (1978), and Putnan and Woodburry (1980). These found favorable evidence for the exchange rate models of the 1970s: significant coefficients with the expected signs, fine model in-sample fit and satisfactory performance in the diagnosis tests. However, the empirical results changed drastically beginning in the 1980s with Meese and Rogoff’s (1983) seminal paper. Using the United States-related exchange rate data for the United Kingdom, Japan, and Germany, they concluded that, in a one- to twelve-month forecasting horizon, the random walk model performs at least as well as the exchange rate models of that time, namely, the flexible price and sticky price monetary models and a hybrid model by Hooper and Morton (1982). A plethora of studies followed Meese and Rogoff’s (1983) work. Some claimed to reverse the no-predictability results, such as Mark (1995). Using innovative bootstrapping techniques and exchange rate data from 1973 to 1991 for Canada, Germany, Japan and Switzerland relative to the US dollar, the author found support for forecasting monetary models at horizons between 12 and 16 quarters for some countries. However, predictability evidence was short lived. Subsequently, criticism came from Kilian (1999), who demonstrated that Mark’s results were not robust for sample modifications and that they crucially depended on the assumed data generating process. Furthermore, Mark’s (1995) implicit assumption of cointegration of the exchange rate and monetary fundamentals has also been subject to criticism. Berkowitz and Giorgianni (2001) showed that if the assumption of cointegration is not valid, then tests are biased toward rejection of the null of no predictability. Inconclusive results were common until the early to mid-2000s. Sarno and Taylor (2002), who surveyed the literature of the 1980s and 1990s, claimed: ‘the empirical results tended to be fragile in the sense that they were hard to replicate in different samples or countries.’ Cheung, Chinn, and Pascual (2005) tested predictability for the US dollar-based exchange rates of the Canadian dollar, British pound, Deutsche mark and Japanese yen by assessing a wider set of models than those used in the 1980s and 1990s. Their results were inconclusive: ‘model/specification/currency combinations that work well in one period do not necessarily work well in another period’. 1 This system, established in 1944, determined that each country should fix its exchange rate in relation to the U.S. dollar, which was convertible to a fixed amount of gold. 2 Surprisingly, in the last half of the 2000s a large number of studies claimed evidence of exchange rate out-of-sample performance. According to Engel, Mark and West (2007), emphasizing the importance of the monetary policy rule, using exchange rate models determined by expected present values of fundamentals, longer data spans and panel data provided more hope for the existence of exchange rate predictability. Basically, these studies focus on two alternative approaches. Some use larger panel data sets in a set of similar countries, such as Groen (2005), Rapach and Wohar (2004) and Mark and Sul (2001). These studies use unit root and panel cointegration techniques and find evidence of predictability for the monetary model, especially over longer horizons. However, the models used in most of these studies are the old monetary models of the 1970s and 1980s. Investing in more innovative and realistic models, another line of research still focuses on country-by-country estimation but assumes endogenous monetary policy in exchange rate Taylor models. Some recent studies on this include the following: Molodtsova and Papell (2009), Engel and West (2005) and Engel, Mark and West (2007) for industrialized countries and Moura (2008), Moura, Mendonça and Lima (2008) and Ketenci and Uz (2008) for developing economies. The basic approach of the Taylor exchange rate model is to conciliate uncovered interest parity with interest rates determined endogenously, as they are in practice, by a Taylor rule reaction function. In summary, all of these studies found significant evidence of exchange predictability for the Taylor model. However, despite the large number of studies with evidence of exchange rate predictability, the controversy was not over. Rogoff and Stavrakeva (2008) claimed that most of the predictability found in recent results is due to the misinterpretation of new out-of-sample tests, as in Clark and West (2006, 2007), and failure to test for robustness using different alternative time windows. Finally, we can answer the question we posed in the beginning of this section. Our study adds to the recent developments in research of exchange rate determination on emerging economies. More specifically, this study groups the recent promising approaches and responds to criticism of them. In fact, we can specify three main contributions. First, instead of looking at just one or two models, the panel data are estimated for an extensive set of models to provide a better comparison group. Second, we contribute to the study of emerging economies with similar characteristics: countries that, despite their increasing importance in the world economy, are not as well studied as the industrialized economies. Third, we improve forecasting accuracy evaluation by using a larger, robust set of out-of-sample statistics. The remainder of this work is divided into five sections. Section 2 explains the Taylor rule exchange rate model. Section 3 describes the data and the panel unit root and cointegration tests run in our selected series and models. Section 4 details the forecasting approach and the bootstrapping methodology. Section 5 discusses the results, and the last section presents the conclusions, limitations, and likely extensions of this work. 2. TAYLOR MODELS OF EXCHANGE RATE DETERMINATION Since the mid-1980s, most central banks have started to use interest rate as their policy instrument instead of the control of some aggregate measure of the money supply. This characteristic has an important implication for exchange rate models: instead of using an exogenous interest rate as an explanatory variable for the exchange rate, it is important to use an endogenous monetary policy rule, a point already made by Engel, Mark and West (2007). 3 Engel, Mark and West’s (2007) approach Their approach builds an exchange rate model that incorporates such characteristics. Interest rates are set by the central bank through a reaction function determined by: it = q qt Et t 1 y yt it 1 ut (2.1), where it is the logarithm of one plus the nominal interest rate at time t, qt is the logarithm of the real exchange rate at time t, t 1 is the logarithm of one plus the inflation rate at time t 1, yt is the logarithm of one plus the output gap at time t, and q , , y and are parameters for which we assume q > 0, > 0, y > 0, 0 < 1 . For our benchmark country, which will be the United States, a similar Taylor reaction function is defined as: it = * Et t1 y yt it1 ut (2.2), where the same notation applies, with an asterisk denoting that the variable refers to the benchmark country. One important assumption we made is that the interest rate reacts to the real exchange rate for our emerging economies (see equation (2.1)) but does not for the United States (equation (2.2)). This assumption is quite reasonable for emerging economies: Moura and Carvalho (2009) estimated Taylor rules for seven Latin American emerging economies and found that Taylor rules including exchange rates as explanatory variables yield superior predictability results. The last part of the Taylor model assumes uncovered interest parity, that is: it it = Et st 1 st (2.3), where st is the logarithm of the nominal exchange rate, and Et denotes the conditional expectation operator. Using equations (2.1) through (2.3) and assuming that the home and benchmark countries have similar parameters, we have: st = Et st 1 q qt * Et t 1 t1 y yt yt it 1 it1 ut ut (2.4). Solving this finite difference equation forward implies: st pt pt * b nj =0b j X t j t (2.5), where pt and pt * are the respective logarithms of consumer price indices for the reference and benchmark countries and: b 1 , 1 q 4 X t j * 1 Et t 1 j t1 j y yt j yt j it 1 j it1 j and = b nj =0b j ut j ut j t To estimate (2.5), we assume the same approach used by Moura (2008), where expectations for the near future are a proxy for future expected values. Formally, we will assume that we can approximate expectations for all future dates j= 1, 2, 3, … by expectations at a fixed date K 12. E y E i Et t 1 j t1 j Et t K t K , t and yt j Et yt K yt K , t t j t t 1 j it1 j Et it K it K vt vt 1 . This assumption leads us to the final empirical specification, which we define as the EMW symmetric model: st pt p*t 1 Et t 12 t12 2 Et yt 12 yt12 3 Et (it 12 i t 12 (2.6). ) 4 qt 1 vt An alternative specification would assume no asymmetry in the reaction function parameters, leading to the forward-looking EMW asymmetric model: st pt p*t 1 Et t 12 1* Et t12 2 Et yt 12 2* Et yt12 3 Et (it 12 ) 3* Et (it12 ) 4 qt 1 vt (2.7). Molodtsova and Papell’s (2009) approach An alternative formulation of the Taylor model is based on Molodtsova and Papell (2009), hereinafter denoted the MP model. We now assume contemporaneous Taylor rules for both the home and foreign countries: it = t y yt it 1 ut (2.8) it = * t y yt it1 ut (2.9). and In addition, the uncovered interest parity holds without expected values, st 1 = st it it (2.10). The model is then solved by substituting equations (2.8) and (2.9) into (2.10). If we additionally assume symmetrical parameters in the reaction functions, this leads to the following empirical specification: 5 st st 1 1 t 1 t1 2 y t 1 y t1 3 ( it 2 it 2 ) vt (2.11). If we instead assume asymmetrical parameters in the Taylor rules, we have: st st 1 1 t 1 1* t1 2 yt 1 2* yt1 3it 2 3*it 2 vt (2.12). We will call equation (2.11) the MP symmetric model and (2.12) the MP asymmetric model. One possible criticism of the approach followed by Molodtsova and Papell (2009) is that the Taylor rules are misspecified because it is likely that Central Banks react not to contemporaneous inflation and output gap but instead to expected values. In these forward-looking specification, we replace inflation and output gap in (2.8) and (2.9) with their respective expected values. With this modification, the empirical specifications for the symmetrical and asymmetrical cases are: st st 1 1 Et t 12 t12 2 Et yt 12 yt12 3 Et (it 12 it12 ) vt (2.13) and E i E i v st st 1 1 Et t 12 1* Et t12 2 Et yt 12 2* Et yt12 3 t t 12 * 3 t t 12 (2.14). t Exchange rates derived from (2.13) and (2.14) will be denoted as, respectively, the MP-expected symmetric and the MP-expected asymmetric models. 3. PANEL UNIT ROOT AND COINTEGRATION TESTS Our data set constitutes an unbalanced panel of monthly data from January 1995 to December 2008 for fifteen inflation targeters in developing countries: Brazil, Chile, Colombia, Mexico, Peru, Czech Republic, Hungary, Poland, Romania, Turkey, Israel, Thailand, Philippines, South Korea and South Africa. The data were collected from Thomson DataStream and International Monetary Fund Statistics. A detailed description of each series is shown in the Appendix. The criterion for choosing the countries and the size of the sample was that all of the countries, during most of the sample period, adopted the independently floating exchange regime and the monetary framework given by the inflation target system according to the International Monetary Fund (IMF) definition. Table 1 provides a detailed explanation of the exchange rate regime classification and the monetary policy framework adopted for each country. We can see that the majority of the countries adopted the current regime (at the time of this writing) during the late 1990s and the remainder in the early 2000s. There is also significant homogeneity across countries in terms of exchange rate regime, entity that defines the inflation targets, situations where the target can be disregarded, target indicator and inflation target level. Therefore, at least in terms of monetary policy and exchange rate regimes, it makes sense to group those countries in a panel data model. Our process of estimation for a posteriori evaluation of the forecasting potential extends the methodology of Cheung, Chinn and Pascual (2005) of country-by-country models to an unbalanced one-way error component model, as described in Baltagi (2008). More specifically, we can nest all of the models 6 discussed above, as well as equations (2.6), (2.7), (2.11), (2.12), (2.13) and (2.14) presented in Section 2, into the model: sit X it uit uit i vit i 1, 2,..., Nt t 1, 2,..., T (3.1), where Nt N 15 is the number of countries observed at time t , X t is the vector of economic fundamentals, and is a vector of coefficients. Notice that the error has two components: An unobservable country effect i and a stochastic disturbance term vit . We assume i to be a fixed parameter to be estimated and the remainder of the disturbance to be stochastic, vit ~ IID(0, v2 ) . Before we proceed with the estimation of the exchange rate models based on equation (3.1), we run some diagnostic panel tests. The importance of these tests will become clear in section 4, when we will introduce our error correction model to forecast exchange rates. As mentioned in Westerlund and Basher (2007), cointegration implies and is implied by an error correction model. Therefore, first, we test for the stationarity of our variables by running panel unit root tests. These tests have a higher power than unit root tests of individual time series. Then, we test for cointegration among the variables in each of the exchange rate models of section 2. Similarly to panel unit root tests, panel cointegration tests are motivated by having more power than individual time-series cointegration tests. By pooling countries with similar characteristics, we increase the span of the data by adding cross-sectional variation, which will increase the power of the unit root and cointegration panel tests; see Baltagi (2008). Phillips and Moon (1999) studied a range of regressions within panel vectors with and without cointegrating relations. Differently from pure time-series spurious regression, where OLS estimates of the coefficient are not consistent, the use of panel data gives consistent estimates of the coefficients. According to Baltagi (2008), the result found by Phillips and Moon (1999) is due to the fact that the panel estimator averages out across individuals because it samples from independent cross-sections. This leads to a stronger overall signal than is obtained in the pure time series case. In Table 2 we show the results for three alternative unit root tests developed by Levin, Lin & Chu (2002), hereinafter referred to as LLC; Im, Pesaran and Shin (2003), hereinafter referred to as IPS; and Hadri (2002), hereinafter referred to as HAD. These three alternative tests were chosen because they allow for different null assumptions. LLC assumes a null of a common unit root process, whereas the IPS test has the null of an individual unit root process. Finally, the HAD test reverses the null, assuming stationarity. In general, the results in Table 2 point to the rejection of the null of non-stationarity, implying that most of the series are stationary processes. The only exceptions are the inflation rate, the relative interest rate and the relative output gap, which have inconclusive results. In Table 3, we perform panel cointegration tests developed by Kao (1999). The goal is to test for a unit root in the residuals of each estimated Taylor rule exchange rate model, equations (2.6), (2.7), (2.11), (2.12), (2.13) and (2.14). We chose to use Kao’s (1999) panel cointegration tests, which use ADF-type unit root tests of the panel data residuals to check for the null of no cointegration. Like the two-step Engle and Granger (1987) cointegration test for single time-series, if the variables are cointegrated, the residuals should be stationary. Table 4 displays the results of Kao’s tests, which reveal strong evidence of cointegration for all of the assumed Taylor models. 7 4. FORECASTING METHODOLOGY The forecasting exercise extends the error correction methodology adopted by Cheung, Chinn, and Pascual (2005) for country-by-country equations to a one-error component panel data model. More specifically, we first estimate specification (3.1) for each model, obtaining, for each country, the fundamental value for the exchange rate: sˆit X it ˆ ˆ i i 1, 2,..., N t 1, 2,..., T (4.1). Then, we estimate a country-specific error correction model, stripped from the short-run dynamics. This error correction model is created on a country-by-country basis by the following equation: si ,t k sit ik ik ( sˆit sit ) vit (4.2). For each country, the estimated parameters of equation (4.2) are used to forecast the future values of the exchange rate at one, six and twelve months ahead. The parameter ik is essential in the sense that it will dictate convergence of the exchange rate to its fundamental value. An alternative formulation to the error correction model defined in equation (4.2) is to pool the constant, ik , and the slope parameters, ik . This procedure will imply a pooled error correction model: si ,t k sit k k ( sˆit sit ) vit (4.3). The pooled error correction model is adopted in Mark and Sul (2001) and is tested by Westerlund and Basher (2007). Basically, it assumes that the predictability of the exchange rate is homogeneously distributed across the emerging economies in our panel. Given the similarities across our sample data in terms of exchange rates, regimes and monetary policies, as previously discussed, we believe this assumption is not so strong. For robustness purposes, however, we will test the predictability of both approaches: the country specific error correction model, equation (4.2), and the pooled error correction model, equation (4.3). Therefore, to build an out-of-sample forecast for the exchange rate, we perform this two-step procedure recursively using rolling regressions. Equations (3.1) and (4.2) or (4.3) are estimated for an initial sample of fixed size — in our case, 48 periods — and result in forecasts for one, six and twelve months ahead. Using the rolling regressions method, we displace the estimation of the models one period ahead, keeping the size of the initial sample constant. We repeat the procedure up to sample exhaustion. The results from this procedure were then compared with those obtained iswith the forecasting of a model that assumes the exchange rate following a driftless random walk given by: sirw,t k sit i 1, 2,..., N t 1, 2,..., T (4.4). In order to compare the out-of-sample predictive accuracy of these forecasts we use asymptotic and bootstrapped versions of three testing statistics: the Theil’s U ratio (TU), the Diebold and Mariano (1995) statistic (DM), and the Clark and West (2006, 2007) statistic (CW). The bootstrapped distributions of these statistics are generated following a similar procedure as that proposed by Westerlund and Basher (2007). Specifically, for each country in our sample we estimate, by least squares, the data generating 8 process (DGP) of the exchange rate and its deviation from the fundamentals as an error correction model under the null hypothesis of no predictability, as shown in equation (4.5). Δsi,t μˆ i vˆi,t p q k 1 k 1 Δzi,t αˆi γˆi zi,t δˆi,k Δsi,t k φˆi,k Δz i,t k uˆi,t (4.5) Where zit sit sˆit is the deviation of the exchange rate from its fundamental value predicted by the Taylor rule models, equations (2.6), (2.7), (2.11), (2.12), (2.13) and (2.14) presented in Section 2, and the lag orders p and q are selected using the Akaike information criteria. The residuals obtained from the estimation of equation (4.5) are subsequently resampled with replacement, and the resulting bootstrapped residuals are then used to recursively 2 construct the bootstrapped sample of zi,t and si,t. These simulated series are then used to estimate equations (4.2), (4.3) and (4.4). Finally, the out-of-sample test statistics are obtained and this bootstrapping procedure is repeated 1,000 times in order to draw the empirical distribution of these statistics. 5. RESULTS Tables 4.a and 4.b present the results of the forecasting exercise for the country-specific and pooled error correction models, respectively, by reporting the statistics proposed by Diebold and Mariano (1995) with bootstrapped confidence intervals, hereinafter referred to as DMB. The DMB statistic is computed as the mean of the difference in the squared forecasting errors between the random walk benchmark and the specified exchange rate model. Under the null hypothesis, this difference is zero. Positive values of this statistic, associated with the rejection of the null at 10% or lower, are considered in cases where the exchange rate model outperforms the random walk. We find the best predictability performance for the EMW Taylor model using the country-specific models. This model, using the methodology proposed by Engel, Mark and West (2007), presents evidence of better forecasting than the random walk for 13 of our 15 countries included in the sample and in 27 out of 45 country/horizon combinations, or 60% of the cases. To give a better visual idea of how accurate these forecasts are, Figure 1 presents the EMW symmetric Taylor model using the country-specific models, with values forecasted six months ahead and the realized values for the logarithm of the exchange rates for all countries. To avoid distortion caused by scale, the realized logarithms of nominal exchange rate values were normalized to zero in January 1993. The EMW symmetric model in the pooled error correction specification shows performance similar to that of its country-specific counterpart; see Table 4.b. The model beats the random walk in 56% of the overall country/horizon combinations and for 12 out of 15 countries in our sample. The EMW asymmetric model has slightly lower performance than its symmetric counterpart. This result is coherent with the known fact that imposing restrictions, such as the symmetry in parameters, can sometimes improve predictability because it involves estimating a considerably smaller number of coefficients. Regarding the MP specifications, the performance is very modest. In fact, predictability is found in less than 10% of all country/horizon combinations for the variants of Molodtsova and Papell’s (2009) Taylor rule model, less than our significance level for the test. This poor performance of the MP model was 2 We use the actual data for starting values of the recursion, and discard the first 100 simulated observations in order to attenuate potential bias. 9 already reported by Rogoff and Stavrakeva (2008) for industrialized economies when measuring out-of-sample performance with a bootstrapped Diebold and Mariano (1995) statistic. Thus, there was not much surprise when we found the same result for emerging economies in this study. In general, we also find that predictability worsens as we increase the forecasting horizon from one to six and twelve months. This is a different result from most of the literature for industrialized economies, but it makes much more economic sense if the convergence of the exchange rate to equilibrium values is fast enough. To evaluate results in a more systematic way, in panel A of Tables 5.a and 5.b we present the hit rate (number and percentage of times the model outperformed the random walk) for the DMB statistic. To verify the robustness of our results, we present in the same tables the hit rates of the bootstrap versions for the Clark and West (2006, 2007) and Theil’s U statistic, hereinafter denominated, respectively, CWB and TUB. Qualitatively, the relative performances of the models are the same for the DMB, CMW and TUB statistics. Quantitatively, TUB has the highest hit rates in both country-specific and pooled error correction models, while the CMW is about the same as the DMB in the country-specific version and slightly higher in the pooled version. Finally, in Tables 6.a and 6.b we present the DM and CW statistics using asymptotic distributions for constructing confidence intervals. The reported results confirm the criticism reported by Rogoff and Stavrakeva (2008). In general, the use of the asymptotic distribution instead of the bootstrapped version decreases predictability for the DM statistic and increases it for the CW. In summary, our results indicate three important facts. First, compared to the literature on exchange rate predictability for industrialized countries, the predictability of Taylor rule exchange rate models applied to this group of emerging countries performed much better. Second, compared to other emerging economies studies using country-by-country analysis, the use of pooling information significantly improved predictability. Our interpretation is that this last result comes from the fact that we grouped countries with similar characteristics and that we increased efficiency in estimation by using panel data regressions. Third, we also verified that some heterogeneity existed by using country fixed effects in our panel, and permitting different adjustment coefficients on the country-specific error correction specification, equation (4.2), improves results. 6. CONCLUSIONS, LIMITATIONS AND FUTURE EXTENSIONS This study contributes to the literature by linking the study of inflation targeting to exchange rate determination and by linking Taylor models to panel data forecasting. From this, we find that inflation targeting in emerging economies appears to have exchange rates driven by forward-looking macro variables. Our endogenous monetary policy Taylor model for the EMW specification indeed outperforms the random walk for 60% of the analyzed country/horizon combinations. Another important conclusion is that significant predictability results can be obtained by pooling information for countries with similar monetary policies and exchange rate frameworks. Because we do not possess longer time series for developing economies, the use of panel data regressions more than compensates for the homogeneity constraints that are imposed. One possible reason for the apparent success of pooling information may also come from the fact that global market investors analyze these countries in a similar manner, leading to common responses to macroeconomic fundamentals. The study has many limitations that may lead to promising future studies. To name one important limitation, we dealt with partial equilibrium analysis. 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Testing the Taylor Model Predictability for Exchange Rates in Latin America”, Open Economies Review, doi:10.1007/s11079-008-9098-0. Moura, Marcelo L., Lima, Adauto R. S. and Mendonça, Rodrigo M., “Exchange Rate and Fundamentals: The Case of Brazil”, Revista de Economia Aplicada, Vol.12 (3), 2008, 395 - 416. Moura, Marcelo L. and Carvalho, Alexandre, “What Can Taylor Rules Say About Monetary Policy in Latin America?”, Journal of Macroeconomics, doi:10.1016/j.jmacro.2009.03.002, 2009. Neely, Christopher. J. and Sarno, Lucio, “How well do monetary Fundamentals forecast Exchange Rates?” Working paper series: The Federal Reserve Bank of St. Louis, WP 2002–007, 2002. Obstfeld, Maurice, Rogoff, Kenneth., “Exchange Rate Dynamics Redux”, Journal of Political Economy, Vol. 103 (3), 1995, 624–660. Phillips, P. C. B., Moon, H. “Linear regression limit theory for nonstationary panel data”, Econometrica, 12 Vol. 58, 1999, 165-193. Putnam, Bluford. H. and Woodburry John R., “Exchange Rate Stability and Monetary Policy”, Review of Business and Economic Research, Vol. 15 (1), 1980, 1–10. Rapach, David E. and Wohar, Mark E., “Testing the Monetary Model of Exchange Rate Determination: A closer Look at Panels”, Journal of International Money and Finance, Vol. 23 (6), 2004, 867–95. Sarno, Lucio and Taylor, Mark P., The Economics of Exchange Rates, Cambridge University Press, Cambridge, 2002. Westerlund, Joakim and Basher, Syed A., “Can Panel Data Really Improve the Predictability of the Monetary Exchange Rate Model?, Journal of Forecasting, Vol. 26, 2007, 365–-383. APPENDIX: DATA DESCRIPTION Data for all fifteen emerging economies plus the United States exist in an unbalanced way from January 1995 to December 2008. The data sources for all variables are DataStream and the IMF’s International Financial Statistics. All of the expected values for macroeconomic variables were obtained from the Consensus Economic Forecast Survey available from DataStream. Because expected values are available on a monthly basis for current-year and next-year values, 12-month-ahead values were computed as an average of the current year’s and next year’s values, where weights are proportional to the respective number of months in the current year and the next year for a 12-month period. ‘Exchange rate’ is the logarithm of the end of the month values of the nominal exchange rates, defined as home currency per US dollar. ‘Expected inflation’ is the logarithm of the ratio of one plus the country’s expected inflation over one plus US expected inflation. We add one because the expected inflation less target can be negative. ‘Expected industrial production gap’ is the logarithm of one plus the country’s expected industrial production gap divided by one plus the US expected industrial production gap. Again, we add one to avoid a logarithm of negative values. First, the expected 12-months-ahead industrial production series was computed using Consensus Economic Forecast values; then, a Hodrick-Prescott filter was applied to this series to capture the expected industrial production gap. ‘Expected interest rates’ is the logarithm of the country’s nominal interest rate divided by the nominal interest rate of the US. ‘Real exchange rate’ is defined as the logarithm of the nominal exchange rate multiplied by the country’s price level ratio to the US price level. ‘Price level’ is the consumer price index normalized to the value of one at the initial date, January 1999. ‘Industrial production’ is the logarithm of the seasonally-adjusted industrial production index of each country divided by its US counterpart. ‘Interest rate’ is the logarithm of the short-term monetary policy nominal interest rate divided by the US federal fund rates. 13 Table 1 - Exchange rate regime classification and monetary policy framework for the selected emerging economie Start date of the Inflation Targeting IMF exchange rate Country Regime classification Entity who defines the target Situation where the target can be disregarded Brazil Jun-99 Independently Government in consultation None floating with central bank Chile Jan-91 Independently Central bank in consultation None floating with government Colombia Sep-99 If managed floating Jointly by government and None with no precentral bank Czech Jan-98 Independently Central bank Natual disasters, price and exchange rate Republic floating schocks that are not consequence of the domestic monetary policy Hungary Jan-01 Independently Jointly by government and None floating central bank Israel Jan-92 Independently Government in consultation None floating with central bank Korea Jan-98 Independently Central bank in consultation None floating with government Central bank None Mexico Jan-99 Independently floating Peru Jan-94 If managed floating Central bank in consultation None with no prewith government Philipines Jan-02 Independently Jointly by government and None floating central bank Poland Oct-98 Independently Central bank None floating Romania Aug-05 If managed floating Jointly by government and Events that cannot be foreseen or that are out with no precentral bank of Central Bank control South Feb-02 Independently Central bank Events that cannot be foreseen or that are out Africa floating of Central Bank control Thailand Apr-00 If managed floating Government in consultation None with central bank with no preTurkey Jan-02 Independently Jointly by government and None floating central bank Indicator for the target Headline CPI Headline CPI Headline CPI Core CPI (excl. regulated prices and inderect taxes) Headline CPI Headline CPI Headline CPI(before 2000)/Core inflation Headline CPI Headline CPI Headline CPI Headline CPI Headline CPI Core CPI (excl. interest costs) Core CPI ( excl. raw food and energy Headline CPI Note: Information on inflation targets was obtained from the respective Central Banks’ websites. Information on the exchange rate classifications was obtained from the IMF website: http://www.imf.org/external/np/mfd/er/2008/eng/0408.htm. 14 Table 2 - Unit Root Panel Tests Series Nominal Exchange Rate Inflation Rate Output Gap (S.A.) Monetary Policy Interest Rate Expected Interest Rate (t+12) Expected Inflation Rate (t+12) Expected Outuput Gap (t+12) Relative Inflation Rate to the U.S. Relative Output Gap (S.A.) to the U.S. Relative Interest Rate to the U.S. Relative Expected Interest Rate (t+12) to the U.S. Relative Expected Inflation Rate (t+12) to the U.S. Relative Expected Outuput Gap (t+12) to the U.S. Rlative Price Level to the U.S. Real Exchange Rate Levin, Lin & Chu (t-value) -7.72187 *** 42.7841 -6.06282 *** -2.95529 *** -6.01859 *** 3.99509 -11.9397 *** -2.87019 *** 42.6943 -4.2458 *** -3.07767 *** -4.41728 *** -1.761 ** -3.29341 *** -11.9397 *** Im, Pesaran and Shin (W-stat) -3.4495 *** 0.85231 -11.8641 *** -2.33125 *** -4.71155 *** -5.78669 *** -7.52095 *** -2.32548 ** 0.8479 -11.5362 *** -3.70912 *** -2.57669 *** -9.01665 *** -3.79184 *** -7.52095 *** PP - Fisher (Chi-square) 59.9117 *** 287.387 *** 663.302 *** 63.5501 *** 57.6064 *** 295.598 *** 336.089 *** 47.5094 ** 288.191 *** 690.898 *** 88.6203 *** 39.3604 454.195 *** 65.0789 *** 336.089 *** Note: All series are monthly values and are defined as the natural logarithms of their respective nominal values. All tests assume the unit root as the null. The first test, Levin, Lin & Chu, assumes a common unit root process, whereas all other tests assume individual unit root processes for each country. The asterisks to the right of the numbers, ***, ** and *, denote statistical significance at 1%, 5% and 10%, respectively. 15 Table 3 - Cointegration Panel Tests - Kao (1999) Model Statistic EMW - Symmetric -28.008 *** EMW - Asymmetric -29.990 *** MP - Symmetric -4.936 *** MP - Asymmetric -4.756 *** MP Expected - Symmetric -3.325 *** MP Expected - Asymmetric -3.799 *** Note: All series are monthly values and are defined as the natural logarithm of the ratios of their respective nominal values for the reference country and the United States. All tests assume no cointegration as the null. The asterisks to the right of the numbers, ***, ** and *, denote statistical significance at 1%, 5% and 10%, respectively. 16 Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals – Country-specific error correction model EMW EMW MP MP Expected MP Expected Symmetric Asymmetric MP Symmetric Asymmetric Symmetric Asymmetric Country BRA CHI MEX PER COL KOR 1 m. 0.000964*** 3.37 0.000677*** 2.59 -0.00022 -1.62 -0.000222 -1.62 -0.000345 -2.37 -0.000324 -2.38 6 m. -0.000603 -0.33 -0.003787 -1.38 -0.003288 -1.03 -0.003163 -1.00 -0.004751 -2.32 -0.004754 -2.32 12 m. -0.017681 -2.87 -0.026014 -2.91 -0.026578 -1.97 -0.026115 -1.97 -0.025276 -2.98 -0.024929 -3.04 1 m. 0.000829*** 2.56 0.000767*** 2.56 -0.000358 -0.71 -0.000328 -0.72 -0.00071 -0.93 -0.000411 -0.80 6 m. 0.005763*** 1.61 0.004873** 1.31 -0.002409 -0.53 -0.002669 -0.59 -0.00292 -0.64 -0.002595 -0.58 12 m. -0.008957 -0.87 -0.008555 -0.87 -0.013161 -1.02 -0.017074 -1.20 -0.013771 -1.05 -0.010857 -0.86 1 m. 0.000221*** 1.67 0.0000762** 0.95 -0.0000215 -1.36 -0.00000588 -0.35 -0.0000152 -1.12 -0.000026 -1.30 6 m. -0.000154 -0.36 -0.000629 -1.01 -0.00043 -1.66 -0.000443 -1.63 -0.000435 -1.63 -0.000431 -1.64 12 m. 0.000304 0.30 -0.000186 -0.13 -0.001067 -1.15 -0.001125 -1.21 -0.001016 -1.09 -0.000979 -1.07 1 m. 0.0000278*** 1.18 -0.0000106* -0.51 -0.0000197 -1.29 -0.0000259 -1.83 -0.0000368 -1.48 -0.000048 -1.87 6 m. 0.000426*** 1.91 0.000109** 0.34 -0.000473 -1.79 -0.000442 -1.69 -0.000548 -2.07 -0.000566 -2.09 12 m. -0.00075 -1.47 -0.001877 -2.09 -0.00213 -2.56 -0.002 -2.40 -0.002265 -2.74 -0.002228 -2.58 1 m. 0.00000635 2.43 0.00000357 1.17 0.0000061 2.71 0.00000291 1.03 0.00000548 2.20 0.000000563 0.12 6 m. 0.00016 2.92 0.000149 2.13 0.000122 1.81 0.000142 2.21 0.000124 1.75 0.000149 2.41 12 m. 0.000472 3.12 0.000411 2.25 0.000328 1.66 0.00038 1.95 0.000291 1.37 0.000381 2.01 1 m. 0.000238*** 3.17 0.000177*** 3.11 -0.0000286 -1.13 -0.0000183 -0.89 -0.0000341 -1.14 -0.0000212 -0.87 6 m. 0.002095*** 2.20 0.001796*** 1.73 -0.000468 -0.88 -0.000457 -0.86 -0.000467 -0.66 -0.000458 -0.70 12 m. 0.000987* 0.85 0.001629* 1.05 0.0000469 0.04 0.000182 0.15 -0.000142 -0.14 -0.0000714 -0.07 17 Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals – Country-specific error correction model Country PHI 1 m. THA ISR SAF POL CZE EMW Symmetric EMW Asymmetric MP Symmetric MP Asymmetric MP Expected Symmetric MP Expected Asymmetric 0.0000455*** 1.01 0.00013** 1.52 0.0000479** 0.71 0.000659*** 2.31 0.000536*** 2.19 0.000106*** 1.61 6 m. 0.001913*** 1.88 0.001618** 1.73 -0.000641 -0.47 -0.000586 -0.43 0.0000659 0.04 0.000189 0.12 12 m. 0.004944** 2.17 0.003963* 1.56 -0.002737 -0.87 -0.002398 -0.78 0.003998 1.57 0.004214* 1.63 1 m. 0.00104*** 2.64 0.000965*** 2.84 0.000037 0.12 0.000031 0.10 -0.000221 -1.04 -0.000206 -0.97 6 m. -0.004467 -1.63 -0.004333 -1.45 0.000476 0.04 0.000358 0.03 -0.016103 -2.54 -0.016372 -2.55 12 m. -0.062881 -2.82 -0.063851 -2.75 -0.02679 -0.60 -0.027129 -0.61 -0.093392 -3.02 -0.09341 -3.05 1 m. 0.0000986*** 2.57 0.000124*** 2.98 0.0000161* 0.57 0.0000139* 0.48 0.0000225** 0.80 0.0000214** 0.79 6 m. 0.000502** 0.70 0.000443** 0.48 -0.000263 -0.29 -0.000286 -0.30 -0.000257 -0.28 -0.000265 -0.29 12 m. -0.000645 -0.38 -0.000364 -0.17 -0.001899 -0.81 -0.002097 -0.90 -0.002148 -0.91 -0.001911 -0.81 1 m. 0.0000266*** 0.59 0.0000202** 0.45 -0.0000284 -1.04 -0.0000296 -1.10 -0.0000272 -0.99 -0.0000305 -1.10 6 m. 0.000656*** 2.37 0.000384** 0.81 -0.00041 -0.65 -0.000381 -0.60 -0.000387 -0.61 -0.000329 -0.52 12 m. 0.000164* 0.12 -0.001426 -0.78 -0.001573 -0.73 -0.001473 -0.68 -0.001541 -0.70 -0.001459 -0.66 1 m. 0.000373*** 2.48 0.000153*** 1.10 0.000047** 0.88 0.0000138* 0.24 0.0000537* 0.75 0.00000513 0.07 6 m. 0.00225*** 2.30 0.001777*** 1.69 0.0000537 0.04 0.00013 0.10 0.000757 0.49 0.000893 0.57 12 m. 0.005192*** 1.66 0.004167*** 1.24 -0.000653 -0.18 -0.000448 -0.12 0.006237 1.87 0.006411 1.93 1 m. 0.000482*** 2.88 0.000419*** 3.14 -0.00000383 -0.04 -0.00000266 -0.03 -0.0000104 -0.11 -0.0000114 -0.12 6 m. 0.002302*** 2.03 0.002033*** 1.66 -0.001473 -0.87 -0.001615 -0.95 -0.001609 -0.93 -0.001642 -0.97 12 m. -0.001973*** -0.47 -0.002525 -0.59 -0.008574 -1.57 -0.00825 -1.55 -0.008513 -1.57 -0.00825 -1.55 18 Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals – Country-specific error correction model Country HUN 1 m. ROM TUR EMW Symmetric EMW Asymmetric MP Symmetric MP Asymmetric MP Expected Symmetric MP Expected Asymmetric 0.000165*** 1.30 -0.000041* -0.27 -0.000199 -1.00 -0.000108 -1.19 -0.000155 -0.95 -0.0000766 -1.07 6 m. 0.001083*** 1.70 0.000159** 0.18 -0.001422 -1.55 -0.001224 -1.47 -0.001433 -1.55 -0.001303 -1.48 12 m. -0.002418 -1.30 -0.004772 -1.72 -0.003358 -1.20 -0.003426 -1.21 -0.00355 -1.24 -0.003455 -1.20 1 m. 0.0000781 0.54 0.0000913 0.77 0.000186 1.32 0.000143 1.00 -0.000102 -1.53 -0.000126 -2.05 6 m. -0.007194 -3.15 -0.006203 -2.88 -0.002898 -0.95 -0.003439 -1.09 -0.006518 -3.51 -0.00677 -3.51 12 m. -0.054306 -2.86 -0.045205 -2.97 -0.035269 -3.29 -0.036354 -3.33 -0.041001 -3.74 -0.038856 -3.71 1 m. 0.000363*** 1.63 0.000132** 0.71 -0.000102 -1.54 -0.0000945 -1.49 -0.000122 -1.45 -0.000123 -1.54 6 m. -0.000529 -0.59 -0.001113 -1.20 -0.001876 -1.32 -0.001768 -1.25 -0.001592 -1.21 -0.001401 -1.08 12 m. -0.005248 -1.41 -0.008753 -1.94 -0.013481 -2.86 -0.013392 -2.88 -0.004729 -1.31 -0.00454 -1.30 Note: The Diebold and Mariano (1995) S-statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). For a onesided test where the null assumes that the statistic is not positive, the number of stars following the statistic, ***, ** or *, means rejection of the null at the 99%, 95% or 90% level, respectively. Below the S-statistic value, we present the t-distribution statistic. Rejection of the null implies that we fail to reject that the exchange rate model has better forecasting power than the random walk benchmark. The p-values are the bootstrapped versions of the respective test statistics and are based on 1000 iterations. 19 Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model EMW EMW MP MP Expected MP Expected Symmetric Asymmetric MP Symmetric Asymmetric Symmetric Asymmetric Country BRA CHI MEX PER COL KOR 1 m. 0.000979*** 4.42 0.000762*** 3.91 -0.000101 -0.89 -0.000085 -0.78 -0.000098 -0.86 -0.0000974 -0.88 6 m. 0.003321** 1.70 0.001715** 0.69 -0.003207 -1.06 -0.00324 -1.06 -0.003462 -1.14 -0.003448 -1.13 12 m. -0.005449 -0.75 -0.008965 -1.08 -0.017679 -1.49 -0.0179 -1.51 -0.020434 -1.58 -0.020023 -1.56 1 m. 0.001252*** 2.12 0.001126*** 2.20 0.000217** 1.16 0.000175* 0.90 0.000209** 1.10 0.000169* 0.85 6 m. 0.006898** 1.91 0.005455** 1.45 -0.001938 -0.45 -0.002183 -0.50 -0.001931 -0.45 -0.00213 -0.49 12 m. 0.002029 0.27 -0.000367 -0.04 -0.007895 -0.68 -0.008382 -0.72 -0.008045 -0.69 -0.008205 -0.70 1 m. 0.000246** 1.60 0.0000616 0.53 0.000013 0.53 -0.000000151 -0.01 0.0000132 0.57 -0.00000282 -0.21 6 m. -0.000548 -1.06 -0.001306 -1.64 -0.000906 -1.86 -0.00091 -1.85 -0.000892 -1.84 -0.000885 -1.82 12 m. -0.001254 -0.91 -0.002483 -1.23 -0.00325 -2.08 -0.003271 -2.10 -0.003235 -2.05 -0.003324 -2.15 1 m. 0.00000378 0.08 -0.0000299 -0.79 0.000004 0.32 -0.00000133 -0.10 0.00000843* 0.68 0.00000659* 0.50 6 m. 0.000447*** 2.54 -0.000046 -0.14 -0.000514 -1.89 -0.000498 -1.83 -0.000518 -1.89 -0.000529 -1.90 12 m. -0.0000349 -0.07 -0.00109 -1.36 -0.002253 -2.56 -0.002087 -2.40 -0.002326 -2.60 -0.002335 -2.51 1 m. -0.0000116 -1.94 -0.0000857 -4.02 0.00000619 2.68 0.00000424 1.55 0.00000612 2.65 0.00000413 1.54 6 m. 0.000106 1.75 -0.000324 -1.90 0.000163 2.35 0.000163 2.38 0.000163 2.35 0.000164 2.36 12 m. 0.000643 3.10 -0.000000641 0.00 0.000582 2.28 0.000607 2.46 0.000582 2.27 0.000622 2.50 1 m. 0.000214*** 3.89 0.000163*** 3.61 -0.00000599 -0.30 -0.0000106 -0.49 -0.00000774* -0.39 -0.0000103 -0.49 6 m. 0.001299*** 2.72 0.001158*** 1.75 -0.000326 -0.80 -0.000308 -0.76 -0.000348 -1.05 -0.000352 -1.05 12 m. 0.00074** 0.92 0.000607** 0.46 -0.001 -0.72 -0.000859 -0.62 -0.000653 -0.59 -0.000571 -0.52 20 Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model EMW EMW MP MP Expected MP Expected Symmetric Asymmetric MP Symmetric Asymmetric Symmetric Asymmetric Country PHI 1 m. 0.000597*** 0.000466*** 0.0000828*** 0.0000436*** 0.0000764*** 0.0000396** 3.10 2.87 1.97 0.87 1.83 0.74 THA ISR SAF 6 m. 0.001765*** 2.04 0.000753** 0.81 -0.000339 -0.26 -0.000332 -0.25 -0.000624 -0.46 -0.000629 -0.46 12 m. 0.001587* 0.66 -0.000941 -0.33 -0.000921 -0.30 -0.000599 -0.20 -0.002045 -0.59 -0.002048 -0.58 1 m. 0.001706*** 2.95 0.001479*** 3.20 0.000323 0.86 0.000313 0.82 0.000299 0.84 0.000306 0.85 6 m. 0.017561 1.49 0.015931 1.42 0.004267 0.35 0.004068 0.33 0.003756 0.31 0.003544 0.30 12 m. 0.025417 0.68 0.023813 0.63 0.001342 0.03 0.000725 0.02 -0.00144 -0.03 -0.002052 -0.05 1 m. 0.0000965*** 2.52 0.000122*** 2.88 -0.00000428 -0.15 -0.00000571 -0.19 -0.000000241 -0.01 -0.0000038 -0.14 6 m. 0.001247** 2.04 0.001267** 1.63 -0.000275 -0.31 -0.000284 -0.32 -0.000292 -0.33 -0.000286 -0.32 12 m. 0.001796 0.89 0.001369 0.58 -0.000825 -0.31 -0.00078 -0.29 -0.000908 -0.34 -0.000761 -0.28 1 m. 0.0000403*** 1.04 0.0000275** 0.60 -0.00000135 -0.06 -0.00000616 -0.28 -0.00000257 -0.11 -0.00000743 -0.32 6 m. 0.000789*** 2.93 0.000382* 0.79 -0.000259 -0.43 -0.000252 -0.42 -0.00026 -0.43 -0.00025 -0.41 -0.000828 -0.48 -0.00162 -0.72 -0.001556 -0.69 -0.001647 -0.72 -0.001504 -0.66 12 m. POL CZE 0.000271 0.21 1 m. 0.000388*** 3.29 0.000128*** 1.03 0.0000532** 1.15 0.0000278* 0.52 0.0000226 0.49 -0.000001 -0.02 6 m. 0.001433** 1.61 -0.000772** -0.59 0.000196 0.17 0.000233 0.20 -0.000956 -0.69 -0.000914 -0.66 12 m. 0.001062 0.37 -0.003009*** -0.78 0.000666 0.19 0.000893 0.25 -0.002209 -0.50 -0.002028 -0.46 1 m. 0.000438*** 2.55 0.000384*** 2.65 0.0000464 0.65 0.0000417 0.56 0.000047 0.67 0.0000474 0.65 6 m. 0.004014*** 2.55 0.003813** 2.24 0.0000931 0.05 -0.0000215 -0.01 0.0000258 0.01 -0.0000526 -0.03 12 m. 0.003788*** 0.87 0.002393 0.50 -0.003006 -0.52 -0.00311 -0.54 -0.003174 -0.54 -0.00324 -0.55 21 Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model EMW EMW MP MP Expected MP Expected Symmetric Asymmetric MP Symmetric Asymmetric Symmetric Asymmetric Country HUN 1 m. 0.000272*** 0.000114** -0.0000637 -0.0000565 -0.0000613 -0.0000456 2.07 0.92 -1.04 -1.31 -1.06 -1.28 ROM TUR 6 m. 0.000795** 1.39 -0.0000265 -0.03 -0.001742 -1.82 -0.001786 -1.85 -0.001754 -1.82 -0.001777 -1.82 12 m. -0.003262 -1.64 -0.005175 -1.98 -0.007569 -2.01 -0.007684 -2.02 -0.007476 -2.02 -0.00741 -1.99 1 m. 0.000278 1.19 0.000248 1.60 0.000236 1.28 0.000207 1.12 0.000217 1.29 0.000204 1.21 6 m. 0.001864 0.48 0.002397 0.68 0.0000232 0.01 -0.0000591 -0.01 -0.002028 -0.53 -0.002046 -0.54 12 m. -0.014121 -1.03 -0.013173 -0.98 -0.01731 -1.17 -0.017212 -1.17 -0.023769 -1.59 -0.023977 -1.61 1 m. 0.000354*** 2.09 0.000118** 0.73 -0.000063 -1.17 -0.0000478 -0.99 -0.0000619 -1.20 -0.0000533 -1.14 6 m. -0.00045 -0.39 -0.002466 -1.68 -0.001375 -1.09 -0.001348 -1.06 -0.001464 -1.17 -0.00141 -1.12 12 m. -0.004549 -1.15 -0.008592 -1.74 -0.008591 -1.62 -0.008405 -1.60 -0.009676 -1.77 -0.009605 -1.76 Note: The Diebold and Mariano (1995) S-statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). For a one-sided test where the null assumes that the statistic is not positive, the number of stars following the statistic, ***, ** or *, means rejection of the null at the 99%, 95% or 90% level, respectively. Below the S-statistic value, we present the t-distribution statistic. Rejection of the null implies that we fail to reject that the exchange rate model has better forecasting power than the random walk benchmark. The p-values are the bootstrapped versions of the respective test statistics and are based on 1000 iterations. 22 Table 5.a - Number of times the model outperformed the random walk at the 10% significance level or less - Bootstrapped out-of-sample statistics – Country-specific error correction model EMW Symmet. EMW Asymmet. MP Symmet. MP Asymmet. MP Expected Symmet. MP Expected Asymmet. Average of all models 3 7% 3 7% 3 7% 11 24% Horizon Panel A - Diebold and Mariano statistic (Bootstraped Version) All Number 27 25 3 Hit rate 60% 56% 7% 1m Number Hit rate 13 87% 13 87% 3 20% 3 20% 3 20% 2 13% 6 41% 6m Number Hit rate 9 60% 9 60% 0 0% 0 0% 0 0% 0 0% 3 20% 12m Number Hit rate 5 33% 3 20% 0 0% 0 0% 0 0% 1 7% 2 10% Panel B - Clark and West statistic (Bootstraped version) Number 26 23 5 Hit rate 58% 51% 11% 4 9% 3 7% 4 9% 11 24% 1m Number Hit rate 13 87% 13 87% 4 27% 3 20% 3 20% 2 13% 6 42% 6m Number Hit rate 10 67% 9 60% 0 0% 1 7% 0 0% 0 0% 3 22% 12m Number Hit rate 3 20% 1 7% 1 7% 0 0% 0 0% 2 13% 1 8% Panel B - Theil's U (Bootstraped version) All Number 34 32 Hit rate 76% 71% 15 33% 15 33% 14 31% 17 38% 21 47% 1m Number Hit rate 13 87% 13 87% 7 47% 7 47% 7 47% 7 47% 9 60% 6m Number Hit rate 12 80% 11 73% 5 33% 5 33% 4 27% 6 40% 7 48% 12m Number Hit rate 9 60% 8 53% 3 20% 3 20% 3 20% 4 27% 5 33% Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). The hit rate number corresponds to the number of times, considering the model and horizon combination, when the p-values were significant at the 10% level or less. The p-values are the bootstrapped versions of the respective test statistics and are based on 1000 iterations. In this table, they are presented in basis points, which can therefore be multiplied by 1,000 iterations. 23 Table 5.b - Number of times the model outperformed the random walk at the 10% significance level or less Bootstrapped out-of-sample statistics – Pooled error correction model EMW Symmet. EMW Asymmet. MP Symmet. MP Asymmet. MP Expected Symmet. 3 7% 4 9% 3 7% 10 22% Horizon Panel A - Diebold and Mariano statistic (Bootstraped Version) All Number 25 21 3 Hit rate 56% 47% 7% MP Expected Average of Asymmet. all models 1m Number Hit rate 12 80% 11 73% 3 20% 3 20% 4 27% 3 20% 6 40% 6m Number Hit rate 10 67% 8 53% 0 0% 0 0% 0 0% 0 0% 3 20% 12m Number Hit rate 3 20% 2 13% 0 0% 0 0% 0 0% 0 0% 1 6% Panel B - Clark and West statistic (Bootstraped version) Number 34 30 8 Hit rate 76% 67% 18% 7 16% 8 18% 6 13% 16 34% 1m Number Hit rate 13 87% 14 93% 4 27% 3 20% 4 27% 2 13% 7 44% 6m Number Hit rate 13 87% 11 73% 1 7% 1 7% 1 7% 1 7% 5 31% 12m Number Hit rate 8 53% 5 33% 3 20% 3 20% 3 20% 3 20% 4 28% Panel B - Theil's U (Bootstraped version) All Number 36 29 Hit rate 80% 64% 15 33% 15 33% 18 40% 18 40% 22 49% 1m Number Hit rate 15 100% 13 87% 7 47% 7 47% 9 60% 9 60% 10 67% 6m Number Hit rate 13 87% 9 60% 5 33% 5 33% 6 40% 6 40% 7 49% 12m Number Hit rate 8 53% 7 47% 3 20% 3 20% 3 20% 3 20% 5 30% Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). The hit rate number corresponds to the number of times, considering the model and horizon combination, when the p-values were significant at the 10% level or less. The p-values are the bootstrapped versions of the respective test statistics and are based on 1000 iterations. In this table, they are presented in basis points, which can therefore be multiplied by 1,000 iterations. 24 Table 6.a - Number of times the model outperformed the random walk at the 10% significance level or less - Asymptotic out-of-sample statistics - Country-specific error correction model EMW Symmet. EMW Asymmet. MP Symmet. MP Asymmet. Horizon Panel A - Diebold and Mariano statistic (Asymptotic distribution) All Number 24 19 8 8 Hit rate 53% 42% 18% 18% MP Expected Symmet. MP Expected Asymmet. Average of all models 12 27% 14 31% 14 31% 1m Number Hit rate 10 67% 7 47% 1 7% 1 7% 2 13% 3 20% 4 27% 6m Number Hit rate 9 60% 5 33% 3 20% 2 13% 5 33% 5 33% 5 32% 12m Number Hit rate 5 33% 7 47% 4 27% 5 33% 5 33% 6 40% 5 36% 18 40% 12 27% 12 27% 21 47% Panel B - Clark and West statistic (Asymptotic distribution) Number 34 31 19 Hit rate 76% 69% 42% 1m Number Hit rate 15 100% 15 100% 9 60% 8 53% 5 33% 5 33% 10 63% 6m Number Hit rate 12 80% 11 73% 5 33% 5 33% 3 20% 3 20% 7 43% 12m Number Hit rate 3 20% 1 7% 1 7% 0 0% 0 0% 2 13% 1 8% Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). The hit rate number corresponds to the number of times, considering the model and horizon combination, the p-values were significant at the 10% level or less. The p-values assume asymptotic distributions of the respective test statistics. 25 Table 6.b - Number of times the model outperformed the random walk at the 10% significance level or less - Asymptotic out-of-sample statistics – Pooled error correction model MP MP Average EMW EMW MP MP Expected Expected of all Symmet. Asymmet. Symmet. Asymmet. Symmet. Asymmet. models Horizon Panel A - Diebold and Mariano statistic (Asymptotic distribution) All Number 21 14 10 8 11 9 12 Hit rate 47% 31% 22% 18% 24% 20% 27% 1m Number Hit rate 11 73% 8 53% 2 13% 0 0% 2 13% 0 0% 4 26% 6m Number Hit rate 9 60% 4 27% 4 27% 4 27% 4 27% 4 27% 5 32% 12m Number Hit rate 1 7% 2 13% 4 27% 4 27% 5 33% 5 33% 4 23% 21 47% 21 47% 20 44% 27 59% Panel B - Clark and West statistic (Asymptotic distribution) Number 40 37 21 Hit rate 89% 82% 47% 1m Number Hit rate 15 100% 15 100% 9 60% 9 60% 10 67% 9 60% 11 74% 6m Number Hit rate 14 93% 13 87% 6 40% 6 40% 5 33% 5 33% 8 54% 12m Number Hit rate 8 53% 5 33% 3 20% 3 20% 3 20% 3 20% 4 28% Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). The hit rate number corresponds to the number of times, considering the model and horizon combination, the p-values were significant at the 10% level or less. The p-values assume asymptotic distributions of the respective test statistics. 26 Figure 1 – Realized and predicted exchange rates – EMW/country specific error correction South Africa .8 Brazil 1.4 .7 Chile 6.8 1.2 6.4 .6 1.0 .5 .4 0.8 6.0 .3 0.6 5.6 .2 0.4 .1 5.2 0.2 .0 -.1 0.0 95 96 97 98 99 00 01 02 03 04 05 06 07 08 4.8 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Mexico 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Peru 1.6 .8 1.4 .7 1.2 .6 1.0 .5 0.8 .4 0.6 .3 Colombia .4 .3 .2 .1 0.4 .0 .2 95 96 97 98 99 00 01 02 03 04 05 06 07 08 South Korea .6 -.1 95 96 97 98 99 00 01 02 03 04 05 06 07 08 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Philippines 1.1 Thailand 6 1.0 .5 5 0.9 .4 0.8 4 0.7 .3 0.6 3 .2 0.5 0.4 2 .1 0.3 .0 0.2 95 96 97 98 99 00 01 02 03 04 05 06 07 08 1 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Israel 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Polandl Czech Republic 1.0 .4 1.4 0.8 .2 1.2 0.6 .0 0.4 -.2 0.2 -.4 0.0 -.6 -0.2 -.8 1.0 0.8 0.6 0.4 95 96 97 98 99 00 01 02 03 04 05 06 07 08 .7 0.0 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Hungary .8 0.2 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Romania Turkey 4.5 1.4 4.0 1.2 .6 3.5 .5 1.0 .4 3.0 .3 2.5 0.8 .2 0.6 2.0 .1 .0 1.5 -.1 1.0 95 96 97 98 99 00 01 02 03 04 05 06 07 08 0.4 0.2 95 96 97 98 99 00 01 02 03 04 05 06 07 08 95 96 97 98 99 00 01 02 03 04 05 06 07 08 Exchange Rate (solid) Predicted Exchange Rate (dash) 27