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*Marcelo L. Moura I ; Adauto R. Lima II ; Rodrigo M.*

- The Economics of Exchange Rates
- Purchasing Power Parity and Real Exchange Rate in Japan
- Spillovers and connectedness in foreign exchange markets: The role of trade policy uncertainty

*Faust, J.*

## The Economics of Exchange Rates

Marcelo L. Moura I ; Adauto R. Lima II ; Rodrigo M. E-mail: marcelom isp. E-mail: adautorsl isp. E-mail: rodrigomm1 ibmecsp. Forecasting performance is tested for a broad set of empirical exchange rate models for an emerging economy with independently floating regime and inflation target monetary arrangement. Compared to the recent literature on out-of-sample exchange rate predictability, we include a more extensive set of models.

We test vintage monetary models of the 's, exchange rate equilibrium models of the 's and a Taylor Rule based model. This last model assumes an endogenous monetary policy, where the Central Bank follows a Taylor rule reaction function to set interest rates.

Our results show that Taylor Rule models and Behavioral Equilibrium Exchange Rate models, the last one combining productivity differentials with portfolio balance effect, have superior predictive accuracy when compared to the random walk benchmark. Some out-of-sample predictability is also obtained with parsimonious models based on uncovered interest parity arguments. Keywords: Taylor rule models, monetary models, out-of-sample exchange rate predictability, cointegration, mean correction error models.

In the present study, we test the adequacy of the empirical exchange rate models for an emerging commodity-based economy with independently floating regime. Our analysis replicates for an emerging economy the study carried out in the classic article by Meese and Rogoff but with a broader set of economic models and using true out-of-sample exercises. Meese and Rogoff's research has generated an extensive literature.

Mark argues that the monetary fundamentals might obtain some success to explain the behavior of the exchange rate if the statistical tests were given more power. However, a host of authors, for example, Kilian and Berkowitz and Giorgianni remained skeptics and suggested that the results obtained by Meese and Rogoff may still seem robust, even after all the data and intense academic investigation gathered for over twenty years.

Some exceptions to this skepticism are present in recent works. The author concludes that for Australia and New Zealand the global price of their respective exported commodities is likely to have a meaningful and stable impact on their respective currencies.

However, in the case of Canada, the evidence was less conclusive. Guo and Savikcas make use of variables that reflect the agents' expectation towards the future behavior of the economic fundamentals, like the term structure of interest rates, credit risk, and the idiosyncratic risk of the United States' stock market, among others.

Their analysis suggest that the idiosyncratic risk of those assets forecast the American dollar's behavior facing the G7's main currencies, and conclude that the exchange rate does not follow a driftless random walk.. Cheung, Chinn and Pascual added other models and elements of the s traditional specifications in the determination of the exchange rate, such as, the net foreign assets and the differential of relative productivity in the tradable goods sector between countries, the Balassa and Samuelson effect.

The authors concluded that, in line with a great part of the existing literature, it is very difficult to find empirical estimations of structural models that may consistently outperform a random walk, having the mean-squared errors as basis of comparison.

On the other hand, the structural models provide a better forecasting for exchange rate movements than that provided by the random walk. Specific studies for Brazil, like Muinhos, Alves and Riella , state that the random walk is not the best hypothesis to explain the behavior of the exchange rate in Brazil. Using data from May to December , the authors conclude that a model derived from the theory of uncovered interest rate parity captures the Brazilian exchange rate's behavior better.

This model takes into consideration the sovereign risk premium in the study measured by the C-Bond spread, in relation to Treasury Bills, as a variable in the specification of the uncovered parity. Until mid 's, as highlighted by Sarno and Taylor , though the theory of exchange rate determination had produced a series of models, estimations both in and out-of-sample did not show strong empirical support.

The results tended to be fragile in the sense that they were hard to replicate in different samples or countries. However, new developments in the mid 's changed the perspective and shed some new light in the field. Engel and West analysis of rational expectations present-value model showed that beating a random-walk can be a too strong benchmark, even if the model is true. At the same time, the use of endogenous monetary models, see Molodtsova and Papell , and new panel data techniques, see Rapach and Wohar found improved results in out-of-sample predictability.

In conclusion, the existing literature up to now allows us to draw some important conclusions. First of all, it is difficult to find empirical economic models that consistently outperform a driftless random walk for the out-of-sample estimations. Second, more recent exchange rate models improve the predictive accuracy of the models. Finally, economic variables that have forward-looking components may improve the results of the models for the out-of-sample forecasting.

The purpose and contribution of this work is to carry out a detailed study about the out-of-sample forecasting performance of exchange rate models to an emerging economy like the Brazilian economy.

The following section presents the economic models used in this work. In Section 3, we analyze the forecasting performance of the estimated models against that of the driftless random walk. We follow the mean correction error methodology suggested by Cheung, Chinn and Pascual , in which the assessment criterion is the Mean Squared Predicted Error MSPE , however, we improve on this work in two ways.

First, we test significance using Clark and West , statistic instead of the one in Diebold and Mariano , which is subject to some strong criticism, see Kunst and Clark and West , Second, we include the Taylor Rule Model based on a more realistic hypothesis of endogenous monetary policy.

The last section presents the conclusions of the study. The Flexible Price Monetary Model FPMM was very representative in the s when the floating exchange rates were adopted by the main industrialized economies, after the collapse of Bretton Woods system in According to Sarno and Taylor , this model became the dominant exchange rate model during the s, for earlier studies on this see Frenkell and Mussa , The basic intuition of the FPMM is to assume that, in each country, the equalization of currency supply and demand determines the price level in each country.

Furthermore, relative prices in each country and exchange rates are related by the purchasing power parity relationship. The solution of the FPMM leads to an exchange rate equation where the exchange rate is determined by relative money supplies, output levels and interest rates.

More specifically, in econometric terms, the equilibrium equation to be estimated can be presented by:. Despite the fact that the FPMM was the dominant approach to determine the exchange rate in the early s, its weak empirical results led to the conception of models that took over frictions in the economy, inducing another form of convergence for long-run market equilibrium. The existence in the system of variables that jump, in this specific case, the exchange rate and the interest rate, would make up for the stickiness in other variables, that is, the prices of goods.

Thus, the adjustment velocity in various markets would be different. The Dornbusch SPMM, captures price stickiness in both economies by the following equilibrium equation:.

The monetary models formerly shown, flexible prices and sticky prices, assume the perfect substitution between home and external assets and their effects on the exchange rate.

However, the existence of home-bias home agents' preference for home assets , liquidity difference, solvency risk, tributary differences and even the currency-exchange risk can affect the presumed equilibrium in the monetary models, which makes the home assets and the external assets imperfect substitutes.

Following Sarno and Taylor , the main idea in the Portfolio Balance Model - hereafter PBM - is to consider that net financial wealth can be allocated into money, domestic issued bonds and foreign bonds. At the equilibrium, exchange rate and nominal interest rates equate supply and demand of those three financial assets. In the reduced-form, the equilibrium exchange rate will be a function of relative money supplies and the stock of domestic and foreign bonds.

However, longer data span and estimation for an emerging economy, like the Brazilian, motivates us to test this model as well. In particular, we use the following empirical specification for the portfolio model:. Asteriks denote the same variables for the reference country, the United States. The next specifications follow a more recent set of exchange rate determination models model in the Balassa-Samuelson tradition. Following Cheung, Chinn and Pascual we use first a productivity Differential model where the productivity gap between tradable and nontradables sectors play a crucial role in determining the equilibrium exchange rate.

The Productivity Differential is given by the following equation:. Besides the Balassa-Samuelson effect, we can also include other well-known familiar effects to the exchange rate in order to establish a link between the exchange rate and the relevant economic variables.

More specifically, the BEER model assumes a reduced form econometric specification where the real equilibrium exchange rate is affected by transitory factors, random disturbances, and the extent to which the economic fundamentals are away from their sustainable values.

We also test a parsimonious model based on uncovered interest rate parity UIP conditions. This model has been extensively tested in the literature with poor results, see Hodrick for survey results. However, recent studies pointed to more hope for the UIP models, for instance, Flood and Rose show that UIP models tend to work better using more recent data from the s, Chinn and Meredith using a larger span of data and incorporating long-term interest rate differentials also achieve better in-sample estimates for the UIP.

Given that an emerging economy is subject to many risks not captured by the interest rate differential, we assume two flexible functional forms. The first assumes that the exchange rate will be a function of short term interest rate differentials,.

As pointed out by Engel, Mark and West , two important characteristics of monetary policy were ignored up to now. First, it is endogenous. Second, since the mids central banks have used interest rate as the instrument policy, not money supply. Therefore, our last model incorporates endogenous monetary policy set by the definition of the short-term interest rate according in the spirit of Taylor central bank reaction function.

Following the line of New-Keynesian monetary models, we apply a Taylor Rule model. The Taylor model for exchange rate determination was employed recently by Engel and West , Mark , Clarida and Waldman and Molodtsova and Papell In general, monetary policy rules are summarized by a Taylor's rule function:.

We assume. Using the two Taylor Rules above with the uncovered interest parity condition:. In particular, using the last expression we can specify this model by the following econometric equation: 5. A general expression for the relation with the exchange rate is:.

Since many of the macroeconomic variables are not stationary, we need to test if [ s t , X t ] has a long-run relationship in order to avoid spurious regressions. Following the seminal work of Engle and Granger we test if [ s t , X t ] co-integrate by using MacKinnon critical values for the Engle-Granger two-step procedure.

Empirical estimation uses monthly data from January to December , a full sample of observations. Then, we run the regression:. For this reason, we use MacKinnon critical values. Results for the Engle-Granger cointegration tests are presented on Table 1.

This means that specifications 2. However, we will keep those models in our forecasting exercise just for scientific curiosity to evaluate if we can obtain any predictive accuracy of them, the theory should say that we will not.

The cointegration tests on Table 1 assume that there is only one cointegration relationship. A more general alternative, given the presence of many macroeconomic series in our models, would be to test for the presence of multiple cointegration relationships. However, for some other models there is evidence of more than one cointegration vector. This last result suggests the use of Vector Error Correction models for those models.

However, the drawback of using VEC in forecasting at long horizons is the need of including short-term dynamics of the explanatory variables. For instance, Groen uses the VEC approach in order to estimate a monetary model and forecasts up to 4 years ahead.

However, information about the values of the short-run dynamics for years 1, 2 and 3 ahead are not available at time t.

## Purchasing Power Parity and Real Exchange Rate in Japan

This paper analyses the directional spillover effects and connectedness for both return and volatility of nine US dollar exchange rates of globally most traded currencies under the influence of trade policy uncertainty. We find two interesting results over the study period ranging from December to July First, there exists asymmetric spillovers and connectedness among the considered exchange rates when trade policy uncertainty is present. Second, the volatility spillover is stronger than the return connectedness between exchange rate and trade policy uncertainty. These findings are robust to the presence of economic policy uncertainty effects.

## Spillovers and connectedness in foreign exchange markets: The role of trade policy uncertainty

Important developments in econometrics and the increasingly large availability of high-quality data have also been responsible for stimulating the large amount of empirical work on exchange rates in this period. Nonetheless, while our understanding of exchange rates has significantly improved, a number of challenges and open questions remain in the exchange rate debate, enhanced by events including the launch of the Euro and the large number of recent currency crises. This volume provides a selective coverage of the literature on exchange rates, focusing on developments from within the last fifteen years.

Using novel real-time data on a broad set of economic fundamentals for five major US dollar exchange rates over the recent float, we employ a predictive procedure that allows the relationship between exchange rates and fundamentals to evolve over time in a very general fashion. Our key findings are that: i the well-documented weak out-of-sample predictive ability of exchange rate models may be caused by poor performance of model-selection criteria, rather than lack of information content in the fundamentals; ii the difficulty of selecting the best predictive model is largely due to frequent shifts in the set of fundamentals driving exchange rates, which can be interpreted as reflecting swings in market expectations over time. However, the strength of the link between exchange rates and fundamentals is different across currencies. Journal of International Economics , 66 , — Google Scholar.

We define the forward price to be the strike K such that the contract has 0 value at the present time. In these cases, some companies can apply hedge accounting procedures to protect their income statement from changes in the fair value of these instruments. The spot exchange rate is 6. The forward rate and spot rate are different prices, or quotes, for different contracts.

*The linearity and stationarity of the real exchange rates of India, Nepal, Pakistan and Sri Lanka are investigated using formal linearity and the recently developed nonlinear stationary test procedures. Results obtained show that these real exchange rates are stationary albeit the presence of nonlinearity. Baum, C.*

o Lucio Sarno and Mark P. Taylor This book is in In the last few decades or so exchange rate economics has seen a number of important developments.

Cambridge Core - Economic Theory - The Economics of Exchange Rates. Lucio Sarno, University of Warwick, Mark P. Taylor, University of Warwick. Foreword.

Indeed, Sarno and Taylor () note that if exchange rates follow a random walk, the estimate of the slope coefficient from the forward.

By Lucio Sarno and Mark Taylor; Abstract: In the last few decades exchange rate economics has seen a number of developments, with substantial contributions.