Can fluctuations in the consumption-wealth ratio help to predict exchange rates?

Abstract

It is accepted that standard macroeconomic variables are not capable of predicting ex ante the majority of short term changes in exchange rates. Lettau and Ludvigson (2001) find that fluctuations in the common long-term trend in consumption, asset wealth, and labour income (hereby, consumption-wealth ratio) is a strong predictor of the excess returns. This study examines the role of the consumption-wealth ratio in predicting the change in the nominal exchange rate for seven industrialized economies. Evidence is found that fluctuations in the consumption wealth ratio help to predict in-sample all currencies. Out-of-sample, the results suggest that the consumption wealth ratio may play a significant role forecasting the Canadian dollar.

Acknowledgements

We are especially gratefull to Pierpaolo Benigno, Sydney Ludvigson and seminar participants at the Central Bank Reserve Bank of Peru and the Central Bank of Chile for helpful suggestions and comments. We also thank Lutz Kilian for making the data available and Michael McCracken for providing his test's codes. The views expressed herein are those of the authors and do not necessarily reflect those of the Central Bank of Chile or the Central Reserve Bank of Perú. Any errors are our own responsibility.

Notes

¹ This finding is often interpreted as evidence of increasing power at higher forecast horizons, however, this result has been questionable in the literature. Nelson and Kim (1993) Bollerslev and Hodrick (1995), Berkowitz and Giorgianni (1997) and Kirby (1997) have documented that conventional long-horizons tests are biased in favour of finding predictability.

² Flood and Hodrick (1990) conclude that the bubble alternative remains unconvincing.

³ Evans and Lyons (2002) find that daily interdealer order explains 60% of daily exchange rate changes and consequently argue that flows are the proximate cause of exchange rate movements.

⁴ Selaive and Tuesta (2003a, 2003b) present empirical evidence, based on an incomplete markets model, suggesting that the net foreign asset position of each country is a key variable in understanding both real and nominal exchange fluctuations. In this sense, an empirical evaluation of the predictability power of the NFA position over exchange rates is also appealing.

⁵ Campbell and Mankiw (1989) show that the consumption-wealth ratio of a representative agent, derived from a budget constraint, is a function of future returns of market portfolio and the consumption growth.

⁶ Like many other assets, the exchange rate should depend on expectations of future variables, and in this sense Obstfeld and Rogoff (1998) suggest to treat the exchange rate as an asset price.

⁷ Inoue and Kilian (2003) conclude that results of in-sample test of predictability will typically be more credible than results of out-of-sample tests.

⁸ Foreign currencies may not be explicit part of the portfolio of a domestic investor, but are implicit in the return – in domestic currency – of a foreign bond (or stock) denominated in foreign currency.

⁹ In an open economy framework when markets are perfectly integrated, an arbitrage condition will imply that the return of assets on domestic currency must equalize the return on assets denominated in foreign currency adjusted by the expected devaluation. Thus one can re-write the term r_{a , t   + 1} using the following equilibrium condition . This condition allows one to directly relate cay_t with expected changes in the nominal exchange rate E_t (Δe_{t +1}).

¹⁰ It is also possible to rationalize in context of open economy, the fact that fluctuations of the consumption-wealth ratio help predicting exchange rate. In a general equilibrium, set up domestic and foreign budget constraints must be combined along with arbitrage condition across countries.

¹¹ The exchange rate is always expressed as American dollar/foreign currency.

¹² It is assumed that Americans and foreign investors hold bilateral positions, i.e. Americans hold foreign assets and foreign investors hold American assets. Both of them denominated in the corresponding domestic currency.

¹³ Standard versions of monetary models relate the exchange to economic fundamentals and the expected future exchange rate. In these models z_t  ≡ e_t  − f_t and . When m_t and corresponds to the money aggregates in both the domestic and foreign economies, and y_t and are the log of domestic and foreign outputs, respectively.

¹⁴ Recently, Wright (2003) applies a Bayesian Model Averaging approach that averages the forecasts of different models. His results suggest that the forecast generated using this approach are very close to those from the random walk forecast.

¹⁵ LL construct the variable cay_t by estimating a cointegrating vector of asset wealth, consumption and income for the period 1952.I to 1998.III.

¹⁶ It is well known that asymptotic critical values for the t-test statistics are biased in small samples.

¹⁷ Mark and Sul (2001) applied the same approximation for a small panel of countries.

¹⁸ Mark's inconsistency in permitting a drift in the bootstrap DGP but not in the benchmark forecast biased the bootstrap critical values. Kilian (1999) emphasized the importance of the treatment of the drift term in the forecasting procedures.

¹⁹ The description of the method of construction of cay_t can be found in their paper.

²⁰ Extending the forecast horizon beyond the sampling interval induces serial correlation in the error. The two methods employed here differ according to the rule used to determine the truncation lag for the Bartlett window. The first method arbitrary sets the truncation lag at 20. The second method employs a data-dependent formula provided by Donald Andrews (1991).

²¹ This results correspond to Fig. 5, p. 504 in Kilian's (1999) paper.

²² In particular they show that the commonly used t-type test of forecast accuracy has lower power than the ENC – NEW tests. For instance, McCracken and Sapp (2002) report strong evidence of exchange rate predictability using the ENC – NEW test.

²³ Clark and McCracken (2002) conclude, based on an empirical application relating GDP growth with the interest rate term spread, that structural breaks can explain why is common to find evidence of predictive content in-sample but not out-of-sample.

²⁴ As Clark and McCracken (2003) pointed out some of the differences between in-sample and out-of-sample results on predictive ability may be due to model instability. Moreover, in an application, they show robust evidence that structural shifts can account for the out-of-sample breakdown in predictive power found in many empirical works.