Integrating indirectly identified unobserved fundamentals into out-of-sample exchange rate forecasting: repairing the exchange rate disconnect

The exchange rate disconnect puzzle is the robust finding, originating with Meese and Rogoff (1983), that nominal exchange rates are largely unexplained by observed macroeconomic fundamentals both in-sample and, more strikingly, in out-of-sample forecasting against a random walk. Chou (2018) applied a Campbell–Shiller-style variance decomposition (a method that splits an asset price's deviation from a benchmark into expected future fundamentals and unobserved components) to a present-value monetary model for the Canadian dollar, Japanese yen, Swiss franc, and pound sterling against the US dollar, and found that deviations from purchasing power parity, the foreign-exchange risk premium, and money-demand disturbances — not observed monetary fundamentals — account for most of the variance of the exchange-rate–fundamentals spread. This leaves open the problem: the unobserved fundamentals are identified only through crude proxies with serious measurement-error problems, and they have not been integrated into out-of-sample forecasting frameworks. The open problem is to refine the empirical identification of these unobserved components and to determine whether incorporating them improves out-of-sample exchange rate prediction relative to random-walk and observed-fundamentals benchmarks.

Background

Since the collapse of Bretton Woods, exchange rates between major currencies have shown large and persistent fluctuations that appear detached from the macroeconomic quantities that standard theory says should drive them. The workhorse monetary model implies that the log nominal exchange rate $s_t$ (home currency per US dollar) is tied to the observed monetary fundamental $f_t=(m_t-m_t^*)-(y_t-y^*)$ — the log relative money supply minus log relative output — through a present-value relation: because the exchange rate is an asset price, it equals the current fundamental plus a discounted sum of expected future changes in fundamentals and of unobserved components, deviations from purchasing power parity (PPP; the failure of the law of one price, so that $s_t$ does not simply track the relative price level $p_t-p_t^*$), the foreign-exchange risk premium $\rho_t$ (the deviation from uncovered interest parity, UIP, under which interest differentials should equal expected depreciation absent a risk premium), and money-demand disturbances $\nu_t^d$ (shifts in money demand not captured by income and interest rates). The empirical failure of this link is the exchange rate disconnect puzzle, coined by Obstfeld and Rogoff (2000) as one of the six major puzzles of international macroeconomics: Meese and Rogoff (1983) showed that no structural model of the 1970s could beat a random walk out of sample, and Cheung, Chinn, and Garcia Pascual (2005) found the same for the models of the 1990s. Engel and West (2005) offered a partial reconciliation: when fundamentals follow unit-root processes and the discount factor approaches one, a fundamentals-driven exchange rate should itself look nearly like a random walk, so weak short-run predictability need not mean fundamentals are irrelevant; Engel, Mark, and West (2007) showed that fundamentals regain some long-horizon, panel-level predictive content. Rossi's (2013) comprehensive survey of exchange-rate predictability nonetheless concludes that predictability "depends" — on predictor, horizon, sample, model, and evaluation method — and that the random walk without drift remains the toughest benchmark. Within this literature, Chou (2018) asked which unobserved components account for the variance of the spread $s_t-f_t$. Using a vector autoregression (VAR — a linear system of regressions of each variable on lags of all variables) for Canada, Japan, Switzerland, and the UK over 1973Q1–2014Q4, with the PPP deviation proxied by the real exchange rate, the risk premium proxied by the ex-post UIP deviation $i_t-i_t^*-\Delta s_{t+1}$, and money-demand disturbances proxied by residuals of estimated money-demand equations, he found that expected future PPP deviations account for the largest share of the variance of $s_t-f_t$, that the risk premium's contribution rose markedly after the creation of the European Economic and Monetary Union (EMU) in 1998, and that expected changes in observed monetary fundamentals explain generally less than 20 percent, often insignificantly. The decomposition itself, however, rests on proxies with acknowledged measurement problems: the real-exchange-rate proxy mechanically contains $s_t$; the ex-post UIP deviation mixes the true risk premium with expectational errors and peso-problem effects (systematic-looking forecast errors that arise when agents rationally weight a rare event, such as a large devaluation, that does not occur within the sample) and is extremely volatile; and money-demand functions are known to be unstable. The open problem left by this diagnosis is to refine the identification of these unobserved fundamentals and to integrate them into out-of-sample forecasting frameworks, since models based solely on observed monetary fundamentals provide little information about exchange rate movements.

Problem Statement

Following from the diagnosis established by Chou (2018), the problem is to repair the exchange rate disconnect by exploiting the unobserved fundamentals that its variance decomposition shows dominate exchange rate movements. Specifically: (i) refine the empirical identification of the three unobserved components of the present-value monetary model — deviations from purchasing power parity, the foreign-exchange risk premium, and money-demand disturbances — so that they are measured with less error than under the current proxies (the real exchange rate as PPP deviation, the ex-post UIP deviation as risk premium, and residuals of estimated money-demand equations), addressing the acknowledged problems that the real-rate proxy mechanically embeds the nominal exchange rate, that the ex-post UIP deviation mixes the true risk premium with expectational errors, and that money-demand functions are unstable; and (ii) integrate these indirectly identified unobserved fundamentals into out-of-sample forecasting frameworks and determine whether doing so improves predictive performance for nominal exchange rates relative to the random-walk benchmark and to models based solely on observed monetary fundamentals. The two parts form one scientific objective: converting the diagnosis that unobserved fundamentals account for most of the exchange-rate–fundamentals spread into demonstrated (or decisively refuted) out-of-sample forecasting value.

References

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