As Europe teeters on the edge of recession , and the United States remains mired in slow growth, expectations of what interest rates, and hence exchange rates, are shifting. Here’s a familiar depiction of where policy rates in the US and the euro area have been, and where they are predicted to go.
Figure 1: Policy rates and predictions. Source: Deutsche Bundesbank, Global Economic Perspectives July 21, 2008.
As long the euro area rate is projected to be above, and rising relative to, the US interest rate, the euro should remain strong against the dollar. These expectations are popularly thought to be a function of output and inflation gaps. This suggests that output and inflation gaps usefully be thought of as fundamentals for exchange rates. In other words, Taylor rule fundamentals can be used as empirical determinants of exchange rates. 
A number of economists have already taken up this approach including Engel and West (2006), papers by Papell et al., and Rogoff and Stavrakeva (2008). They have studied the in-sample and out-of-sample predictions of these Tayor rule fundamentals models. Currently I’m working on a paper examining how the predictability varies with different measures of output gaps, with a focus on the dollar/euro rate, following the spirit of Molodtsova et al. (2008), but focusing on the in-sample characteristics.
As noted in a previous post on output gaps , there are number of ways to measure the output gap. I will focus on the output gap measured as a deviation from a quadratic trend applied to real GDP data. I will assume the Taylor rule incorporates an output gap, and inflation gap, a real exchange rate gap where the interest rate responds nonlinearly with respect to the exchange rate gap. This leads to a specification for the four quarter change in the exchange rate of the following form:
st-st-4 = 0.114 – 7.072 ogt-4 – 4.790 pit-4 + 0.313 qt-4 – 9.982 (q3)t-4 + 1.381 it-5 + ut
where adj.R2 = 0.89, SER = 0.052, sample 1999q1-08q1; bold face indicates significance at the 10% level.
In Figure 2, I present the standard error of regression (SER) statistics for the Taylor rule fundamentals regressions at 1, 4, and 20 quarters horizons, and compare them against the corresponding SERs for a sticky-price monetary model error correction model, interest rate differential regressions, purchasing power parity, and an external imbalances model a la Gourinchas-Rey (2007).
Figure 2: Standard error of regression (SER) statistics for five models and for three horizons. Source: Author’s calculations.
What is true is no model fits well for 1 quarter changes in exchange rates, and none do particularly well for 5 year changes. Interestingly, at the 1 year horizon, the Taylor rule fundamentals do as good a job as the monetary model ECM.
In Figures 3 and 4, I present the in-sample predictions of the five models at the one year horizon.
Figure 3: Log dollar/euro rate (black), in-sample 4 quarter ahead prediction from Taylor rule fundamentals (blue), monetary model (red), interest differentials (green). Source: author’s calculations.
Figure 4: Log dollar/euro rate (black), in-sample 4 quarter ahead prediction from Taylor rule (blue), PPP (red) and external imbalances model (green). Source: author’s calculations.
What these graphs make clear is that the Taylor rule does about as well as the monetary model, and noticeably better than the other models. What makes the Taylor rule fundamentals model preferable to the monetary model is the fact that most of the key parameters in the monetary model regressions (money, income, sometimes inflation) have the wrong sign.
Update: The entire paper is here
Armed with these results, I forecast out the one year ahead dollar/euro exchange rate, based upon 2008q1 data. This prediction is presented in Figure 5, along with the plus/minus 2 standard error bands (note that the sample ends in 2008q1, so one year ahead is 2009q1). I also include the Deutsche Bank forecast for end of July 2009.
Figure 5: Dollar/euro rate (blue), dollar/euro rate for 6/30 (blue square), in-sample 4 quarter ahead prediction from Taylor rule fundamentals estimated over 1999q1-08q1 (solid blue square) and associated +/- 2 standard errors (teal +), and DB forecast for 7/09 (red square). Source: author’s calculations and Deutsche Bank Exchange Rate Perspectives, July 24, 2008.
What the figure illustrates is that a sharp reversal in the dollar/euro rate is predicted by the model. Some component of this is being driven by the nonlinearity in the PPP relationship. In the absence of this nonlinearity, the dollar would be predicted to continue to depreciate, largely because of the large negative output gap differential (nearly 3 ppts in 2008q1).
Would I ever bet on this prediction? The answer is no. First, I never put any money in the forex market. Second, despite the success of the equation on statistical grounds, the standard errors are still quite large. Third, there is a complication arising from the fact that in this analysis I have used a mixture of final data (the data older than a year) and final data that has not been through the annual benchmark revision, for the US. Presumably, a similar caveat applies to the euro area GDP data. And it is unclear whether the relationships that obtain for data post-revisions obtain for, say, the 2008Q1 data. For that, the analysis of Molodtsova et al. (2008), which uses real time data, might shed more light (although they too encounter the issue of how to use pre-EMU data).
And of course, these types of macro models are “business as usual” models — they do not address what would happen if there were a large scale shift out of dollar assets by central banks and sovereign wealth funds due to depegging or some other discrete event.
[Update 17 August] An example of the application of a Taylor-rule based exchange rate forecasting procedure is provided by Mike Rosenberg of Bloomberg. I’ve posted his analysis here.