Several months ago, I discussed the implications of a model of the exchange rate wherein Taylor rule fundamentals — the output , inflation and exchange rate gaps — were central (post). In that paper [pdf], I showed that Taylor rule fundamentals outperformed purchasing power parity, interest rate parity, and the monetary model of exchange rates in terms of in-sample fit, at least insofar as the dollar/euro exchange rate is concerned.
Unfortunately, events have outrun modeling. Policy rates in the key economies have either already hit zero (Japan, US) or are forecast to (UK, euro area).
Figure 2 from B. Chadha, “Quant Easting and the Dollar,” Global Economic Perspectives (Deutsche Bank, 19 December 2008), not online.
Now, remember the steps involved in getting a relationship between the exchange rate and these “gaps”. The gaps are related to changes in the policy rates; the policy rates are linked to expected appreciation (not depreciation) since prices are sticky (the Dornbusch-Frankel model).
This leads to the following specification for the four quarter change in the dollar/euro exchange rate of the following form:
st-st-4 = 0.114 – 7.072 ogt-4 – 4.790 πt-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
And where the output gap (og) is measured as a deviation from a quadratic trend applied to real GDP data, the underlying Taylor rule incorporates an output gap, and inflation gap (π), a real exchange rate gap (q), and the interest rate (i) responds nonlinearly with respect to the exchange rate gap. The one-year-ahead forecast (for data ending 2008Q2, as discussed in this post) is shown in Figure 2, with the 22 December observation on the USD/EUR rate, and the Deutsche Bank forecast from 12/19 for one-year-ahead. So far, the actual, forecast still seems plausible.
Figure 2: Dollar/euro rate (blue), 22 December observation (blue +), in-sample 4 quarter ahead prediction from Taylor rule fundamentals estimated over 1999q1-08q2 (solid red square) and DB forecast for 12/18/09 (teal square). Source: author’s calculations and Deutsche Bank Exchange Rate Perspectives, December 19, 2008.
But now the link is broken, as the interest rate is no longer a policy instrument. It is true that long term interest rates can still be influenced by policymakers, but not via the term structure. Rather, for the near future, policy will be effected via quantitative easing. This breaks the obvious link between the fundamentals and the exchange rate.
I don’t have a good answer for what will work in future. One could go back to the monetary model of the exchange rate (discussed here). And this has the advantage of using money stocks, which are observable (as opposed to unobservables like output and inflation gaps). On the other hand, the model also presupposes a stable relationship between money, interest rates and incomes, something that those familiar with the money demand literature will know is difficult to show.
Figure 3: M1 to GDP ratio (blue) and M2 to GDP ratio (red), all series seasonally adjusted. Source: BEA, GDP release of 25 November, and Federal Reserve Board via St. Louis Fed FRED II.
This point actually leads me to another, more general, observation. Many of the monetary policy multipliers are based upon the supposition that the interest rate can be moved in either direction to influence aggregate output. However, as we’ve come to the zero interest bound, this supposition can no longer be supported. Perhaps, we’ll have to move back to defining monetary policy multipliers in terms of money aggregates, instead of in terms of policy rate changes , not that these monetary policy multipliers will look like those that would obtain in normal times (see Krugman’s take here [pdf]). In any case, modeling monetary policy effects in this new environment will likely be one of the major challenges for macro modelers going forward.