The Cockroach Exchange Rate Index

In an earlier post, I noted how Ragout properly criticized this attack post from Don Luskin. But it seems that Brad DeLong felt it was necessary to get some stronger bug spray to finish off what he calls the intellectual cockroach (comparing cockroaches to Luskin strikes me as a but harsh – doesn’t Professor DeLong owe the cockroach species an apology here?). The more effective bug spray comes from a review of the last graph Luskin provides in the cockroach case that a 1982 CEA memo on inflation was somehow flawed. DeLong writes:

Moreover, what Luskin has plotted here is not the real exchange rate: the U.S. real exchange rate did not change by a factor of three between 1973 and 1988. I suspect that what Luskin has done has been to divide a nominal exchange rate series by the home country’s price level, rather than by the ratio of the home to the foreign price level, and thus created a series that is essentially meaningless.

Luskin’s graph shows the price of foreign currency in dollars relative to the U.S. consumer price index, which indeed is an odd series that we shall call the cockroach exchange rate index. The Federal Reserve provides indices of exchange rate (in terms of the value of the dollar) both in nominal terms and in real terms, which has me wondering under what conditions if any would this cockroach exchange rate index makes any sense.

One of the special cases of the more general rule for defining real exchange rates might be a situation where the foreign price level is constant so that an unchanged real exchange rate implies that any domestic inflation is accompanied by nominal devaluations of the currency. In this case, the cockroach exchange rate index would be flat over time and any variation of it would represent changes in the real exchange rate. A second special case is a situation where domestic and foreign inflation are equal so that variations in the nominal exchange rate and the real exchange rate are the same.

If we turn the light on the cockroach’s graph, we can see a sharp distinction between Luskin’s graph for the period from 1973 to 1980 versus the period from 1981 to 1989. Looking at the average changes for three 5-year periods: (a) from Jan. 1976 to Dec. 1980; (b) from Jan. 1981 to Dec. 1985; and (c) from Jan. 1986 to Dec. 1990, we see very sharp distinctions between the behavior of inflation rates and nominal exchange rates. For the period from Jan. 1976 to Dec. 1980, U.S. inflation was just over 9% while average foreign inflation was just under 9%, which implies that the most of the 8.9% nominal depreciation of the dollar was reflected in a real depreciation (6.2% over the period). Luskin properly notes that U.S. inflation was lower during the 1980’s as it averaged only 4.5% for the decade. Now had foreign inflation remained at 9%, his cockroach index would predict a rise in the price of foreign currency in dollars relative to the U.S. consumer price index that would track this supposed 9% foreign inflation rate if there was no change in real exchange rates. What Luskin fails to recognize as he scurries in the dark is that foreign inflation also averaged about 4.5% during the decade. So most of the 25.7% nominal appreciation during the first half of the decade was reflected in a massive real appreciation (20.4%), while the second half of the decade saw a 29.9% nominal devaluation and a 27.4% real devaluation.

So what was Mr. Luskin’s point here? Did he really believe the the real appreciation of the early 1980’s was a permanent change in the terms of trade or did he simply misforecast foreign inflation not realizing that it was also declining? Odd for someone who was attacking the forecasting abilities of the CEA back in 1982 that even many years after this period did the cockroach who hides in the dark fail to see the light on what historically happened to foreign prices.