Economists come under fire when things go wrong, and the main line of attack comes from forecasts gone awry. Forecasting is an integral part of many economists’ jobs, and a valuable tool for public policy. The problem is that forecasts are very often wrong—after all, as the famous quote goes, “It is difficult to make predictions, especially about the future.”

Economists have fought back, explaining that their forecasts are just estimates and better considered as a range rather than a precise, fixed-point prediction. Still, there’s no denying that the power to divine the future is valuable, so economists are continuously working to find ways to make their methods of spotting future trends more accurate.

This week, the European Central Bank published a working paper (pdf) on forecasting foreign exchange rates. The authors say they have identified a method so simple that it can be done “on the back of a napkin.”

Ultimately, the researchers say that two features of currency markets in advanced countries (with flexible exchange rates) allow forecasts to be calculated more accurately. The first is that real exchange rates (adjusted for the inflation rates in a country) are mean-reverting—that is, the rate will always return to a long-term average. This long-term level is implied by Purchasing Power Parity theory. The second is that this reversion to the mean is mostly driven by the nominal exchange rate, and not other factors like relative inflation in country-currency pairs.

“The secret is to avoid estimating the pace of mean reversion and assume that relative prices are unchanged,” the paper’s authors, Michele Ca’ Zorzi and Michał Rubaszek, add.

So far, so simple, right? Right?!

Glad you’re following along. So the best method for forecasting, say, the euro-dollar exchange rate at some point in the future is “a calibrated PPP model,” which assumes that the inflation-adjusted exchange rate slowly returns to its sample mean, with half of this adjustment completed in three years.

As the authors suggest, “this approach is so simple that it can be implemented even on the back of a napkin in two steps.” So, napkins ready? Here’s how you do it:

Step 1 consists in calculating the initial real exchange rate misalignment with an eyeball estimate of what is the distance from the sample mean. Step 2 consists in recalling that, according to this model, one tenth of the required adjustment is achieved by the nominal exchange rate in the first 6 months, one fifth in one year, just over a third in two years and exactly half after 3 years.

Got it? Good, because that comes from the paper’s “non-technical summary.” 🤔

Clearly, what passes for simple conversation in the cafes around the ECB’s Frankfurt headquarters may be a little different from what people elsewhere chat about over coffee.