Radar Perene / Archive / science

Exchange rates: 'expensive dollar' is a data question

◦ Index methodology v2.2 (working papers with DOI). See the methodology.

Science

In March 2020, the dollar closed at R$ 4.88 and the entire country declared it expensive. In December 2024, it closed at R$ 6.09 and the declaration was repeated, word for word. Between one date and the other, the sentence did not change — but prices in Brazil and in the United States changed, both countries' interest rates changed, and therefore the ruler against which "expensive" would make sense changed too. Whoever repeated the adjective without redoing the arithmetic did not issue the same opinion twice; they issued two different opinions without noticing.

Purchasing power parity (PPP) is the hypothesis that, over the long run, the exchange rate between two currencies tends to offset the inflation differential between the two countries — so that the same basket of goods costs, once converted, roughly the same in both places. It does not say where the exchange rate will be next month; it says what it makes sense to compare it against. "Expensive" and "cheap" are fractions, and parity supplies the denominator.

The idea is a century old — the Swedish economist Gustav Cassel named it shortly after the First World War — and it remains the starting point of any serious discussion about exchange-rate levels, precisely because it turns an adjective into a calculation.

The ruler and its versions

The popular version of parity is the Big Mac Index, published by The Economist since 1986: a one-item basket, sold worldwide, converted into dollars. The research version is the real exchange rate — the nominal rate adjusted by the two countries' price levels — and its more complete sibling, the real effective exchange rate, which weights a basket of trading partners. The Central Bank publishes these series as open data, and the PTAX quotation, the official dollar reference, is series 1 of the SGS — the same system described in open data from the Central Bank.

The distinction the ruler imposes is the one the news cycle tramples: the nominal exchange rate can rise year after year without the dollar becoming "more expensive" in real terms, if Brazilian inflation runs above American inflation over the same period. The headline number is a loose numerator; parity forces the denominator to be declared.

There is a second parity, less famous and more rigorous: covered interest parity, which ties the price of the forward dollar to the interest-rate differential between the two countries. It is not a theory about the future — it is an arbitrage identity: if the forward dollar cost anything different from what the rates imply, there would be riskless profit in closing the circuit. The consequence disarms an entire folklore: the forward price of the dollar is not "the market's bet" on where the exchange rate is going; it is, essentially, the cost of carrying the position.

What the data shows about parity

The empirical literature has a double and honest verdict. In the short run, purchasing power parity fails systematically: the exchange rate fluctuates far more than prices do, and enormous deviations open and persist. In the long run, there is evidence that deviations correct — slowly. Kenneth Rogoff's classic 1996 survey named the discomfort the purchasing power parity puzzle: the half-life of deviations measured in the literature runs in years, not months. The ruler works as a decade's anchor, not a week's compass.

For the Brazilian case, the practical consequence is documentable: over any short window, the level of the exchange rate says more about the environment — global risk appetite, terms of trade, domestic premiums — than about any "fair price." That is why the house doctrine, recorded in the entry the dollar as thermometer, treats the exchange rate as a gauge of regime, not as a term of judgment.

Two levels, the same question

The house archive keeps both episodes from the opening, and they yield more read together than apart. In numbers: the R$ 4.8839 close of March 2020 and the R$ 6.097 close of December 2024 were both recorded by the monitoring as statistical anomalies — rare departures from each era's own historical pattern, documented in the ruler of March 2020 and in the dollar in anomaly, December 2024.

Notice what the record asserts and what it refuses to assert. Stating that the exchange rate was far from its own history is verifiable arithmetic. Stating that it was "expensive" would require the full denominator — relative prices, interest rates, terms of trade — and an equilibrium reference the literature estimates with wide margins and legitimate disagreements. The house writes the first sentence and leaves the second to those with courage and no data.

Frequently asked questions

Does purchasing power parity predict the exchange rate?

Not over any horizon useful for short-term decisions. The evidence points to slow correction of deviations, measured in years. Parity serves to anchor long-period comparisons, not to anticipate the next move.

Is the Big Mac Index serious?

It is an honest illustration with declared limitations: a single item, embedded local service costs, no income adjustment. Research versions use broad baskets and adjustments — but the sandwich's intuition is the same as the full ruler's.

What is the real effective exchange rate?

The exchange rate adjusted for inflation and weighted by the country's trading partners. It is the measure that answers "how much the currency has actually strengthened or weakened" better than any isolated nominal quotation.

If the forward dollar is not a forecast, what is it?

Interest-rate arithmetic. Under covered parity, the forward price reflects the rate differential between the two currencies — the cost of carrying the position until then. Reading it as a consensus about the future is attributing intent to an accounting identity.

If the exchange-rate level is a denominator question, the next piece of the trail asks what the "cycle" everyone claims to see in the data actually is: business cycles — describing is not predicting →

House readings: each day's exchange rate is in today's note, in the Daily; the episodes when it left its pattern, in the precedents, in the Atlas.

Rebuilding the real exchange rate for a specific period, with declared deflators, is an exercise the house conducts on request.

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