Grande Latte Prices Around the world. What'

Grande Latte Prices Around the world.

What's the fair value of a euro? That depends on whether the answer comes from Berlin or Paris.

German Chancellor Angela Merkel on Wednesday weighed in on what the currency should be worth, saying the euro's exchange rate is "normal in the historical context." French Finance Minister Pierre Moscovici had a different take earlier this month, calling the euro "perhaps too strong."

Economists say Ms. Merkel is right—technically. The euro's buying power is roughly where it should be, according to the Peterson Institute for International Economics, which judges currencies based on countries' current-account balance. But others caution Germany's relatively robust economy props up the euro's value; if weaker countries like Spain or Italy still had their own currencies, they'd be worth much less.

A weaker euro could help Europe's struggling economies by making their exports more competitive. However, a too-cheap currency can trigger runaway inflation.

"What is fair for one part of the zone, is very unfair for other parts of the zone," said Amer Bisat, a managing partner at Traxis Partners, which has $300 million in assets, and who teaches a course on monetary theory at Columbia University. "The euro is arguably undervalued for the North, and overvalued for the South."

Similar debates over what constitutes "fair" in the currency world are playing out in legislatures and central banks around the world. Some U.S. politicians have accused China of keeping the yuan unfairly depressed to give its exports a leg up. Leaders across Asia have complained this year that Japan is pushing the yen too low, saying they will match with currency-weakening policies of their own. Some analysts say the rhetoric has snowballed into a global currency war, where countries are competing to devalue their currencies.

It is a fight that is complicated by the lack of a universally acknowledged measuring stick for a currency's proper value. Economists use a battery of data points, including comparing what the same product would cost in different countries or measuring the value of income and investment an economy takes in versus what it spends. Even then, they can come out with wildly different ideas of which major currencies are artificially strong or weak.

While most models peg the euro's value—about $1.32 on Thursday—as roughly correct, they are split on the yen. Makena Capital Management, which ranks currencies using eight economic variables, including inflation and the state of a country's finances, says Japan's currency may fall as low as ¥120 against the dollar as the country adjusts its monetary policies. Meanwhile, according to the Peterson Institute, the yen has already fallen 12% below its fair value of ¥84.

"It could be a bit of a judgment call," said Aroop Chatterjee, chief foreign-exchange quantitative strategist at Barclays in New York. He looks at several models, keeping an eye out for instances where they all agree a currency is too strong or weak.

One way to determine how currencies stack up is purchasing-power parity, or PPP, which compares the amount of currency needed to buy the same item in different countries. A grande latte at Starbucks , SBUX +0.60% for example, costs $4.30 in New York, but the equivalent of $9.83 using Norwegian krone in Oslo, and just $3.92 in Turkish lira in Istanbul. Economists say PPP is of limited use, however, as it doesn't account for factors like a country's finances and trade flows.

Even the International Monetary Fund—whose economic models serve as a benchmark for financial firms and governments world-wide—is re-evaluating how it assesses exchange rates.

The IMF has for many years used three separate calculations to create a rough range for how a currency's value compares with a basket of its rivals. Its formulas rely on economic data, including comparing a country's trade deficit or surplus to where it should be based on its underlying economic characteristics, or an exchange rate's long-term average.

On a trial basis, the fund is expanding its models to include how much a country has influenced its exchange rate by buying or selling its own currency in the open market.

IMF Managing Director Christine Lagarde said on Feb. 15 that there had been "no major deviation from fair value" in major currencies recently.

"Yes, the euro strengthened. Yes, the yen depreciated. But that was caused by recent good policies taken in Europe and recently revised, looser monetary policy taken in Japan," she told Group of 20 finance ministers and central bankers in Moscow.

For certain currencies, models broadly agree they are too expensive, or too cheap.

The New Zealand dollar, known as the kiwi, is almost 19% stronger than it should be based on economic fundamentals, according to the Peterson Institute. Its value has been buoyed by investors attracted to the country's bonds, which yield more than most other developed economies' debt. Reserve Bank of New Zealand Gov. Graeme Wheeler Wednesday called the kiwi "significantly overvalued" and said the central bank would intervene "when the circumstances are right."

On the other side of the equation, most models point to the Swedish krona as undervalued, even though it has strengthened more than any other major currency against the dollar this year.

As difficult as it is coming up with the perfect currency model, many of the systems available now tend to work—if given enough time.

"Around 50% of undervaluations tend to be erased within five years," said Alan Ruskin, a strategist at Deutsche Bank in New York. "Over the long term, these models do provide value."