Some thoughts on “overvalued” and “undervalued” exchange rates

Benn Steil and Emma Smith have a new post on the Big Mac Index:

The Economist magazine’s famous Big Mac Index uses the price of McDonald’s Big Macs around the world, expressed in a common currency (U.S. dollars), to estimate the extent to which various currencies are over- or under-valued. The Big Mac is a global product, identical across borders, which makes it an interesting one for this purpose.

But burgers travel badly.  So in 2013 we created our own index—one that better meets the condition that the product can flow quickly and cheaply across borders.

The Geo-Graphics Little Mac Index compares the price of iPad minis across countries. iPad minis are a global product that, unlike Big Macs, do in fact travel the earth with their owners.

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Overall, the Little Mac Index suggests that the dollar has become slightly more overvalued (up from 5 percent) since the beginning of 2015.  The euro is undervalued by 11 percent, and the yen by 10 percent.  Having been fairly valued at the beginning of last year, the renminbi – following on the heels of China’s large devaluation in August – is now 5 percent undervalued.  This compares with an implausible 46 percent undervaluation on the Big Mac Index.  Maybe Congress is Lovin’ It, but we think the Economist needs to hold the mustard.

Given recent events, only a complete moron, or Donald Trump, would claim the yuan is undervalued.  So that’s a point in favor of the Little Mac Index.  But let’s step back and think about what terms like ‘overvalued’ and ‘undervalued’ actually mean.  Do they mean the exchange rate is artificially set at a different level from the black market rate?  Perhaps in cases like Venezuela, but in most cases these are actual market exchange rates, where you can freely buy and sell the currency in question.  So clearly that’s not what the creators of the Big Mac and Little Mac indices have in mind.

But then what does it mean to say an asset price is under or overvalued?  Does it mean the market is in some sense wrong, as when there is a bubble?  Perhaps, but then why would you expect these “Mac” excises to find the right exchange rate? Yes, PPP predicts a certain relationship between prices, but we have very good economic theories, such as Balassa/Samuelson theory, which explain why we should not expect PPP to hold for all goods.  So a deviation from the prediction of PPP actually tells us nothing about under and overvaluation.

Nor is it clear why Steil and Smith think it’s better to use a traded good than a non-traded good.  Let’s take that to the logical extreme, and use a good that is so easily traded that the law of one price holds, say gold.  AFAIK, the price of gold in New York, London, Hong Kong, Tokyo, Zurich, etc., is virtually identical, when measured in a common currency.  So Steil and Smith have picked a good that is more easily traded that Big Macs, but less easily traded than gold.  But why is that optimal? Using gold, PPP would always seem to hold true.  Even worse, a sudden adjustment in the exchange rate (such as Switzerland’s 15% appreciation a year ago), would leave the price of gold in Zurich exactly the same as before, when measured in dollar terms.  In other words, if they had chosen a very easily traded good like gold, instead of Little Macs, Steil and Smith would have found the Swiss franc to be correctly valued right before, and right after, a sudden 15% adjustment.  Does that make sense?

It seems to me that if you really want to look for exchange rates that are out of line with PPP, you’d use non-traded goods like Big Macs, not traded goods like gold. Little Macs fall in between, and offer no obvious advantage over either extreme.

In my view all of these exercises miss the point.  Exchange rates should not be set to make PPP come true. Nor should exchange rates be set to generate a current account balance of zero.  Trying to set rates to make these equalities hold would create a macroeconomic disaster.  Exchange rates should be set at a level that provides macroeconomic equilibrium, something like low and steady growth in NGDP.  The only meaningful sense that an exchange rate can be said to be overvalued is if it leads to below target NGDP growth (or inflation, if you prefer.) For instance, despite falling from 80 to the dollar, to 120 to the dollar, the yen is still overvalued, as most experts forecast about 1% inflation going forward, which is below their 2% target.

This sense in which an exchange rate can be overvalued is exactly the same as saying the short term interest rate is too high, or the TIPS spread is too low, or the nominal price of zinc is too low.  A counterfactual monetary policy that produced on target NGDP growth, would (by assumption) lead to a lower short-term nominal interest rate, a higher TIPS spread, and a higher nominal price of zinc.  And a lower domestic currency value in the forex markets.  That doesn’t mean the market is “wrong” in a “violation of the EMH” sense, rather it means monetary policy is too tight to achieve macroeconomic equilibrium.

So far I’ve talked about nominal exchange rates.  But what about real exchange rates, can they also be overvalued or undervalued?  Elsewhere I’ve argued that real and nominal exchange rates are so different that they should not even be discussed in the same course.  And yet many people foolishly talk about them synonymously. What would it mean to say the China’s real exchange rate is undervalued?  In that case you’d be arguing that China’s government policies encourage too much saving, too little investment, or both.  In other words, the policies encourage too big a S-I gap, which of course is the current account surplus.  I’m not saying that’s true (I doubt it) but that would be the argument.  In that case it would be stupid to adjust the exchange rate (doing so would produce a depression) you’d want to change the saving/investment policies.

Off topic, I love the ambition in this post by C. Harwick, where he derives NGDP targeting from first principles.  I don’t know anything about this blogger, but based on this post he seems much younger and much smarter than I am.  However I disagree with the final two bullet points in item #13.

PS.  I have a new post on IS shocks, over at Econlog.



10 Responses to “Some thoughts on “overvalued” and “undervalued” exchange rates”

  1. Gravatar of Derivs Derivs
    9. January 2016 at 09:56

    As reading about PPP for the first time was something that had a real influence on my career path. I was broken hearted to see how poorly it held up. Then one day I realized it is actually very good. What is very bad is that people do not correctly calculate the frictions between the 2 places (taxes,labor,rents). Lazy analysis!!!

    Much like why gas on 1 corner trades at a different price than the opposite corner that is in another higher taxed county. It’s not PPP that is broken, it’s someones shitty model that is missing variables (not always but usually).

    Brasil looks like a PPP disaster to the U.S., but when you know the taxes you can usually reconcile prices to U.S. prices almost perfectly.

    Obviously some frictions are impossible to predict the $value-friction of, take pharmaceuticals, where they are simply illegal to transport.

  2. Gravatar of ssumner ssumner
    9. January 2016 at 10:36

    Derivs, Good points.

  3. Gravatar of Luis Pedro Coelho Luis Pedro Coelho
    9. January 2016 at 11:27

    With tradeable goods, the law of one price holds; with non-tradable goods, you have to be very careful to take into account quality differences (as well as taxes & regulations, which sometimes do increase the quality as they increase the costs).

  4. Gravatar of Benjamin Cole Benjamin Cole
    9. January 2016 at 17:37

    As Scott Sumner says, and I sloppily and liberally paraphrase, “exchange rates, scmachange rates.”

    Who cares? The Fed must have US monetary policy at a level that is right for us.

    By the way, the Monetary Authority of Singapore and also the central bank of Hong Kong are courting recession by pegging the exchange rates of their currencies. So was the People’s Bank of China, and I hope they move to having no peg at all.

    One quibble: Sumner says monetary policy should target low and steady rates of NGDP growth. I suppose it is a matter of semantics what means the word “low.” I prefer robust growth. Let it rip. Print money and build houses.

    Central bankers make monetary policy the way that spinster schoolmarms run nightclubs.

  5. Gravatar of Ray Lopez Ray Lopez
    9. January 2016 at 18:01

    @Derivs, Sumner – the iPad Mini index is a poor substitute for the Big Mac index for the reason given by the former’s authors on their blog: “The iPad mini is a global product … and its manufacturer, Apple, is highly attuned to shifting currency values. “We made some pricing adjustments due to changes in foreign exchange rates,” Apple spokesman Takashi Tabayashi told Bloomberg News after Apple raised Japanese iPad prices 15% in May, offsetting the early effect of Abenomics on the yen” – notice Apple is deliberately pricing the iPad differently in different countries depending on foreign exchange values. By contrast, most of McDonald’s stores are franchises, which are not controlled by a central ‘boss’ and thus don’t make these global adjustments.

    Gratuitous insult (routine): don’t you read your primary sources?

    PS- the C. Harwick post does NOT derive NGDPLT from first principles. He simply is outlining various believes in bullet form. Where is the analysis? Not in the link cited. And curiously Sumner rejects the one principle that G. Selgin and myself would agree on: “However, #5 suggests something like Free Banking would be far more stable and robust than even an ideal monetary policy target.”

  6. Gravatar of C Harwick C Harwick
    9. January 2016 at 23:03

    Thanks for the link! I have to agree with Ray though; “derives NGDP targeting from first principles” is a far too generous description of semi-connected bullet points.

    Since you brought up point 13, I wonder why you’re skeptical of nominal gross output as a monetary target (as I gathered from Googling all instances of Gross Output on this site). It seems very much in the spirit of your “Lower Interest Rates Are Not Contractionary” post the other day. If consumption spending is not relevant for the equation of exchange, why would anything short of total spending – final spending included – be important either?

    Sure gross output double counts things and is a poor measure of an economy’s wealth for that reason, but that would seem to be exactly what you’d want for a monetary target. If I buy a bike and then sell it, it shouldn’t count toward GDP, but it does affect the velocity of money, which should influence a monetary target. No? Better econometric reliability is the only reason I can think of for preferring NGDP.

    Related: the equation of exchange is not very useful if you interpret M as base money.

    (If this is off topic for the comments on this post, I’m happy to move the discussion elsewhere; though if there’s anything obviously wrong with my logic here I’d like to be told so before I stake anything bigger than a blog comment on it)

  7. Gravatar of ssumner ssumner
    10. January 2016 at 06:37

    C Harwick, Yes you are right. I suppose I meant “derives from first principles” as a sort of joke–but it wasn’t a very good one. Rather you went from the very general to the very specific, that’s what I was referring to. I thought it was an excellent post.

    On NGO, this recent post explains my views:


    The short answer is that NGDP is better than NGO because it’s what matters for labor and credit market stability.

    I disagree about the equation of exchange, I think it’s actually more useful if you use base money. But I think the equation is also more useful in the Cambridge version:

    M = kPY

    That version makes it clearer that we are looking at the demand for money (as a share of income.)

    Your mistake is assuming that velocity is the average number of times a dollar is spent. That’s not true. V is NGDP/M, nothing more. There is a different V for every M.

  8. Gravatar of C Harwick C Harwick
    10. January 2016 at 10:01

    Aha, so I was searching in the wrong place. Somehow I’d missed Vincent’s post too. I’ll continue in the comments over there, then.

  9. Gravatar of rob rob
    11. January 2016 at 03:44

    There is so much wrong with that index for China that I don’t even know where to begin.
    1# iPads sold in China are different, in order to be imported the Gov needs to ensure it can “control” the device more or less. So there are especially high barriers to moving foreign iPads into China
    2# There is a thing companies with market power do in the presense of barriers to reselling, it is called price discrimination.
    3# In terms of many non tradeable things, things like vegetables and energy are way cheaper, but that isn’t really tells us nothing about the future of the exchange rate
    4# Had they instead went with a burberry tie index, or an iPhone index or some other random good which is more expensive here the result would be opposite
    5# Big macs here are not the same either, they use different meat and have tweeked things, it is significantly different. Also Mcdonalds workers make about 1 dollar an hour.

  10. Gravatar of Jack’s Links – The Zeitgeist Log Jack’s Links – The Zeitgeist Log
    17. January 2016 at 22:00

    […] Scott Sumner on Exchange Rates – Everybody understand on some intuitive level what it means for one country’s currency to be ‘strong’ versus another – that they can buy more goods in the ‘weak’ country than they could buy of similar goods in the ‘strong’ country. This is usually best seen by going to a developing country from a developed one, and whenever the scenario deviates from this familiar one, people start making errors, conflating cause and effect, and being generally confused. […]

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