What's the deal with PPP?

In a previous post I suggested that there might some problems with using Purchasing Power Parity (PPP) measures of income per capita, the traditional measure of well-being used by the World Bank, for example. And although some might think that the main problems are basically empirical, my fundamental preoccupation is theoretical (see this paper, which in fact comes from my thesis).

PPP was developed by Gustav Cassel as an extension of the Quantity Theory of Money (QTM) to international matters. The quantity of money determined domestically the internal price level, and the exchange rate was determined as the ratio of domestic and foreign prices (or vice versa depending on how you define the exchange ratio), or in dynamic versions, the change in the exchange rate was defined as the difference of the inflation rates.

Wicksell was very critical of Cassel's theory, as I note in my paper [there were significant personal differences between the two main authors of the Swedish school, beyond their divergences on economic theory]. He basically suggested that the rate of interest, the natural rate determined by the productivity of capital and the savings decisions of economic agents, was the key variable, not the money supply. Hence, the bank rate, if it was lower than the natural rate, would not only generate his famous cumulative process of inflation, but it would also lead to flows of capital, provided that it was not in line with the bank rate of interest in other countries, and would basically determined the foreign exchange rate [note that Wicksell, and not the Keynes of the Tract, as is often argued, is the first, in 1919, to defend what we would today refer to as the uncovered interest parity condition].

From our perspective what matters here is that, even within the marginalist approach, the notion that the Quantity of Money, and prices, determine the equilibrium exchange rate is ultimately incorrect, once money is endogenous, as Wicksell assumed [note that the modern consensus in macroeconomics, both the New Keynesians and the so-called New Neoclassical Synthesis, assume an exogenous rate of interest, using some sort of rule, typically a variation of Taylor's rule]. Further, if we assume free capital movement, which implies a uniform rate of profit, marginalism would require that capital would flow to places in which it is scarce, and eventually (in the long run) the rate of profit or the natural rate of interest would be equalized.* Hence, the exchange rate that would be establish after the process is complete, would correspond to the uniform natural rate, which governs the bank rate, which as we saw is what Wicksell suggested determines exchange rate. So there must exist a natural exchange rate that corresponds to the natural rate of interest (and the natural rate of unemployment and its correspondent real wage, Friedman would argue).

It is obvious that there are 'imperfections' and the natural rate of interest is not equalized in the real world, so the exchange rate also deviates from the natural rate. But that isn't the main problem with the mainstream view. As we saw, the capital debates undermine the theoretical basis for a natural rate of interest, and hence for a natural exchange rate (or a natural rate of unemployment for that matter). Hence, it is the Keynesian (and Sraffian) institutional rate of interest, as determined by monetary authorities that rules the roost. The conventional rate of interest is then connected to a conventional exchange rate [then institutional factors become relevant, like the existence or not of capital controls, etc.].

Leave aside the theoretical problems of purchasing power parity measures, since they are NOT attractors of the actual exchange rates [the reasons why Argentina had a 1 to 1 exchange rate with the dollar for a decade, or Greece has a 'fixed' parity too are political and institutional], and even if for some purposes you may want to use PPP rates as a measure of material welfare, one may also be interested in actual market exchange rates for other purposes. Indeed, for most of the relevant matters that concern economic well being, particularly in peripheral countries, like the capacity to repay foreign debt and avoid default and import capital goods to promote growth, it is the market exchange rate that is central to convert incomes in different countries into a common numeraire.**

* The fact that capital does NOT flow to developing countries is something that still puzzles very much mainstream economists like Robert Lucas (see here).

** Which means that China is considerably less developed than Argentina and Brazil, even if it is growing fast, it has a regional hegemonic project, and is, by sheer size, one of the most important economies in the world.

Comments

  1. There are two questions here. First, under what conditions are PPP and UIP consistent? And second, does *either* condition describe actual exchange rates (in the short/medium/long run)?

    Neither UIP nor PPP depends on the existence of a natural rate of interest, so I don't think the Cambridge controversy is relevant to the questions in this post. Nor is the problem of "perverse" capital flows, which don't seem to bother the mainstream much at all these days -- just assume there is some immobile third factor, "technology" or "institutions" or some such.

    The key question, it seems to me, is the relationship between PPP, UIP, and a central bank policy rule.

    I think the mainstream view goes like this:

    (1) The real interest rate is pinned down by the world interest rate. (Again, no assumptions about a natural rate are needed here, just small country and free capital mobility.)

    (2) The central bank sets the nominal rate.

    (3) UIP ensures that a country with a nominal rate below the world rate must be experiencing *nominal* appreciation, and conversely.

    (4) So, when a central bank announces a new rate below the world rate, its currency undergoes an instantaneous depreciation, proportional to the difference between the rates and the amount of time it is expected to persist.

    (5) The currency then appreciates at a rate equal to the difference between the domestic and world (nominal) rates. If market expectations were correct, the nominal exchange rate will return to its original value at exactly the moment that the central bank returns the nominal interest rate to the world level.

    (6) There will be no change in relative price levels.

    (7) So UIP is satisfied continuously, but there can be departures from PPP in the short run. In fact, it is theses departures from PPP that make monetary policy effective in a world of free capital mobility. With mobile capital, the central bank cannot move real interest rates, but it can move real exchange rates.

    I don't think this is a good description of the world, but I don't think there is any *logical* contradiction in it. What I don't know is, what (in the mainstream view) would happen if a central bank tried to maintain an interest rate different from the world rate indefinitely? To the extent that a low interest rate is inflationary, it will tend to produce a depreciation, which means the market adjustment will be away from UIP rather than towards it.

    Question: How do *you* think exchange rates are determined?

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    1. Nope, wrong. A few replies. If the natural rate (and there is no mainstream theory that does not have it) determines the bank rate (the Taylor rule is one way in which the rate of interest that produces stable prices, the natural one, determines the one the bank should set), then by definition UIP demands (in equilibrium) a natural rate, and hence you do have a natural exchange rate (PPP also demands since, prices are not stable becuase you print to much money for a given supply constraint, the natural limit; and that natural limit is associated to the full utilization of capital which takes place when Investment equals full employment savings, given by (you guessed) the natural rate. I do say how it is determined, in the paper and the post. It is a conventional rate, controled among other things by central banks.

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    2. I'm not arguing, just trying to understand.

      So the policy rule plus the (domestic) Phillips curve, pin down both the nominal interest rate and the inflation rate, meaning UIP determines the exchange rate, meaning you have to drop PPP or the system would be overdetermined?

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    3. Let me clarify. PPP is a rule with exogenous money. With endogenous money it must be the rate of interest that is central to determine the exchange rate and you must have some sort of UIP rule. However, as I say in my paper (and the thesis) in both cases what underpins the marginalist logic is that capital is fully utilized, and you do have with exogenous or endogenous money a rate of interest that equalizes the investment to full employment savings. Now (forget short term deviations and imperfections) that means that once that rate is achieved prices are stable and the exchange rate is in equilibrium. So the neoclassical theory implies, whether they get it or not, a natural exchange rate. Note that this is true for all relevant macro prices, a natural rate of interest is connected to the natural exchange rate and to the natural real wage (Friedman called the quantity natural rather than the price in the labor market, but the point is clear, and he directly alluded to Friedman). But yes, you are correct that you can have only one rule otherwise the system would be overdetermined.

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  2. So the question I have here is on the "empirical" side. I tend to take all economic statistics with a grain of salt, as just guesstimates, some more or less faulty in method, but with claims to too much precision dubious. So are you saying that there actually is an empirically accurate explanatory and predictive account of fluctuating FX rates and PPP should play no role in such an account? I tend to think not, given the massiveness of FX flows nowadays and the numerous speculative factors that seem to drive FX rates far from any theoretical "equilibrium" for persistent periods of time. (I found explanations of the strengthening U.S. $ during the GFC as a "flight to safety" ridiculous, as fairly clearly what was happening was a re-patriation of U.S. $ from speculative investments abroad to cover domestic losses or to cover $ investment losses by foreigners in the Euro-dollar market). So granted PPP estimates are all over the place, (since after all they are not used on a regular basis for practical business), but isn't there nonetheless a persistent gap between nominal FX and PPP "values" between major first world currencies, (with high global market demand) and third world currencies, (with little market demand? And aren't MNCs and mega-banks (and their speculative clients) consistently arbitraging that difference, so as to suck rents out of the globalized economy?

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    1. Nope. PPP is terrible as a theoretical explanation for exchange rates since it is not an attractor of the actual exchange rates. Second, while on the empirical side you may want to know the purchasing power of a peasant in rural India, for example, that does not give you a precise measure of the country's problems. India must import capital goods in international markets at the current exchange rate. So you may want to use current rates too.

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  3. And by the way, all measures should be taken with a grain of salt, but that does not mean that they are all guesstimates. GDP is a pretty decent measure, in spite of its critics, and it is NOT just a guess. Richard Stone and Simon Kuznets are two of the few 'Nobels' that were deserved.

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  4. Further, if measured consistently, almost any measure gives you at least the time series to analyze.

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