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.
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