Some thoughts on currency crises and overshooting

So I've been teaching an international finance class, after a long while I might add. The discussion of currency crises models I think is interesting, since it is very revealing of the mainstream assumptions about the long run. Typical discussion would imply that in the long run the Quantity Theory of Money (QTM) and Purchasing Power Parity (PPP) hold. PPP means simply that the exchange rate adjusts for differences between the domestic and foreign price levels. Hence, we have that S =P/P*, where the star indicates foreign variable. If in addition we believe with the QTM that the central bank (CB) controls prices by controlling the money supply, then the CB can control the exchange rate indirectly.

In the figure below the 45o line shows the equilibrium levels of the exchange rate (S) as the price level, which is related to the money supply. Now suppose that the central bank fixes the exchange rate at S1 (the graph is based on Dornbusch representation in his classic paper; for now disregard the QQ curve). If the money supply is below the level that corresponds to P1, then the fixed exchange rate is too depreciated for the current stock of money, stimulating exports, discouraging imports, and leading to Current Account (CA) surpluses. In this case, the central bank would accumulate international reserves. The accumulation of reserves leads to increasing money supply and the economy moves to a new equilibrium.

If the central bank follows the rules of the game and it is credible (and the assumptions are also valid, meaning the economy has a tendency to full employment and increase in money supply only affect prices) then the money supply increases/decreases with the CA surpluses/deficits and the system converges to a stable equilibrium. However, if the commitment to the fixed-peg is not credible, and the rules of the game are not followed, then problems might arise. Imagine a situation in which the monetary authority continues to print money, to finance fiscal deficits for example, and the fixed exchange rate would now be below its equilibrium value (below the 45o line). Beyond the equilibrium point the central bank would start losing reserves. At some point, say when the money supply reaches the money supply level compatible with P2, the stock of reserves would be depleted. At this point, the central bank cannot defend the exchange rate anymore and the exchange rate jumps to S2. The Krugman model basically assumed exactly this, with the difference that if agents have rational expectations (perfect foresight in this case), then they would have an advantage to try to speculate against the currency before reserves are exhausted.*

In the model above the currency crisis occurs because the CB does not follow a monetary policy consistent with the fundamentals, that is, prints too much money to finance the government. Although, not immediatly obvious the model above is a simplified version of the Mundell-Fleming (MF) model, in the long run, when prices rather than income is the adjusting variable.In this case, the MF model can be represented with the exchange rate and prices, rather than output, as the adjusting variables. The QQ curve is a downward sloping curve, since higher prices increase money demand (or reduce the real money supply), leading to a higher rate of interest and a more appreciated exchange rate (lower S). Note the QQ curve is just the old LM for an open economy.

Also, because the QTM and PPP hold it must be true that increases in money supply lead to higher prices which lead to a proportional change in the nominal exchange rate, for a given foreign price and foreign money supply. In other words, the 45o degree line which corresponds to the proportional changes in domestic prices and the nominal exchange rate must still hold. We can derive the IS curve too, which would be upward sloping, but it is unnecessary, since if PPP holds then the economy must be in the long run on the 45o degree line.**

Dornbusch's trick, which was considered the first New Keynesian model (featuring both rational expectations and price rigidities), is that the nominal exchange rates adjusts faster than prices, then an increase in money supply would shift the QQ (LM) curve upwards. An increase in money supply reduces the domestic interest rate, leading to a depreciation of the currency. The economy moves from point A to point B. Then as depreciation increases net exports, and a lower rate of interest leads to more investment, there will be excess demand in the goods market, and for an economy that is at full employment, prices would go up. As prices go up, then the economy moves down the new QQ’ curve from point B to C, since with higher prices money demand increases and the rate of interest must increase (less than the initial decrease) causing some appreciation (less than the initial depreciation). At the new equilibrium the exchange rate is more depreciated than at the original equilibrium, but because of the short run rigidity of prices, the exchange rate overshoots its equilibrium value in the short-run. The point was that even if markets were efficient, in the sense that with price flexibility they tend to full employment and to the equilibrium exchange rate (PPP), the use of the exchange rate to deal with shocks might lead to excessive volatility.

There are many problems with the long run MF model (meaning the one solved in the S-P space). The obvious one is the notion that price flexibility leads to full employment, something that Keynes long ago suggested was NOT the case. Although Keynes was aware of the possibility of the system returning to full employment with price flexibility, he suggested that if lower prices had a negative impact on firms that are indebted, then investment would fall. In his own words: "indeed if the fall of wages and prices goes far, the embarrassment of those entrepreneurs who are heavily indebted may soon reach the point of insolvency, — with severely adverse effects on investment." In other words, with price flexibility the IS shifts back, and there is no tendency to full employment. That means that one should stick with the solution of the model in S-Y space, if one wants to introduce the open economy (one such model, without full employment and many other mainstream characteristics is available here).

Alternative (classical-Keynesian, post-Keynesian or whatever you prefer to call them) models would not only emphasize the role of quantity adjustments, but also the the sustainability of the current account (CA), rather than fiscal deficits in the explanation of currency crises. While conventional currency crises models of all generations (including the more heterogeneous 3rd generation models) suggest that at the heart of currency crisis there is a fiscal crisis, post-Keynesians emphasize terms of trade shocks and hikes to foreign rates of interest, highlighting the role of the balance of payments constraint in currency crises. Note that the economy in this view is not at full employment, and, hence the effect of fiscal expansions is not on prices, but on the level of activity. Higher level of income leads to increasing imports and a deteriorating CA. It’s the deteriorating CA and not the fiscal deficits that matter and the CA position might worsen even if the fiscal accounts are balanced. Further, after a currency crisis the central bank hikes the rate of interest, increasing the costs of debt-servicing, and, hence, government spending, at the same time that the recession reduces the revenue, leading to a weakening of the fiscal accounts. In this case, it is the external currency crisis that causes the domestic fiscal crisis. Causality is reversed. My two cents.

* Later models, like Obstfeld's, shown that if the costs of defending the parity are high, for example because in order to preclude the loss of reserves associated with a currency attack, the central bank hikes the rate of interest and pushes the economy into a recession, then there is a chance that self-fulfilling speculation might lead to a crisis.

** The IS curve would be positively sloped and steeper than a 45o line, since depreciation creates excess demand in the goods market. To restore equilibrium, domestic prices would have to increase, though proportionately less, since an increase in domestic prices affects aggregate demand, both via the relative price effect and via higher interest rates.

PS: I had posted before on my course here, were there is a link to Serrano and Summa's critique of the MF model.

Labor productivity comparisons

A simplified graph with the GDP per worker employed in 2013 (i.e. labor productivity) in US dollars converted to Purchasing Power Parity (PPP) is shown below.

Note that it is better than per capita income (which is more of a measure of living standards) as a measure of the economic potential of an economy, and that labor productivity avoids the pitfalls of Total Factor Productivity (TFP). The measure in PPP rather than market exchange rates distorts things a bit (but that is another issue). The graph with all the countries, and the link to the Conference Board data set here.

PS: Picture changes a little with productivity per hours worked, which is also available. For example, Norway would be slightly more productive if we used the labor productivity per hour measure.

Real wage growth in the center and the periphery

From the International Labor Organization's Global Wage Report 2012/13 the rates of growth of real wages around the globe.

Note that Eastern Europe and Central Asia and Asia (China playing a big role) lead the pack. Developed countries basically have stagnant wages and the Middle East is the only region with some real contraction.

Note that these are rates of growth, and that levels are very different in each region. According to the report (p. 10):

"The hourly rate of pay varied from almost US$35 in Denmark, through a little more than US$23 in the United States, to US$13 in Greece, between US$5 and US$6 in Brazil, and less than US$1.50 in the Philippines. Using a different and non-comparable methodology, total hourly compensation costs in manufacturing were estimated at US$1.36 in China for 2008 and at US$1.17 in India for 2007 (United States Department of Labor, Bureau of Labor Statistics, 2011)."

These levels are measured in current exchange rates (not Purchasing Power Parity, PPP), which is in my view good, since it reflects the actual costs that firms do face in international markets.

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.

China and Latin America

Back in the late 1960s and early 1970s the topic in economic development was the so-called Brazilian Miracle. Rates of growth were a staggering 7.5% on average, and in the last phase of the boom were in the two digit level. Forty years later the Brazilian economy is far from that kind of performance. Only the Chinese can boast such a miracle (at least so far). The graph below shows the relative performance of China with respect to both Argentina and Brazil from the 1950s until 2009.

The chart shows that until 1980 Brazil income per capita grew slightly faster than China, while Argentina did basically at the same rate, and both Latin American countries were considerably wealthier than China. By 2007 China's income per capita had surpassed that of Brazil and was approaching fast that of Argentina. Also, it is clear that in the 2000s the comparative performance of Argentina was better than that of Brazil.

These measures are with Geary-Khamis Purchasing Power Parity (PPP) 1990 dollars, which should be taken with some skepticism. From our perspective the important thing is that the data provides a good picture of the relative growth of China, even if the absolute level (whether the average Chinese is better off than the average Brazilian) might be less than precise. The source is from Fundación Norte y Sur, headed by Orlando Ferreres , but the original data (my guess is that with the exception of Argentina for the last few years) is from Angus Maddison.

I'll have more on the problems of PPP measures in a different post.