48. The Fleming- Mundell diagram

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1 48. The leming- Mundell diagram Russell Boyer and Warren Young MUNDELL- LEMING AND MUNDELL S DIAGRAMS The open economy IS- LM- BP curve diagram has been one of the most widely used in macroeconomic textbooks. Although other diagrammatic representations of the open economy have been developed, such as the Salter- Swan- Corden- Meade dependent economy approach, IS- LM- BP has proved its value through its standard form, simplicity and versatility, since it first appeared in Mundell (1963) (where these curves are denoted by - LL-, notation that we will utilize here). Although the diagram is usually cited as a key element in the Mundell- leming model, perhaps a better description of the construct is Mundell s diagrammatic representation of the leming [equational] model (Cooper 1976). Indeed, Mundell (1963) provided a diagram which could be said to represent leming s (1962) equations, similar to the case of IS- LM, where Hicks (1937) provided a diagram representing the equations of Harrod and Meade (see Chapter 47, on IS- LM). Mundell s construct (1963, see igure 48.1 and 48.2) develops this diagrammatic representation for the specific case of perfect capital mobility. The diagram, as drawn in Mundell (1963), has two panels to it (see igure 48.1). The horizontal axis is common to the two panels, and measures real output. The upper panel has the interest rate measured on its vertical axis, and this is the panel that all textbooks which utilize the diagram reproduce in their presentations. The lower panel measures the value of the exchange rate on its vertical axis, but the information provided by it is not clear- cut. One needs the further direction which is supplied by the upper panel before it is possible to know how much to shift the loci in the lower panel. In the case of fixed exchange rates, the lower panel provides no new information at all. It is incumbent on the analyst to shift the curves in such a way that the value of the exchange rate does not change, but we knew that before we began. or the case of flexible exchange rates, the size of the movement in the value of the exchange rate is of interest. 356 M BLAUG PRINT.indd 356 6/7/10 15:14:41

2 The leming- Mundell diagram 357 r L L Q P S Y L L Y 0 Q P Source: Mundell (1963) igure 48.1 Mundell s diagram: monetary policy But this information is available from the upper panel, since precisely the same parameter values are relevant to the shifts there that appertain to the movements in the lower panel. Two of the loci are from Hicks (1937) IS- LM paper:, represents equilibrium in the domestic goods market, and LL, equilibrium in the domestic assets market. The former has a negative slope, because some expenditure is sensitive to interest rate. With a higher value for the interest rate, such expenditures are reduced, and, ceteris paribus, the level of output will be lower. One of the variables held constant is the value of the exchange rate. Defining this as the domestic- currency price of a unit of foreign currency, a rise in the exchange rate will raise the price of foreign goods relative to domestic goods. The resulting lower relative price for domestic goods increases demand for them and output responds accordingly, so that shifts to the right. The LL locus is positively sloped, for a given quantity of money and given values of domestic- currency prices. Everywhere along this locus, the quantity of money demanded is constant, consistent with its supply being given, so that for these points there is equilibrium M BLAUG PRINT.indd 357 6/7/10 15:14:41

3 358 amous figures and diagrams in economics r L L Q P S Y L L Y 0 R Q P Source: Mundell (1963) igure 48.2 Mundell s diagram: fiscal policy in the domestic financial assets market. The reason is that an increase in interest rates causes the quantity of money demanded to be lower, since bonds, an alternative form in which to hold funds, are providing a higher yield. If this is matched by an increase in output, then the resulting higher volume of transactions necessitates an increase in the quantity of money held. In the right proportions, these two influences on money demand exactly offset each other and demand is back at its original (equilibrium) value. An increase in the money supply will cause a rightward shift in LL. The final curve,, was added by Mundell so as to represent equilibrium in the foreign exchange market. In the perfect capital mobility case shown, this locus is horizontal, a situation which has a very simple interpretation: if domestic bonds are perfect substitutes for foreign bonds, then their rates of return must be equated. No matter what the level of domestic output, the yield on domestic bonds must equal the yield available from holding foreign financial instruments. The economy is assumed to start in equilibrium at point Q, where there is market clearing (so that supply and demand are equated) of all the markets analyzed above. M BLAUG PRINT.indd 358 6/7/10 15:14:41

4 The leming- Mundell diagram 359 Earlier Mundell diagrams (1960, 1961a) bear a resemblance to this definitive version, in that they have the interest rate measured along the vertical axis, where the curves in these diagrams represent internal and external balance. These earlier diagrams seem applicable to both the fixedand the flexible- exchange- rate cases, just as is the later 1963 diagram. It was widely recognized that switching between these regimes amounted merely to an inversion, in terms of their endogeneity and exogeneity, of the roles of the money supply and the exchange rate. This point had been noted by Meade (1951, 190) and highlighted by riedman and Schwartz (1963, 89). All the earlier Mundell figures (1960, 1961a) are seemingly like the IS- LM diagram with a curve added to represent the effects of an economy s openness in its trading relationships with the rest of the world, and with the capacity to analyze either fixed or flexible exchange rate regimes within its confines. Such an interpretation, however, is misleading. In fact, the diagrams are quite different. Only the last Mundell contribution (1963) serves all these purposes, and that is why it has been so widely utilized. or example, Mundell (1960) has the terms of trade (rather than income) along the horizontal axis. urthermore the terms of trade by definition include in their calculation the value of the exchange rate. Thus a change in the exchange rate would amount to a movement along these curves, rather than a shift in either of them, which one finds in the later 1963 diagram. In addition, although this earlier diagram is meant to represent both the fixedand the flexible- exchange- rate cases, the argument is that in terms of comparative statics, there is no distinction between the two in the determination of the values of real variables (the point that had been emphasized by Meade for the simplest benchmark case). Indeed, the switch of roles which this early Mundell paper envisages is entirely in the dynamics, since he fully accepts Meade s argument. In order to isolate most clearly the dynamical dissimilarities of the two exchange rate regimes, it is assumed that money prices are flexible. It is the actions of the Central Bank which cause an inversion of the roles, in the dynamic adjustment process, of the terms of trade and the rate of interest (Mundell 1960, 228). The reader may be surprised to find that, although the title of Mundell s 1960 article is The Monetary Dynamics of International Adjustment under ixed and lexible Exchange Rates, the money supply never makes an appearance as a separate variable, nor does the exchange rate play an important role. Moreover, this paper does not conduct any comparative static exercises, but faults Meade (Mundell 1960, 242) for referring to ease of adjustment, without distinguishing dynamic effects from static ones. What one finds is that Mundell s argument is phrased entirely in terms of differential equations, with an analysis of the conditions needed for stability, and for direct (rather than cyclical) approach. M BLAUG PRINT.indd 359 6/7/10 15:14:41

5 360 amous figures and diagrams in economics A similar reading of Mundell (1961a) identifies differences from the later Mundell diagram, so that it is problematic to see it as the first appearance in print of the famous diagrammatic framework. On the horizontal axis is money income. While the reader is encouraged to think in terms of either a classical model (for which real income is given, and price is the adjusting variable) or a Keynesian model (for which real output is changing, and prices are fixed), the IS- LM diagram and the Mundell (1963) diagram are quite specific that only the Keynesian case is being considered. At the end of this paper, Mundell (1961a, 168) considers an economy which is in recession. But the diagram cannot persuasively be used to analyze this case, since the low level of money income could be due to a low price level, rather than to a depressed level of economic activity. In turn, the obvious remedy, expansionary financial policies, may have no effect on employment, because their impacts may be entirely on the price level rather than on production. At this point, it should be noted that Mundell (1961c) and (1962) are derivatives of the Mundell (1961a) framework. In particular, Mundell (2002, 9) readily concedes that the 1962 paper is merely a dynamization of the argument in the earlier article. In addition, Mundell s earlier 1961(a) diagram portrays the low capital mobility case in which the locus is steeper than the LL locus. While this may be considered a small point, it is nonetheless true that Mundell (1969, 263) faults leming for countenancing such a case, since this leads to an ambiguity as to the effect of expansionary fiscal policy on the state of the balance of payments. urthermore it is quite the opposite case from the one that appears in Mundell s l963 paper. Perfect capital mobility, of course, causes the locus to be horizontal, and therefore necessarily it is less steep than the LL locus. It is interesting to note that Mundell (1963, 482) says that his purpose in writing his 1963 paper was to deal with defects that arose in the earlier (1960) paper for the perfect capital mobility case. But, in fact, in the original published version of the 1960 paper, the locus is horizontal in two of the nine figures in the paper. Although Mundell (1960, 237) says at first that the locus is flat if capital is perfectly mobile, he then goes on to assert that the horizontal curves shown in igures IV and V are drawn on the assumption that capital is almost completely mobile. It is curious that the condition is described in these terms, but the wording indicates that Mundell understood the conflict that arises between a Central Bank s setting the values of interest rates, and the pressures on those yields that are due to a high degree of capital mobility. On the other hand, the discussion in Mundell (1961a) focuses on a single policy initiative (monetary policy), and a single exchange rate regime M BLAUG PRINT.indd 360 6/7/10 15:14:41

6 The leming- Mundell diagram 361 (fixed rates). This paper appears very much to be a formalization of the argument which one finds in riedman s (1953) celebrated essay The Case for lexible Exchange Rates, but there is no acknowledgement of any debt to that source, but rather a nod towards Hume s famous mechanism for balance of payments adjustment. Mundell s 1961 paper (1961a) considers a general degree of capital mobility. Had it dealt in that general setting with both fixed and flexible exchange rates, its diagram would have had priority over Mundell (1963). Instead, by focusing exclusively on fixed exchange rates, this portrayal fails to exploit the power which arises from the later 1963 diagram. In any case, by ignoring fiscal policy in this paper, Mundell failed to discover the key crowding- out result which is leming s (1962, 372, 378) celebrated achievement. Mundell s 1963 Diagram and leming s 1962 Equations Mundell s (1963) paper deals with the perfect capital mobility case and does so without equations written out explicitly. Mundell s half of the Mundell- leming model for the small- country case is not presented in a mathematical or equational form that distinguishes between markets for stocks and markets for flows. Mundell (1963, 479) says that monetary policy is ineffective under fixed exchange rates with perfect capital mobility, and this result is shown clearly in igure 1 of the 1963 paper (see igure 48.1). The question is whether ineffectiveness occurs if capital mobility is less than perfect. The answer is that in the time frame which Mundell (1963) considers, and within the confines of leming s equations, monetary policy has no impact on real output, no matter what the degree of capital mobility (see Mundell 1961a, 159). In contrast, with a proper specification of the asset markets, this result does indeed depend on the degree of substitutability between domestic and foreign assets (Marston 1985, 872). Mundell (1963) says that fiscal policy is ineffective under flexible exchange rates with perfect capital mobility. The second figure of that paper demonstrates this result (see igure 48.2). The same question arises in this case. Does this result hinge on the degree of capital mobility? leming (1962) notes in his text, and in his mathematical appendix, that in his equational framework, this result holds only with perfect capital mobility. In contrast, with a proper specification of the asset markets, this result does not depend on the degree of substitutability between domestic and foreign assets. On the contrary, it depends entirely on the M BLAUG PRINT.indd 361 6/7/10 15:14:41

7 362 amous figures and diagrams in economics assumption, which both leming (1962) and Mundell (1963) adopt, that asset market conditions are not directly dependent on the value of the exchange rate. inally, Mundell (1963) says numerous times that with perfect capital mobility, the level of real output and the nominal quantity of money are proportional in equilibrium positions. So under flexible exchange rates (for which the Central Bank can set and maintain any quantity of money which it chooses), an expansionary monetary policy will cause output to increase by the same percentage amount as the money supply is augmented. This result is a valid deduction only of the leming model (1962, 374, 379). It is not a valid deduction of the (verbal) model which Mundell (1963) presents. No attempt is made to demonstrate this result in Mundell s (1963) igure 1 (see igure 48.1). This is not surprising, since it is not a valid deduction of his model. Indeed, the diagram as drawn is not consistent with this result, since the LL loci in it do not converge as one proceeds leftward along them. Limitations of Mundell s 1963 Diagram: theory and pedagogy Most recent presentations of international economic theory have Mundell s 1963 diagram playing only a minor role. The reason is that in a twodimensional diagram, for which there are only two separate axes available, the user does not want to obviate the function of one of them. But this is precisely what this diagram does. We know from the start that the value of the interest rate cannot change (unless it is changed exogenously, presumably due to changing financial- market conditions in the rest of the world). To measure the interest rate on the vertical axis amounts to wasting that axis. A far more informative presentation of these results can be made with the money supply or the exchange rate measured along one of the axes, replacing the unchanging value of the interest rate. Indeed, Mundell s 1963 diagram is sufficiently complex that some authors and textbooks feel a step- by- step derivation is justified. One finds such derivations in articles by Michaely (1968) and Wrightsman (1970), and in textbooks such as Branson (1972), or Caves, rankel and Jones (2002). In contrast, many textbooks feel that the mechanisms highlighted by leming (1962) and Mundell (1963) are no longer of interest (see, for example, Krugman and Obstfeld 2006). More common today are diagrams which capture the essence of the Dornbusch (1976) view rather than the Mundell- leming model (see, for example, Obstfeld and Rogoff 1996). As an example of the inconsistencies which one finds in identifying M BLAUG PRINT.indd 362 6/7/10 15:14:41

8 The leming- Mundell diagram 363 models in the open macroeconomy, Obstfeld and Rogoff (1996, 609) declare the mechanism which Dornbusch championed as being the essence of what they call the Mundell- leming- Dornbusch model. They use the expression at least seven times in their graduate textbook. In contrast, the identical mechanism is central to the key framework employed in the undergraduate textbook by Krugman and Obstfeld (2006). In that book, this expression is not to be found. More precisely, in that textbook, Mundell s name is not attached to this macromodel, and leming s name does not make any appearance whatsoever. References Branson, W Macroeconomic Theory and Policy. New York: Harper and Row. Caves, R., renkel, J. and Jones, R World Trade and Payments 9th ed., Boston, MA: Addison- Wesley. Cooper, R Monetary Theory and Policy in an Open Economy. Scandinavian Journal of Economics 78: Dornbusch, R Expectations and Exchange Rate Dynamics. Journal of Political Economy 84 December: leming, J Domestic inancial Policies under ixed and under loating Exchange Rates. IM Staff Papers 9: riedman, M The Case for lexible Exchange Rates in Essays in Positive Economics, Chicago, IL: University of Chicago Press. riedman, M. and Schwartz, A A Monetary History of the United States Princeton, NJ: Princeton University Press. Hicks, John Mr. Keynes and the Classics : A Suggested Interpretation. Econometrica 5: Krugman, P. and Obstfeld, M International Economics: Theory and Policy 7th ed. Boston, MA: Addison- Wesley. Marston, R Stabilization policies in open economies, in R. Jones and P. Kenen (eds), Handbook of International Economics, volume 2, Amsterdam: North- Holland, chapter 17, Meade, J The Balance of Payments. Oxford: Oxford University Press. Michaely, M The Impact of Alternative Government Policies under Varying Exchange Systems: Comment. Quarterly Journal of Economics 82: Mundell, R The Monetary Dynamics of International Adjustment under ixed and lexible Exchange Rates. Quarterly Journal of Economics 74: Mundell, R. 1961a. The International Disequilibrium System. Kyklos 14: Mundell, R. 1961b, A Theory of Optimum Currency Areas, American Economic Review 51: Mundell, R. 1961c. lexible Exchange Rates and Employment Policy. Canadian Journal of Economics and Political Science 27: M BLAUG PRINT.indd 363 6/7/10 15:14:41

9 364 amous figures and diagrams in economics Mundell, R The Appropriate Use of Monetary and iscal Policy for Internal and External Stability. IM Staff Papers 9: Mundell, R Capital Mobility and Stabilization Policy under ixed and lexible Exchange Rates. Canadian Journal of Economics and Political Science 29: Mundell, R Contribution to Summary of Discussion, in R. Mundell and A. Swoboda eds, Monetary Problems of the International Economy, Chicago, IL: University of Chicago Press, Mundell, R Notes on the Development of the International Macroeconomic Model, in A. Arnon and W. Young (eds) The Open Economy Macromodel: Past, Present and uture. London and New York: Kluwer- Springer. Obstfeld, M. and Rogoff, K oundations of International Macroeconomics. Cambridge, MA: MIT Press. Wrightsman, D IS, LM, and External Equilibrium: A Graphical Analysis. American Economic Review 60.1: M BLAUG PRINT.indd 364 6/7/10 15:14:41

IS-LM-BP: An Inquest. Warren Young and William Darity Jr.

IS-LM-BP: An Inquest. Warren Young and William Darity Jr. IS-LM-BP: An Inquest Warren Young and William Darity Jr. Open economy macroeconomics is not a new field of theoretical inquiry. Its origins can be traced back to mercantilist and classical notions of the