APPENDIX: Stability Conditions
and where η=1-c1+c2P3-rFL1 is the marginal propensity to save. The signs of n1 and n2 are ambiguous on the basis of assumptions in the text.
The Routh-Hurwicz necessary and sufficient conditions for stability in the neighborhood of
On the basis of assumptions made in the text, it can be shown that
It can also be shown that, if n1 is negative, the expression (n2e1 -n1e2) must also be negative. Applying these results, together with the partial derivatives derived previously, to the Routh-Hurwicz conditions above, it follows that n1<0 and n2 > 0 are jointly sufficient to guarantee the local stability of the system (45). In substituting for ϕ5 in the expressions for n1 and n2, one finds that these signs will hold if
where β = 1 - θc1 + θc2 P3 > 0 is the inverse of the Keynesian multiplier for this model. The first expression stipulates that wealth effects on consumption are sufficiently strong that an increase in real wealth reduces saving. The second requires substitution effects on consumption to exceed a threshold value to ensure that a reduction in the price of nontraded goods (an increase in eR) will increase private saving. With the assumption of constant expenditure shares and initial eR = 1, this substitution effect is given by (1 - θ)θc, or (1 - θ)cN. This increase in consumption of nontraded goods increases real saving by ηβ-1(1-θ)cN. Inequality (46b) requires that this positive effect on saving exceed negative effects because of an increase in real wealth given by θnPT and a decrease in the domestic real interest rate equal to P1.
Barro, Robert J., and Herschel I. Grossman, “A General Disequilibrium Model of Income and Employment,” American Economic Review (Nashville, Tennessee), Vol. 61 (March 1971), pp. 82-93.
Chopra, Ajai, “The Speed of Adjustment of the Inflation Rate in Developing Countries: A Study of Inertia,” Staff Papers, International Monetary Fund (Washington), Vol. 32 (December 1985), pp. 693-733.
Cuddington, John T., Per-Olov Johansson, and Karl-Gustaf Löfgren, Disequilibrium Macroeconomics in Open Economies (Oxford, England: Basil Blackwell, 1984).
Fleming, J. Marcus, “Domestic Financial Policies Under Fixed and Floating Exchange Rates,” Staff Papers, International Monetary Fund (Washington), Vol. 9 (November 1962), pp. 369-79.
Frenkel, Jacob A., Thorvaldur Gylfason, and John F. Helliwell, “A Synthesis of Monetary and Keynesian Approaches to Short-Run Balance-of-Payments Theory,” Economic Journal (London), Vol. 90 (September 1980), pp. 582-92.
Gordon, Robert J., “Inflation in Recession and Recovery,” Brookings Papers on Economic Activity: 1 (1971), The Brookings Institution (Washington), pp. 105-66.
Johnson, Harry G., “The Monetary Approach to Balance-of-Payments Theory,” in The Monetary Approach to the Balance of Payments, ed. by Jacob A. Frenkel and Harry G. Johnson (London: Allen & Unwin, 1976), pp. 147-67.
Montiel, Peter J., “A Monetary Analysis of a Small Open Economy with a Keynesian Structure,” Staff Papers, International Monetary Fund (Washington), Vol. 32 (June 1985), pp. 179-210.
Mundell, Robert A., “The Optimum Balance of Payments Deficit,” in Stabilization Policies in Interdependent Economies, ed. by Emil Claassen and Pascal Salin (Amsterdam: North-Holland; New York: Elsevier, 1972), pp. 69-90.
Mussa, Michael, “Tariffs and the Balance of Payments: A Monetary Approach,” in The Monetary Approach to the Balance of Payments, ed. by Jacob A. Frenkel and Harry G. Johnson (London: Allen & Unwin, 1976), pp. 187-221.
Nordhaus, William D., “Recent Developments in Price Dynamics,” in The Econometrics of Price Determination Conference, ed. by Otto Eckstein (Washington: Board of Governors of the Federal Reserve System, 1972).
Officer, Lawrence H., “The Purchasing-Power-Parity Theory of Exchange Rates: A Review Article,” Staff Papers, International Monetary Fund (Washington), Vol. 23 (March 1976), pp. 1-60.
Parkin, Michael, “The Causes of Inflation: Recent Contributions and Current Controversies,” in Current Economic Problems, ed. by Michael Parkin and A.R. Nobay (New York: Cambridge University Press, 1975), pp. 243-91.
Rodriguez, Carlos A., “Money and Wealth in an Open Economy Income-Expenditure Model,” in The Monetary Approach to the Balance of Payments, ed. by Jacob A. Frenkel and Harry G. Johnson (London: Allen & Unwin, 1976), pp. 222-36.
Whitman, Marina V. N., “Global Monetarism and the Monetary Approach to the Balance of Payments,” Brookings Papers on Economic Activity: 3 (1975), The Brookings Institution (Washington), pp. 491-556.
Mr. Montiel, an economist in the Developing Country Studies Division of the Research Department, holds degrees from Yale University and the Massachusetts Institute of Technology.
As will be seen below, the assumption that quantities are demand determined when markets fail to clear also characterizes the market for nontraded goods. A more reasonable assumption in both cases would be that, in the presence of disequilibrium, quantities are determined by the short side of the market. This assumption will be inconsistent with the approach adopted here when excess demand exists in either the labor market or the market for nontraded goods. The recognition of such cases has given rise to an extensive literature on closed-economy general disequilibrium models (for example, Barro and Grossman (1976) and Malinvaud (1977)). Research on disequilibrium models for open economies, however, is in its infancy. The state of the art can be examined in Cuddington, Johansson, and Löfgren (1984). The assumption of demand determination made here is traditional in conventional Keynesian models. It simplifies the analysis by assuming essentially that behavior characteristic of the “Keynesian” region of wage-price space carries over into the “classical” and “repressed inflation” regions as well (see Malinvaud (1977)), thus obviating the need for separate analyses of those cases. Of course, to the extent that the deviations from long-run equilibrium that are of interest here involve short-run Keynesian unemployment, the assumption that quantities are demand determined will be appropriate. In any case, since the model’s long-run equilibrium is Walrasian (as shown in Section II), its long-run properties are not affected by this assumption.
Allowing for a variable markup has no effect on the qualitative conclusions in Montiel (1985). As is intuitively clear, adjustments in the markup increase the slope of the economy’s short-run Phillips curve in
The partial derivatives rely on the assumption that the marginal propensity to save is positive. This assumption ensures that an increase in the supply of nontraded goods reduces excess demand in that market.
It can easily be shown that, if the credit expansion finances an increase in gT, the balance of payments deterioration will occur in the trade balance; if the expansion is directed toward the private sector, the capital account will deteriorate.
The Appendix derives a set of conditions that are sufficient to guarantee local stability. These conditions involve strong wealth and substitution effects on consumption.
Note that, since a positive effect of inflation on consumption was already operative in the model through the real interest rate, no previous results are qualitatively affected by this modification.