This appendix derives the effects of various shocks on w, r, π, inflation tax payments πm, the trade account T, and the current account CA. The effects on w and r are obtained from equations (7) and (11).
where △ and Ώ are defined by
where Φ is defined by
where Γ is defined by
Adams, Charles and Daniel Gros, “The Consequences of Real Exchange Rate Rules for Inflation: Some Illustrative Examples”, IMF Staff Papers, 33 (September 1986), pp. 439–476.
Dornbusch, Rudiger, “PPP Exchange-Rate Rules and Macroeconomic Stability”, Journal of Political Economy, 90 (February 1982), pp. 158–165.
Lizondo, Jose Saul, “Real Exchange Rate Targets, Nominal Exchange Rate Policies, and Inflation”, Revista de Analisis Economico, 6, (June 1991), pp. 5–21.
Montiel, Peter J. and Jonathan D. Ostry, “Macroeconomic Implications of Real Exchange Rate Targeting in Developing Gountries”, IMF Staff Papers, 38, (December 1991), pp. 872–900.
Montiel, Peter J., and Jonathan D. Ostry, “Real exchange Rate Targeting Under Capital Controls: Can Money Provide a Nominal Anchor?”, IMF Staff Papers, 39, (March 1992), pp. 58–78.
I would like to thank, without implication, Jose Fajgenbaum, Peter Montiel, Jonathan Ostry, Brian Stuart, and Carlos Vegh for useful comments on a previous version of this paper.
Previous papers have discussed related issues within different theoretical frameworks. Dornbusch (1982) examines the effect of nominal exchange rate rules on the trade-off between output stability and price level stability in a model defined in terms of deviations from trends. Adams and Gros (1986) assume an exogenously given long run real exchange rate and discuss the inflationary consequences of purchasing power parity rules for the nominal exchange rate.
The real exchange rate is defined as the relative price of traded to nontraded goods, so that an increase in the real exchange rate indicates a real depreciation.
Lizondo (1991) allows for a demand for money with elasticity above unity over a certain range and examines the implications of this assumption. Keeping with the usual practice in papers on this subject, however, the discussion here will focus on the inelastic section of the demand for money.
Since the public sector is subject to an intertemporal budget constraint, these policies may need to be accompanied by a future fiscal adjustment that ensures solvency, as explained below.
This formulation of the production structure abstracts from any influence that real exchange rate targeting may have on employment and thus on aggregate supply. Therefore, the model focuses primarily on the effects that operate through the demand side of the economy.
Importables and exportables are aggregated into traded goods by assuming free trade and constant terms of trade.
For simplicity, real factor income y will be treated as constant throughout the paper. If the real exchange rate is kept fixed, y is effectively constant so that no additional assumption is needed. However, if the real exchange rate changes, we need to assume that (yt/ct)=(yn/cn) at the initial equilibrium.
In the context of an optimizing model this would be consistent with a Cobb-Douglas utility function.
Assuming non-indexed bonds would not affect the conclusions.
For a constant real exchange rate, the real interest rate on foreign bonds is equal to the foreign currency interest rate on foreign bonds minus the rate of change of the foreign currency price of traded goods. Assuming that the price of traded goods is constant in terms of foreign currency, r* can be interpreted as both the real interest rate on foreign bonds and the foreign currency interest rate on foreign bonds.
Thus the demand for f depends positively on w, r*, and π, and negatively on r and y.
Thus, h5<0 assumes C3>r*, h6>0 assumes r>r*, and h7<0 holds under the assumption that the elasticity of the demand for money is below unity.
If the central bank lends to the private sector (and charges a real interest rate r) the analysis below is unaltered, with b denoting public sector domestic bonds net of central bank credit to the private sector.
The “operational” deficit includes non-interest payments and receipts, and the real interest component of interest payments and receipts. Thus, it is equal to (eθ•1gn + eθgt • t) + rb + r*b*.
Clearly, the adjustment in public sector expenditure on traded goods that ensures solvency could also take place in the present. However, we prefer to set the problem in terms of a future adjustment so as to separate clearly the effect of a current policy or exogenous shock from the effect of the corrective measures that will be needed to ensure solvency.
In an optimizing intertemporal model, the policy composition and the timing of the fiscal adjustment would have implications not only for the long run rate of inflation but also for private sector current behavior.
The assumption that b is a policy variable implies that the public sector decides how much domestic debt to place in the market. Since at each point in time total net liabilities of the public sector are given, and the stock of money is demand determined by the private sector, the stock of public sector net foreign debt is an endogenous variable.
This sequence for the presentation also applies to the discussion of the other shocks below.
Choosing a more depreciated real exchange rate target requires on impact a higher (S/P) and a lower w, which according to (5) can only be obtained by an upward jump in the price level and a proportionally higher upward jump in the exchange rate.
The tendency for wealth to increase from its new (lower) level, before any change in the rate of inflation, can be interpreted in terms of equation (8). It is necessary to look at the effects of changes in r and w on
Unless there is a change in the foreign interest rate, any given shock has the same effect on the trade balance and on the current account.
In the steady state private capital flows are zero (f is constant) and, therefore, policies can have only an impact effect on those flows.
This can be looked also in terms of the wealth constraint (5). The level of wealth falls, but the demand for money also falls and the stock of domestic bonds is constant. So the effect on foreign asset holdings is undetermined.
In terms of the wealth constraint, the level of wealth increases, but the demand for money also increases and the stock of domestic bonds is constant. So the effect on foreign asset holdings is undetermined.
This counter-intuitive result can be explained also in terms of a decline in aggregate spending (private sector expenditure declines by more than public sector expenditure increases). Private sector expenditure on nontraded goods must decline by the same amount that public sector expenditure on nontraded goods increases so as to keep equilibrium in this market at an unchanged real exchange rate. However, since the private sector is facing unchanged relative prices, private demand for both types of goods move together. Thus, lower private expenditure on nontraded goods is necessarily accompanied by lower private expenditure on traded goods, thereby resulting in lower aggregate spending for the economy as a whole.
In terms of the wealth constraint, the level of wealth falls but the demand for money also falls and the stock of domestic bonds is constant. So the effect on foreign asset holdings is undetermined.
A sufficient condition for this to hold is r*<(b3b/b1). If the foreign interest rate were “too high*#x201D;, a private capital inflow (which would reduce public sector net foreign debt by the same amount) could conceivable reduce public sector foreign interest payments by an amount sufficiently large to reduce the operational deficit.
In terms of the wealth constraint, wealth increases while the demand for money falls and the stock of domestic bonds is constant. Thus, holdings of foreign assets necessarily increase.
In terms of the wealth constraint, the level of wealth increases and the demand for money falls, but the stock of domestic bonds also increases. So the effect on foreign asset holdings is undetermined.