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 Δ and Ω are defined by
where Φ is defined by
The effects on inflation tax payments πm are obtained from the set of equations (A2):
where Γ is defined by
Adams, Charles, and Daniel Gros, “The Consequences of Real Exchange Rate Rules for Inflation: Some Illustrative Examples,” Staff Papers, International Monetary Fund, Vol. 33 (1986), pp. 439–76.
Dornbusch, Rudiger, “PPP Exchange Rate Rules and Macroeconomia Stability,” Journal of Political Economy, Vol. 90 (February 1982), pp. 158–65.
Lizondo, Jose Saul, “Real Exchange Rate Targets, Nominal Exchange Rate Polides, and Inflation,” Revista de Analisis Economico, Vol. 6 (June 1991), pp. 5–21.
Montiel, Peter J., and Jonathan D. Ostry, “Macroeconomic Implications of Real Exchange Rate Targeting in Developing Countries,” Staff Papers, International Monetary Fund, Vol. 38 (1991), pp. 872–900.
Montiel, Peter J., and Jonathan D. Ostry, “Real Exchange Rate Targeting Under Capita! Controls; Can Money Provide a Nominal Anchor?” Staff Papers, International Monetary Fund, Vol. 39 (1992), pp. 58–78.
J. Saul Lizondo is a Deputy Division Chief in the Western Hemisphere Department and holds a Ph.D. from the University of Chicago. The author would like to thank José Fajgenbaum, Peter Montiel, Jonathan Ostry, Brian Stuart, Christopher Towe, and Carlos Végh for useful comments on a previous version of this paper.
Previous papers have discussed related issues using 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 by 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 certain range of money demand with elasticity above unity and examines the implications of this assumption. Keeping with the usual practice, however, the discussion here focuses on the inelastic portion 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.
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 is treated as a 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, one needs to assume (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 nonindexed 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, h5 < 0 means that the higher the level of wealth, the tower is the speed at which consumers would accumulate additional wealth; for this to hold, an increase in wealth must increase consumption by more than the income obtained by investing the extra wealth in foreign assets, that C3, > r*. Second, h6>0 means that an increase in the stock of domestic bonds increases the speed at which the private sector accumulates wealth; for this to hold, domestic bonds must pay a higher interest rate than the alternative interest-bearing asset (foreign bonds), that is, r > r*. Third, h7 < 0 necessarily 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 noninterest 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*.
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 current private sector 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 since the stock of money is determined by private sector demand, the stock of public sector net foreign debt is an endogenous variable.
Choosing a more depreciated real exchange rate target requires a higher (S/P) and a lower w on impact, which according to equation (5) can only be obtained by an upward jump in the price level and a proportionally higher 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 ˙ w, for a constant π. Notice first that private sector consumption declines owing to the increase in r and the fall of w on impact, and that the demand for money declines owing to the increase in r. Thus (for a given rate of inflation), wealth tends to increase because of (i) a decline in consumption (the term in square brackets increases), (ii) the higher interest receipts on domestic debt owing to the higher interest rate (the term [r − r*] b increases), and (iii) the gain in income that the private sector obtains by reducing its money holdings and allocating those resources to foreign assets (the term (r* + π)L(r + π; y) declines). Wealth tends to decline because of the loss of foreign interest receipts that results from the decline in wealth on impact (the term r*w declines). The net effect on ˙ w of all these changes is positive, so inflation has to increase to compensate for this (to keep ˙w = 0), as shown in the Appendix. This type of reasoning can also be applied when discussing the other shocks in order to see whether wealth tends to increase or decrease after impact. However, the explanation for the other shocks is not included in this paper as it would be rather cumbersome and tedious.
Unless there is a change in the foreign interest rate, any given shock has the same effect on the trade balance and the current account.
In the steady state, private capital flows are zero (f is constant). Therefore, policies can have only an instantaneous once-and-for-all impact on those flows.
This can be looked at in terms of the wealth constraint (5). The leve! 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 counterintuitive result can also be explained 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 is “too high,” a private capital inflow (which would reduce public sector net foreign debt by the same amount) could conceivably 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 fails 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.
While the various results mentioned above would also hold under perfect asset substitutability, the conclusions regarding this policy are specific to the model in this paper, in which domestic and foreign assets are imperfect substitutes.