ACTIVE EXCHANGE rate management has become increasingly prevalent among developing countries in recent years. With a view toward preserving competitiveness, these countries have frequently adopted rules under which the nominal exchange rate is depreciated continuously to offset differences between domestic and foreign inflation rates. Because such rules, which effectively target the real exchange rate, establish a feedback from domestic inflation to the nominal exchange rate, countries adopting them sacrifice the role of the exchange rate as the nominal anchor for the price level. Since price level stability remains an important macroeconomic goal in such countries, the question naturally arises as to whether the role of nominal anchor can instead be provided by a policy-controlled financial aggregate, such as the money supply.
In an earlier paper (Montiel and Ostry (1991)), we investigated the effects of real shocks on price level stability under real exchange rate targeting.1 We found that the stock of domestic credit could not replace the exchange rate in the role of nominal anchor under such a regime. While the money supply may represent a more obvious candidate for this role, our previous paper incorporated the assumption of perfect capital mobility, which prevented the authorities from treating the money supply as a policy variable. To examine the implications of money supply targeting under a real exchange rate rule, we now consider the case in which capital controls are imposed, thereby making sterilization feasible, and ask whether fixing the money supply can stabilize the price level in response to shocks. The analysis leads naturally to a consideration of the case in which the effectiveness of capital controls is less than perfect, and we examine the implications of money supply targeting in this case as well. We find that using money as a nominal anchor is problematic in both cases.
The paper is organized as follows: the next section presents an abbreviated description of our previous model, modified for the presence of effective capital controls, and demonstrates the inflationary consequences of a real—specifically, a terms of trade—shock in the absence of money supply targeting. The money supply is then fixed through a policy of active sterilization in Section II, and the macroeconomic implications of the terms of trade shock are reexamined under these circumstances. Section III considers how the analysis is affected when capital controls are imperfect. Our findings regarding the role of money as a nominal anchor are summarized in a brief concluding section.
I. The Basic Model Under Capital Controls and No Leakages
We consider a small open economy in which competitive firms combine labor (available in fixed supply) and a sector-specific factor to produce home goods and exportables, using a standard concave technology. All prices are flexible, ensuring that full employment is continuously maintained.
The income generated from production of the two goods is received by consumers who use it to buy home goods and importables. Consumers have Cobb-Douglas utility, which implies that they allocate a constant fraction of their total expenditures to each of the two goods in every time period. The real value of aggregate consumption expenditures is assumed to depend upon the real value of factor income net of taxes, the real interest rate, and real financial wealth. Real factor income, which we denote by y, is the value of output of exportables and home goods, deflated by the consumer price index. As shown in Khan and Montiel (1987), under the assumption that the external trade surplus is zero in the initial steady-state equilibrium, real factor income depends only on the terms of trade (the price of exports relative to imports), denoted by ρ, with y’(ρ) > 0.
Real household financial wealth consists of real money balances (m = M/P), plus the real value of foreign securities (vFp/P), less the real value of loans extended to households by the banking system (dp = Dp/P), where P is the domestic price level. To permit it to control the domestic money supply, the central bank in this economy refrains from engaging in foreign exchange transactions for financial purposes. We assume that, as a result of this policy, a parallel foreign exchange market emerges in which private individuals trade foreign exchange at the market-determined exchange rate, v. The central bank continues to operate an official exchange market, however, for all commercial transactions. Since trade in the official market is limited to commercial transactions, interest earnings on foreign securities are converted into domestic currency at the parallel market exchange rate.
To simplify the analysis, it is assumed that the foreign inflation rate is equal to the nominal interest rate on foreign securities and, therefore, that the foreign real interest rate is zero. This implies that inflows into the parallel market (in the form of interest earnings on the stock of foreign securities) are just sufficient to offset the rate at which the real value of the stock of foreign securities is eroded by foreign inflation, and therefore, that the real stock of foreign securities (in terms of traded goods), denoted fp, is constant when capital controls are perfect.
For the composition of the household portfolio, we assume that uncovered interest rate parity holds continuously:
where i is the domestic cost of borrowing, and i* is the return on foreign securities. The demand for money depends on the nominal interest rate and on real income:
where subscripts denote partial derivatives with respect to the corresponding arguments. For the purposes of this section, we shall assume that monetary policy takes the form of holding the real stock of credit to the private sector (dp) constant.
Under real exchange rate targeting, the authorities continuously adjust the commercial exchange rate, denoted by s, in order to keep the real exchange rate (the relative price of importables to home goods) constant at a base period level. Therefore, the rate of devaluation of the commercial exchange rate is adjusted according to the difference between the rate of inflation of home goods and the foreign currency rate of inflation of importables, which we denote as π*.2 Because the domestic price index is a weighted average of the domestic price of importables and home goods, under this rule the domestic rate of inflation, denoted by π, will be equal to the rate of inflation of home goods. Thus, the real exchange rate targeting rule can be expressed as
We assume that the real exchange rate rule is implemented from an initial steady state characterized by a fixed nominal exchange rate (that is, ŝ = 0) with no capital restrictions. The resulting equilibrium real exchange rate (see Khan and Montiel (1987)) represents the base period value for the application of the real exchange rate rule. From equation (3), therefore, domestic inflation will be equal to ŝ* in the initial equilibrium. The description of the financial sector is completed by using the Fisher equations, r = i – ŝ and r* = i* – ŝ*, together with equations (1) and (3), to write the following expression for the domestic real interest rate:
where b = v/s represents (1 plus) the premium between the financial and commercial exchange rates,
An equilibrium for this economy requires, first, that the supply of nontraded goods, denoted yn, equal the sum of the demand for such goods from the private and public sectors, cn + gn (internal balance). Denoting by θ the share of total private expenditure devoted to home goods, the internal balance condition may be written as
where t represents the real value of taxes and where units are chosen so that the value of the real exchange rate is unity in the base period.3 In equation (5), ρ and fp are exogenous variables, while gn, t, and dpare policy determined. The real money supply, m, however, is an endogenous variable. Its behavior over time can be derived from the household budget constraint.4 This yields the following expression for the accumulation of real money balances:
Using equation (3) and the definition of
Solving this expression for the domestic inflation rate, π, yields
Finally, equation (9) can be substituted into equation (7), permitting us to express the model as a system of two differential equations in b and m. It can readily be shown, however, that the equilibrium defined by
Imposing the conditions
The combinations of b and π that satisfy equations (11) and (12) are portrayed in Figure 1. The schedule labeled NN is the locus of combinations of b and π that clear the market for home goods (equation (11)). The slope of the NN schedule is
where a subscripted number denotes a partial derivative, so that L1 is the partial derivative of money demand with respect to its first argument (namely, the interest rate), which is negative. The intuition underlying equation (13) is that a rise in b raises the real value of the private sector’s financial wealth and creates an incipient excess demand for home goods. To restore market clearing, a rise in the inflation rate, which reduces real wealth by lowering real money balances, is required.
The schedule labeled SS is the locus of combinations of b and π that maintain the rate of growth of real money balances equal to zero (equation (12)). Its slope is given by
Figure 1.Macroeconomic Equilibrium Under Capital Controls
Note: ρ0 is the initial terms of trade defined as the price of exports relative to imports.
Consider now the effect of an improvement in the terms of trade—that is, a rise in ρ. An improvement in the terms of trade raises the value of the marginal product of labor in the exportables sector and causes employment to shift from home goods production to export production.7 In addition, the rise in ρ raises real income and, hence, the demand for home goods. For both reasons, an incipient excess demand for non-tradables develops, the elimination of which requires a reduction in real wealth and, hence, in private spending on all goods, including non-tradables. This is brought about by the adverse real balance effect of a rise in inflation. Thus, the NN schedule in Figure 1 shifts vertically upwards to N’N’, with the magnitude of the displacement given by
Turning to the SS schedule, a rise in ρ raises real factor income, y, which by itself would tend to raise the rate of money accumulation. However, it also raises real consumption spending, both directly through the marginal propensity to consume, and indirectly by increasing real wealth (through a positive real balance effect). In addition, the positive effect of an improvement in the terms of trade on money demand increases the inflation tax, πL, thereby reducing
As can be seen, the shifts in both curves contribute to a rise in the inflation rate, although they have opposite effects on the parallel market premium. Solving for the effects of the terms of trade shock on inflation gives
The denominator of this expression is positive under our maintained assumption that
II. Can a Money Supply Rule Stabilize Prices?
Suppose now that the authorities, anticipating the inflationary effects of a shock under real exchange rate targeting, attempt to stabilize the inflation rate (that is, set π = π*) by pursuing a monetary target. Under this regime, the nominal money supply continues to grow at the world rate of inflation, π*. This rule therefore implies
Of course, holding the nominal money supply on this path requires abandoning the assumption that the real stock of credit, dp, is constant, since credit policy must now be geared to sterilizing the effects of the balance of payments on the money supply. Returning to the system consisting of equations (5), (6), and (9), the new monetary policy regime implies replacing
The new system consists of equations (5), (19), (9), and (18). To solve this system, it is convenient to define a variable, w = bfp – dp, which represents households’ nonmonetary financial wealth. Since
Next, the equilibrium condition for the nontraded goods market (equation (5)) can be solved for
It can be readily shown that the roots of this system are positive. Since m and w are both jumping variables, this implies that the unique perfect foresight path is given by the solution of (22) and (23), with
The immediate implication of this result is that the money supply targeting rule considered in this section stabilizes the domestic inflation rate at the world rate, π*, even in the face of a terms of trade shock. This follows from equation (22), with
where Δ = -mc3(π* - w/L1)/c2 < 0 is the determinant of the system (equations (22) and (23)). Thus, the favorable terms of trade shock results in an increase in the real demand for money, the accommodation of which requires a once-for-all expansion of credit to prevent a discrete fall in the domestic price level. At the same time, the free exchange rate must undergo a discrete appreciation. This follows from the result in equation (24b) that real wealth falls. Since m + w = m + bfp – dp, and since credit-financed changes in m leave m - dp unchanged, the exogeneity of fp under perfect capital controls implies that m + w can fall only through a reduction in the premium, b.
In addition to the finding that monetary targeting can indeed stabilize the domestic inflation rate, the second key result of this section is that this initial change in the premium is not the end of the story. In fact, the premium will continue to change over time, even while m and w remain at their stationary values. To see this, notice from equation (20) that the increase in p and decline in m + w will tend to move the rate of increase in the premium—which effectively represents movements in the domestic real interest rate—in opposite directions. The favorable terms of trade shock tends to induce an excess demand for nontraded goods, requiring an increase in the domestic real interest rate (that is, in
Thus, the exchange rate (or equivalently, the premium) in the parallel market undergoes a discrete initial drop and then appreciates continuously at a constant rate. The permanent rate of appreciation represents a reduction in the domestic real interest rate required to maintain equilibrium in the market for nontraded goods in the face of the reduction in the demand for such goods caused by the decline in real household wealth.
Under real exchange rate targeting, then, the only way that a permanent wedge between the domestic and foreign real interest rates can emerge is with an ever-widening gap between the commercial and financial exchange rates (that is,
III. The Model with Leakages
The results of the previous section suggest that our model should explicitly incorporate the effects of incentives to engage in cross transactions that arise when a substantial gap begins to emerge between the financial and commercial exchange rates. In this section, we incorporate such leakages between markets in the simplest way possible. We make the conventional assumption that when the financial exchange rate, v, is depreciated (appreciated) relative to the commercial rate, s—that is, b > 1 (b <1)—arbitrage flows are created between these two markets.12 Thus, inflows into the parallel market will be an increasing function, k(.), of the premium, b – 1 :
where the second term in (26) represents interest earnings on holdings of foreign securities (which we have already assumed to be exchanged through the parallel market). Using the definition of the real value of foreign securities, fp, we can rewrite equation (26) as13
Thus, given the properties of the k(.) function, it is clear that when b = 1, so that there is no premium, inflows into the parallel market in the form of interest earnings are just sufficient to offset the erosion in the real value of foreign securities due to foreign inflation, as in the last section. When b > 1, however, households are able to direct foreign exchange into the free market, implying that
Consider now the regime of Section I in which the authorities keep the real stock of credit, dp, constant. The internal balance condition continues to be given by equation (5), which can be solved for
A rise in b, fp, or m raises real private holdings of financial wealth and creates an excess demand for home goods, the elimination of which requires a rise in the domestic real interest rate and, hence, in
Substituting equation (28) and the definition of
A rise in b or fp raises the domestic interest rate, thereby lowering money demand and creating excess supply in the money market. Equally, a rise in m creates an excess supply of real balances. In all three cases, therefore, a fall in the inflation rate, π, is required to restore money market equilibrium. Substituting equations (26), (28), and (29) into the private sector’s budget constraint and setting
where R = (m – dp) represents the central bank’s holdings of foreign exchange reserves, which are assumed to be positive.14 Under the assumption that
Rather than solve for the dynamics of the system, which are not of immediate interest, we proceed directly to analyze the effects of a terms of trade shock on the long-run equilibrium, focusing particularly as before on the effects on the steady-state rate of inflation.
Since in the steady state, the real stock of foreign securities must be constant (that is,
The analysis of this section thus indicates, first, that the incorporation of leakages into the basic model of capital controls implies that, rather than adjusting instantaneously to terms of trade or other shocks, the economy moves gradually toward a steady-state equilibrium, with its position at any instant being driven by the value of the system’s only predetermined variable, fp. In the steady state, the only differences between the models with and without leakages concern the values of b and fp. In the model of Section I, fp is exogenous while b is endogenous, and vice versa in the model with leakages. Since b and fp only enter the system as a product, it is clear that the value of bfp must be the same in both cases. Equally, it is clear that the values of all other endogenous variables, and specifically the inflation rate, to which the economy ultimately converges in the steady state, are the same in both models. Therefore, as in Section I, an improvement in the terms of trade is inflationary under real exchange rate targeting in the model with leakages, with the long-run effect on π being given by the expression in equation (17). With this result in hand, we now proceed to address the issue of whether a monetary policy rule can contain this inflationary impact once the possibility of leakages is taken into account.
IV. Effect of a Monetary Rule in the Model with Leakages
To analyze the consequences of monetary targeting in the presence of leakages, we again assume that the authorities adopt the money supply rule (18). To derive the required rate of credit expansion, substitute (18) in (6) as before, and solve for
which differs from equation (19) only by the inclusion of the term, b
The resulting model consists of the nontraded goods market clearing condition (5), the money market equilibrium equation (9), equation (18) describing the evolution of the real money supply, the leakage function (27), and the credit rule (31). Proceeding as in Section II by making use of the variable, w = bfp – dp, and noting that now
The introduction of leakages, however, turns out to have radical implications for the model of Section II. The interpretation of the system is exactly as before, except that corresponding to the new leakage function (27), the variable fp now becomes predetermined, rather than exogenous. Since the system is forward looking, the solution implies working backward from a steady-state configuration. Consider, then, the steady-state version of the model. For the system to reach a steady state, the predetermined variable, fp, must satisfy
The economics underlying this result are straightforward. In brief, the presence of leakages implies that in the long run the economy effectively exhibits perfect capital mobility. Changes in the stock of credit will not, therefore, affect the real money supply. Instead, since the system determines an equilibrium value of the stock of real nonmonetary assets, w, changes in dp will simply be offset by corresponding changes in fp, just as in our previous model, and monetary policy will be powerless to alter the economy’s steady-state inflation rate. The only steady-state solution of the system, therefore, is that of the previous section, with π π π* in response to a permanent improvement in the terms of trade. Money supply targeting cannot provide an alternative nominal anchor in this case, simply because monetary policy cannot control the money supply in the long run in the presence of leakages.
Suppose, however, that, in full awareness of this result, the authorities nevertheless respond to a terms of trade shock by temporarily supplementing their real exchange rate target with capital controls and a money supply target, intending to abandon such controls at some future date. Could such a policy, while it is in place, succeed in stabilizing the domestic inflation rate at the world rate π*?
This question is addressed in Figure 2. Setting
A favorable terms of trade shock in a context of real exchange rate and monetary targeting causes the
In the presence of leakages, however, point C no longer represents an equilibrium. To study the economy’s dynamics in this case, consider the family of loci in Figure 2 corresponding to constant values of real private wealth, m + w, which for convenience we will call a (that is, a = m + w). Each member of this family has a slope of –1, and one such member, denoted DE, is indicated in Figure 2. Another such locus, corresponding to a higher value of a, passes through the initial equilibrium at A, while yet a third, with the lowest value of a, passes through C. The relationship between the value of a at C and its initial value at A is derived in equation (24b). It is also possible to show that, once capital controls are abandoned, the long-run equilibrium value of a, which we refer to as a*, will settle somewhere between its value at C and at A—that is, the long-run free capital mobility equilibrium must be along a locus such as DE.18
To see how the economy gets from A to its long-run position along DE in the presence of leakages, notice that, along a perfect foresight path, neither the premium, b, nor the aggregate price level can be expected to move discontinuously, since this would create arbitrage opportunities among assets or across time. The implication of this is that household wealth cannot jump at the instant that capital controls are abandoned—that is, the perfect foresight path must move the economy on to the locus DE at that instant.19 On impact, then, the economy must move into a region in the m-w plane, from which it can reach DE at the appropriate instant. Notice that both m and w can jump to the perfect foresight path, as in Section II. Because the nominal values of the stocks of money, foreign assets, and credit are all predetermined, these jumps must come about through changes in the premium, b, and in the aggregate price level. From such an initial point, the dynamics of the system must obey the directional arrows indicated in Figure 2, which are derived with reference to the
To see where the economy moves on impact, consider, first, the locus of all points that can be reached from A by a jump in the price level, with b unchanged at its initial value of unity. This locus is labeled b = 1 in Figure 2. It has a negative slope (because an increase in the price level reduces both m and dp, and the latter increases w), which is greater than unity in absolute value. To reach points to the left of this locus, b has to fall, while to reach points to the right, b has to rise. Points that are simultaneously below the b = 1 and DE loci, such as J, cannot be on a perfect foresight path, because such points are characterized by b < 1 and m + w < a*. The latter implies, from equation (21), that
Figure 2.Dynamics Under Temporary Capital Controls
The relevant observation about this path for our purposes is that along MN, the real money supply is continuously falling. Since, from equation (22), this implies that π < π* along MN, it follows that targeting the growth rate of the money supply at its preshock level succeeds neither in stabilizing the price level—which jumps on impact—nor the rate of inflation, which remains above the world rate even as the domestic money supply is targeted to grow at the world inflation rate, π*, by continuous sterilization with capital controls. Moreover, it can also be shown (see Montiel and Ostry (1991)), that the steady-state domestic inflation rate remains above the world rate when capital controls are eventually abandoned. It follows, then, that in the presence of leakages, targeting the money supply fails to stabilize the rate of inflation over all time horizons.
The intuition behind these results is as follows: the favorable terms of trade shock creates an incipient excess demand in the market for non-traded goods, both because production shifts to the exportables sector (away from nontraded goods) and because the positive income effect of the favorable terms of trade shock increases the demand for nontraded goods. Since the real exchange rate rule prevents the relative price of domestic goods from rising (that is, through a real exchange rate appreciation), the burden of adjustment on impact is borne by an increase in the domestic price level that reduces the real value of private wealth, m + w.
The combination of increased real income due to the terms of trade improvement and reduced real spending on the part of households gives rise to a trade surplus on impact. This makes necessary the adoption of a contractionary credit policy in order to keep the growth of the money supply at its targeted level. Because domestic credit and foreign currency assets are taken to be close substitutes, continuous credit contraction will result in a continuous appreciation of the parallel exchange rate while capital controls remain in place.
However, since at the moment that capital controls are abandoned foreign currency assets must sell at par, holders of such assets would expect to reap a windfall. This causes arbitrageurs to bid up the price of foreign currency assets (that is, to increase b) at the instant that the shock hits, to the point where potential windfall gains are eliminated. Notice that the reduction in the real value of private wealth must be such that m + w falls in spite of the fact that, due to the increase in b and the reduction in the real stock of credit, real private nonmonetary wealth, w, actually rises. The decrease in real wealth thus comes about through a reduction in the real money stock, m. The combination of lower real money stock, higher real income, and lower domestic real interest rate results in an incipient excess demand for money. Money market equilibrium thus requires that the domestic nominal interest rate increase. This can happen along the perfect foresight path only if the domestic rate of inflation rises on impact and remains higher than the world rate during the transition from M to N.
This paper has examined whether the money supply can serve as a nominal anchor for the price level under real exchange rate targeting when the nominal exchange rate cannot serve this purpose. It was argued that, when capital controls are perfect, so that the government can permanently segment official and unofficial markets for foreign exchange, the inflation rate can indeed be stabilized in the face of exogenous shocks when the authorities follow an appropriately chosen money supply rule. However, we also showed that the stabilization of the inflation rate carried with it the implication that in the long-run equilibrium, an ever-widening gap between the official and unofficial exchange rates would emerge. Since this growing gap between the two exchange rates would ultimately create unbounded incentives to engage in cross transactions between official and unofficial markets, we argued that the effectiveness of capital controls could not ultimately be sustained.
The paper then examined whether monetary targeting could effectively stabilize the inflation rate when these incentives for cross transactions create leakages between official and unofficial markets for foreign exchange. Our finding once again was that using money as a nominal anchor for the price level is problematic. Although the model with cross transactions did not have the problem of a continuously growing gap between official and unofficial exchange rates in the steady state, and hence avoided some of the difficulties that were inherent in the model with perfect capital controls, our conclusion was nonetheless that a money supply rule could not prevent the emergence of inflation when the economy was subjected to a permanent terms of trade shock. The reason was simply that, in the presence of leakages, the long-run behavior of the economy must be identical to that of an economy without any capital controls—that is, with perfect capital mobility. Since, under perfect capital mobility, changes in the stock of credit cannot affect the real money supply, so too in the model with leakages, the money supply becomes endogenous and, hence, cannot be used as a nominal anchor for the domestic price level. In addition, however, the paper showed that if capital controls are used temporarily to target the rate of growth of the money supply, a monetary rule would still fail to stabilize the rate of inflation, even in the short run. To conclude, then, this paper finds little support for the view that a money supply rule can stabilize the inflation rate when the authorities target the real exchange rate.
AdamsCharles and DanielGros“The Consequences of Real Exchange Rate Rules for Inflation: Some Illustrative Examples,”Staff Papers International Monetary FundVol. 33 (September 1986) pp. 439–76.
BhandariJagdeep S. and Carlos A.Végh“Dual Exchange Markets Under Incomplete Separation,”Staff Papers International Monetary FundVol. 37 (March 1990) pp. 146–67.
DornbuschRudiger“PPP Exchange Rate Rules and Macroeconomic Stability,”Journal of Political EconomyVol. 90 (February 1982) pp. 158–65.
GuidottiPablo E.“Insulation Properties Under Dual Exchange Rates,”Canadian Journal of Economics21 (November 1988) pp. 799–813.
KhanMohsin S. and Peter J.Montiel“Real Exchange Rate Dynamics in a Small Primary-Exporting Country,”Staff Papers International Monetary FundVol. 34 (December 1987) pp. 681–710.
Lizondo J.Saúl“Real Exchange Rate Targets, Nominal Exchange Rate Policies, and Inflation,”Revista de Analisis Economico 6 (June 1991) pp. 5–22.
MontielPeter J. and Jonathan D.Ostry“Macroeconomic Implications of Real Exchange Rate Targeting in Developing Countries,”Staff PapersInternational Monetary FundVol. 38 (December 1991) pp. 872–900.
Peter J. Montiel was Deputy Division Chief of the Developing Country Studies Division of the Research Department when this paper was written and is currently Danforth/Lewis Professor of Economics at Oberlin College. He is a graduate of Yale University and the Massachusetts Institute of Technology.
Jonathan D. Ostry, an Economist in the Research Department, holds a doctorate from the University of Chicago, as well as degrees from the London School of Economics and Political Science, Oxford University, and Queen’s University.
The authors would like to thank Guillermo A. Calvo and Mohsin S. Khan for useful comments.
In the absence of terms of trade shocks, π* is the foreign currency rate of inflation of traded goods, which will be referred to in what follows simply as the foreign inflation rate.
We have suppressed the real exchange rate as an argument from the supply of nontradables function, since, under the real exchange rate rule, this relative price does not change.
The private sector budget constraint assumes that inflation tax revenues that accrue in the first instance to the central bank are not handed back to the private sector. This assumption was necessary to ensure the existence of a unique steady state in our previous paper (Montiel and Ostry (1991)), and is also necessary under the assumption of imperfect capital mobility. A related point is made by Woodford (1988) in his discussion of the macroeconomic effects of pegging the interest rate.
The instability of the system defined by
Our comparative statics results with respect to inflation do not, however, depend on the assumption that the SS schedule is negatively sloped. If the slope of SS is positive, then the result requires only that SS be steeper than NN, which is assured by previous assumptions.
The fact that
Again, our comparative statics results do not depend on this assumption.
Notice that this condition is equivalent to the requirement that the product of the share of seigniorage in real income and the income elasticity of money demand be less than unity, something that would be easily satisfied for any plausible values of the parameters.
By contrast, under a fixed exchange rate regime, this shock would lead to a real exchange rate appreciation in the model, with no change in the steady-state rate of inflation (see Khan and Montiel (1987)).
In this case,
Recall the assumption, i* = π*.
If the central bank extends credit to the government, m – dp is reserves plus credit to the government; in either case, m – dp is positive.
As mentioned previously, all results are evaluated around an initial steady state with b = 1.
We assume that the
The magnitude of the shift is given by
This can be shown as follows. Totally differentiating equation (5) under the assumption of perfect capital mobility, so that b = 1 (and therefore b = 0), we have
Since m + w cannot jump at the moment that controls are abandoned, equation (5) implies that b also cannot change discontinuously.