Comparing the Welfare Costs and the Initial Dynamics of Alternative Temporary Stabilization Policies

BoardofGovernorsoftheFederalReserveSystem InternationalFinanceDiscussionPapers Number539 February 1996 COMPARINGTHEWELFARECOSTSANDTHEINITIALDYNAMICSOF ALTERNATIVETEMPORARYSTABILIZATIONPOLICIES MartinUribe NOTE: InternationalFinanceDiscussionPapersarepreliminarymaterialscirculatedtostimulate discussionandcriticalcomment. ReferencesinpublicationstoInternationalFinanceDiscussionPapers (otherthananacknowledgmentthatthewriterhashadaccesstounpublishedmaterial)shouldbe clearedwiththeauthoror authors.

ABSTRACT This paper compares the We]fare costs and initial dynamics of three alternative inflation stabilization policies using the staggered price model with imperfect credibility and currenc~’ substitution de~-elopedby Calvo and V4gh (1990). In addition to the policies analyzed by Call*oand V6gh (1990) — a temporarv. exchange-rate based stabilization program (ERB), and a temporary money based program (MB) — this paper considers a third stabilization policj’ consisting of a temporary money based program with initial reliquefication —i.e., an initial once-and-for-all increase in the money supply— that keeps the nominal and real exchange rate from appreciating on impact (MBR). Simulation results suggest that the welfare costs associated with ERB and NfBR programs are lower than those generated by MB programs. This seems to be the case even for highly temporary programs and for economies with low degree of currency substitution. ERB and MBR programs produce similar welfare costs except in two cases: when the policy change is very temporar~*,MBR programs do better. while for high values of the elasticity of currency substitution ERB programs outperform MBR programs.

Comparing the Welfare Costs and the Initial Dynamics of Alternative Temporary Stabilization Policies Nlart~n Uribe” 1 I A long debate in open economy macroeconomic policy isconcerned with the issue of identifying the best nominal anchor for stopping high inflation. Two ofthe most popular instruments generally discussed are the money supply and the nominal exchange rate. One of the reasons for this long lasting discussion might be found in empirical evidence suggesting that exchange-rate based programs are associated with an initial boom in aggregate consumption and an eventual recession. whereas in money based programs the recession is born right at the outset. so it is unclear which strategy is the less costly.1 This paper addresses this issue by performing welfare comparisons in the basic analytical framework developed by”Calvo and V6gh (1990). The reason for choosing this framework is that succeeds in reproducing the “recession nowversus recession later’”empirical regularity, together with several other stj’lized facts associated with exchange-rate based and monej~ based stabilization programs. Four elements of the Calvo-V6gh model are important in replicating these stj’lized facts: (1) inflation acts as a tax on consumption via a cash-inad~’anceconstraint, (2) currencjTsubstitution, (3) staggered price setting in the home-good market a la (‘alvo (198:3)and (4) the temporariness hypothesis, by which agents percei~’e the stabilization programs as lasting for only a finite period of time. 1 1 Calvoandv~gh(1993a).

This paper evaluates three different types ofstabilization policies: a temporary reduction in the devaluation rate, a reduction in the money growth rate, and a temporary reduction in the money growth rate accompanied by an initial increase in the money supply that keeps the nominal exchange rate from appreciating on impact. This last policy, which is frequently advocated by pohcymakers, as a way to avoid high interest rates and recession during the initial phase of inflation stabilization programs, has not been formally analyzed in the literature on temporary stabilization. This policy will be referred to as a money based program with initial reliquefication. The next section presents the Calvo-V6gh model, emphasizing the method used for computing dynamics and welfare costs. Particular functional forms are assumed for preferences and technologies. Following Calvo and V6gh (1990), the instantaneous utility function is assumed to be additively separable in home and traded goods and logarithmic in each of the two goods. Thus, the welfare comparisons are restricted to the case of a unitary intertemporal elasticity of substitution. This assumption was made here for computational convenience but is certainly a limitation, (see section 7 for more discussion on this). The liquidity technology is assumed to be of the CES type in domestic and foreign currency. The supply of traded goods is assumed to be exogenously given, while output in the nontraded good sector is assumed to be demand determined. Sections 3to 5 are devoted to comparing the initial dynamics ofthe model under the three alternative stabilization policies described above. Section 6 describes the welfare criteria used to compare the alternative stabilization policies and performs welfare comparisons for different parameter \’alues. Section 7 closes the paper with some remarks. 2 S (1990) This section presents a closed form solution to the Calvo-V6gh (1990) model under exchangerate based programs and exact numerical solutions for money based and money based with initial reliquefication programs (see Calvo and V6gh, 1990for a diagrammatic exposition of exchange-rate based and money based programs). The main features of the model are staggered prices in the nontraded sector a la Calvo (1983), currency substitution, and imperfect credibility about monetary policy. 2 H Consider an economv“ populated b.v a large number of identical households with preferences defined over paths of consumption of traded goods, c;, and non-traded goods, c~,and de- 2

scribed by the fo ~m (1) $ > 0 denotes the subjective discount factor. Households are assumed to have access to three assets. Domestic currency, m:, foreign currency, $~,and a foreign-currency denominated bond, b:, that pays the constant interest rate r in foreign currency. These three variables are expressed in terms of traded goods. The budget constraint of the household is given by2 m m + + J rn+~f.+ I e + c + ( + r)mf + trft]di = b/. + e ytEt - T (2)r’ o 0 where Ctdenotes the devaluation rate, et denotes the real exchange rate (i.e., the relative price of the traded good in terms of home goods), y; and y~denote the household’s income of traded and home goods respectively, and rt denotes a lump-sum transfer received from the government. expressed in terms of the foreign currency. The foreign-currency price of the traded good is assumed to be equal to one. Households can use domestic and foreign currenc}”to purchase goods. These transactions are assumed to be subject to a cash-inad~’anceconstraint of the form q j’t) > C +CA) ~: (3) where Q > 0 and L(”.“) is a CES function with elasticity of substitution (1 + p)-l >0 and share parameter O< ~ ~ 1. that is. –l + JL(m,)-) E (1– (4) The household’s problem consists in choosing paths for consumption and asset holdings so as to maximize (1) subject to (2) and (3). For simplicity, it is assumed that /?= r. The first order conditions corresponding to this problem are 1 ft + r 1 l+cl (5) c; [ Ln (d? A) a tYPe limt-m e -“’(b, + f, + m:) 20 + + the

I Ct — = et (6) (7) where Aisa Lagrange multiplier associated with the budget constraint (2). It followsfrom (7) and from the fact that the liquidity function islinearly homogeneous, that the ratio offoreign to domestic currency depends only on ct. 2 A s It is assumed that the path of the price levelof home goods is continuous but that its growth rate can “jump?’;moreover, its right-hand time-derivative is assumed to be proportional to the log-difference between “full-employment” and current output, that is, * = –0 ln(yt/ij) (8) where m~denotes the inflation rate ofhome goods, ~ denotes full-employment output and Ois a positive parameter. The dot on ~~denotes its right-hand time-derivative. This specification follows the model of staggered price setting developed by Calvo (1983). We assume that fr~ is proportional to the log-difference, rather than to the difference between potential and current output. This slight departure from Calvo (1983) and Calvo and V4gh (1990,1993b) makes it possible to obtain a closed form solution of the model in the case of a temporary exchange-rate based stabilization program. Importantly, the modification does not violate any of the original framework’s micro-foundations.3 2 T g The government is assumed to perform lump-sum transfers, ~~,to the public. to hold foreigncurrenc~’denominated bonds, ~, and to be allowed to print domestic currency. The money supply, expressed in terms oftraded goods, isdenoted by rn~.The right- hand time-derivative of b~is given by @= p~m,~+ rt$ – T~ 3F d e X ti = p K ! S S i OI – 6E 4

where p~denotes the right-hand growth rate of the nominal money supply. The right-hand time derivative of real balances is in turn given by, m; (p~– t~) (9) = Combining these last two expressions, one can express the present-value budy It constraint of the government as4 (lo) where ~ – m: is taken as ven by the government. 2 Eq In equilibrium. the home-good market clears and the money supply equals money demand, that is y~= c~ (11) m; = m: (12) It is also assumed perfect capital mobility, so the domestic nominal interest rate, it , is given by it = r + tt (13) Combining (2). (10). (11) and (12) gives r ~-r’(c~+ rft )dt = 1# (14) /o where I/’ denotes permanent income and is given by + J F b: + fo) + r e-rtyr at (113) o The (right-hand) growth rate ofthe real exchange rate, isgiven by the difference between the de~’aluationrate and the home-good inflation rate, that is, (16) Using the C’E5’form for liquidity ser~’icesassumed in (4), the ratio of foreign to domestic in a 1 c - = - m

currency can be written as ‘=[(1j7)(~)]*~Zf-J(i~) Withw,(i)>(l (17) mt Combining (5), (13). and (17), c; can be expressed as a function of the nominal interest rate and of the Lagrange multiplier, (18) ~~ithz~(~)> 00 Using (~), (4), (6), (1’7)and (18) one can write ~t as, -~2(Yw(i J f, A (19) L(I, ?0(2,)) and combining and (19), 2raw(i J c; + rjt = A 1+ = A 2 (20) L(l, W(2J) – [ 1 where x’(i~) z O. Using (20) and the economy’s resource constraint (14), one can then solve for the value of the Lagrange multiplier A, as a function of the time path of the nominal interest rate and of the permanent income, r w A=— e - ”d t 2 ( i ~(21) )x yp/o 2 I c Suppose that previous to the announcement ofthe stabilization program (t < O),the economy is in a steady--state in which both the devaluation and the inflation rates are constant. Suppose also that in this steady state the devaluation rate is CH. The nomillal interest rate is then also constant at i~ = r + eH. From (21) the pre-stabilization value of A is A- = :(~H)~(~H)/Yp (the subscriPt “-” denotes pre-stabilization values), and using this in (18), the consumption of tradables is c*= @’/z(iH). Since the inflation rate is constant, equation (8) implies that consumption (and production) ofhome goods isat full-employment. c- = J. It then follows from the constancy of the consumption of traded and home goods that the real exchange rate is also constant at e. = UX(ZH)/YP”FinallY?from ’16) the pre-stabilization inflation rate is ~.-= ~~.

3 T e s The purpose of this section is to use the model described above, in order to numerically simulate its response to a temporar~’ exchange-rate based inflation stabilization program. This simulations will later be compared to those arising from money-based stabilization programs. It turns out that for exchange-rate based stabilization programs, the functional forms assumed for preferences and technologies, allow us to obtain a close form solution of the model.5 .4s it will be shown below, this is not the case under money-based stabilization. Suppose that at time t = O,the government unexpectedly announces a stabilization plan H t. ELfor T Perio “ that lowers the de~’aluationrate from ~ d that is, for Os t < T Ct= (22) # for t.> T { Suppose also that the gok’ernmentguarantees free convertibility of the domestic currency. It follows from (13) that the nominal interest rate is then given by The marginal utilit~’of wealth. .\. can then be obtained by substituting this expression into equation (21), 1 A= – 1 – Ls-rT + It is not clear what. the ‘“announcement effect” on Ais. When domestic currency is the sole means of exchange a~-ailablein the economy (~ = 1), it follows from (20) that x(i~) = 1. so Abecomes a weighted a~”erageof Z(ZH)/y~ and :(zL)/y~, which, given that z’(i~) < 0, is greater than the pre-announcernent value ;(iH)/y~.G Under currency substitution, on the other hand, ~’(i~) > 0. so the product z(i~)x(zf) can be increasing or decreasing in it. If it was increasing in if. then Awould decrease with the announcement of the stabilization program (this case is nat,irallj more likel“v the larger is the elasticity of currencv. substitut ~~n). - ~ J = solutionsarestill a itutlonisZero.Inthisc~e ~(~~)isnotZero .

The time path of tradables is a step function of the form A-’z(zL) for O<—t < T c; = (24) ~- Iz(iH) for t z T { Two things are apparent from this expression. First, the program generates an initial boom in the consumption of tradables7 Also, since the supply of traded goods is assumed to be constant, the trade balance deteriorates on impact. These two features are consistent with the stylized facts associated with this type of programs, see V6gh (1992) and Kiguel and Liviatan (1992a)8 At t = T c; jumps down to its long-run steady state level, which can be lower or higher than the pre-stabilization level (see below). 3 S s Consider a long-run state of the economy, in which all real variables and inflation are constant. From (23). the steady state of consumption of tradables is reached at T, c== c where variables without a time subscript refer to long-run values. From (8) and (11), in turn. the steady state of consumption of home goods is c = P Using (6) one can express the long-run \’alue of the real exchange rate as e = J/c; From (16). (22) and (23) the steady states of the devaluation rate, the nominal interest rate and the inflation rate are ~= # ‘Theratio ) – + < 0 > 8

T = fH+ r i = 3 D In analyzing the initial dynamics of the model in response to a temporary reduction in the devaluation rate, it is convenient to express some of the variables of interest as deviations or log-deviations from their steady state levels. Define, h, = – Aq = t~– It will also proi’econvenient to write Ac: and Act in the following way. A = A (1 – Z@(t)) Aq = A6~(1– q’(f)) where UT(t) denotes the unit step function, defined as, O for Os t < T Udt) = 1 for t z T { Using (6), one can express (S) and (16) as a system of two linear differential equations ~r~ and Act. [H=L‘~l[:::l+l[(-lf-:uc’T(’)) “ (213) whered~ & Since, gi~.enthe policj rule, neither the price of the home good nor the nominal exchang rate can jump, the initial valueofthe real exchange rate isgiven by C.= e- and so Aro = Zn(e-/e). On the other hand. Lzo is chosen in such a wa~’that n~iscontinuous for t >0 and converges 9

to An easy way to solve linear systems like (25) Containing a non-linear forcing term> isdescribed in Boyce and DiPrima (1965), and consists in applying the Laplace transform on it, solving the resulting algebraic linear system and applying the inverse Laplace transform operator to recover the original variables. Let X(S) be the Laplace transform of Ztevaluated ~.10 LaPlace transform of (25) is then given bYJ Given s. this is an algebraic linear system in [MI(s) Al?(s)]’ whose solution is given b“v {[-f:cT-:sT+‘2[’:a) } The original variables can be recovered by applying the inverse Laplace transform operator, to (26),11 Figures 1 and 2 show the transitional dynamics of some variables of interest in response to a temporary reduction in the devaluation rate12 The baseline set of parameter values were chosen arbitrarily and are shown in table 1.13 The time unit is a quarter. The economy starts in a steady state with an inflation rate of 107o(6H = 0.1) and the pl c k on setting the devaluation rate at 170(~~ = 0.01) for 10 quarters (T = 10); ~~then resumes derivedinthestaggeredprices a – ( 6 II (] provideatable “ AT~ = – – + [ – – C + 1– 4AeOsinh(@) + A – Aet = I - – r + 1– w – 1[ – – s – l + A s – C s + e l 1 10

to its original level of 10%. Figure 1 shows the case in which only domestic currency can be used as a means of exchange (~ = 1). Qualitatively identical figures are shown in Cal}’o and V6gh (1993b) and V6gh (1992). The model captures the main empirical regularities of exchange-rate based stabilization episodes. Consumption of both goods display a boomrecession cycle, the real exchange rate appreciates and the trade balance deteriorates during the initial phase of the program. Adding currency substitution does not change the qualitative response of the model. For high enough values of the elasticity of currency substitution, however, it might happen that the steady state consumption of tradables ends up being higher than its pre-stabilization level. This possibility arises because of the wealth effect associated with the substitution of domestic for foreign currency in response to the temporary reduction in the devaluation rate. This is shown in figure 2. which displays the dynamics of consumption of tradables for 7 = .75and for two valuesofthe elasticity}o’f currenc~.substitution, 1and 2.5. The figure also shows the behavior of the ratio of domestic to foreign currency. Between t = Oand t = T, the increase in the demand for domestic currency is materialized via exchanging foreign for domestic currency at the central bank, who in turn invests them at the international interest rate and returns the proceeds to the public in a lump-sum fashion, generating the positi~’ewealth effect mentioned abo~’e.This effect is obviously stronger the easier it is for the public to substitute currencies. i.e., the higher 1/(1 + p) is. The high-elasticity case is also associated with a stead~. state real exchange rate (not shown in the figure) lower than its pre-stabilization level. This followsfrom the fact that the steady state of consumption of home-goods is exogenously given and the real exchange rate equals the ratio of consumption of home goods to consumption of tradables. In the next sections, the initial dynamics and welfare implications of this type of stabilization programs w~illbe compared with money based stabilization programs. 4 T s Consider now a stabilization program by which the government lowers the money growth rate from pH to /!Lf<’ pH, for T periods; that is, pL for O~ t < T pt = (27) pH for t~ T { The nominal exchange rate and the devaluation rate are now in the previous section. the emphasis will be put 11

I the time paths of the variables of interest. In this case, however, it will not be possible to obtain close form solutions. Nevertheless, it will be shown that it is easy to compute numerical solutions using very standard routines. Let us first derive the time paths of the nominal interest rate and domestic real balances. Using (3)1(6), (17) and (18) one can write rnt as 2 = ?-n~= X A (28) L(I, Z@)) where v’(it) < 0 because s‘(i,) <0 and w’(z,) >0. Using this expression together with (12) and (13), one can write (9) as.14 ; = - (2,- ( Jo)) (29) since –v’(z)/v(z) is always positive, it follows from this expression and (27), that the unique non-explosive solution for t ~ T is the steady state, that is i = r + pH for t z T For O~ t < 7’, the time path of it can be found by solving the following initial value problem: Let gt a i~-~; then the e~’olutionof g~is governed by the following differential equat ion]5 ) = (g~ h) ~ with g(0) = r+p ~. !Numericalsolutions to this equation can be easily (and quickly) obtained using an~’computer math package equipped with routines for solving initial value problems.lG In order to get the time paths of consumption of tradables and domestic and foreign real balances. it is necessar~’to first calculate the value of the multiplier Awhich, from (21), is p ~ Y= a andrealbalancesarecontinuous a a u MALA 8 a ~ O< t ~ M A T LA

given by T - ) d + + + UP/~ c The first term on the right hand side can be evaluated using a computer math package capable ofsolving integrals. 17Once ~and the path ofthe nominal interest rate are computed, it is straight forward to obtain the paths of c?from (18), j’~from (21), mt from (28) and c~ from (13). Since these variables depend only on ~ and the contemporaneous nominal interest rate, they all reach their steady states at t = T. The dynamics of the real exchange rate and inflation are determined by a system similar to (25) (30) The difference between this s~”stemand (25) is that the forcing term is no longer a step function. The initial condition for Aef is given by AeO= /n(eO/e), where e = ~/c~ is the steady state of the real exchange rate and C. is the initial value of the real exchange rate, which is no longer predetermined because the nominal exchange rate may jump at t = O. Howe\’er. one can use the initial value of domestic real balances, whose path was already calculated, to determine eo. Since given the policy rule neither the nominal money supply nor the price of the home good can jump at,t = O,it follows that the following condition has to hold como= e.m- (31) w’heree- and m- are the pre-stabilization values of the real exchange rate and of domestic real balances obtained above II]order to calculate the initial value An. z T. —(r + ~H), is con~’enientto define the following variable, h, z M, – @q From (30) it follo}~’tshat the e~’olutionof h~isgiven b~’the followingdifferential equation, h~= Oh,– @(At~+ &Ac;) (32) Since the forcing term of this equation is zero for t z T, and since ~ > 0, the unique . ! 4 A TL 1:3

. non-explosive solution for this equation satisfies ht = Ofor t 2 T o AT, = $Ae, for t —> T (33) The condition h~ = Ocan then be used to write (32) as an initial value problem in exactly the same wa~’as was done above with equation (29); the solution to this problem gives ho, which in turn determines Am. = h. + ~A~. Given ATOand Aeo, (30) becomes an initial value problem which can be solved numerically for Amtand Ae~for O< t ~ T.18 Condition (33) and the second equation in (30) then give the solution for t >—T, Act = C-o(t-T) Lle~ Figure 3 shows the transitional dynamics of a plan that reduces the money growth rate from 10%)to 1%for 10quarters for an economy that usesonly domestic currency as a means of exchange (~ = 1). For comparison, the figure also includes the dynamics of an exchange-rate based program (the same shown in figure 1). The initial dynamics ofthe nominal interest rate are very similar in both t}’peof programs and correspondingly, the paths of consumption of tradables also look alike. As t approaches T, however, the nominal interest rate starts rising in the money based program. and this implies that the recession in the traded sector starts earlier for this type of plan. With respect to the consumption of home goods, the money based program does not induce an early boom but neither an early recession. In this singlecurrency economy, the consumption of home goods isproportional to real balancm measured in terms of home goods, and since both the price level and the nominal mone;~supply are predetermined at t = O.the consumption of home goods is also predetermined. This means that at / = Othe real exchange rate (e. = ~/c;) jumps down by the same proportion as C; does. This, in turn, can only happen if on impact the nominal exchange rate appreciates by that proportion. Finall~.,the domestic real interest rate is pretty flat during the whole stabilization period and takes off only after the plan is abandoned. Compare this with the initial period of low real interest rates in the exchange-rate based program. Figure 4 shows the d~’namicsin an economy with currency substitution (~ = .75). The differences between the two stabilization strategies are much more dramatic now. To start with, the consumption boom is much more pronounced under exchange-rate stabilization l M B s ~ uOA hbandlesTsystremsDT o hue LEA4 t i ~ ne Onecan calculate a lS = – + 14

for two reasons: first the nominal interest rate is always lower under exchange-rate based stabilization than it is under money base stabilization, and second in the exchange-rate based stabilization program the wealth effect associated with the substitution of domestic for foreign currenc~’when the devaluation rate falls induces higher consumption of tradables in both. the transition and the long run. In the money based program. the higher demand for domestic currency materializes partly through a decrease in the nominal and real exchange rate on impact (recall that the price of home goods cannot jump). This discourages the consumption of home goods. So, while the exchange rate program is associated with an initial boom in this sector, the money based program generates an initial recession. The model then succeeds in replicating the empirical regularity of “recession now versus recession later”. The initial recession in the money based program, in turn. is accompanied by deflation and high real interest rates during the initial phase of the plan, in contrast with what happens in the exchange rate based program in which the real interest rate is low throughout the transition. 5 T s u 1[is frequentl~’argued that money based stabilization programs should be accompanied by an initial once-an-for-all increase in the money supply in order to avoid high real interest rates and recession. caused h}’the credit crunch associated with the initial increase in money demand. In this section reliquefication willadopt the form ofan initial increase in the nominal money supply that keeps the nominal and real exchange rate from falling on impact.lg Technically, rcli{~ueficationmeans that the initial condition for the real exchange rate derived above (equation (31)) is now replaced by20 q = programirnp]emented . a ( ( centralbankcmitsreservesarereturned a

I Figure 5 and 6 show the transitional dynamics implied by money based programs with and without initial reliquefication. as wellas the initial dynamics of the exchange-rate based plan, in a single-currenc~reconomY (figure 5) and in one with currency substitution (figure 6). The last case is the most interesting because reliquefication has more evident effects, so only figure 6 will be discussed. Let us first comment on the variables that are unaffected by reliquefication. The paths of real balances? consumption of tradables, and the nominal interest rate were derived independently of the initial value of the real exchange rate, so they are completely unaffected by reliquefication. The effect of reliquefication on the rest of the variables, is to induce dynamics that look very similar to those arising from exchange-rate based programs during the initial phase of the plan and to money-based programs without reliquefication during the final phase of the program. For example. the money based program with initial reliquefication induces an initial boom in the consumption ofhome goods as does the exchange-rate based program, but only a mild recession by the time the program is abandoned, as is the case with the money based program without initial reliquefication. Something similar occurs with the behavior of the real interest rate: the money based program with initial reliquefication shares with the exchange rate program low rates in the initial phase but avoids the high rates induced by these plans by the time they are abandoned. The conclusions are similar for the real exchange rate and the inflation rate. 6 W c d s This section compares the welfare implications of the three alternative temporary stabilization policies discussed above: exchange-rate based (ERB), money based (MB), and money based with initial reliquefication (MBR). These comparisons include sensitivity analysis aimed at highlighting which parameters of the model are important in determining the cost of each policy. The measure of the welfare cost associated with each type ofplan isdefined as the fraction by which the pre-stabilization consumption streams oftraded and home goods, c: and c- have to be decreased in order to leave the consumer indifferent between consuming the decreased but constant path and the one arising from given stabilization program. Formall--- let f a 16

denote the welfare cost. Then f solves In(c-) + /n(c-) + 2Zn((l - ~)) = r ~~ e-r’[in(c;) + zn(c~)]~t The welfare comparisons are shown in figures 7 to 10. Figure 7 shows the welfare costs l as a function of the bdegreeof temporariness” ~T. For the three different policies analyzed and when -~= .75, the cost goes to zero as 7’ gets very small, increases initially, reaches a maximum and then starts to decrease until eventually turns into a welfare gain at long horizons. When currenc~’substitution is shut down (i.e., ~ = 1), the pattern changes only in that for large values of T the welfare cost tends to zero. This is related to the fact that in this case the model shows superneutrality to permanent changes in either the money growth rate or the devaluation rate. If the degree of temporariness is interpreted as the degree of lack of credibility,21the figure shows that it is not clear that for low levels of credibility the use of money as a nominal anchor is preferred to the nominal exchange rate, as might be interpreted from Calvo and V6gh (1993b), pages 21-22. In the experiment displayed in figure 7. the ERB program is less costly than the money based program even for low values of T regardless of the presence of currency substitution. On the other hand the MBR program does better than the ERB program in cases of ~’erylow credibility. In figure S the welfare costs are computed for different values of the long-run (and prestabilization \’alueofthe) inflation rate, ~~. Under currency substitution, the costs associated with ERB and MB programs are non-monotonic in e‘. Two forces going in opposite directions are responsible for this. on the one hand, temporary changes in the nominal interest rate prrturb the consumption paths from being constant, and thus are costly for agents with concave instant utility functions. on the other hand, there is a positive welfare effect associated with the substitution of domestic for foreign currency even when the devaluation rate is reduced tcmporaril~~. In the }IB program, the first effect dominates right from the beginning for the parameter values chosen. To disentangle these two effects, panel (b) of figure S shows the same computations for a single-currency economy, ~ = 1.22 In this case, t = p l

I the welfare cost of ERB programs is always decreasing in the long-run inflation rate. Since the MB and the XIBRprograms display identical dynamics for the consumption oftradables, all the difference in welfare costs between these two programs stems from the behavior of the consumption of home goods. Under currency substitution, the .MBR programs avoids the initial recession in this market and in the single-currency economy it generates a boom. This translates in lower welfare costs when the economy is reliquefied on impact. Figure 9 shows the welfare costs for different values of the elasticity of currency substitution, (1 + p)-l. As this elasticity increases, the welfare costs are always decreasing for the ERB program, initially decreasing for the MBR program, and always increasing for the MB program. The reason for this pattern is that the higher is (lp)-l, the stronger is the welfare effect associated with the substitution of currencies in response to a temporary reduction in inflation. In the MB program, however, a higher elasticity of currency substitution induces a stronger initial deflation and recession in the home-good market, because, given the money supply, that is the only way by which the increase in domestic-money demand can be materialized. The initial reliquefication prevents the deflation from happening and thus does better than the MB program. Figure 10 shows the cost of temporary stabilization programs as a function of the parameter 0, that relates the speed of adjustment of the inflation rate as a fraction, 0, of the “unemployment rate”’ in the home-good market. These costs associated with temporary seem to be very sensitive to changes in O,and are always decreasing in it. This is not surprising if one remembers that a low value of Omeans that either firms do not revise their prices very frequently, or that when they do, the price changes do not respond much to the degree of excess demand. or both. Figure 11,clarifies this point by showing the dynamics of inflation and consumption of home-goods for two t~aluesof 0, .04 and .4.23The inflation rate takes a longer time to catch-up with the devaluation rate when 9 is small. Consequently, the real exchange rate (not shown in the figure) appreciates much more in the ERB and .MBR programs and the initial appreciation takes much longer to disappear in the MB program. This, in turn, translates in an amplification of the eventual recession in the ERB and MBll programs, and in a longer and more pronounced initial recession in the NIBprogram. O 18

7 C The welfare comparisons performed above suggest that exchange-rate based programs and mone~’based programs with initial reliquefication are lesscostly than money based programs, even at lowlet’elsof credibility and low degrees ofcurrency substitution. This might explain in part why pure money based stabilization episodes are so infrequent. Exchange-rate based and money based programs with initial reliquefication produce similar welfarecosts, except in two cases: at lowlevelsofcredibility (or high degrees oftemporariness), mone}’based programs with initial reliquefication do better, while for high elasticities of currenc~’substitution exchange-rate based programs appear to be less costly. There are at least two reasons for why, although frequently advocated. money based programs with initial reliquefication are seldom observed. First, in the very short-run money based programs with initial reliquefication are observationally equivalent to exchange-rate based programs and hence it is conceivable that episodes that fall into the category of mone~-based programs with reliquefication are actually labeled exchange-rate based program. Second. from a reputational standpoint, it might be difficult for policy makers to announce a program that limits the rate of money growth and at the same time implement a once-andfor-all increase the stock of money. From this perspective it might be easier to implement an exchange-rate based program and convince the public that under such regime the central bank has no control mwr the stock of mone~’,and that any increase in it reflects an increase in the public’s demand for real balances. The speed at which inflation adjusts to its long-run level measured in the model by the parameter 0. is an in~portant determinant of the welfare cost for all of the policies studied. Low~’aiursof 0 are associated with high welfare costs because the inflation rate takes longer to dmraluation rate, amplifying the degree of real exchange rate appreciation r and the recession in the home-good market. It is worth recalling that all the computations performed in this paper were constrained to the case of logarithmic and additively separable instantaneous utility functions. Specifically}’t.he anai~’sisignores the effects of varying the degree of intertemporal substitution in consumption. This omission is particularly important for two reasons: first, most,of the real effects in the model used above come from intertemporal substitution induced by a temporar~’reduction in inflation. which in the model acts as a tax on purchases of goods through the cash-in-advance constraint. Second, empirical estimates of the intertemporal elasticity of substitution (Gio\’annini. 1985;and R,einhart and V6gh, 1993)suggest values of arou d .2 for de~-elopingcountries, way below unity. In general, it would be important to perform the welfare comparisons using calibrated versions of the model in order to obtain quantitative 19

values for the costs of engaging in each of the different inflation stabilization strategies. This task is left for future research.

R Boyce. W:illiarnE. and DiPrima, Richard C., Elementary Differential Equations and Boundary Wlue Proldems, (1965), N. York, J. Wiley. Calve, Guillermo .~.. “Staggered Prices in a Utility-Maximizing Framework,” JournaZ of Monetary Economics, 1983, 12, pp. 383-98. Calve, Guillermo A. and V6gh, Carlos ,4., “Credibility and the Dynamics of Stabilization Policy: A Basic Franlework.9’ IMF (1990) WP #90/110, also in Christopher Sims editor, Advances in Econometrics, Sixth World Congress, Cambridge University Press. Calve, Guillermo A. and Carlos A. V6gh. “Inflation Stabilization and Nominal Anchors,” mimeo, 1993a. Calve, Guillermo .4. and Carlos A. V6gh, “Exchange Rate Based Stabilization Under Imperfect Credibility}’,” in Helmut Frisch and Andreas Worgotter Eds., Open Economy Macroeconomics, London MacMillan Press, 1993b, Chapter 1, pp. 3-28. Giovannini, Alberto. “Sa~’ingsand the Real Interest Rate in LDC’S,” Journal of Development Economics , 19S5. 17 ~p 197-217. Kiguel. Miguel A. and Li\’iatan, Nissan. “The Business Cycle Associated with Exchange- Rate Based Stabilizations.’* The World Bank Economic Review, 1992a, 6 pp 279-305. Kiguel. .MiguelA. and Lii’latan. Xissan, “Stopping Three Big Inflations.” mimeo, World Bank. 19Wlj Reinhart Carmen }1. and \;&gh. Carlos .4., “Intertenlporal Consumption Substitution and Inflation Stabilization: An Empirical Investigation.” mimeo IMF, Januar~’ 1993. Carlos A \ “Stopping High Inflation: An .Analytical overview,” IMF Stafl Papers, September 1992. 39:3 pp 626-695.

Table 1: Parameter values used in the simulations ! Parameter Value Description 0.5 fraction of GNP subject to cash constraint 0.’7,5 share of domestic currency in CES liquidity function 1.0 elasticity of currency substitution 0.4 speed of adjustment of inflation 10 duration of the program (quarters) 2.*5% real interest rate lo% long-run devaluation and money growth rates 1.0%1 devaluation and money growth rates during the transition 1.0 permanent (traded) income 1.0 full emplo}”rnentoutput in the home-good sector I

Figure 1: Exchange-Rate Based Stabilization: A Single-Curre~~ EcanornY Transition period: 10 quarters Long run devaluation rate: 10% Devaluation rate during transition: 1% Real interest rate: 1.5% consumption of traded goods consumption of home goods 1.04- I 1.05( # I r I I 1.02 - n ‘ - I i 0.98 1 1 t ().g~ -5 0 5 10 15 20 -5 0 5 10 15 20 . . real exchange rate 0“11~ 1.05 r I 1 1 / o.g~ -5 0 5 10 15 20 inflation and devaluation rates 0.15 ~ 1 1 T 0.1 , I ------------ 0.1 - /7 0.05- 0.05v Lt--_---/-:------------f--t o -5 0 5 10 15 20 inflation ---- devaluation 23

Figure 2: Exchange-Rate Based Stabilization Under Currency Substitution The Dynamics of consumption of Tradables and Real Balances for Different Values of the Elasticity of Substitution Between Domestic and Foreign Currencies, Il(l+rho) consumption of tradables consum~tion of tradables 0.98P I 1 1 1 1“02~ ‘*97-1+ I I I 1“ I I 0.961 i 0.95 H I 1 I l/(l+rho)= 1 l/(l+rho)=2.5 Domestic-to-Foreign-Currency Ratio 4.5 ,- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- , I I I I b 4 , , , 1 ! 8 I 1 , : ! I I 1 1 I I 3.5 t I ! I 1 I \ 1 1 : I 1 3 t I 2.5 I 1 1 1 1 t ! ; 1 , 1 I I t I I 1 I ! I I 2 t I ; 1 t I 1 1 : I : I I 1.5 ; t t I I ! I I 1 I I ! 1 , I 1 ! 0.5 4 I 1 \- - -- 1 : o ._-- 1 1 t ! -5 0 5 10 15 20 l/(l+rho)= 1 ---- l/(l+rho)=2.5

Figure 3: Comparin Money and Exchange-Rate Based Stabilization A Single-6 urrency Economy Money Based StabiliaztiOn ------ Exchange-Rate Based Stabilization See also headings on figures 1 and 2 consumption of traded goods consumption of home goods 1.04- , 1 1 1 1.05! I I I t I , I 1.02 - 1 ! I ( 1 0.98-: 1 1 1 1 I 0.?; ~ ; 1 1 I o 5 10 15 20 10 15 20 domestic real interest rate 0.1 ‘ r T 1 ), 0.05 - i;, ,. .. ‘. ‘. , IL ; o - ‘:,,’’”-””-=:,i ,. t = +; v -0.05-5 ~ 1 i 1 I 0.91 1 1 1 1 I 5 10 15 20 -5 0 5 10 15 20 . . 0 0.1 - 0.05- ()~ 0 1 1 1 I -5 0 5 10 15 20 -5 0 5 10 15 20

# Figure 4: Comparing Mone and Exchange-Rate Based Stabilization Under Currency 1ubstitution Money Based Stabiliaztion ------ Exchange-Rate Based Stabilization See also headings on figures 1 and 2 consumption of traded goods 1.02 1 T 1 1 :’-. ! , - - - 1 1 - - - - - - - 1 - - - ---------------- - - - -, 1 0.9“ 0.98 0.8- .. og(j~ “ -5 0 5 10 15 20 domestic real interest rate 0.2: 1 1 I I 1- ‘ 0.1 :, 8 ‘\ 0.9 -~--lQ--------- 0 “--”---- --’-: 0.8 1 [ I i ‘-‘ 07~ “-5 0 5 10 15 20 ‘“zI-. -- . --l 0 , . -- 0.1 ---- 1 /’ 0.1- -------------------“ 0 P“<- : 0.05- -0.1 t t--------------------t t 01 1 1 1 1 J -5 0 5 10 15 20

Figure 5: Reliquefication in a Single Currency EconOrnY Money Based Stabiliaztion ------ Exchange-Rate Based Stabilization ...x...x Money Based with InitiaI RELIQLJEF1cAnON See also headings on figures 1 and 2 consumption of traded goods consumption of home goods 1.04‘ 1 r 1.05 1 I I 1 :% t\ 1.02- 1? ‘ ‘ ~ \ I I o98‘~ ocJ5~ “ -5 0 5 10 15 20 o 5 10 15 20 domestic real interest rate real exchange rate 0.1i r I 1 1 1.05I 1 I r 1 I :, 0.05- IJ‘x~~ h, \ x * “ ‘x.x a o- i~’x- - . 0.95v -0.05-5 ~ 1 1 I 0.9- 1 t ! I 5 10 15 20 -5 0 5 10 15 20 inflation rate nominal interest rate 0.2- 1 1 1 0.15, I 1 1 1 1 0.15 “ )[ N- “ “ O. - O*1~J~~* 0.05- 0.05 “ N“v ww 1 0’ I ! 1 I ()~ -5 0 5 10 15 20 -5 0 5 10 15 20 2

Figure 6: Reliqueficaticm Under Currency Substitution Money Based Stabiliaztion ------ Exchange-Rate Based Stabilization ...x...x Money Based with Initial RELIQUEFICATION See also headings on figures 1 and 2 ‘ . consumption of home goods 1.1I 1 I 1 I I I #,--------------------, 1 1\ I 1- I I -\ 0.9- 0.98“ 0.8“ J+x-xii- 0.96-5 ~ j 1. 15 Z. real exchange rate domestic real interest rate 0.2 3 r 1 1*1~ “ “ “ J1 1- ‘ 0.1 “ ;, 0.9“ o’L“ “ “7 0.8- I [ 1 I I -oo1j- ~ ; 1. 15 ‘0 0.7[ -5 0 5 10 15 ‘0 . . 0*15~ inflation rate 0.2 1 i i I 0.1’‘“q J[ h \ 0.1- 0.05“ ,I--------------------i I I ()~ -5 0 5 1“ 15 ‘0 2

Figure 7 (a): Welfare Costs as a Function of T. ~=.75 0.4~ I I , - - - - - - - - - - - - -- ,- .. -- -- - -- -.-.. -... 0.3- ‘“’”-- ---- -.. ... -.. I -.. -...-.. 0.2~ “ .-. -- - -. - 1- O *J , I -0.2- 1 -0.3- -.i -0.4- ! 5~ , “o 5 10 15 20 25 30 35 40 45 50 ERB ----MB ..x..x.. MBR T (in quarters) 5 Figure 7(b): Welfare CoStsas a Function OfT. =1 0.16 , [ , 1 I - -- - - - - - -- I .-- . 0.14- -- .. .... , , 0.12- ; I -1 o 1 5 10 15 20 25 30 35 40 45 50 ERB ---- MB ..X..X..MBR T (in quarters) 29

Figure 8 (a): Welfare Costs as a Function of long-run inflation. 6 =.75 1.2i , , 1 , I 1 0.8 0.6 $ 0.4 0.2 x : 0 x 1 , ) 1 1 ! -0.20 5 10 15 20 25 30 35 40 45 50 ERB ---- MB ..X..X..MBR v Figure 8 (b): Welfare Costs as a Function long-run inflation. =1 1 r ... .... , , ! 0.9 . 0.8 0.7 I ““ / ,, 0.2I - , .“”4> ~ ~ O.i- I 1 i K 1 t I 0 ~ j 10 15 20 25 30 35 40 45 50 ERB ---- MB ..X.,X..MBR ~ti(7) o 30

# Figure 9: Welfaie Costs as a Function of the elasticity of currency substitution. =.75 Y 1, r r , , 1 . ----J ---------- ----- -z-- ---- 0.8 ---- ------ ---- 1 . - 1 ~. ..- 4 0.6r ”- I I 0.4- , .- 0.2 , .- 0 x x x x x x x x x x x x x x \: -0.2 -0.40 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ERB ----MB ..x..x..MBR elast. curr. subst.

Figure 10 (a): Welfare Costs as a Function of o . =.75 4.5r I 1 1 1 4 3.5 1 1 I , . 3 L 2.5 o , 2 I 4 1.5 -1 tI I 1 I \ \ ““ , ,, I 0.5-i “-. i I - - --------------------------J.------------ - - ._ _ _ -- _ ‘~ x x x . , . , . , x x x 1 , 1 i J -o.so~ 0.5 1 1.5 2 2.5 3 3.5 4 0 ERB ---- MB ..x..x.. MBR 0 Figure IO(b):Welfare Costs asa Functionof . =1 3.5 I 1 [ I I 3! ~ I -! 25.! ‘1 ,1 2~ I ] ! j 1.5‘, ,; I ! l! \ 1 i I 0.5~‘j, J ,( v------ 0 --—------ ------------ ------ ----- * ------- --_-_—- ---—w-----. -——--_—.—- I .— Oj 0.5 1 i5 2 2.5 3 3.5 4 ERB ----MB . MBR. X . .X 0

Figure 11: Inflation and Consumption of Hbrne Goods as a Function of theta ERB = Exchange-Rate Based Program MB = Money Based Program MBR Money Based with Initial Reliquefication ERB: inflation ERB: consumption of home goods 1 I 1.1; T I I o:n~~...,,,,,,,,;>;j-j 1 0 L - .-1 - - - - - - -- [ .‘ , 1 0.05 [ /’”’‘ I 1 ‘L-----=’ 0.8} \ \J/” ‘.. --- --------- 1 I I ...—.— 0 o.7~~——————— -5 0 7 10 15 20 -5 0 5 .10 15 20 theta= .04 ----- theta=.4 theta= .04 ----- theta =.4 MB: infIation MB: consumption of home goods 0.2 , -~ 1.1f I [ 0.1;— ,- -...--—-—------—-- 1: ~~------.-_-----,.---------------- ! ,“ , /-6 :7 ! (). ‘x < , 0.9i i ~’ -0.1 ; :‘ 0.8 y, “ ‘~1- I -0.2 1 1 (-)7~~ -5 0 5 10 15 io “-5 0 5 10 15 20 theta= .04 ----- theta =.4 theta= .04 ----- theta =.4 MBR: consumption of home goods 1.05; 1 1 T 1 J //;... 0.11—, ------------- \ - . 1 1 , 0.95 //: 4 0.05 - 0.9 H ; -- \ /“ j \ “L// 0 0.85-5 t 1 -5 0 5 10 15 20 5 10 15 20 0 theta= .04 ----- theta=.4 theta= .04 ----- theta =.4

International Finance Discussion Papers IFDP umbu mks A ut J996 539 C ot Welfar m eCostsand p theInitialDa hrey M i nUr ng aamr of A l T t eS e t mrPa nbp o ia o l lt ir i zi avea cirtyi 538 L M in I e Eno x f Emp el v c noga Jt i aEt Garytdeosioi on f I n Ft eMri r nna a a torm ni okc n iaalet 537 U M o Ee s x ta Ip tehis d c u t Aelnga rD B t nt eis ruon E of a M f P o Sf n o e eh ic t otsciac ry 536 R S eiwth D i Rg yt e lci n a hCht aHme ii omnig ns b t F e F Re t an I duwn i hen aete ond rven a al ti N o R n be o s r er o r w v ed es 535 T R a I m io Ep Fl xhe i s i ncdt n aEd e kMtsa Tr i rnnc o ns S L h f Me o s e c ro s xk o s: ic ns 534 C C u i E rr Mm ra A a e e s r r nJ hk gA Fcry ef eteisn E Tm r p e i a r t i Amc K Real nd nt 533 R P e i tha Lag o Ont Pi t o r e nC Erinc al ha ns T R of G ves.oC o u heg rl rr Jo eaHesRo np ci hy 1 99 532 A Pg r gan oth P r d r ue o c gd t uS ai cBav teust i iv ty of A g g r e g a Jo G tFe es 531 A C of T e E l fon Cra Js t a t a iau Jna c M riy padade t ar ie a t U S n t ind hea t te ed 530 M Io i nAd fue lls alt Gtir d Birnag or onli Ne R E ri 529 H y pa S e t r aCi bn i f l la ndia Mst Maii gatonar i on R e v i s i Lt Zh ed 528 On t I o th Cn oM v iv he eaa r G r Vtr.i St ase nc P Ao nr t a f l o y l s io is 527 I n Ct eo o trhmL n op Ua aet ri Peoi veHonnis al o ns L C in M aa o n u bf sa c E otr tsVul r raiz in P a r l d f ce tedI q no Frt ua De p ieer oirPse n Dssnisas a oct its ani uesspe ovni I n Ft eS i24r B non G a aottooth Fi vn oR eneSacr oaepl r deey,s sneo W a DC 2s h 0i n 5g t o5 n, 1. 3

International Finance Discussion Papers I F DP I 1 99 5 U n I c nCe asrn26th hUtt a nr o i iu Dna iWqmtH uy,eceen ennt of N E q Mu a ai canl r i o b e shNric S iZo un mo: mi M a cE r xo e a c o m n op m lic es 5 T Ia i ntrh 1 fg2R5 C l9e he at a9 Rti cl T Fing0icls eonnerne J L Wo i na 5 E Dc e ano Iv 2n4 ent el ro og empMun FmeIy icr e a tnt i on E Mc oo bn io lm i ic ty 5 H C A uac Fc 23 puan e mm iru l Mt uatrnaat F. Iyitigun ail li “o n, G A R r e o- A w n a t l hy: s is 5 E R a x R e a th L22cEtn o th isue ndon Alr Dss B ns ru T M r A E ae GAa r Aps k RpuDa e PCSriry t:Ho-a 5 T M T r Moa 21nei M she cn m ehi M s aeyC xsi arn iop oisn A Ml We ej 5 W is M P o E h 20nfo f e le etn Joc Amiac t riy ve Al D B ru 5 C B Ie n dI n 19eaann pt fe nr l Pdnk aLeal ran t ouc ioe, G in T r rE a c o n o s wn i No tthSh m i at ioen 5 A l A t p t Re pE18r rR nx o a eca at Hata JhciEd vhe an es a R I R n T U etaan T ndDeh t r h aWl reeseR oMwe il rest 5 P m rc o aano th1m7i pord em utk Vi i Gphact t et i on p u n on i rc n es ve r i e tv s a omPit cei Lm nd ra e toyu ennt f U m a in r un. f d a uc om t Ss. u t r ir ng ie 5 B D i M l s fo S 1te6 r o o t i bl hJ ckuFa v otd ed in M u El tc Mi o - n c o oo um dRan e Tr t t reyl r ic 5 S u s p o i op n15l uf y l- r sa P ictL drae i oeus on O c o Eu n t CPD r Sw hii es 5 C F fa th C l p 1i4oT ir iru a n tg nN t Ssohmal hrtiat tiie S T a E h Eom vpe i i nmdoe r d i rye ca nc 5 B L a Ee Aa c13n i J co d tnanndk Ail i oD B pa nvgmi ru it D “ FF Ci a not th cR anid tnt e crSo BiiKacer tebal s”ut D o w n t u r n? 3