UNIVERSITY OF CALIFORNIA Los Angeles
Stabilization Programs, Monetary Policy and Exchange Rate Movements in Emerging Markets Economies
A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy
in Economics
Alexandre Soriano Alencar
Trang 2UMI Number: 3121215
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Trang 3The dissertation of Alexandre Soriano Alencar is approved Amartya Lahiri ⁄L——— a7 Andrew Atkeson Hans Shollhammer — “TẢ —
Carlos Vegh(Ø ommittee Chair
University of California, Los Angeles 2004
Trang 4DEDICATION
Trang 5
1 Temporary Exchange Rate-Based Stabilization Programs Under
Asset Market Segmentation i
1.1 Introduction 1
1.2 Exchange Rate-Based Stabilization: Examples and Empirical Regularities 7
1.3 Model il
1.3.1 Households’ problem 11
13.2 Government 17
1.3.3 Equilibrium conditions 18
1.3.4 Solution of the model 20
1.4 Conclusion 4]
Tables and Figures 44
Bibliography 52
2 Monetary Policy with Dollarized Liabilities 56
Trang 62.3 Equilibrium
2.4 Unexpected Shocks and Monetary Policy
2.4.1 Increase in borrowing restrictions (decrease in 1) 2.4.2 Monetary policy
2.5 Conclusion Bibliography
3 Exchange Rate Overshooting: the Role of Trade Frictions 3.1 Introduction 3.2 Model 3.2.1 Households 3.2.2 Firms 3.2.3 Government 3.2.4 Equilibrium conditions 3.2.5 Solution of the model 3.3 Conclusion
Trang 7
List Chapter 1
Table 1.1 — Stabillzation programs
Table 1.2 — Inflation tax redistribution and welfare changes
Vi
Trang 8Chapter Í
Figure 1.1 — Type B households’ consumption path
Figure 1.2 — Type NB households’ consumption path when endowment is constant
Figure 1.3 — Type NB households’ consumption path when endowment increases at T
Figure 1.4 — Change in welfare for type NB Figure 1.5 —- Change in welfare for type B
Figure 1.6 — Change in the present value of consumption for type NB Figure 1.7 — Change in the present value of consumption for type B Figure 1.8 — Rate of devaluation after T
Chapter 3
Figure 3.1 — Effects of a negative terms of trade shock when trade and credit frictions are present
Figure 3.2 ~ Effects of a negative terms of trade shock when only trade frictions are present
Trang 9ACKNOWLEDGEMENTS
I am grateful to Carlos Vegh for his support and guidance ] am also indebted to Amartya Lahiri, Gustavo Adler and David Rahman for their helpful advice and suggestions
Trang 10August 5, 1971 1995 1995 1997 1997-1998 1997-1998 1999 1999 2000-2003 2002 VITA
Born, Belo Horizonte, MG, Brazil Trainee
Promon Engenharia, Campinas, SP, Brazil
B.S., Electric Engineering
State University of Campinas, Campinas, SP, Brazil Teaching Assistant
Department of Economics
Pontifical Catholic University, Rio de Janeiro, RJ, Brazil Research Assistant
Department of Economics
Pontifical Catholic University, Rio de Janeiro, RJ, Brazil Lecturer
Department of Economics
Pontifical Catholic University, Rio de Janeiro, RJ, Brazil M A., Economics
Pontifical Catholic University, Rio de Janeiro, RJ, Brazil
Equities Analyst
Banco BBM, Rio de Janeiro, RJ, Brazil
Teaching Fellow/Associate/Assistant Department of Economics
University of California, Los Angeles
Candidate of Philosophy, Economics University of California, Los Angeles
PUBLICATIONS
Alencar, A S (2002) “Testing the CCAPM Through Volatility Frontiers and the Euler Equation” (in Portuguese), in M Bonomo, ed., Financas
Trang 11ABSTRACT OF THE DISSERTATION
Stabilization Programs, Monetary Policy and Exchange Rate Movements in Emerging Markets Economies
by
Alexandre Soriano Alencar Doctor of Philosophy in Economics University of California, Los Angeles, 2004
Professor Carlos Vegh, Committee Chair
This dissertation examines issues on monetary policy and exchange rate behavior in developing countries The first chapter studies welfare consequences of temporary exchange rate-based stabilization programs The second chapter studies how currency mismatch between revenues arid Habilities may affect optimal monetary policy Chapter three shows how a negative terms of trade shock may generate an overshooting of the exchange rate when the economy faces trade and financial
Trang 12Chapter 1 analyses the welfare consequences of temporary exchange rate-based stabilization programs The assumption that only a fraction of households participate in asset market transactions differentiates this analysis from previous work Households with access to the assets markets are better able to protect themselves from the changes in the inflation rate, at the cost of distorting their consumption path However, the temporary reduction in the inflation tax is equivalent to a government loan that will be repaid later in the form of a higher seigniorage
Therefore, households without access to the assets markets, when credit constrained,
may also be able to improve their welfare This chapter attempts to show that, contrary to the predictions of traditional literature, temporary exchange rate-based stabilization programs may end up benefiting households
Chapter 2 studies how private dollarized liabilities may affect monetary policy Private firms in developing countries commonly contract debt denominated in foreign currency However, these countries face frequent and strong financial shocks, which generate pressures for a high depreciation of the exchange rate Firms with a currency mismatch between revenues and liabilities could face liquidity problems In this chapter, we are able to show that a tight monetary policy could alleviate firms facing financial distress due to their dollarized debts, since it would appreciate the exchange rate The cost would be an initial contraction However, a healthier balance sheet would allow higher investments and higher future growth
Trang 13rate Therefore, when the economy also faces financial constraints, a negative terms of trade shock would generate an initial sharp fall on imports, which is driven by an overshooting of the exchange rate
Trang 14Temporary Exchange Rate-
Stabilization Programs Under Asset Market Segmentation
1.1 Introduction
Trang 15as-set traders, it may allow a smoother, and consequently better, consuraption path for
credit constrained households
Exchange rate-based stabilization programs have been extensively studied in the last decades Rodriguez (1982), contradicting the traditional literature at the time, was the first to show that a credible decline in the devaluation rate can originate an initial expansion Assuming adaptive expectations a la Cagan for the inflation rate - and taking into consideration the lower nominal interest rate that, by the interest parity condition, follows a lower devaluation rate -, he pointed out that
real interest rates decrease This interest rate decrease leads to an initial boost in demand However, since the inflation inertia leads to an overvaluation of the real
exchange rate, an eventual correction is necessary and the initial expansion is followed by a contraction in demand Rodriguez’s analysis was the first of many analyses to consider inflation inertia as a central justifying argument for the main regularities of exchange rate-based stabilization programs, such as an overvaluation of the real exchange rate, a initial boom in consumption and activity followed by a bust, and the usual ’temporariness” of the programs itself
Trang 16The result is a lower consumption rate once the program is discontinued One feature of these models is the lack of credibility itself validates the boom-bust cycle Even if the government would be able to keep inflation under control, the initial higher
consumption would imply an eventual lower consumption
A common and clear conclusion of the literature is that these temporary stabi- lization programs decrease welfare, with the exception of very few models that rely on additional supply side effects' Even if a balance of payment crisis does not take place at the moment of the programs’ discontinuity, households’ consumption path is distorted Unrestricted access to the asset markets by all households is an important assumption for this conclusion It is only with assets market access that households are able to follow an optimal consumption path in first place This access also allows households to trade assets by/for currency and then model their consumption path
according to the opportunity cost of consumption
However, these papers are ignoring the important fact that a large fraction of developing countries’ populations lack the access to the asset markets’ Only house-
'There is one exception to this literature that does not rely on supply side channels Alfaro (1999), making the conjecture that part of the population is endowed with tradable goods while the other part is endowed with nontradable goods, was able to show that a temporary stabilization program could make the owners of the nontradable endowment better off
Trang 17hoids with access to the assets markets are able to trade assets to increase their
consumption at the moment the stabilization program is announced For example,
with access to the international bonds market, households can borrow and exchange
bonds by domestic currency at the central bank The central bank must buy and sell
reserves (bonds) at the target exchange rate to control the devaluation rate With these higher cash balances, households thus increase their consumption while the program is being implemented Households later exchange excess cash balances by reserves at the central bank and pay back their debt just before the program is dis- continued The payment of inflation tax is consequently reduced The incurred cost is a distortion in the consumption path, which is no longer smooth
Households lacking access to the bonds market are not able to trade these financial
assets and thus cannot hold more cash balances to increase their consumption once
the program is launched Likewise, these households cannot get rid of excess cash balances, which will be heavily taxed by inflation once the program is abandoned
Hence, since the first group is able to better protect itself from the changes in the inflation rate, there will be an inflation tax redistribution The burden of this tax
will decrease for the first group and, consequently, increase for the second
open economy context, these papers help to resolve some puzzles in international finance, such as volatile and persistent real exchange rate movements, and the excess volatility of nominal exchange
rates,
Trang 18However, it is possible for households without access to the bonds market to benefit
from the temporary stabilization program, if the households were credit constrained For example, an expected increase in income would result in a willingness to borrow
to allow a smoother consumption path These households, however, are not able to borrow from financial markets But the government is temporarily decreasing the
inflation tax through the stabilization program, increasing households’ net disposable
income These households are then abie to start accumulating cash balances and
consuming more Once the program is terminated, inflation tax increases However,
since consumers’ income has already increased during the program, the government has effectively extended a loan to these households that will be repaid in the form of a higher inflation tax
As it is already apparent from the previous explanation, the degree of market segmentation seems to play a crucial role in the welfare analysis of the economy When all households have access to asset markets, as in standard models, there is no inflation tax redistribution and welfare decreases due to the distortion in the consumption path When there is no access to assets markets, but households are credit constrained, all households benefit from the program® The question is, then, what happens in the more realistic intermediate case, where only a fraction of the population is able to trade in asset markets This present work shows that the smaller
Trang 19
the fraction of the population that can trade in asset, markets, the bigger the benefits - or the smaller the costs - for both types of households The final result could be higher welfare for all households Some other factors addressed in this paper are how the elasticity of intertemporal substitution and other parameters affect the results
The rest of the chapter is organized as follows Section 1.2 lists the main exchange
rate based stabilization programs implemented in Latin America in the last 40 years
Trang 201.2 Exchange Ì ased Stabilization: Examples and Empirical Regularities
Exchange rate-based stabilization programs have been vastly documented and stud- ied in the literature’ In the attempt to fight inflation, these programs have been implemented by policy makers for decades, with different degrees of success They
have been used to overcome from moderate levels of inflation to hyperinflations The
main interest of this paper is the analysis of chronic inflation cases Latin America
constitutes a very rich source of case studies where these programs have been ap- plied During the 1960s, for example, Argentina, Brazil and Uruguay implemented programs that relied on fixed exchange rates - or with periodic devaluations in the Brazilian case - and different types of income policies With the exception of Brazil, the lower inflation was not sustained, mainly due to the lack of fiscal discipline More orthodox programs that relied on a policy of pre-announced devaluation schedules and no price or wage controls were implemented during the 1970s Argentina, Chile and Uruguay followed these programs However, even with fiscal adjustments in Chile and Uruguay, these stabilization attempts ended in an exchange and financial crisis The real appreciation of the exchange rate, due to the low convergence of inflation to the rate of devaluation, is attributed to be the main source of failure for these
Trang 21
programs
More heterodox programs are implemented im mid 1980s Argentina, Brazil and Mexico used wage and price controls to overcome the inertial component of inflation in the attempt to avoid the overvaluation of the exchange rate The programs in Argentina and Brazil soon failed due to a lack of fiscal control Finally, during the 1990s, Argentina, Brazil and Uruguay again implement more orthodox exchange rate based stabilization programs And, once again, lack of fiscal control and overvaluation of the exchange rate end up contributing to the collapse of these programs
Table 1.1 shows some major stabilization programs in Latin America in the last
forty years As we can see, they have shown to be sustainable only temporarily The exact reasons for the systematic failure of the programs are still object of discussion The real appreciation of the exchange rate is pointed out as one of the main reasons
Once the program is implemented, the exchange rate is kept fixed or devalued ata
pre-specified rate, but an inflationary process, though smaller, is still in place in these economies, causing an appreciation of the real exchange rate This overvaluation of
the currency contributes strongly for a deterioration of the trade and current account,
which proves to be unsustainable at the end The other main explanation for the failure of these programs is the lack of fiscal adjustment Only the programs that had made some fiscal adjustments were able to keep inflation at lower rates after their abandonment
Trang 22rate-based temporary stabilization programs The first one that stands out is a boom
in consumption and real activity This behavior is even more interesting when we compare it with the contraction in consumption and real activity that usually follows amoney based program This boom in consumption leads to another fact, which is the current account and trade balance deterioration Other main empirical regularities we should point out are: a slow convergence of the inflation rate to the rate of
devaluation; a sustained real appreciation of the domestic currency; an increase in
real wages measured in units of the tradable goods; and a large fiscal adjustment in
temporarily successful programs
Our goal is to build up a model that could not only match all these facts®, but could also explain the popular support for these temporary programs In order to achieve this objective, we work with the more realistic assumption that a significant fraction of the population does not have complete access to the asset markets In fact, many of the households in these developing countries do not even have access to a banking account And it is known that the main source of loans in most developing countries
is the banking sector For example, in Brazil, there were 55 millions checking accounts
in 2000° Given that many of these accounts belong to firms and many of its citizens
5 We are not going to explicitly model all the above empirical regularities in our research However, with smail changes in our model, which would not affect its main results, it is possible to incorporated ail fo them For example, Calvo (1986), and Calvo and Vegh (1999) built up very similar models to ours that incorporate a bigger range of empirical regularities
Trang 23have more than two or three accounts, a big fraction of its 176 million inhabitants does not have one Even if you look at the United States, where asset markets are much bigger, access to these markets are not a reality for many individuals In 1989, 59 percent of its citizens did not hold any interest bearing assets’ And 25 percent did not even have a checking account
As we have already said, adding a segmented markets framework to traditional models may change completely their predictions on the welfare consequences of tem- porary programs And it may help to explain one more fact, although we are not going to model it explicitly During the program, the boom in the consumption of durable goods is much bigger than the overall boom in consumption One possible explanation for this behavior is the fact that part of the population is credit constrained Durable goods usually are relatively more expensive and many times households rely on credit lines to buy them (for example, through many installments) Once a stabilization is
in motion, it is easier for the population - without access to the asset markets - to
save enough cash balances to buy the durable goods*
"Interest bearing assets encompass money market accounts, certificate of deposit, bonds, mutual funds and equities Source: Mulligan and Sala-i-Martin (2000) Data from the Survey of Consumer Finance
Trang 241.3 iodel
Consider a small open economy perfectly integrated with the rest of the world in the
goods market This economy is populated by a continuum of households of mass 1,
which are blessed with perfect foresight There exists only one tradable and non- storable good, whose price in terms of the foreign currency is assumed to be constant Since there is free movement of the good, purchasing power parity holds Perfect capital mobility also prevails, but only a fraction \ of the domestic population has
access to the asset markets Interest parity, together with the Fischer equation for
the rest of the world, implies that
?¿ =T +ế¡ (1.1)
where i; is the domestic nominal interest rate, r is the rate of return in the interna-
tionally traded bonds, and ¢, is the devaluation rate of the domestic currency
Let’s explain in more details the role of each agent and how this economy works
1.3.1 Households’ problem
Trang 25or lend internationally traded bonds at the international interest rate r? The other type, called type NB, does not have access to the bonds market Their only asset is
domestic cash balances
Each agent 7 (7 € B, NB) maximizes her lifetime utility function given by
Maz | u(c])e" tát (1.2)
0
where c; is consumption at time t by an individual of type j; 0<@<1 is the constant
rate of time preference; and the utility function u(.) is assumed to be increasing, twice continuously differentiable, and strictly concave
Households are subject to a cash-in-advance (CIA) constraint given by
IV Đ +, (1.3)
where mi is the amount of real cash balances held by individual j at time t m2 is,
Mỹ T £
therefore, given by m? = upre, where MM? is the amount of nominal cash balances, 5,
is the nominal exchange rate!’, and P?* is the price of one unit of the consumption 3
°OFf course, they can do so as long as they satisfy their intertemporal budget constraint, which will be defined in this section
10Measured as the domestic currency value of one dollar, our international currency
Trang 26good measured in units of the international currency As we said, this price is assumed
to be constant
Type B households
Depending on their types, consumers face different budget constraints Let’s de- note the amount of the internationally traded bond held by one type B individual
as bP bP is already measured in terms of the tradable good 78 is the amount
of government transfers for a type B consumer, again also measured in terms of the
consumption good Finally, y? is the amount of the good the household has as endow- ment each period The flow budget constraint of a representative type B consumer
can, therefore, be written as
BBs B_.B_;.B
a, =Ta, +y + Tị — G — im, (1.4)
where a? = mP + b?
Trang 27me = ack Vt (1.5)
Integrating forward the flow budget constraint, applying the transversality condi- tion iim đ2e~”!dt = 0 and taking into consideration the fact that the CIA constraint —0o binds, we get her intertemporal budget constraint
[ (1+ aiePe "dt = a? + | (yP +7? edt (1.6)
0 0
As expected, the present value of the real cost of consumption - after we take into
consideration the cost of holding cash balances - is equal to present value of house- holds’ assets, plus the present value of their endowment and government transfers
Finally, maximizing the lifetime utility of a type B individual (1.2), subjected to the above budget constraint, we get her optimality condition
ul(eP) = AF (1 + ai) (1.7)
where \? is the constant Lagrangian multiplier of the intertemporal budget con- straint We have also assumed in the above derivation that the rate of intertemporal
Trang 28discount Ø is equal to the international interest rate r This assumption allows a flat path for consumption when the nominal interest rate is constant Therefore, for a constant nominal interest rate, during periods of a lower endowment, households
borrow in the international markets or use their stock of international bonds to keep their consumption level When the endowment is high, they pay back their debts and save for the low endowment periods This feature is important, as we will see, since temporary stabilization plans distort their consumption path
Type NB households
Type NB individuals do not have access to the asset markets This means that they are not allowed to borrow And, if they want to save, they will have to do so through domestic cash balances Their flow budget constraint is given by
NB NB NB NB - NB
Thị =U TT, ~& erm, (1.8)
NB and 7" are already measured in terms of the consumption good
where m
Trang 29attain ourselves to the case in which their CIA constraint binds!!
NB NB
mi? = ac Ví (1.9)
Given this assumption, their real cash balances path follows the following first order differential equation
_NB ; ; 1 ;
m, =yNP+7N8 - c +eumV? (1.10)
This equation shows clearly how dependent is consumption on the path of the endowment and on the monetary policy of the government For example, for a given rate of devaluation, consumers cannot borrow to consume more today even when they
expect a big increase in their disposable income
11 We can build up the hamiltonian and get the first order conditions for type NB maximization: He= ule) + Ag lye + 74 — ce ~ cerns) + pe, frre — xe]
FOC:
ul (cz) = At + Op, (a)
m > ace py > 0 iby [TM — œœ] = O (b) Ae = [B+ ee] At — be (c)
Me = Ye + Te — Ce Ee (d)
Then, with the following assumption Ty wae Vf,Vas > †
it is easy to verify that m, = ac; is part of the solution of the system given by the FOCs
Trang 301.3.2 Government
The government issues domestic money +2 holds international reserves - foreign bonds - and makes lump sum transfers to the households Its flow budget constraint can be
written as
Ah, = “Me if teJ
„ (1.11)
hy = hy bm + em —T ¡Ƒ tự j
where J is a finite set, h are the international reserves, m represents the real cash
balances in the economy and 7 are the transfers The variables are denoted in per
capita terms This equation basically says that the rate of accumulation of reserves
by the government is given by the difference between its revenues - interest on current reserves plus revenues from money creation - and its costs - the transfers to house- holds Taking into account the government transversality condition jim he"'dt = 0,
—>©O
equation (1.11) gives us the government intertemporal budget constraint
oo lo)
| Tre "tị = hạ — Tạ + [ (izm,)e7 "dt (1.12)
0 0
Trang 31We will assume that the government has a fiscal constraint, that is, r will be fixed
along the model!* Hence, the monetary authority has to adjust its policy to satisfy
the government budget constraint If it temporarily reduces seigniorage, a higher
inflation tax will have to be collected in the future, as it is clear from the government intertemporal budget constraint
1.3.3 Equilibrium conditions
First of all, since r is denoted in per capita terms, we have that
t= dt? 4 (1—A)jrX8 (1.13)
And from the money market equilibrium condition
mm = Am? + (1~ A)mN® (1.14)
l?Tn the complete markets case, the results are the same if the government transfers could be
adjusted to the seigniorage revenue During the stabilization program, the transfers would be re- duced Once this is abandoned, they would increase back again Here, we don’t want the transfers to the type NB households to be reduced, since we want to explore the fact that they may be credit constrained and the stabilization program increases the net disposable income while being imple mented At the same time, we don’t want any wealth transfers from one group to the other due to changes in the government transfers Therefore, although a fixed 7 is not strictly necessary for our main results, it will make them clearer
Trang 32‘he current account for the economy follows from the households and government
flow constraints - equations (1.4), (1.10) and (1.11) -, taking into account (1.13) and `
the equilibrium in the money market (1.14)
hụ + b, = (hy + bQ) + yS— AeP — (1— AjeNF (1.15) Here, 6; is the per capita amount of international bonds held by households There-
fore, b; = AbP For simplicity, we have assumed that y® = yN® = y, As expected,
asset accumulation will be given by the interest in the current assets, plus the endow-
ment of the economy, minus the total consumption of households Integrating forward and using the transversality conditions for the government and type B households, we get the economy intertemporal budget constraint
af cPeTdt + (1 — » | fe" dt = hy +.by + [ ye dt (1.16)
0 0 0
Trang 331.3.4 Selution of the Model
Initially, we solve the model for the case in which all households have access to the bonds market In this case, we are going to get the known result that a temporary exchange rate-based stabilization reduces welfare, since it distorts households’ con-
sumption path With this result in mind, we then analyze the segmented markets case Once part of the population does not have access to the asset markets, a tem-
porary stabilization program may affect positively the welfare of different segments of society As discussed in the Introduction, this is possible due to two channels The first one is based on the fact that part of the population - type NB consumers - may be credit constraint In this case, a temporary program would reduce the inflation tax initially, allowing the credit constrained households to consume more The second channel is an inflation tax redistribution that takes place with the program Since type B households are able to better adjust their consumption path when facing dif- ferent effective consumption costs - different nominal interest rates -, they are able to transfer part of their inflation tax burden to the rest of the population
Non-segmented markets case
In this section, we assume that all households have access to the bonds market That
is, A = 1 and we only have type B consumers Along the paper, we will keep the assumption that the government faces a fiscal constraint That is, it cannot decrease
Trang 34is expenditures, the transfers to households, even temporarily!”,
Let’s suppose that the initial devaluation rate - which in our model is equivalent to the inflation rate - is set at a constant value that satisfies the government intertem- poral budget constraint (1.12) If, together with this budget constraint, we take into account the households’ first order condition (1.7) and the economy’s resource constraint (1.16), this constant rate of devaluation must be equal to
G — ho
65 = — © lhe + bp +Y) (1.17)
where G= [(° re-"'dt and Y = [>° ye "dt
From the interest parity condition (1.1), we get that the nominal interest rate is constant Therefore, consumption is also constant, as can be verified by the house- holds’ first order condition (1.7) Then, using the economy’s resource constraint, we get that
eP =r(hạ + bạ + Y}) (1.18)
Equation (1.17) is reflecting the fact that the present value of the inflation tax must
Trang 35
be equal to the present value of the government net deficit - its expenditures minus its
reserves’ And equation (1.18) is just telling us that (constant) consumption must
be equal to each period return on the present value of this economy wealth
Now, suppose the government implements an exchange rate based stabilization program In our model, this program will consist of a lower devaluation rate €1(< £g)
Given the fiscal constraint of the government, it is easy to see that this policy is not
sustainable’ The stabilization program will be temporary We make the natural as-
sumption that the initial rate of devaluation is set such that seigniorage falls during the program!® More specifically, we assume that i,m, falls while the program is not discontinued Since the government has to satisfy its budget constraint (1.12), ism: will eventually have to increase to higher values than the pre-plan ones More intu- itively, during this stabilization period, the monetary authority has to use its reserves
14 Equation (1.17), together with equation (1.18) and the cash in advance constraint (1.5), can be
written as 69" = G — hg
15Suppose it were From the first order condition of consumer maximization (1.7), consumption should be constant Then, from the resource constraint of the economy (1.16), this consumption should not change from its initial level c? Consequently, seigniorage would fall - i,m, would fall This means that it is impossible to satisfy the government intertemporal budget constraint (1.12)
\8Tf the government is at the right side of the Lafer curve, we should expect this decrease in seignoriage with a lower inflation (devaluation) rate - and an increase once the devaluation rate is set at a higher level’ That is what we observe when countries decrease their inflation rates Given the parameters of the model, the chosen devaluation rate ¢ should be such that
dim ‘ i
“a, >0 (a)
In the present paper, we work with the following constant elasticity of substitution form for the utility function
yank
c, 7
ules) = TT
Since we want a strictly concave utility function, we set the intertemporal elasticity of substitution o > 0 For o <1, (a) is always satisfied And for o > 1, we can use the first order condition and the CIA to show that we have to guarantee that « < wert —r
X
Trang 36- or borrow from households - to keep the desired lower devaluation rate!’ In order to fiance its expenditures, the government prints more money than it is consistent
with the lower devaluation rate Households get rid off these excess cash balances
by buying reserves from the government at the target exchange rate Since these re-
serves were a source of revenue, through their interest payments, the government will need even more seigniorage after the program is abandoned Therefore, ¢ will have to increase and so will the inflation tax!® We also assume that this new devaluation
rate will be constant from the day of the abandonment on!’
In our perfect foresight environment, households know exactly the moment T in
17 We can rewrite the government flow constraint as
hy = rhe — rm time + ms — 7
In the initial steady-state equilibrium, with the constant devaluation rate ¢9, we have that
h=O= rho — rmo + igrng — T
During the implementation of the exchange rate based stabilization program, the rate of devalu-
ation €4 is set at a constant lower level By the first order condition, this means that m, = my is
also constant during the plan At t = 0, when the program starts, households change bonds by cash balances:
Aho, = Amo+
We can, therefore, rewrite the government flow constraint as
ho = rho + Aho) — r(mo + Amo.) +0+iym,-7
which implies
hạ = nhọ — r?ma -È 111m — T
Since we have assumed that im < igmo, ho < 0 Togheter with the fact that the fow constraint of the government is an unstable differential equation, we have that the government continuously looses reserves during the implementation of the program
18We could associate the eventual abandonment of the stabilization program with a BOP crisis The assumptions in the present model are similar to the ones in Krugman (1979) and Flood and Garber (1984), (1996) models of BOP crises due to fiscal constraints We could, therefore, think that, once the reserves reach a certain threshold, a crisis takes place with the government abandoning its stabilization plan and leting the exchange rate float
Trang 37which the government will abandon the stabilization program From the consumers’ frst order condition (1.7) and the assumption of a strictly concave utility function, we see that consumption will be higher while the program is not discontinued, compared with its level after T By the economy resource constraint (1.16), this means that
consumption will increase once the plan is implemented, and it will drop below its
original level cf after its abandonment, as it is shown in F Igure 1.129
In summary, when the government implements its temporary stabilization pro- gram, setting a lower devaluation rate ¢, households take advantage of the lower
nominal interest rate - lower opportunity cost of consumption - and consume more
Once the program is discontinued and a higher devaluation rate > is set to satisfy the government’s budget constraint, they start consuming less This temporary sta- bilization decreases households’ welfare, since it distorts their consumption path To show this more clearly, let’s define
Ve fPulaje fd and As a We can write
Ov Ly Bey (Ee PP) re) Aen ev At
ak = U(C)DA + U'(€2) BRAS
20By the economy resource constraint fo be dt =W
where W = ho +89 + Io aye "tái
With the first order condition, we get that c& =rW
We can, therefore, write that
c[(1~ e ?) +cÿ(e~7?) = cỡ
Trang 38Using the economy resource constraint (1.16), we get that
gE (4 _ evr) = —yxerr
Plugging this expression in the previous one, we get that
để = (w(oa) —w (en [8=]
Using the first order condition (1.7) and the economy resource constraint (1.16), we have already shown that „ > 0 and 22 <0 And since u'(c,) > u! (ce), we have BẠ that = < 0, that is, welfare decreases with the temporary stabilization program Segmenied markets
In this section, we analyze the economy when it is populated by both types of agents,
that is, A < 1 Note that type NB consumption path will depend not only on the
government monetary policy, but also on the exogenous endowment path This is very intuitive, since this group is not able to borrow during moments in which its endowment is low
In order to get more intuition, we will first start with a qualitative analysis for the constant endowment path case”! Assuming we are along a stationary equilibrium,
type NB flow constraint (1.10) gives us
21 For simplicity, we will assume that type NB cash-in-advance constraint binds When the endow- ment path is constant, this assumption only holds if the elasticity of intertemporal substitution is sufficiently big Otherwise, households could start saving - using their cash balances for this purpose - during the temporary stabilization program For this constant endowment path case, we will go only through a qualitative analysis Latter, when we assume a future increase in the endowment,
Trang 39; NB
cXP Y +7 ° 1+ aéq
and the first order condition for type B individuals (1.7), together with their intertem- poral budget constraint (1.6), gives us
Be rb +y+r78
2 1.2
0 1 + aeg ( 0)
Note that, as we have already mentioned, we assume that government’s transfers
to households are fixed From the above steady-state relations, the economy resource constraint (1.16) and equation (1.13), we get the devaluation rate ¢) Since we have a constant consumption path for both groups, this rate of devaluation is the same as before, given by (1.17)
Again, the government is not able to reduce the rate of devaluation permanently We have already showed that, if the government is at the right side of the Lafer curve, seigniorage coming from type B households decreases while the program is not discontinued Now, using the flow constraint for type NB individuals (1.10), we also
get that Sữa ^^ ã— >0, V?, Inflation tax paid by these consumers also decreases when
??Erom type NB flow constraint, in the stationary equilibrium with a constant rate of devaluation
€, we have that
Trang 40the nominal interest rate is set at a lower level Hence, since by the government intertemporal budget constraint (1.12), the present value of the inflation tax cannot be reduced, a permanent decrease in the devaluation rate is not possible If the
government implements an exchange rate-based stabilization program without fiscal
reforms, this program is bounded to fail Eventually the government will have to increase the devaluation rate And in order to satisfy its budget constraint, the rate
of devaluation will have to be set at an even higher level than the original one”
The temporary stabilization program has an intertemporal effect on the consump- tion profile of both groups For the individuals that are able to trade bonds, this effect is the same as before They borrow to consume more while the program is not dis- continued; and they consume less once this is abandoned, as it is clear from their first order condition
For the individuals without access to the asset markets, we also observe an increase in consumption while the program is not discontinued But this increase is smooth Since they cannot borrow, households can only take advantage of the smaller inflation
= -W+T
mss = lfate
which we can rewrite as
im = +
#m =U-+T + — 1/2)
Since, for any reasonable values of the parainetbers, 1 /œ > r, whenever the governimnent decreases £,
imgg also decreases Besides, since m > 0 during the pian, ¿my < iM (< íomŠ s) forO<t<T
We have that 2 > 0,