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THESIS

(mm)

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1293 01789 4001

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

ESSAYS ON THE EFFECTS OF CHANGES IN THE
DOMESTIC RISK ON SMALL OPEN ECONOMIES
presented by

Ramén E. Pineda S.

has been accepted towards fulfillment
of the requirements for

Ph 11 degree in MS.

ail/4,4 my“

 

Major professor

 

Date /l//(/387

MS U 1': an Affirmative Action/Equal Opportunity Institution 0- 12771

PLACE iN RETURN BOX
to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

DATE DUE

MTE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1M WM“

ESSAYS ON THE EFFECTS OF CHANGES IN THE DOMESTIC RISK
ON SMALL OPEN ECONOMIES

By

Ramon E. Pineda S.

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Economics

1998

II
open ecm
economy

changes ir
risk lllLlUL
dei‘filOpini:
agents' an
general eql
mean presc
CEUSQS Cam
instantancoi
the dOmem
deri‘allte 0
bCCaUsQ SUM
assumptions

In Ch

lHflHIlOn Talc

ABSTRACT

ESSAYS ON THE EFFECTS OF CHANGES IN THE DOMESTIC RISK
ON SMALL OPEN ECONOMIES

By

Ramon E. Pineda S.

This dissertation examine the effects of changes in the domestic risk on small
open economies. In Chapter 1 we investigate how resident investors in a small open
economy adjust their holdings of domestic and foreign assets (portfolios), in response to
changes in the internal risk. A general wisdom maintains that an increase in the domestic
risk induces the native capital to flee out especially, but not exclusively, of the
developing economies. In this chapter, we establish sufficient conditions (restrictions on
agents’ attitude toward risk) under which this claim is true both in a partial and in a
general equilibrium level. We find that an increase in the domestic risk (modeled as a
mean preserving spread in the domestic bond’s real return distribution) unambiguously
causes capital flight if agents’ preferences show either: i) a positive third derivative of the
instantaneous utility function, relative risk aversion no larger than one and increasing in
the domestic return, and non-decreasing absolute risk aversion; or ii) a null third
derivative of the instantaneous utility function. This outcome is somewhat controversial
because sufficient conditions for the conventional wisdom imply very restrictive sets of
assumptions about agents’ attitude toward risk.

In Chapter 2 we evaluate how an increase in domestic risk affects the equilibrium

inflation rate in a small open economy. An increase in the domestic risk (modeled as a

mean pit

reallocatii

 

adjustmcn
expenditur
the domes

expansion

 

inflation. V
consequcm
aVersion u.
one. If I}:
intematim-

IlSk InduC.

mean preserving spread in domestic bond’s nominal return distribution) induces a
reallocation of domestic agents’ portfolios between foreign and domestic bonds. The
adjustment in agents’ portfolios affects domestic government’s ability to finance its
expenditure stream, since domestic investors could be willing to reduce their holdings of
the domestic bond. This situation makes the domestic government rely more on the
expansion of money supply as a source of fiscal revenue, and this could lead to higher
inflation. We find that a sufficient condition to unambiguously determine the inflationary
consequences of an increase in the domestic risk if we use a constant relative risk
aversion utility function is to assume a coefficient of relative risk aversion no larger than
one. If this is the case, and the domestic government has limited access to the
international financial markets and a given expenditure stream an increase in the domestic

risk induces a rise in the equilibrium inflation rate of a small open economy.

To Adriana Bermudez
for all the wonderful things that you have done to me

and
To Rosa, Ramon,

Scarlet, Jose’ and Adriana Pineda
for your love, encouragement and understanding.

iv

 

 

like to 1
Rouena
For all t
pancnce.

I ;
some oft}
likcio than
my studies
Jeffrey “'0‘
Carl Dax'ids

My 1
“ODOmisL l
Amuedo‘ ”c

SOO'VUDQ Jam.

I‘Voul

ACKNOWLEDGMENTS

Many people had made possible the completion of this dissertation and I would
like to thank some of them briefly. First, my most sincere thanks to Gerhard Glomm,
Rowena Pecchenino and Robert Rasche who have been the members of my committee.
For all the time they put into this project, their friendship, constant encouragement,
patience, guidance and advice, I am truly grateful.

I am deeply indebted to Jack Meyer and Corinne Krupp who took time to read
some of the essays in this dissertation, and provided very useful comments. I would also
like to thank the faculty at the Department of Economics for their help and support during
my studies at Michigan State University. In particular, I want to thank John Strauss,
Jeffrey Wooldridge, Peter Schmidt, Steve Matusz, Charles Ballard, Richard Baillie and
Carl Davidson for the knowledge that I received from them.

My fellow graduate students have played at major role in my formation as an
economist. I especially would like to thank Pablo Fajnzylber, Yali Molina, Catalina
Amuedo, Heather Bednarek, Min Chang, Bonnie Anderson, Hirokatsu Asano and
Sooyung Jang.

I would also like to thank my friends at the Economics Institute, Woo Jung,
Emmanuel Skoufias, Jeffrey Zax, Hamid Baghestani, Charles Becker and Maureen
Kilkenny, without them things would have been a lot harder in graduate school.

I want to thank Leopoldo Lopez Gil and George McCandless, because it was their

idea that has made all this possible. I want to acknowledge the financial support of “La

 

 

 

Fundacni
C ientific:
family. th

I a
haVe signi.

the Mcdin.

 

thank the \

The

been a gun:

have been is

and Rflmtin
execPlion. ’1
M.“ sisters z
easier and h
Pineda JULI]
tendemcSS‘ u

the best in II):

I “nu

Diego RCStui

F undacién Gran Mariscal de Ayacucho” and “El Consejo Nacional de Investigaciones
Cientificas y Tecnolégicas”. I am truly grateful to these institutions, and to the Barreto
family, their help and trust have been critical during all this time.

I am indebted to the Venezuelan and Latin American communities in MSU; they
have significantly improved my standard of living. I especially want to thank the Mendez,
the Medina, the F ajnzylber, the Sorzano and the Uzcategui families. I would also like to
thank the volleyball group at Spartan Village. What a nice group of people!

The greatest thanks, however, go to my family. My wife Adriana Bermudez has
been a constant source of inspiration and encouragement. Her dedication and support
have been great. For all of this and more, she is “la mujer de mi vida”. My parents, Rosa
and Ramén Pineda, have always helped and supported me in everything; this was not the
exception. Their love, patience and trust are things that I would never be able to repay.
My sisters and brother, Adriana, Scarlet and Jose’ Pineda, have always made my life
easier and happier. It is impossible to have better siblings. My grandparents Eumelia
Pineda, Juana and Claudio Salazar, have always encouraged me, with love and
tenderness, to do my best. My aunts, uncles, cousins. and friends have always offered me
the best in them.

I would also like to thank those “brothers” that life has given me, Omar Bello,
Diego Restuccia, Giovanni Di Placido, Rodolfo Mendez, Simén Lamar, Alexander
Elbittar and Eduard Sanchez. All of them, and their families, have played a significant

role in my life.

vi

i

' 1A"-

13!

 

".‘w-'v.: ,, I“

i s'lr‘. ,
mp} -

.4. ”WI: m-‘~._- _-,.

 

[0 have
longer.
Jacinta'

theulifl

I would also like to thank my in-laws for their support and trust. It is not possible
to have better in-laws. Finally, I want to remember a very special group people that are no
longer among us “la abuelita” Maria Figueroa, Angel Octavio and Octavio Colina, “la tia
Jacinta”, Yolanda Hernandez and Virginia Milano. Their love and support throughout

their lifetime were truly invaluable.

vii

 

 

 

LIST OF

LISI OF

C HAPTE1

 

CAPITAL
The Role 0

1.1. Introdt
1.1. Genet:
1.3. Capita.
1.4. Equnm
1.5. Risk A
1‘6' Capital
1.7. Some I
REFERENI
APPENDI)

TABLE OF CONTENTS

CHAPTER 1

CAPITAL FLIGHT AND CHANGES IN DOMESTIC RISK

The Role ongents’ Preferencesl
1.1.Introduction1
1.2. General Characteristics ofthe Economy7
1.3. Capital Flows and Changes in Risk12
1.4. Economy Wide Effects (General Equilibrium Effects)..........................................23
1.5. Risk Aversion (A D1gressron)30
1.6. Capital Outflows (Two Numerical Examples) ............................................... 32
1.7. Some Final Comments38
REFERENCES ...................................................................................... 41
APPENDIX 1.A ..................................................................................... 52

viii

CHAPT
CHANG
ECONO)

2.1. lntroc

 

 

3.2. Genet
3.3. Effect:

2.4. Chang

 

3.5. Final Ii

REFEREN.

 

 

APPENDI)

CHAPTER2

CHANGES IN DOMESTIC RISK AND INFLATION IN SMALL OPEN

2.1. Introduction69
2.2. General Characteristics ofthe Economy76
2.3. Effects ofan Increase in Risk (Partial Equilibrium)............................. . . . . . . . . . . . . .....90
2.4. Changes in Domestic Risk and Inflation (General Equilibrium Effects) ............... 97
2.5. Final Remarkle4

 

 

 

.
l
{pH-vs: ' "-""

 

Table I
Table 1.

Table 1..

Table 1.4
Table 1.5
Table 1.6 -
Table 1.7 -
Table 1.8 -
Table 1.9 - ’

Table 2.1 - 1

LIST OF TABLES

Table 1.1 - Capital Flight: Modified-World Bank Measure

Table 1.2 - Stock of Capital Flight: Morgan Guaranty Trust’s Measure ...................

Table 1.3 - Estimates of Capital Flight Stocks (1970-87) for Some Developing

Economies using Different Methodologies

Table 1.4 - Estimates of Coefficient ofRelative Risk Aversion

Table 1.5 - Marginal Expected Utility ofthe Risky Asset

Table 1.6 - Indirect Effect on Savings Mean Preserving Spread .

Table 1.7 - TPEE on Savings Mean Preserving Spread

Table 1.8 - Total PEE on Domestic Assets Mean Preserving Spread ........................

Table 1.9 - Total PEE on Foreign Assets Mean Preserving Spread
Table 2.1 - Partial Equilibrium Effects of a MP8 in Domestic Bond’s Nominal Return

Distribution

...44

.45

..46

.46

...60

...62

..63

.64

..66

..95

 

 

 

 

Figure 1.

Figure 1..

Figure 1.4
Figure 1.5
Figure 1.6-
Figure 1.7 -
Figure 2.1 -

Fligure 2.3 -

LIST OF FIGURES

Figure 1.1 - Effects of a First Degree Stochastic Deterioration: Constant Absolute Risk
Aversion 47

Figure 1.2 - Effects of a Mean Preserving Spread: Constant Absolute Risk Aversion. . .48

Figure 1.3 - Effects of a First Degree Stochastic Deterioration: Constant Relative Risk

Aversion 49

Figure 1.4 - Effects of a Mean Preserving Spread: Constant Relative Risk Aversion ....50

Figure 1.5 - Estimates of Capital Flight (1983) As Percentage of GDP ...................... 51
Figure 1.6 - First Degree Stochastic Deterioration Going from F to G ...................... 68
Figure 1.7 - Mean Preserving Spread Going from F to G ....................................... 68
Figure 2.1 - Average Inflation and Political Risk 42 Countries (1985-1995) .............. 109
Figure 2.2 - Average Inflation and Political Risk 112 Countries (1973-1981) ............ 110

xi

 

 

 

 

1.1. him
A g
capital to 71
this chapte
€C0n0m}- 2
IESPODSC I
(restriction
LCS
{that} Ilces
dECadeS Si,
economics
Until 1991
represent 1 1
41.12%...0 in E u“

Chapter 1

Capital Flight and

Changes in The Domestic Risk
The Role of Agents’ Preferences

1.1. Introduction

A general wisdom maintains that an increase in the domestic risk induces resident
capital to flee especially, but not exclusively, from developing economies. The purpose of
this chapter is twofold. First to determine how domestic investors in a small open
economy adjust their holdings of domestic and foreign assets (their portfolios) in
response to changes in domestic risk. Second, to establish sufficient conditions
(restrictions on agents’ preferences) that validates the conventional wisdom.

Lessard and Williamson (1987) define capital flight as: “...the resident capital
(that) flees because of the perception of abnormal risk at home...”. During the last two
decades significant amounts of resources have departed suddenly from developing
economies under the form of capital flight. Claessens and Naude’ (1993) document that
until 1991 the cumulative value of the resources that have migrated as capital flight
represent 118% of the GDP in North Africa and Middle East, 85% in Sub-Saharan Africa,
40% in Europe and Central Asia, 35% in Latin American and the Caribbean and 15% for

East Asia and the Pacific.l

 

' See Tables 1.1-1.3 for additional estimates of capital flight.

 

 

—_'

 

{actor
studic
(1986)
Naude’
among 1
the gmu
etc. not
because It
On
an operatic
alternatives
direct app“

Operational c

’ Recently i

Instability in

flight Over I

 

Since the debt crisis in the early 1980’s several works have tried to determine
factors that explain episodes of capital flight in developing countries.2 Some of these
studies --Khan and U1 Haque (1987), Cuddington (1986 and 1987), Cumby and Levich
(1986), Dooley (1986), Lessard and Williamson (1987), Padilla (1991), Claessens and
Naudé (1993), Kant (1996) and Schineller (1997)-- are empirical. A common feature
among these empirical studies is the use of variables such as the interest rate differential,
the growth of domestic output, the domestic inflation rate, and internal fiscal imbalances,
etc., not only because their relevance in the process of resource allocation, but also
because researchers want to utilize them as proxies for changes in domestic risk.3

One of the first problems that any empirical study in this area must face is to find
an operational (empirical) definition of capital flight. The literature offers several
alternatives that are based on two estimation approaches: the balance of payments or the
direct approach, and the residual or the indirect approach.4 After the empirical or

operational definition is selected country-specific or regional time series of capital flight

 

2 Recently, interest in the analysis of capital flight has increased considerably due to the
instability in the international markets caused by the Mexican crisis of 1994-95 and the
Asian crisis that started during 1997.

3 For instance, Dooley (1986) considers the rate of return variables as proxies for different
perceptions of financial and expropriation risk.

4 As its name may suggest, the balance of payments or direct methodology uses the
capital account of the balance of payments to directly determine estimates of capital
flight. Cuddington (1986) uses this methodology and defines as capital flight the short-
terrn speculative outflows. The residual approach «introduced by the World Bank
(1985)-- tries to determine the changes in a country’s holdings of foreign assets. This
method is called indirect or residual because both the uses and the sources of foreign
assets must be determined before we can estimate the amount of capital flight. See
Cumby and Levich (1986) and Kant (1996) for a good summary of different definitions
of capital flight. See also Cumby and Levich (1986), Padilla (1991) and Claessens and
Naudé (1993) that construct estimations of capital flight applying several definitions of
capital flight over a common data set.

 

 

are crca
inappro
changes .
results. TL
and Willi.
which ‘ev
present.
0th
between Ch
Open econm
domestic fir
assets. In 011'

may IndUCC E

FunhennOre. \

{Tommie

are created. Nevertheless, this way of constructing capital flight time series may be
inappropriate because researchers apply their operational definitions to periods in which
changes in domestic risk may not have taken place, casting doubt on the validity of the
results. Thus, we think that to stay close to the (generally accepted) definition of Lessard
and Williamson the operational definition must be estimated only in those periods in
which ‘evidence’ (or at least a strong presumption) of changes in the domestic risk are
present.

Other studies --Khan and U1 Haque (1985) [KU]-- try to model the connection
between changes in the distribution of domestic return and capital outflows in a small
open economy.5 They show that when the probability that the government may confiscate
domestic firms goes up, domestic investors tend to increase their holdings of foreign
assets. In other words, they find that an increase in (what they call) the expropriation risk
may induce an increase in the amount of domestic capital sent abroad.

The present study is in some sense an extension of Khan and U1 Haque (1985).6
As they do, we study how individuals (investors) that maximize expected-utility adjust
their portfolios as a result of changes in the distribution of domestic asset returns.
Furthermore, we analyze how those reactions may induce capital outflow in a small open

economy.

 

5 The literature of currencies crises —-that started with the works of Krugman (1979) and
Obstfeld (1986)-- is also closely related with the study of capital flight.

6 However Khan and U1 Haque (1985) address issues that are outside the scope of the
present study. For instance, they address topics such as expropriation and debt
repudiation.

 

11131 “R

 

consum p

consumpt

receive nt

 

assume th;

 

domestic er
market. anc
15 known (1
”SALV- We a
dOmESIic QC
dilmE‘SIIC {jg

This
domesfic ret
mOde] the C:
treated its em
[1131 are OUISi
We Consider ‘

Wham-C ( FE

We assume that the domestic economy is inhabited by a large number of agents
that live for two periods. Agents maximize expected lifetime utility by choosing a
consumption stream. In the first period of their life, each agent receives an endowment of
consumption goods that are traded in a perfectly competitive. international market. Agents
receive no endowment in the second period.

Agents save part of their endowments to finance second period consumption. We
assume that agents use two saving alternatives: foreign and domestic bonds. Since the
domestic economy is small, the return on foreign bonds is determined in the international
market, and it is taken as given by the domestic investors. Furthermore, we assume that it
is known with certainty. The other kind of asset in this economy, domestic bonds, is
risky. We assume that agents know the domestic bond’s return distribution function. The
domestic economy also has a government that collects taxes from and sells bonds to the
domestic agents.

This is the context in which we study the effects of changes in the distribution of
domestic returns on domestic investors’ equilibrium portfolio allocations. We do not
model the causes of the assumed changes in the domestic return distribution; they are
treated as exogenous. With this exogeneity assumption we try to illustrate changes in risk
that are outside the control of (are not affected by the actions of ) the domestic agents.7
We consider two forms of transformation of the domestic return distribution: first degree

stochastic (FDS) and mean preserving (MP) changes. By using F DS changes we focus on

 

7 The causes of the change in the domestic retum’s distribution may be induced by
instability either in the international (contagion eflect) or the domestic financial markets;
all that matter is that domestic agents, for some reason, perceive an exogenous change in
the distribution of domestic returns.

 

 

 

the effe

distribu‘

Ir
distributit
transfomt;
sense.’ Fur
least based
as capital Ill

To (1
literature of
3 Partial equ
ini‘estors: ii) ;
and [he domes

DUring

 

 

the effects on agents’ (and the economy’s) equilibrium outcomes of alterations in the
distribution of domestic returns that involve changes in its expected value. Notice that
KU’s expropriation risk is a particular form of FDS transformation in which agents face
changes in the expected value of the domestic return.

In contrast to KU, we also consider mean preserving transformations in the
distribution of the domestic return. We think that it is also important to assume MP
transformations because they represent changes in risk in a Rothschild and Stiglitz (1970)
sense.8 Furthermore, this assumption seems to be more appropriate than F DS changes, at
least based on Lessard and Williamson’s definition, if we want to interpret capital flows
as capital flight (flows induced by changes in domestic risk).

To do the comparative statics analysis we use standard methodology in the
literature of decision making under uncertainty. We carry out the analysis at two levels: i)
a partial equilibrium level in which we evaluate only the behavior (of the domestic
investors; ii) a general equilibrium level where the interactions between the private agents
and the domestic government are considered.9

During the investigation we ask to what extent can we use assumptions about
domestic agents’ attitudes toward risk to establish sufficient conditions such that changes

in domestic risk unambiguously induce capital outflows. We find that:

 

8 FDS changes are used to illustrate situations in which we compare higher/better
outcomes with lower/worse ones; MP transformations allow us to focus in situations in
which the trade-off between risk and expected return is not present since by definition in
MP transformations the expected value of the risky return is held constant.

9 Capital movements may produce several effects on the domestic economy but for the
purpose of this paper the most (the only) relevant one is that it has on the government’s
financial process. See Cardoso and Helwege (1995) for a complete summary of the cost
associated with capital flight.

 

 

rcIaIin
FDS d
holding
increase

2
reduction
and an int
absolute ri
of relative
return: or ii
be Inlcrprct
This finding
trisdum 1m}
preferences.
CUmpaj-au' \‘e

Stfindard ass u r

1) If agents’ preferences exhibit risk aversion together with a coefficient of
relative risk aversion no larger than one, and nondecreasing absolute risk aversion, then a
F DS deterioration of the distribution of domestic returns induces a reduction in the
holdings of the domestic asset, an increase in the holdings of the foreign asset and an
increase in total savings.

2) A mean preserving spread of the distribution of domestic returns causes a
reduction in the holdings of domestic bonds, an increase in the holdings of foreign assets
and an increase in total savings if preferences show either: i) risk aversion, nondecreasing
absolute risk aversion, a positive third derivative of the utility function, and a coefficient
of relative risk aversion no larger than one which is also increasing in the domestic
return; or ii) a null third derivative of the utility function. In this case capital outflows can
be interpreted as flight because the outflows are induced by changes in domestic risk.
This finding is somewhat controversial since sufficient conditions for the conventional
wisdom imply a very specific and restrictive sets of assumptions about agents’
preferences. In particular, it is troublesome that we cannot obtain unambiguous
comparative static results when domestic investors’ attitudes toward risk exhibit the

standard assumption of decreasing absolute risk aversion.

The rest of the chapter has the following structure. In part II we describe the
characteristics of the economy and define a competitive equilibrium. In part III we
evaluate how changes in the distribution of the domestic bond return affect the behavior
of the domestic investors. In this part we establish some results at a partial equilibrium

level. Part IV contemplates the analysis at a general equilibrium level. Part V contains a

._..~““ ’

 

‘ ._w,__._____ i..?

 

duress”
numeric
50me [rd
use two
ConSIanl
FDS and
depending

final Com”

 

1.2. Gene.
The
of identical
The domesti
foreign asset
domestic age
period consur
utility. The c
insets. The f0
knoun “111] C,
an uncertain

E (H
“éLDOUS and

digression concerning some of the assumptions used in this chapter. Part VI contains two
numerical examples. Here we ask what is the relationship between capital outflows and
some traditional measures of domestic agents’ degree of risk aversion? To answer this we
use two very common utility functions, constant absolute risk aversion (CARA) and
constant relative risk aversion (CRRA) utility functions. We find that in cases of both
F DS and MP changes, the smaller the coefficient of risk aversion (relative or absolute
depending on the case) the larger the capital outflows. Lastly, in part VII we make some

final comments.

1.2. General Characteristics of the Economy

The following is the setup of a small open economy inhabited by a large number
of identical agents. We assume that both the economy and agents live for two periods.
The domestic agents engage in trade of consumption goods and financial assets with the
foreign assets at prices determined in the international markets. In the first period, the
domestic agents receive endowments of consumption goods. Then, they choose their first
period consumption and the amount of savings such that they maximize expected lifetime
utility. The domestic agents could use two saving alternatives, foreign and domestic
assets. The foreign asset’s real return is determined in the international markets, and it is
known with certainty by the domestic agents. On the other hand, the domestic asset has
an uncertain return, but agents know its distribution function. This distribution is

exogenous and therefore taken as given.

 

 

 

 

1.2.1.1)

1
m0 Pcrl
Agents;/
1) (
“'th (i 1

times 35 ’3

pel'lod Coll:

 

 

random \‘ZIF
At t1
of consump
Individuals .
consumptinr
domestic (a)
consumption
has a known
ébsume that I
qudntities are

good. that is al

1.2.1. Private Agents
In this economy there exist a large number of identical individuals that live for
two periods. Each agent maximizes the expected lifetime utility from consumption.

Agents’ preferences are represented by:
1) UtC.i+r E{U[521}
where U is a strictly increasing, strictly concave, continuous and differentiable (as many

times as needed) utility function. Here ,6 is a discount factor with fle(0,1). CI is first

period consumption and C2 is consumption in period two. The tilde indicates that 52 is a

random variable. Finally, E represents the expectation operator.

At the beginning of period one each individual receives an endowment of 8 units

of consumption goods. In period one, agents pay lump sum taxes, 2', to the government.
Individuals do not receive a goods endowment in the second period, so to finance their
consumption in the second period they must save. Agents can use foreign (m) or/and

domestic (a) assets to save. The foreign assets yield a certain real net return of r units of

consumption goods per unit invested. The domestic asset’s net yield )7 is random, and
has a known cumulative distribution function (cdi), F'0 To simplify notation, let us
assume that population size N is equal to one and therefore, aggregate and per capita
quantities are the same. Notice that all the variables are in terms of the consumption

good, that is all variables are in real terms.

 

'0 The support of the random variable 3? is the interval [x0, x1]. In what follows we use
capital letters to denote cumulative distribution functions F, and small letters to denote
densities f

 

 

 

maximize (

Let

 

Mime Let u '

Dr X) _ '
titreont‘lrtmnS

pendlx 1

1.2.1.1. Households Budget Constraints

It follows that the first period household budget constraint (HBC) is given by
F=C, +a+m+r or Y=C, +a+m, where Y: 17-7. The second period HBC is

given by C2 : a(1+3c’)+m(1+r).

1.2.1.2. Households Maximization Problem
Then, given preferences (1) and the HBCS, households choose C, , C2 , a and m to
maximize (1) subject to their HBCs.

Let S denote total savings, then S=a+m and therefore, 2) Y = C, + S and 3)

C, = a('f - r) + S (1 + r) . Thus, we can write the maximization problem in terms of a and

A-

S as:

Max U[Y— S]+,6.j‘{U[a(x — r)+ S(l +r)]}f(.r)dx-

{.S'. a}

The first order conditions (FOC’S) of this maximization problem are given by:

FOC’s: 4) VS: —U'[Y — S]+ flj{U'[a(x — r) + S(1 + r)](1+ r)}f(x)dx = 0

5) Va: ,ij'wx — r) + 5(1+ r)](x — r)}f(x)dx = 0.

From now on we focus only on interior solutions in which a, S and m are all

positive. Let a° , S ' and m’be the values of a, S and m that satisfy the F OC’s. the second

order conditions (SOC’s), and are all positive.ll

 

" See Appendix 1.A.

 

 

1.2.2. (

first per .
individu.
(a) 10 ll.
gmemmc
1n
matches 11
realized do

by 31:01 I r:

 

 

 

 

re"~lUircment.

endowment .

1.2.3. DOmes

“0ng
expeCted lll‘et
Lhat lhe markc

Lites. and the ,

pCFIO(

1.2.2. Government

The domestic economy has a public sector that lives for two periods. During the
first period the government levies lump sum taxes on, and sells bonds to the domestic
individuals. The government uses the resources collected through taxation (r) and bonds
(a) to finance a given level of first period expenditure, g. Hence, the first period
government budget constraint is g=a+ r.

In the second period the government receives an endowment A that exactly
matches the requirements to repay its debt namely, a(l+x). Here x e[x,_,,x,] is the
realized domestic return. Thus, the second period government budget constraint is given
by A=a(1+x). Given these assumptions the government is concerned about its financial
requirements only in the first period. In the second period the government uses the

endowment A to repay all its debt.‘2

1.2.3. Domestic Bonds Market

Households choose the desired level of domestic assets so as to maximize their
expected lifetime utility. On the other hand, the government supplies enough bonds such
that the market clears given the distribution of domestic return and the levels of income,

taxes, and the foreign return.

 

‘2 We make this assumption to ensure that the domestic government can repay its debt in
the second period.

 

 

 

 

1.2.4. 1

them on

1.2.5. (it
\\

total cons
Therefore.

For the Sc

 

 

 

Value of 10

aVailable for

1.2.4. Foreign Bonds Market

Domestic private agents determine their desired foreign bond purchases, and buy

them on the international markets.

1.2.5. Goods Market Equilibrium
We define an equilibrium in the consumption good market as a situation in which
total consumption of both private and public sectors is equal to the total supply of goods.

Therefore, in period one we have: C, +g= 17— (a + m+ r) + (a + r) or C, + g: F— m.

For the second period, C, + a(1+ x) = a(1+ x) + m(l + r) + A or C, = m(1+ r) + A.
Using these conditions, we have that if the goods markets are in equilibrium, the present
value of total domestic consumption is equal to the present value of all resources

available for the domestic economy to consume.

5‘ . )1
C,+g+ 2 =Y+ .
(1+r) (1+r)

 

 

1.2.6. Competitive Equilibrium

A

We define a competitive equilibrium as a sequence { (7,, C,, a, m, Y, g, r, A}
such as, given the foreign return (r) and the domestic (risky) return (3? ), households solve
their maximization problem, government budget constraints (GBC) are satisfied, and both

goods and asset markets are in equilibrium.

 

 

 

1.3. C

asset.S r
vve C0115
ThCn' \u
P05511313 '

cOmIlarc I

 

1.3.1. Cha‘
Let
random varl

FIG] be the .
1

HF}3

Let I ‘1
respectively. 1

how the dome“

 

asset‘s return d7
distribution G c‘

' A
‘ v

S ' 1
r .u, are differ‘

 

 

1.3. Capital Flows and Changes in Risk

In this section we try to determine how changes in the distribution of the domestic
asset’s return affect private agents’ positions in both foreign and domestic assets. First,
we consider first degree stochastic changes in the distribution of the domestic return.
Then, we look at the effects of mean preserving transformations of F. To learn about the
possible effects of the assumed changes in the distribution of the domestic return, we

compare the equilibrium outcomes of two economies in which this is the only difference.

1.3.1. Changes in the Distribution of Domestic Returns

Let F and G be two different cumulative distribution functions (cdf) of the
random variable 2' . Define V[F] as the expected utility when the cdf is F. Likewise, let
V[ G] be the expected utility under G. Therefore, V[ F] and V[ G] are given by

V[F] _=_ U[C, 1+ dbl/[5, ]} f(x)dx and, V1012 UIC. l +fl ”1152 ]}g(X)dX.

x0 x0
Let {S ',a'} and {S,ci} denote the arguments that maximize V[F] and V[G],

respectively. Then if we compare the values of {S ’,a' } and {S,ci } we can determine
how the domestic private agents adjust portfolios in response to changes in the domestic

asset’s return distribution. We know that if the expected marginal utility of savings under

distribution G evaluated at { S i ,a' }, V_,.[G]l J]. , is different from zero, then { S ' .a' }and

.S' ‘

{S,ci } are different. However, if V,,.[G]|S.,u. is zero, then {S .,a' } and {S,d } are equal.

 

 

fir [

1n thus

to estab

the effec
into the t
\tith ttvn
the exoge
11011....8
variables...
immediate

distribution

 

obtain the ir,
mar $111111 ext
Change- This

at the Optimal

13.1.1. First 1
(.111 en ,
fim deere

6 810,

mm“ Under /

 

r ..
. mic/x, for al

 

 

In those cases where VJG] and Vu[G]

 

do not vanish, their signs may allow us

.S".u‘ S'Jl‘

to establish the relationships that exist between a’ and ti , and between S. and S .
Following Eeckhoudt, Meyer and Ormiston (1997) [EMO], we try to disentangle
the effects of changes in the distribution of domestic return on agents’ optimal choices
into the direct and the indirect effects. As in the present paper, EMO analyze a problem
with two endogenous variables in which agents face a change in the distribution of one of
the exogenous variables of the problem. They determine the direct effect by looking at
how “...a parameter shift alters the marginal expected utility for each of the decision
variables...” while holding everything else constant. This effect shows the most
immediate response of a decision variable to changes in the exogenous variables’
distribution without considering other possible consequences. On the other hand, EMO
obtain the indirect eflect by looking at how changes in the exogenous variables affect the
marginal expected utility of one of the decision variables once we allow the other to
change. This effect reflects that there may exist interactions between the choice variables

at the optimal levels since agents set them simultaneously.

1.3.1.1. First Degree Stochastic Changes

Given F and G, we say that the distribution F dominates the distribution G in a
first degree stochastic sense if for all the agents with positive U’, the expected utility is
greater under F than under G. A necessary and sufficient condition for this is that

F(X)SG(x) for all the x in the domain.l3

 

'3 See Eeckhoudt and Gollier (1995)-

13

 

 

 

Thus. 1
proposi
distribut

determir.

and 8.

Lemma 1
”3331115. 1

Proof} See

”Optimum
If agents . Dr,

110 larger that

Prtlgf: SEC ‘4‘]

1.3.1.1.]' 1),,”e
DE

%

[rider Fisk ave
l'a]

”9 OfS Lines 1

 

Let us assume that F and G are the initial and the new distribution, respectively.
Thus, going from F to G implies a first degree stochastic deterioration. Lemma 1 and
proposition 2 help us to establish how first degree stochastic (FDS) changes in x’s
distribution affect agents’ marginal expected utility. These results are used later to
determine the signs of the direct and the indirect effects of a FDS deterioration on both a

and S.

Lemma 1:
If agents’ preferences exhibit risk aversion, then VS [G]|S, 0, >0.

Proofi See Appendix 1A..

Proposition 2:
If agents’ preferences exhibit risk aversion and have a coefficient of relative risk aversion

<0.

.8" ,u‘

 

no larger than one for all x, then V, [G]

Proof: See Appendix 1.A. I

1.3.1.1.1. Direct Effect (DE)

DE Total Savings:

 

 

Under risk aversion V,.[G] ,>0, and to restore the equilibrium (V_,.[G] =0) the

 

.8",u S’JI’

value of S goes up since V5,, is negative. thus lemma 1 shows that a FDS deterioration in

14

 

 

Proposition 3.

a

l.

the di
dislike
DE DO.
3." PM
one. the
equilibrit
T1
asset’s rct
Similarly.
{direct effct
Notice that
direct effecz
“Ithour fur-1h
T0 es;
relationsh,p n:
1001; a, hou- Ch

prOPOSJUOn hCl

 

l If pFCFErchC

a. ell

the distribution of the risky asset’s return induces an increase in total savings if agents
dislike risk, i.e., S’ < S .

DE Domestic Assets:

 

By proposition 2 we know that if the coefficient of relative risk aversion is no larger than

one, then Va [G]

 

<0. Since V0,, is negative, a must go down to restore the

S‘Jl’
equilibrium; therefore, a. > d .

Thus, as a consequence of the direct effect of a F DS deterioration in the domestic
asset’s return, the level of total savings tends to increase when agents are risk averse.
Similarly, a FDS deterioration induces a reduction in the holdings of the domestic asset
(direct effect) in cases where the coefficient of relative risk aversion is no larger than one.
Notice that if the coefficient of relative risk aversion is larger than one the sign of the
direct effect on the holdings of risky assets is ambiguous. and we cannot determine it
without further information.

To establish the signs of the indirect effects we need to find out what kind of
relationship may exist between a and S at their optimal levels. In other words, we need to
look at how changes in a affect the expected marginal utility of S and vice versa. The next

proposition helps us to determine this relationship.

Proposition 3:
a) If preferences are characterized by decreasing absolute risk aversion (DARA), then

.>0.

(1.8

 

 

Proof? 5

act as C1

preferencr

1.3.1.1.2. 1
1E Total Sa‘
Proposition
holdings of t}
one. B); propr
level off “he,
0.1M NARA

Preferences pre

Other.

 

    

Old/nos of l

   

b) If preferences are characterized by increasing absolute risk aversion (IARA), then
V. <0.
c) If preferences are characterized by constant absolute risk aversion (CARA), then
VA. =0.

1

Proof: See Appendix LA. I

Thus, proposition 3 tells us that the holdings of the risky asset and total savings
act as complements, substitutes or independent goods at equilibrium when agents’

preferences display decreasing, increasing or constant absolute risk aversion.

1.3.1.1.2. Indirect Effect (IE)

IE Total Savings:

 

Proposition 2 suggests that a FDS deterioration of x’s cdf induces a reduction in the
holdings of the domestic asset if the coefficient of relative risk aversion is no larger than
one. By proposition 3 the reduction in a causes a negative (positive) effect on the desired
level of S when a and S act as complements (substitutes), i.e., when preferences exhibit
DARA (IARA). Finally, changes in a do not cause indirect effects on savings if
preferences present CARA since the optimal levels of a and S are independent of each
other.

IE Holdings of Risky Assets:

 

Lemma 1 establishes that a FDS deterioration causes an increase in the level of savings as

long as agents dislike risk. Thus, it follows that this effect on savings induces a reaction

16

 

 

declfli“

pre fer" ’ 1"

to dCIC’ml’
,ambles .;
that this is
of the econ.
b}: E110 sin

The

 

domestic bot

Corollary IA
11 agents pret
at'ersion no la
deterioration oi

Proof: See :1 PI”

Notice 11

Cl
.111. even for L

 

 

 

on the holdings of the risky asset of the same (opposite) sign when preferences have
decreasing (increasing) absolute risk aversion. Nevertheless, the effect is null when

preferences have CARA.

1.3.1.1.3. Total Partial Equilibrium Effect (TPEE)

The TPEEs combine the information about both the direct and the indirect effects
to determine how the changes in the exogenous variables affect each one of the decision
variables at its optimum level. We call it the total partial equilibrium effect to emphasize
that this is the total effect at the individual level, given that we have not allowed the rest
of the economy to adjust its behavior. Notice that the TPEE is the total efect as defined
by EMO since they evaluate the effects at the individual level.

The following corollaries establish the sign of the TPEEs of FDS changes in

domestic bonds’ return distribution on agents’ savings and portfolio mix.

Corollary 1.A: (TPEE on Savings)
If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS

deterioration of x’s cdf induces an increase in total savings.

Proof: See Appendix LA. I

Notice that the TPEE on savings is positive if preferences show risk aversion and

CARA, even for cases when relative risk aversion is larger than one.

_._~..n r‘ “its. \

 

 

Coroll

1

1f agen

aversior

 

 

 

deteriora

Prim/f St

C orollarj
If agents'
aversion n

deterioratio

PTO/5 See

 

1.3.1.2. .‘ICa,
Novv 1
all

.OCQIIOns an

Presen'ing [A],

 

Corollary LB: (TPEE on Domestic Assets)
If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS

deterioration of x’s cdf induces a reduction in the holdings of domestic assets.

Proof: See Appendix 1.A. I

Corollary 1.C: (TPEE on Foreign Assets)
If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS

deterioration of x’s cdf induces an increase in the holdings of foreign assets.

Proof See Appendix LA. I

1.3.1.2. Mean Preserving Transformations
Now let us consider how agents’ optimal choices of savings and portfolio
allocations are affected when the distribution of domestic returns experiences a mean

preserving [MP] transformation.

18

 

 

 

transfc
in risk.

transt’or

F 01
determine ;
dOmestic re

eSlabIISI] the,“

13.2.1. Dire,

PTOPOsirion 4
If I is eith.

Under 0 mama

PFOOf SEE ,App

Proposition 5,

 

lite expecled ma

T 6‘ ”Dim.

At least since Rothschild and Stiglitz (1970 and 1971) [RS], mean preserving
transformations have been considered a reasonable and convenient way to model changes
in risk. A random variable a“ experiences a MP spread transformation if its initial cdf F is

transformed into a new cdf G such that the next two conditions hold:

a) ]G(x)dx 2 ]F(x)dx Vxe[x0,x,] and,

b) xj‘G(x)dx = XIF(x)dx.
to x0
Following the approach used evaluating the effects of F DS changes, we first try to
determine the direct and the indirect effects of a MP spread of the distribution of the
domestic returns on both S and a. Then, we combine those pieces of information to

establish the total partial equilibrium effects.

1.3.2.1. Direct Effects (DE)
Proposition 4:

If U "' is either positive, negative or zero, then the marginal expected utility of savings

under G evaluated at {a*,S*}, VSIG]

 

5* a, , has either a positive, negative or zero value.

Proof: See Appendix 1.A. I

Proposition 5:

 

The expected marginal utility of the risky asset under G evaluated at {a*,S*}, V216]

S",a"I

is negative if preferences exhibit either i) a positive third derivative of the utility function,

 

 

 

a coef.‘
variabl t

risk avc

 

 

 

Proof:~ 5

From pro;
x’s distrib
utility funt'

Proof: See

Pmposition ;
the risk." aSSt
positive third
Smaller than 0
ofthe utility ]
lllll’d defil'alivc

ProtlfI See APP;

 

a coefficient of relative risk aversion smaller than one and nondecreasing in the random
variable; ii) a positive third derivative of the utility function and a coefficient of relative
risk aversion equal to one; or iii) a null third derivative of the utility function.

Proof: See Appendix 1.A. I

DE Total Savings:

 

From proposition 4 it follows that the sign of the direct effect on saving of a MP spread in
x’s distribution is either positive, negative or null if the sign of the third derivative of the
utility function is positive, negative or zero, respectively.

Proof: See Appendix LA. I

DE Holdings of Domestic Assets:

 

Proposition 5 tells us that the direct effect of a mean preserving spread on the holdings of
the risky asset is negative if preferences exhibit one of the next sets of assumptions: i) a
positive third derivative of the utility function, a coefficient of relative risk aversion
smaller than one and nondecreasing in the random variable; ii) a positive third derivative
of the utility function and a coefficient of relative risk aversion equal to one; iii) a null
third derivative of the utility function.

Proof: See Appendix LA. I

20

 

 

 

 

1.3.2.2
By 1116
Spread 4
3\L’F510r
{61311.16 -
and eitlic
aWrgjon l
the Utllll}

Prod/5 SC"

from PT “1’05
asset is posi ti
utility functio.
indirect effect
utility function
utility function:

Proof See .1 ppt

 

 

1.3.2.2. Indirect Effects (IE)

IE Total Savings:

 

By the results of propositions 3 and 5 we know that the indirect effect on savings of a MP
spread is negative if preferences show: i) DARA plus either a coefficient of relative risk
aversion smaller than one and nondecreasing in the random return; or ii) a coefficient of
relative risk aversion equal to one. The indirect effect on savings is positive under IARA
and either: i) a positive third derivative of the utility function, a coefficient of relative risk
aversion less than one and increasing in the random return; or ii) a null third derivative of
the utility function. Finally, the indirect effect is null if preferences exhibit CARA.

Proof: See Appendix LA. I

IE Holdings of the Domestic Asset:

 

From propositions 3 and 4 we know that the indirect effects on the holdings of the risky
asset is positive if preferences exhibit either: i) DARA and positive third derivative of the
utility function; or ii) IARA and a negative third derivative of U. On the other hand, the
indirect effect is negative if preferences exhibit IARA and positive third derivative of the
utility function. The IE is null if preferences exhibit either: i) a null third derivative of the
utility function; or ii) CARA.

Proof: See Appendix LA. I

21

 

To

 

 

and the

mean pt

Corollar
A mean 1
savings it
third deri
increasing

13’0in See

Corollary ,1
A mean prc.
ofthe risk)‘ ,
POSitive thin.
lnr; 0“'1) a n

Proof See A ,.

 

1.3.2.3. Total Partial Equilibrium Effects
The following corollaries combine the pieces of information given by the direct
and the indirect effects to establish the TPEEs (on agents’ savings and portfolio mix) of a

mean preserving spread in the domestic bond’s return distribution.

Corollary 2.A: (1‘ PEE on Savings)

A mean preserving spread of x’s distribution causes an increase in the level of optimal
savings if preferences exhibit either: i) nondecreasing absolute risk aversion, a positive
third derivative of U, a coefficient of relative risk aversion smaller than one and

increasing in x; or ii) a null third derivative of U.

Proof: See Appendix LA. I

Corollary 2.B (TPEE on Domestic Assets)

A mean preserving spread in x’s distribution induces a reduction in the optimal holdings
of the risky assets if preferences exhibit either: i) nondecreasing absolute risk aversion, a
positive third derivative of U, and relative risk aversion no larger than one and increasing

in x; or ii) a null third derivative of U.

Proof: See Appendix LA. I

Corollary 2.C: (TPEE on Foreign Assets)
A mean preserving spread in x’s distribution causes an increase in the optimal holdings of

foreign assets if preferences show either: i) nondecreasing absolute risk aversion, a

 

posith

andinc

 

Proo/i 5

those cas
DARA tl:
total pani

direct and

14. Econ

 

The

mnrbuos 1,“

“am [0 e‘iall

 

positive third derivative of U and a coefficient of relative risk aversion no larger than one
and increasing in x; or ii) a null third derivative of U.

Proof: See Appendix LA. I

Notice that the TPEE on savings is also positive if preferences exhibit CARA. In
those cases in which the conditions of propositions 3, 4 and 5 hold and preferences show
DARA the direct and the indirect effects have opposite signs. Therefore, the signs of the
total partial equilibrium effects are ambiguous; they depend on the relative size of the

direct and the indirect effects.

1.4. Economy Wide Effects (General Equilibrium Effects)

The previous section describes how the domestic individuals adjust their
portfolios because of shifts in the distribution of the domestic assets’ return. Now we
want to evaluate the economy wide effects of those changes in the distribution.

Given our assumptions about the government financing process, any change in
agents’ holdings of the domestic bonds alters the government budget constraint (GBC). In
particular, if there is a reduction of the holding of the domestic bonds, given g, the
government has to increase the taxes levied on the domestic agents. This reaction of the
government induces additional responses in agents’ optimal choices and therefore, in the

GE outcomes of the economy.

23

1.4.1. General Equilibrium Effects of FDS Changes

Following Diamond and Stiglitz (1974), let a be an index of a family of
cumulative density functions of the random variable 32’ , such that an increase (a
reduction) in 0' implies a FDS improvement (deterioration) in x’s distribution. Then,
given two distributions F and G, we say that distribution F dominates distribution G in a

first degree stochastic sense if 0",, <0“. Here 0,, and 0",. represent the indexes

 

. _ . . g . c9 a a" m (7 S
assoc1ated to the dlstrtbutions F and (1, respectively. Let 7—, — and denote
0 0' 8 0' c9 0'

the TPEE of FDS changes in x’s distribution on domestic assets, foreign assets and level
of savings, respectively.

From the GBC it follows that --given a fiscal expenditure g-- any change in the
equilibrium holdings of the risky assets is compensated by equivalent changes in taxes,
da+dr=0. Thus, taking into account the interactions between the domestic private agents
and the domestic government, we can write the general equilibrium effect on the

domestic assets of F DS changes in x’s distribution as

 

(3a (7a (9a 67a
da=——do+—dr or dal+—-— = do.
0’0“ 51 fit (3

Hence, the sign of the general equilibrium effect of FDS changes in the

distribution of the domestic return is given by the sign of

Notice that to determine the sign of this expression we need to know the sign of

a a 0
its denominator. By construction &_ is equal to —E and, as borrowing is not
1

possible, the sign of the denominator is positive and, therefore, the sign of the GE effect

is given by the sign of the TPEE.”

1.4.1.1. GE Effect on the Domestic Assets

From corollary 1.B we have that if agents’ preferences exhibit risk aversion, a coefficient
of relative risk aversion no larger than one, and nondecreasing absolute risk aversion,
then a FDS deterioration (improvement) on x’s cdf induces negative (positive) GE effects

in the holdings of domestic assets.

1.4.1.2. GE Effects on Total Savings

We can write the general equilibrium effect on savings caused by F DS changes as:

 

 

as 55 . . as as
615 = do + dr. Alternatively, usmg the GBC and the fact that —= — , we
5 0' 0" r a 7 fl Y
0" S 0" S
can write the GE effect as d— — _ __da '5

dozflo armi

 

.. . 3 a 5 a dY (7 a
'4 Recall that we define Y = Y — 1. Thus it follows that — = —— = — —.
0" Z' (3 Y d 2' (7 Y
c? S 5 S dy (7 S
§r_§Ydr_ ar’
therefore, by construction, the effects of changes in taxes on agents’ saving rate is the
negative of the effects changes in income.

and

 

'5 Because we assume lump sum taxes, we have that

 

25

Corollary 1.A establishes some conditions under which we can determine the
sign of the first part of the right-hand-side (RHS) expression. However, we still need to
know the sign of the second part of the RHS expression. In particular, we must determine

the sign of the total partial equilibrium effect on savings of changes in disposable income.

Proposition 6:

Under risk aversion, the TPEE on savings due to changes in income is positive.

Proof: See Appendix LA. I

Since the TPEE on savings of changes in income is positive and under the

conditions of corollary 1.B the GE effect on a of a FDS change is negative, the

. 5 S da . . .
expressron — —— lS posrtive.
§ Y do
GE Effects on Savings

If agents’ preferences show risk aversion, a coefficient of relative risk aversion no larger
than one, and nondecreasing absolute risk aversion, then a F DS deterioration
(improvement) of x’s cdf induces an increase (reduction) in the general equilibrium level

of savings.

26

1.4.1.3. GE Effects on the Foreign Assets

By construction, the holdings of foreign assets is equal to total savings minus the
holdings of domestic assets, m=S—a. Thus, it follows that dm =dS-da. Then, if the results
of the previous GE effects hold, we have that a FDS deterioration (improvement) induces

an increase (a reduction) in the GE holdings of foreign assets.

Summary:

We have seen that if agents’ preferences are characterized by a specific set of
properties we can sign the partial and general equilibrium effects --on a, m, and S—- of
first degree stochastic changes in x’s distribution. In particular, we show that a FDS
deterioration induces unambiguously a reduction in the holdings of domestic assets, and
an increase in the holdings of foreign assets and total savings when preferences show risk
aversion, nondecreasing absolute risk aversion, and a coefficient of relative risk aversion
no larger than one. Those findings hold both at partial equilibrium and at a general
equilibrium level.

These results are similar to those in Khan and. U1 Haque (1985) in the sense that a
first degree stochastic change in the distribution of domestic returns induces an increase

in the holdings of foreign assets.

1.4.2. General Equilibrium Effects of MP Transformations
Let xi be an index of a family of cumulative density functions of the random

variable 3? such that an increase (decrease) in 1 implies a mean preserving spread

27

(contraction) of x’s distribution. Then, given two distributions F and G, we say that
distribution G is riskier than distribution F in a Rothschild and Stiglitz sense if 1,, is
smaller than xi“.

é’a 8m é’S

the domestic and the foreign assets. and on total savings, respectively.

1.4.2.1. GE Effects on Domestic Assets
As in the case of first degree stochastic changes, the general equilibrium effect of
a mean preserving transformation on the holdings of domestic assets is given by

c7 a a
do = Edi + 7dr. Consequently, the sign of the general equilibrium effects of mean
. r

preserving changes in the distribution of the domestic assets’ return is given by the sign

of:
flu
da {7/1
dl_1 aa'
”a?

Assuming that people do not borrow, we have that the GE effect has the same sign
of the total partial equilibrium effect. Thus, under the conditions of part B of corollary 2,
the GE effect on the holdings of the domestic assets is negative, i.e., a MP spread induces

a reduction in the general equilibrium value of a.

28

1.4.2.2. GE Effects on Savings

The GE effect on savings of mean preserving transformations of the distribution of the

dS 0" S é’ 5 da . .
= —— — ———. From the results of proposmon 6 and
d2 é xi. 0" Y d2

 

domestic return is given by

parts A and B of corollary 2 we know that a MP spread in x’s cdf induces an increase in

the GE level of savings.

1.4.2.3. GE Effects on Foreign Assets

Under the conditions of part C of corollary 2 and proposition 6, a MP spread in x’s cdf
induces an increase in the holdings of the foreign assets, capital flight.

Summagy:

Under the conditions of corollary 2 and propositions 6 and 7, a mean preserving
spread (contraction) on the distribution of the domestic return induces a reduction (an
increase) in domestic investors holdings of domestic assets. At the same time, the MP
spread (contraction) motivates an increase (a reduction) in the holdings of foreign assets
and total savings. In this context the increase in agents’ holdings of the foreign bond can
be interpreted as capital flight, since the capital outflows are induced by an increase in
domestic risk. Domestic agents also raise their total savings as protection against the

increase in the domestic risk.

29

1.5. Risk Aversion (A Digression)

1.5.1. Absolute Risk Aversion

We place restrictions on the forms of absolute risk aversion to establish some of
the results of sections 111 and IV of this chapter. We find that nondecreasing absolute risk
aversion (together with other assumptions) allows us to unambiguously determine the
total partial equilibrium and general equilibrium effects of both FDS and MP changes in
x’s distribution. The assumption of nondecreasing absolute risk aversion is convenient,
since the direct and the total partial equilibrium effects have the same sign. This is the
case because the indirect effect either has the same sign as the direct effect (IARA) or is
null (CARA).

However, at least since Arrow (1965) and Pratt (1964), the perception that
absolute risk aversion is decreasing or at least nonincreasing is generally accepted. We
find that when preferences exhibit the desired DARA the direct and the indirect effects
have opposite signs, and, therefore, the sign of the TPEE is ambiguous. A possible
solution to eliminate the ambiguity is to impose additional assumptions on preferences.
For instance, if we assume that either the direct effect or the indirect effect dominates the
other (it is larger in absolute value) we can still determine the signs. The results of
corollaries one and two are still valid, in the cases where the direct effect is the dominant
effect. Nevertheless, the results of corollaries one and two are reversed, when the indirect

effect dominates the direct effect. Even though DARA is a widely accepted and desired

30

property, nondecreasing absolute risk aversion has often been used in both empirical and

theoretical studies.'6

1.5.2. Other Measures of Risk Aversion

In this paper we use many assumptions about agents’ attitude toward risk that are
controversial, nondecreasing absolute risk aversion is only one of them (but perhaps it is
the most controversial one). In corollaries 1 and 2 we place restrictions on the size of the
coefficient of relative risk aversion. In the literature of decision making under
uncertainty it is common to assume that this coefficient is smaller than one.l7 However,
several empirical studies find that in a variety of countries the coefficient of relative risk
aversion is larger than one.‘8

We also employ assumptions about the sign of U’” in the comparative static
analysis. The sign of U'" is closely related to the form of absolute of risk aversion. A

positive U’" is a necessary condition for nonincreasing absolute risk aversion (either

 

'6 Hall (1978) assumes a quadratic utility function which implies IARA. Caballero
(1990) uses a CARA.

'7 Fishburn and Porter (1976), Rothschild and Stiglitz (1971), Levhari and Srinivasan
(1969) and Hadar and Seo (1990) are some of the papers that use relative risk aversion
smaller (no larger) than one doing comparative static under uncertainty.

'8 Studies as Binswanger (1981), Morduch (1990) estimate this coefficient for Indian
households using the ICRISAT data finding values larger than one. Ogaki, Ostry, and
Reinhart (1996) estimate the intertemporal elasticity of substitution (IES) for a large
number of economies. Given the forms of the utility functions that they use (isoelastic or
constant relative risk aversion) the coefficient of relative risk aversion can be computed
as the inverse of the IES. The implied values for the relative risk aversion are larger than
one. Other studies as Zeldes (1989), Carroll and Samwick (1997) and Caballero (1990)
use a coefficient of 3. Nevertheless, Hansen and Singleton (1983) find estimates of the
relative risk aversion coefficient that are both larger and smaller than one using US data.
See Table 1.4 for a summary of these estimates.

3]

CARA or DARA). On the other hand, a nonpositive (1” implies increasing absolute risk
aversion.

The sign of the third derivative of the utility function is generally associated with
the existence of a precautionary saving motive. Leland (I968), Sandmo (1970) and
Kimball (1990) show that a positive third derivative of the utility function indicates a
precautionary saving motive. Here we find that when preferences have some specific (and
restrictive) characteristics an increase in the interest-income risk induces an increase in
total savings. From corollary 2.A we know that this happens if preferences exhibit CARA
and therefore, U "'> 0, and also if preferences exhibit IARA, U ”'> O and relative risk
aversion less than one and decreasing in the domestic return. So a positive third
derivative of U is still associated with a precautionary savings motive. Nevertheless, a
precautionary saving motive (an increase in savings as the result of an increase in risk)
take place even if preferences exhibit U ' "= 0 because of the indirect effect. Even though
the direct effect of a MP spread on savings is null when U "'= 0 (proposition 4) the
reduction in the holdings of domestic assets (a) induces an indirect increase in optimal

savings (in this case preferences exhibit IARA «proposition 3).

1.6. Capital Outflows: (Two Numerical Examples)

So far we have analyzed how agents adjust their portfolios because of changes in
the domestic return distribution using a general utility function. Next we evaluate the
effect of those changes in domestic returns’ cdf on the equilibrium outcomes of small

open economies using specific forms of the utility function. We use two very common

32

utility functions namely, constant absolute risk aversion (CARA) and constant relative
risk aversion (CRRA) to conduct some simulations. We choose values for all the relevant
exogenous variables to carry out the simulations and try to connect the preferences’
parameters with domestic agents’ responses.

With these two numerical examples we want to extend the findings of part III and
IV of this chapter. In particular, in the first exercise we assume that preferences exhibit
CARA, and test the predictions of corollaries 1 and 2 for cases in which the coefficient of
relative risk aversion is greater than one. In the second example our goal is to extend the
results of the corollaries for the case in which absolute risk aversion is decreasing. In this

example we assume a CRRA utility function that also implies the commonly accepted

DARA.

1.6.1. Example 1: CARA

Consider a constant absolute risk aversion utility function, thus U [c] = —e
Let us assume a discrete cdf for the domestic assets’ return. Let p1= p2=0.5, xl=0.01 and
x2=0.07; where the x’s represent the possible values of the random variable (the domestic
return) and the p’s represent the probability that each one of those values is realized.
Then, the expected value of the random variablei7 is 0.04. Let ,B=0.94, Y=500. r =0.0398
be the discount factor, income level and safe (foreign) asset’s return, respectively.

To model the FDS and MP changes in x’s distribution we define the new values of

x’s so that they satisfy the FDS deterioration and MP spread conditions.‘9 Let xll and xl2

 

‘9 See Appendix LB.

33

.'_.-~ 0.491: ill“. ,

 

 

be the new values of x’s that satisfy the FDS conditions. Then, we can write those new
values of x as x.,=xl-kl and xlz=x2-kl. Here kl represents a F DS shift factor. If we add
(subtract) kl from the initial values of x we obtain a FDS improvement (deterioration).
Likewise, let x2, and x22 be the new values of x that satisfy the MP spread conditions. We
write those values as x2,=x,-k2, and x22=x2+k22, where k3,=c2/pl and k22=c2/p2. Here kg,
and k22 represents the MP shift factors. Notice that these terms contain both additive (c3)
and multiplicative shifts (l/p’s) such that the MP conditions hold. Set k,=c2=0.0001.

The Figures 1.1 and 1.2 illustrate the effects of a FDS deterioration and a MP
spread when preferences exhibit constant absolute risk aversion, respectively. In each
graph we show the relationship between the coefficient of absolute risk aversion and the
effect on each one of the equilibrium outcomes. To compute the effects on the holdings of
domestic and foreign assets and on total savings, we compare the equilibrium outcomes
of two economies that differ only in the distribution functions of the random return, x. In
the graph where we evaluate the effects on the variable 2, Var. represents the difference
between 2 and z * , hence Var = 2' — z *. Here 2 * and 2 are the equilibrium outcomes
for the economies with the initial and new distribution, respectively.

In these numerical examples we find that a FDS deterioration in the distribution of
the random return induces an increase in total savings. a reduction in the holdings of
domestic (risky) assets and an increase in the holdings of foreign assets (see Figure 1.1).
On the other hand, similar results hold in the case of a mean preserving spread of x’s cdf.
There is an increase in total savings, a reduction in the holdings of domestic (risky) assets

and an increase in the holdings of foreign (safe) assets (see Figure 1.2). These results

34

imply that the predictions of corollary 1 and 2 are still valid for cases where the
coefficient of relative risk aversion is larger than one.20 Then, in an economy with these
characteristics (CARA is one of them), capital outflows are the consequence of domestic
agents’ reactions to changes in the domestic risk, and, therefore, they can be interpreted

as capital flight.

1.6.2. Example 2: CRRA

l-p
Now let us assume a constant relative risk aversion utility fimction, U [c] =

 

Let p,= p2=0.5, x,=0.0l and x2=0.07, ,6=0.94, Y=500, r=0.0398. As in example 1, x’s
represent the possible values of the random variable, p’s represent the probability that
each one of those values is realized, ,6 is the discount factor, Y is the income level and r is
the safe asset’s return. Again the expected value of the random variable)? is 0.04. Let
{xmxn} and {x2,,x22} be the new values of x’s that satisfy the FDS and the MP spread
conditions, respectively. We can write those new values of x as xn=x,-k,, x,2=x2-kl,

x2|=x.-k2| and x32=x2+k32. where the k’s and c2 are define as before. Let us assume that

k,=c,=0.0001.

 

2° Here yis the coefficient of absolute risk aversion. Hence, the coefficient of relative risk
aversion p, is given by p = y C, . We find that p_<1 if 750. 01402.

One of the properties of a constant relative risk aversion (CRRA) utility function
is that it exhibits decreasing absolute risk aversion. DARA is not included among the
conditions of corollaries l and 2 because the signs of the total partial equilibrium effects
(TPEE) cannot be determined without ambiguity. In those cases, the signs of the TPEE
depend on the relative size of the direct and the indirect effects.

Notice that for this example it appears that the direct effect is the dominant one
explaining the behavior of the holdings of both domestic and foreign assets.2| So, a FDS
deterioration (Figure 1.3) or a MP spread (Figure 1.4) induces a reduction in the holdings
of domestic assets and an increase in the holdings of foreign assets. The signs of these

effects are valid even for cases in which the coefficient of relative risk aversion, p, is

larger than one. Thus, at least for p6(0.6,10), a first degree stochastic deterioration or a

mean preserving spread in x’s cdf induces capital outflows.22 For total savings the

indirect effect appears to be the dominant effect for p<l. In those cases the TPEE is

negative, hence a FDS deterioration (or a MP spread) reduces the total savings of the
domestic agents. Whereas, for cases where p>l a FDS (or a MP) change induces an

increase in total savings. At p =1 there is no effect on total savings.

 

2' If the appropriate conditions hold and the direct effect dominates the indirect effect,
then a FDS deterioration or a MP spread in x’s cdf may induce: a) a reduction in the
holdings of domestic assets; b) an increase in the holdings of foreign assets; c) an
increase in total savings. However, if the indirect effect dominates the direct effect we
have that a FDS deterioration or a MP spread in x’s distribution may induce: a) an
increase in the holdings of domestic assets; b) a reduction in the holdings of foreign
assets, c) a reduction in total savings.

22 For those values of p the optimal values of a, m and S are all interior solutions of the
form a>0, m>0, and S>O.

36

Notice that these numerical examples suggest a negative relationship between the
size of the coefficient of relative risk aversion and the amount of capital flight. This
negative relationship is also suggested by Figure 1.5 that relates estimates of capital flight
and relative risk aversion for 13 developing economies. We. use estimates of capital flight
during 1983 (the first year after the beginning of the debt crisis) taken from Schineller
(1997). We also use the values of the intertemporal elasticity of substitution (the inverse
of the coefficient of relative risk aversion) estimated by Ogaki, Ostry and Reinhart
(1996)?“

This negative relationship between capital flight and relative risk aversion seems
to imply that if two small open economies in similar situations face an increase in their
domestic risk the country in which agents exhibit smaller relative risk aversion tend to be
affected more severely. This could be explained because in general the investors in the
country with the smaller (relative) risk aversion tend to hold higher positions of the risky
asset, and consequently, their portfolio adjustments tend to be larger. Thus, in general,
countries with smaller risk aversion tend to be more exposed to severe capital flight

pI‘OCCSSCS.

 

2" The sample of 13 countries includes: Argentina, Brazil, Chile, Colombia, Costa Rica,
Ecuador, Mexico, Malaysia, Peru, Philippine, Thailand, Uruguay and Venezuela.

2" By no means do we pretend that these are conclusive proof, nevertheless it is
interesting that at least for this small sample of countries the predictions of the
simulations seem to be correct.

37

1.7. Some Final Comments

According to general wisdom an increase in domestic risk induces domestic
capital to flee from developing economies. Here we show sufficient conditions (some
restrictions on agents’ attitude toward risk) under which this claim is true.

Using standard methodology in the literature of decision making under
uncertainty, we analyze how domestic private investors adjust their portfolios in response
to changes in the distribution of the domestic asset’s return. We consider two different
changes namely, first degree stochastic (FDS) changes and mean preserving (MP)
transformations.

We find that if preferences exhibit risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS
deterioration induces an increase in the holdings of foreign assets, a reduction in the
holdings of domestic assets and an increase in total savings.

On the other hand, if we assume that x’s cdf experiences a MP spread, then we
can show that domestic agents increase their holdings of foreign assets, decrease their
holdings of domestic assets and increase total savings when we impose one of the
following sets of assumptions: i) a positive third derivative of the utility function, a
coefficient of relative risk aversion smaller than one and increasing in the random return,
and nondecreasing absolute risk aversion; ii) a null third derivative of the utility function.

Furthermore, if those conditions prevail similar results hold also at a general

equilibrium level. In those cases, an increase in domestic risk induces an increase in the

38

holdings of foreign assets, and at the same time, a reduction in the holdings of the
domestic assets and an increase in total savings.

These findings are extensions of Khan and U1 Haque (1985)’s results, since they
analyze capital flights in the context of a particular form of FDS deterioration
(expropriation risk). Here we show that similar results can be obtained even for general
forms of FDS changes. Nevertheless, this generalization of KU is at the expense of
imposing more restrictions on agents’ preferences. In addition to risk aversion (employed
by KU), we assume that the coefficient of relative risk aversion is no larger than one, and
either IARA or CARA.

Moreover, the results in the paper are extensions of KU also because we use a
more appropriate form to represent changes in domestic risk than the one considered by
KU, namely, MP transformations of the domestic return. In the case of a MP spread the
capital outflows are interpreted as capital flight because they are induced by changes in
the domestic risk.

The findings of parts III and IV of this chapter are confirmed and extended in the
numerical examples conducted in part VI. For instance, we find if we use a constant
absolute risk aversion (CARA) utility function, then the previous predictions about the
effects of a FDS deterioration or a MP spread are valid even for cases in which the
coefficient of relative risk aversion is larger than one. Furthermore, using a constant

relative risk aversion (CRRA) utility function, we find that if the coefficient of relative

risk aversion p is smaller than one, then a FDS deterioration (or a MP spread) in x’s

distribution causes a reduction in the holdings of domestic assets, and an increase in the

39

holdings of foreign assets. Those results are still valid even when the coefficient of

relative risk aversion is larger than (or equal to) one. However, the assumed changes in
x’s distribution induce domestic private agents to decrease total savings if p is smaller

than one, and to increase it if p is larger than one. The effect on savings is null if the
coefficient of relative risk aversion is equal to one.

The examples also suggest a negative relationship between the size of the
coefficient of risk aversion and the amount of capital flight, that is the amount of capital
outflows induced by an increase in the domestic risk (a MP spread of the domestic

returns’ distribution) tends to be higher the lower the coefficient of risk aversion.

40

 

11“.,
..

REFERENCES

Arrow, K. (1965). “ Aspect of a Theory of Risk Bearing ” .Ytjo Jahnsson Lectures,
Helsinki. Reprinted in Essays in the Theory of Risk Bearing (1971). Chicago.
Markham Publishing Co.

 

Binswanger, H. P. (1981). “ Attitudes Toward Risk: Theoretical Implications of an
Experiment in Rural India ”. The Economic Journal. Vol. 91. #364. pp. 867-890.

 

Caballero, R. (1990). “ Consumption Puzzles and Precautionary Savings ”. Journal of
Monetary Economics. Vol. 25. pp. 113-136.

 

Calvo, G., L. Leiderman and C. Reinhart (1996). “ Inflows of Capital to Developing

Countries in the 19905 ”. Journal of Economic Pergaectives. Vol. 10. #2. pp. 123-
139.

 

Cardoso, E. and A, Helwege. (1995). Latin America’s Economy. Diversity, Trends, and
Conflicts. The MIT Press. Cambridge, Massachusetts.

 

Carroll, C. and A. Samwick. (1997). “ The Nature of Precautionary Wealth ”. Journal of
Monetary Economics. Vol. 40. pp. 41-7].

 

Claessens, S. and D. Naudé. (1993). “ Recent Estimates of Capital Flight ”. International
Economics Department the World Bank. Policy Research Working Papers. #1186.

 

 

Cuddington, J. (1986). “ Capital Flight: Estimation, Issues, and Explanations ”. Princeton
Studies in International Finance. #58. Princeton. NJ. International Finance
Section. Department of Economics. Princeton University.

 

. (1987). “ Macroeconomics Determinants of Capital Flights: An Econometric
Investigation ” in Lessard and Williamson Ed. Capital Flight and Third World
Debt. Institute for International Economics. 1987. Washington DC pp. 85-96.

 

Cumby, R. and R. Levich. (1987). “ Definitions and Magnitudes. On the Definitions and
Magnitudes of Recent Capital Flight ” in Lessard and Williamson Ed. Capital
Flight and Third World Debt. Institute for International Economics. 1987.
Washington DC pp. 27-67.

 

Diamond, P. and J. Stiglitz (1974). “ Increase in Risk and in Risk Aversion ”, Journal of
Economic Theory, 8, pp. 337-360.

 

4l

Dooley, M. (1986). “ Country-Specific Risk Premium, Capital Flight and Net Investment
Income Payments in Selected Developing Countries ”. DM 86/17. IMF.
Washington. DC

Eeckhoudt, L. and C. Gollier (1995). Risk: Evaluation, management and sharing. First
Published in French in 1992 by Ediscience International, Paris. Translated by V.
Lambson. Published 1995 by Harvester Wheatsheaf.

 

Eeckhoudt, L., Meyer J., and M. Ormiston (1997). “ The Interaction Between the
Demand for Insurance and Insurable Assets ”. Journal of Risk and Uncertainty.

 

Fishburn, P. and R. Burr Porter. (1976). “ Optimal Portfolios with One Safe and One
Risky Asset: Effects of Changes in Rate of Return and Risk ”. Management
Science. Vol. 22. No 10. pp. 1064-1073.

 

Hadar, J. and T. Sec. (1990). “ The Effects of Shifts in a Return Distribution on Optimal
Portfolios ”. lntemational Economic Review. Vol. 31. #3. pp. 721-736.

 

Hall, R. (1978). “ Stochastic Implications of the Life Cycle-Permanent Income
Hypothesis: Theory and Evidence ”. Journal of Political Economy. Vol. 86. #6.
pp. 971-87.

 

Hansen, L. P. and K. Singleton. (1983). “ Stochastic Consumption, Risk Aversion, and
Temporal Behavior of Assets Returns ”. Journal of Political Economy. Vol. 91.
#2. pp. 249-265.

 

Kant, C. (1996). “ Foreign Direct Investment and Capital Flight ”. Princeton Studies in
International Finance. #80. Princeton. NJ. International Finance Section.
Department of Economics. Princeton University.

 

 

Khan, M. and N. U] Haque. (1985). “ Foreign Borrowing and Capital Flight: A Formal
Analysis ”. IMF Staff Papers. Vol. 32. #4. pp. 606-628.

 

99

.(1987). “ Capital Flight From Developing Countries Finance and

Development.

 

 

Kimball, M. (1990). “Precautionary Saving in The Small and in The Large”.
Econometrica. Vol. 58. #1. pp. 53-73.

 

Krugman, P. (1979). “ A Model of Balance of Payments Crises”. Journal of Money,
Credit and Banking. Vol. 11. #3. pp. 311-325.

 

 

Leland, H. (1968). “ Saving and Uncertainty: The Precautionary Demand for Savings ”,
Quarterly Journal of Economics. Vol. 82. pp. 465-473.

 

 

Lessard, D. and J. Williamson. (1987). “ The Problem and Policy Responses ” in Lessard
and Williamson Ed. Capital Flight and Third World Debt. Institute for
lntemational Economics. 1987. Washington DC pp. 201-254.

Levhari, D. and T. Srinivasan. (1969). “ Optimal Savings Under Uncertainty ”. Review of
Economic Studies. Vol. 36. #2. pp. 153-163.

 

Morduch, J. (1990). “ Risk, Production and Saving: Theory and Evidence From Indian
Households ”. Mimeo. Harvard University.

Morgan Guaranty Trust Company of New York. World Financial Markets. March 1986,
June/July 1987 and December 1988.

 

Ogaki, M., J. Ostry and C. Reinhart. (1996). “Savings Behavior in Low- and Middle-
Income Developing Countries. A Comparison ”. IMF Staff Papers. Vol. 43. #1.

 

Padilla del Bosque, R. (1991). Estimacion de la Fuga de Capitales Bajo Diversas
Metodologias para los Casos de Argentina, Brasil, Mexico y Venezuela. Serie de
Documentos de Trabajo. Instituto Torcuato Di Tella.

Pratt, J. W. (1964). “ Risk Aversion in the Small and in the Large Econometrica. Vol.
32. pp. 122-136.

 

Rothschild, M. and J. Stiglitz (1970), “ Increasing Risk I: A Definition Journal of
Economic Theory. pp. 225-243.

 

. (1971). “ Increasing Risk II: Its Economic Consequences ”, Journal of Economic
Theory. pp. 66-84.

 

Sandmo, A. (1969). “ Capital Risk, Consumption, and Portfolio Choice ”. Econometrica.
Vol. 37. No. 4. pp. 586-599.

 

Sandmo, A. (1970). “ The Effects of Uncertainty on Savings Decisions Review of
Economics and Studies. pp. 353-360.

 

Schineller, L. (1997). “ An Econometric Model of Capital Flight From Developing
Economies ”. Board of Governors of the Federal Reserve System. lntemational
Finance Discussion Papers # 579.

 

 

World Bank (1985). “International Capital and Economic Development. World
Development Indicators”. World Development Report.

 

Zeldes, S. (1989). “ Optimal Consumption with Stochastic Income: Deviations from
Certainty Equivalence ”. Quarterly Journal of Economics. Vol. 104. pp. 275-298.

 

43

 

 

 

 

 

 

Table 1.1

Capital Flight: Modified-

World Bank Measure.
(Percent of GDP)

1983 1 990

 

 

Argentina -2.92 -15.84
Bolivia 6.68 0.12
Brazil 2.66 0.31
Chile 14.96 -10.58
Colombia 5.18 079
Costa Rica 3.54 -20.3
Ecuador -3.18 3.51
Mexico 7.52 0.55
Peru -2.77 1.45
Uruguay 27.15 -3.9

- Venezuela . 21.3 -17.46
Average 7-28 -5-72
India 1.74 1.1 1
Indonesia -1.7 7.94
South 1.54 -4.26
Korea
Malaysia 5.45 -25.1 1
Philippines -5.39 -2.19
Thailand . -2.67 -11.78

{:5 Average -1-72 -5-72

 

 

 

 

Source: Schineller (1997). “An Econometric Model of Capital
F light from Developing Countries”.

44

 

 

 

Table 1.2

Stock of Capital Flight:
Morgan Guaranty Trust’s Measure

Billions of $ at
YeahEnd

1980 1982 1987

 

 

 

Argentina 1 1 35 46
Bolivia 1 1 2
Brazil 6 8 31
Chile 0 1 2
Colombia 0 0 7
Ecuador 3 4 7
Ivory Coast 1 1 0
Mexico 19 44 84
Morocco 0 0 3
Nigeria 6 13 20
Peru 0 1 2
Philippines 11 19 23
Uruguay 0 2 4
Venezuela 15 33 58
Yugoslavia 3 3 6

 

 

 

Source: Morgan Guaranty Trust Company. (1988). World Financial Markets

 

45

 

. ex“

‘v

 

.4l___-L‘—

 

 

 

Table 1.3
Estimates of Capital Flight Stocks {1970-87)
for Some Developing Economies
using Different Methodologies

 

 

 

 

 

 

 

 

 

Millions of US Dollars

Definitions Argentina Brazil Mexico Venezuela
World Bank 53,366 35,716 100,085 53,082
Morgan 51,341 30,150 96,868 51,509

Guaranty Trust
Cline 35,485 16,962 29,612 32,914
Cuddington 20,917 -681 58,777 18,103
Dooley 25,016 9,432 53,464 16,342
Source: Padilla del Bosque, R. (1991)
Table 1.4

Estimates of the
Coefficient of Relative Risk Aversion

 

Study
Binswanger (1981)a
Morduch (1990) a
Hansen and Singleton (1983)b
Ogaki, Ostry and Reinhart (1996)c

 

Range of the Estimates
(1.84 - 68.4)
(1.18 - 2.22)
(0 - 2)
(1.557 - 21.276)d

 

 

a.- Study uses Indian Data
b.- Study uses US Data
c.- Study uses data for 85 countries.

d.- The smallest CRRA is for the United Arab Emirates and the largest for Uganda.

 

46

 

 

 

 

 

 

Figure 1.1

Effects of a First Degree Stochastic Deterioration
Constant Absolute Risk Aversion

Var Total Savings

 

1.2t 1

 

0.21K
‘

O" 9 - A ‘ +4
0 2 4 6 8 10

 

 

 

 

Coefficient of A bsolute Risk A version

 

 

 

 

 

 

 

 

 

 

 

 

V‘" Assets Variation
1 . 5, ' '
1.
O . 5l K [Foreign Assets]
0 . . -.
-0 . 5. 5,! [Domestic Assetsj
_1, i
—1 . 5
O 2 4 6 8 10

Coefficient of A bsolute Risk A version

47

 

Figure 1.2
Effects of a MeanPreserving Spread

Constant Absolute Risk Aversion

Var Total Savings

 

 

 

0.05’ K
‘

O 2 4 6 8 l O
Coefficient of A bsolute Risk A version

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V‘" Assets Variation
0 . 4 ’ T
O . 2 '
[Foreign Assets I
a" .
g" [Domestic Assets I
- o . 2 . ~>
3v.
- o . 4 - -
O 4 6 8 l O

2
Coefficient of A bsolute Risk Aversion

48

 

Figure 1.3

Effects of a First Degree Stochastic Deterioration
Constant Relative Risk Aversion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V‘” Total Savings
0.0004}
0.0002
0
—0.0002
L- . m
0 2 4 6 8 1 0
Coefficient of Relative Risk Aversion
V‘" Assets Variation
4 O ‘
2 0 [Foreign Assetfl
O
- 2 O flJeStic Assets]
_ 4 0 ,
O 2 4 6 8 1‘0

Coefficient of Relative Risk Aversion

49

Figure 1.4

Effects of a Mean Preserving Spread
Constant Relative Risk Aversion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V‘" Total Savings
W
-6»
7.5 10
—6i i
5 10 l
—6
2.5 10
0
-6'
-2.5 10 »
_6[
—5 10 ; i
0 2 4 6 8 10
Coefficient of Relative Risk Aversion
V‘” Assets Variations
1.5
i
1.
0.5» [Foreign Assets I
l
0
.0,51 MicAssetsl
...l.
—1.5'- - - - 1
0 2 4 6 8 10

Coefficient of Relative Risk Aversion

50

 

 

 

Figure 1.5
Estimates of Capital Flight (1983)

 

 

as Percentage of GDP
KF83
27,15 4 U“
jvan
A
7A CHL
A
MEX 323.
uvs \‘ ‘ COL
.33
‘ BRA cm ii "A
A
pen ’3
ARG ECU THA PHI.
3’————-———a
5 39 ~
T l l f j—
1.6233 1.3416
CRRA

Source: Capital Flight Estimates taken from: Schineller (1997).
Estimates of the CRRA (lntertemporal Elasticity of Substitution) taken from:
Ogaki, Ostry and Reinhart, (1996).

 

51

 

 

APPENDIX 1.A

Households Maximization Problem

Given preferences (1) and the HBC, households solve:

Max VEU[C,]+,BI‘[{U[C2]}f(x)dx subject to Y=Cl+a+m and

gr, .(', ,a.m) 1‘
' ()

CZ=a(l+3F)+m(l+r).

 

Let S denote total savings, then S=a+m and therefore, 2) Y =Cl +5 and, 3)

C2 = a()? - r) + S(1+ r). Thus, the maximization problem can be rewritten in terms of a

and S as:

ii/hiii U[Y—S]+,B[{U[a(x —r)+S(1+r)]}f(x)dx

Foes: 4>V.: -U'[Y—S]+flj{U'[a(x—r)+S(l+r)](1+r)}f(x)dx=0

xn

5) V.,: ,6 [{U'tao — r) + S(1+r)1(x — r)}f(x)dx = 0

x0

SOC’s: V.: U"[Y—S]+,BI-[{U"[a(x-r)+S(1+r)](1+r)2}f(x)dx

AS

,‘ ‘)

Vm: fl [{U”[a(3? — r) + so +r)1(1+ rxx — r)}f(x)dx

V0,; [2’ [{U' ' [a(x — r) + so + r>](x — r)’}f(x)dx

52

V...= flitU'tatx — r) + 50 + r)1(1+ r)(x — r)}f(x)dx

V (“I

U.“ (Ill

V.. V.
Let H=[ "" ’":[. Then. the SOC’s are given by V“ <0, V <0, and

[HI : [Vss'I/uu — (V

( IS

)2] > 0. By strict concavity of U both V“ and V are negative. We

(Ill

assume that [H] is positive. We focus only on interior solutions in which a, S and m are

all positive.

Effects of a FDS Deterioration

Here we assume that the economy goes from F to G such as F dominates G in a first
degree stochastic sense.

Lemma 1:

>0.

S ‘ ,u‘

If agents’ preferences exhibit risk aversion, then VS[G]

 

Proof

By definition of {9161*} and FOC’s (4), VJGIsI-w has the same sign that

 

 

VSIG] 5.0. — VilFl 3.,“ since V_.IFl

 

is

.\".(t‘

is equal to zero. Hence, the sign of V5[G]

 

S’,a‘
given by the sign of A [{U'ta‘a — r) + 5‘0 + r)1(1+ r)}[g<x) — f(x)]dx-

Using integration by parts we can write that expression as:

‘1

2,}—I{U"[C21a'}[G(x>— F<x>]dx.

x0

 

160+ r>{[U"[C. lIGlx] — thn]

53

 

Thus, the sign of VS[G] W, is the same that the sign of [{U"[C2 ]a'}[F(x) — G(x)]dx .

’0

Therefore, if preferences exhibit risk aversion we have that V,[G] > 0 by the F DS

 

S‘xl"
deterioration assumption, F (x).<G(x) 17x.-

Proposition 2:

If agents’ preferences exhibit risk aversion and have a coefficient of relative risk aversion

<0.

S‘fl‘

no larger than one for all x, then V"[G]

 

Proof:

We know that the sign of VU[G]

 

since

S",a’ ’

is equal to the sign of VU[G]

 

-V..[F]

 

S ' .u‘ S ‘ ,u‘

by F OC’s the latter expression is null. Then:
A [{U'ta‘tx — r) + 5'0 + r)1(x — r)}[g(x) - f(x)]dx-

Using integration by parts we have that the sign of V“ [G]

 

is given by the sign of:

S" at
I T

' i U'[C21[1— A,1[F(x)—G(x)1dx-'[U"[CzlS(1+r)[F(x)—G(x)1dx.

Xu X"

_U"[Cl

Where A, represents the coefficient of relative risk aversion, A, = U'[C]

C . Since by

definition of F DS deterioration F (x)SG(x) 17%, and concavity of U the second term of that
expression is negative. The sign of the first part of the expression depends on the sign of

(1- A). If the A, is not larger than one for all values of x in the domain, then the sign of

the whole expression is negative. Therefore, VU[G]

 

is negative if U"<0 and A,_<l. I

.8" ,u’

54

Proposition 3:
a) If preferences are characterized by decreasing absolute risk aversion (DARA), then

Va, >0.

b) If preferences are characterized by increasing absolute risk aversion (IARA), then

I/uS < 0'

c) If preferences are characterized by constant absolute risk aversion (CARA), then
K1S=0

Proof

From SOC’s Vus = ,Bi[{U"[a(?c’ — r) + S(1 +r)](1 + r)('f —r)}f(x)dx . This expression

X"

can be rewritten as (I+r)fli[{[:%_"i[_[_§f2_]]]lj'[c~2](f_r)}.f(x)dx or using the
2

x0

coefficient of absolute risk aversion as -(1 + rm [{A..U'1521(Y _ r)}f(x)dx . Here A”

r“

 

represents the coefficient of absolute risk aversion, thus A” = —%T[[—g]l. Then, it follows
+ <:> IARA —
3 Au
that if a" = — c: DARA , then VHS 2 + . I
x o <::> CARA o

55

 

Total Partial Equilibrium Effects (TPEE)
Corollary 1.A: (T PEE on Savings)
If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS
deterioration of x’s cdf induces an increase in total savings.
Proof:
From lemma 1 the direct effect of a F DS deterioration on total savings is positive as long
as U "< 0. On the other hand, the indirect effect is: a) Negative under DARA and AS 1.
b) Positive under IARA and A,.<_1. c) Null under CARA. Then, combining those pieces
of information we have that the TPEE is positive if preferences show U "< 0, AS] and
either IARA or CARA.

Notice that the sign of the TPEE on S is positive under CARA and U”<0, but
cannot be determined under DARA.I
Corollary 1.8: (TPEE on Domestic Assets)
If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a FDS
deterioration of x’s cdf induces a reduction in the holdings of domestic assets.
Proof:
From proposition 2 the direct effect of a FDS deterioration on the holdings of the risky
assets is negative if AS]. The indirect effect is: a) positive under DARA and U "< 0. b)
Negative under IARA and U "< O. c) Null under CARA. Hence, the TPEE is negative if

preferences show A,SI , U "< 0 and either IARA or CARA. I

56

Corollary 1.C: (TPEE on Foreign Assets)

If agents’ preferences are characterized by risk aversion, a coefficient of relative risk
aversion no larger than one, and nondecreasing absolute risk aversion, then a F DS
deterioration of x’s cdf induces an increase in the holdings of foreign assets.

Proof:

By construction TPEE on m is given by (TPEE on S - TPEE on a). From corollary LA
the TPEE on savings is positive. From corollary 1B the TPEE on risky assets is negative.

Therefore, the TPEE on the foreign assets is positive. I

Effects of a MP Spread

Here we assume that the domestic return’s distribution goes from F to G, such as G is a
mean preserving spread transformation of F.
Proposition 4:

If U "' is either positive, negative or zero, then the marginal expected utility of savings

 

under G evaluated at {a*,S*}, V,[G] SM, , has either a positive, negative or zero value.
Proof:

From FOC’s the sign of V,[G]

 

 

is the same of V,[G] —- V,[F]

 

. Thus, the sign

S‘fi‘ S".a‘ S',a‘

is given by the sign of (l + r),B [U'[C2 ][g(x) — f(x)]dx.

I"

of V..[G]

 

S ’ .a’

57

Following Rothschild and Stiglitz (1970) [RS] we can determine the sign of VJG]

 

S ‘ ,a’

by looking at the concavity of U '[Cz] with respect to the random variable it“ . Then,

'1' convex
V..[G]

 

= — ifU'[C2]is concave inx.

S ' .a‘

0 linear

dZU ' C
Furthermore, since ——a——[—,——2-l = U "'a2 the concavity of U '[C 2] depends on the sign of

‘7

x

+ +
= — if U"'= — .I
O 0

U"'. Hence, V,[G]

 

S ‘ .(1‘

Proposition 5:

 

The expected marginal utility of the risky asset under G evaluated at {a*,S*}, ValG]

S*.a*
is negative if preferences exhibit either i) A positive third derivative of the utility
function, a coefficient of relative risk aversion smaller than one and nondecreasing in the
random variable; ii) A positive third derivative of the utility function and a coefficient of
relative risk aversion equal to one; or iii) A null third derivative of the utility function.

Proof:

The sign of Vu[G]|S.’u, is equal to the sign of a [U'[C,](x—r)[g(x)—f(x)]dx.

X”

Following RS we can establish the sign of the later expression by looking at the concavity

of U '[C2 ](x - r) with respect to x. Thus, we must find the sign of:

a 2U'[C2 ](x Tr)
d x2

 

= a[2U"[C2 ] + U"'[CZ ]a(x — r)].

58

 

To find the sign of this expression we place some restrictions on the coefficient of

relative risk aversion A, and about the sign of the third derivative of U.

. . a" A, a
By defimtlon we know that = —
a x U'[C21

 

 

[U"' C2 +U" (1+ A,)]. Furthermore, we

know that:

a) If U"'> 0,then U'” C2>U"' a(x—r).
b) If Ar<1,then U" (1+A,)>U” 2.
c) If U"'<O,then U'” C2<U"' a(x—r).
d) If A,>l,then U" (1+A,)<U" 2.

If we use some of these assumptions about U and about A, we can establish the sign of

 

VU[G] For instance, if we assume that ' >0, then we know that

x

 

.5" ,u‘

0> U"'[Cz] C2 +U"[C2] (1+ A). If in addition to that we assume that U"'> 0 and
A,<l , then it follows:
0>U"'[C2] C2 +U"[C2] (1+A,)>2U"[C2]+U"'[C2]a(x-r).

The following table summarizes the results that are obtained when we make assumptions

 

d A,
about U’", and A,.
d x

59

 

I—_-' — n—

 

Table 1.5

Marginal Expected Utility of the Risky Asset

 

 

Va U"’>0 U"=0 U"'<0
Ag<0 An=0 A4>O A§<O Ag=0 Ag>0 An<0 A420 An>0
Ar<l ? — — .. .. — .. .. ?
Ar=l —
Ar>1 9 a ‘7 __ ‘7

 

 

 

 

 

 

 

Here an outcome (1’) tells us that the sign of Vu[G]

 

is ambiguous. On the other hand,

0" .8"

an outcome (..) means that a particular set of assumptions cannot hold at the same time.

r

 

For example, if preferences exhibit a null third derivative of U, then = 0 is not

x

possible. A null .031: requires DARA, and DARA requires U "'> 0.

(3x

Total Partial Equilibrium Effects

Corollary 2.A: (TPEE on Savings)
A mean preserving spread of x’s distribution causes an increase in the level of optimal

savings if preferences exhibit either: i) Nondecreasing absolute risk aversion, a positive

60

 

l-‘_ '1- —-..«~

third derivative of U, a coefficient of relative risk aversion smaller than one and
increasing in x; or ii) A null third derivative of U.

Proof:

To determine the TPEE on total savings we must establish the signs of both the direct and
the indirect. The sign of the direct effect is give by proposition 4, whereas to determine
the sign of the indirect effect we combine the results of propositions 3 and 5. Tables 1.5
and 1.6 contain information about the signs of the indirect effect and the total partial

equilibrium effects, respectively.

Each entry in this first table represents the product of the signs of VU[G]

 

and V..s. . For

(1‘,.\"

1nstance, if we assume that U ">0, r = 0 and Ar<1, then the negatrve s1gn rs the result
(7 x

of the product of the negative sign of VJG]

 

and the positive sign of V...»-

(I’,.\"

61

 

 

Table 1.6

Indirect Effect on Savings
Mean Preserving Spread

 

 

 

 

InlSav U">O U"=O U"<0

Arx<0 szo Arx>0 Ax<0 4:0 #90 Arx<0 Arx=0 Arx>0
Ar<1 ? — — .. .. .. .. .. ..
Azl .. — .. .. .. .. .. .. .. D4RA
Ar>1 .? ? ? "'
Ar<l .. .. 0 .. .. .. .. .. ..
Ar=1 .. .. .. .. .. .. .. .. .. CARA
Ar>1 .. .. 0
A<1 .. .. + .. .. + .. .. ?
Ar=l .. .. .. .. .. .. .. .. .. IARA
Avl .. .. ? .. .. + .. .. a ?

 

 

 

 

 

 

In Table 1.7 each outcome represents the sum of the signs of the direct and the indirect
effects of a mean preserving spread on total savings. Thus, we combine the information
about the direct effect with the results of the indirect effect to determine the sign of the

TPEE on total savings.

62

 

Table 1.7

TPEE on Savings
Mean Preserving Spread

 

 

 

TotSav U">0 U"=O U"<0
Arx<0 4:0 Ai;>0 Ar,<0 Arx=0 An>0 Arx<0 Ar,=0 Arx>0

Ar<l ‘7 ? ’7

Ar: ?

4>l 9 ? 9

Ar<l +

Ar:

4>l + ..

Ar<l + + 9

Ar=1 ..

Ar>l ‘7 + ‘7

 

 

 

 

Notice that we may obtain a (‘2) output when the TPEE is ambiguous either because the
indirect and the direct effects have opposite signs or because the sign of one of the effects

is ambiguous in its own.

Corollary 2.B: (TPEE on Domestic Assets)
A mean preserving spread in x’s distribution induces a reduction in the optimal holdings

of the risky assets if preferences exhibit either: i) Nondecreasing absolute risk aversion, a

63

 

 

 

positive third derivative of U, and a coefficient of relative risk aversion no larger than one
and increasing in x; or ii) A null third derivative of U.

Proof:

Proposition 5 tells us under what conditions we can unambiguously sign the direct effect
on the risky assets of a MP spread. Using propositions 3 and 4 we can establish the sign
of the indirect effect. Then, combining those pieces of information we have that the TPEE

of a MP spread on the holdings of the risky assets is given in Table 1.8.

 

Table 1.8

Total PEE on Domestic Assets
Mean Preserving Spread

 

m Ris U"'>0 U"'=0 U"'<0
Arx<0 Ar,-_-o Arr>0 Ar,<o Ar,=0 Arx>0 Ar,<o Ar,=o Arx>0
Ar<1 7 '2 ? .. . .. .. .. ..
Ar=l .. ? .. .. .. .. .. .. .. DARA
Ar>1 ? '2 ?
Ar<1 .. .. — .. .. .. .. .. ..
Ar: .. .. .. .. .. .. .. .. .. CARA
Ar>l .. .. ? .. .. .. .. .. ..
Ar<l .. .. — .. .. — .. .. ?
Ar: .. .. .. .. .. .. .. .. .. IARA
Ar>l .. .. ? .. .. - .. .. ?

 

 

 

 

 

 

 

64

 

Corollary 2.C: (TPEE on Foreign Assets)

A mean preserving spread in x’s distribution causes an increase in the optimal holdings of
foreign assets if preferences show either: i) Nondecreasing absolute risk aversion, a
positive third derivative of U and a coefficient of relative risk aversion no larger than one
and increasing in x; or ii) A null third derivative of U.

Proof: !
By definition, we can express the total partial equilibrium effect on risky assets as a

function of the TPEE on total savings and the TPEE on the holdings of risky assets, thus

 

TPEE on m= TPEE on S - TPEE on a. Therefore, the TPEE on the foreign assets is given
in Table 1.9.

Proposition 6:

Under risk aversion, the TPEE on savings due to changes in income is positive.

Proofi

(If!

—V l/SY. + VS'ul/ul’l]

 

By definition we have that —'—— = [ then it follows that since V = 0

a}: I H[ i ‘ ul'.

V. V .
the indirect CffCCt --given by w" vanishes. On the other hand, by SOC’s V < 0

(It!

and [H[ > 0 , therefore the Sign of Ey— rs equal to the Sign of VS,l . Notice that under risk
I

‘1

aversion the sign of VS,l = — [{U"[C,]}f(x)dx is positive. I

”‘0

65

 

Table 1.9

Total PEE on Foreign Assets
Mean Preserving Spread

 

Tot For U"'>0 U"'=0 U"'<0

 

 

Art<0 Arr=0 Arx>0 Arr<0 Arx=0 Arx>0 Arx<0 Arx=0 A’}>0
Ar<l ? ? ?

Ar=l .. ? .. .. .. .. .. .. .. DARA

Ar>l ? ? ?

Ar<1 .. .. + .

Ar=l .. .. .. .. .. .. .. .. .. CARA
Ar>l .. .. ?

Ar<l .. .. + .. .. + .. .. ?

Ar=1 .. .. .. .. .. .. .. .. .. IARA
Ar>1 .. .. ? .. .. + .. .. ?

 

 

 

66

 

 

 

APPENDIX 1.B

FDS Changes

By definition the cdf F dominates the cdf G in a FDS sense iff FSG for all x. We assume
that F and G are given by [F(x,)=p,, F(x2)=1], and [G(x,,)=p., G(x.2)=1]. To show that F
dominates G we must show that F .<_G for all x. Since x”: xl-kl and x12=x2-k, it follows
that G(x,,)>F(xH). By the same token, G(x,)>F(x1), G(x,2)>F(x,2), and finally,
G(x2)=F(x2). Graphically, a F DS dominance condition implies that the function G is never
below the function F. (See Figure 1.6).

MP Changes

Let us use Figure 1.7 to show that when going from F to G the distribution of the random
return experiences a MP spread. Condition 1 of a MP spread implies that the area under G
is no smaller than the area under F, for all x in the domain. This condition holds for x<x2.
The area A represents the difference between the area under G and F for values of x lower
than x2. This area is given by:

Pi"[Xi-Xzil=Pi*[Xi-Xi+(cz/pi)l=cs-

Let B be the difference between the areas under F and G for x larger than x2. If condition
2 holds, i.e., if the expected values of x under the two distributions are equal, then the B-
area should be equal to the A-area. Furthermore, if the B-area is equal to the A-area, then
condition 1 holds for all the values of x, and therefore, the condition 1 is satisfied. The
value of the B-area is given by: (1-p,)[x2-x22]=(1-p‘)*[x2 +(c2/(1-p,))-x2]=c2. Thus, since

the two areas are equal conditions 1 and 2 of a MP spread are satisfied.

67

 

 

 

Figure 1.6

First Degree Stochastic Deterioration

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Going From F to G
F(x) G(x)
I E x11 =X1 “k1
FE x12 :x2 -k1
pl
X
x11 x1 x12 X7
Figure 1.7
Mean Preserving Spread
Going from F to G
F(x) G(x)
x2i=xi'(czlpil
x22=x2+[02/(1-p,)]
B '
p1 ,
-; A
X
x21 XI x2 x22
68

 

'F‘nu‘. 1-..'-

Chapter 2

Changes in Domestic Risk and Inflation
in Small Open Economics

2.]. Introduction

Recent empirical studies (Erb, Harvey and Viskanta (1995, 1996) and Diamonte,
Liew and Stevens (1996)) have found a positive correlation between asset return volatility
and political risk (indicators) in a variety of countries. In other words, these studies find
that countries with higher political risk tend to exhibit higher return volatility.l This
evidence seems to suggest that changes in a country’s (political) risk affect domestic
assets’ return distribution in that country.

Our purpose in this chapter is twofold. First, we try to determine how an increase
in the domestic risk of small open economies (modeled as a mean preserving spread in
domestic bond’s return distribution) affects domestic agents’ optimal saving and portfolio
choices. Second, we investigate whether these changes in domestic agents’ choices
translate into higher inflation by altering the government’s financing process.

Lately, a large body of literature has tried to establish the existence of empirical
relationships between changes in an economy’s political stability and the behavior of

variables such as economic growth, investment, saving and inflation. Those studies try to

 

' These studies also find that the (political) risk indicators predict future returns of stocks
and bonds.

69

 

uncover possible links between the decision-making process of both public and private
agents and the (negative) incentive effects that a reduction in political stability may
generate.

Studies such as Ades and Chua (1997), Alesina, Ozler, Roubini and Swagel
(1996), Barro (1991), Barro and Sala-i-Martin (1995) and Kormendi and Meguire (1985)
look for a relationship between economic growth and political stability. These studies
find that the higher the political stability the higher the growth rate of an economy.2

Alesina and Perotti (1996) analyze how income distribution affects investment.
They try to establish the connection between these variables by exploring how these two
variables relate to political stability. Alesina and Perotti claim that an increase in political
instability may affect investment among other things because it can disrupt production
activities and trade, and because higher political instability increases agents’ uncertainty
about the returns of (potential) investment opportunities. Then, given those possible
effects of changes in the political stability on investment, Alesina and Perotti show
evidence that an increase in income inequality induces a reduction in political stability,
hence it induces a reduction of investment.

Venieris and Gupta (1986) assume that the risky asset’s return distribution
function contains information about the political stability of an economy, and analyze

how well political stability, together with income distribution, explains an economy’s

 

2 Nevertheless, Levine and Renelt (1992) find that the results of some of these studies are
not very robust. Using similar data sets to those used in Barro (1991) and Kormendi and
Meguire (1985), Levine and Renelt find that the statistical significance of the variable
that measures political stability is very sensitive to the set of explanatory variables used
in the model.

70

 

saving rate. Venieris and Gupta find evidence that the level of political stability that
characterizes a given economy is a significant explanatory variable of the saving rate in
that economy. In particular, they find that a country’s saving is negatively affected by
increases in political instability. Venieris and Gupta claim. that the distortions introduced
by an unstable political system may induce risk averse agents to alter the way in which
they accumulate income and wealth. Venieris and Gupta conjecture that a possible
explanation for the low saving rates in poor economies is that those countries do not

provide a political environment that encourages saving.

2.1.1. Political Stability and Inflation

Figure 2.1 shows the average political risk (as measured by lntemational Country
Risk Guide)3 and the average inflation rate for a sample of 42 countries during the period
1985-1995. This figure suggests that countries with higher political stability tend to have
lower inflation. Here a large value of the index indicates a low level of political risk.4

Some studies have looked for this relationship between an economy’s inflation
rate and the stability of its political system, and find evidence of its existence. For
instance, Cukierman, Edwards and Tabellini (1992) find evidence in favor of a (negative)
relationship between inflation and political stability. As an explanation for this
relationship they highlight the role that institutions in politically unstable countries

(dependent central banks and inadequate tax systems) play explaining the inflation rate in

 

3 We provide information about the International Country Risk Guide’s index in
Appendix 2.

4 Similar results are obtained if we use alternatives measures of political risk as the one
used by Barro (1991) or that of Alesina and Perotti (1996). See Figure 2.2.

71

 

those economies. Cukierman, Edwards and Tabellini maintain that economies with an
unstable political system are less likely to have the institutions that are necessary to
overcome problems such as the dynamic-inconsistency of the economic policy. Thus,
political instability creates conditions that allow governments to behave with a pro-
inflation bias.

Another study that examines this relationship is Romer (1993). He studies how
the degree of openness of an economy affects the inflation rate of this economy. There he
introduces a measure of political stability and determines that politically unstable
economies tend to have higher inflation rates than stable economies. Romer also suggests
that differences in the institutions between stable and unstable economies have a
significant role in explaining the connection between inflation and political stability.

The present study, even though it relates to those works that analyze the political
stability-inflation relationship, departs from them, and suggests another link through
which political stability may affect inflation. Instead of looking at the role that
institutions in politically unstable economies may have in explaining inflation, we try to
determine how changes in the level of political stability (changes in domestic risk) could
affect agents’ saving and portfolio decisions, and how those changes can translate into

higher inflation by altering the government financing process.
2.1.2. Changes in Domestic Risk and Inflation

To analyze the inflationary consequences of changes in domestic risk, we use a

one-good, two-country (domestic and foreign) world economy framework. We assume

72

 

 

 

 

that this economy is characterized by free trade in the consumption good market and by
an imperfect financial capital market.

The domestic country is inhabited by a large number of infinitely-lived agents that
maximize expected lifetime utility and trade the single consumption good and one
financial asset (foreign bond) with the rest of the world (the foreign country). We assume
that domestic agents face a cash-in-advance constraint, so they must have domestic
currency to participate in the domestic economy’s good market.

In the initial period domestic agents receive an endowment of the single
consumption good. During the rest of their life agents receive no other endowment and to
finance their consumption they must save. We assume that agents may use two saving
alternatives: domestic and foreign bonds. Because of the size of the foreign market, we
assume that the foreign bond’s nominal return is determined outside of the domestic
economy. Furthermore, we assume that this return is known with certainty and taken as
given by domestic agents. The domestic bond’s nominal return is random, with a known
distribution function, and behaves as an independent and identically distributed random

variable.

The domestic economy also has a government that sells units of the domestic
bond and issues domestic currency to finance its spending. The domestic government
does not have access to international financial markets, and, therefore, it can sell the
domestic bond only to domestic agents. We assume that the domestic government holds a
constant level of international reserves (foreign currency), and that the domestic economy

has a managed exchange rate system. As a consequence of these two assumptions

73

 

 

(constant international reserves and managed exchange rate system), the domestic
government can alter the money supply only by changing the rate at which agents
exchange domestic and foreign currencies.

This is the context in which we evaluate the effects of an increase in the domestic
risk on domestic inflation. Following Rothschild and Stiglitz (1970), we model changes
in risk as mean preserving spreads of the risky asset’s return distribution. Hence to
represent an increase in the domestic risk we assume that the domestic bond’s nominal
return distribution experiences a mean preserving spread.

To conduct the comparative static analyses we compare the equilibrium outcomes
of two economies that differ only in the distribution functions of their random asset’s

return. We do the comparisons both at a partial and at a general equilibrium level.

Doing the partial equilibrium analysis (the analysis at the individual level) we
follow the methodology developed by Levhari and Srinivasan (1969), Samuelson (1969),
and Rothschild and Stiglitz (1971). We ask what assumptions about agents’ attitude
toward risk are sufficient to unambiguously sign the effects of changes in the domestic
risk on agents’ optimal savings and portfolios. We find that when agents’ preferences are
characterized by constant relative risk aversion and the coefficient of relative risk
aversion is no larger than one, an increase in domestic risk induces domestic agents to
reduce their holdings of the domestic bond, and, at the same time, to increase their
positions in the foreign asset (the standard results in the literature on risk).

Then using those results at the individual level we study the general equilibrium

implications of an increase in domestic risk. We find that a reduction in domestic

74

 

 

investors’ willingness to hold the domestic bond (due to the increase in domestic risk)
forces the domestic government to expand the money supply to compensate for the
shortfall in fiscal revenue.5 To augment the money aggregate the domestic government
increases the devaluation rate of the domestic currency, and a higher devaluation rate
translates into higher inflation. Therefore an increase in a country’s domestic risk (an
increase in its political instability) induces an increase in that country equilibrium
inflation rate when agents’ preferences exhibit a coefficient of relative risk aversion no
larger than one.

The rest of the chapter has the following structure. Part 11 describes the
characteristics of the economy and defines a competitive equilibrium. In part III we
analyze how a mean preserving spread in the distribution of the domestic bond’s nominal
return affects both domestic investors’ saving and the configuration of domestic
investors’ portfolios. Part IV presents the analysis at a general equilibrium level. There
we evaluate how changes in domestic investors’ actions affect the financing process of
the domestic government, and how changes in the way the government finances its

spending can produce higher inflation. Finally, part V contains some comments.

 

5 The money aggregate expansion takes place (in part) because of the domestic
government’s inability to borrow on the international financial market, and to levy taxes
on the domestic agents.

75

 

2.2. General Characteristics of the Economy

The following is the setup of a one-good, two-asset (domestic and foreign bonds),
two-country (domestic and foreign) world economy.

The domestic country is a small open economy inhabited by a large number of
infinitely lived agents that maximize expected lifetime utility. Domestic agents trade a
single consumption good and one financial asset (foreign bond) with the rest of the world
(foreign country). Given the relative size of the domestic economy, the price of the
consumption good (in units of the foreign currency), is determined in the foreign country,
and domestic agents take it as given.

We assume that in the domestic economy the only source of income is from
savings. To save domestic agents could use two alternatives: domestic and foreign bonds.
The foreign bond has a nominal return that is known with certainty, and it is taken as given
by domestic agents. The domestic bond is risky, and even though its nominal return is
random agents know its distribution function. This distribution function is exogenous.6

In this model the international financial capital market is imperfect, because the
domestic government cannot participate in it. Here, any bond issued by the domestic

government can be bought only by domestic agents.7

 

6 Following Venieris and Gupta (1986), Erb, Harvey and Viskanta (1995, 1996) we
assume that domestic return reflects information about the political stability, and,
therefore, this is the (main) source of risk for the domestic bond. In particular, here we
interpret the domestic risk as coming from the political environment that agents (both
private and public) face, and that is exogenous to them.

7 Even though this is a very strong assumption, there have been several episodes in which
the governments of developing economies have had very limited access to international
financial markets. An example of these episodes is the period after the debt crisis in the
1980’s in which many developing economies, especially in Latin America, had very

76

 

2.2.1. Households
The domestic economy is populated by a large number (that we normalize to one) of
identical households that live forever. These households maximize expected lifetime utility

from consumption. We assume that agents’ expected lifetime utility is given by:

(1) 15,25 ’ U(c,)

(=0

where ,6 is a stationary subjective discount factor, such that ,8 e(0,1). U is a strictly
increasing, strictly concave, continuous and twice differentiable utility function,
e, > 0 denotes consumption in period t, and E0 is the expectation operator. We assume
that at the beginning of their life all agents receive an initial endowment, W0, of the
consumption good.

As a simplifying assumption, in the domestic economy there is no production so,
domestic households receive utility from the consumption of a good that is produced

abroad and sold in a perfectly competitive international market. The price of this good on

the international markets, Pf, is expressed in foreign currency, and we assume that it is

constant and equal to one. Then, under free trade and by the law of one price (arbitrage

condition), P, = P,’ e, . Here e, denotes the nominal exchange rate of domestic currency

per unit of foreign currency, whereas P, represents the price of consumption good in the

t

. . . . P e
domestic market. Furthermore, srnce P = 1, 1t follows that P, = e, and ’ ’ El.

' 1’.

 

 

limited access to international financial markets. See Agénor and Montiel (1996, Chapter
13). Another example is given by the sudden reduction of inflows of financial resources
into Mexico after the first quarter of 1994. See Atkeson and Rios-Rull (1996).

77

 

 

We assume that domestic households face a cash-in-advance constraint (CIAC),

hence:

(2) m," 21’, c

I

where m," represents households’ demand for money.

In this economy interest-earning from saving is the only source of income for the
domestic households. Thus, domestic agents must save to transfer resources between
periods. To save households determine their desired levels of both domestic bonds, b, and
foreign bonds, b* , in each period. These bonds are denominated in nominal terms in their
respective currencies, and have a one period maturity.

The domestic bond (issued by the domestic government) can be purchased only
by domestic agents. This bond has a random nominal net return, i , with a cumulative
distribution function denoted by F. Furthermore, we assume that 36 is an independent and
identically distributed (iid) random variable. We also assume that domestic households
make their resources allocation decisions before 36”, is revealed, where 36,” is the net

rate of return of a domestic bond bought at period t that matures at period t+1. The

foreign bond is denominated in foreign currency, and the domestic currency value of b,‘+l

units of the foreign bond (at the buying time) is e, b. The nominal net return of a

I+1'

foreign bond bought at period t and that matures at t+1, r is determined in the

[+1 ’
international financial market and it is known with certainty. We assume that agents take

both F and r,+l as given. Given this set up, we can write the domestic households’

intertemporal nominal budget constraint (HBC) as:

78

 

(3) P, c, + m1, +1)”, + e,b,‘,, = (1 + r,)b, +(1 +r,)e,b,‘ + m," v t_>_1.

Thus domestic households use the financial resources available at the beginning of
period t to buy consumption goods and to acquire financial assets.

Notice that e,b,'+l is the nominal value in domestic currency of bf” units of the
foreign bond when agents buy (at the beginning of period t). However we can rewrite this
expression in terms of the domestic currency value at the beginning of period t+1, by

)
c(+1

 

multiplying e b' by

l 1+l

, and expression (3) becomes:

eH—l

e
.1 1+1 ' _ ~ ° 1
RC, +m +b,+I +e, —b,+l — (1+x,)b, +(l+r,)e,b, +m,‘ .

1+1
H]

e .
Let a, = ——’—’-—‘—, then 1t follows that:
e

l

(I

1 t ~ ‘ (I
PIC! +"11H +br+l +el+l :bnl =(l+x1)bt +(1 +r,)e,b, +ml

l

1 . . . . .
where e,+l ——b,+l represents the domestic currency value of b,+1 units of the foreign bond
6

at beginning of period t+1. (e, )'I denotes changes in the domestic currency value of bf“
that take place because of changes in the exchange rate of the domestic and the foreign
currencies between the beginning of period t and the beginning of period t+l.

In real terms the HBC is given by:

 

" . 1 ~ b . "
C, + mt+l + bt+l el+l i ”l = ( +x,) I +(1+rl )b, .84-+23,—
P P P 6‘, P

l l l l l l

and assuming that P, = e, for all periods, we have:

79

 

 

‘l b . l 7' b . "
c,+—’h+—”i+n,ib,,,=(—:£’)—’+(1+r,)b,f’-+m—’ or
P, P, if. I P, P,

m" b . (1+r)]; . m"
(3’) c,+—’*'—+—fi+b,+,=—P’L+(l+r,)b, +—1;’—.

I I I I ,

2.2.1.1. Solving the Households’ Maximization Problem

The households’ problem is to maximize their lifetime utility by choosing an
optimal sequence of consumption, foreign and domestic bonds, and money holdings given
the CIAC and the HBC. Thus given some positive initial endowment, W0, the foreign
bond’s nominal return (a constant for all t), the domestic bond’s nominal return distribution
(and the realizations of this return until period t), the period t exchange rate between the
domestic and the foreign currencies (and past realizations) and the price in domestic

currency of the consumption good (and past realizations) households solve:

(1) Max , EOZfl’ U(c,)subject to:

h . '
[1,. "—'.h,,..'fl’—l[ I :0

 

8 If e,+l at e, agents face a (nominal) capital gain or loss depending on the direction that
the exchange rate moves. Thus, it looks as if agents confront exchange rate risk (ERR)
investing in the foreign bond, since e,+1 is unknown when they choose b,’,, . If this were
the case, agents would be choosing between two risky assets. Nevertheless, in this case
since the nominal rate of return of the foreign assets (ignoring capital gain or loses) is
known with certainty, and, since PH1 1+1 , the real rate of return is also known with
certainty, and it is equal to the nominal rate of return. Hence, even though in nominal
terms there exists ERR when investing in the foreign bond, the ERR is not present when

we do the evaluation in real terms, and, therefore, in this set up we can consider the
foreign bond as a risk-free asset.

=6

80

 

_,A___‘.._

w?

. ‘4"

 

(2) m," 2 P c, and

l

(I ~ I
b . 1 b . ‘
(3’) a +——'",’." +—-’*' +1)... =————( H” ' +<1+r,>b, +3; '

l I l f
Equivalently, we can rewrite the maximization problem in terms of real wealth

using the result of the next proposition.

Proposition 1:
If the domestic nominal net return, 3c“, , is positive, then the cash-in-advance constraint (2), is
binding.
Proof:

Let us define W, as real wealth at the beginning of period t, thus for t Z 1,
P,_,W,_, = b, + e,_,b,' + m," and PW, = (1 + 17,)b, + (1 + r, )e,b,‘ + m," — P,c,.

Then, by substitution of the first expression into the second we have:
P,W, = (1 + 32', )[P,_,W,_, — e,_,b,’ — m;’] + (1 + r, )e,b,' + m," - P,c,,

5(RWI)
d =—x,

~

and therefore

 

é’m

Then, as long as if, > O households have incentives to set m," 2 —oo in order to
maximize nominal wealth. However, by the cash-in-advance constraint (CIAC), the lowest

possible level of money that agents can hold is given by P, c, , and, therefore, agents set

m," = P,c, . Thus, if f, ’3 support is given by [xO ,xl ] , where x0 is positive, then the CIAC

binds.-

81

 

 

 

 

A convenient way to solve the households’ maximization problem is to rewrite the

HBC in terms of agents’ saving and portfolio mix. Let us define agents’ total (nominal)
saving as P,S, = b,+l + e,b,‘,,. On the other hand, let a, be the share of the domestic bond

in agents’ portfolios (or total saving), a, = (b / P, S,) . Then it follows that:

I+l

(1+x',)b,+(1+r,) e, b,‘ =[(1+sc,)a,_l +(l+r,) g,_, (1—a,_,)[r,_,s,_,

where £,_, denotes the gross rate of change of the exchange rate, i.e., £,_, = (8’ e j . Let
I-l

us define R, as the return of agents’ portfolios, hence
R, ER(a,,3c’,+l,r,,,,e,)=[(1+3F,,,)a,+(1+r,+,) .s, (1-a,)[.

Using the result of proposition one, we can write the households’ intertemporal

 

1+1

budget constraint as: W =[ P’ ][R, (W, —c,)[ or

H]

 

Thus we can write households’ maximization problem as:

Max Eoiflt U(c,) subject to W =[R, (W —c,)[.

l+l I
'c ,a .W
ll I “ll 1-0

 

 

 

In the following analysis we use a specific functional form for the utility function. In
particular, we assume that the utility function, U, exhibits constant relative risk aversion

l-r
y7¢l
(CRRA), and therefore U (c) = 1— 7 .
Ln(C) if)’ =1

 

From Samuelson (1969) we know that this maximization problem can be broken
into two separate maximization problems when agents’ preferences are characterized by
CRRA. In the first problem agents determine the optimal size of their portfolios (savings

rate), whereas in the second maximization problem agents select their optimal portfolios’

mix, a, .

2.2.1.1.1. Case 1: 7 >0 and y at]
Optimal Savings
To determine the optimal saving rate, we solve the following dynamic programming

problem:

 

0 Sc SW

.l-r ..
(5) V[W,a] = Max [1‘ + p E[V[(R(W—c)),a[[[.
7
Since it” is iid, the value function and the optimal policy rules for consumption and

saving are given by: V[W,a]=[f_l_[[1_[fl E[R81-y [[r ]‘7 Wi—r
”7

c, =[1—[p E[1i,'-7][W[W, and s, =[,8 E[R,"’[[WW,.

83

 

 

Notice that those policy firnctions depend on E [R,"’ [ , and therefore, they depend

on the optimal portfolio’s mix, the foreign asset’s nominal return, the domestic asset’s
nominal return, the rate of change of the exchange rate and the inflation rate.9

Optimal Portfolio

To select the optimal composition of their portfolios, agents maximize (if y < l)

a,(1+f,+,)+(1—a,)e,(l +r,,,)

fl'

 

l-r
(minimize (if y > 1)) E I: :[ with respect to (1,. This is

1

equivalent to maximizing (minimizing) E [R,"7 [ with respect to a, , taking as given both

 

 

 

a,” and am. Then, the optimal portfolio is given by the a, that solves:
((1+ in ) _ 8I(1+ rl+l ))
E ”' , =0
[a,(1 +23”) +(1 -a,)e,(l +r,+,))
7r, -

 

 

and, therefore, period toptimal portfolio mix, a,, is a function of 36”,, r,+l , 7t, and e,

2.2.1.1.2. Case 2: 7 = 1
Optimal Savings

If we assume a Log-utility function the functional equation is given by:

(6) V[W,a] = Max Ln(c) + p E[V[R(W—c)[[.

031' SW

 

9 Levhari and Srinivasan (1969), Rothschild and Stiglitz (1971) and Sargent (1987, Chapter
I) obtain similar results.

84

 

 

Since 3? is iid we can write the value function and the policy fimctions as:

V[Wa]=[1—_1——fl[Lnl(—fl)+[(l _flfl)[Ln+(fl) [-_—,[Ln(1+[(,_flfl),[E[Ln(R)]

c,=(1—/3)W, and S.=AW.

 

 

Notice that in the Log-utility case none of the policy functions depend on the

portfolio’s return, R,. In other words, if the coefficient of relative risk aversion is equal to
one, 7 = 1, consumption and saving rates do not depend on either the optimal portfolio’s
mix, the foreign asset’s nominal return, the domestic asset’s nominal return, the rate of
change of the exchange rate or the inflation rate. They only depend on ,0.

Optimal Portfolio

In this case, agents choose a, to maximize: E[Ln(a, (l +x,,,)+(1— a ,,)e (l +r ,.,,))]

[(1+x,..)— a.r<1+ ,..)]
[a (1+x,,,)+(1— a,’,r)8(1+r,..)[

 

The optimal a, is the one that solves E =0. As

in the case when y rat 1, here the period t optimal portfolio configuration, a, , does depend

onx r

l+l’

(+1’ ”I and 8! '
2.2.2. Government

The domestic economy has a public sector that lives forever. The domestic
government issues bonds and adjusts the level of money supply to finance some
exogenously given stream of expenditure. We assume that government’s consumption, g,,

does not produce any effect on the consumers’ utility, and therefore, we consider it a pure

85

 

 

destruction of the consumption good.'0 The domestic government buys its consumption
goods in the domestic market, just as domestic households do.

We assume that the domestic government cannot sell bonds to foreign residents
even though the domestic government always honors its debt.‘l We summarize the

activities of the domestic government using its intertemporal budget constraint (GBC), that
can be written as: m,“ = P, g, = B,H —(1+fc’,)B,+ M,+1 — M, for all t2]
where B,+1 represents the amount of domestic bonds issued by the government, and M 1+1

represents the money supply. Here m,“ represents the amount of nominal resources that
domestic government needs to finance its expenditure.

The domestic government is in charge of the money creation process. However,
the monetary activities of the government are restricted by its fiscal actions. In other words,
the domestic government must collect enough resources to finance its given expenditure
stream by selling bonds and expanding the money supply. We assume that the domestic
government expands domestic currency to finance the difference between fiscal spending
and government’s debt.

Given the assumption of a managed exchange rate system, let us define the

domestic money supply as M, = e, IR, , where IR, is the amount of international reserves

held by the domestic government at period t. In this case the money supply could be

affected either by movements in the amount of foreign reserves held by domestic

 

'0 Following Lucas and Stokey (1983), we consider government’s consumption as
defense expenditures that have to be made to face an unlikely war.

” Notice that the kind of risk in domestic bonds that we try to model is not default risk.
Here we assume that the nominal return is always positive.

86

 

 

government or by variations on the exchange rate, thus a change in the money supply is
given by:

(7) M,+| - M, = e,,l AIR, +(e, —-1)M,

where A indicates absolute variation, and 5, represents the gross rate of changes in the
exchange rate. From (7) it follows that if AIR, > 0, i.e., the international reserves go up
(holding everything else constant), the stock of domestic currency increases. On the other

hand, given the stock of international reserves, money aggregates can be affected by

variations in the exchange rate. We assume that at the end of period t the domestic
government determines the exchange rate e”, , by intervening in the exchange rate market

such that the desired level is achieved. In other words, the domestic economy has a system
of managed exchange rates. Given the level of international reserves, a devaluation of the
domestic currency, (8, — l) > 0 , induces an increase of the money supply whereas when
the domestic currency experiences a revaluation, (e, - 1) < O , the domestic money supply

decreases. Using (7) we can rewrite the GBC as:

(8) P

,g,=B,,,—(1+'f,)B,+e AIR,+(g,—1)M, 121

1+]
hence to finance period t spending and to repay its debt, the domestic government must sell
domestic bonds, and alter either the domestic currency exchange rate or the level of
international reserves. Here we assume a given level of international reserves, and,
therefore, the policy variable in control of the domestic govermnent is the rate of change of

the nominal exchange rate.

87

n.

 

2.2.3. Domestic Currency Market

We define an equilibrium of the domestic currency market as a situation in which

the demand for money is equal to the money supply, M, = m," + m,“ . Notice that we add to

the money demand the nominal resources that government uses to finance its expenditure.

2.2.4. Domestic Bond Market

The domestic government does not have access to international financial markets,
and, therefore, the bond issued by the domestic government cannot be bought by foreign
agents. Domestic households choose their desired level of the domestic bond so as to
maximize their expected lifetime utility. The domestic government’s supply of this bond
must be enough to clear the market (31+: 2 b,+,), given the distribution of the domestic
nominal return, the domestic inflation, the devaluation (revaluation) of the domestic

currency and the foreign nominal return.

2.2.5. Foreign Bond Market

Given the size of the foreign country, the foreign bond’s nominal return is
determined in the foreign country’s financial market, and, therefore, domestic private agents
take it as given. Thus, the domestic agents determine their desired foreign bond purchases

and buy them on the international market.

88

 

 

 

2.2.6. Consumption Good Market
Given the size of the domestic economy, the international price of the consumption
good is fully determined in the foreign market. Under the assumption of free trade the

domestic price of the consumption goods, ,, is equal to [the international price of the
consumption good in foreign currency, P,’ , times the exchange rate of the two currencies,

e, . Furthermore, since we assume that P,’ = 1 for all I, the price of the consumption good in
the domestic market is equal to the exchange rate, P, = e,. At this price, domestic

households choose their optimal consumption, and the domestic government carries out its
expenditure stream. We define an equilibrium in the consumption good’s market as a
situation in which domestic consumption (both private and public) is feasible. Then using

the HBC and the GBC an equilibrium in the consumption goods market is given by:

O

P, c, +P, g, =e, [(1+r,)b,' —b,,,] or

(9) 8! (rt bl.)_1)l (CI +gl):el [bill _bl‘]
Expression (9) represents the domestic economy’s balance of payments at period t,

where the right-hand-side expression indicates the capital account balance and the left-

hand-side expression indicates the current account balance.

2.2.7. Competitive Equilibrium

We define a competitive equilibrium as a sequence

I
bt+l ’

MeP

I+|’ t+l’ l+l’ t+l},=0

X
a,,S,,g,,m, ,B

I+l " I+l ’

[c,,m" b

89

 

 

such that given F, {Z,,,r,+,}:0 and the initial endowment W0, households solve their
maximization problems, the government budget constraint is satisfied, the domestic and
foreign bond markets clear, the domestic money market clears and the domestic
consumption allocations (both private and public) are feasible.

Alternatively, we can define a competitive equilibrium as a sequence

a, ,5, 9g. am,“ «3

1+l’ I+l" l+l’

II CD
{Cl’m b b I+I’Ml+l’el+l’])l+l},___0

such that given F, {f,,,,r,,,}:0 and the initial endowment W0, the balance of payment
condition of the domestic economy, expression (9), is satisfied.

Notice that in this model if both c, and g, are greater than zero, a competitive

equilibrium requires a positive value of b,‘ for all t. This implies that the optimal portfolio
mix, a,, must be greater than or equal to zero and strictly less than one, a, e[0,l) , for
t 2 1 . However, from now on we assume that the portfolio maximization problem has an
interior solution, and, therefore, a, 6 (0,1) for all t 21 .

In the following sections, and to simplify notation, we drop the time subscript in all

the variables. We represent R, as R, f as 36 , r,,, as r, e, as e,e

1+1

ase, 7r,asn,

I+|

P

H]

as P , s, as s , and a, as a. There s denotes agents’ saving rate.

2.3. Effects of an Increase in Risk (Partial Equilibrium)

In this section we try to determine the effects on domestic agents’ positions in

both foreign and domestic bonds that an increase in the domestic risk may induce.

9O

 

 

Following Rothschild and Stiglitz (1970) [RS], we model an increase in the domestic risk
as a mean preserving spread in the distribution of the domestic asset’s (nominal) return.

To determine the effects of a mean preserving spread (MPS) in domestic bond’s
nominal net return distribution on domestic agents’ behavior, we compare agents’
optimal choices in two economies that differ only in the cumulative distribution function
of their random return. Furthermore, we ask what assumptions about agents’ relative risk
aversion are sufficient to determine the signs of those effects of a MPS in domestic
bond’s nominal net return distribution on agents choices.
Changes in Domestic Risk

Let /i be an index of a family of the cumulative distribution functions (cdf) of the
random variable Y , such that an increase (a reduction) in /i indicates an increase (a
reduction) in the risk of the random variable’s cdf. In other words, given F and G, two
different cdfs of the random variable 5? , we say that G is riskier than F in a Rothschild
and Stiglitz’s sense if A ,, < /i 0. . Here, /i ,, and /i,,. represent the indexes associated to the

distributions F and G, respectively.”

Let [Sta/i} and {330?} denote domestic households’ optimal saving rate and

portfolio configuration when agents face the distributions F and G, respectively. Then by

comparing [5" ,a‘} and {5,61} we can determine how domestic private agents adjust their

portfolios in response to MPS in the domestic asset’s return distribution.

91

 

 

 

2.3.1. Effects on Households’ Optimal Choices

The next analysis follows Levhari and Srinivasan [1969] and Rothschild and
Stiglitz (1971), closely.
2.3.1.1. Case 1: y>0 and #1
Proposition 2:
A mean preserving spread in the domestic asset’s return distribution induces an increase
(a reduction) in domestic agents’ savings rate if the coefficient of relative risk aversion is
greater (smaller) than one.
Proof

From the households’ maximization problem we know that the saving rate is
. A]- /7 "1_ .
grven by: s=[,6 E[R ’ [I or s7 = ,6 E[R 7 J. Followrng RS we must look at the

concavity (convexity) of H 5 R"’ with respect to the random variable, 5c” , to determine
the effect of a mean preserving spread in it" ’5 distribution on the saving rate.

7

1-
By definition RM 2 [:[i][a (1 + ic')+(1— a)e (1 + r)][ . Hence the concavity of
It

H with respect to Y is given by:
2 1 1—7 ~ -(|+r)
H” =—[7(1 —7) a] —- [a (1+x)+(1—a).e (1 +r)]
It

It follows that if y is smaller (greater) than 1, then a MPS in the domestic bond’s

return distribution induces a reduction (an increase) in the savings rate. '3 I

 

‘2 We follow Diamond and Stiglitz (1974) in the use of these indexes for the random
variable’s cdf to indicate changes in risk.
‘3 Here Ojj denotes the second derivative of variable 0 with respect variable j.

92

REY- f-r-r" a.

 

1m .-
1 _

Proposition 3:
A mean preserving spread in the domestic asset’s return distribution induces a reduction in

the proportion that the domestic bond represents in households’ portfolios (a reduction in

a), if the coefficient of relative risk aversion is less than one.
Proof

From households’ maximization problem we know that the optimal portfolio mix,
' i
((1 +x)—e (1+r))

a,is given implicitly by: E v =0.
[a (1+Y)+(1—a)e (1+r)]

71'

b d

 

 

 

 

 

((1+r)—s (1+r))
[a (l+'f)+(1-—a)£ (1+r)]7

72'

b d

 

LetZE

 

 

 

 

Then we can determine the effect of a MPS in domestic bond’s nominal return
distribution on a if we can establish the concavity (convexity) of Z with respect to it” . It
follows that
r A

_ ay [a(l—7)(l+Y)]+[2(l—a)+a(1+y)]g(1+r)
Ir’ (a (1+x)+(1—a)g (1+r))“2

72'

— a—l

 

 

 

 

 

is negative if y< l, and therefore, a MPS in f ’5 distribution induces a reduction in a. Since
the sign of Zn is ambiguous when 7 >1 , the effects of a MPS in f ’5 distribution on the

optimal portfolio configuration are also ambiguous. I

93

2.3.1.2. Case 2: 7 =1
Proposition 4:
A mean preserving spread in the domestic asset’s return distribution induces a reduction
in the proportion that the domestic bond represents in households’ portfolios (a reduction in
or), if the coefficient of relative risk aversion is equal to one.
Proof

From households’ maximization problem with a Log-utility firnction we know that
the optimal portfolio mix is given by the a that solves:

((1+r)—a(l+r))
(a (l+?c’)+(1-a)e (1+r))

 

=0.

Then to determine the effect of a MPS in it“ ’5 distribution we must establish the

((1+r)—e (1+r))
(a (1+r)+(1-a)g (1+r))

 

concavity of: Z 2 with respect to f .

. 2a (1+r)e _ . .
Srnce Z = — , 1S negatrve, we have that a MPS 1n

(a (1 +r)+(1—a)g (1 +r))‘

 

it” ’s distribution induces a reduction in a .I

Notice that in the Log-utility case the domestic agents’ saving rate does not
depend on the random variable, 3? , and therefore, it cannot be affected by MPS changes
in domestic bond’s nominal net return distribution. Table 2.1 summarizes the results of

propositions 2-4.

94

 

 

 

Table 2.1

Partial Equilibrium Effects of a MP8 in Domestic Bond’s
Nominal Return Distribution

 

 

 

 

 

7 Effects on Saving Rate Effects on a
(0,1) (-) (-)

1 0 (-)
(1,00) (+) (17)

 

 

2.3.1.3. Demand for Domestic Bond

In this section we use the results of propositions 2-4 to establish the sign of the

 

 

partial equilibrium (PE) effects of a mean preserving spread in the domestic bond’s return
distribution on the demand for domestic bonds. To conduct the comparative static
analysis we compare the optimal holdings of the domestic bond of agents that inhabited

two economies that differ only in the risky (domestic) bond’s return distribution.

95

 

Corollary 1: (PE Effects on Agents’ Demand for Domestic Bonds)

A mean preserving spread in the domestic bond’s nominal return distribution
induces a reduction in domestic agents’ demand for domestic bonds if the coefficient of
relative risk aversion is less than or equal to one.

Proof
By definition households’ demand for the domestic bond can be written in terms of the

optimal portfolio mix and the level of savings as: b,l =a,P,S, or equivalently,

I

b,,, = a,s,P,W, , where s, represents period t agents’ saving rate. Then, for a given level

of period t wealth, any effect of a MPS in I? ’5 distribution on the demand for domestic

bond must be induced by changes in agents’ portfolio mix and savings rate, and therefore:

db da
1 -—’*' = .' PW -———’ PW
( 0) d1 [SI I I] d], +[al I I]

ds,
11,1 ‘

l4

 

From the results of propositions 2-4 and expression (10), we know that we can
sign the effect of a mean preserving spread (MPS) on the demand for domestic bond
when the coefficient of relative risk aversion is less than or equal to one.

If the coefficient of relative risk aversion is equal to one, agents’ saving rate does
not depend on f (therefore, it does not depend on xi). In this case, the effects of a MPS in

if ’3 distribution on domestic agents’ demand for domestic bonds are driven only by

changes in agents’ portfolio configuration.

 

'4 Here A is the Rothschild and Stiglitz’s index of change in risk, and $- represents the

changes in variable 2 in response to changes in the risk of the risky asset’s nominal return
distribution.

96

 

I
14..
_.‘.!'L'-

Thus, a MPS in 3? ’5 distribution induces a reduction in agents’ demand for
domestic bonds if the coefficient of relative risk aversion is equal to one.

In the most general case of the constant relative risk aversion utility function
(#1), the effects of a MPS in the domestic asset’s nominal return distribution on agents’
demand for domestic bonds are given by the combined effects on agents’ portfolio
configuration and savings rate. We find that when the coefficient of relative risk aversion
is less than one, the effects of a MPS in Tc’ ’5 distribution in agents’ savings rate and
portfolio configuration go in the same direction, the two effects are negative, and
therefore, the effect of a MPS in 3? ’3 distribution in domestic agents’ demand for
domestic bond is negative.

Notice that if the coefficient of relative risk aversion is greater than one, we
cannot determine the effect of a MPS in it” ’5 distribution on domestic agents’ demand for

domestic bonds because we cannot sign the effect on agents’ portfolio configuration. I

2.4. Changes in Domestic Risk and Inflation

(General Equilibrium Effects)

In this section, we try to determine how an increase in domestic risk may affect
the domestic economy as a whole. In order to do this evaluation we try to connect
domestic agents’ reactions to this change in risk with the behavior of the domestic
government. In particular, we analyze how changes in agents’ demand for the domestic
bond may induce revisions in the form by which the domestic government finances its

spending.

97

 

 

'Ir-t'- ‘
1
l

 

 

 

2.4.1. Government Financing Process

In general, a reduction (an increase) in agents’ demand for domestic bonds
induces the domestic government to increase (reduce) the use of changes in monetary
aggregates as a source of revenue. From expression (7), the domestic government can
affect the money supply either by changing the devaluation rate of the domestic currency
or by changing the level of international reserves. However, if we assume that the stock
of international reserves held by the domestic government is constant, changes in the

money supply take place only because of changes in the devaluation rate.

2.4.2. Effects of an Increase in Risk
2.4.2.1. Demand for Domestic Bonds

If we assume that the coefficient of relative risk aversion is no larger than one, an
increase in domestic risk (represented as a mean preserving spread in the domestic bond’s
nominal return distribution) induces a reduction in agents’ demand for domestic bonds.IS
This reduction in the demand for domestic bonds limits the ability of the domestic
government to issue new bonds, and drives the domestic government to increase the
money supply by increasing the domestic currency’s devaluation rate to finance its
consumption. This reaction of the domestic government may induce additional responses
in domestic agents because an increase in the devaluation rate may imply changes in the

real returns of the financial assets.

 

'5 We focus in cases where the coefficient of relative risk aversion is no greater than one
because we know that the effect of a mean preserving spread in domestic bond’s nominal
return distribution on households’ demand for domestic bonds can be unambiguously
determined, and it is negative (Corollary 1).

98

 

 

 

In section III, we assumed that agents adjust their optimal choices because an
increase in domestic risk, taking as given the devaluation rate (and for that matter all
government activities). Now we evaluate both agents’ and government’s behaviors once
we take into account their interactions, and the fact that s, = 7r,.

To determine the general equilibrium effects of changes in the domestic risk we
must determine how agents’ saving and portfolio mix depend on the domestic currency
devaluation rate. The next two propositions help us to establish the signs of those
effects.'6
Proposition 5:

An increase in the devaluation rate of the domestic currency induces a reduction (an
increase) in the saving rate of the domestic agents if the coefficient of relative risk
aversion is less (larger) than one. Furthermore, if the coefficient of relative risk aversion
is equal to one an increase in the devaluation rate does not affect agents’ saving rate.
Proof

If the coefficient of relative risk aversion (7) is different from one, by the FCC and

because the devaluation and the inflation rate are identical we know that

(1 + ma “‘7’
s7 = ,6 E[:-——— + (l + r)(1 — a):[ and therefore,
8

 

'6 Once again, we drop the time subscripts.

99

 

 

 

 

...qlirl-

 

 

 

 

— (1+ Ba _
(3‘7 2
(,8 = ——/3(1 -— 71E 1 ,. 5 ,
[LT—’93 + (1 + r)(l - (2)]
t 8 -

Thus an increase in the devaluation rate induces an increase (a reduction) in the

saving rate if the coefficient of relative risk aversion, y, is less (larger) than one. Notice

that when the coefficient of relative risk aversion is equal to one the saving rate does not

(3.7

 

depend on the devaluation rate (it just depends on ,0) and therefore, is null.I

 

Proposition 6:
An increase in the devaluation rate of the domestic currency induces a reduction in the

proportion that the domestic bond represents in households’ portfolios (a reduction in a), if

 

the coefficient of relative risk aversion is no larger than one.
Proof

If 7 $1 we have that the optimal portfolio mix is given by the a that solves:

 

 

 

 

 

(l+3c’)—e(1+r) i
E g = 0. By the implicit function theorem, the sign of @
[a(l+x’)+(1—a)e(1+r)[7 a;
l .- _
é’a

 

is given by the derivative of the first order condition with respect to .9. Thus the sign 0,,
e

100

 

 

 

P [am — 7)(l + Y)’ + e(1+ r)(l + r)(1 — a(l — ”[7
3
is given by the sign of E —- 8 1+ . Then,
[a(l+r)+(1—a)s~(1+r)[ ’
8

 

 

 

 

if 7 < 1 an increase in the devaluation rate reduces the proportion that the domestic bond
represents in agents’ portfolio.

On the other hand, if 7 = 1, we have that the optimal portfolio mix is given by the

(1+f)—e(1+r)
[a(l +i’)+ (1— a)e(1+ r)]

 

a that solves E[ [2 0. Therefore, the sign of % is given by
e

(1 +r)(1+ r)
[a(1+ Y) + (1 - a)e(1+ r)]2

 

the sign of E[— [. Thus, if the coefficient of relative risk

aversion equals one, an increase in the devaluation rate induces a reduction in the

. . . , . é’a
proportion that domestic bonds represent in agents portfolros and therefore, 7 < 0 .I
(5

Next, using the results of propositions 2-6 we establish the general equilibrium

(GE) effects of changes in the domestic risk.

Corollary 2: (GE Effects on the Demand for Domestic Bonds)
A mean preserving spread in the domestic bond’s nominal return distribution induces a
reduction in the (general equilibrium) demand for domestic bonds if the coefficient of

relative risk aversion is no larger than one.

101

 

 

Proof
Notice that if the coefficient of relative risk aversion is equal to one, from expression (10)

and because in this case the PE effect on the savings rate is null, the general equilibrium
. . . db, , da
effect on the demand for domestic bonds rs given by: 71—;- = [,6P,W,] 71’— .

On the other hand, the general equilibrium effect of a MPS in 3c“ ’5 distribution on

q

da, 0a 67a, 0'19,

I I

. . . do: . .
the optimal portfolio configuration, — , rs grven by: -—— = + .
dxi dxi cixi (28, (32c

 

 

 

,a,

 

From proposition (4) we know that < 0 . To compensate for the reduction in

the demand for domestic bonds, the domestic government must increase the devaluation

é’e . . . . . .
rate and therefore, 5: > 0. By proposrtron (6) an increase in the devaluatlon rate induces

I

. . . do . . . . . .
a reductton in a, 1.e. :— 1s negatrve. Then, we have that the Sign of the GE equrlrbrrum
(8

I

effect of an increase in the domestic risk on the proportion that the domestic bond

represents on agents’ portfolios (a,), is negative which indeed implies that the sign of

b . . .
the GE on the demand for the domestic bond, i—d’i—l’ 18 also negative. Therefore, a mean

preserving spread in the domestic bond’s nominal return distribution (an increase in
domestic risk) induces a reduction in the general equilibrium demand for domestic bonds.

For coefficients of relative risk aversion less than one the general equilibrium
effects on the demand for domestic bonds of a mean preserving spread in the domestic

bond’s nominal return distribution is also given by expression (10). In this case, the sign

102

 

 

 

 

d . . . . .
of 731’— rs strll negative (proposrtrons (4) and (6)). On the other hand, from the results of

propositions (3) and (5) we know that the sign of the GE effect of an increase in the
. . , . ds, . . . as, 63' . .
domestrc rrsk on agents savrng rate, —— , 1S negative (both — and ——’— are negatrve) 1f
dxi cixi (9.9

the coefficient of relative is less than one. Therefore, if the coefficient of relative risk

aversion is less than one, the sign of the GE effect of an increase in the domestic risk on

H]

 

the demand for the domestic bonds, , is also negative.-

Then under the conditions of corollary (2) «relative risk aversion no larger than
one-- an increase in the domestic risk induces a reduction in domestic agents’ demand for
the domestic bonds. Now we study the inflationary implications of changes in demand for

the domestic bond as result of changes in domestic risk.

2.4.2.2. Effects on the Inflation Rate

Let us assume that the coefficient of relative risk aversion is no larger than one.
Then, the reduction experienced in agents’ demand for domestic bonds (because of the
MPS in ic’ ’s distribution) forces the domestic government to increase the devaluation rate
of the domestic currency, and consequently, the money supply. Furthermore, given our

assumptions about the consumption good market (free trade and a constant international
price of the consumption good, P,’ = 1), an increase in the devaluation rate implies a one-
to-one increase in the inflation rate, since P = e,. Thus, as a consequence of a mean

I

103

 

 

preserving spread in the domestic bond’s nominal return distribution (an increase in

domestic risk) the domestic inflation increases, since the devaluation rate increases.

2.5. Final Remarks

In this chapter we study how an increase in the domestic risk influences the
equilibrium inflation rate of a small open economy. We modeled an increase in domestic
risk as a mean preserving spread in the domestic bond’s nominal return distribution. We
find that if agents’ preferences exhibit constant relative risk aversion and the coefficient
of relative risk aversion is no larger than one a mean preserving spread in the domestic
asset’s return distribution induces a reallocation of domestic agents’ portfolios away from
domestic assets and into foreign assets.

The adjustments in agents’ portfolios affect the domestic government’s ability to
finance its expenditure stream by issuing new units of domestic bonds. To compensate
for the fall in public revenue the domestic government is forced to expand the
money supply. Then if we assume a system of managed exchange rates and that the
domestic government has limited access to international financial markets, the expansion
of the money supply requires an increase in the devaluation rate of the domestic currency,
and a higher devaluation rate implies an increase in the inflation rate. Thus, we have that
with a constant relative risk aversion utility function, if the coefficient of relative risk
aversion is less than or equal to one, an increase in domestic risk produces a higher

equilibrium inflation rate.

104

 

 

 

In this very simple model we restrict the sources of revenue available to the
domestic government. We assume no taxes and limit the domestic government’s access to
the international financial markets. These strong constraints in government financing
alternatives fit, in some sense, the conditions in which. the government acts in several
developing economies. In some of these economies, fiscal revenue relies in an important
way on domestic borrowing and money creation because of inefficient tax systems and
limited access to international financial markets.

Recently, some empirical studies present evidence in favor of a negative
relationship between political stability and inflation rate. Studies as Cukierman, Edwards
and Tabellini (1992) and Romer (1993) find that countries with the lower political
stability tend also to have higher inflation rates. These studies argue that a possible
justification for this negative correlation is that politically unstable countries are less
likely to have institutions that help to overcome problems such as the dynamic-

inconsistency of the economic policy.

Even though changes in domestic risk can be generated by factors others than
changes in an economy’s political stability, to the extent that changes in domestic risk are
caused by political instability, we can interpret the main result of this paper as an
additional mechanism through which political stability affects inflation. Here higher
political instability implies higher inflation, but not because of the differences that the
degree of political instability induces on an economy’s institutions but rather because of
the effects that changes in the level of political instability by itself induces on domestic

investors’ decisions and therefore on the behavior of the domestic govemment. Here we

105

 

 

show that given the institutions, higher political stability implies a lower need for the
domestic government to expand money aggregates, and, therefore, a higher degree of

political stability induces a lower inflation rate.

 

 

 

106

REFERENCES

Ades, A. and H. Chua. (1997). “ Thy Neighbor’s Curse: Regional Instability and Economic
Growth ”. Journal of Economic Growth. Vol. 2. pp. 279-304.

 

Agénor, P. and P. Montiel (1996). Development Macroeconomics. Priceton University
Press.

 

Alesina, A. and R. Perotti. (1996). “ Income Distribution, Political Instability, and
Investment”. European Economic Review. Vol. 40. pp. 1203-1228.

 

Alesina, A., Ozler, S., Roubini, N. and P. Swagel. (1996). “Political Stability and Economic
Growth”. Journal of Economic Growth. Vol. 1. pp. 189-211.

 

Atkeson, A., and IV. Rios-Rull. (1996). “The Balance of Payments and Borrowing
Constraints: An Alternative View of the Mexican Crisis”. Research Dgpartment
Staff Report 212. Federal Reserve Bank of Minneapolis.

 

 

Barro, R. (1991). “ Economic Growth in a Cross Section of Countries”. Quarterly Journal of
Economics. Vol. 106. pp. 407-443.

 

Barro, R. and X. SaIa-i-Martin. (1995). Economic Growth. McGraw-Hill

 

Cukierman, A., Edwards, S. and G. Tabellini. (1992). “ Seigniorage and Political
Instability”. American Economic Review. Vol. 82. No 3. pp. 537-555.

 

Diamond, P. and J. Stiglitz. (1974). “Increase in Risk and in Risk Aversion”. Journal of
Economic Theory. Vol. 8. pp. 337-360.

 

Diamonte, R., Liew, J. and R. Stevens. (1996). “ Political Risk in Emerging and Developed
Markets ”. Financial Analysts Journal. pp. 71-76.

 

Erb, C., Harvey, C. and T. Viskanta. (1996). “Political Risk, Economic Risk, and Financial
Risk”. Financial Analysts Journal. pp. 29-46.

 

Hahn, F. (1970). “ Savings Under Uncertainty ”. Review of Economic Studies. Vol. 37, pp.
21-24.

 

Kormendi, R. and P. Meguire (1985). “Macroeconomic Determinants of Growth”. Journal
of Monetary Economics. Vol 16. pp. 141-163.

 

Levine, R. and D. Renelt. (1992). “A Sensitivity Analysis of Cross-Country Growth
Regressions”. American Economic Review. Vol. 82. No. 4. pp. 942-963.

 

107

 

 

Levhari, D. and T. Srinivasan. (1969). “ Optimal Savings Under Uncertainty ”. Review of
Economic Studies. Vol. 37. pp. 153-164.

 

Lucas, R. and N. Stokey. (1983). “Optimal Fiscal and Monetary Policy in as Economy
without Capital”. Journal of Monetary Economics. Vol. 12. 1983.

 

Romer, D. (1993). “ Openness and Inflation: Theory and Evidence Quarterly Journal of
Economics. Vol. 108. No. 4. pp. 869-903.

 

Rothschild, M. and J. Stiglitz. (1970). “ Increasing Risk 1: A Definition ”. Journal of
Economy Theory. pp. 225-243.

 

Rothschild, M. and J. Stiglitz. (1971). “ Increasing Risk 11: Its Economics Consequences
Journal of Econony Theory. pp. 66-84.

 

Samuelson, P. (1969). “Lifetime Portfolio Selection by Dynamic Stochastic
Programming”. Review of Economics and Statistic. Vol. 5. pp. 239-246.

 

Sargent, Thomas. (1987). Dmamic Macroeconomics Theory. Cambridge: Harvard
University Press, 1987.

 

Stewart, D. and Y. Venieris. (1985). “ Sociopolitical Instability and the Behavior of Savings
in Less-Developed Countries ”. Review of Economics and Statistic. pp. 557-563

 

Venieris, Y. and D. Gupta. (1986). “Income Distribution and Sociopolitical Instability as

Determinants of Savings: Across-sectional Model”. Journal of Political Economy.
Vol. 94. No. 4. pp. 873-883.

 

108

 

 

 

 

Figure 2.1

Average Inflation and POIiticaI Risk’
42 Countries (1985 - 1995)

 

Log of Average Inflation

 

6.77457 4 e

 

 

d b'\\
\\_ o
O \ O
K\\ o
O ‘\’\\ O
o o O o o \i‘ \\\
——1 \\\‘ .
o o o \\ _\\
o \ty.\\ 0
o o -\‘b\
C ,9 o 0 DO I) \O
o
0
.33647 r 0
I l l l l
40 91.5

Political Risk Average (Low Index = High Risk)

Source: World Bank (1997) and Diamonte, Liew and Stevens (1996)
* As measured by the lntemational Country Risk Guide’s Index

 

 

109

 

 

 

Figure 2.2

Average Inflation and Political Risk”
1 12 Countries (1973 - 1981)

 

 

 

5.3312 r «:3
Q
a o o
O
O
O 1
O Q.) /,

8 o, g ,2
O O F Q (Q- // “/1 1’11
0 O c o \) >/“’T /

ti} 9 t) 10’ 3 Ar/‘/J 3
O .J? O ., /- “- e,

i g, /// ..//” O \. DO U r

- $86000 8 8 ‘e’ O s 2

_ = O O r) ‘
g 8 O O O o
. O

O
6 O O

o O
8 O 0
1.2809 8 O
6 l I I [
1. 5

Index of Political Instability (Low Index = Low Risk)

Source: Romer (1993)
** As measured by Barro (1991)’s Index

 

 

110

APPENDIX 2

(Based on Diamonte, Liew and Stevens (1996)’s appendix.)
The Political Risk Services, a country-risk Consultant firm, publishes the
lntemational Country Risk Guide (ICRG) since 1980. The ICRG provides survey

measures of political risk for more than 130 countries (nevertheless, only 45 countries are

\LlIw—‘I [
'1. : L 1.1—Lu

reported by Diamonte, Liew and Stevens in their study). Analysts rating of 13 political

risk attributes combine to form one overall political risk index for each country. The

 

maximum score assigned to each attribute is set so that each country’s overall score falls _.
between 0 (highest risk) to 100 (lowest risk). The political attributes taken into account
to form the ICRG political index are:

1.- Economic Expectations Vs Reality.
2.- Economic Planning Failures.

3.- Political Leadership.

4.- External Conflicts.

5.- Corruption in the Government.
6.- Military in Politics.

7.- Law and Order Tradition.

8.- Racial and Nationality Tensions.
9.- Organized Religion in Politics.
10.- Political Terrorism.

11.- Civil War Risk.

12.- Political Party Development.
13.- Quality of Bureaucracy.

The countries reported by Diamonte, Liew and Stevens (1996) are: Hong Kong,
Spain, Italy, Singapore, Ireland, France, Belgium, United Kingdom, Australia, United
States, Canada, Germany, Japan, New Zealand, Sweden, Norway, Denmark, Netherlands,
Austria, Finland, Switzerland, Peru, Colombia, Chile, Argentina, Brazil, Venezuela,
Mexico, Pakistan, Sri Lanka, Philippines, India, Indonesia, Thailand, Korea, Malaysia,
Taiwan, Nigeria, Jordan, Zimbabwe, Turkey, Poland, Greece, Portugal and Hungary.

111

 

 

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