Download The Current Account and the International Distribution of Wealth Under Uncertainty

DISCUSSION PAPERS IN ECONOMICS
Working Paper No. 98-11
Precautionary Saving and the International Distribution of Wealth
Kenneth R. Beauchemin
Department of Economics, University of Colorado at Boulder
Boulder, Colorado
Betty Daniel
University at Albany, State University of New York
Albany, NY
August 1998
Center for Economic Analysis
Department of Economics
University of Colorado at Boulder
Boulder, Colorado 80309
© 1998 Kenneth R. Beauchemin, Betty Daniel
Kenneth R. Beauchemin
University of Colorado at Boulder
University at Albany
August, 1998
IThe authors would like to thank seminar participants at Dartmouth College for
helpful comments.
Send correspondence
to:
Ken Beauchemin, Department of
Economics, University of Colorado at Boulder, Boulder, CO 80309-0256. E-mail:
[email protected].
Abstract
This paper provides a simulation analysis of savings and current account behavior in
a two-country world with heterogeneoustime preferenceand precautionary saving.
The differencein time preferencebetweeneachcountry's representative agentinitially
leads to a systematic redistribution of wealth through the current account. This
redistribution strengthens the precautionary savings motive for the impatient country
and weakens it for the patient country. Systematic current account imbalance ends
once net foreign assets enter the neighborhood in which "risk-adjusted" rates of time
preferenceare equated. This is analogous to equilibrium in an endogenous time
preferencemodel, in which wealth is redistributed until time preferencerates are
equated, but without the unappealing assumption that wealthier agents are more
impatient. Quantitatively, small differences in time preference generate realistic mean
debt-GDP ratios.
Key words: current account, uncertainty, precautionary saving.
JEL classification: F32, D91, E21.
1
Introd uction
Current account imbalance often persists over horizons longer than the business
cycle, even in the industrial countries. The literature attributes such persistent imbalance to a difference in time preference rates of the representative agents in each
country (Helpman and Razin, 1982). Yet, this explanation is not entirely satisfactory
in the two-country certainty models put forward to date. In the standard constant
time preference model, the impatient county is destined for a steady state of minimal consumption, determined by an internationally imposed borrowing constraint.
Given the implausibility of this steady state for a deficit country like the US, Obstfeld
(1981) introduced endogenous time preference (Uzawa, 1968), in which time prefer-
ence is decreasingin wealth. This allows differencesin time preferenceto explain
systematic current account imbalance without the unappealing result of one country
eventually owning most of the world's wealth.
Over time, wealth is redistributed,
ending current account imbalance, without appeal to a borrowing constraint. How-
ever, the assumptionthat an agent becomesmore impatient as he becomeswealthier
is counter-intuitive.
The standard, constant time preference, certainty equivalence model (CEQ) in international finance views the current account as independent of wealth. Uzawa utility
makes the current account dependent on the distribution of wealth, eliminating the
implausible steady state, but at the cost of an implausible assumption about the
dependence of time preference on wealth. The main purpose of this paper is to show
that the introduction of uncertainty into the standard constant time preference model
makes the current account dependent on the distribution of wealth through precautionary saving behavior.
Therefore, under uncertainty, persistent current account
imbalance can be explained by differences in time preferences. However, as wealth
is redistributed, the precautionary motive for the impatient agent is strengthened
1
as a small open economy, whose representative agent has a rate of time preference
greater than that of the representative agent in the rest of the world, then the analog
implies that, the small impatient country will initially run a systematic current account deficit. As wealth falls, the precautionary motive to saveis strengthened,and
it eventually becomesstrong enoughto offset impatience, allowing persistent current
account imbalance to end, prior to reaching a borrowing constraint. The analysis does
not extend to a small relatively patient country, however,becauseboth patience and
precautionary behavior yield current account surpluses. General equilibrium analysis, in which the interest rate can change, or equivalently a two country model, is
necessary here. A two country model is also necessary to deal with the problem in
large countries, like the US and Japan, for which interest rates cannot be considered
exogenous to domestic economic activity.
This paper provides the general equilibrium analysis for a two-country world endowment economy in which time preference ratffi of the representative agent in each
country differ. Since an analytical description of the equilibrium is not possible, we
follow much of the literature in dynamic stochastic general equilibrium theory by
using numerical techniques to approximate the equilibrium decision rules. In tech-
roque, it is similar to heterogeneousagent accounts of assetprices including Telmer
(1994), Lucas (1994), and Lucas and Heaton (1997). It is also related to papers by
Aiyagari (1994), Krusell and Smith (1995), and Quadrini and Rios-Rull (1997) which
quantitatively assessthe effect of precautionary saving on the aggregate stock of capital (Aiyagari and Krusell and Smith) and the distribution of wealth (Quadrini and
Rios-Rull), when agents face idiosyncratic income shocks. In contrast, our primary
interest is in precautionary saving as the mechanism by which world wealth is redis-
tributed. We focus on this issue in two ways. First, utility discounting is the sole
source of agent heterogeneityso that there is no idiosyncratic income risk. GODSequently, the economic environmenthas a complete markets interpretation. Second,
3
Agents
.b2t.
have accessto a one-period risk-free pure discount bond, which is zero in
net su~ply, and which they can trade with agents of the other country.
Since the
only difference in agents is in their rate of time preference, agents use this bond to
achieve their desired expected rate of change of consumption over time. Letting the
price of the bond be Pt, and the number of bonds held at the beginning of period t
be bit, each agent maximizes expected lifetime utility subject to a sequence of budget
constraints
t
Yt + bit,
Cit+ Ptbi,t+l
0,1,
(1)
and borrowing constraints
t = 0,1,
bit ~ b*
(2)
The borrowing constraint is necessaryto assure that the agent obeys his intertemporal
borrowing constraint with probability one (Aiyagari 1994).
Both the bond market and the goods market clear in each period:
Clt + C2t
(3)
2Yt
bIt + b2t = 0
(4)
where either one implies the other by Walras's Law. Since, by equation (4), bIt = -b2t,
in what follows we simplify notation by letting bt represent the domestic country's
bond holdings, i.e. bt = bIt
In this simple model, an increase in a country's quantity of bonds represents a
current account surplus. The current account for the domestic country is defined as
the accumulation of net foreign assets according to:
bt+l -bt =
I-pt
Pt
1
bt + -(Yt
Pt
Cl,t)
When the borrowing constraint (2) is not binding, the Euler equations from the
agents' optimization problem require the expected marginal rates of substitution in
6
consumption to equal the bond price for both agents:
(5)
Considerthe implications of equation (5) for the current account The results for
the certainty case are well-known. The impatient country usesthe bond to achieve
falling real wealth and consumption through a current account deficit, until debt
reachesa lower bound. The current account deficit ends and consumptionremains
at the low level permanently. While it may seem reasonableto postulate current
account imbalance due to differencesin time preferencerates, it seemsunreasonable
to expect an impatient county, perhaps a country like the U.S., to exhaust its wealth
and then to subsist on a permanently low level of consumption.
Obstfeld (1981) introduced the Uzawa utility function, in which time preference is
an increasing function of wealth, to avoid the corner solution while allowing agents to
have different time preference. Under Uzawa assumptions, as wealth is redistributed,
making the impatient
agent poorer, he becomes more patient.
Analogously, the
patient agent becomesless patient as he becomeswealthier. Hence, current account
imbalance ends once wealth has been redistributed to equate time preference rates.
The problem with this story is the intuitively unappealing assumption that increasing
wealth makes agents more impatient. This paper shows that precautionary savings
can play the same role in redistributing wealth as endogenous time preference.!
For the uncertainty case, equilibrium is described in terms of stationary steady-state
distributions which cannot be computed analytically. Therefore, this paper simulates
simple artificial economies to characterize the behavior of the current account and
net external debt. It shows that, with the addition of uncertainty and precautionary
savings behavior, there is an equilibrium distribution
of wealth for which persistent
lObstfeld and Rogoff (1996, p.95) suggeststhat precautionary savings can imply dynamic behavior similar to endogenoustime preference.
7
current account imbalance ends. Specifically, if agents have convex marginal utility
and face uncertainty in their incomes, then a difference in time preference does not
send agents monotonically to their borrowing constraints. As the impatient country
decumulates, his precautionary motive to save is strengthened. Accumulation weakens the precautionary motive for the patient agent. Together, these forces generate
an equilibrium distribution of wealth in which current account imbalance is generally
small.
2.2 Calibration and Computational
Algorithm
The parameter settings are chosen to facilitate comparison of our model with in-
come uncertainty to the benchmark certainty neoclassicalmodel. Since borrowing
constraints are present only asymptotically in the neoclassical model, they are chosen
very large for the simulations. Borrowing constraints are chosen to be eight, which
is eight times the unconditional expectation of GDP. This assures that the agent's
intertemporal budget constraint is satisfied with probability one, and does not allow
an independent role for tight borrowing constraints.2 The constraints bind less than
5 percentof the time in simulation.
The focus of the study is on current account behavior generated when representative agents differ in time preference. We found that only small differences in time
preference are necessary to generate a distribution of debt/GDP ratios of the order
of magnitude of those actually observed.3 Heterogeneity in rates of time preference
is created by setting the discount factors of the domestic agent and foreign agentto
.948 and .952, respectively.
2The role of tight liquidity
constraints in an uncertainty economy would also be interesting to
investigate.
30bstfeld and Rogoff (1996, p. 69) calculate debt/GDP ratios for'selected countries. They vary
from being very small to a maximum of 4.8 for Nigeria.
8
We investigatethe effects of increasedrisk aversionand prudence, in the senseof
Kimball (1990), by simulating economieswith a = 2 and a = 4. The remaining two
parameters, 0" and 4>,determine the distributional properties of the stochastic world
income process. We study the effects of increased income variability
by allowing
the standard deviation of shocks to be both 2.5 percent (0" = .025) and 5.0 percent
(0" = .05). These settings are large compared with aggregate income volatility
small compared with individual income volatility.
but
Since our representative agent is
both the individual and the economy, and since the two face identical volatility only
if markets are really complete, the settings are probably reasonable.4 Finally, we
consider increased persistence in world income shocks with two different values of the
transition probability:
<I>
= .50 and <I>= .75. The former setting corresponds to serially
uncorrelated or i.i.d. shocks. Using the approximating technique of Tauchen (1986),
the latter setting corresponds to an AR(l) process with first-order serial correlation
of .50.5 These settings are summarized in Table 1.
The algorithm constructed to solve for the equilibrium is conceptually related to
those used by Telmer (1993) and Lucas (1994), who adapt the discrete state-space
Euler equation method, used by Baxter, Crucini and Rouwenhorst (1990), for use in
multiple agent settings.6 The goal of the algorithm is to describe the world equilibrium
distribution of wealth (bt+l) as a function of the current state, which is given by the
vector Zt = (bt, Yt). This requires a decision rule for the domestic agent's asset
accumulation along with the equilibrium asset pricing function.
Let bt+l = b (Zt) denote the time-invariant function, mapping the current state
4More desirable, of course, would be to have an economycomposedof many individuals with
idyiosyncratic risk of the appropriate magnitude and aggregaterisk of the appropirate magnitude.
This is beyond scopeof the present paper.
5First-order serial correlation of .50 at an annual frequencytranslates into approximately .84 at
a quarterly frequency-rougWy the value obtained using HP filtered quarterly data on output.
6Details of the algortithm are available upon request.
9
into the domestic agent's accumulation decision, and let Pt = P (Zt) denote the timeinvariant equilibrium asset pricing function. Therefore, b (Zt) is the equilibrium law
of motion for the world economy. Substituting these into the budget constraints in
(1), and applying the asset market clearing conditions, gives equilibrium consumption
for each agent. Assuming that the borrowing constraints (2) are not binding, combining the expressions for equilibrium consumptions with the first order conditions
(5), the time-invariant accumulation rule b (Zt) and equilibrium price function p (Zt)
are implicitly
given by the following system of equations:
{32Et [Yt+l -b
p (Zt) -[Yt
(Zt) + P (b (Zt) , Yt+l) b (b (Zt) , Yt+l)]-O
-bt + P (Zt) b (Zt)]-a
"}
where the conditional expectation is computed using the transition probabilities appropriate to the incomestate Yt. If the borrowing constraint is binding for an agent,
then the assetprice is strictly greater then the marginal rate of substitution. In this
case, the equilibrium price is determined by the marginal rate of substitution of the
unconstrained agent.
To compute the stationary distributions, an income sequence {Yt} of 25,000 periods is constructed according to the transition probability cPoThis sequence is used
to generate the asset quantity sequence {bt} and the asset price sequence {Pt} by
solving bt+l = b(bt, Yt) and Pt = p(bt, Yt) forward through time. Linear interpolation
is used between grid points. The first 5,000 values are subsequently dropped to erase
distortions caused by initial realizations outside of the ergodic set.7.
71n a limited number of cases,we compared the results of this procedure to those obtained from
a repeated sampling procedure in which 1000repetitions of simulations 1000periods in length were
run; the final realization in each run was retained to construct the stationary distributions. We
found no significant differencesin the results and opted for the computationally efficient method.
10
In the following section, we use the settings a = 2, 0" = .05 and <I>= .50 in
graphs which characterize the equilibrium.
This implies that agents have relatively
low risk aversion and high income volatility, and that income shocks are independent
and identically distributed (i.i.d.).
In Section 4 we compare the results from all
simulations.
3
Characterizing
the Equilibrium
As a benchmark, consider an economy with no uncertainty (0" = 0). In this case,
interior solutions for consumption and the current account are described by equating
marginal rates of substitution across the two agents as in (5). This expression can be
rearranged as:
1-
(32)
Q
Cl,t+l/ Clt
C2,t+l/C2t -..B1/
which implies that Cl,t+l/ Clt > C2,t+l/C2tunder the assumption that the foreign agent
is more patient than the domestic agent (.f32> .f31).
Since the world endowment is fixed, market. clearing implies that consumption
growth is negative for the domestic agent and positive for the foreign agent. Therefore, beginning from a position of autarchy or zero external debt, the impatient
country runs a successionof current account deficits to finance a downward sloping
consumption profile until a borrowing constraint is reached. At that point, both consumption growth and the current accountbecomezero and the existing external debt
is rolled over in perpetuity.
The size of the transitory current account imbalances is a function of two properties. First, larger differences in discounting (i.e. larger 1321131)'
generate steeper
equilibrium consumption profiles, and, hence, larger transitional current account im-
balances.The secondinfluencecomesthrough the coefficientof relative risk aversion,
a. In the deterministic economy,a simply gauges an agent's desire to smooth con11
sumption across time periods. With relatively large a's, agents want consumption in
different periods to look very similar. Consequently, they dislike any growth, either
positive or negative, in their intertemporal consumption profile. In general equilibrium, therefore, larger a's imply smaller current account imbalances and a longer
transition period as more periods are required for the impatient country to amassthe
constraining level of debt.
Figure 1 shows two asset decision rules for the domestic agent, corresponding to
economies with Q = 2 and Q = 4. A 45-degree line is drawn as a benchmark.8 Note
that the function b (bt, 1) is uniformly below the 45-degree line in both cases, with
the function corresponding to Q = 2 uniformly lower than the function for Q = 4.
The impatient country marches monotonicallyto its borrowing constraint, with the
size of current account deficits and the speed of adjustment decreasing in o. The
asymptotic steady-state is the implausible one with the impatient country subsisting
on minimal consumption, while the patient country enjoys the fruits of most of the
world's wealth.
Next, consider the economy with uncertainty in the world endowment (0' > 0).
Equating expectedmarginal rates of substitution betweendomesticand foreign agents,
as in equation (5), yields:
.al Et [( Cl,t+l) -0]
.82Et [( C2,t+ 1) -Q ]
-0
-Q
C2t
Clt
Pt.
(8)
In this case, a not only controls the desire of agents to smooth consumption across
time periods but also across states of nature. Therefore, a larger a implies that the
agent is more risk averse in that he is less tolerate of differences in consumption across
states. More importantly, however, with CRRA utility the convexity of marginal
8.\lthough these decision rules were computed using a borrowing limit of eight (as in all other
experiments), only a portion of the bond spaceis shown for better resolution; the picture is qualitatively the same throughout the bond space.
12
utility (i.e. U'" > 0) generates precautionary saving in the senseof Leland (1968)
and Sandmo(1970). Roughly stated, a mean preservingspread in income increases
discounted expected marginal utility relative to current marginal utility.
With a
constant interest rate, an agent savesmore. In general equilibrium, the additional
demand for saving raises the price of bonds, decreasing the world interest rate.
Kimball (1990) gauges the strength of the precautionary motive with the concept
of absolute and relative prudence. In the current environment with CRRA utility,
the coefficient of relative prudence is given by -W
= 1+a.
In a fashion similar to
Pratt's (1964) measure of relative risk aversion, relative prudence measures the degree
of convexity in the marginal utility function. Although this concept was developed
in a strictly partial equilibrium setting for a two-period lived consumer, the intuition
carries overto the more generalsetting. In our model,therefore, a not only gaugesan
agent'sdistaste for consumptionrisk, it alsogaugesthe strength of the precautionary
motive.
Precautionary behavior is present in the equilibrium law of motion for assets and
in the stationary distribution
of external debt. The equilibrium law of motion for
assets over the entire asset space, b (bt, Yt), is depicted in Figure 2A. An enlargement
in the neighborhood of zero assets is presented in Figure 2B. The function b (bt, yi)
maps current bond holdings into future bond holdings, conditional on a low income
state, while the function b (bt, yh) is the analogous mapping conditional on a high
income state. Both cross the 45-degree line, with the mapping conditional on low
(high) income relatively steeper (flatter) than the forty-five degree line.
At the initial position of autarchy (bo = 0), both functions are below the 45-degree
line. .Therefore, from a position of zero net external debt, wealth is redistributed
awayfrom the domestic (impatient) agenttoward the foreign (patient) agent through
a current account deficit, regardless of the state. In this region, behavior mimics
that in the certainty case. However, once the level of debt reaches b, the domestic
13
agent begins to save in a high income state, running a current account surplus, and
to dissave in a low income state, running a current account surplus. From b, the
economy enters an ergodic set for wealth, formed by the closed interval with the
borrowing constraint b* as its minimum and b as its maximum: [b*, b].
In our model, precautionary savings is the mechanism by which w~alth is redistributed, very much like that in the certainty world of Uzawa utility.
To understand
how precautionary savingsredistributes wealth to eliminate systematic current account imbalance, it is useful to rewrite the domesticand foreign first order conditions
isolating the degreeof convexity in marginal utility.9 Define 1 + 8it for each agent
i
1,2 as:
where {jit > 0 by Jensen's inequality.
In our setup with two exogenous income
states, the variation in consumption is captured by the distance between Ci,t+l in each
state. Given a value for a, an increase in the conditional expectation of consumption,
EtCi,t+l' holding the variation in consumption constant, decreases bit- Alternatively,
an increase in consumption variation, holding the conditional expectation constant
(i.e., a mean-preserving spread in Ci,t+l), increases {jit. Combining the two effects, we
can say that as expectedconsumption becomeslarye relative to its variance, {jit be-
comessmall (zero in the limit).10 Using this definition, equation(8) can be rewritten
as:
.BI (1 + bIt)
= .B2(1 + 82t)
= Pt.
(9)
To compare the results with those of the certainty case, define {3(1 + Oit) as the
"risk-adjusted discount factor", (RADF) for each agent i = 1,2
For the certainty
case, the discount factor for the domestic agent is always smaller than its foreign
9A similar discussionis found in Daniel (1997).
loBlanchard and Mankiw (1988) derive this using a quadratic approximation of utility.
simulations have the sameimplication.
14
Our
set, raisesconsumption and decreases(increases)variance for the impatient (patient)
agent. Therefore, within the ergodic set, tilt is always lower in a high income state.
However, for the patient agent, ti2t is lower in a high income state when the distribution of wealth is not too unequal, and higher otherwise. This is because, as the
distribution of wealth becomes more unequal in favor of the patient agent, the effect
of a good income state on consumption volatility begins to dominate the effect on
mean consumption for the patient agent.II
Figure 4 plots risk-adjusted discount factors for domestic and foreign agents. The
solid lines represent the low income state, while the dashed lines represent the high
income state. Figure 4B is an enlargement of Figure 4A in the neighborhood where
RADF's are equal. Risk-adjusted discount factors for the domestic agent rise, as
domestic bonds fall, while risk-adjusted discount factors for the foreign agent fall, as
domesticbond holdings fall (and equivalentlyas foreign bond holdings rise.
In the certainty case with Uzawa utility, systematic accumulation ends once discount factors are equated. Something analogous happens in the uncertainty case. In
Figure 4B, conditional on obtaining a low income state (solid lines), risk-adjusted
discount factors are equal at bi. Therefore, if bIt = bi, and income is low, equa(9) ImD
. 1Ies
"
"
bon
t hat E(Cl,t+llbi,yi)
,~,
~
Clt
"
= E(C2,t+llbi,yi)
" However. COnsl
der w hat h aDDens
C2t
~ ~
in a high income state, with bIt = bi. Figure 4B shows that in a high income
state (compared with a low income state), the risk adjusted discount factor falls
for the domestic agent and rises for the foreign agent. Therefore, from equation
(9), domestic consumption growth is expected to be lower than foreign consumption
gr
Efc""lblyh'
owth:~\~l.t+ll-'If
Clt
J < EfC2t'llblyh'
~\~".'+J.I-'If J. Since each income state has a non-zero proba-
bility of occurring, E (~
C2t
I bi) < E (~
I bi) .Therefore, as bonds reach bi, the
expected percentage change in domestic consumption is less than the expected percentage change in foreign consumption.
110f course, the same applies as b increases for the impatient
16
agent outside of the ergodic set.
17
Now,
tional
consider
the
point
on a high income
bIt = bh, and income
.E(
IS equal:
at which
state.
is high,
Cl.t+llbh,yh) =
with
domestic
This
occurs
equation
discount
factors
at bIt = bh in Figure
(9) implies
that
E( C2,t+llbh,yh).However,
Clt
state,
risk-adjusted
expected
..
consIder
Figure
3, the
agent and falls for the foreign
risk adjusted
what
discount
agent so that expected
hig h er t han .1t s £oreIgn
.E( counterpart:
'
gr owt h IS
Cl,t+llbl,yl)
>
This
utility
state has a non-zero
probability
suggests
between
function.
an analogy
There
Clt
at b. The analogy
they reach a point
domestic
skewed to the left.
for the
consumption
S.Ince
eac h
E (~
I bh) > E (~
saving
model
consumption
I bh) .
and the Uzawa
bh < b < bi., at which
growth
rates are equal
C2t
with
the certainty
equating
the mass of the bond
The distribution
if
growth
rises
E(
C2,t+llbl,yl\,N J.
~\~",.-rJ.I~
given by b , such that
I b; = b ) , Expected
Therefore,
C2t
the precautionary
is a level of bonds,
I bt = b ) = E ( ~
E (~
of occurring,
condi-
hap p ens In a bad
factor
Clt
income
4B.
consumption
C2t
bIt = bi.. From
are equal,
expected
distribution
of bonds
Both
world
consumption
should
is shown
suggests that
growth
bonds
are redistributed
rates.I2
be in the neighborhood
in Figure
bi. and bh are contained
until
This suggests
containing
that
(bh, bi.) .
3. The distribution
is bell-shaped
and
in the densest part
of the distribution.
The skewness reflects the asymmetric response by the agent to the low probability
events of a string of low versus high income states. With a string of low income
states, the impatient agent will let bond holdings drift a substantial amount away
from their mean, while, with a string of high income states, the patient agent never
lets bonds drift above b. 13Virtually all of the mass of the distribution is well above
the liquidity constraint of eight. The equilibrium distribution of bonds does not pile
12Theanalogy is not exactly correct due to a Jensen'sinequality term. When consumption levels
differ and expected percentage changes in consumption are equal, the expected levels change in
consumption for the poorer agent must be lower, due to a lower base level consumption. This
implies that the expected change in consumption is negative at b. The level of bonds, at which
consumption is no longer expected to change,is somewhatlower than b.
13TheJensen'sinequality term is also likely to be playing a role here. Seethe previous footnote.
up on the borrowing constraint, as it would in the certainty case. Uncertainty implies
an equilibrium distribution of bonds such that the country does not systematically
run surpluses or deficits in the stochastic steady-state equilibrium.
4
Comparative
Quantitative
Results
Table 2 presents the results of the simulations with differing risk aversion and income variance for i.i.d. world income shocks. The state-dependent debt levels (almost
debt/GDP ratios since GDP is on averageunity), where risk-adjusted discount factors are equated, are reported along with various moments of the domestic country's
stationary distribution of debt.14,15The results provide a good representation of the
adjustment mechanism generated by precautionary saving. With precautionary savings, a redistribution of wealth eliminates systematic current account imbalance. The
stronger are precautionary forces, the smaller the equilibrium divergence in debt/GDP
ratios should be. The simulations show that the more important is precautionary saving, as represented by higher income variation and greater prudence, the smaller the
mean equilibrium debt/GDP ratios. Quantitatively, the effects are considerable. An
increase in the coefficient of relative risk aversion from 2.0 to 4.0 with low income
variation reduces the mean debt-GDP ratio from 3.27 to 0.81; with high income variation the ratio falls from 1.28 to 0.16. Viewed slightly differently, a doubling of the
standard deviation of income shocks (from 2.5 percent to 5.0 percent) reduces the
debt-GDP ratio by approximately a factor of three when Q = 2 and a by over a factor
of four when a = 4.
14Although the domestic country's net foreign asset position is negative in the ergodic set,. we
report the moments for the debt/GDP distribution levels to avoid the superfluous use of minus
signs.
15Skewness
is reported as the difference betweenthe mean and the standard deviation divided by
the standard deviation which can take on values between -1 and + 1.
18
In all simulations, bf.and bhare contained in the densest portion of the distributions.
The mean debt/GDP
ratios typically lie somewhat to the left of both bf.~nd bh,
reflecting the skewness of the bond distributions.
Finally, we document the effects of persistence in world income shocks in Table 3.
In this set of experiments, the (symmetric) transition probability is set to 4> .75 so
that annual first-order serial correlation is .50. The main difference in results is that
the mean debt/GDP levels increase in all four experiments. Intuitively, persistence
enables agents to anticipate future income thereby decreasing consumption variation
and therefore precautionary motives. Although debt rises, it remains within a broad
range of levels observedin actual economies.
5
Conclusion
Systematic current account imbalance can be explained by differences in time pref-
erence for the representativeagents in different countries, without either extreme
asymptotic behavior, or the unappealing assumption that wealthier agents are more
impatient. Small differencesin time preferenceinitially generatesystematic current
account imbalance, independent of the income realization. This eventually gives way
to an equilibrium distribution of wealth, in which current accountsbalance on average. Countries do not march systematically to borrowing constraints, as in a certainty
model. Additionally,
with small differences in time preference and standard choices
for other parameters, equilibrium distributions for debt/GDP ratios are consistent
with the magnitudes of theseratios observedin actual economies.
The mechanismby which precautionary savings redistributes wealth, ending systematic current account imbalance, can be explained using an analogy to Uzawa
utility.
In Uzawa utility, the redistribution
of wealth raises the discount factor of
the impatient agent and reduces the discount factor of the patient agent until they
19
are equated. With precautionary saving, the redistribution
of wealth raises the risk-
adjusted discount factor of the impatient agent and reduces the risk-adjusted discount
factor of the patient agent. The mass of the equilibrium distribution of bonds is in
the neighborhood where these risk-adjusted discount factors are equal.
20
[11] Leland, Hayne E., "Saving and Uncertainty:
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The Precautionary Demand for Saving,"
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23
Table 1
Parameter Value(s)
b*
8.0
a
2,4
.B1
948
.B2
.952
(J"
025, .050
<P
.50, .75
24
Table 2 (i.i.d. shocks)
"Low" Income Variability
(0" = .025)
Property
a
bi , bh
2
"High" Income Variability
Variability
4
a
Q;
2
(0"
.050)
a=4
2.019,2.238 0.643, 0.752 0.770,0.925 0.120,0.158
Mean
3.269
0.809
1.284
0.158
Median
3.072
0.596
1.038
0.124
Std. Dev
1.251
0.718
0.874
0.124
Skewness
0.158
0.297
0.282
0.276
Binding freq.
.0026
.0005
0004
.0000
Table 3 (Persistent shocks)
25
FIG. 1. Domestic agent's bond function: deterministic case.
26
..,.
~
..'+
D
"
-8
-y~
--y.
-7
-6
-5
-4
-)
-2
-1
.
2345678
oCt]
3.
FIG. 2. Domestic agent's bond function: stochasticcase.
27
-7
-6
-5
-4
-3
-2
Debt/GDP
FIG. 3. Stationary distribution of domestic debt.
28
-1