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The Implications of First-Order Risk
Aversion for Asset Market Risk
Premiums
Geert Bekaert, Robert J. Hodrick and
David A. Marshall

Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
December 1994 (W P-94-22)

FEDERAL RESERVE BANK
OF CHICAGO

T h e Implications of First-Order Risk Aversion
for Asset M a r k e t Risk P r e m i u m s

Geert Bekaert
Stanford University

Robert J. Hodrick
Northwestern University and NBER

David A. Marshall
Federal Reserve Bank of Chicago and
Northwestern University

January 14, 1994

The authors have benefitted from the comments of Stan Zin and Andy Abel as well as numerous
participants at seminars and conferences. We thank the seminar participants at Duke University,
the Federal Reserve Bank of Chicago, Northwestern University, the University of Chicago, the
University of Pennsylvania, the University of Southern California, the American Finance
Association, a CEPR conference at the University of Limburg, and a conference on Capital
Market Integration at the London School of Economics.




T h e Implications of First-Order Risk Aversion
for Asset Market Risk P r e m i u m s

Abstract

Existing general equilibrium models based on traditional expected utility preferences have been
unable to explain the excess return predictability observed in equity markets, bond markets, and foreign
exchange markets. In this paper, we abandon the expected-utility hypothesis in favor of preferences that
exhibit first-order risk aversion. We incorporate these preferences into a general equilibrium two-country
monetary model, solve the model numerically, and compare the quantitative implications of the model
to estimates obtained from U.S and Japanese data for equity, bond and foreign exchange markets.
Although increasing the degree of first-order risk aversion substantially increases excess return
predictability, the model remains incapable of generating excess return predictability sufficiently large
to match the data. We conclude that the observed patterns of excess return predictability are unlikely to
be explained purely by time-varying risk premiums generated by highly risk averse agents in a complete
markets economy.




T h e Implications of First-Order Risk Aversion
for Asset M a rket Risk P r e m i u m s

1. Introduction
It is generally accepted that excess returns on a variety of assets are predictable. This is true for
returns in the equity markets, bond markets, and foreign exchange markets of various countries. One
interpretation of this evidence is that equilibrium risk premiums on all assets are highly variable. Yet,
existing rational expectations general equilibrium models based on traditional expected utility preferences
have been unable to generate risk premiums that are sufficiently variable to be consistent with the
observed predictability of returns.
Consequently, in this paper we abandon the expected-utility hypothesis in favor of preferences
that exhibit first-order risk aversion.1 With these preferences, agents are substantively averse to even
small gambles. Hence, a small degree of uncertainty in the exogenous environment of economic agents
can potentially induce relatively large fluctuations in agents’ intertemporal marginal rates of substitution.
This, in turn, implies large fluctuations in expected rates of return on a variety of assets. Our goal is to
determine whether a general equilibrium model incorporating preferences that exhibit first-order risk
aversion is quantitatively consistent with the predictability of returns and with other time series properties
observed in the data from the foreign exchange market, the equity markets, and the bond markets of the
U.S. and Japan.
Other papers that propose first-order risk aversion as an explanation for asset pricing anomalies
include Epstein and Zin (1990, 1991) and Bonomo and Garcia (1993). In particular, Epstein and Zin
(1991) are unable to reject the overidentifying restrictions implied by a closed economy model, analogous
to the model of Hansen and Singleton (1982), when first-order risk aversion is assumed. Their approach

1 The concept o f first-order risk aversion was introduced by Segal and Spivak (1990).




1

requires the researcher to choose a proxy for the unobservable rate of return on aggregate wealth, and
their inference about the validity of the model depends on this choice. In an open economy setting, the
choice of a proxy for the return on aggregate wealth is problematic. Hence, we do not follow the
approach of Epstein and Zin (1991). Instead of testing the first-order conditions of the model, we
explicitly solve a two-country monetary model for the endogenous moments of interest.
In our model, consumption of two goods equals the outputs of two countries, which are assumed
to be exogenous endowment streams. The two money supplies are also exogenous. The growth rates
of these exogenous processes follow a discrete Markov chain that is estimated from U.S and Japanese data
using the method of Tauchen and Hussey (1991). The equilibrium processes for returns and other
endogenous variables are found by numerically solving a system of Euler equations. Having solved the
model, we generate a variety of statistics that provide evidence on the predictability of the model’s
returns. The performance of the model is evaluated by comparing these statistics to the corresponding
statistics in the data.
The remainder of the paper is organized as follows. In section 2, we present evidence on the
predictability of excess rates of return in the dollar-yen foreign exchange market, in the dollar and yen
discount bond markets, and in the equity markets. These stylized facts provide the set of statistics that
we would like the model to match. In section 3, we discuss intuitively why time-varying equilibrium risk
premiums could be an explanation of the statistics described in section 2. Section 4 introduces the
concept of first-order risk aversion, and section 5 incorporates these preferences into a formal dynamic
model. In section 6 we derive the model’s equilibrium conditions for endogenous financial variables.
Section 7 describes our procedure for calibrating the model, and section 8 presents our results. Section
9 compares our results with Epstein and Zin (1991), and section 10 provides concluding comments.
2. Some Stylized Facts on Excess Return Predictability
In this section we document the predictability of excess rates of return on discount bonds,




2

equities, and foreign money markets using regression analysis. Since U.S. and Japanese data are the
exogenous processes of the model, we report results only for these two countries. Nevertheless, the
evidence is consistent across the markets of most developed countries as documented by the recent
empirical studies of Harvey (1991), Bekaert and Hodrick (1992, 1993), and Solnik (1993), among others.
We begin by developing notation for own-country money market and equity investments. Let
If (If) be the dollar (yen) return at time t+1 from investing one dollar (yen) at time t in the nominally
risk-free dollar (yen) bond. Let Rf+1 (Rf+1) be the analogous one-period dollar (yen) return in the equity
market of the U.S. (Japan). Throughout the paper, lower case letters will represent either the natural
logarithms of upper case counterparts or variables measured as continuously compounded rates of return.
Hence, the continuously compounded excess dollar (yen) rate of return in the U.S. (Japanese) equity
market is rf+1 - if (rf+1 - if). The conditional expectation of an excess return is often referred to in the
literature as a risk premium, and we will use this terminology interchangeably with expected excess
return.2
A. The Foreign Exchange Market
If S, is the spot exchange rate at date t of dollars per yen, the dollar return to investing one dollar
in the yen money market and bearing the foreign exchange risk is St+1If/St. Let Ft be the forward
exchange rate of dollars per yen quoted at date t for date t+1 transactions. Then, the dollar return to
investing one dollar in the yen money market and eliminating the foreign exchange risk with a forward
contract is F,If/S,. Since this investment also provides a risk-free return of dollars, covered interest
arbitrage implies interest rate parity:

2
An excess rate of return is the nominal rate of return on an asset in excess of the short-term interest
rate. If inflation is stochastic, conditional expectations of excess rates of return will be non-zero even
if agents are risk neutral, which makes use of the term "risk premium" for these conditional expectations
somewhat imprecise. Engel (1992) provides a recent discussion of this issue for the risk premium in the
foreign exchange market.




3

(1)

The right-hand side of equation (1) is the continuously compounded forward premium or discount in the
foreign exchange market. Notice that the continuously compounded excess dollar rate of return from
investing in the Japanese money market is if + s,+1 - st - if, which from equation (1) is st+1 - ft.
A common 'way of testing the predictability of the excess rate of return on an uncovered foreign
money market investment is to regress the excess return on the forward premium:
s«m

- ft = & + 0,(f, " st) + W

(2)

The null hypothesis that the excess rate of return is unpredictable implies 0, = 0. If the point estimate
of /S, differs significantly from zero, there is evidence that ex ante excess rates of return vary over time.
In the empirical analysis we focus on a quarterly holding period since that is the frequency we use for
the exogenous processes in simulating the model.3 The sample period for our exchange rate data is
January 1976 to December 1989. The data are described more completely in Appendix A.
The first row of Table 1, Panel A, displays the regression results for equation (2) using the threemonth forward premium as the predictor. As is typical in the literature, the slope coefficient of -4.016
is significantly negative.4 The R2 for the regression is .22, and the standard deviation of the fitted value
of the excess return, reported in Table 1, Panel B, is 12.36%.5 These statistics indicate that excess

3 The availability of monthly observations on the three-month holding period allows us to use
additional observations that increase the power of the tests but induce autocorrelation in the errors. As
in Hansen and Hodrick (1980), the standard errors in Table 1 allow for the autocorrelation induced by
the overlapping error structure and, additionally, for possible conditional heteroskedasticity as in Hansen
(1982).
4 For the dollar values of other major foreign currencies, the estimated coefficients are also
significantly below zero. Similar results arise in regressions using non-dollar exchange rates as
demonstrated in Bekaert (1992) and Hodrick (1992). Bossaerts and Hillion (1991) use French franc
exchange rates and find slope coefficients that are all less than zero, but not all are significantly negative.
5 All rates of return in this paper are expressed in percentage points per annum.




4

returns are quite predictable and risk premiums are quite variable.
B. The Discount Bond Market

Similar evidence of predictable excess holding period rates of return can be found in the discount
bond market using a forward premium computed from bond prices as a predictor. Specifically, let Vkk
denote the date t price of a nominally risk-free pure discount bond which pays one unit of currency at
*

date t+k. When necessary to avoid confusion, there will be a superscript $ or ¥ symbol on

to denote

the currency. Let i^k be the continuously compounded yield to maturity on a k-period bond expressed
in percent per period. By definition,
v,k = exp(-ki^k).

(3)

Let the one-period continuously compounded holding period rate of return on a k-period bond realized
at time t+1 be h,+l k = ln(Vt+I k.,/Vuk), which from equation (3) can be written as
K

im

= " (k -

+ ki..k-

(4)

In the empirical analysis we examine the one-period excess holding period rate of return on a twoperiod bond, h,+12 - i„ in a regression analogous to equation (2). For parallel structure, we define the
forward premium in the bond market, denoted fb„ as the logarithm of the contractual price today for a
one-period bond delivered one period from now minus the logarithm of the price today of a one-period
bond:
fbt = ln(Vt2/Vu ) -ln(Vu) = - 2 ^ + 2it.

(5)

The bond market analogue to equation (2) is
hf u " i> = 00 + 0i(A\) + W

<6)

If excess holding period returns are unpredictable, /3, should be zero.
In rows two and three of Table I, we report estimates of equation (6) for the U.S. dollar and
Japanese yen discount bond markets. Since our timing interval is one quarter, ht+1>2 is the three-month




5

return on a six-month bond and fbt is the forward premium on a three-month bond to be purchased three
months in the future. For the empirical analysis we have monthly observations on three-month and sixmonth Euro-dollar and Euro-yen interest rates from October 1975 to June 1990.
For both the dollar and the yen markets, the estimate of /S, is -0.45, and both are significantly
negative.6 While the estimated /5,’s are not as negative as the estimates from the foreign exchange
market, there is strong evidence of predictability of the excess rates of return. The R2 for the U.S.
market is .03, and the R2 for the yen market is .09. The standard deviations of the fitted values of the
excess returns in the two markets are 0.318% for the U.S. and 0.370% for Japan. These statistics are
much smaller than those in the foreign exchange market.
C. The Equity Markets
A similar set of results emerges from examining excess rates of return in equity markets. We
focus on results in Bekaert and Hodrick (1992), who show that excess rates of return to U.S. and foreign
equities are predicted by the forward premium in the foreign exchange market. Consistent with our twocountry framework, we construct a dollar world equity market excess rate of return as an equallyweighted average of the dollar excess rates of returns on the equity markets of the U.S. and Japan:
r«!i - i* = [(r*, - it) * (r*. - i*) + (st<1- f,)](l/2).

<7)

We regress this excess return on the three-month forward premium in the dollar-yen foreign exchange
market:
r,:, - i* = P0 + 0,(f.

-

s.) + «,

(8)

The fourth row of Table 1, Panel A, reports a slope coefficient of -3.543, with a standard error of 0.816.
As equation (7) indicates, there are three components to this world equity excess rate of return: the excess

6 These results are similar to those reported by Fama (1984b) and Stambaugh (1988) for monthly
U.S. data.




6

dollar rate of return in the U.S. equity market, the excess yen rate of return in the Japanese equity
market, and the excess rate of return in the foreign exchange market. The regression of the third
component on the forward premium is discussed above. Regressions of the first two components on the
forward premium are contained in rows five and six of Table 1, Panel A. Each of the components has
a negative slope coefficient, and all but the Japanese equity coefficient are significantly negative.
3. Time-Varying Risk Premiums
The patterns of predictability in excess returns documented above can, in principle, be explained
by time variation in equilibrium risk premiums.7 Our paper considers this point of view. In this section
we formally relate the regression evidence of the previous section to time-variation in risk premiums
using a decomposition of the forward premium introduced by Fama (1984a). We then discuss what is
required from an equilibrium model if it is to be consistent with the patterns observed in the data.8
Define the logarithmic risk premium in the foreign exchange market as rp, = Et(st+1) - ft.
Following Fama (1984a), the forward premium can be decomposed into the expected rate of depreciation
of the dollar relative to the yen minus this risk premium:
fpt s ft - s, = Et(Ast4l) - rp„

(9)

where A is the first difference operator.

7The literature modelling asset returns as the outcome of a dynamic, stochastic equilibrium is too vast
to be reviewed here. Examples of recent papers that model excess returns in foreign exchange markets
using approaches related to that used in this paper include Backus, Gregory, and Telmer (1992), Bansal,
Gallant, Hussey and Tauchen (1991), and Bekaert (1993a,b). Kandel and Stambaugh (1991) use a similar
approach to model excess returns in equity markets.
8 There are at least two other potential explanations of the data, which we take seriously but do not
pursue in this paper. First, the stylized facts may not be representative of the true population
distributions. Rather, they may be examples of problems in statistical inference caused by the adoption
of a rational expectations perspective in non-experimental data. Such problems could be caused by
infrequent regime changes, learning, peso problems, data snooping biases, and so forth. Second, these
stylized facts may be evidence of market inefficiency.




7

Now, consider the regression of st+1 - ft on a constant and fp„ as in equation (2). By rational
expectations, st+1 - ft = rpt 4- et+I, where the innovation, et+1, is orthogonal to the time t information set.
Consequently, only the risk premium covaries with the regressor in equation (2), and the slope coefficient
in that regression is
= :cov(st4t - f t, fpt) =
cov(rpt, Et(AstJ ) - var(rpt)
1
var(fpt)
var(Et(Ast4l)) + var(rpt) - 2cov(rp„ Et(Ast4l))'

(1Q)

A decomposition similar to equation (9) can be performed for the bond market. Define the risk
premium in the bond market to be rb, = E,(h,+l2 - ij. Then, the forward premium in the bond market,
fbt, can be decomposed into the expected rate of change of the logarithm of the one-period bond price
minus the risk premium:
fbt = Et(Avu l) - rb,,

(11)

where vl+1 = ln(Vt+t). The slope coefficient in equation (6) would then be given by an expression
analogous to equation (10) with rp, replaced by rbt and Ast+1 replaced by Av,+1.
Clearly, if var(rp,) = 0, the slope coefficient in equation (2) is zero. Similarly, if var(rb,) = 0,
the slope coefficient in equation (6) is zero. To generate the negative slope coefficients found in the data,
the risk premiums rp, and rb, must vary through time. The decomposition (10) provides intuition
regarding the amount of time-variation in risk premiums required to match the data. Consider first the
case of foreign exchange. The explained variance in regression (2) is /S?var(fpl), so the finding of /3, < 1 implies
var(rp,) > var(fpt).

(12)

Furthermore, if /3X< -1, equation (10) implies
var(rpt) > cov(rpt, Et(As,4l)) > var(Et(Astn)).

(13)

Hence, regression results like those in the actual data require that the risk premium in the foreign




8

exchange market be more variable than the expected rate of depreciation and that the risk premium and
the expected rate of depreciation covary positively. Similarly, since the slope coefficient for the equity
market regression is comparable to that in the foreign exchange market regression, the implied variability
of the equity risk premium is comparable to the implied variability of the risk premium in the foreign
exchange market.

*

In the case of the bond market regressions (6), the estimated slope coefficients are insignificantly
different from -0.5. Equation (10), applied to the dollar and yen bond markets, then implies
var(Et(Avt<1)) ~ var(rbt)

(14)

That is, the variabilities of the risk premiums in the two bond markets are roughly equal to the
variabilities of the expected rates of change of the logarithmic bond prices.
The general asset pricing framework of Hansen and Richard (1987) provides insight into what
is needed from an equilibrium model if it is to generate the requisite time-variation in risk premiums.
Let Rj>l+, denote an arbitrary dollar return realized in period t + 1 from investing one dollar at time t.
Hansen and Richard (1987) show that there exists a stochastic discount factor, Q*+1, satisfying9:
Et[Qt»iRu*,] = 1-

(15)

In equilibrium models with effectively complete markets, Q*+1 equals each agent’s intertemporal marginal
rate of substitution of wealth divided by the gross rate of change in the dollar price level.
Equation (15) implies that substantial time variability in excess returns can be achieved only if
there is substantial time-variation in the conditional second moments of the joint {Rft+1, Q?+1} process,

9 Hansen and Richard (1987) require that (i) the space of portfolio payoffs is a Hilbert space of square
integrable random variables, and (ii) there are no arbitrage opportunities.




9

which, in turn, requires substantial volatility in the marginal rate of substitution.10 One way of
generating highly volatile marginal rates of substitution is to assume that agents have a high degree of
risk aversion. In effect, the extreme nonlinearity associated with high risk aversion can transform the
uncertainty due to conditionally homoskedastic exogenous inputs into endogenous risky asset returns
whose moments are conditionally quite variable. Alternatively, high volatility in marginal rates of
substitution can be generated by directly assuming time-varying conditional heteroskedasticity in the
exogenous driving processes (as in Bekaert (1993b)).11
It should be noted that increasing the variance of risk premiums is not sufficient to insure that
conditions (12), (13), and (14) hold. The forward premiums and the expected rates of change of asset
prices are also endogenous variables in the model. Changes in the model specification that increase the
variances of risk premiums may also increase the variances of E,(Ast+1) and Et[Avt+1], leaving the relative
variances unchanged. Furthermore, the covariances between the risk premiums and the expected rates
of change of asset prices may change. Thus, while it is likely that extreme risk aversion will increase
the variability in intertemporal marginal rates of substitution, it is unclear whether this is sufficient to
induce the patterns of predictability in excess returns that are observed in the data. Hence, to explore
the effects of increasing risk aversion we must solve the model explicitly.
4. First-Order Risk Aversion
The preceding discussion makes clear the role that substantial risk aversion may play in
generating the regression results described in section 2. Models using expected-utility preferences have

10 Hansen and Jagannathan (1991) develop restrictions on the mean and variance of the intertemporal
marginal rate of substitution implied by the stochastic properties of observed asset returns. Cochrane and
Hansen (1992) use this methodology to survey equilibrium approaches to asset pricing. They demonstrate
how difficult it is to generate sufficient variability in Qf+, within the context of an equilibrium model.
11 In principle, these two approaches could be combined. For the model of this paper, however,
incorporating time-varying conditional heteroskedasticity substantially increases the dimensionality of the
state space, rendering the approach computationally intractable.




10

not fared well in this regard. Even the models of Backus, Gregory, and Telmer (1993) and Bekaert
(1993b), which incorporate substantial time-nonseparabilities in the form of habit persistence, fail to imply
sufficient predictability in excess rates of return. The reason for this failure is not difficult to see.
Expected-utility preferences display second-order risk aversion. That is, in response to a lottery which
is close to perfect certainty, an expected utility maximizer exhibits behavior close to risk neutrality. This
is a problem for consumption-based asset pricing models because, at any given date, the conditional
variance of next period’s aggregate consumption is small.
One way of addressing this problem is to abandon preferences that display only second-order risk
aversion in favor of preferences that imply first-order risk aversion. With this type of preference
specification, agents are substantially averse to even small gambles. Epstein and Zin (1991) examine a
variety of such preferences, including Gul’s (1991) disappointment aversion preferences, in order to
increase the variability of agents intertemporal marginal rate of substitution. Disappointment aversion
was introduced by Gul (1991) as a way of accommodating the Allais paradox within a parsimonious
extension of expected utility. Camerer’s (1989) review of the experimental economics literature suggests
that expected utility cannot explain the experimental evidence on preference orderings under uncertainty.
Rather, what is required is a preference ordering in which outcomes are evaluated relative to some
reference point. Disappointment aversion has this property.
We follow Epstein and Zin (1991) in using the following simple model of disappointment
aversion. A preference ordering over the space of probability distributions T (e.g., over alternative
lotteries) can be represented by a certainty equivalent function /*: 7*-*R. For P €

T, fi(P)

is implicitly

defined by
A ^ 1,

where K = A-prob(z >




y)

+ prob(z <

fi).

a

< 1.

(16)

If A = 1, the preferences described by equation (16)

11

correspond to expected utility with a coefficient of relative risk aversion equal to 1 - a . If A differs from
unity, equation (16) can be interpreted as follows. Those outcomes below the certainty equivalent are
disappointing, while those above the certainty equivalent are elating. If A < 1, the elation region is
down-weighted relative to the disappointment region. The next section embeds these preferences in a
two-country monetary model.
5. A Two-Country Monetary Model
In the model asset prices and exchange rates are determined in a competitive equilibrium in which
the demands for assets and goods are the optimal choices of a representative agent. As in Marshall
(1992) and Bekaert (1993b), money is demanded by agents because consumption transactions are costly,
and increasing real balance holdings decreases these transaction costs. Specifically, let the two countries
be denoted as x and y, respectively. The representative agent’s consumption of the good produced in
country x is c \ and the representative agent’s consumption of the good produced in country y is cy.
Consumption of cx involves transaction costs measured by
(17)

denominated in units of c\ where Mf+, is the amount of currency x (which we call the dollar) acquired
by the representative agent in period t; and Px is the price of cx at date t in units of M\ Consumption
of cy involves a transaction cost of
(18)

denominated in units of good y, where Mf+, is the amount of currency y (which we call the yen) acquired
by the representative agent in period t; and P( is the yen price of cy at date t.
The timing in this model differs from the transaction-cost models of Feenstra (1986) and Marshall
(1992) in that money provides transaction services in period t when it is acquired. However, money must




12

be held until the following period, so losses in purchasing power due to inflation accrue in period t + 1.
This timing is imposed for tractability. With our timing, the only endogenous state variable affecting an
individual agent’s decisions is the agent’s stock of wealth. If money only provided transaction services
if acquired one period earlier, the agent’s stock of money would represent a second endogenous state
variable. The optimality conditions would then involve the derivatives of the (unknown) value function
with respect to the money-wealth ratio. To solve such a model numerically would be extremely
burdensome computationally.
In addition to monies, agents can hold n capital assets. Let Zj t+1 be the value (in units of cx) of
the representative agent’s investment in asset i, chosen at t, and which pays off at t + 1. The gross real
return to asset i (measured in units of good x received in t + 1 per unit of good x invested at date t) is
denoted Ri>l+1.
If St denotes the exchange rate (dollars/yen), the budget constraint for the representative agent
in units of consumption good x is

c,* +

♦ ^ i ( c ly + tf) + £ z.i,t*l
P.x
'
M
P
« '

m ,:

< W

(19)

P,x

where W, denotes the representative agent’s wealth at the beginning of period t:
Mt* + S, M,y
"
W. - - l- - ‘ ■ * £ z, A ,

(20)

The representative agent’s preferences over current and uncertain future consumption incorporate
disappointment aversion as in equation (16), and are specified using the approach of Epstein and Zin
(1989).

Specifically, let Jt denote the vector of exogenous state variables which span the agent’s

information set at date t. The utility value of Wt in the state Jt is denoted V(Wt, JJ, and is defined
recursively by




13

i/p
V(Wt, Jt) =

max
{c,*, Cyt M,:„ M*,, r

( k i v r r

* ^ [ P v W „ u u,])'

(21)

0 < 6 < 1, p < 1,

subject to the budget constraint (19) and the wealth constraint (20), using the definition of p from
equation (16).

The expression p|PV(W

s )|Jtj

denotes the certainty equivalent of the conditional

%

distribution of the value function at date t+1, given information at date t. When agents make their
consumption and portfolio choices, they care about two distinct effects: how their choices affect currentperiod utility, and what happens to the probability distribution of their future utility. In an expected
utility framework, the latter effect is incorporated by taking the conditional expectation of next-period’s
value function. In equation (21), effects of the probability distribution of future utility on current utility
are captured by the certainty equivalent function p. In addition, the two effects are aggregated in
equation (21) by the CES function of the form (a" + bp)tl/p), while, in the expected-utility framework, the
two effects are simply added.
The parameter p governs intertemporal substitution in the following, somewhat unconventional,
sense: The elasticity of substitution between current utility (c’t)i(cy)1', and the certainty-equivalent of
future utility, p{PV(W , , | JtJ, is given by 1/(1+p). Therefore, p determines the optimal tradeoff between
present and future utility. When p is near unity, there is an extremely high degree of substitutability
between these two sources of utility. Extremely negative values of p imply almost no substitutability.
It should be noted that this elasticity of substitution does not directly correspond to the elasticity of
substitution between current and future consumption (as studied, for example, by Hall (1988)). The more
conventional notion of intertemporal substitution elasticity is a function of all the preference parameters
of the model.




14

6. Equilibrium Determination of Exchange Rates and Asset Returns
In order to derive equilibrium asset prices and exchange rates, we must solve the representative
agent’s decision problem and impose market clearing. The agent’s optimal behavior is characterized by
a set of Euler equations that involve the real return on optimally-invested aggregate wealth, which we
denote R,. (An explicit characterization of Rt can be found in Appendix B.) These equations also involve
the real returns, inclusive of marginal transaction cost savings, from holding dollars and yen. Let
' p,x
p,:.
denote the real return from holding dollars, where

i
i +&

(22)

denotes the period t partial derivative of \p* with

respect to its i* argument. (\^, is defined similarly.) The real return from holding yen is

Ry .t* l

X .

p .x

s,p,:,

i

(23)

i + ^

Note that both Rxt+, and Ry,t+i are measured in units of good x received in t+1 per unit of good x
invested at date t.
The first-order conditions for the representative agent’s optimal consumption, money holdings,
and portfolio choices are the following:12

12
request.




The derivation is a modification of the arguments in Epstein and Zin (1989), and is available upon
15

(2 4 )

Et{lA(ZtM)[ZrM - 1]} = 0,

E{lA(Zt4l)Z “1Rt;11Rit4l] = Et[IA(Zt4l)], V i = x , y , l ........N,

(25)

where

0

1/p

y P<l-i)
X pa-i
c,:i
C..I
’1 +

(26)

'
*.♦«

C,x

c,y

1 + flu.

and

A if Z ^ 1
*a(Z) -

(27)

1 if Z < 1

In developing the solution to the model, it is useful to define the endogenous processes for
consumption-velocities of the two monies. Let vj and vj denote the consumption-velocities in countries
x and y:
v, ■

c‘P‘

cyPy

M,t*l

M,y
t*l

' ‘ y•
- v
v —
=
vty

1 •

(28)

Other endogenous variables are the nominally risk free, continuously compounded interest rates
on dollars and yen, denoted i* and i*. Nominally risk-free interest rates are functions of the marginal
transaction costs with respect to real balances:

its = In

1
); *i.rt = In
111
1 +^2,

The exchange rate S, is given by




16

1

(29)

ptx

1 + tit

V '

pty

1 + tit

c,y

1 -6
6

(30)

Given interest rates and the spot rate, the forward rate F, can then be computed using covered interest
parity as in equation (1).

7. Calibration and Solution o f the Model
In this section we describe our procedures for choosing the parameters of the stochastic processes
for the exogenous variables and of the transaction cost functions. The outputs and money supplies of the
two countries are assumed to be exogenous. There are no data series corresponding precisely to the
endowment constructs of the model. The difficulty is that a two-country mode) cannot replicate the
complexity of trade patterns that we observe in the real world. As a result, we do not take seriously the
predictions of the model for quantity variables. However, the implications of the model for asset return
predictability can be investigated with a plausible specification of the endowment driving processes.
We calibrate the endowments and money supplies of the two countries to consumption data and
money supply data from the U.S. and Japan. The growth rates of these four exogenous processes are
assumed to follow a vector autoregression, which we will approximate as a discrete Markov chain. We
find that a first-order VAR with conditionally homoskedastic errors fits the data well. In Table 2, Panels
A and B, we display OLS estimates of this VAR.

Table 2, Panel C reports statistics testing the

appropriate lag length for the VAR. The Akaike and Schwarz criteria, as well as the sequential likelihood
ratio tests, support the first-order VAR specification. Table 2, Panel D provides statistics testing for
normality, autocorrelation, and conditional homoskedasticity of the VAR residuals. Only in the residual
for the growth rate of Japanese consumption is there marginal evidence of serial correlation. For none
of the residuals is there significant evidence against normality or conditional homoskedasticity.
The growth rates of these four exogenous processes are approximated by a discrete first-order




17

Markov chain in which each variable can take four possible values, implying a state space with 256
possible values. The Markov chain is calibrated to the estimated VAR using the Gaussian quadrature
method of Tauchen and Hussey (1991). In Table 3, we display the parameters of the first-order VAR
implied by this Markov chain approximation. The parameters characterizing the Markov process VAR
are virtually indistinguishable from those of the estimated VAR reported in Table 2. All parameters of
the Markov process VAR (including the elements of the covariance matrix decomposition) are within onetenth of one standard error of the corresponding parameters in the estimated VAR. We take this as
evidence that the discrete approximation is unlikely to distort the economic implications of the model.
The parameters of the transaction cost functions (17) and (18) are chosen by fitting equations (29)
to U.S. (for

\p*)

and Japanese (for V'5') data, as described in Appendix A. Specifically, we set
^ x(c,m) = 0.0008c4-35,m ''° 31; ^(c,m) = 0.0166c2“ ’’m*-2109.

(31)

Given this exogenous process, the three unknown endogenous processes R,, v}, and v{ are found
by solving the three Euler equations (24) and (25) (for i = x and y) simultaneously. Since the state space
is discrete, the Euler equations can be solved exactly for the 256 values of each endogenous variable.
The only approximation is in the initial discretization of the driving processes. A detailed description of
the solution procedure can be found in Appendix B. Once R,, vj, and v( have been determined, all other
endogenous variables can be calculated from definitions and equilibrium conditions.
8. Implications of the Model for Excess Return Predictability
In this section, we report results obtained from solving the model for a variety of parameters
governing preferences. The quarterly subjective discount parameter /3 is fixed at (0.96)025. The choice
of 6 (the weight on cx in the current-period utility) is irrelevant, since we examine rates of depreciation
, rather than levels of exchange rates. The remaining parameters are varied over the following grid: A
€ {1.0, 0.85, 0.70, 0.55, 0.40, 0.25},




p

€ {0.50, -0.33, -4.0, -9.0}. We experimented initially with

18

values of a between 0.5 and -9 and found that the choice of a had virtually no effect on the moments of
interest. Consequently, we only report results for a

=

-1. This corresponds to a coefficient of relative

risk aversion of 2 in an economy with expected-utility preferences over timeless gambles.
We first discuss the ability of the model to replicate the predictability of excess returns
documented in section 2. We focus on three measures of predictability: the slope coefficient in the excess
return regressions analogous to equations (2), (6), and (8); the R2, measured as the ratio of the variance
of the expected excess return to the variance of the realized excess return; and the standard deviation of
the expected excess return. All three statistics can be computed exactly given the discrete Markov chain
driving process.
Consider the model’s implications for the slope coefficients in the excess return regressions
analogous to equations (2), (6), and (8). The results are displayed in Tables 4, 5, and 6 for the foreign
exchange market and the dollar and yen discount bond markets, respectively. Table 7 displays the slope
coefficient when the excess return to the aggregate wealth portfolio (which we interpret as an analogue
to an unlevered equity portfolio) is regressed on the foreign exchange forward premium.
It is clear from these tables that the model cannot match the slope coefficients estimated from
observed data. For no combination of parameters do the regression coefficients implied by the model
come close to the magnitudes reported in Table 1. For example, for the foreign exchange market
regression, the estimated slope coefficient in Table 1 Panel A is -4.016, with an estimated standard error
of 0.766. The most negative slope coefficient implied by the model is -0.191, which is approximately
five standard errors away from the estimated value. Similarly, the slope coefficients implied by the
model for the term structure regressions analogous to equation (6) (reported in Tables 5 and 6) and the
equity return regressions (reported in Table 7) are extremely small, and they are all more than 3.4
standard errors away from the corresponding estimates reported in Table 1.
The second measure of predictability is the model’s R2 as defined above. This theoretical R2




19

cannot be observed in the data, but a lower bound is provided by the estimated R2s reported in Table 1,
Panel A. Whereas the R2s in the data are substantive, ranging between 1% and 22%, the corresponding
R2s in the model are negligible, all being less than .2%.
The third measure of the predictability of excess returns is the variability of the explained
component of excess returns. As with the R2discussed above, a lower bound for this measure in the data
is provided by the standard deviation of the fitted value of the excess return regressions reported in Table
1, Panel B. As with the previous two measures, the model is unable to reproduce the variability observed
in the data. For example, the standard deviation of the fitted value of St+, - f, in Table 1 is 12.4%. The
largest value of the standard deviation of E,(s,+l - f,) from the model, reported in Table 4, is 0.356%,
which is over thirty times too small. Analogously, the standard deviation of the fitted value of the excess
world equity return in Table 1 is 10.9%. The largest standard deviation of Et(rt+1 - ij from the model,
reported in Table 7, is 0.175 %, which is over sixty times too small. The standard deviations of the fitted
values of the excess returns in the discount bond markets are 0.318% and 0.370% for the dollar and the
yen markets, respectively. The maximum value of the standard deviations of the expected excess returns,
reported in Tables 5 and 6, are 0.13% and 0.06% respectively.
These results are somewhat disappointing to those who favor risk-based explanations for the
predictability of excess returns. To further explore the role of risk aversion in generating predictability
in excess returns, we next examine how the predictions of the model change as we increase the
importance of the first-order risk aversion by lowering A. In all cases, setting A = 1 results in extremely
small values for the slope coefficients. However, it is not generally true that increasing the amount of
risk aversion (decreasing A) implies more negative slope coefficients. Furthermore, a large degree of
risk aversion is not systematically associated with a particular sign of the regression coefficient. For
example, the coefficients corresponding to A = .40 and A =.25 in Tables 4 through 7 are as likely to
be positive as to be negative. Thus, even if it were assumed that agents in the economy display extreme




20

risk aversion, it is not at all clear whether this would improve the performance of the model along this
dimension.
To see why the model fails to replicate the observed slope coefficients, it is useful to return to
the discussion of section 3. In that section, we argued that substantial time-variation in risk premiums
is necessary if a model is to match the patterns found in the data. Examination of Tables 4 through 7
reveals that the variances of the ex ante risk premiums are unambiguously increasing as the degree of
first-order risk aversion increases. For foreign exchange, the standard deviation of the risk premium
increases by a factor of 100 when A moves from 1 to .25. For discount bonds and the aggregate wealth
portfolio, the standard deviation of the risk premium increases at least twenty-fold when A moves from
1 to .25. Similarly, the R2’s in all markets increase dramatically as first-order risk aversion is increased.
The reason why these dramatic increases in risk-premium volatility do not imply comparable
increases in the magnitude of the slope coefficients in the prediction regressions is that these coefficients
are functions of moments in addition to the variances of the risk premiums. As shown in equation (10),
the slope coefficients also depend on the variances of the expected asset price changes and on the
covariances between the expected changes in asset prices and the risk premiums. These moments are also
affected by changes in the parameter governing first-order risk aversion. In particular, Tables 5 and 6
show that the variances of the expected changes in the prices of one-period discount bonds actually
decrease unambiguously as A decreases. The variance of the expected change in the spot foreign
exchange rate is not monotonic in A. As shown in Table 4, decreasing A from unity initially reduces
this variance, while further reductions in A increase it. The value of A at which this variance is at a
minimum depends on p. The effects of increased first-order risk aversion on the covariances between
the ex ante risk premiums and the expected changes in asset prices are also in Tables 4 through 6. In
the foreign exchange market, decreasing A unambiguously increases this covariance. In the discount
bond markets, the response of this covariance to increased risk aversion is not monotonic, and depends




21

on the value of p.
Our model also has implications for the unconditional mean equity premium and the unconditional
standard deviations of financial variables, which provide additional dimensions to assess the model’s
performance. In Table 7, increasing the amount of first-order risk aversion dramatically increases the
unconditional mean excess equity return. As A is reduced from 1 to .25, the mean equity risk premium
increases by a factor of approximately 20. This increase is not sufficient to match the data as the largest
mean equity premium generated by our model simulations is 3.5%. While this is substantially below the
value of 8.4% estimated from our data set, the equity return data correspond to a levered portfolio, while
the equity return computed in our model is unlevered. The result are comparable to those of Bonomo
and Garcia (1993) for homoskedastic driving processes. These authors are able to increase the mean
equity risk premium significantly by employing a richer driving process that incorporates regime
switching.
Table 8 displays standard deviations implied by the model. In comparing Table 8 with Table 1,
Panel B, notice that the magnitudes of the standard deviations in the model are almost always smaller than
the corresponding statistics in the data. In particular, the standard deviation of currency depreciation is
approximately 2.5 times higher in the data than in the model, and the standard deviation of the equity risk
premium is approximately three times higher in the data than in the model. When p = -9, the standard
deviation of the forward premium in the model is only 50% lower than that in the data; for the other
values of p, the variability of the forward premium is almost an order of magnitude too low.
Although the model underpredicts the variability of both expected and realized excess returns,
the parameterizations of the model that generate the largest variances of expected rates of return tend to
overpredict the variances of the forward premiums in the discount bond markets. For example, with p
= -9 and A = .25, the standard deviations of the forward premiums in the dollar and yen discount bond
market are 3.81% and 2.56%, compared to 0.71% and 0.83% in Table 1, Panel B.




22

The source of this problem is as follows. In order to generate high volatility in excess returns,
the model must generate high volatility in the conditional second moments of intertemporal marginal rates
of substitution. Unfortunately, parameterizations of the model which do this also imply highly volatile
spot interest rates. A similar problem has been noted in a closed-economy model by Heaton (1991).
Consequently, one challenge for this class of models is to accommodate highly variable expected and
realized excess returns on risky assets while keeping short-term interest rates relatively non-volatile.
9. On the Success of Epstein and Zin (1991)
Epstein and Zin (1991) are unable to reject the overidentifying restrictions implied by their single­
country model with preferences incorporating first-order risk aversion, which suggests considerable
support for this approach to asset pricing. Our approach is less successful. How can we explain the
differences in findings?
According to the Euler equation (25), the implications of these models for asset returns are
summarized in the behavior of the asset pricing operator

Et[IA(Zt-,)]

-1
♦1•

This operator is a function of Rt+1, the return to the aggregate wealth portfolio. Euler equation estimation
requires an observable analogue to this asset pricing operator, and Epstein and Zin use the return on a
value-weighted portfolio of equities as their empirical measure of Rt+1. This procedure is clearly subject
to Roll’s (1977) critique, a point acknowledged by Epstein and Zin. Furthermore, with this approach,
the empirical asset pricing operator is a function of the returns on the equity assets being priced. The
operator partially inherits the statistical properties of observed equity returns, so it has less difficulty
replicating the behavior of observed excess equity returns. In contrast, we derive Rt+1 by explicitly
solving the model’s equilibrium as a function of the growth rates of output and money in the two




23

countries. Nowhere do we use data on asset returns in deriving the asset pricing operator. To ask the
pricing operator, derived in this way, to replicate the stochastic properties of equity returns is a much
tougher test of the model than the Epstein-Zin procedure. It is not surprising that we find more evidence
against the model.
10. Conclusions
In this paper, we ask whether high levels of risk aversion can explain the observed predictability
of excess returns within the context of a frictionless, representative agent model. In order to give this
explanation the best chance for success, we assume that agents’ preferences display first-order risk
aversion. This preference specification implies that agents respond more strongly to consumption risk
than would be the case under conventional Von Neumann-Morgenstern preferences. Yet, even this more
extreme form of risk aversion can explain only a small fraction of the predictability of excess returns
found in the data. Furthermore, we find that the slope coefficients in equations predicting excess returns
do not increase monotonically with increased risk aversion. The level of risk aversion affects not only
the variability of risk premiums, but also the second moments of other endogenous variables which affect
predictability. The resulting implications for the signs and magnitudes of these slope coefficients are
ambiguous.
Taken together, the results of this paper suggest that the predictability of excess returns cannot
be fully explained simply by modifying preference assumptions. A more promising approach may be to
abandon the assumption that the empirical distribution in the data set is a good proxy for agents’
subjective distribution over future variables.

Rational optimizing models that do not impose this

assumption include learning models, models with peso-problems, and some models with regime
switching. It is hoped that these alternative approaches will have more success in explaining excessreturn predictability than approaches based solely on modelling agents’ aversion to consumption risk.




24

APPENDIX A: DESCRIPTION OF DATA
The interest rate data are monthly series on three-month and six-month Euro-dollar and Euro-yen
rates, obtained from the Harris Bank database at the University of Chicago. Monthly exchange rate data
are from daily bid and ask rates from Citicorp Database Services and are described in detail in Bekaert
and Hodrick (1993):
The money supplies for the U.S. and Japan are quarterly series taken from International Financial
Statistics (IFS Series 34). Growth rates are deseasonalized by regressing on four dummies. The
consumption data are Nondurables and Services from the OECD Quarterly National Accounts. The
Japanese data include the Semi-durables category, as this category is included in the U.S. Nondurables
series. Per capita data on money supplies and consumption were derived by using linear interpolations
from the annual population series 99z from IFS.
The transaction cost technology parameters are considered to be part of the exogenous
environment and are calibrated from the model’s implications for money demand, as summarized by
equations (29). These equations imply linear relationships between the logs of current dollar and yen
velocities of circulation and the logs of the respective interest rate divided by one plus the interest rate.
The calibration is done by linear regression using quarterly Eurocurrency interest data and nominal
velocity. The velocity series used is computed using nominal GDP, taken from OECD Quarterly
National Accounts, divided by the money series described above. GDP velocity is used because it implies
more reasonable parameters for the transaction cost function than consumption velocity. The use of GDP
velocity can be justified by noting that money in actual economies intermediates many more transactions
than just consumption transactions. See Marshall (1992) for a fuller discussion of this issue.

APPENDIX B: SOLUTION PROCEDURE
The key step in solving the model is to solve numerically the Euler equations (24) and (25) for




25

the endogenous variables vj, v(, (defined in equations (28)) and R,+i (the return to the aggregate wealth
portfolio). We do so by using a finite-state Markov chain to approximate the exogenous driving process
(see Tauchen and Hussey (1991)). We then solve the model exactly for this approximate driving process.
In this appendix we describe the solution procedure in greater detail.
Let ej denote the total output of good x at date t, let

denote the output o f good y at date t, and

let Mt+i and M(+1 denote the supplies o f dollars and yen respectively, available for use in mediating
transactions at date t. (These money stocks are dated t + 1 because it is assumed that the loss in value
from inflation accrues to the agent in t+ 1 .) Let g, denote the vector o f growth rates o f outputs and
money supplies in the two countries:

S,

It is assumed that {ej, e^, MJ+I, M^+,} is an exogenous process whose law o f motion is known.
First, we show how equations (24) and (25) can be written in terms o f g, and the three
endogenous processes {vf, v(, Rt+1}.

Using (17), (18), and the requirement that, in equilibrium, the

output o f each good must either be consumed or used as transaction costs,

we can write consumption growths, marginal transaction costs, and inflation rates as functions o f {gt, vf,




^x
^X
ct+l _ et+l
_X
X
Ct

i +

(32)

= e& ' i
cty

ety

i + tfvtr,)£-‘

rn =

(34)

c-i

(35)

tf, = & { w )

& = X(1 -i/)(vt‘)'

& =

p,:. _ vt:, c,x h *
m

K

ii

p,y

> \

p,y
*.

C,y m

V,y C,y,

(38)

,:,

,!2

(39)

M tyi

The next step is to formally characterize R,+„ the return to the aggregate wealth portfolio. Since
we define the return to money inclusive of marginal transaction costs, $ jit and $ !>t, we must incorporate
these marginal transaction costs into the definition of the portfolio weights for the aggregate wealth
portfolio. Formally, let




27

w t ■ w t-

S , I l (c,’ * t f )

Pt

+ --- V'zt
p.

s t—
Pt

(40)

Wt denotes wealth available for asset purchases at date t, adjusted for marginal transaction costs. The
portfolio weights on the aggregate wealth portfolio are defined in terms o f \Vt. Let wxt+1 and wyt+1
denote the portfolio' weight on MJ+1 and

respectively:

M,t*l

(41)

(i + &)) /W.

K

M y

(42)

W y.ul S
P,
Let wi t+1 denote the portfolio weight on asset i:

w.

= Z,MX

(43)

i =

Note that the weights sum to unity:
N

w.i,t*l
E
i-1

+ W

(44)

x,t*l + wy,t*l = 1A*

The return to the aggregate wealth portfolio is defined as follows:

R .-i s

’

i-1

(45)

where RM+l and Ry,t+, are defined in equations (22) and (23). Aggregate wealth evolves according to

w,., -

m

In a single-good nonmonetary model, the market return can be expressed as a function o f the
wealth/consumption ratio and the growth rate o f consumption. It is convenient to express R,+1 in a similar




28

way. To do so, define c, = W, - W„ and let the "wealth/consumption ratio" Wt/ct be denoted wc,.
Equation (46) then implies

R- '

WC.-1

''

* '

The transaction cost functions \p* and ^ are homogeneous o f degree one, so one can use Euler’s theorem,
along with equation (30), to show that

' c '
C«

C,x

■ 1

(48)

1 + 'Put

By using equations (32) - (39) and equation (48) in equations (22), (23), (26), and (47), one can write
the endogenous processes Rx>t+1, Ry.,+i, Zt+1, and R,+l as functions o f (gt+1, vj, v?+1, v(, v(+1, wc„ wct+,}.
It follows that the three-equation system consisting of equation (24) and equation (25) with i = x and i
= y, can be expressed in terms of {gl+1, vf, vf+1, v(, v(+„ wct, wct+1}. Let this three-equation system
be denoted

Et[f

vt*l»vt*>v£i,vty,wct4l,wcj

= 0

(49)

where f is a known function.
Our task then is to find a stochastic process {vj, v(, wc,} which satisfies equations (49) for the
given g, process. Following Tauchen and Hussey (1991), we approximate g, by a finite-state Markov
chain. The discretization uses Gaussian quadrature. In the results presented in section 7, we allow each
o f the four elements o f g, to take on 4 values, implying 256 possible states o f the economy.

The

endogenous processes, vj, v(, wc,, are then represented by vectors with 256 elements each, to be
determined by solving system (49).

The conditional expectation can be evaluated exactly (given the

discrete approximation) since the state transition probabilities are known. We reduce the computational
burden of this solution algorithm by assuming that the growth rates of c} and c( are observed, rather than




29

the growth rates of output in the two countries. This enables us to solve system (49) recursively: the
elements of {wc„ vx} do not depend on the third equation in (49). Therefore, the 512 elements of {wc,,
vx} are found by simultaneously solving the 512 equations represented by the first two equations of (4 9 ),
each evaluated at each of the 256 states. Given these values for {wq, vx}, the 256 elements of vy are
found by solving the% 256 equations represented by the last equation of (49) evaluated at each of the 256
states. Having solved for (wc„ vx, vy}, the remaining endogenous variables can be computed using
equation (47) and equations (32) - (39).




30

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33




Table 1

Panel A: Regression Results
Dependent
Variable

Coef. on
constant

$t+i ”
%

16.271
(3.674)

Coef.
on fpt

Coef. on
ft?

Coef. on
ft?

-4.016
(0.766)

R2
.2 2 0

+1.2 * i?

0.038
(0.050)

hi+,.2 - s

0.075
(0.019)

rT+, - i?

21.540
(4.864)

-3.543
(0.816)

.139

r?+. - i?

11.413
(4.971)

-2.024
(0.900)

.041

rT+i -

15.397
(4.807)

-1.045
(0.954)

.013

i\

-0.450
(0.129)

.028
-0.448
(0.028)

Panel B: Means and Standard Deviations
Variable

Mean

Standard Deviation

Ast+1

5.119

25.019

fa

3.698

3.077

fitted st+, - f,

1.421

12.355

ft?

0.124

0.707

0.094

1.892

fitted h*+1.2 - i*

0.094

0.318

ft?

0.116

0.826

M
ut +l,2 - iv
ll

0.128

1.259

fitted h*+12 - i*

0.128

0.370

rw - is
rt-i
*t

8.440

29.204

fitted r", - i*

8.440

10.899

^t +1,2 "

34

.086

Table 1 (continued)

Notes: The data are monthly observations on quarterly rates. The sample period is from January 1976
to December 1989 for exchange rates and equities and from October 1975 to June 1990 for interest rates.
All rates are measured as percentage points per annum. Time subscripts denote quarters. The logarithms
of the dollar/yen spot and forward exchange rates are denoted st and ft. The quarterly rate of depreciation
is Ast+1; the three-month forward premium on the yen in terms of the dollar is denoted
the quarterly
dollar excess return on the world equity market (an equally-weighted average of the dollar excess returns
to U.S. and Japanese equities, defined in equation (7)) is r*+, - i*; the three-month dollar excess return
to U.S. equities is rf+1 - i*; the three month yen excess return to Japanese equities is r*+3 - if; h?+1>2 it (hl+i.2 * •*) is the quarterly excess dollar (yen) return from t to t + 1 obtained by holding dollar (yen)
discount bonds that mature at t+ 2 ; fbf (fbj) is the one-quarter-ahead forward premium, defined in
equation (5), in the dollar (yen) discount bond market. In Panel B, the variable "fitted s, +1 - ft" is the
fitted value of regression (2 ); the variable "fitted hf+1>2 - i?" ("fitted h*+12 - i*") is the fitted value of
regression (6 ) using data from the dollar (yen) bond market; the variable "fitted r* +1 - i*" is the fitted
value of regression (8 ). The numbers in parentheses are standard errors, which are heteroskedasticityconsistent and are corrected for the serial correlation induced by the overlap in the data using the method
of Newey and West (1987).




35

Table 2

VAR Estimates and Diagnostics for the Exogenous Processes

Panel A: Parameter Estimates for the VAR

constant

gm,.,

gXt-i

g°t-i

gy«-i

R2

gmt

.610
(.446)

.195
(.151)

.022
(.437)

-.182
(.074)

.368
(.184)

.074

gx,

.629
(.141)

.033
(.038)

.281
(.118)

-.016
(.024)

.076
(.062)

.057

gi\

.439
(.835)

.023
(.228)

1.310
(.763)

-.493
(.129)

-.259
(.370)

.198

gyt

1.118
(.287)

.137
(.085)

-.060
(.246)

-.015
(.050)

-.171
(.142)

.009

Panel B: Cholesky Decomposition of the Covariance Matrix of the VAR Residuals




.01261
(.00152)

.00114
(.00034)

.00054
(.00287)

-.00056
(.00073)

.00382
(.00043)

.00332
(.00272)

-.00038
(.00087)

.02326
(.00177)

.00371
(.00097)
.00762
(.00059)

36

Table 2 (Continued)

Panel C: Selection Criteria for the VAR Order
VAR order

Akaike Criterion

Schwarz criterion

1

-36.61

-36.05

2

-36.45

-35.33

3

-36.43

-34.74

Likelihood ratio tests
2

19.06 (.266)

2 vs. 3

23.94 (.091)

1

vs.

Panel D: Residual Diagnostics
1(4)

Q2(4)

Ku

Sk

BJ

Eq. 1

2.481
(.894)

5.916
(.206)

.172
(.784)

.005
(.987)

0.075
(.963)

Eq. 2

6 .1 1 0

(.191)

7.039
(.134)

1.137
(.070)

-.046
(.883)

3.308
(.191)

7.198
(.126)

4.036
(.401)

-.547
(.383)

.2 0 0

1.169
(.558)

Eq. 3

(.523)

14.27
-.500
.232
2.123
1.182
(.426)
(.007)
(.713)
(.459)
(.554)
Notes: The sample period is 1974:4 to 1990:1. gm, denotes the growth rate of the dollar money supply;
gxt denotes the growth rate of U.S. consumption; gn, denotes the growth rate of the yen money supply;
gyt denotes the growth rate of Japanese consumption. Estimates of the VAR coefficients and the
decomposition of the error covariance matrix are obtained by OLS and reported in Panels A and B with
heteroskedasticity-consistent standard errors in parentheses. The appropriate lag length for the VAR
minimizes the Akaike or Schwarz criterion in Panel C. The likelihood ratio test is a sequential test of
a VAR(n) versus a VAR(n+1). The test statistic has a x 2 distribution with degrees of freedom equal to
the number of coefficients being restricted by the lower VAR order. The statistic incorporates the Sims
(1980) correction. Marginal levels of significance are in parentheses. Panel D reports statistics and
associated p-values for various residual diagnostic tests. Column 1 reports the Cumby-Huizinga (1992)
1-test for serial correlation of the residuals. Column 2 reports the Ljung-Box test statistic, applied to
squared residuals, as a test for ARCH. Columns 3, 4, and 5 test for normality of the residuals. Ku is
the normalized kurtosis coefficient and Sk the normalized skewness coefficient. Their asymptotic
distribution is N(0,24/T), N(0,6/T) respectively, with T the sample size, under the null of normality.
BJ is the Bera-Jarque (1982) test fpr normality and is x2(2).
Eq. 4




37

Table 3
VAR Parameters Induced by the Discretized Markov Chain Approximation

(i) Implied VAR Coefficients

constant

gm,.,

gXt-l

gn,-,

gy»-i

gpl,

.610

.194

.022

-.181

.368

gXt

.629

.033

.280

-.016

.075

gn.

.443

.023

1.299

-.489

-.255

gy.

1.118

.137

-.062

-.014

-.170

(ii) Cholesky Decomposition of the Implied Residual Covariance Matrix

.01261

.00114

.00054

-.00056

.00382

.00331

-.00038

.02312

.00369

.00762
Notes: The discrete state space approximation to the VAR in Table 2 is computed using the Gaussian
quadrature procedure of Tauchen and Hussey (1991). Each variable is allowed to take four possible
values, implying a discrete state space with 256 elements. Variable definitions are given in the notes to
Table 2.




38

Table 4
Implications of the Model for the Foreign Exchange Market Regression

•
p = .5

A = 1.0

A = .85

A = .70

A = .55

ft

-.007

- .0 1 2

-.068

-.097

R2

l.OxlO"7

2 . 1xl 0 '5

8 . 8 xl 0 '5

.00016

00030

.00133

= -3

.042

.085

.116

.159

.332

ff[Et(As,+1)]

.228

.229

.226

.230

.274

.370

-.0004

.0 0 1 1

.0038

.0087

.0269

.1017

13,

-.007

-.023

-.057

-.107

.035

-.044

R2:

l.OxlO"7

1 .8 xl 0 '5

7.7xl0'5

.00015

.00029

.00116

.003

.039

.080

.113

.155

.309

.236

.231

.229

.228

.269

.363

-.0004

.0003

.0034

.0076

.0256

.0941

Pi

-.0 0 1

-.003

-.006

- .0 2 1

-.009

.057

R2

l.OxlO'7

2 . 1 xl 0"5

8 .6 xlO-J

.00017

.00032

.00133

.003

.042

.085

.118

.164

.334

.485

.472

.461

.443

.438

.509

- .0 0 0 1

.0 0 1 1

.0061

.0099

.0255

.1190

.0 0 1

.003

.005

.007

.008

.009

2 . 1 xl 0'5

8 .2 xl 0 '5

.00015

.00032

.00138

.004

.044

.088

.1 2 0

.173

.356

2.284

2 .2 0 0

2 .1 0 0

1.973

1.807

1.575

.0157

.0311

.0422

.0570

.1472

ff[rpJ
ff[E,(Ast+1)]

^[rpJ
a[Et(Ast+I)]
cov[rp„ E,(Ast+1)]
Pi

R2
p = -9

-.191

.003

cov[rp„ El(Ast+1)]

P

.038

A = .25

ff[rpj
cov[rp„ El(Asl+1)]

p = -.33

A = .40

ff[rpj
a[Et(Asl+1)]
cov[rp„ El(Ast+,)]

1.7x1O'7

.0046

Notes: The logarithms of the dollar/yen spot and forward exchange rates are denoted s, and f„ and rpt
= El(st+1-Q. /?, denotes the slope coefficient in the regression st4l - ft = /S0 + j8 ,(ft - st) + et4l.
EtCXj+j) denotes the expectation of x, +1 conditional on date t information, a[xj denotes the unconditional
standard deviation of xt, and cov[xt, yj denotes the unconditional covariance.
R2 =
var(Et(sl4,-ft))/var(st4l-ft). All moments reported are the exact population moments implied by the model
at the indicated parameter specifications, given the Markov transition matrix for the exogenous process
gt. This transition matrix was computed using Gaussian quadrature from the estimated VAR, as described
in Appendix B.




39

Table 5
Implications of the Model for the Dollar Discount Bond Market Regression

p = .5

A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

is,

- .0 0 0 0 1

- .0 0 0 2 2

-.00026

.00013

-.00196

.00084

R2

1 .0 x 1 0 '*

7.7X10-6

2 .6 x 1 0

5.4xl0's

.00014

.00053

.00067

.0 0 1 2 1

.00172

.00272

.00512

.2 2 0

.218

.215

.2 1 1

.206

.199

-5.0xl0'7

- 1 .0 x 1 0 s

-l.OxlO-5

8 .6 x 1 0 *

-7.6xl0'5

-7.2x10*

Pi

.00005

.00042

-.00031

.00046

.00048

-.00205

R2:

5.0x10'*

1.4xl0'5

5.1x10 s

.0 0 0 1 2

.00024

.00087

ff(rpt)
Et[Av*+1]

.00005

.00078

.00146

.00219

.00297

.00528

.230

.226

.2 2 1

.214

.206

.192

3X10-6

-2 .2 x 1 0 s

.00013

2 .6 x 1 0

2.9xl0'5

-4.8x10 s

Pi

-.00006

-.00031

-.00113

-.00128

-.0 0 1 2 2

-.00491

R2

4.0x10*

4.7x10^

2 .2 xl 0 '5

4.9xl0'5

.0 0 0 1 0

.00034

.00003

. <*rb*)
E,[Av2+I]
covfrbf, E,(Av*+1)]

p = -.33

covfrb*, Et(Av*+1)]

p = -3

s

a(rb*)

.0 0 0 2

.0 0 2 1

.0044

.0062

.0083

.0135

E,[Av*+1]

1.109

1.074

1.030

.977

.910

.805

-.00036

-.00118

-.00119

-.00095

0.00303

-.0006

- .0 0 1 2

-.0018

-.0025

-.0047

1.9x10 s

7.4x10 s

.00019

.00045

.0 0 1 1 2

cov[rb*), Et(Av*+1)]

P = -9

s

-.00007

Pi

- .0 0 0 1

R2

1 . 1x 1 0 ^

a(rb?)

.006

.024

.045

.067

.093

.123

E,[Av*+l]

5.995

5.725

5.406

5.016

4.516

3.798

-.0047

-.0176

-.0318

-.0421

-.0342

-.0528

cov[rbf), E,(Avf+,)]

Notes: h*+u denotes the continuously compounded one-period holding period returnon two-period dollar
discount bonds; ifdenotes the continuously compounded dollar spot interest rate; Av*+,denotes the rate
of change in the logarithm of the price of one-period dollar bonds; and rb* = Et(h*+12-is). /S, denotes
the

slope

coefficient

in

the

regression

h*,>2- i,s =

var^E,(ht*l2-i*))/var(h**,2-it$). See also the note to Table 4.




40

P0

+ /S,(fbts) + et4,.

R2

=

Table 6
Implications of the Model for the Yen Discount Bond Market Regression

P =

-5

A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

fit

-.00013

.0 0 0 0 2

-.00044

-.00052

.00214

.00169

R2

2 .0 xl 0 '7

5.0xl0'5

.0 0 0 1 2

.00024

.00054

.00195

?(rb»)

.00007

.00091

.00176

.00247

.00352

.00658

.249

.247

.243

.238

.230

.223

-8 x 10 ‘6

2x1O'4

-2.3xl0'5

-2.3x10 s

.000126

.000127

fit

- .0 0 0 2 1

-.00024

-.00095

-.00118

.00059

-.00036

R2:

3.5xl0'7

3.1xl0‘5

.00013

.00027

.00059

.00193

<r(rb?)

.0 0 0 1 2

.00113

.00226

.00313

.00442

.00757

.347

.340

.333

.322

.306

.288

-2 xl 0 6

-3x1O'6

- .0 0 0 1 0

- .0 0 0 1 1

.00007

.00003

fit

-.00027

-.00081

-.00176

-.00256

-.00276

-.00532

R2

3 .2 x 10 ‘7

1.2x1 O’5

4.8x10‘5

.0 0 0 1 0

.0 0 0 2 0

.00067

o i jb \)

.0004

.0023

.0045

.0062

.0080

.0131

.950

.919

.883

.836

.774

.690

-.00024

-.00068

-.00136

-.00176

-.00160

-.00239

fix

-.0003

-.0009

-.0017

-.0028

-.0039

-.0065

R2

7.2xl0 7

1.4x10 s

5.3xl0'5

.00013

.00029

.00073

a [ E ,( Av*+I)]

cov[rbI, E,(AvI+1)]

p = -.33

a[Et(AvI+I)l
cov[rb][) E,(Av*+1)]

p = -3

a[E,(Av*+I)]
cov[rb^, Et(Avf+I)]

p = -9

o is b \)

.036

.013

.024

.034

.046

0628

a[E,(Av{+1)]

4.062

3.872

3.648

3.374

3.025

2.541

0.00422

-.01396

-.02262

-.03069

-.03398

-.03876

cov[rb*, E,(Av*+,)]

Notes: h*+1>2 denotes the continuously compounded one-period holding period return on two-period yen
discount bonds; i* denotes the continuously compounded yen spot interest rate; Avf+, denotes the rate of
change in the logarithm of the price of one-period yen bonds; and rbf = E ^+ ^-if). /S, denotes the slope
coefficient in the regression ht4i,2 - i* = /S0 + /3,(fbtr) + et<l. R2 = v a ^ E ^ ^ -i^ /v a r^ h ^ -i* ). See
also the note to Table 4.




41

Table 7
Implications of the Model for the Excess Dollar Return on Aggregate Wealth

Panel A: Predictability of Excess Dollar Return on Aggregate Wealth
A = 1.0
,
R2
0

P

= -5

o[E,(rl+1-i«)]
p

=

-.33

/S,
R2
^[Et(rt+j-iJ]
,
R2
0

p = -3

<r[Ei(rt+l-i,)]
,
R2
0

p = -9

^[E,(rt+rO]

A = .85
.003

- .0 0 1

l.OxlO"8

A = .70

A = .55

-.015

-.039

4.2x10-6

2 . 1x 1 0

.0 0 1

.013

- .0 0 1
1 .0 x 1 0 '*
.0 0 1
.0 0 0
1 .0 x 10 '8

s

A = .40
-.034

A = .25
-.085

4.6x10 s

.0 0 0 1 2

.00042

.028

.042

.068

.128

-.0 0 1

-.004

-.049

-.040

.006

3 .6 x 1 0 "*

2 .0 x 1 0 s

4.6x10 s

.0 0 0 1 1

.00039

.0 1 2

.028

.042

.067

.123

-.008

- .0 2 0

.0 0 2

.0 0 2

.025

3.1x10-*

1.4x10 s

3.4x10 s

.0 0 0 1 0

.00033

.0 0 1

.0 1 2

.025

.039

.068

.1 2 2

.0 0 1

.003

.006

.0 1 0

8 . 1 x 10 -*

2 .8 xl 0"5

.028

.051

3.7xl0'7
.006

.009

.009

7.5xl0"s

.00016

.00040

.082

.115

.175

Panel B: Mean of (rt+, - i,)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

0.060

0.227

0.430

0 .6 8 8

0.999

1.510

p = -.33

0.062

0.238

0.447

0.718

1.047

1.563

p = -3

0.077

0.315

0.597

0.940

1.356

1.991

p = -9

0.168

0.655

1.205

1.843

2.591

3.566

Notes: r, denotes the continuously compounded dollar return to the aggregate wealth portfolio; i, denotes
the continuously compounded dollar spot interest rate. /S, denotes the slope coefficient in the regression
r«.i " », = /30 +
- st) + etM. R2 = var(Et(rul -it)) / var(rl4l -it). See also the note to Table 4.




42

Table 8
Implications of the Model for Unconditional Standard Deviations

Panel A: (st+1 - s,)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

9.118

9.121

9.122

9.125

9.110

9.093

p = -.33

9.166

9.121

9.120

9.125

9.111

9.081

p = -3

9.184 '

9.186

9.188

9.193

9.175

9.167

p = -9

10.066

10.026

9.921

9.978

9.833

9.702

Panel B: (ft - st)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

.230

.227

.225

.221

.215

.209

p = -.33

.237

.233

.228

.223

.212

.198

p = -3

.486

A ll

.456

.436

.410

.364

9 = “9

2.282

2.193

2.087

1.955

1.784

1.521

Panel C: (r, +1 - i,)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

6.152

6.157

6.165

6.170

6.178

6.188

p = -.33

6.230

6.235

6.240

6.249

6.255

6.254

p = -3

6.802

6.791

6.782

6.765

6.741

6.714

P = -9

10.002

9.850

9.672

9.458

9.163

8.746

Panel D: (hf+12 - i*)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

0.244

0.242

0.239

0.235

0.230

0.222

p = -.33

0.214

0.210

0.205

0.200

0.193

0.179

p = -3

0.998

0.966

0.928

.0.882

0.822

0.728

P = -9

5.759

5.503

5.199

4.827

4.352

3.699




43

Table 8 (Continued)

Panel E: (hf+u - if)
A = 1.0

A = .85

A = .70

A = .55

A = .40

A = .25

p = .5

0.166

0.164

0.162

0.159

0.154

0.149

p = -.33

0.206

0 .2 0 2

0.197

0.191

0.182

0.172

p = -3

0.697

0.674

0.647

0.612

0.567

0.505

P = -9

3.685 •'

3.510

3.304

3.054

2.735

2.292

Notes: See Tables 4-7.




44

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.

REGIONAL ECONOMIC ISSUES
Estimating Monthly Regional Value Added by Combining Regional Input
With National Production Data

WP-92-8

Philip'R. Israilevich and Kenneth N. Kuttner

Local Impact of Foreign Trade Zone

WP-92-9

David D. Weiss

Trends and Prospects for Rural Manufacturing

WP-92-12

William A. Testa

State and Local Government Spending—The Balance
Between Investment and Consumption

WP-92-14

Richard H. Mattoon

Forecasting with Regional Input-Output Tables

WP-92-20

P.R. Israilevich, R. Mahidhara, and G.J.D. Hewings
A

Primer on Global Auto Markets

WP-93-1

Paul D. Ballew and Robert H. Schnorbus

Industry Approaches to Environmental Policy
in the Great Lakes Region

WP-93-8

David R. Allardice, Richard H. Mattoon and William A. Testa

The Midwest Stock Price Index—Leading Indicator
of Regional Economic Activity

WP-93-9

William A. Strauss

Lean Manufacturing and the Decision to Vertically Integrate
Some Empirical Evidence From the U.S. Automobile Industry

WP-94-1

Thomas H. Klier

Domestic Consumption Patterns and the Midwest Economy

WP-94-4

Robert Schnorbus and Paul Ballew




1

Working paper series continued

To TradeorNot toTrade: Who ParticipatesinRECLAIM?

WP-94-11

Restructuring& WorkerDisplacementintheMidwest

WP-94-18

ThomasH.KlierandRichardMattoon

PaulD.BallewandRobertH.Schnorbus

ISSUES IN FINANCIAL REGULATION
IncentiveConflictinDeposit-InstitutionRegulation: Evidencefrom Australia

EdwardJ.KaneandGeorgeG.Kaufman

WP-92-5

CapitalAdequacy and theGrowth ofU.S.Banks

WP-92-11

Bank Contagion: Theory and Evidence

WP-92-13

TradingActivity,ProgarmTradingandtheVolatilityofStockReturns

WP-92-16

PreferredSourcesofMarket Discipline: Depositorsvs.
SubordinatedDebt Holders

WP-92-21

HerbertBaerandJohnMcElravey
GeorgeG.Kaufman
JamesT.Moser

DouglasD.Evanoff

An InvestigationofReturnsConditional
onTradingPerformance

JamesT.MoserandJackyC.So

The EffectofCapitalon PortfolioRiskatLifeInsuranceCompanies
ElijahBrewerHI,ThomasH.Mondschean,andPhilipE.Strahan

W P-92-24

WP-92-29

A Framework forEstimatingtheValueand
InterestRateRiskofRetailBank Deposits
DavidE.Hutchison,GeorgeG.Pennacchi

WP-92-30

CapitalShocks andBank Growth-1973 to 1991

WP-92-31

The ImpactofS&L FailuresandRegulatoryChanges
on theCD Market 1987-1991

WP-92-33

HerbertL.BaerandJohnN.McElravey

ElijahBrewerandThomasH.Mondschean




2

Working paper series continued

Junk Bond Holdings, Premium Tax Offsets, and Risk
Exposure at Life Insurance Companies

WP-93-3

Elijah Brewer III and Thomas H. Mondschean

Stock Margins and the Conditional Probability of Price Reversals

WP-93-5

Paul Kofman and James T. Moser

Is There Lif(f)e After DTB?
Competitive Aspects of Cross Listed Futures
Contracts on Synchronous Markets

WP-93-11

Paul Kofman, Tony B o u w m a n and James T. Moser

Opportunity Cost and Prudentiality: A RepresentativeAgent Model of Futures Clearinghouse Behavior

WP-93-18

Herbert L. Baer, Virginia G. France and James T. Moser

The Ownership Structure of Japanese Financial Institutions

WP-93-19

Hesna Genay

Origins of the Modern Exchange Clearinghouse: A History of Early
Clearing and Settlement Methods at Futures Exchanges

WP-94-3

James T. Moser

The Effect of Bank-Held Derivatives on Credit Accessibility

WP-94-5

Elijah Brewer III, Bernadette A. Minton and James T. Moser

Small Business Investment Companies:
Financial Characteristics and Investments

WP-94-10

Elijah Brewer III and Hesna Genay

MACROECONOMIC ISSUES
An Examination of Change in Energy Dependence and Efficiency
in the Six Largest Energy Using C o u n tries-1970-1988

WP-92-2

Jack L. Hervey

Does the Federal Reserve Affect Asset Prices?

WP-92-3

Vefa Tarhan

Investment and Market Imperfections in the U.S. Manufacturing Sector

WP-92-4

Paula R. Worthington




3

Working paper series continued

Business Cycle Durations and Postwar Stabilization of the U.S. Economy

WP-92-6

Mark W. Watson

A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues
and Recent Performance

W P -92-7

James H. Stock and Mark W. Watson

Production and Inventory Control at the General Motors Corporation
During the 1920s and 1930s

W P -92-10

Anil K. Kashyap and David W. Wilcox

Liquidity Effects, Monetary Policy and the Business Cycle

W P -92-15

Lawrence J. Christiano and Martin Eichenbaum

Monetary Policy and External Finance: Interpreting the
Behavior of Financial Flows and Interest Rate Spreads

W P -92-17

Kenneth N. Kuttner

Testing Long Run Neutrality

W P -92-18

Robert G. King and Mark W. Watson

A Policymaker's Guide to Indicators of Economic Activity
Charles Evans, Steven Strongin, and Francesca Eugeni

W P -92-19

Barriers to Trade and Union Wage Dynamics

W P -92-22

Ellen R. Rissman

Wage Growth and Sectoral Shifts: Phillips Curve Redux

W P -92-23

Ellen R. Rissman

Excess Volatility and The Smoothing of Interest Rates:
An Application Using Money Announcements

W P -92-25

Steven Strongin

Market Structure, Technology and the Cyclicality of Output

W P -92-26

Bruce Petersen and Steven Strongin

The Identification of Monetary Policy Disturbances:
Explaining the Liquidity Puzzle

W P -92-27

Steven Strongin




4

Working paper series continued

Earnings Losses and Displaced Workers

WP-92-28

Louis S. Jacobson,Robert J. LaLonde, and Daniel G. Sullivan

Some Empirical Evidence of the Effects on Monetary Policy
Shocks on Exchange Rates

WP-92-32

Martin Eichenbaum and Charles Evans

An Unobserved-Components Model of
Constant-Inflation Potential Output

WP-93-2

Kenneth N. Kuttner

Investment, Cash Flow, and Sunk Costs

WP-93-4

Paula R. Worthington

Lessons from the Japanese Main Bank System
for Financial System Reform in Poland
Takeo Hoshi, Anil Kashyap, and Gary Loveman

WP-93-6

Credit Conditions and the Cyclical Behavior of Inventories

WP-93-7

Anil K. Kashyap, O w e n A. Lamont and Jeremy C. Stein

Labor Productivity During the Great Depression

WP-93-10

Michael D. Bordo and Charles L. Evans

Monetary Policy Shocks and Productivity Measures
in the G-7 Countries

WP-93-12

Charles L. Evans and Fernando Santos

Consumer Confidence and Economic Fluctuations

WP-93-13

John G. Matsusaka and Argia M. Sbordone

Vector Autoregressions and Cointegration

WP-93-14

M a r k W. Watson

Testing for Cointegration When Some of the
Cointegrating Vectors Are Known

WP-93-15

Michael T. K. Horvath and M a r k W. Watson

Technical Change, Diffusion, and Productivity

WP-93-16

Jeffrey R. Campbell




5

Working paper series continued

Economic Activity and the Short-Term Credit Markets:
An Analysis o f Prices and Quantities

WP-93-17

Benjamin M. Friedman and Kenneth N. Kuttner

Cyclical Productivity in a Model of Labor Hoarding

WP-93-20

Argia M. Sbordone

The Effects of Monetary Policy Shocks: Evidence from the Flow of Funds

WP-94-2

Lawrence J. Christiano, Martin Eichenbaum and Charles Evans

Algorithms for Solving Dynamic Models with Occasionally Binding Constraints

WP-94-6

Lawrence J. Christiano and Jonas D.M. Fisher

Identification and the Effects of Monetary Policy Shocks

WP-94-7

Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans

Small Sample Bias in GMM Estimation of Covariance Structures

WP-94-8

Joseph G. Altonji and Lewis M. Segal

Interpreting the Procyclical Productivity of Manufacturing Sectors:
External Effects of Labor Hoarding?

WP-94-9

Argia M. Sbordone

Evidence on Structural Instability in Macroeconomic Time Series Relations
. Stock and M a r k W. Watson

WP-94-13

The Post-War U.S. Phillips Curve: A Revisionist Econometric History

WP-94-14

James H

Robert G. King and M a r k W. Watson

The Post-War U.S. Phillips Curve: A Comment

WP-94-15

Charles L. Evans

Identification of Inflation-Unemployment

WP-94-16

Bennett T. McCalhun

The Post-War U.S. Phillips Curve: A Revisionist Econometric History
Response to Evans and McCallum

WP-94-17

Robert G. King and M a r k W. Watson




6

Working paper series continued

Estimating Deterministic Trends in the
Presence of Serially Correlated Errors

WP-94-19

Eugene Canjels and M a r k W. Watson

Solving Nonlinear Rational Expectations
Models by Parameterized Expectations:
Convergence to Stationary Solutions

WP-94-20

Albert'Marcet and David A. Marshall

The Effect of Costly Consumption
Adjustment on Asset Price Volatility

WP-94-21

David A. Marshall and Nayan G. Parekh

The Implications of First-Order Risk
Aversion for Asset Market Risk Premiums

WP-94-22

Geert Bekaert, Robert J. Hodrick and David A. Marshall




7