James L. Swofford

English

Research Papers in Economics

129
James L. Swofford
James L. Swofford is a professor and chafr of the Department
of Economics, University of South Alabama.
•i Commentary
‘JOUG FISHER AND ADRIAN FLEISSIG
develop and estimate a Dynamic Fourier Expen-
diture System in an attempt to meet some criti-
cisms that have been raised against the literature
on expenditure systems. First, I will discuss Fish-
er and Fleissig’s model in terms of their own
criteria set forth in their introduction. Then I
will discuss their specification in terms of some
criteria for’ an ideal model that Carl F Christ
proposed in his paper at last year’s Federal
Reserve Bank of St. Louis Economic Policy
Conference. Finally, I will make some general
comments about research on money stock
measurement.
FISHER AND FLEISSIG’S
CRITERIA
In their introduction, Fisher and Fleissig men-
tion five of what they feel are the most telling
shortcomings of the expenditure system litera-
ture. The first they mention is a failure to link
theory and application. On one level they have
met this criticism admirably. They chose to use
the Fourier form as a flexible form specification
that is able to approximate any unknown in-
direct utility function. They have also modeled
the dynamics in a way that makes economic
sense with their dynamic utilit function specifi-
cation. On another’ level they have not linked
theory and application. ‘l’heir discussion of the
elasticities of substitution that they have estimnat-
ed is fairly terse. While they show that the
elasticity of substitution between two assets is
more stable with one dynamic specification,
they do not discuss the sign, magnitude or eco-
nomic interpretation of their estimated elastici-
ties more than in passing. They say that their
elasticities are typical for this literature, hut is
that good or bad? They do not cite specific
previous studies nor do they mention the size
or sign of elasticities from other studies. Are we
surprised that old consumer Mt and other
checkable deposits (OCD) and savings accounts
are substitutes but old consumer Ml and OCD
and small time deposits are complements? These
results make sense to me hut their implications
should be explained in the paper. What about
the size of these elasticities? What is their
meaning? My view is that other economists may
miss the importance of the expenditure system
literature, if those of us doing research using
such systems continue to omit a thorough dis~
cussion of the elasticities that these systems
produce and a comparison of these elasticities
with those produced by previous research.
The second shortcoming of the expendi-
ture system literature that Fisher and Fleissig
address is improper aggregation o~’ei-goods. In
my view they have handled this problem in a
very nice way. Expenditure systems like the F’ou-
ncr system are very parameter-intensive, and
aggregation over goods is required to make
them tractable. Fisher’ and Fleissig have used
both revealed preference results and good
1udgment about which goods to aggregate. I feel
that in estimating s stems such as these both
are needed. Howeven I feel I must point out
that Fisher and Fleissig have used a revealed
preference test for a direct utility function to
MAROHIAPRIL 1994130
back up the specification of an indirect utility
function. Direct utility function r’esults may be
suggestive of the structure of the indirect utility
function, but they are not necessarily more than
suggestive.
Fisher and Fleissig’s third and fourth problems
with the expenditure system literature are
imprecise estimations of partial derivatives and
use of locally integrable models, for which the
first- arid second-order conditions do not obtain
at some data points. The Fourier System was de-
veloped to handle these cm’iticisms of other
specifications, such as the translog, so Fisher
and Fleissig have admirably handled these criti-
cisms as they set out to do.
The last problem Fisher and Fleissig set before
themselves to solve is misspecification, often
nonspecification, of dynamics in expenditure
systems. They model the dynamics with two
very general specifications. One, the time ser’ies
model, is statistical in nature. Another, the dy-
namic utility function model, is consistent with
economic theory. My view is that they are cor~
rect to model the dynamics in very general
ways. Gerald Whitney and 1 (1994) have found
that data in similar categories to those that Fish-
er and Fleissig have used can only be rational-
ized by a well-behaved direct utility function
with some incomplete category adjustment wi~
thin some quarters. But since Fisher’ and Fleissig
are unable to choose between their two dynarn-
ic specifications, we cannot yet say that they
have correctly specified the dynamics. They
have, however, certainly done a better job
modeling the dynamics than other researchers
in this area. In a sense they have begun the de-
bate on how to correctly model the dynamics
within flexible consumer expenditure systems.
In summary, with a couple of reservations,
Fisher and Fleissig have done a good job in
meeting the criteria they set forth for their
model. Next, I turn to the question of how their
models compare with someone else’s criteria for
an ideal econometric specification.
(~Jij~j~ CHRISTS CRFI’ER.I.A FOR
.4.1.5 ECIDNGi.VLETRI(: •MGIJEi.j
At last year’s St. Louis Fed conference, Carl F
Christ suggested seven characteristics of an ideal
econometric model. I will next examine Fisher
and Fleissig’s paper in light of this ideal.
Christ’s first cr’iterion is that the estimated
model should provide a good description of
some interesting set of past data. Certainly, Fish-
er and Fleissig’s model has been used to inves~
tigate an intet-esting issue—money holdings.
There ar’e also a reasonable number of coeffi-
cients that are statistically different from zero,
and they test and find the residuals of their’
model are white noise.
The second criterion that Chr’ist sets out (and
one that he stressed) is that the model should
be testable against data that were not used to
estimate it and were not available when it was
specified. Fisher and Fleissig have not done this.
Since their sample ends in 1985, and Fisher and
Fleissig have presumably formulated their model
in recent years, this would be a tough challenge.
A model estimated on data that ends eight years
ago could not be expected to predict today’s
data very accurately. The new data set collected
by the research staff of the St. Louis Fed could
be used to estimate a dynamic flexible model,
which then could be put to this test over the
next few years.
Christ’s third criterion, related to his second,
is that the estimated model should describe
events for at least a few quarters after it was
formulated and estimated. As with Christ’s se~
cond criterion, Fisher’ and Fleissig’s specification
cannot be reasonably put to this test. But a
specification estimated with the St. Louis Fed’s
updated data could be.
‘the fourth criterion is that the model should
make sense in the light of our knowledge of
economics. Of course, the dynamic Fourier
specification is flexible with respect to arbitrary
elasticities, and it also does not generate negative
shares. But Fisher and Fleissig’s specification
does generate asset pairs that switch from sub-
stitutes to complements over their sample. This
is a puzzling result that they do not explain.
Christ’s fifth criteria is that a simple model is
superior to a complex model. Fisher and Fleis-
sig’s model is not simple, leaving open the possi-
bility that an otherwise equal but simpler model
will be found. Of course, this could be said of
any specification. This does suggest that some-
one might want to test Barnett’s Asymptotically
Ideal Model with this type of data since it has
similar characteristics to the Fourier model and
may be simpler, depending on the formulation
used.
F.OFERAL RESERVE SANK OF ST.131
The sixth criteria for judging a model is that,
other things being equal, a model that explains
a wide variety of data is better. Fisher and Fleis-
sig’s model does explain a wide variety of data,
but some of it has been aggr’egated. An argu-
ment could be made to estimate this model be-
fore aggregating the data. But Fisher and Fleissig
have used the soundest aggregation techniques
in the literature, the model they necessarily
used is very parameter-intensive, and the disag-
gregate data series is of a r’elatively short du-
ration.
Christ’s seventh and final criterion is that
models that nest special cases are preferable.
Fisher and Fleissig’s dynamic Fourier models
nest the static Fourier and, in that respect, meet
Christ’s ideal. Unfortunately, these models do
not nest other Flexible Functional forms nor do
the dynamic specifications nest each other.
Of course, Fisher and Fleissig’s dynamic
Fourier flexible functional form does not meet
all of Christ’s ideals. Fisher and Fleissig did not,
nor would they, claim that it does, and I do not
mean to give the impression that they would
make such a bold claim for their model. Their
model seems to meet the first and the fourth
through the seventh criteria fairly well. Criteria
two and three concern the ability of flexible ex-
penditure systems to predict future behavior,
which seems a worthwhile area of investigation
to pursue with such specifications.
For the most part, Fisher and Fleissig’s specifi~
cations meet their own criteria that they set out
to meet, and Christ’s criteria for an ideal specifi-
cation that they were probably only generally
trying to meet. Their paper is an important con-
tribution to a growing literature on economic
monetary aggregates. I want to close with a few
comments on this literature.
‘I’HE FC )N()MIC 1UOT4ff:9T%~PIT
.zU•;CII.EG.A1I’ES I,~IT.E:R.NFIJR.E
I feel that Fisher and Fleissig’s paper is an im-
portant contribution to the question of what is
money. Much of my work in this area has in-
volved nonstochastic revealed preference tests.
Not much is known about the power of such
tests, and there are doubts about the validity of
these tests, so work such as Fisher and Fleissig’s
showing that per capita behavior is consistent
with stochastic models is very important.
The hterature on economic monetary ag-
gregates suggests that the aggregates on which
the central bank focuses may not be the ones
that people use. If people are using one ag-
gr-egate and the central bank is controlling
another, then stable “policy” may lead to an un-
stable price level. Policy in such a situation
might be destabilizing, because the public and
the central bank are engaged in a two-sided
game, with each side having a different
objective—the monetary aggregate each uses.
This implies that it is important for central
banks to attempt to identify what the public in
their country is using as money.
Also, there may not be an economic monetary
aggregate in an area. When looking for an eco-
nomic monetary aggregate, the question we are
really asking is, “Is there a common currency
for a particular area?” This area may or may
not be a nation state. If there is no economic
monetary aggregate in an area, then, again,
“monetary” policy would not likely lead to
predictable results.
Finally, there may be multiple economic mone-
tary aggregates in use. Consumers may be using
one aggregate and business another. Controlling
both aggregates may be mutually exclusive. In
such a case, optimal monetary policy may re-
quire minimizing some loss function over the
aggregates, with each one weighted by how
closely related each aggregate is to the price
level.
R.EFERE.N{]ES
Christ, Carl F. “Assessing Applied Econometric Results;’ this
Review (March/April 1993), pp. 71—94.
Swofford, James L. “Microeconomic Foundations of a Com-
mon Currency Area,” working paper, University of South
Alabama, 1991.
_______ and Gerald A. Whitney. “A Revealed Preference
Test for Weakly Separable Utility Maximization with Incom-
plete Adjustment,” Journal of Econometrics (January! Febru-
ary 1994), pp. 235—49.
MARON/APRiL 1994

Money demand in a flexible dynamic Fourier expenditure system (commentary)

http://research.stlouisfed.org/publications/review/94/03/9403jswofford.pdf

Money demand in a flexible dynamic Fourier expenditure system (commentary)

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