Transaction Costs and Nonlinear Adjustment Towards Equilibrium in the US Treasury Bill Market
| Date | 01 November 1997 |
| DOI | http://doi.org/10.1111/1468-0084.00078 |
| Published date | 01 November 1997 |
| Author | Heather M. Anderson |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 59, 4 (1997)
0305-9049
TRANSACTION COSTS AND NON-LINEAR
ADJUSTMENT TOWARDS EQUILIBRIUM IN
THE US TREASURY BILL MARKET*
Heather M. Anderson
I. INTRODUCTION
Studies of yield curves frequently use arbitrage arguments to explain the
comovement of yields associated with bills of different maturity. Such
arguments assert that rational investors will buy and sell bills in an
attempt to profit on any yield spreads which are not justified by risk,
liquidity or other considerations, and they further assert that this specula-
tive behaviour causes yields to adjust so as to eliminate any potential
profit making opportunities. The implied equilibrium is attained when
yield spread allow no opportunity for arbitrage, and if yield spreads are
inconsistent with this equilibrium then arbitrage causes yields to adjust.
Recent work by Hall, Anderson and Granger (1992), shows that error
correction models1are useful for the empirical study of this theory of
yield comovement. Focussing on the modelling of changes in yields to
maturity, and using yield spreads as the error correcting variables, these
authors find empirical support for an error correction hypothesis which
asserts that yields will adjust whenever yield spreads deviate from long-
run equilibrium. Their resulting error correction model of yield changes
passes standard specification tests and it shows potential for forecasting,
but it does not study the yield adjustment process in detail, and in
particular it does not attempt to study how transaction costs might affect
yield movements.
Transaction costs are often ignored in studies of asset markets, in part
because they complicate the analysis of such markets, but mainly because
they are known to be small, and their effects are therefore assumed to be
negligible. Aiyagari and Gertler (1991) use simulations to show that trans-
*I am grateful to Nathan Balke, Vince Geraci, Clive Granger, Takeo Hoshi, Pu Shen, Ross
Starr, Timo Ter¨asvirta and Farshid Vahid for useful comments and suggestions, but I retain
the responsibility for any errors and/or omissions.
1These models were first suggested by Sargan (1964), and then related to Granger’s (1981)
definition of cointegration by Engle and Granger (1987). They incorporate long-run equi-
librium relationships between the variables of interest, as well as mechanisms which induce
short-run adjustment towards these equilibria.
465
© Blackwell Publishers Ltd, 1997. Published by Blackwell Publishers, 108 Cowley Road, Oxford
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action costs may be partly responsible for Mehra and Prescott’s (1985)
well known ‘equity premium puzzle’, and in a similar study, Marshall’s
(1993) simulations of a general equilibrium asset pricing model show that
extremely small costs of consumption adjustment at the individual level
can cause large differences between observed aggregate consumption and
the prediction derived from a frictionless model. These simulations show
that the aggregate effects of small transaction costs are potentially
important, implying that research based on observed asset market
behaviour should not overlook these possible effects.
This paper argues that non-linear error correction models provide an
appropriate framework for studying how transaction costs affect yield
movements in the primary US Treasury bill market. Since economic
theory predicts that arbitrage and corresponding yield adjustment will
only occur when disequilibrium in the bill market is a large enough to
imply net gains to investors after transaction costs,2portfolio adjustment
is modelled as an ‘on/off’ threshold error correction process, which
becomes active only when the market is ‘sufficiently far’ from equilibrium.
The threshold is determined by agents’ transaction costs, which deter
agents from responding to small deviations from equilibrium.
Two types of non-linear error correction models are studied and
compared. The first, based on Balke and Fomby’s (1997) threshold error
correction model, incorporates a transaction cost threshold which is
assumed to be the same for all agents. In this model, movement towards
equilibrium (error correction) is observed when agents find deviations
from equilibrium sufficiently large to justify the transaction costs associ-
ated with portfolio adjustment.3The second model generalizes the
threshold model by allowing for heterogeneous transaction costs. This
heterogeneity implies that the proportion of investors with transaction
costs low enough to allow them to profit from disequilibrium, gradually
increases with the extent of disequilibrium. This leads to a ‘smooth transi-
tion’ between regimes in which aggregate adjustment is strong and those
in which aggregate adjustment is weak. Linearity tests find statistically
significant evidence for each of the proposed non-linear adjustment
mechanisms, and estimated models which incorporate these non-linear-
ities outperform their linear counterparts, both in and out of sample. The
smooth transition model does not forecast as well as its threshold
counterpart, but unlike the linear and threshold models, it passes a
battery of diagnostic tests.
2See Bertola and Caballero (1990) for a survey of economic models which incorporate
adjustment costs, and Constantinides (1986) for an analysis which specifically relates to the
capital market. These papers show that small and frequent adjustments are not optimal in the
presence of adjustment costs, and that the investor’s optimal adjustment strategy implies a
‘band of inaction’ around the equilibrium.
3One could justify a common observed threshold by assuming that the trader with the
lowest threshold can arbitrage all of the ‘unpriced deviation’ away, but this assumes that such
a trader never experiences binding legal or liquidity constraints.
© Blackwell Publishers 1997
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