1997 V.P.I. & S.U. Department of Economics Working Paper
Series
1997 V.P.I. & S.U. Department of Economics Working
Papers
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the abstract of the paper.
 E9701
 Richard Ashley
 A New Technique for Postsample Model Selection and Validation
 February 1997
 E9702
 Tan Hui Boon and Richard Ashley
 An Elementary Method For Detecting And Modeling
Regression Parameter Variation Across Frequencies
With An Application To Testing The Permanent Income Hypothesis
 March 1997
 E9703
 Susan K. Snyder
 Nonparametric Tests of Household Behavior
 March 1997
 E9704
 Robert P. Gilles
Dimitrios Diamantaras
 Pricing in Economies with a Variable Number of Commodities
 April 1997
 E9705
 Hans H. Haller and Roger Lagunoff
 Markov Perfect Equilibria in Repeated Asynchronous Choice Games
 April 1997
 E9706
 Jean Derks, Hans H. Haller, and Hans Peters
 The Selectope for Cooperative Games
 April 1997
 E9707
 Hui Boon Tan and Richard Ashley

On the Inherent Nonlinearity of Frequency Dependent Time Series Relationships
 June 1997
 E9701
 Richard Ashley
 A New Technique for Postsample Model Selection and Validation
 February 1997

The model selection and Grangercausality literatures have generally focused on insample rather
than postsample hypothesis testing. In large part this is due to the fact that feasible postsample
model validation periods are usually quite short, whereas largesample methods are ordinarily
required in order to deal with the serial correlation and crosscorrelation typically found in
postsample forecast error series. This paper describes a resampling based postsample inference
procedure which enhances the usefulness of the inference significance levels it produces by
explicitly estimating the uncertainty which its own largesample approximation induces in
these levels.
For a given target level of inferential precision (such as significance at the 5% level) this
procedure also estimates both how strong the postsample forecasting efficiency evidence in
favor of one of two models must be for a given length postsample period and how long a
postsample period is necessary if the evidence is of given strength. These results indicate
that a postsample model validation period substantially longer than the 5 to 20 periods
typically reserved in past studies is necessary in order for a 20 to 30 percent MSE reduction
to be significant at the 5% level. This approach also quantifies the inferential impact of
different forecasting efficiency criterion choices (MSE vs. MAE vs. asymmetric criteria) and
allows for the use of either expected loss ratios or the expected loss differentials introduced
in Diebold and Mariano (1995). The value of the procedure is illustrated using postsample
forecasting error data from Ashley, Granger, and Schmalensee (1980), in which evidence is
presented for unidirectional Grangercausation from fluctuations in aggregate consumption
expenditures to fluctuations in aggregate expenditures on advertising using U.S. data.
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 E9702
 Tan hui Boon and Richard Ashley
 An Elementary Method For Detecting And Modeling
Regression Parameter Variation Across Frequencies
With An Application To Testing The Permanent Income Hypothesis
 March 1997

A simple technique for directly testing the parameters of a time series regression model
for instability across frequencies is presented. The method can be easily implemented
in the time domain, so parameter instability across frequency bands can be conveniently
detected and modeled in conjunction with other econometric features of the problem at
hand, such as simultaneity, cointegration, missing observations, crossequation
restrictions, etc. The usefulness of the new technique is illustrated with an
application to a cointegrated consumptionincome regression model, yielding a
straightforward test of the permanent income hypothesis.
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Richard Ashley
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 E9703
 Susan K. Snyder
 Nonparametric Tests of Household Behavior
 March 1997

This paper extends the analysis of testable restrictions of nonparametric equilibrium models to a
model of household labor supply. As an alternative to the assumption that households act as a
single utilitymaximizing agent, Chiappori (1988) has proposed an extremely general model of
collective rationality within the household. This paper shows how to test for consistency with
collective rationality within the household without making any assumptions concerning the
parametric form of underlying individual utility functions or the form of intrahousehold
bargaining behavior. Using technniques from algebraic geometry that were introduced to
economists in Brown and Matzkin's (1996) work on testing general equilibrium models, we
derive the necessary and sufficient conditions for data on household consumption and nonlabor
income, prices, and household members' labor choices to be consistent with the collective
rationality model. Thus without observing the allocation of consumption within the household,
we can nonparametrically test whether households behave like one agent or like a collection
of individually rational agents. We apply these tests to data from the National Longitudinal
Surveys on U.S. households and find that most households behave consistently with both models.
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Susan K. Snyder
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 E9704
 Robert P. Gilles
Dimitrios Diamantaras
 Pricing in Economies with a Variable Number of Commodities

 We present a general equilibrium model which is general enough to encompass
the endogenous selection of a set of tradeable commodities. At its
foundation we introduce the notion of a trade infrastructure as a set of
social institutions describing the trade as well as the production
possibilities open to the agents in the economy. Our model bridges the
analyses of economies with a finite number of commodities and those with an
infinite number, and it provides a general framework for investigating a
very large class of possible applications. The endogenization of the
marketability of commodities makes it possible to investigate the dynamic
institutional development such as occured during the industrial revolution
and the recent developments in the 20th century. We discuss in detail a
simple example that expresses the development of a guild economy into a
market based economy.
We introduce an equilibrium concept that describes the pricing of trade
infrastructures, based on the notion of valuation equilibrium for economies
with abstract public goods, as in Diamantaras and Gilles (1996,
International Economic Review, 37, 851 860). Through this concept we are
able to price the tradeability of a commodity by itself. As our main result
we obtain the decentralization of Pareto efficient allocations using the
concept of valuation equilibrium.
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Robert P. Gilles
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 E9705
 Hans H. Haller and Roger Lagunoff
 Markov Perfect Equilibria in Repeated asynchronous Choice Games

 This paper examines the issue of multiplicity of equilibria in alternating
move repeated games with two players. Such games are canonical models of
environments with repeated, asynchronous choices due to inertia or
replacement. We focus our attention on Markov Perfect Equilibria (MPE).
These are Perfect equilibria in which individuals condition their actions
on payoffrelevant state variables. Our main result is that the number of
MPE is generically finite with respect to stage game payoffs. This holds
despite the fact that the stochastic game representation of the alternating
move repeated games is “nongeneric” in the larger space of state dependent
payoffs. We also compare the MPE to nonMarkovian equilibria and to the
(trivial) MPE of standard repeated games. Unlike the latter, it is often
true when moves are asynchronous that Pareto inferior stage game
equilibrium payoffs cannot be supported in MPE. Also, MPE can be
constructed to support cooperation in a Prisoner’s Dilemma despite limited
possibilities for constructing punishments.
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Hans H. Haller
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 E9706
 Jean Derks, Hans H. Haller, and Hans Peters
 The Selectope for Cooperative Games


The selectope of a cooperative transferable utility game is the convex hull
of the payoff vectors obtained by assigning the Harsanyi dividends of the
coalitions to members determined by socalled selectors. The selectope is
studied from a settheoretic point of view as superset of the core and the
Weber set; and from a valuetheoretic point of view, as containing weighted
Shapley values, random order values, and sharing values.
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Hans H. Haller
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 E9707
 Tan hui Boon and Richard Ashley
 On the Inherent Nonlinearity of Frequency Dependent Time Series Relationships
 June 1997

On theoretical grounds, a number of important macroeconomic relationships are thought to
be different in intensity and/or sign for low frequency ("permanent") fluctuations than
for high frequency ("transitory" or "unanticipated") fluctuations. Examples include
the consumptionincome relation, the Fisher effect, and the relationships between
macroeconomic policy variables (e.g., government spending and the supply of money)
and variables like output and prices.
We provide a fundamental argument showing that such frequency dependent relationships
cannot be captured by linear causal models. Indeed, where the actual relationship is
frequency dependent, the coefficient in the linear model is unstable (across frequencies)
precisely because the linear model is misspecified. What, then, is the significance of
the frequency dependencies commonly detected and analyzed using linear techniques, such as
the coherence function or the (related) measure of linear dependence/feedback put forward
by Geweke (1982)? We elucidate via a simple example and provide an example of bona fide
frequency dependence in the CPI PPI relationship using a straightforward alternative
technique proposed by Tan and Ashley (1997).
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Richard Ashley
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Virginia Tech Department of Economics
Send Comments to: ashleyr@vt.edu"
Revised: May 13, 1997
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