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1. E97-01

   Richard Ashley

   A New Technique for Postsample Model Selection and Validation

   February 1997

   
   

2. E97-02

   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

   
   

3. E97-03

   Susan K. Snyder

   Nonparametric Tests of Household Behavior

   March 1997

   
   

4. E97-04

   Robert P. Gilles Dimitrios Diamantaras

   Pricing in Economies with a Variable Number of Commodities

   April 1997

   
   

5. E97-05

   Hans H. Haller and Roger Lagunoff

   Markov Perfect Equilibria in Repeated Asynchronous Choice Games

   April 1997

   
   

6. E97-06

   Jean Derks, Hans H. Haller, and Hans Peters

   The Selectope for Cooperative Games

   April 1997

   
   

7. E97-07

   Hui Boon Tan and Richard Ashley

   On the Inherent Nonlinearity of Frequency Dependent Time Series Relationships

   June 1997

E97-01

Richard Ashley

A New Technique for Postsample Model Selection and Validation

February 1997

The model selection and Granger-causality 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 large-sample 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 re-sampling based postsample inference procedure which enhances the usefulness of the inference significance levels it produces by explicitly estimating the uncertainty which its own large-sample 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 Granger-causation from fluctuations in aggregate consumption expenditures to fluctuations in aggregate expenditures on advertising using U.S. data.

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E97-02

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, cross-equation restrictions, etc. The usefulness of the new technique is illustrated with an application to a cointegrated consumption-income regression model, yielding a straightforward test of the permanent income hypothesis.

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E97-03

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 utility-maximizing 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 intra-household 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 non-labor 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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E97-04

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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E97-05

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 payoff-relevant 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 “non-generic” in the larger space of state dependent payoffs. We also compare the MPE to non-Markovian 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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E97-06

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 so-called selectors. The selectope is studied from a set-theoretic point of view as superset of the core and the Weber set; and from a value-theoretic point of view, as containing weighted Shapley values, random order values, and sharing values.

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E97-07

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 consumption-income 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 mis-specified. 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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Revised: May 13, 1997

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