Knowledge that Transforms

Fully modified least squares (FM-OLS) regression was originally designed in work by Phillips and Hansen (1990) to provide optimal estimates of cointegrating regressions. The method modifies least squares to account for serial correlation effects and for the endogeneity in the regressors that results from the existence of a cointegrating relationship. This paper provides a general framework which makes it possible to study the asymptotic behavior of FM-OLS in models with full rank I(1) regressors, models with I(1) and I(0) regressors, models with unit roots, and models with only stationary regressors. This framework enables us to consider the use of FM regression in the context of vector autoregressions (VAR's) with some unit roots and some cointegrating relations. The resulting FM-VAR regressions are shown to have some interesting properties. For example, when there is some cointegration in the system, FM-VAR estimation has a limit theory that is normal for all of the stationary coefficients and mixed normal for all of the nonstationary coefficients. Thus, there are no unit root limit distributions even in the case of the unit root coefficient submatrix (i.e., I n-r , for an n-dimensional VAR with r cointegrating vectors). Moreover, optimal estimation of the cointegration space is attained in FM-VAR regression without prior knowledge of the number of unit roots in the system, without pretesting to determine the dimension of the cointegration space and without the use of restricted regression techniques like reduced rank regression. The paper also develops an asymptotic theory for inference based on FM-OLS and FM-VAR regression. The limit theory for Wald tests that rely on the FM estimator is shown to involve a linear combination of independent chi-squared variates. This limit distribution is bounded above by the conventional chi-squared distribution with degrees of freedom equal to the number of restrictions. Thus, conventional critical values can be used to construct valid (but conservative) asymptotic tests in quite general FM time series regressions. This theory applies to causality testing in VAR's and is therefore potentially useful in empirical applications.

The paper studies the representation and characterization of risks generated by a continuum of random variables. The Main Theorem is a characterization of a broad class of continuum processes in terms of the decomposition of risk into aggregate and idiosyncratic components, and in terms of the approximation of the continuum process by finite collections of random variables. This characterization is used to study decision making problems with anonymous and state-independent payoffs. An Extension Theorem shows that if such a payoff function is defined on simple processes, then it has a unique continuous extension to the class of processes characterized in this paper. This extension is formulated without reference to sample realizations and with minimal restrictions on the patterns of correlation between the random variables. As an application, the theory is used to develop a new model of large games which emphasizes the explicit description of the players' randomizations. This model is used to study the class of environments in which Schmeidler's (1973) representation of strategic uncertainty in large games is valid.

The authors consider a k-player sequential bargaining model in which the size of the cake and the order in which players move follow a general Markov process. For games in which one agent makes an offer in each period and agreement must be unanimous, the authors provide characterizations of the sets of subgame perfect and stationary subgame perfect payoffs. With these characterizations, they investigate the uniqueness and efficiency of the equilibrium outcomes, the conditions under which agreement is delayed, and the advantage to proposing. Copyright 1995 by The Econometric Society.

A modification of the official Sen poverty index yields an index which is not only continous in individual incomes and consistent with the transfer axiom, but also admits a geometric interpretation in terms of the area beneath a graph called the inverse generalized Lorenz curve for normalized poverty gaps by Jenkins and Lambert (1993) or the poverty gap profile by Shorrocks (1994).

This paper develops and estimates a model of the U.S. automobile industry. On the demand side, a discrete choice model is adopted, which is estimated using micro data from the Consumer Expenditure Survey. The estimation results are used in conjunction with population weights to derive aggregate demand. On the supply side, the automobile industry is modeled as an oligopoly with product differentiation. Equilibrium is characterized by the first-order conditions of the profit-maximizing firms. The estimation results are used in counterfactual simulations to investigate two trade policy issues: the effects of the voluntary export restraint, and exchange rate pass-through. Copyright 1995 by The Econometric Society.

Using a simulated method of moments approach, the author evaluates a representative consumer asset pricing model in which the consumer is assumed to have time nonseparable preferences of several forms. Examining the model's implications for several moments of asset returns, he finds evidence for the local substitution of consumption with habit formation occurring over longer periods of time. The interaction between these two effects is important. The author also shows that, when accounting for sampling error, a model with local substitution and long-run habit persistence is consistent with the Hansen and Jagannathan (1991) bounds. Copyright 1995 by The Econometric Society.

Christopher Harris, Philip Reny, Arthur Robson, The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization, Econometrica, Vol. 63, No. 3 (May, 1995), pp. 507-544

If an agent's preferences over subjectively uncertain acts are consistent with him having a subjective probability distribution over the states of nature, then those preferences can induce consistent preferences over 'objectively' risky lotteries. Such 'probabilistically sophisticated' behavior allows us to treat decision making under uncertainty as though it is under risk. This paper first characterizes exactly what probabilistic sophistication entails for an agent's beliefs about the likelihood of states of nature. Secondly, it presents characterizations of probabilistically sophisticated individuals whose induced lottery preferences obey neither the independence axiom nor a monotonicity property that is shown to share some of the nature of independence. Copyright 1995 by The Econometric Society.

We add a round of pre-play communication to a finite two-player game played by a population of players.Pre-play communication is cheap talk in the sense that it does not directly enter the payoffs.The paper characterizes the set of strategies that are stable with respect to a stochastic dynamic adaptive process.Periodically players have an opportunity to change their strategy with a strategy that is more successful against the current population.Any strategy that weakly improves upon the current poorest performer in the population enters with positive probability.When there is no conflict of interest between the players, only the efficient outcome is stable with respect to these dynamics.For general games the set of stable payoffs is typically large.Every efficient payoff recurs infinitely often.

Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method of moments estimators and tests can be constructed using these moment conditions. The resulting econometric methods are designed to be applied to discrete-time data obtained by sampling continuous-time Markov processes.