Reconstructing dynamics from intertemporal economic data

Venkatesh Bala
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Venkatesh Bala: Department of Economics, McGill University, 855 Sherbrooke Street W., Montreal, Quebec H3A 2T7, CANADA

Economic Theory, 1997, vol. 9, issue 2, 325-339

Abstract: This paper is concerned with the relationship between a continuous dynamical system and the trajectory generated by such a system. The main result provides necessary and sufficient conditions for an infinite data stream to be rationalized as the output of a continuous law of motion. The paper develops concepts of informativeness of a given set of intertemporal data and shows that informativeness is maximal when the data is chaotic. It also demonstrates that with probability one the sample paths from a non-trivial independent and identically distributed stochastic process cannot be rationalized as the output of a continuous deterministic system. Two impossibility results are discussed which show that even with an infinite amount of data the hypothesis that the data has been generated by a non-monotonic function cannot be ruled out. An application concerning the recovery of the excess demand function from a sequence of price observations from the tatonnement process is also given.

Date: 1997
Note: Received: April 25, 1994; revised version December 29, 1995
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