Reduction of State Variable Dimension in Stochastic Dynamic Optimization Models which Use Time-Series Data

Abstract

Statistical procedures are developed for reducing the number of autonomous state variables in stochastic dynamic optimization models when these variables follow a stationary process over time. These methods essentially delete part of the information upon which decisions are based while maintaining a logically consistent model. The relatively simple linear autoregressive process as well as the general case is analyzed and the necessary formulae for practical application are derived. Several applications in agricultural economics are discussed and results presented which quantify the relative amount of information sacrificed with the reduction in number of state variables. Empirical stochastic dynamic optimization problems frequently become unwieldy with too many state variables required to fully summarize the entire history of the decision process. Bellman has called this problem the of dimensionality. Although continuing advances in computing power and available memory cause this curse to fade appreciably, empirical practitioners must still use considerable ingenuity as well as good judgment in arriving at computationally operational yet acceptably accurate models. Burt discussed various ways of reducing the dimensionality problem, one of which was to deliberately discard part of the information contained in the full set of state variables. This paper provides a practical methodology for implementing a reduction in the number of state variables when a subset of these variables emanates from timeseries data. In many actual and potential applications of dynamic optimization to problems in agricultural economics, there are some sets of state variables that are unaffected by the decisions.