Assessing Markov chain approximations: A minimal econometric approach

Markov chain approximations of continuous state-space processes are common in economic models. Increasing the dimensions of the state space is costly; this paper develops a procedure to evaluate the tradeoff between the number of dimensions devoted to modelling dynamics and those devoted to modelling the contemporaneous state space. The methodology borrows from a previous literature which formalizes inference within calibrated models. Approximations for post-war real per capita US consumption growth are compared. Standard business cycle theory is used to generate needed information regarding state transition probabilities. In this application it is useful to trade some accuracy in defining the state space for more realistic dynamics.