Fitting a Complex Markov Chain Model for Firm and Market Productivity

Abstract

This thesis develops a methodology of estimating parameters for a complex Markov chain model for firm productivity. The model consists of two Markov chains, one describing firm-level productivity and the other modeling the productivity of the whole market. If applicable, the model can be used to help with optimal decision making problems for labor demand. The need for such a model is motivated and the economical background of this research is shown. A brief introduction to the concept of Markov chains and their application in this context is given. The simulated data that is being used for the estimation is presented in detail. The underlying economical problem is described as a stochastic process. Available data for a single firm is limited, therefore a 2-step method is used to estimate the probability matrix for the firm Markov chain. Under a time homogeneity assumption, maximum likelihood estimation techniques are used to estimate the parameters of a Markov chain for one firm based on all firms in the market. These parameters are refined using a linear combination approach. The expectation and variance of the proposed estimator are analyzed. The method's validity is established using various goodness-of-fit tests. Theoretical explorations for the estimation of a market Markov chain are made. In the end, a summary of results and an outlook for further research directions is given.