Buy-Sell Dependence and Classification Error in Market Microstructure Time-Series Models : A Markov Switching Regression Approach

Abstract

This paper conducts an empirical test of a market microstructure

model using a new econometric approach. I treat the direction of a trade

as a discrete latent variable following a stationary Markov chain. By

overlaying a three-state Markov chain on a familiar market

microstructure model, I can extract information on the directions of

trades efficiently from time-series data. An analysis of 100 large and

100 small firms for the year 1990 yields several important results: (1)

Order types (sale, cross, purchase) are serially correlated, and the mean

transition probability matrix is very similar for large and small firms. (2)

Information asymmetry is greater for smaller firms. (3) The per share

order processing cost is greater for larger firms. (4) When trades are

classified by the bid-ask test supplemented by the tick test, the

estimated misclassification probabilities are typically small for sales

and purchases, but they are often fairly large for crosses. (5) Buy-sell

classification error results in systematic biases for regression

coefficients.