An Ordered Probit Analysis of Transaction Stock Prices

74 Pages Posted: 27 Dec 2006 Last revised: 18 Aug 2010

See all articles by Jerry A. Hausman

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

A. Craig Mackinlay

University of Pennsylvania - Finance Department; National Bureau of Economic Research (NBER)

Date Written: October 1991

Abstract

We estimate the conditional distribution of trade-to-trade price changes using ordered probit, a statistical model for discrete random variables. Such an approach takes into account the fact that transaction price changes occur in discrete increments, typically eighths of a dollar, and occur at irregularly spaced time intervals. Unlike existing continuous-time/discrete-state models of discrete transaction prices, ordered probit can capture the effects of other economic variables on price changes, such as volume, past price changes, and the time between trades. Using 1988 transactions data for over 100 randomly chosen U.S. stocks, we estimate the ordered probit model via maximum likelihood and use the parameter estimates to measure several transaction-related quantities, such as the price impact of trades of a given size, the tendency towards price reversals from one transaction to the next, and the empirical significance of price discreteness.

Suggested Citation

Hausman, Jerry A. and Lo, Andrew W. and MacKinlay, Archie Craig, An Ordered Probit Analysis of Transaction Stock Prices (October 1991). NBER Working Paper No. w3888. Available at SSRN: https://ssrn.com/abstract=467658

Jerry A. Hausman (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Andrew W. Lo

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Archie Craig MacKinlay

University of Pennsylvania - Finance Department ( email )

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