Trading Costs and Returns for US Equities
This paper by Hasbrouck is about estimating trading costs from transaction prices. One of the classic models used for estimating trading costs is the Roll model. For a plain version of Roll model where the price increments are modeled in a univariate sense, an estimate for the costs is given by a formula that involves square root of negative auto correlation. In cases where there is a positive autocorrelation between the transaction prices, the formula loses its power.
Hasbrouck uses Bayesian methods to obtain a Gibbs estimate of trading costs. The motivation of the author is, the unavailability of high frequency data before1983 and hence the absence of trade signs for all the trades. The author tries to create an efficient Gibbs estimate of the cost and compare it with the cost estimate in the post high frequency data world. Once the performance of the estimator is good enough, the trade directions and hence the estimated cost can be obtained from 1920s.
From a pure stats perspective, the paper is a delightful read as it shows a interesting application of Bayes methods / Gibbs sampling methods in finance.
What did I learn from the paper ?

How to simulate trade signs given a set of transaction prices and a stylized model, in this case, Roll’s model ?

How can one can use High frequency quote data to verify or check cost estimates computed via Gibbs Sampling ?

What are the common liquidity measures of a market ?

Box and Whisker plot can be used to show nonstationarity of a time series

The level of trading costs are positively related to expected returns

Controlling the spread or the scale of the prior distribution is critical.