Time and the Process of Security Price Adjustment
Link : Paper
This paper was published in Journal of Finance(1992) by Cornell professors, David Easley and Maureen O’Hara. It is one of the classic papers in market microstructure that shows that timing of the trade is not exogenous to price formation process. In this post, I will briefly go over the contents of the paper. The paper starts off giving some basic history of the models where time dimension of the trade is never explored or does not impact the price process. It then introduces a sequential trade set up considering the following probabilities:

What is the probability of an information event ?

What the probability that the information event will be caught by a signal ?

What’s the probability that a trader is informed ?

What’s the fraction of uninformed traders are buyers ?

What’s the probability that an uninformed buyer buys ?

What’s the probability that an uninformed buyer doesn’t trade ?

What’s the probability that an uninformed seller sells ?

What’s the probability that an uninformed seller doesn’t trade ?
With the above probabilities defined for a trading day, the paper then goes on to derive the bid and ask equilibrium quotes for a market maker. Once the structure of the model is set, the paper then goes on to stating and proving 7 propositions :

The information content of a notrade observations differs from that of a transaction

Bid and ask move in response to the absence of a trade(Absence of trade leads to smaller spread)

Volume of trade, market maker inventory and time all matter in adjustment of prices to information

Spread is correlated to the volume

In the absence of abnormal price changes, prices converge to a level contained in the interval of initial quotes

Quotes and transaction prices, converge to their strong form efficient values at exponential rate(in clock time)

Even assuming that following an information event all trades are from the informed does not remove the effects of normal volume on the price path.
The empirical implications of the paper are :

Time affects the behavior of prices.

Spread will decrease, the longer the time between transactions

Interval between trades cannot be viewed as exogenous to the price process

Analysis of quotes is better than trades for certain analysis as the former is not plagued by optional sampling problem
Conclusion:
If information events are not certain to have occurred, then the lack of trade may provide a signal to market participants. This imparts information content to the time between trades, causing time per se to no longer be exogenous to the price process.