In order to address the issue of the welfare costs of informed trade, a new Glosten-Milgrom type model is constructed with elastic uninformed trade. Since uninformed trade is elastic, there are some uninformed who choose not to trade because their idiosyncratic valuation lies within the spread. This lack of trade is a welfare loss and the model can be used to estimate the magnitude of the loss. Calculations show that the welfare loss tends to be single-peaked in the amount of informed trade, reaching a maximum at an internal point. That is, after some point, the welfare loss is decreasing in the amount of informed trade because with more informed trade information gets into prices faster and spreads decline. For short term information (information likely to be revealed in a short amount of time) the maximum loss occurs at a very high probability of informed trade meaning that the welfare loss is mostly increasing in informed trade. For longer term information, the maximum occurs at a relatively small probability of informed trade suggesting that over some range welfare loss is actually declining in informed trade.
Glosten, Lawrence. "Welfare cost of informed trade." Working paper, NBER & Columbia Business School, August 10, 2010.
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