We do find that dealers do compete more aggressively when their competitors cannot benefit from their own price discovery.
The question that motivated the Bayesian approach in this paper is what are the sizes of the posterior bands around the yields under the model, to an agent who does not know precisely what the current factor(s) is (are). Under the model, we find these are fairly tight, and the data and the model behave differently in important ways that cannot be explained by parameter and factor uncertainty.
The second way, which has been more common in the literature, is to look at this as a volatility forecasting horserace. We have two interesting applications in this vein. First, we put the implied volatility on the right-hand side in a GARCH specfication. Despite the maturity mis-match, it is generally statistically significant, with a positive coefficient. Second, we conduct out-of-sample tests--comparing RMSE's of forecasts and using encompassing regressions. We provide further evidence that GARCH does fairly poorly for forecast horizons of 90 - 180 calendar days, as it tends to overstate the importance and persistence of recent volatility shocks. The historical variance has a lower RMSE than the implied volatility for 9 of the 10 individual stocks that we analyze.
The question of whether stock market returns are predictable is a fascinating one, and has naturally been studied from a variety of perspectives. Most of the attention on this question looks at the use of conditioning information such as interest rates and dividend yields to forecast returns. But there was also interest in whether past returns themselves could predict future returns. We decompose returns into white noise and a predictable (autoregressive) process to ask how much predictability there is. The answer: not much. We can't disentangle whether there is an infinitessimally small predictable component, or a large predictable component with virtually no predictability--but both imply no predictability of returns.
As Chris Sims had pointed out, frequentist tests of unit roots have peculiar properties. This paper provides another example of this fact.
But we also look at bid-ask spreads and trading activity, and we find surprisingly large spreads for the smallest stocks as well as low trading activity.