The model uncertainty associated with the three-model set is 1.29%, which is less than the average within-model uncertainty of 1.51%. As оq grows large, within-model uncertainty increases, since it includes uncertainty about a, and model uncertainty typically declines (although the latter effect is somewhat non-monotonic for Bay State). Thus, in terms of contributions to the overall uncertainty about Bay State’s cost of equity, uncertainty about the values of the parameters within a given model is greater than uncertainty about which model to use.
Panel В of Table VIII reports the averages across the 1,994 stocks of each value in Panel A. For the typical stock, both model uncertainty and overall uncertainty are higher than for Bay State Gas, a utility. Otherwise, the conclusions are similar. In particular, even with aa — 0, the average model uncertainty is less than the average within-model parameter uncertainty: 2.26% versus 3.71%.
The average overall uncertainty about ц in that case is 4.40%, only 0.69% higher than the average within-model uncertainty. As cra grows large, the average model uncertainty decreases and the average within-model uncertainty increases. In general, although model uncertainty is substantial, it appears to be less than the within-model parameter uncertainty in estimating costs of equity for individual firms using the factor-based models entertained here.
We conduct a similar analysis for the utilities industry. Figure 9 displays the plots corresponding to those in Figures 6-8 for aa set to 3% and 5%, the plots corresponding to those in Figures 6-8. That is, each utility’s expected excess returns estimated using two different models are plotted against each other, where the utility-specific prior is used instead of the all-stock prior. The associations between the estimates obtained from different models appear to be stronger than those observed in Figures 6-8 for the whole cross-section of stocks.
All three models typically produce rather similar estimates, and the fit between the estimates from the CAPM and the three-factor CK model is especially close. Note that, contrary to the observation for the whole cross-section, the cross-model plots in Figure 9 are less disperse than the within-model plots in Figure 5. In other words, the disagreements across models in utilities’ estimated expected excess returns appear to be smaller than the disagreements within a given model produced by changing the degree of prior mispricing uncertainty (cra) from 0 to 5%.