Figure 3.

Results from 5,000 Monte Carlo simulations with N^* = 100, σ² = 0.1,1.0,4.0, and N ranging from 100 to 10,000. The vertical axis shows the difference between standard deviation (SD) of β̂_X from the misspecified and correct exposure models. A positive difference indicates that the correctly specified model is more efficient. For all values of σ², the average exposure model prediction accuracies are ${\overline{R}}_W^2$ between 0.73 and 0.75 and ${\overline{R}}_W^{2\prime }$ between 0.49 and 0.50 $0.50.N=N^{*}={\overline{R}}_W^2\mathrm{V}\overline{\mathrm{a}}\mathrm{r}(W)R_W^2{\widehat{\alpha }}_3{\widehat{\beta }}_X{\widehat{\beta }}_X{\widehat{\beta }}_{X}0.001N=N^{*}={\sigma }^2=1.0{\overline{R}}_W^2=0.740.12-0.007{\overline{R}}_W^{2\prime }=0.490.21-0.001{\widehat{\alpha }}_{3}0.41{\widehat{\alpha }}_{3}N=N^{*}={\sigma }^2=0.1{\overline{R}}_W^2=0.730.23-0.035{\overline{R}}_W^{2\prime }=0.500.160.001R_W^{2}144{\widehat{\alpha }}_{3}1.37{\widehat{\alpha }}_3{N}^{*}={\sigma }^2=0.1,1.0,4.0N{\widehat{\beta }}_X{\sigma }^2{\overline{R}}_W^{2}0.730.75{\overline{R}}_W^{2\prime }0.490.50$.