DGP: Poisson. Null model estimated by PPML.

Size and Power - omitted squared term

Size

Unadjusted power

Size-adjusted power

DGP: log-Normal $y$ with GLM variance assumption (Case 1).

Size

Power: omitted variable that is correlated to $x_1$

Unadjusted power

Size-adjusted power

Power: omitted term $x_1^2$

Unadjusted power

Size-adjusted power

DGP: log-Normal $y$ with PPML variance assumption (Case 2).

Size

Power: omitted variable that is correlated to $x_1$

Unadjusted power

Size-adjusted power

Power: omitted term $x_1^2$

Unadjusted power

Size-adjusted power