A careful consideration of CLARIFY: simulation-induced bias in point estimates of quantities of interest

Some work in political methodology recommends that applied researchers obtain point estimates of quantities of interest by simulating model coefficients, transforming these simulated coefficients into simulated quantities of interest, and then averaging the simulated quantities of interest (e.g., CLARIFY). But other work advises applied researchers to directly transform coefficient estimates to estimate quantities of interest. I point out that these two approaches are not interchangeable and examine their properties. I show that the simulation approach compounds the transformation-induced bias identified by Rainey (2017), adding bias with direction and magnitude similar to the transformation-induced bias. I refer to this easily avoided additional bias as “simulation-induced bias.” Even if researchers use simulation to estimate standard errors, they should directly transform maximum likelihood estimates of coefficient estimates to obtain point estimates of quantities of interest.