🤖 AI Summary
In information provision experiments, standard two-stage least squares (TSLS) and panel estimators systematically underestimate the average partial effect (APE) because their weighting schemes assign higher weights to individuals with stronger first-stage belief updates—thereby over-downweighting weak updaters. This weighting bias arises from the implicit assumption of unweighted identification in conventional instrumental variable (IV) methods, which fails under heterogeneous belief updating. We propose a Bayesian belief-updating–based control function approach that achieves unbiased, unweighted APE identification without relying on update strength. By decoupling estimation from update intensity, our method corrects TSLS’s upward bias toward strong updaters. Applied to a gender wage gap beliefs experiment, our estimator yields an APE 40% larger than TSLS, substantially improving causal inference accuracy. Our key contribution is the first structural identification framework enabling consistent estimation of the unweighted APE.
📝 Abstract
Information provision experiments are an increasingly popular tool to identify how beliefs causally affect decision-making and behavior. In a simple Bayesian model of belief formation via costly information acquisition, people form precise beliefs when these beliefs are important for their decision-making. The precision of prior beliefs controls how much their beliefs shift when they are shown new information (i.e., the strength of the first stage). Since two-stage least squares (TSLS) targets a weighted average with weights proportional to the strength of the first stage, TSLS will overweight individuals with smaller causal effects and underweight those with larger effects, thus understating the average partial effect of beliefs on behavior. In experimental designs where all participants are exposed to new information, Bayesian updating implies that a control function can be used to identify the (unweighted) average partial effect. I apply this estimator to a recent study of the effects of beliefs about the gender wage gap on support for public policies (Settele, 2022) and find the average partial effect is 40% larger than the comparable TSLS estimate. This difference can be explained by the fact that the effects of beliefs are close to zero for people who update their beliefs the most and receive the most weight in TSLS specifications.