Measurement error, fixed effects, and false positives in accounting research

We show theoretically and empirically that measurement error can bias in favor of falsely rejecting a true null hypothesis (i.e., a “false positive”) and that regression models with high-dimensional fixed effects can exacerbate measurement error bias and increase the likelihood of false positives. We replicate inferences from prior work in a setting where we can directly observe the amount of measurement error and show that the combination of measurement error and fixed effects materially inflates coefficients and distorts inferences. We provide researchers with a simple diagnostic tool to assess the possibility that the combination of measurement error and fixed effects might give rise to a false positive, and encourage researchers to triangulate inferences across multiple empirical proxies and multiple fixed effect structures.