Unbiased Estimation as a Public Good
Bias and variance help measure how bad (or good) an estimator is. When considering a single estimate, minimizing variance plus squared bias (i.e., mean squared error) is optimal in a certain sense. Sometimes a smoothing parameter is explicitly chosen to produce such an optimal estimator. However, important parameters in economics are often estimated multiple times, in many studies over many years, collectively contributing to a public body of evidence. From this perspective, the bias of each single estimate is relatively more important, even if mean squared error minimization remains the goal. This suggests some tension between the single best estimate a paper can report and the estimate that contributes most to the public good. Simulations compare instrumental variables and linear regression, as well as different levels of smoothing for instrumental variables quantile regression.