Econometrics Session in Honor of Gary Chamberlain
Paper Session
Sunday, Jan. 3, 2021 12:15 PM - 2:15 PM (EST)
- Chair: Joshua Angrist, Massachusetts Institute of Technology
Robust Empirical Bayes Confidence Intervals
Abstract
We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual empirical Bayes estimator, but use a larger critical value to account for the effect of shrinkage. We show that in this setting, parametric EBCIs based on the assumption that the means are normally distributed (Morris, 1983) can have coverage substantially below the nominal level when the normality assumption is violated, and we derive a simple rule of thumb for gauging the potential coverage distortion. In contrast, while our EBCIs remain close in length to the parametric EBCIs when the means are indeed normally distributed, they achieve correct coverage regardless of the means distribution. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1−α on average across the n EBCIs for each of the means. We illustrate our methods with applications to effects of U.S. neighborhoods on intergenerational mobility, and structural changes in factor loadings in a large dynamic factor model for the Eurozone. Our approach generalizes to the construction of intervals with average coverage guarantees in other regularized estimation settings.Inference with Many Weak Instruments
Abstract
We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson-Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator (JIVE). This new pre-test is valid under heteroscedasticity and with many instruments.Fairness, Equality, and Power in Algorithmic Decision-Making
Abstract
Public debate and the computer science literature worry about the fairness of algorithms, understood as the absence of discrimination. We argue that some leading definitions of fairness have three limitations. (1) They legitimize inequalities justified by ``merit.' (2) They are narrowly bracketed, considering only differences of treatment within the algorithm. (3) They consider only between-group differences. We compare fairness to two alternative perspectives overcoming these limitations. The first asks what is the causal impact of the introduction of an algorithm on inequality? The second asks who gets to pick the objective function of an algorithm? We formalize these perspectives, characterize when they give divergent evaluations of algorithms, and provide empirical examples.When Should You Adjust Standard Errors for Clustering?
Abstract
In empirical work in economics it is common to report standard errors that account for clustering of units. Typically, the motivation given for the clustering adjustments is that unobserved components in outcomes for units within clusters are correlated. However, because correlation may occur across more than one dimension, this motivation makes it difficult to justify why researchers use clustering in some dimensions, such as geographic, but not others, such as age cohorts or gender. This motivation also makes it difficult to explain why one should not cluster with data from a randomized experiment. In this paper, we argue that clustering is in essence a design problem, either a sampling design or an experimental design issue. It is a sampling design issue if sampling follows a two stage process where in the first stage, a subset of clusters were sampled randomly from a population of clusters, and in the second stage, units were sampled randomly from the sampled clusters. In this case the clustering adjustment is justified by the fact that there are clusters in the population that we do not see in the sample. Clustering is an experimental design issue if the assignment is correlated within the clusters. We take the view that this second perspective best fits the typical setting in economics where clustering adjustments are used. This perspective allows us to shed new light on three questions: (i) when should one adjust the standard errors for clustering, (ii) when is the conventional adjustment for clustering appropriate, and (iii) when does the conventional adjustment of the standard errors matter.JEL Classifications
- C3 - Multiple or Simultaneous Equation Models; Multiple Variables