Concerns that algorithms may discriminate against certain groups have led to numerous efforts to ‘blind’ the algorithm to race. We argue that this intuitive perspective is misleading and may do harm. Our primary result is exceedingly simple, yet often overlooked. A preference for fairness should not change the choice of estimator. Equity preferences can change how the estimated prediction function is used (e.g., different threshold for different groups) but the function itself should not change. We show in an empirical example for college admissions that the inclusion of variables such as race can increase both equity and efficiency.

This paper proposes tools for robust inference in difference-in-differences and event-study designs where the parallel trends assumption may be violated. Instead of requiring that parallel trends holds exactly, we impose restrictions on how different the post-treatment violations of parallel trends can be from the pre-treatment differences in trends (“pre-trends”). The causal parameter of interest is partially identified under these restrictions. We introduce two approaches that guarantee uniformly valid inference under the imposed restrictions, and we derive novel results showing that they have desirable power properties in our context. We illustrate how economic knowledge can inform the restrictions on the possible violations of parallel trends in two economic applications. We also highlight how our approach can be used to conduct sensitivity analyses showing what causal conclusions can be drawn under various restrictions on the possible violations of the parallel trends assumption.

There are widespread concerns that the growing use of machine learning algorithms in important decisions may reproduce and reinforce existing discrimination against legally protected groups. Most of the attention to date on issues of “algorithmic bias” or “algorithmic fairness” has come from computer scientists and machine learning researchers. We argue that concerns about algorithmic fairness are at least as much about questions of how discrimination manifests itself in data, decision-making under uncertainty, and optimal regulation. To fully answer these questions, an economic framework is necessary--and as a result, economists have much to contribute.

There is growing concern about "algorithmic bias" -that predictive algorithms used in decisionmaking might bake in or exacerbate discrimination in society. We argue that such concerns are naturally addressed using the tools of welfare economics. This approach overturns prevailing wisdom about the remedies for algorithmic bias. First, when a social planner builds the algorithm herself, her equity preference has no effect on the training procedure. So long as the data, however biased, contain signal, they will be used and the learning algorithm will be the same. Equity preferences alone provide no reason to alter how information is extracted from data -only how that information enters decision-making. Second, when private (possibly discriminatory) actors are the ones building algorithms, optimal regulation involves algorithmic disclosure but otherwise no restriction on training procedures. Under such disclosure, the use of algorithms strictly reduces the extent of discrimination relative to a world in which humans make all the decisions.

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Social scientists are often interested in estimating causal effects in settings where all units in the population are observed (e.g. all 50 US states). Design-based approaches, which view the treatment as the random object of interest, may be more appealing than standard sampling-based approaches in such contexts. This paper develops a design-based theory of uncertainty suitable for quasi-experimental settings, in which the researcher estimates the treatment effect as if treatment was randomly assigned, but in reality treatment probabilities may depend in unknown ways on the potential outcomes.We first study the properties of the simple difference-in-means (SDIM) estimator. The SDIM is unbiased for a finite-population design-based analog to the average treatment effect on the treated (ATT) if treatment probabilities are uncorrelated with the potential outcomes in a finite population sense. We further derive expressions for the variance of the SDIM estimator and a central limit theorem under sequences of finite populations with growing sample size. We then show how our results can be applied to analyze the distribution and estimand of difference-in-differences (DiD) and two-stage least squares (2SLS) from a design-based perspective when treatment is not completely randomly assigned. * We thank Isaiah Andrews, Iavor Bojinov, Peng Ding, Pedro Sant'Anna, Yotam Shem-Tov, and Neil Shephard for helpful comments and suggestions. Rambachan gratefully acknowledges support from the NSF Graduate Research Fellowship under Grant DGE1745303.

In panel experiments, we randomly expose multiple units to different treatments and measure their subsequent outcomes, sequentially repeating the procedure numerous times. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For the leading example, known as the lag-p dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution. We then derive the finite population limiting distribution of our estimators as either the sample size or the duration of the experiment increases. Our approach provides a new technique for deriving finite population central limit theorems that exploits the underlying Martingale property of unbiased estimators. We further describe two methods for conducting inference on dynamic causal effects: a conservative test for weak null hypotheses of zero average causal effects using the limiting distribution and an exact randomization-based test for sharp null hypotheses. We also derive the finite population limiting distribution of commonly-used linear fixed effects estimators, showing that these estimators perform poorly in the presence of dynamic causal effects. We conclude with a simulation study and an empirical application in which we reanalyze a lab experiment on cooperation.

In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For a rich class of dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution and derive its finite population limiting distribution as either the sample size or the duration of the experiment increases. We develop two methods for inference: a conservative test for weak null hypotheses and an exact randomization test for sharp null hypotheses. We further analyze the finite population probability limit of linear fixed effects estimators. These commonly‐used estimators do not recover a causally interpretable estimand if there are dynamic causal effects and serial correlation in the assignments, highlighting the value of our proposed estimator.