Knowledge that Transforms

Abstract This article presents a theoretical case for replacement of conventional heteroskedasticity-consistent and cluster-robust variance estimators with jackknife variance estimators, in the context of linear regression with heteroskedastic and/or cluster-dependent observations. We examine the bias of variance estimation and the coverage probabilities of confidence intervals. Concerning bias, we show that conventional variance estimators have full downward worst-case bias, while our jackknife variance estimator is never downward biased. Concerning confidence intervals, we show that intervals based on conventional standard errors have worst-case coverage equalling zero, while the jackknife-based confidence interval has coverage probability bounded by the Cauchy distribution, under the auxiliary assumption of normal errors. We also extend the Bell and McCaffrey (2002) student t approximation to our jackknife t-ratio, resulting in confidence intervals with improved coverage probabilities. Our theory holds under broad assumptions, allowing arbitrary cluster sizes, regressor leverage, within-cluster correlation, heteroskedasticity, regression with a single treated cluster, fixed effects, and delete-cluster invertibility failures. Our theoretical findings are consistent with the extensive simulation literature investigating heteroskedasticity-consistent and cluster-robust variance estimation.

Abstract We study the effect of risk on how firms organize their supply chains. We use transaction-level data on U.S. manufacturing imports to construct a novel measure of input sourcing risk based on the historical volatility of ocean shipping times. Our measure isolates the unexpected component of shipping times that is induced by weather conditions along more than 331,000 maritime routes. We first document that unexpected shipping delays significantly reduce importers’ sales, profits, and employment. We then show that firms actively diversify weather risk by using more routes and foreign suppliers, although their import values decline. To rationalize these findings, we introduce shipping time risk into a general equilibrium model of importing with firm heterogeneity. Our quantitative analysis predicts substantial costs for the U.S. economy associated with supply chain risk.

Abstract Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating non-negatively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general. Instead, the TSLS estimator will, in general, reflect treatment effects for both compliers and always/never-takers, and some treatment effects for the always/never-takers will necessarily be negatively weighted. We show that the only specifications that have a LATE interpretation are “saturated” specifications that control for covariates nonparametrically, implying that such specifications are both sufficient and necessary for TSLS to have a LATE interpretation, at least without additional parametric assumptions. This result is concerning because, as we document, empirical researchers almost never control for covariates nonparametrically, and rarely discuss or justify parametric specifications of covariates. We apply our results to thirteen empirical studies and find strong evidence that the LATE interpretation of TSLS is far from accurate for the types of specifications actually used in practice. We offer concrete recommendations for practice motivated by our theoretical and empirical results.

Abstract This article reconsiders the question of optimal labour income taxes for the very rich in the context of a flexible moral hazard model. In this setting, risk is not exogenous. Rather, each agent can affect the probabilities of all possible income outcomes by allocating a fixed time endowment across a variety of distinct tasks. I prove that the optimal income tax rates on high-end earners and the optimal Pareto tail index of the pre-tax labour income distribution are both endogenously determined by agent preferences. In particular, a society with less risk-averse agents will find it optimal to impose a lower tax rate on the rich, even though its members’ choices give rise to a smaller Pareto right tail index. In contrast, this kind of negative co-movement between inequality and optimal tax rates is a suboptimal response in the classical Mirrlees (1971)–Diamond (1998)–Saez (2001) setup to changes in the exogenous distribution of skills.

Abstract Multiple hypothesis testing (MHT) practices vary widely, without consensus on which are appropriate when. This article provides an economic foundation for these practices designed to capture leading examples, such as regulatory approval on the basis of clinical trials. MHT adjustments are appropriate in our framework to the extent that research costs are invariant to the number of hypotheses. Control of average size, as for example via a Bonferroni correction, emerges in the limit case where all costs are fixed; in the opposite limit, where costs vary in proportion to the hypothesis count, no correction is needed. We illustrate implications by calculating explicit critical values using data on actual costs in the drug approval process and in program evaluation research; these suggest that some MHT adjustment is warranted in these applications, but not as much as implied by standard practice.

Abstract The seminal paper by Baron and Ferejohn (1989) leaves significant gaps in our understanding of open rule bargaining. We aim to fill these gaps by providing a fresh analysis of open rule bargaining. Our approach relies on an appealing class of stationary equilibria. In this class, we show that delays tend to be longer and allocations tend to be less egalitarian than originally predicted by Baron and Ferejohn. Our results shed new light on the efficiency and fairness implications of using an open vs. closed rule in legislatures and of bargaining processes in general.

Abstract Discrete choice data allow researchers to recover differences in utilities, but these differences may not suffice to identify policy-relevant counterfactuals of interest. In fact, in the case of dynamic discrete choice models, only a narrow set of counterfactuals are point-identified. In this paper, we explore how much one can learn about counterfactual outcomes of interest within this framework. We focus on the partial identification of counterfactuals, while allowing for (mild) model restrictions that can gradually shrink the identified set. We derive bounds for low-dimensional objects (such as average welfare) as arguments of optimization programmes, along with a uniformly valid inference procedure. Furthermore, we develop new and tractable computational tools and algorithms suitable for dealing with high-dimensional problems like this. Finally, we illustrate in Monte Carlos, as well as an empirical exercise of firms’ export decisions, the informativeness of the identified sets, and we assess the impact of (common) model restrictions on results.

Abstract Existing tests of reference-dependent preferences assume universal loss aversion. This paper examines the implications of heterogeneity in gain-loss attitudes for such tests. In experiments on labour supply and exchange behaviour, we first measure gain-loss attitudes and then study a canonical treatment effect that distinguishes different models of reference dependence. We document substantial heterogeneity in gain-loss attitudes and evidence against universal loss aversion. Moreover, we find heterogeneous treatment effects over gain-loss attitudes consistent with formulations of expectations-based reference points. Assuming homogeneous preferences would lead to different and potentially incorrect conclusions in these tests. Our findings provide foundational support for reference points derived from expectations and help reconcile inconsistencies in prior empirical exercises.

Abstract While men and women make joint decisions about fertility, women give birth and are more likely to learn about a significant cost of childbearing—maternal health risk. Within couples in Zambia, men have systematically lower awareness of maternal risk factors and higher desire for children than their wives. We develop a model in which information asymmetries between partners over maternal health risk can persist in equilibrium due to strategic incentives and can generate disagreement over fertility that cannot be resolved with transfers. To study the effect of communication barriers on fertility, we design an experiment that varies whether the husband or the wife receives information about maternal health risk. One year after the intervention, men told about such risk exhibit significant gains in knowledge, report lower demand for children, and communicate this information to their wives, who also update their beliefs. Pregnancy falls significantly, while transfers remain unchanged relative to the control group. Meanwhile, when women are told about risk, they update their beliefs, but fail to transmit the information to their husbands, who do not change their demand for children. While pregnancy also falls among these couples, the decline is accompanied by a significant reduction in transfers and support to the wife. When childbearing costs, particularly those borne by one party, cannot be easily communicated within the household, targeting information can help overcome asymmetries and improve household decision-making.

Abstract We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter θ and the decision maker can use a point-identified parameter μ to deduce restrictions on θ. Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity. Our notion of optimality combines a minimax approach to handle the ambiguity from partial identification of θ given μ with an average risk minimization approach for μ. We show how to implement optimal decision rules using the bootstrap and (quasi-)Bayesian methods in both parametric and semiparametric settings. We provide detailed applications to treatment choice and optimal pricing. Our asymptotic approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.