Knowledge that Transforms

We study the role of public risk-sharing in markets where firms face substantial cost uncertainty, focusing on public reinsurance in health insurance. We develop a model where insurers internalize cost uncertainty through risk charges that raise effective marginal costs and create a role for reinsurance. Public reinsurance lowers both expected costs and cost volatility, particularly for smaller insurers, reducing prices and enhancing competition. Using an event study of staggered state-level reinsurance programs, we show that public reinsurance leads insurers to lower prices and private reinsurance purchases, benefiting financially constrained insurers the most. Structural estimates indicate that risk charges account for a substantial share of the premium-cost wedge and highlight public reinsurance’s comparative advantage over premium subsidies by providing risk protection and enhancing competition. Our results underscore the importance of accounting for firms’ risk exposure in policy design and provide a general framework for understanding public risk-sharing policies.

We consider an oligopoly model in which each firm chooses not only its price but also its advertising strategy regarding how much, and what, product information to provide. To highlight firms’ strategic incentives, we impose no structural restrictions on feasible advertising content, so that each firm can disclose or conceal any information. We obtain a comprehensive characterization of the equilibrium advertising strategy and provide some sufficient conditions for the existence of symmetric pure-price equilibria. We show that intense competition induces firms to provide accurate product information; firms usually obfuscate consumers’ relatively low or high values; and requiring firms to provide more product information can reduce social surplus and also be harmful to consumers.

We study the labour market effects of permanent 30%–64% reductions on unemployment insurance benefits available in seven states. Leveraging linked firm-establishment data, we find that establishments based on reform states experience employment increases that are 0.8%–1.3% larger than those of the same firm’s establishments in other states. Using a similar multi-state firm design, starting salaries are 1.2%–5.5% lower in reform states and posted salaries for the same job fall by 3.2%–3.5%. The negative co-movement of employment and wages after the reform suggests a labour supply shock and mitigates against confounding changes in labour demand driving the results. Our findings are consistent with workers lowering their reservation wages as outside options fall, and employers take advantage of this by offering lower wages and increasing employment.

Manager pay has increased considerably since 1980, and so has inequality in manager pay. Over the same period, there has been a sharp rise in market power. We start from the premise that the role of managers is to increase firm productivity. When markets are imperfectly competitive, productivity not only helps firm grow in size, productivity also affects market power. We model how imperfect competition in product markets affects manager pay, and break down the contributions of firm size and market power to compensation. We find that market power, on average, accounts for 45.2% of total manager pay. Notably, there is substantial variation across managers. Top managers are disproportionately employed by firms with market power, and they benefit from it: in 2019, 80.3% of top manager pay is attributable to market power. Our main conclusion is that rise of market power explains half of the increase in average manager pay, and nearly all of the increase in manager pay inequality.

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.

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.

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.

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.

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.

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.