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Equilibrium Effects of Pay Transparency

Econometrica 2023 91(3), 765-802 open access
The discourse around pay transparency has focused on partial equilibrium effects: how workers rectify pay inequities through informed renegotiation. We investigate how employers respond in equilibrium. We study a model of bargaining under two‐sided incomplete information. Our model predicts that transparency reduces the individual bargaining power of workers, leading to lower average wages. A key insight is that employers credibly refuse to pay high wages to any one worker to avoid costly renegotiations with others. When workers have low individual bargaining power, pay transparency has a muted effect. We test our model with an event‐study analysis of U.S. state‐level laws protecting the right of private sector workers to communicate salary information with their coworkers. Consistent with our theoretical predictions, transparency laws empirically lead wages to decline by approximately 2%, and wage declines are smallest in magnitude when workers have low individual bargaining power.

General Equilibrium Effects of (Improving) Public Employment Programs: Experimental Evidence From India

Econometrica 2023 91(4), 1261-1295 open access
Public employment programs may affect poverty both directly through the income they provide and indirectly through general equilibrium effects. We estimate both effects, exploiting a reform that improved the implementation of India's National Rural Employment Guarantee Scheme (NREGS) and whose rollout was randomized at a large (sub‐district) scale. The reform raised beneficiary households' earnings by 14%, and reduced poverty by 26%. Importantly, 86% of income gains came from non‐program earnings, driven by higher private‐sector (real) wages and employment. This pattern appears to reflect imperfectly competitive labor markets more than productivity gains: worker's reservation wages increased, land returns fell, and employment gains were higher in villages with more concentrated landholdings. Non‐agricultural enterprise counts and employment grew rapidly despite higher wages, consistent with a role for local demand in structural transformation. These results suggest that public employment programs can effectively reduce poverty in developing countries, and may also improve economic efficiency.

Bidding in Common‐Value Auctions With an Unknown Number of Competitors

Econometrica 2023 91(2), 493-527 open access
This paper studies a first‐price common‐value auction in which bidders do not know the number of their competitors. In contrast to the case of common‐value auctions with a known number of rival bidders, the inference from winning is not monotone, and a “winner's blessing” emerges at low bids. As a result, bidding strategies may not be strictly increasing, but instead may contain atoms. Moreover, an equilibrium fails to exist when the expected number of competitors is large and the bid space is continuous. Therefore, we consider auctions on a grid. On a fine grid, high‐signal bidders follow an essentially strictly increasing strategy, whereas low‐signal bidders pool on two adjacent bids on the grid. The solutions of a “communication extension” based on Jackson, Simon, Swinkels, and Zame (2002) capture the equilibrium bidding behavior in the limit, as the grid becomes arbitrarily fine.

Mitigating Disaster Risks in the Age of Climate Change

Econometrica 2023 91(5), 1763-1802 open access
Emissions abatement alone cannot address the consequences of global warming for weather disasters. We model how society adapts to manage disaster risks to capital stock. Optimal adaptation—a mix of firm‐level efforts and public spending—varies as society learns about the adverse consequences of global warming for disaster arrivals. Taxes on capital are needed alongside those on carbon to achieve the first best. We apply our model to country‐level control of flooding from tropical cyclones. Learning rationalizes empirical findings, including the responses of Tobin's q , equity risk premium, and risk‐free rate to disaster arrivals. Adaptation is more valuable under learning than a counterfactual no‐learning environment. Learning alters social‐cost‐of‐carbon projections due to the interaction of uncertainty resolution and endogenous adaptive response.

Nexus Tax Laws and Economies of Density in E‐Commerce: A Study of Amazon's Fulfillment Center Network

Econometrica 2023 91(1), 147-190 open access
We quantify the distortionary effects of nexus tax laws on Amazon's distribution network investments between 1999 and 2018. We highlight the role of two features of the expansion of Amazon's network: densification of the network of distribution facilities and vertical integration into package sortation. Densification results in a reduction in the cost of shipping orders, but comes at the expense of higher facility operating costs in more expensive areas and lower scale economies of processing shipments. Nexus laws furthermore generate additional sales tax liabilities as the network grows. Combining data on household spending across online and offline retailers with detailed data on Amazon's distribution network, we quantify these trade‐offs through a static model of demand and a dynamic model of investment. Our results suggest that Amazon's expansion led to significant shipping cost savings and facilitated the realization of aggregate economies of scale. We find that abolishing nexus tax laws in favor of a non‐discriminatory tax policy would induce the company to decentralize its network, lowering its shipping costs. Non‐discriminatory taxation would also entail lower revenue, however, as tax‐inclusive prices would rise, resulting in a fall in profit overall. This drop and the decline in consumer welfare from higher taxes together fall short of the increases in tax revenue and rival profit, suggesting that the abolishment of nexus laws would lead to an increase in total welfare.

Constrained Conditional Moment Restriction Models

Econometrica 2023 91(2), 709-736 open access
Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper, we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods are based on the minimum of the generalized method of moments (GMM) objective function with and without shape restrictions. Uniformly valid critical values are obtained through a bootstrap procedure that approximates a subset of the true local parameter space. In an empirical analysis of the effect of childbearing on female labor supply, we show that employing shape restrictions in linear instrumental variables (IV) models can lead to shorter confidence regions for both local and average treatment effects. Other applications we discuss include inference for the variability of quantile IV treatment effects and for bounds on average equivalent variation in a demand model with general heterogeneity.

Nonparametric Estimates of Demand in the California Health Insurance Exchange

Econometrica 2023 91(1), 107-146 open access
We develop a new nonparametric approach for discrete choice and use it to analyze the demand for health insurance in the California Affordable Care Act marketplace. The model allows for endogenous prices and instrumental variables, while avoiding parametric functional form assumptions about the unobserved components of utility. We use the approach to estimate bounds on the effects of changing premiums or subsidies on coverage choices, consumer surplus, and government spending on subsidies. We find that a $10 decrease in monthly premium subsidies would cause a decline of between 1.8% and 6.7% in the proportion of subsidized adults with coverage. The reduction in total annual consumer surplus would be between $62 and $74 million, while the savings in yearly subsidy outlays would be between $207 and $602 million. We estimate the demand impacts of linking subsidies to age, finding that shifting subsidies from older to younger buyers would increase average consumer surplus, with potentially large impacts on enrollment. We also estimate the consumer surplus impact of removing the highly‐subsidized plans in the Silver metal tier, where we find that a nonparametric model is consistent with a wide range of possibilities. We find that comparable mixed logit models tend to yield price sensitivity estimates toward the lower end of the nonparametric bounds, while producing consumer surplus impacts that can be both higher and lower than the nonparametric bounds depending on the specification of random coefficients.

A Sieve‐SMM Estimator for Dynamic Models

Econometrica 2023 91(3), 943-977 open access
This paper proposes a Sieve Simulated Method of Moments (Sieve‐SMM) estimator for the parameters and the distribution of the shocks in nonlinear dynamic models where the likelihood and the moments are not tractable. An important concern with SMM, which matches sample with simulated moments, is that a parametric distribution is required. However, economic quantities that depend on this distribution, such as welfare and asset prices, can be sensitive to misspecification. The Sieve‐SMM estimator addresses this issue by flexibly approximating the distribution of the shocks with a Gaussian and tails mixture sieve. The asymptotic framework provides consistency, rate of convergence, and asymptotic normality results, extending existing results to a new framework with more general dynamics and latent variables. An application to asset pricing in a production economy shows a large decline in the estimates of relative risk aversion, highlighting the empirical relevance of misspecification bias.

Unemployment and Endogenous Reallocation Over the Business Cycle

Econometrica 2023 91(3), 1119-1153 open access
This paper studies the extent to which the cyclicality of occupational mobility shapes that of aggregate unemployment and its duration distribution. We document the relation between workers' occupational mobility and unemployment duration over the long run and business cycle. To interpret this evidence, we develop a multisector business cycle model with heterogenous agents. The model is quantitatively consistent with several important features of the US labor market: procyclical gross and countercyclical net occupational mobility, the large volatility of unemployment and the cyclical properties of the unemployment duration distribution, among many others. Our analysis shows that occupational mobility due to workers' changing career prospects, and not occupation‐wide differences, interacts with aggregate conditions to drive the fluctuations of the unemployment duration distribution, and the aggregate unemployment rate.

A Preferred‐Habitat Model of the Term Structure of Interest Rates

Econometrica 2023 89(1), 77-112 open access
This document contains a list of one typo in the main text and six typos in the online appendix of the article. Each typo is followed by an explanation of why it is only a typo and does not affect the analysis in the article. The main text and online appendix refer to the documents in the journal’s website https://www.econometricsociety.org/publications/ econometrica/2021/01/01/preferred-habitat-model-term-structure-interest-rates.