We propose a new tractable general framework for sorting – composite sorting. Composite sorting comprises of (1) distinct workers being assigned to the same job and (2) a given worker type simultaneously being part of both positive and negative sorting. We show that composite sorting generically arises in a class of sorting models when fixed investments can mitigate the variable costs of mismatch. We develop a complete characterization of equilibrium sorting as well as the corresponding equilibrium wages. Wages exhibit a local hierarchical structure meaning the relative wages depend solely on sorting patterns within narrow skill groups. Using this framework, we study within–job wage dispersion and demonstrate that quantitatively composite sorting may explain a sizable portion of wage dispersion within occupations in the United States.
We argue that noisy aggregation of dispersed information provides a unified explanation for several prominent cross-sectional return anomalies such as returns to skewness, returns to disagreement and corporate credit spreads. We characterize asset returns with noisy information aggregation by means of a risk-neutral probability measure that features excess weight on tail risks, and link the latter to observable moments of earnings forecasts, in particular forecast dispersion and accuracy. We calibrate our model to match these moments and show that it accounts for a large fraction of the empirical return premia. We further develop asset pricing tools for noisy information aggregation models that do not impose strong parametric restrictions on economic primitives such as preferences, information, or return distributions.
We analyze the consequences of noisy information aggregation for investment. Market imperfections create endogenous rents that cause overinvestment in upside risks and underinvestment in downside risks. In partial equilibrium, these inefficiencies are particularly severe if upside risks are coupled with easy scalability of investment. In general equilibrium, the shareholders' collective attempts to boost value of individual rms leads to a novel externality operating through price that amplifies investment distortions with downside risks but o sets distortions with upside risks.
We characterize optimal policies in a multidimensional nonlinear taxation model with bunching. We develop an empirically relevant model with cognitive and manual skills, firm heterogeneity, and labor market sorting. The analysis of optimal policy is based on two main results. We first derive an optimality condition − a general ABC formula − that states that the entire schedule of benefits of taxes second order stochastically dominates the entire schedule of tax distortions. Second, we use Legendre transforms to represent our problem as a linear program. This linearization allows us to solve the model quantitatively and to precisely characterize the regions and patterns of bunching. At an optimum, 9.8 percent of workers is bunched both locally and nonlocally. We introduce two notions of bunching – blunt bunching and targeted bunching. Blunt bunching constitutes 30 percent of all bunching, occurs at the lowest regions of cognitive and manual skills, and lumps the allocations of these workers resulting in a significant distortion. Targeted bunching constitutes 70 percent of all bunching and recognizes the workers’ comparative advantage. The planner separates workers on their dominant skill and bunches them on their weaker skill, thus mitigating distortions along the dominant skill dimension. Tax wedges are particularly high for low skilled workers who are bluntly bunched and are also high along the dimension of comparative disadvantage for somewhat more skilled workers who are targetedly bunched.
In this paper, we introduce the weighted-average quantile regression framework, R 1 0 qY |X(u)ψ(u)du = X0β, where Y is a dependent variable, X is a vector of covariates, qY |X is the quantile function of the conditional distribution of Y given X, ψ is a weighting function, and β is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters β. We show that our estimator is √ T-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where T is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.
We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auctiondesign problem can be reduced to the problem of continuous optimal transportation introduced by Beckmann (1952). We establish the strong duality between the two problems and demonstrate the existence of solutions. We then develop a new numerical approximation scheme that combines multi-tosingle-agent reduction and the majorization theory insights to characterize the solution.
We develop a model of political competition with endogenous turn-out and endogenous platforms. Parties trade off incentivizing their supporters to vote and discouraging the supporters of the competing party from voting. We show that the latter objective is particularly pronounced for a party with an edge in the political race. Thus, an increase in political support for a party may lead to the adoption of policies favoring its opponents so as to asymmetrically demobilize them. We study the implications for the political economy of redistributive taxation. Equilibrium tax policy is typically aligned with the interest of voters who are demobilized.