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Recent Submissions

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    Wild boostrap inference for penalized quantile regression for longitudinal data
    (University of Waterloo, 2022-10-18) Lamarche, Carlos; Parker, Thomas
    The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator. The model puts no restrictions on individual effects, and the estimator achieves consistency by letting the shrinkage decay in importance asymptotically. The new method is easy to implement and simulation studies show that it has accurate small sample behavior in comparison with existing procedures. Finally, we illustrate the new approach using U.S. Census data to estimate a model that includes more than eighty thousand parameters.
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    Uniform inference for value functions
    (University of Waterloo, 2022-11-10) Firpo, Sergio; Galvao, Antonio F.; Parker, Thomas
    We propose a method to conduct uniform inference for the (optimal) value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. Marginal optimization is not Hadamard differentiable (that is, compactly differentiable) as a map between the spaces of objective and value functions, which is problematic because standard inference methods for nonlinear maps usually rely on Hadamard differentiability. However, we show that the map from objective function to an Lp functional of a value function, for 1 ≤ p ≤ ∞, are Hadamard directionally differentiable. As a result, we establish consistency and weak convergence of nonparametric plug-in estimates of Cramer-von Mises and Kolmogorov-Smirnov test statistics applied to value functions. For practical inference, we develop detailed resampling techniques that combine a bootstrap procedure with estimates of the directional derivatives. In addition, we establish local size control of tests which use the resampling procedure. Monte Carlo simulations assess the finite-sample properties of the proposed methods and show accurate empirical size and nontrivial power of the procedures. Finally, we apply our methods to the evaluation of a job training program using bounds for the distribution function of treatment effects.
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    Fighting for fares: Uber and the declining market price of licensed taxicabs
    (University of Waterloo, 2022-04-22) Garnham, Alina; Stacey, Derek
    In this paper, we study how the emergence of Uber in a large North American city affects the financial value of taxicab licenses. A taxicab license provides a claim to a stream of dividends in the form of rents generated by operating the taxicab or leasing the license. The introduction of Uber undoubtedly affects the anticipated stream of dividends because Uber drivers capture part of the farebox revenue that might otherwise go to the owners/drivers of licensed taxicabs. At the same time, the launch of Uber's innovative technology-driven approach to the provision of ride-hailing services can be viewed as a partial obsolescence of the traditional taxicab approach. The economic incentives facing market participants may therefore change as Uber gains momentum in the ride-hailing market, which could further affect the market value of licensed taxicabs. Using transaction-level data, we apply a theory of asset pricing to the secondary market for Toronto taxicab licenses to explore these potential price effects. We learn that both the farebox and innovation effects contribute to the overall decline in market value, with the farebox effect account for just over half of the $170K price decline from 2011 to 2017. We explore the welfare implications for taxicab license owners with counterfactual simulations. We find that, consistent with the anti-Uber protests organized by Toronto taxi drivers, there was a high willingness to pay among license holders to prevent or postpone the launch of Uber's ridesharing services.
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    Learning new bias: Misspecifications and consequences
    (University of Waterloo, 2023-09) Hu, Lin; Kovach, Matthew; Li, Anqi
    We study how a decision maker (DM) learns about the bias of unfamiliar news sources. Absent any frictions, a rational DM uses known sources as a yardstick to discern the true bias of a source. If a DM has misspecified beliefs, this process fails. We derive long-run beliefs, behavior, welfare, and corresponding comparative statistics, when the DM has dogmatic, incorrect beliefs about the bias of known sources. The distortion due to misspecified learning is succinctly captured by a single-dimensional metric we introduce. Our model generates the hostile media effect and false polarization, and has implications for fact-checking and misperception recalibration.
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    Rationally inattentive statistical discrimination: Arrow meets phelps
    (University of Waterloo, 2023-08) Echenique, Federico; Li, Anqi
    When information acquisition is costly but flexible, a principal may rationally acquire information that favors "majorities" over "minorities" unless the latter are strictly more productive than the former. Majorities therefore face incentives to invest in becoming productive, whereas minorities are discouraged from such investments. The principal, in turn, focuses scarce attentional resources on majorities precisely because they are likely to invest. We give conditions under which the resulting discriminatory equilibrium is most preferred by the principal, despite that all groups are ex-ante identical. Our results add to the discussions of affirmative action, implicit bias, and occupational segregation and stereotypes.