School Seminar Series | Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities by Tim Christensen
Invites you to a
School seminar presented by
(New York University)
Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities
Co-authors
Xiahong Chen (Yale University)
Sid Kankanala (Yale University)
Thursday 25 August
11.00am – 12.30pm
Via Zoom: Meeting Link
Abstract: We introduce two practical methods for estimation and inference on a nonparametric structural function and its derivatives—such as elasticities or other marginal effects—using instrumental variables. The first procedure is a data-driven choice of sieve dimension and the second is a data-driven approach for constructing uniform confidence bands (UCBs) for the structural function and its derivatives. Both procedures are simple to implement and do not require prior information about the smoothness of the function or instrument strength. Despite their simplicity, both procedures have strong theoretical justifications. Our first procedure leads to estimators of the structural function and its derivatives that are efficient in the sense that they converge at the best possible (i.e., minimax-optimal) rate for sup-norm loss. Our second procedure yields UCBs for the structural function and its derivatives that have correct coverage asymptotically and that contract at, or within a logarithmic factor of, the minimax rate. As such, our UCBs are asymptotically more efficient (i.e., narrower) than UCBs based on the usual approach of undersmoothing. We illustrate both methods with empirically-calibrated simulations and a real-data application in which we estimate the elasticity of the intensive margin of firm exports in a monopolistic competition model of international trade. Our results provide evidence against common parameterizations of the distribution of unobserved firm heterogeneity.
For further information contact: School seminar series coordinators Dr Ye Lu (ye.lu1@sydney.edu.au) & Dr Alastair Fraser (alastair.fraser@sydney.edu.au)
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