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  3. 2021
  4. Preliminary Program
  5. Optimization-Conscious Econometrics
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Optimization-Conscious Econometrics

Paper Session

Monday, Jan. 4, 2021 10:00 AM - 12:00 PM (EST)

Hosted By: American Economic Association
  • Chair: Elie Tamer, Harvard University

Optimization Over Quantiles

Guillaume Pouliot
,
University of Chicago

Abstract

Quantiles and quantile regression estimates obtain as the solution of linear programming problems.  While this implies that optimization problems where the feasible set is composed of quantiles may be formulated as two-level problems, these are often intractable, especially when additional constraints are introduced.  A standard approach is then to rely on strong duality and represent the feasible set in terms of feasibility and optimality criteria.  We discuss powerful applications of this simple approach in econometrics.  First, we produce a mixed integer linear programming formulation of the inverse quantile regression estimator of the instrumental variables quantile regression (IVQR) model.  We show that this construction naturally rehabilitates regression rankscore inference for IVQR, thus producing inference that is more robust and, under homoskedastiticy assumptions, even pivotal with respect to the bandwidth parameter.  The inference method is extended to allow for weak-identification robust subvector inference.  Second, we produce mixed integer programming formulations for quantile regression with interval censored regressors --or omitted categorical variables-- and likewise treat the case of ordinary least-squares with censored regressors.  Third, we show how this strategy can be leveraged to invert, under additional assumptions, permutation tests for the average treatment effect allowing for treatment effect heterogeneity. 

The Proximal Bootstrap

Jessie Li
,
University of California-Santa Cruz

Abstract

We propose a bootstrap that can consistently estimate the limiting distribution of $\sqrt{n}$ consistent estimators with nonstandard asymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to a convex optimization problem, which can have a closed form solution under certain designs. Applications include constrained optimization for possibly non-smooth, non-convex objectives, and finite dimensional regularized estimators, such as the Lasso, $\ell_1$ norm regularized quantile regression, $\ell_1$ norm support vector regression, and trace regression via nuclear norm regularization. Work in progress attempts to look at the high dimensional de-sparsified $\ell_1$ regularized estimators.

An Adversarial Approach to Structural Estimation

Elena Manresa
,
New York University
Tetsuya Kaji
,
University of Chicago
Guillaume Pouliot
,
University of Chicago

Abstract

We propose a new simulation-based estimation method for structural models that leverages adversarial machine learning techniques. In addition to a structural model, the method requires a classification algorithm whose task is to predict the provenance of a given draw: the true distribution of the data vs. the model-generated distribution. The estimator is then defined as the value of the structural parameters for which the classifier cannot distinguish the corresponding simulated data from the observed data.  Different classification models define different estimators and we show that when using a logistic regression as a discriminator the estimator is asymptotically equivalent to the optimally weighted Simulated Method of Moments.  We provide a complete analysis and implementation of the case with discriminators based on Neural Networks (NN) with multiple layers.  On the computational side, combining the stochastic gradient descent methods developed for NN estimation with a modified Nesterov accelerated gradient approach produces reliable point estimation.  On the theory side, we show that when using a sufficiently rich NN the resulting estimator achieves the Cramer Rao bound.  The method can be combined with recent developments in robust inference to account for misspecification, and is amenable to conduct sensitivity analysis using different aspects of the data in estimation. We showcase the good properties of the framework by revisiting the savings motives of the elder in the U.S., following up on DeNardi, French, Jones (2010). Including health profiles and gender in the estimation provides more informative estimates of the relative importance of bequest motives versus the risk of large medical expenses toward the end of life.

Inference by Stochastic Optimization: A Free-Lunch Bootstrap

Jean-Jacques Forneron
,
Boston University
Serena Ng
,
Columbia University

Abstract

Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model is complex. This paper uses iterates of a specially designed stochastic optimization algorithm as draws from which both point estimates and bootstrap standard errors can be computed in a single run. The draws are generated by the gradient and Hessian computed from batches of data that are resampled at each iteration. We show that these draws yield consistent estimates and asymptotically valid frequentist inference for a large class of regular problems. The algorithm provides accurate standard errors in simulation examples and empirical applications at low computational costs. The draws from the algorithm also provide a convenient way to detect data irregularities.
Discussant(s)
Elie Tamer
,
Harvard University
Francesca Molinari
,
Cornell University
Alexander Torgovitsky
,
University of Chicago
Xiaohong Chen
,
Yale University
JEL Classifications
  • C1 - Econometric and Statistical Methods and Methodology: General
  • D0 - General