arXiv subjects

Whitney K. Newey

Publications and source records attributed to Whitney K. Newey.

At least 19 recordsLinked to original sources

arXiv2026

Linear Estimation of Structural and Causal Effects for Nonseparable Panel Data

This paper develops linear estimators for structural and causal parameters of nonseparable models using panel data. These models incorporate unobserved, time-varying, individual heterogeneity, which may be correlated with the regressors. Estimation is based on an approximation of a conditional average potential outcome by a linear sieve specification with individual-specific parameters. Effects of interest are estimated by a bias corrected average of individual ridge regressions. We demonstrate how this approach can be applied to estimate causal effects, counterfactual consumer welfare, and averages of individual taxable income elasticities. We show that the proposed estimator has an empirical Bayes interpretation and possesses a number of other useful properties. We formulate Large-$T$ asymptotics that can accommodate discrete regressors and which bypass partial identification in this case. We employ the methods to estimate average equivalent variation and deadweight loss for potential price increases using data on grocery purchases.

econ.EM↗

arXiv2026

Panel Data Estimation of Individual Demand in Markets with Many Consumers

The purpose of this paper is to consider whether and how panel data can be used to estimate individual demand, as opposed to market-level demand, while accounting for simultaneity resulting from prices being determined in markets. We consider linear demand models and random coefficient demand models, together with linear supply models. We find that the bias of individual demand estimates obtained using familiar panel data methods, like differencing, disappears as the number of consumers in each market grows, as long as the time-varying, i.e. idiosyncratic, component of preferences is orthogonal to the unobserved, time-varying component of supply. This approximate control is assumed in many panel discrete choice models and is plausible in other models where idiosyncratic preferences represent random variation in preferences over time. Macroeconomic effects can be allowed for by including regressors characterizing time effects, such as trends and time period dummies, or fixed time effects.

econ.EM↗

arXiv2026

Higher-Order Neyman Orthogonality in Moment-Condition Models

We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error and, as such, offer a unified and tractable route to higher-order debiasing in a wide range of econometric models. The number of additional nuisance parameters required by our construction, beyond those already present in the original moment conditions, is independent of the order of orthogonalization and can be reduced to a single scalar if desired.

econ.EM↗

arXiv2026

Semiparametric Efficient Empirical Higher Order Influence Function Estimators

Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $ψ$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous covariates; their estimator, in contrast to previous estimators, is semiparametric efficient under the minimal conditions of Robins et al. (2009b), together with an additional (non-minimal) smoothness condition on the density g of X, because the Robins et al. (2008, 2017) estimator depends on a nonparametric estimate of g. In this paper, we introduce a new HOIF estimator that has the same asymptotic properties as the original one, but does not impose any smoothness requirement on g. This is important for two reasons. First, one rarely has the knowledge about the properties of g. Second, even when g is smooth, if the dimension of X is even moderate, accurate nonparametric estimation of its density is not feasible at the sample sizes often encountered in applications. In fact, to the best of our knowledge, this new HOIF estimator remains the only semiparametric efficient estimator of $ψ$ under minimal conditions, despite the rapidly growing literature on causal effect estimation. We also show that our estimator can be generalized to the entire class of functionals considered by Robins et al. (2008) which include the average effect of a treatment on a response Y when a vector X suffices to control confounding and the expected conditional variance of a response Y given a vector X. Simulation experiments are also conducted, which demonstrate that our new estimator outperforms those of Robins et al. (2008, 2017) in finite samples, when g is not very smooth.

math.ST↗

arXiv2025

Minimax Semiparametric Learning With Approximate Sparsity

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of parameters are precisely non-zero. This excludes models where linear formulations only approximate the underlying data distribution, such as nonparametric regression methods that use basis expansion such as splines, kernel methods or polynomial regressions. Many recent methods for root-$n$ estimation have been proposed, but the implications of exact model sparsity remain largely unexplored. In particular, minimax optimality for models that are not exactly sparse has not yet been developed. This paper formalizes the concept of approximate sparsity through classical semi-parametric theory. We derive minimax rates under this formulation for a regression slope and an average derivative, finding these bounds to be substantially larger than those in low-dimensional, semi-parametric settings. We identify several new phenomena. We discover new regimes where rate double robustness does not hold, yet root-$n$ estimation is still possible. In these settings, we propose an estimator that achieves minimax optimal rates. Our findings further reveal distinct optimality boundaries for ordered versus unordered nonparametric regression estimation.

math.ST↗

arXiv2025

Identification of Treatment Effects under Limited Exogenous Variation

Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. With control variables to correct for endogeneity, nonparametric identification of treatment effects requires strong support conditions. To alleviate this requirement, we consider varying coefficients specifications for the conditional expectation function of the outcome given a treatment and control variables. This function is expressed as a linear combination of either known functions of the treatment, with unknown coefficients varying with the controls, or known functions of the controls, with unknown coefficients varying with the treatment. We use this modeling approach to give necessary and sufficient conditions for identification of average treatment effects. A sufficient condition for identification is conditional nonsingularity, that the second moment matrix of the known functions given the variable in the varying coefficients is nonsingular with probability one. For known treatment functions with sufficient variation, we find that triangular models with discrete instrument cannot identify average treatment effects when the number of support points for the instrument is less than the number of coefficients. For known functions of the controls, we find that average treatment effects can be identified in general nonseparable triangular models with binary or discrete instruments. We extend our analysis to flexible models of increasing dimension and relate conditional nonsingularity to the full support condition of Imbens and Newey (2009), thereby embedding semi- and non-parametric identification into a common framework.

econ.EM↗

arXiv2024

Panel Estimation of Taxable Income Elasticities with Heterogeneity and Endogenous Budget Sets

This paper introduces an estimator for the average of heterogeneous elasticities of taxable income (ETI), addressing key econometric challenges posed by nonlinear budget sets. Building on an isoelastic utility framework, we derive a linear-in-logs taxable income specification that incorporates the entire budget set while allowing for individual-specific ETI and productivity growth. To account for endogenous budget sets, we employ panel data and estimate individual-specific ridge regressions, constructing a debiased average of ridge coefficients to obtain the average ETI.

econ.EM↗

arXiv2024

Conditional Influence Functions

There are many nonparametric objects of interest that are a function of a conditional distribution. One important example is an average treatment effect conditional on a subset of covariates. Many of these objects have a conditional influence function that generalizes the classical influence function of a functional of a (unconditional) distribution. Conditional influence functions have important uses analogous to those of the classical influence function. They can be used to construct Neyman orthogonal estimating equations for conditional objects of interest that depend on high dimensional regressions. They can be used to formulate local policy effects and describe the effect of local misspecification on conditional objects of interest. We derive conditional influence functions for functionals of conditional means and other features of the conditional distribution of an outcome variable. We show how these can be used for locally linear estimation of conditional objects of interest. We give rate conditions for first step machine learners to have no effect on asymptotic distributions of locally linear estimators. We also give a general construction of Neyman orthogonal estimating equations for conditional objects of interest.

math.ST↗

arXiv2024

Automatic Debiased Machine Learning via Riesz Regression

A variety of interesting parameters may depend on high dimensional regressions. Machine learning can be used to estimate such parameters. However estimators based on machine learners can be severely biased by regularization and/or model selection. Debiased machine learning uses Neyman orthogonal estimating equations to reduce such biases. Debiased machine learning generally requires estimation of unknown Riesz representers. A primary innovation of this paper is to provide Riesz regression estimators of Riesz representers that depend on the parameter of interest, rather than explicit formulae, and that can employ any machine learner, including neural nets and random forests. End-to-end algorithms emerge where the researcher chooses the parameter of interest and the machine learner and the debiasing follows automatically. Another innovation here is debiased machine learners of parameters depending on generalized regressions, including high-dimensional generalized linear models. An empirical example of automatic debiased machine learning using neural nets is given. We find in Monte Carlo examples that automatic debiasing sometimes performs better than debiasing via inverse propensity scores and never worse. Finite sample mean square error bounds for Riesz regression estimators and asymptotic theory are also given.

math.ST↗

arXiv2024

Efficient Bias Correction for Cross-section and Panel Data

Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.

econ.EM↗

arXiv2022

A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees

Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is $n^{-1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.

stat.ML↗

arXiv2022

RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests

Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. $\sqrt{n}$-consistent and asymptotically normal estimation of the object of interest requires debiasing to reduce the effects of regularization and/or model selection on the object of interest. Debiasing is typically achieved by adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality. We implement an automatic debiasing procedure based on automatically learning the Riesz representation of the linear functional using Neural Nets and Random Forests. Our method only relies on black-box evaluation oracle access to the linear functional and does not require knowledge of its analytic form. We propose a multitasking Neural Net debiasing method with stochastic gradient descent minimization of a combined Riesz representer and regression loss, while sharing representation layers for the two functions. We also propose a Random Forest method which learns a locally linear representation of the Riesz function. Even though our method applies to arbitrary functionals, we experimentally find that it performs well compared to the state of art neural net based algorithm of Shi et al. (2019) for the case of the average treatment effect functional. We also evaluate our method on the problem of estimating average marginal effects with continuous treatments, using semi-synthetic data of gasoline price changes on gasoline demand.

cs.LG↗

arXiv2022

Constrained Conditional Moment Restriction Models

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. We find in Monte Carlo examples that the critical values are conservatively accurate and that tests about objects of interest have good power relative to unrestricted GMM.

math.ST↗

arXiv2021

Heterogeneous Coefficients, Control Variables, and Identification of Multiple Treatment Effects

Multidimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the heterogeneous coefficients are mean independent from treatments given the controls, a simple identification condition is that the generalized propensity scores (Imbens, 2000) be bounded away from zero and that their sum be bounded away from one, with probability one. Our analysis extends to distributional and quantile treatment effects, as well as corresponding treatment effects on the treated. These results generalize the classical identification result of Rosenbaum and Rubin (1983) for binary treatments.

econ.EM↗

arXiv2021

The Influence Function of Semiparametric Estimators

Many useful parameters depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, constructing debiased machine learning estimators, in efficiency comparisons, and in formulating primitive regularity conditions for asymptotic normality, We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application.

stat.ME↗

arXiv2020

Locally Robust Semiparametric Estimation

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps. We show that orthogonal moment functions can be constructed by adding to identifying moments the nonparametric influence function for the effect of the first step on identifying moments. Orthogonal moments reduce model selection and regularization bias, as is very important in many applications, especially for machine learning first steps. We give debiased machine learning estimators of functionals of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that adding to identifying moments the nonparametric influence function provides a general construction of orthogonal moments, including regularity conditions, and show that the nonparametric influence function is robust to additional unknown functions on which it depends. We give a general approach to estimating the unknown functions in the nonparametric influence function and use it to automatically debias estimators of functionals of high dimensional conditional location learners. We give a variety of new doubly robust moment equations and characterize double robustness. We give general and simple regularity conditions and apply these for asymptotic inference on functionals of high dimensional regression quantiles and dynamic discrete choice parameters with high dimensional state variables.

math.ST↗

arXiv2019

Testing the Drift-Diffusion Model

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that corresponds to that boundary. This model has been widely used in psychology, neuroeconomics, and neuroscience to explain the observed patterns of choice and response times in a range of binary choice decision problems. This paper provides a statistical test for DDM's with general boundaries. We first prove a characterization theorem: we find a condition on choice probabilities that is satisfied if and only if the choice probabilities are generated by some DDM. Moreover, we show that the drift and the boundary are uniquely identified. We then use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic.

econ.EM↗

arXiv2018

Cross-Fitting and Fast Remainder Rates for Semiparametric Estimation

There are many interesting and widely used estimators of a functional with finite semiparametric variance bound that depend on nonparametric estimators of nuisance functions. We use cross-fitting (i.e. sample splitting) to construct novel estimators with fast remainder rates. We give cross-fit doubly robust estimators that use separate subsamples to estimate different nuisance functions. We obtain general, precise results for regression spline estimation of average linear functionals of conditional expectations with a finite semiparametric variance bound. We show that a cross-fit doubly robust spline regression estimator of the expected conditional covariance is semiparametric efficient under minimal conditions. Cross-fit doubly robust estimators of other average linear functionals of a conditional expectation are shown to have the fastest known remainder rates for the Haar basis or under certain smoothness conditions. Surprisingly, the cross-fit plug-in estimator also has nearly the fastest known remainder rate, but the remainder converges to zero slower than the cross-fit doubly robust estimator. As specific examples we consider the expected conditional covariance, mean with randomly missing data, and a weighted average derivative.

math.ST↗