Chernozhukov, Victor
Overview
Works: 
124
works in
193
publications in
1
language and
383
library holdings

Roles: 
Author, Other, Editor

Classifications: 
HB1,
330.072 
Most widely held works by
Victor Chernozhukov
Quantile regression under misspecification with an application to the U.S. wage structure by Joshua David Angrist (
Book
)
11
editions published
in
2004
in
English
and held by
41
libraries
worldwide
Quantile regression(QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR can be interpreted as minimizing a weighted meansquared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile correlation concept, similar to the relationship between partial correlation and OLS. We also derive general asymptotic results for QR processes allowing for misspecification of the conditional quantile function, extending earlier results from a single quantile to the entire process. The approximation properties of QR are illustrated through an analysis of the wage structure and residual inequality in US Census data for 1980, 1990, and 2000. The results suggest continued residual inequality growth in the 1990s, primarily in the upper half of the wage distribution and for college graduates
Learning and disagreement in an uncertain world by Daron Acemoglu (
Book
)
9
editions published
in
2006
in
English
and held by
22
libraries
worldwide
Most economic analyses presume that there are limited differences in the prior beliefs of individuals, as assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with different priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the literature establish that when individuals are certain about the interpretation of signals, under very mild conditions there will be asymptotic agreementtheir assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the interpretation of signals, meaning that they have nondegenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we prove the following results: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteriors about the underlying parameter will fail to converge. (3) Observing the same sequence of signals may lead to a divergence of opinion rather than the typically presumed convergence. We then characterize the conditions for asymptotic agreement under "approximate certainty"i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has "rapidlyvarying tails" (such as the normal or exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of probability distributions has "regularlyvarying tails" (such as the Pareto, the lognormal, and the tdistributions), asymptotic agreement does not obtain even in the limit
Bootstrap confidence sets under model misspecification by Mayya Zhilova (
file
)
1
edition published
in
2015
in
English
and held by
16
libraries
worldwide
Quantile regression with censoring and endogeneity by Victor Chernozhukov (
Book
)
9
editions published
in
2011
in
English
and held by
9
libraries
worldwide
In this paper, we develop a new censored quantile instrumental variable (CQIV)estimator and describe its properties and computation. The CQIV estimator combines Powell(1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol
Inference on counterfactual distributions by Victor Chernozhukov (
Computer File
)
5
editions published
between
2008
and
2013
in
English
and held by
5
libraries
worldwide
In this paper we develop procedures for performing inference in regression models about how potential policy interventions affect the entire marginal distribution of an outcome of interest. These policy interventions consist of either changes in the distribution of covariates related to the outcome holding the conditional distribution of the outcome given covariates fixed, or changes in the conditional distribution of the outcome given covariates holding the marginal distribution of the covariates fixed. Under either of these assumptions, we obtain uniformly consistent estimates and functional central limit theorems for the counterfactual and status quo marginal distributions of the outcome as well as other functionvalued effects of the policy, including, for example, the effects of the policy on the marginal distribution function, quantile function, and other related functionals. We construct simultaneous confidence sets for these functions; these sets take into account the sampling variation in the estimation of the relationship between the outcome and covariates. Our procedures rely on, and our theory covers, all main regression approaches for modeling and estimating conditional distributions, focusing especially on classical, quantile, duration, and distribution regressions. Our procedures are general and accommodate both simple unitary changes in the values of a given covariate as well as changes in the distribution of the covariates or the conditional distribution of the outcome given covariates of general form. We apply the procedures to examine the effects of labor market institutions on the U.S. wage distribution. Keywords: Policy effects, counterfactual distribution, quantile regression, duration regression, distribution regression. JEL Classifications: C14, C21, C41, J31, J71
Program evaluation with highdimensional data
(
file
)
4
editions published
between
2013
and
2015
in
English
and held by
4
libraries
worldwide
We consider estimation of policy relevant treatment effects in a datarich environ ment where there may be many more control variables available than there are observations. In addition to allowing many control variables, the setting we consider allows heterogeneous treatment effects, endogenous receipt of treatment, and functionvalued outcomes. To make informative inference possible, we assume that reduced form predictive relationships are approx imately sparse. That is, we require that the relationship between the covariates and the outcome, treatment status, and instrument status can be captured up to a small approximation error using a small number of controls whose identities are unknown to the researcher. This condition allows estimation and inference for a wide variety of treatment parameters to proceed after selection of an appropriate set of control variables formed by selecting controls separately for each reduced form relationship and then appropriately combining this set of reduced form predictive models and associated selected controls. We provide conditions under which postselection inference is uniformly valid across a widerange of models and show that a key condition underlying uniform validity of postselection inference allowing for imperfect model selection is the use of approximately unbiased estimating equations. We illustrate the use of the proposed treatment effect estimation methods with an application to estimating the effect of 401(k) participation on accumulated assets
Inference on parameter sets in econometric models by Victor Chernozhukov (
Book
)
2
editions published
in
2006
in
English
and held by
4
libraries
worldwide
This paper provides confidence regions for minima of an econometric criterion function Q([theta]). The minima form a set of parameters, [theta]I, called the identified set. In economic applications, [theta]I represents a class of economic models that are consistent with the data. Our inference procedures are criterion function based and so our confidence regions, which cover [theta]I with a prespecified probability, are appropriate level sets of Qn([theta]), the sample analog of Q([theta]). When [theta]I is a singleton, our confidence sets reduce to the conventional confidence regions based on inverting the likelihood or other criterion functions. We show that our procedure is valid under general yet simple conditions, and we provide feasible resampling procedure for implementing the approach in practice. We then show that these general conditions hold in a wide class of parametric econometric models. In order to verify the conditions, we develop methods of analyzing the asymptotic behavior of econometric criterion functions under set identification and also characterize the rates of convergence of the confidence regions to the identified set. We apply our methods to regressions with in terval data and set identified method of moments problems. We illustrate our methods in an empirical Monte Carlo study based on Current Population Survey data. Keywords: Set estimator, level sets, interval regression, subsampling bootsrap. JEL Classifications: C13, C14, C21, C41, C51, C53
Improving point and interval estimates of monotone functions by rearrangement by Victor Chernozhukov (
Book
)
2
editions published
between
2007
and
2008
in
English
and held by
4
libraries
worldwide
Suppose that a target function ... is monotonic, namely, weakly increasing, and an original estimate of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. The improvement property of the rearrangement also extends to the construction of confidence bands for monotone functions. Suppose we have the lower and upper endpoint functions of a simultaneous confidence interval that covers the target function with a prespecified probability level, then the rearranged confidence interval, defined by the rearranged lower and upper endpoint functions, is shorter in length in common norms than the original interval and covers the target function with probability greater or equal to the prespecified level. We illustrate the results with a computational example and an empirical example dealing with ageheight growth charts. Keywords: Monotone function, improved estimation, improved inference, multivariate rearrangement, univariate rearrangement, Lorentz inequalities, growth chart, quantile regression, mean regression, series, locally linear, kernel methods. JEL Classifications: 62G08, 46F10, 62F35, 62P10
Posterior inference in curved exponential families under increasing dimensions by Alexandre Belloni (
Book
)
2
editions published
between
2007
and
2013
in
English
and held by
3
libraries
worldwide
N this work we study the large sample properties of the posteriorbased inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions, such as moment restrictions, on the model, and plays a fundamental role in various branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties of estimation and inference procedures based on the posterior. We also discuss the multinomial model with moment restrictions, which arises in a variety of econometric applications. In our analysis, both the parameter dimension and the number of moments are increasing with the sample size. Keywords: Bayesian Infrence, Frequentist Properties. JEL Classifications: C13, C51, C53, D11, D21, D44
Inference for extremal conditional quantile models, with an application to market and birthweight risks by Victor Chernozhukov (
Computer File
)
3
editions published
in
2011
in
English
and held by
3
libraries
worldwide
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional valueatrisk, production efficiency, and adjustment bands in (S, s) models. In this paper we provide feasible inference tools for extremal conditional quantile models that rely upon extreme value approximations to the distribution of selfnormalized quantile regression statistics. The methods are simple to implement and can be of independent interest even in the nonregression case. We illustrate the results with two empirical examples analyzing extreme fluctuations of a stock return and extremely low percentiles of live infants' birth weights in the range between 250 and 1500 grams
Inference on treatment effects after selection amongst highdimensional controls by Alexandre Belloni (
Computer File
)
3
editions published
between
2012
and
2013
in
English
and held by
3
libraries
worldwide
We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly nonGaussian and heteroscedastic disturbances where the number of controls may be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "postdoubleselection" method. Our results apply to Lassotype methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard postmodel selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates. Keywords: treatment effects, partially linear model, highdimensionalsparse regression, inference under imperfect model selection, uniformly valid inference after model selection. JEL Classification: C10, C51
Conditional valueatrisk : aspects of modeling and estimation by Victor Chernozhukov (
Book
)
2
editions published
in
2000
in
English
and held by
3
libraries
worldwide
This paper considers flexible conditional (regression) measures of market risk. ValueatRisk modeling is cast in terms of the quantile regression function  the inverse of the conditional distribution function. A basic specification analysis relates its functional forms to the benchmark models of returns and asset pricing. We stress important aspects of measuring very high and intermediate conditional risk. An empirical application illustrates. Keywords: Conditional Quantiles, Quantile Regression, Extreme Quantiles, Extreme Value Theory, Extreme Risk. JEL Classifications: C14, C13, C21, C51, C53, G12, G19
Conditional quantile processes based on series or many regressors by Alexandre Belloni (
Computer File
)
3
editions published
in
2011
in
English
and held by
3
libraries
worldwide
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantilespecific coefficients and estimate the functionvalued coefficients from the data. We develop large sample theory for the empirical QR coefficient process, namely we obtain uniform strong approximations to the empirical QR coefficient process by conditionally pivotal and Gaussian processes, as well as by gradient and weighted bootstrap processes. We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence, large sample distributions, and inference methods based on strong pivotal and Gaussian approximations and on gradient and weighted bootstraps. All of the above results are for functionvalued parameters, holding uniformly in both the quantile index and in the covariate value, and covering the pointwise case as a byproduct. If the function of interest is monotone, we show how to use monotonization procedures to improve estimation and inference. We demonstrate the practical utility of these results with an empirical example, where we estimate the price elasticity function of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption. Keywords: quantile regression series processes, uniform inference. JEL Classifications: C12, C13, C14
Symposium on transportation methods
(
Book
)
1
edition published
in
2010
in
English
and held by
3
libraries
worldwide
Intersection bounds : estimation and inference by Victor Chernozhukov (
Computer File
)
3
editions published
between
2009
and
2012
in
English
and held by
3
libraries
worldwide
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased infinite samples, routinely underestimating the size of the identified set, we also offer a medianbiascorrected estimator of such bounds as a natural byproduct of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernelbased empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus nonDonsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.  Bound analysis ; conditional moments ; partial identification ; strong approximation ; infinite dimensional constraints ; linear programming ; concentration inequalities ; anticoncentration inequalities ; nonDonsker empirical process methods ; moderate deviations ; adaptive moment selection
Local identification of nonparametric and semiparametric models
(
Computer File
)
3
editions published
between
2011
and
2012
in
English
and held by
3
libraries
worldwide
In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models, singleindex IV models, and semiparametric consumptionbased asset pricing models
Identification and efficient semiparametric estimation of a dynamic discrete game by Patrick L Bajari (
Book
)
4
editions published
in
2015
in
English
and held by
3
libraries
worldwide
In this paper, we study the identification and estimation of a dynamic discrete game allowing for discrete or continuous state variables. We first provide a general nonparametric identification result under the imposition of an exclusion restriction on agent payoffs. Next we analyze large sample statistical properties of nonparametric and semiparametric estimators for the econometric dynamic game model. We also show how to achieve semiparametric efficiency of dynamic discrete choice models using a sieve based conditional moment framework. Numerical simulations are used to demonstrate the finite sample properties of the dynamic game estimators. An empirical application to the dynamic demand of the potato chip market shows that this technique can provide a useful tool to distinguish long term demand from short term demand by heterogeneous consumers
Symposium on computation on nash equilibria in finite games
(
Book
)
1
edition published
in
2010
in
English
and held by
2
libraries
worldwide
Extremal quantities and valueatrisk by Victor Chernozhukov (
Book
)
1
edition published
in
2006
in
English
and held by
2
libraries
worldwide
This article looks at the theory and empirics of extremal quantiles in economics, in particular valueatrisk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings in the last 20 years. In the discussion, we put a particular focus on conditional extremal quantile models and methods, which have applications in many areas of economic analysis. Examples of applications include the analysis of factors of high risk in finance and risk management, the analysis of socioeconomic factors that contribute to extremely low infant birthweights, efficiency analysis in industrial organization, the analysis of reservation rules in economic decisions, and inference in structural auction models. Keywords: Extremes, Quantiles, Regression, Valueatrisk, Extremal Bootstrap. JEL Classifications: C13, C14, C21, C41, C51, C53
On the computational complexity of MCMCbased estimators in large samples by Alexandre Belloni (
Book
)
1
edition published
in
2007
in
English
and held by
2
libraries
worldwide
This paper studies the computational complexity of Bayesian and quasiBayesian estimation in large samples carried out using a basic Metropolis random walk. The framework covers cases where the underlying likelihood or extremum criterion function is possibly nonconcave, discontinuous, and of increasing dimension. Using a central limit framework to provide structural restrictions for the problem, it is shown that the algorithm is computationally efficient. Specifically, it is shown that the running time of the algorithm in large samples is bounded in probability by a polynomial in the parameter dimension d, and in particular is of stochastic order d2 in the leading cases after the burnin period. The reason is that, in large samples, a central limit theorem implies that the posterior or quasiposterior approaches a normal density, which restricts the deviations from continuity and concavity in a specific manner, so that the computational complexity is polynomial. An application to exponential and curved exponential families of increasing dimension is given. Keywords: Computational Complexity, Metropolis, Large Samples, Sampling, Integration, Exponential family, Moment restrictions. JEL Classifications: C1, C11, C15, C6, C63
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Alternative Names
Chernozhukov, V.
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