Andriy Norets
Assistant Professor at the Economics Department
Princeton University
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Contact Information Personal Information Research Interests |
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Work in progress
“Credibility
of confidence sets in nonstandard econometric problems,” with Ulrich Mueller.
“Posterior consistency and concentration rates in Kullback-Leibler divergence with applications to misspecified infinite dimensional models”.
Research Papers
·
Dynamic Discrete Choice Models
·
Bayesian Nonparametrics
and Flexible Modeling
Dynamic Discrete Choice Models
“Semiparametric Inference in Dynamic Binary Choice Models,” pdf, with Xun Tang (revision requested by
the Review of Economic Studies).
We
introduce an approach for semiparametric inference in
dynamic binary choice models that does not impose distributional assumptions on
the state variables unobserved by the econometrician. The proposed framework
combines Bayesian inference with semiparametric
identification results. The method is
also applicable to estimation of dynamic binary action games of incomplete
information. We demonstrate the method
on Rust's model of bus engine replacement and a dynamic game-theoretic model of
firms' entry and exit. The estimation
experiments show that the parametric assumptions about the distribution of the
unobserved states can have a considerable effect on the estimates of per-period
payoffs. At the same time, the effect of
these assumptions on counterfactual conditional choice probabilities can be
small for most of the observed states.
An
extension of the proposed method to dynamic multinomial choice models is here: pdf.
“On the Surjectivity
of the Mapping between Utilities and Choice Probabilities,” 2012, pdf, with Satoru Takahashi
This
note considers a standard multinomial choice model. It is shown that if the distribution of
additive utility shocks has a density then the mapping from deterministic
components of utilities to choice probabilities is surjective. In other words, any vector of choice
probabilities can be obtained by selecting suitable utilities for alternatives. This result has implications for at least
three areas of interest to econometricians: Hotz and
Miller (1993) estimator for structural dynamic discrete choice models,
nonparametric identification of multinomial choice models, and consistency of
conditional density estimators based on covariate dependent mixtures.
“Continuity and Differentiability of Expected Value
Functions in Dynamic Discrete Choice Models,” pdf, Quantitative
Economics 1 (2010), pp. 305-322.
This
paper explores the properties of expected value functions in dynamic discrete
choice models. The continuity with
respect to state variables and parameters and the differentiability with
respect to state variables are established in this paper under fairly general
conditions. The differentiability with
respect to parameters is proved when some state variables do not affect the
state transition probabilities and thus the expected value functions. The paper shows that such variables are needed
in order to apply the implicit function theorem used in the proof. The results of the paper are of particular
relevance to estimable dynamic discrete choice models.
“Inference in Dynamic
Discrete Choice Models with Serially Correlated Unobserved State Variables,” pdf, Econometrica, Vol. 77, No. 5
(September, 2009), pp. 1665–1682.
Web Supplement with proofs: pdf
This
paper develops a method for inference in dynamic discrete choice models with
serially correlated unobserved state variables.
Estimation of these models involves computing high-dimensional integrals
that are present in the solution to the dynamic program and in the likelihood
function. First, the paper proposes a Bayesian Markov Chain Monte Carlo
estimation procedure that can handle the problem of multidimensional
integration in the likelihood function. Second, the paper presents an efficient
algorithm for solving the dynamic program suitable for use in conjunction with
the proposed estimation procedure.
“Implementation of Bayesian
Inference in Dynamic Discrete Choice Models,” 2008, pdf.
This
paper experimentally evaluates a recently developed methodology for Bayesian
inference in dynamic discrete choice models.
It provides a sequence of steps for implementation of reliable and
computationally efficient estimation procedure.
The experiments are conducted on a model with serially correlated
unobserved state variables.
“Estimation of Dynamic
Discrete Choice Models Using Artificial Neural Network Approximations,” pdf, 2012,
Econometric Reviews, Volume 31, Issue 1, pp. 84-106.
I propose a method for inference in dynamic discrete choice models (DDCM) that utilizes Markov chain Monte Carlo (MCMC) and artificial neural networks (ANN). MCMC is intended to handle high-dimensional integration in the likelihood function of richly specified DDCMs. ANNs approximate the dynamic program (DP) solution as a function of the parameters and state variables prior to estimation to avoid having to solve the DP on each iteration. Potential applications of the proposed methodology include inference in DDCMs with random coefficients, serially correlated unobservables, and dependence across individual observations. The paper discusses MCMC estimation of DDCMs, provides relevant background on ANNs, and derives a theoretical justification for the method. Experiments suggest this to be a promising approach.
Bayesian Nonparametrics and
Flexible Modeling
“Bayesian
regression with nonparametric heteroskedasticity,”
2011, submitted, pdf.
This paper presents a large sample justification for a semiparametric Bayesian approach to inference in a linear regression model. The approach is to model the distribution of the error term by a normal distribution with the variance that is a flexible function of covariates. It is shown that even when the data generating distribution of the error term is not normal the posterior distribution of the linear coefficients converges to a normal distribution with the mean equal to the asymptotically efficient estimator and the variance given by the semiparametric efficiency bound. This implies that the estimation procedure is robust and conservative from the Bayesian standpoint and at the same time it can be used as an implementation of semiparametrically efficient frequentist inference.
“Posterior
consistency in conditional density estimation by covariate dependent mixtures,”
2011, with Justinas Pelenis,
revision requested by Econometric Theory, pdf.
This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel stick-breaking processes for modeling the mixing probabilities. We show that the posterior in these two models is weakly and strongly consistent for a large class of data generating processes.
“Approximation of conditional densities by smooth
mixtures of regressions,” pdf, 2010, Annals of
Statistics, 38(3), pp. 1733-1766.
This paper shows that large non-parametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and variances and mixing probabilities can depend on variables in the conditioning set (covariates.) These models are a special case of models known as mixtures of experts in statistics and computer science literature. Flexible specifications include models in which only mixing probabilities, modeled by multinomial logit, depend on the covariates and, in the univariate case, models in which only means of the mixed normals depend flexibly on the covariates. Modeling the variance of the mixed normals by flexible functions of the covariates can weaken restrictions on the class of the approximable densities. Rates of convergence and easy to interpret bounds are also obtained for different model specifications. These approximation results can be useful for proving consistency of Bayesian and maximum likelihood density estimators based on these models. The results also have interesting implications for applied researchers.
“Bayesian
modeling of joint and conditional distributions”, with Justinas Pelenis,
pdf,
web appendix,
Journal of Econometrics, Volume 168, Issue 2, June 2012, pp. 332–346.
In
this paper we propose a Bayesian approach to flexible modeling of conditional
distributions. The approach uses a
flexible model for the joint distribution of the dependent and independent
variables and then extracts the conditional distributions of interest from the
estimated joint distribution. We use a
finite mixture of multivariate normals to estimate
the joint distribution. The conditional
distributions can then be assessed analytically or through simulations. The discrete variables are handled through
the use of latent variables. The
estimation procedure employs an MCMC algorithm.
We provide a frequentist justification of the
method: the Bayesian estimator of the density is consistent in the total
variation distance. The method can be
used as a heteroscedasticity and non-linearity robust
regression model with discrete and continuous dependent and independent
variables and as a Bayesian alternative to quantile
and kernel regression.
Miscellaneous
“MCMC estimation of a
finite beta mixture,” 2010, pdf, Matlab
code, with Xun Tang.
We describe an efficient Markov chain Monte Carlo algorithm for estimation of a finite beta mixture. The algorithm employs Metropolis-Hastings independence chain for simulation of the parameters of beta distributions. The Metropolis-Hastings transition densities that well approximate the target distributions are constructed from the limiting sampling distribution of the method of moments estimator, which is readily available for beta distribution. This technique can be useful for other models with analytically tractable method of moments estimators. The algorithm demonstrated excellent performance in a Monte-Carlo study.
Teaching
· Econometric Theory I, Part I
· Undergraduate introductory econometrics