Andriy Norets
Assistant Professor at the Economics Department
Princeton University
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Contact Information Personal Information Research Interests |
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Research Papers
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Dynamic Discrete Choice Models
Dynamic Discrete Choice Models
“Inference in
Dynamic Discrete Choice Models with Serially Correlated Unobserved State
Variables,” pdf, Econometrica,
Vol. 77, No. 5 (September, 2009), 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,
submitted.
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,”
2007, pdf,
submitted.
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.
“Continuity
and Differentiability of Expected Value Functions in Dynamic Discrete Choice
Models,” pdf,
submitted.
This
paper explores properties of expected value functions in dynamic discrete
choice models. The continuity with
respect to state variables and parameters and 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 existence of such variables is shown to
be implied by the implicit function theorem used in the proof. The results of the paper are of particular
relevance to estimable dynamic discrete choice models.
Flexible Bayesian Modeling
“Bayesian
modeling of joint and conditional distributions”, with Justinas Pelenis,”
submitted, pdf,
web appendix.
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.
“Approximation
of conditional densities by smooth mixtures of regressions,”
pdf, 2009,
forthcoming in the Annals of Statistics.
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.
Miscellaneous
“Heterogeneity in income processes,”
with Sam Schulhofer-Wohl,
coming soon.
Macroeconomists
are increasingly interested in heterogeneity in individuals' preferences and in
the income risk that they face. Previous
empirical papers have focused on only one or a few aspects of heterogeneity. In this paper, we estimate the entire joint
distribution of risk preferences and income processes. Our model allows individual-specific trends,
persistence and volatility of income and permits all of these characteristics
to be correlated with the individual's risk preferences. We find substantial heterogeneity in all
parameters of the income process. These findings potentially have substantial
implications for the conclusions of microfounded macro models.