Demian Pouzo

Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; others use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly non-compact infinite dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.

Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments

This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are identified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important applications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.

Optimal Taxation with Endogenous Default under Incomplete Markets

In a dynamic economy, we characterize the fiscal policy of the government when it levies distortionary taxes and issues defaultable bonds to finance its stochastic expenditure. Default may occur in equilibrium as it prevents the government from incurring in future tax distortions that would come along with the service of the debt. Households anticipate the possibility of default generating endogenous credit limits. These limits hinder the governments ability to smooth taxes using debt, implying more volatile and less serially correlated fiscal policies, higher borrowing costs and lower levels of indebtedness. In order to exit temporary financial autarky following a default event, the government has to repay a random fraction of the defaulted debt. We show that the optimal fiscal and renegotiation policies have implications aligned with the data.

Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff-relevant consequences as a function of actions. We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. We provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.

Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension

This paper establishes consistency of the weighted bootstrap for quadratic forms

RETROSPECTIVE VOTING AND PARTY POLARIZATION: RETROSPECTIVE VOTING AND PARTY POLARIZATION

\left( n^{-1/2} \sum_{i=1}^{n} Z_{i,n} \right)^{T}\left( n^{-1/2} \sum_{i=1}^{n} Z_{i,n} \right)

Maximum Likelihood Estimation in Possibly Misspecified Dynamic Models with Time Inhomogeneous Markov Regimes

where

A Framework for Modeling Bounded Rationality: Mis-Specified Bayesian-Markov Decision Processes

(Z_{i,n})_{i=1}^{n}

Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals

are mean zero, independent

Estimation and model selection of semiparametric multivariate survival functions under general censorship

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