Semiparametric Estimation of Markov Decision Processeswith Continuous State Space

We propose a general two-step estimation method for the structural parameters ofpopular semiparametric Markovian discrete choice models that include a class ofMarkovian Games andallow for continuous observable state space. The estimation procedure is simpleas it directly generalizes the computationally attractive methodology of Pesendorferand Schmidt-Dengler (2008) that assumed finite observable states. This extensionis non-trivial as the value functions, to be estimated nonparametrically in the firststage, are defined recursively in a non-linear functional equation. Utilizingstructural assumptions, we show how to consistently estimate the infinitedimensional parameters as the solution to some type II integral equations, thesolving of which is a well-posed problem. We provide sufficient set of primitives toobtain root-T consistent estimators for the finite dimensional structural parametersand the distribution theory for the value functions in a time series framework.Discrete Markov Decision Models, Kernel Smoothing, Markovian Games, Semi-parametric Estimation, Well-Posed Inverse Problem.D

Essays on semiparametric estimation of Markov decision processes.

Dynamic models of forward looking agents, whose goal is to maximize expected in-tertemporal payoffs, are useful modelling frameworks in economics. With an exception of a small class of dynamic decision processes, the estimation of the primitives in these models is computationally burdensome due to the presence of the value functions that has no closed form. We follow a popular two-step approach which estimates the functions of interest rather than use direct numerical approximation. The first chapter, joint with Oliver Linton, considers a class of dynamic discrete choice models that contain observable continuously distributed state variables. Most papers on the estimation of dynamic discrete choice models assume that the observable state variables can only take finitely many values. We show that the extension to the infinite dimensional case leads to a well-posed inverse problem. We derive the distribution theory for the finite and the infinite dimensional parameters. Dynamic models with continuous choice can sometimes avoid the numerical issues related to the value function through the use of Euler's equation. The second chapter considers models with continuous choice that do not necessarily belong to the Euler class but frequently arise in applied problems. In this chapter, a class of minimum distance estimators is proposed, their distribution theory along with the infinite dimensional parameters of the decision models are derived. The third chapter demonstrates how the methodology developed for the discrete and continuous choice problems can be adapted to estimate a variety of other dynamic models. The final chapter discusses an important problem, and provides an example, where some well-known estimation procedures in the literature may fail to consistently estimate an identified model. The estimation methodologies I propose in the preceding chapters may not suffer from the problems of this kind

Analyzing subjective well-being data with misclassification

We use novel nonparametric techniques to test for the presence of non-classical measurement error in reported life satisfaction (LS) and study the potential effects from ignoring it. Our dataset comes from Wave 3 of the UK Understanding Society that is surveyed from 35,000 British households. Our test finds evidence of measurement error in reported LS for the entire dataset as well as for 26 out of 32 socioeconomic subgroups in the sample. We estimate the joint distribution of reported and latent LS nonparametrically in order to understand the misreporting behavior. We show this distribution can then be used to estimate parametric models of latent LS. We find measurement error bias is not severe enough to distort the main drivers of LS. But there is an important difference that is policy relevant. We find women tend to over-report their latent LS relative to men. This may help explain the gender puzzle that questions why women are reportedly happier than men despite being worse off on objective outcomes such as income and employment

Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales

Econometric analyses in the happiness literature typically use subjective well-being (SWB) data to compare the mean of observed or latent happiness across samples. Recent critiques show that comparing the mean of ordinal data is only valid under strong assumptions that are usually rejected by SWB data. This leads to an open question whether much of the empirical studies in the economics of happiness literature have been futile. In order to salvage some of the prior results and avoid future issues, we suggest regression analysis of SWB (and other ordinal data) should focus on the median rather than the mean. Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique. We use GSS data to show the famous Easterlin Paradox from the happiness literature holds for the US independent of any parametric assumption

Estimating bayesian decision problems with heterogeneous expertise

We consider the recent novel two-step estimator of Iaryczower and Shum (American Economic Review 2012; 102: 202–237), who analyze voting decisions of US Supreme Court justices. Motivated by the underlying theoretical voting model, we suggest that where the data under consideration display variation in the common prior, estimates of the structural parameters based on their methodology should generally benefit from including interaction terms between individual and time covariates in the first stage whenever there is individual heterogeneity in expertise. We show numerically, via simulation and re-estimation of the US Supreme Court data, that the first-order interaction effects that appear in the theoretical model can have an important empirical implication. Copyright © 2015 John Wiley & Sons, Ltd

Joint Analysis of the Discount Factor and Payoff Parameters in Dynamic Discrete Choice Models

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the discount factor to be known. We show the knowledge of the discount factor is not necessary to identify parts, or even all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. On the other hand it is known the payo¤ function cannot be nonparametrically identified without any a priori restrictions. Our identification of the discount factor is robust to any normalization choice on the payoff parameters. In IO applications normalizations are usually made on switching costs, such as entry costs and scrap values. We also show that switching costs can be nonparametrically identified, in closed-form, independently of the discount factor and other parts of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. We illustrate with a Monte Carlo study and the dataset used in Ryan (2012)

Nonparametric Euler equation identification and estimation

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators

Minimum Distance Estimation of Search Costs using Price Distribution

Hong and Shum (2006) show equilibrium restrictions in a search model can be used to identify quantiles of the search cost distribution from observed prices alone. These quantiles can be difficult to estimate in practice. This paper uses a minimum distance approach to estimate them that is easy to compute. A version of our estimator is a solution to a nonlinear least squares problem that can be straightforwardly programmed on softwares such as STATA. We show our estimator is consistent and has an asymptotic normal distribution. Its distribution can be consistently estimated by a bootstrap. Our estimator can be used to estimate the cost distribution nonparametrically on a larger support when prices from heterogeneous markets are available. We propose a two-step sieve estimator for that case. The first step estimates quantiles from each market. They are used in the second step as generated variables to perform nonparametric sieve estimation. We derive the uniform rate of convergence of the sieve estimator that can be used to quantify the errors incurred from interpolating data across markets. To illustrate we use online bookmaking odds for English football leagues' matches (as prices) and find evidence that suggests search costs for consumers have fallen following a change in the British law that allows gambling operators to advertise more widely

Estimation of structural optimization models: a note on identification

Bajari, Benkard and Levin (2007) propose an estimation methodology for a broad class of dynamic optimization problems. To carry out their procedure, one needs to select a set of alternative policy functions and compare the implied expected payoffs with that from the data. We show that this can generally lead to objective functions that are not capable of consistently estimating an identified model