The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

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Econometric Analysis of Cross Section and Panel Data

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum simulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. No other book incorporates all these fields, which have arisen in the past 20 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

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Discrete Choice Methods with Simulation

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

We consider a class of nonparametric time series regression models in which the regressor takes values in a sequence space and the data are stationary and weakly dependent. We propose an infinite dimensional Nadaraya-Watson type estimator with a bandwidth sequence that shrinks the effects of long lags. We investigate its asymptotic properties in detail under both static and dynamic regressions contexts. First we show pointwise consistency of the estimator under a set of mild regularity conditions. We establish a CLT for the estimator at a point under stronger conditions as well as for a feasibly studentized version of the estimator, thereby allowing pointwise inference to be conducted. We establish the uniform consistency over a compact set of logarithmically increasing dimension. We specify the explicit rates of convergence in terms of the Lambert W function, and show that the optimal rate that balances the squared bias and variance is of logarithmic order, the precise rate depending on the smoothness of the regression function and the dependence of the data in a non-trivial way.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2807757_code2260635.pdf?abstractid=2766822&mirid=3

Nonparametric Estimation of Infinite Order Regression and Its Application to the Risk-Return Tradeoff

Dynamic portfolio choice has been a central and essential objective for institutional investors in active asset management. In this paper, we study the dynamic portfolio choice with multiple conditioning variables, where the number of the conditioning variables can be either fixed or di- verging to infinity at certain polynomial rate of the sample size. We propose a novel data-driven method to estimate the optimal portfolio choice, motivated by the model averaging marginal regression approach suggested by Li, Linton and Lu (2015). More specifically, in order to avoid the curse of dimensionality associated with multivariate nonparametric regression problem and to make it practically implementable, we first estimate the marginal optimal portfolio choice by maximising the conditional utility function for each univariate conditioning variable, and then construct the joint dynamic optimal portfolio through the weighted average of the marginal optimal portfolio across all the conditioning variables. Under some regularity conditions, we establish the large sample properties for the developed portfolio choice procedure. Both simulation studies and an empirical application well demonstrate the performance of the proposed methodology.

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Semiparametric Dynamic Portfolio Choice with Multiple Conditioning Variables

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the high-frequency data contaminated by microstructure noise, we introduce a localised pre-averaging estimation method that reduces the effective magnitude of the noise. We then use the estimation tool developed in the noise-free scenario, and derive the uniform convergence rates for the developed spot volatility matrix estimator. We further combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector. In addition, we consider large spot volatility matrix estimation in time-varying factor models with observable risk factors and derive the uniform convergence property. We provide numerical studies including simulation and empirical application to examine the performance of the proposed estimation methods in finite samples.

Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

We propose a general framework for the specification testing of continuous treatment effect models. We assume a general residual function, which includes the average and quantile treatment effect models as special cases. The null models are identified under the confoundedness condition and contain a nonparametric weighting function. We propose a test statistic for the null model in which the weighting function is estimated by solving an expanding set of moment equations. We establish the asymptotic distributions of our test statistic under the null hypothesis and under fixed and local alternatives. The proposed test statistic is shown to be more efficient than that constructed from the true weighting function and can detect local alternatives deviated from the null models at the rate of $O_{P}(N^{-1/2})$. A simulation method is provided to approximate the null distribution of the test statistic. Monte-Carlo simulations show that our test exhibits a satisfactory finite-sample performance, and an application shows its practical value.

Oliver Linton

Papers

Nonparametric Estimation of Infinite Order Regression and Its Application to the Risk-Return Tradeoff

Semiparametric Dynamic Portfolio Choice with Multiple Conditioning Variables

Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

A Unified Framework for Specification Tests of Continuous Treatment Effect Models

Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form