Moment Restriction-based Econometric Methods: An Overview

Moment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters, this will provide semiparametric estimates or tests. If we use the score to construct moment restrictions to estimate finite dimensional parameters, this yields maximum likelihood (ML) estimates. Semiparametric or nonparametric settings based on moment restrictions have been the main concern in the literature, and comprise the most important and interesting topics. The purpose of this special issue on “Moment Restriction-based Econometric Methods” is to highlight some areas in which novel econometric methods have contributed significantly to the analysis of moment restrictions, specifically asymptotic theory for nonparametric regression with spatial data, a control variate method for stationary processes, method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models, properties of the CUE estimator and a modification with moments, finite sample properties of alternative estimators of coefficients in a structural equation with many instruments, instrumental variable estimation in the presence of many moment conditions, estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments, moment-based estimation of smooth transition regression models with endogenous variables, a consistent nonparametric test for nonlinear causality, and linear programming-based estimators in simple linear regression.Moment restrictions; Parametric; semiparametric and nonparametric methods; Estimation; Testing; Robustness; Model misspecification

Moment Restriction-based Econometric Methods: An Overview

Moment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters, this will provide semiparametric estimates or tests. If we use the score to construct moment restrictions to estimate finite dimensional parameters, this yields maximum likelihood (ML) estimates. Semiparametric or nonparametric settings based on moment restrictions have been the main concern in the literature, and comprise the most important and interesting topics. The purpose of this special issue on “Moment Restriction-based Econometric Methods†is to highlight some areas in which novel econometric methods have contributed significantly to the analysis of moment restrictions, specifically asymptotic theory for nonparametric regression with spatial data, a control variate method for stationary processes, method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models, properties of the CUE estimator and a modification with moments, finite sample properties of alternative estimators of coefficients in a structural equation with many instruments, instrumental variable estimation in the presence of many moment conditions, estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments, moment-based estimation of smooth transition regression models with endogenous variables, a consistent nonparametric test for nonlinear causality, and linear programming-based estimators in simple linear regression.robustness;testing;estimation;model misspecification;moment restrictions;parametric;semiparametric and nonparametric methods

Dynamic probabilities of restrictions in state space models: An application to the Phillips curve

Empirical macroeconomists are increasingly using models (e.g. regressions or Vector Autoregressions) where the parameters vary over time. State space methods are frequently used to specify the evolution of parameters in such models. In any application, there are typically restrictions on the parameters that a researcher might be interested in. This motivates the question of how to calculate the probability that a restriction holds at a point in time without assuming the restriction holds at all (or any other) points in time. This paper develops methods to answer this question. In particular, the principle of the Savage-Dickey density ratio is used to obtain the time-varying posterior probabilities of restrictions. We use our methods in a macroeconomic application involving the Phillips curve. Macroeconomists are interested in whether the long-run Phillips curve is vertical. This is a restriction for which we can calculate the posterior probability using our methods. Using U.S. data, the probability that this restriction holds tends to be fairly high, but decreases slightly over time (apart from a slight peak in the late 1970s). We also calculate the probability that another restriction, that the NAIRU is not identied, holds. The probability that it holds uctuates over time with most evidence in favor of the restriction occurring after 1990.Bayesian, state space model, Savage-Dickey density ratio, time varying parameter model.

Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness

This paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite dimensional unobservable. To analyze the economic restriction, we employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may test the economic restriction by considering quantiles of linear combinations of the dependent variable. For this hypothesis we develop a new empirical process based test that applies kernel quantile estimators, and derive its large sample behavior. We investigate the performance of the test in a simulation study. Finally, we apply all concepts to Canadian individual data, and show that rationality is an acceptable description of actual individual behavior.

Special features of RAD Sequencing data:implications for genotyping

Restriction site-associated DNA Sequencing (RAD-Seq) is an economical and efficient method for SNP discovery and genotyping. As with other sequencing-by-synthesis methods, RAD-Seq produces stochastic count data and requires sensitive analysis to develop or genotype markers accurately. We show that there are several sources of bias specific to RAD-Seq that are not explicitly addressed by current genotyping tools, namely restriction fragment bias, restriction site heterozygosity and PCR GC content bias. We explore the performance of existing analysis tools given these biases and discuss approaches to limiting or handling biases in RAD-Seq data. While these biases need to be taken seriously, we believe RAD loci affected by them can be excluded or processed with relative ease in most cases and that most RAD loci will be accurately genotyped by existing tools

Risk Aversion in a Dynamic Trading Game

The effect of risk aversion on Nash equilibrium trade restrictions is studied using numerical methods. An increase in a nation's level of risk aversion can lead to either an increase or decrease in its equilibrium restriction and either an increase or decrease in its rival's restriction. The linear quadratic dynamic game is generalized to include risk aversion.International Relations/Trade,

Quantifying Privacy: A Novel Entropy-Based Measure of Disclosure Risk

It is well recognised that data mining and statistical analysis pose a serious treat to privacy. This is true for financial, medical, criminal and marketing research. Numerous techniques have been proposed to protect privacy, including restriction and data modification. Recently proposed privacy models such as differential privacy and k-anonymity received a lot of attention and for the latter there are now several improvements of the original scheme, each removing some security shortcomings of the previous one. However, the challenge lies in evaluating and comparing privacy provided by various techniques. In this paper we propose a novel entropy based security measure that can be applied to any generalisation, restriction or data modification technique. We use our measure to empirically evaluate and compare a few popular methods, namely query restriction, sampling and noise addition.Comment: 20 pages, 4 figure