Indirect inference for stochastic volatility models via the log-squared observations.

Model; Models; Stochastic volatility; Volatility;

Asymptotic properties of GMM estimators of stochastic volatility.

Estimator; Stochastic volatility; Volatility;

The Information Matrix Test with Bootstrap-Based Covariance Matrix Estimation

We propose an information matrix test in which the covariance matrix of the vector of indicators is estimated using the parametric bootstrap. Monte Carlo results and heuristic arguments show that its small sample performance is comparable with that of the efficient score form.

The information matrix test with bootstrap-based covariance matrix estimation.

We propose an information matrix test in which the covariance matrix of the vector of indicators is estimated using the parametric bootstrap. Monte Carlo results and heuristic arguments show that its small sample performance is comparable with that of the efficient score form.Covariance; Information; Matrix;

Split-panel jackknife estimation of fixed-effect models

We propose a jackknife for reducing the order of the bias of maximum likelihood estimates of nonlinear dynamic fixed-effect panel models. In its simplest form, the half-panel jackknife, the estimatorisjust 2θˆ−θ1/2,where θˆ!istheMLEfromthefullpaneland θ1/2 istheaverageofthe two half-panel MLEs, each using T/2 time periods and all N cross-sectional units. This estimatoreliminates the first-order bias of θˆ . The order of the bias is further reduced if two partitions of the panel are used, for example, two half-panels and three 1/3-panels, and the corresponding MLEs.On further partitioning the panel, any order of bias reduction can be achieved. The split-panel jackknife estimators are asymptotically normal, centered at the true value, with variance equal to that of the MLE under asymptotics where T is allowed to grow slowly with N. In analogous fashion, the split-panel jackknife reduces the bias of the profile likelihood and the bias of marginal-effect estimates. Simulations in fixed-effect dynamic discrete-choice models with small T show that the split-panel jackknife effectively reduces the bias and mean squared error of the MLE, and yields confidence intervals with much better coverage.jackknife, asymptotic bias correction, dynamic panel data, fixed effects

Asymptotic Results for GMM Estimators of Stochastic Volatility Models

We derive closed-form expressions for the optimal weighting matrix for GMM estimation of the stochastic volatility model with AR(1) log-volatility, and for the asymptotic covariance matrix of the resulting estimator. The moment conditions considered are generated by the absolute observations (which is the standard approach in this literature) or by the log-squared observations. We use the expressions to compare the performances of GMM and other estimators that have been proposed, and to optimally select small sets of moment conditions from very large sets.Stochastic volatility, GMM

Sequential reciprocity in two-player, two-stage games: An experimental analysis.

We experimentally test Dufwenberg and Kirchsteiger’s (2004) theory of sequential reciprocity in a sequential prisoner’s dilemma (SPD) and a mini-ultimatum game (MUG). Data on behavior and first- and second-order beliefs allow us to classify each subject’s behavior as a material best response, a reciprocity best response, both, or none. We found that in both games the behavior of about 80% of the firstmovers was a material best response, a reciprocity best response, or both. The remaining 20% of first-movers almost always made choices that were “too kind” according to the theory of reciprocity. Secondmover behavior, in both games, was fully in line with the predictions of the theory. The average behavior and beliefs across subjects were compatible with a sequential reciprocity equilibrium in the SPD but not in the MUG. We also found first- and second-order beliefs to be unbiased in the SPD and nearly unbiased in the MUG.Sequential reciprocity; Sequential prisoner’s dilemma; Mini-ultimatum game;

Specification and Testing of Models Estimated by Quadrature

This paper proposes a test to check the specification of models with unobserved individual effects integrated out by quadrature and also a simple way of increasing the flexibility of this type of model. The results of a Monte Carlo study and an application using a well-known data set illustrate the finite sample properties of the proposed methods and their implementation in practice.

Testing the Information Matrix Equality with Robust Estimators

We study the behaviour of the information matrix (IM) test when maximum likelihood estimators are replaced with robust estimators. The latter may unmask outliers and hence improve the power of the test. We investigate in detail the local asymptotic power of the IM test in the normal model, for various estimators and under a range of local alternatives. These local alternatives include contamination neighbourhoods, Student's t (with degrees of freedom approaching infinity), skewness, and a tilted normal. Simulation studies for fixed alternatives confirm that in many cases the use of robust estimators substantially increases the power of the IM test.