The thirteen essays: in this volume have been written by the students of Professor Peter C. B. Phillips to recognize, honor, and demonstrate his impact on the practice of econometrics. These writings span parts of Phillips' seminal and enormous research program. His students have continued to work in the areas he helped initiate.

The first section of essays deals with higher-order asymptotics. In “Edgeworth Expansions for the Wald and GMM Statistics for Nonlinear Restrictions,” Hansen derives an Edgeworth expansion for the generalized method of moments (GMM) distance statistic for a real-valued, nonlinear restriction on a normal linear regression. He also provides a refinement of the Edgeworth expansion for the Wald statistic derived by Park and Phillips (1988) and shows that the leading coefficient is the same in these two expansions. This establishes that, to the order of approximation of the Edgeworth expansion, the GMM distance statistic has a better approximation to the chi-square distribution than does the Wald statistic. Finally, the essay updates the Monte Carlo simulation of Gregory and Veall (1985) to include both heteroskedasticity-robust covariance matrix estimation and the GMM distance statistic. He finds that if the robust covariance matrix is calculated under the null, the GMM statistic has near-perfect finite sample Type I error in his experiments – even in sample sizes as small as n = 20.