PANEL UNIT ROOT TESTS WITH CROSS-SECTION DEPENDENCE: A FURTHER INVESTIGATION

An effective way to control for cross-section correlation when conducting a panel unit root test is to remove the common factors from the data. However, there remain many ways to use the defactored residuals to construct a test. In this paper, we use the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) residuals to form two new tests. One estimates the pooled autoregressive coefficient, and one simply uses a sample moment. We establish their large-sample properties using a joint limit theory. We find that when the pooled autoregressive root is estimated using data detrended by least squares, the tests have no power. This result holds regardless of how the data are defactored. All PANIC-based pooled tests have nontrivial power because of the way the linear trend is removed.

A Perturbation Technique for Sample Moment Matching in Kernel Density Estimation

Summary The fundamental idea of kernel smoothing technique can be recognized as one-parameter data perturbation with a smooth density. The usual kernel density estimates might not match arbitrary sample moments calculated from the unsmoothed data. A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation. It is shown that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments. Moreover, the pointwise rate of MISE of the resulting density estimates remains optimal. Relevant simulation studies are carried out to demonstrate the usefulness and other features of this technique.

Semiparametric IV Estimation with Parameter Dependent Instruments

A well-known result in the method of moments literature is that the efficient instruments for the estimation of a model are functions of the conditional expectation of its gradient. Some recent studies have suggested the nonparametric estimation of these instruments when they are of unknown functional form. When these instruments in turn depend on the unknown parameters it has been suggested that these be replaced by preliminary consistent estimates. It is shown here that solving the sample moment equations simultaneously over the instruments and the residuals of the model will generally produce the same asymptotic efficiency and avoid the disadvantages inherent with the use of preliminary estimates.

Strong consistencies of the bootstrap moments

LetXbe a real valued random variable withE|X|r+δ<∞for some positive integerrand real number,δ,0<δ≤r, and let{X,X1,X2,…}be a sequence of independent, identically distributed random variables. In this note, we prove that, for almost allw∈Ω,μr;n*(w)→μrwith probability1. iflimn→∞infm(n)n−β>0for someβ>r−δr+δ, whereμr;n*is the bootstraprthsample moment of the bootstrap sample some with sample sizem(n)from the data set{X,X1,…,Xn}andμris therthmoment ofX. The results obtained here not only improve on those of Athreya [3] but also the proof is more elementary.