Article

# Approximately Exact Inference in Dynamic Panel Models

• ##### Yianna Tchopourian
Society for Computational Economics, Computing in Economics and Finance 2006 01/2006;
Source: RePEc

ABSTRACT This paper develops a general method for conducting exact small-sample inference in models which allow the estimator of the (scalar) parameter of interest to be expressed as the root of an estimating function, and which is particularly simple to implement for linear models with a covariance matrix depending on a single parameter. The method involves the computation of tail probabilities of the estimating function. In the context of dynamic panel models, both the least squares and maximum likelihood paradigms give rise to estimating functions involving sums of ratios in quadratic forms in normal variates, the distribution of which cannot be straightforwardly computed. We overcome this obstacle by deriving a saddlepoint approximation that is both readily evaluated and remarkably accurate. A simulation study demonstrates the validity of the procedure, and shows the resulting estimators to be vastly superior over existing ones

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• ##### Article: Infereni on full or partial parameters based on the standardized signed log likelihood ratio
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ABSTRACT: Suppose that a random sample of size n is drawn from a statistical model ℳ of probability density p(x;ω) where the parameter ω is assumed to be uniquely expressed by χ∈R d and Ψ∈R f . Let ω ^ be the maximum likelihood estimator of ω under ℳ and let 1(ω) be the log likelihood. Further let ℳ Ψ be a submodel obtained by fixing Ψ in ℳ. Suppose that (ω ^,a 0 ) is minimal sufficient under ℳ such that a 0 is approximately ancillary and the conditional density of ω ^ for given a 0 satisfies p(ω ^;ω|a 0 )=[const·|j(ω ^)| 1/2 exp{l(ω)-l(ω ^)}][1+O(n -3/2 )] where j(ω)=∂ 2 l(ω)/∂ω∂ω t . Then it is shown in this paper that there exists a statistic r Ψ * of dimension f under ℳ Ψ which follows f-dimensional normal distribution N(0,I) to relative order O(n -3/2 ). This is used to get confidence regions for the partial parameter Ψ, independently of the nuisance parameter χ. When f=1, r Ψ * is obtained by adjusting the mean and variance of the signed log likelihood ratio statistic given by {sgn(Ψ ^-Ψ)}[2{l(ω ^)-l(χ ^ Ψ ,Ψ)}] 1/2 , where χ ^ Ψ stands for the maximum likelihood estimator of χ under the model ℳ Ψ .
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