DYNAMIC PANEL ANDERSON-HSIAO ESTIMATION WITH ROOTS NEAR UNITY

Limit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson–Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample sizen→ ∞. But whenT→ ∞, either for fixednor asn→ ∞, IV is$\sqrt T$consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy asn→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T) → ∞ with no restriction on the divergence rates ofnandT.When the common autoregressive root$\rho = 1 + c/\sqrt T$the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is$\sqrt n$consistent for fixedTand$\sqrt {nT}$consistent with limit distributionN(0, 4) when (n,T) → ∞ sequentially or jointly. These results are robust for common roots of the formρ= 1+c/Tγfor allγ∈ (0, 1) and joint convergence holds. Limit normality holds but the variance changes whenγ= 1. Whenγ> 1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.

Statistical Analysis of Ratio of Random Variables and Its Application in Performance Analysis of Multihop Wireless Transmissions

The distributions of random variables are of interest in many areas of science. In this paper, the probability density function (PDF) and cumulative distribution function (CDF) of ratio of products of two random variables and random variable are derived. Random variables are described with Rayleigh, Nakagami-m, Weibull, andα-μdistributions. An application of obtained results in performance analysis of multihop wireless communication systems in different transmission environments described in detail. The proposed mathematical analysis is also complemented by various graphically presented numerical results.

A Note on Confidence Intervals in Cost-Effectiveness Analysis

How to obtain confidence intervals for cost-effectiveness ratios is complicated by the statistical problems of obtaining a confidence interval for a ratio of random variables. Different approaches have been suggested in the literature, but no consensus has been reached. We propose an alternative simple solution to this problem. By multiplying the effectiveness units by the price per effectiveness unit, both costs and benefits can be expressed in monetary terms and standard statistical techniques can be used to estimate a confidence interval for net benefits. This approach avoids the ratio estimation problem and explicitly recognizes that the price per effectiveness unit has to be known to provide cost-effectiveness analysis with a useful decision rule.