Closed forms for asymptotic bias and variance in autoregressive models with unit roots

AbstractFor a first-order autoregressive AR(1) model with zero initial value, xt = αxt−1 + εt, we provide closed-form analytical expressions for the asymptotic bias and variance of the maximum likelihood (ML) estimator α = ∑1n xtxt−1∑1n−1 xt2 when ¦α¦ = 1. For the bias, numerical accuracy of up to six significant digits is achieved for sample sizes n > 100

Nonparametric kernel estimation of econometric parameters

Includes bibliographical references (p. 9-10)

Nonhomogeneous Production Functions and Applications to Telecommunications

A form of nonhomogeneous production function is utilized to compute marginal productivities, various elasticities, optimum input ratios, and the like, for different levels of inputs and outputs. Such comparisons are relevant for labor negotiations, capital investment, and control by either a parent corporation or a government regulatory agency. This form of production function can be fitted by simple regression and allows variable returns to scale and variable elasticities of substitution.

Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value

For a first-order autoregressive AR(1) model with zero initial value, x i = ax i−1 ,_, + e i, we provide the bias, mean squared error, skewness, and kurtosis of the maximum likelihood estimator â. Brownian motion approximations by Phillips (1977, Econometrica 45, 463–485; 1978, Biometrika 65, 91–98; 1987, Econometrica 55, 277–301), Phillips and Perron (1988, Biometrika 75, 335–346), and Perron (1991, Econometric Theory 7, 236–252; 1991, Econometrica 59, 211–236), among others, yield an elegant unified theory but do not yield convenient formulas for calibration of skewness and kurtosis. In addition to the usual stationary case |α|