SADDLEPOINT APPROXIMATIONS FOR THE ESTIMATOR ON A LAGGED DEPENDENT VARIABLE

The estimator of the coefficient on a lagged dependent variable in the linear regression model is known to be a ratio of non-central quadratic forms. This paper provides a saddlepoint approximation for its finite sample density and distribution, under the assumption of Gaussian errors. By providing an explicit asymptotic order of error for the approximation, its inferential and methodological usefulness is significantly extended. Asymptotically the approximation remains valid under more general error assumptions and, crucially, upon consistent estimation of the noncentrality. Numerical experiments demonstrate the high accuracy of the approximation.