This paper examines testing for AR(1) disturbances against MA(1) disturbances in the linear regression model. A Monte Carlo experiment compares the small-sample properties of the Cox test, some linearized Cox tests, and an approximate point optimal test, as well as a Lagrange multiplier test of AR (1) disturbances against ARM A (1,1) disturbances. The main findings are that the true sizes of the asymptotic non-nested tests can differ considerably from their nominal sizes, the Lagrange multiplier test's sizes are reasonably accurate and the point optimal test is generally more powerful than the other tests when appropriate critical values are used. When sizes are controlled at an arbitrary value of the AR (1) parameter, the relative power of the Cox test is increased substantially.

Michael McAleer, Gordon Fisher, Paul Volker, Separate Misspecified Regressions and the U.S. Long-Run Demand for Money Function, The Review of Economics and Statistics, Vol. 64, No. 4 (Nov., 1982), pp. 572-583

Extreme bounds analysis attempts to measure the effects of the uncertainty in the specification of the explanatory variables in a regression model on the estimated coefficients of interest. Standard errors for the stochastic extreme bounds are computed using the bootstrap technique. State-by-state cross section data are used to study the deterrent effect of capital punishment in the United States in 1950. The bootstrap standard errors are sufficiently large for some bounds to suggest caution in the interpretation of the empirical results regarding the fragility of inferences for the deterrent effect of capital punishment.

L. G. Godfrey, Michael McAleer, C. R. McKenzie, Variable Addition and Lagrange Multiplier Tests for Linear and Logarithmic Regression Models, The Review of Economics and Statistics, Vol. 70, No. 3 (Aug., 1988), pp. 492-503