"Monte Carlo experimentation in econometrics helps ‘solve’ deterministic problems by simulating stochastic analogues in which the analytical unknowns are reformulated as parameters to be estimated." (Hendry (1980)) With that in mind, Monte Carlo studies may be divided operationally into three phases: design, simulation, and post-simulation analysis. This paper provides a guide to the last of those three, post-simulation analysis, given the design and simulation of a Monte Carlo study, and uses Pesaran's (1974) study of statistics for testing non-nested hypotheses to illustrate the techniques described. A statistic is derived for testing for significant deviations between the asymptotic and (observed) finite sample properties. Further, that statistic provides the basis for analysing discrepancies between the finite sample and asymptotic properties using response surfaces. The results for Pesaran's study indicate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Finally, a method is proposed for adjusting the finite sample sizes of different test statistics so that comparisons of their power may be made. Extensions to other finite sample properties are indicated.

This paper develops Instrumental Variables statistics for testing non-nested hypotheses when the hypotheses considered are single equations from a system of linear dynamic simultaneous equations. Asymptotic distributions of those statistics and of comparable Maximum Likelihood statistics are derived under the null hypothesis, a local non-nested alternative hypothesis, and a local “comprehensive” alternative hypothesis. The asymptotic powers of the non-nested hypothesis tests are compared with those of tests of nested hypotheses, and a numerical application is given.

In a recent article, Aneuryn-Evans and Deaton propose asymptotic formulae for analysing Monte Carlo studies of the Cox statistics for testing non-nested hypotheses. This note shows the invalidity of those formulae by demonstrating that, in general, the Cox statistics do not have a singular joint asymptotic distribution.

Using Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses. Simple numerical-analytical formulae (response surfaces) are obtained which closely approximate the statistics' unknown size and power functions for a dynamic simultaneous-equations model. The analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties. Two practical results arise. The F form and the Wald statistic is favored over its chi-squared form, and "large-sigma" and small "effective" sample size strongly affect the test of over-identifying restrictions and the Cox-type test. Copyright 1991 by The Econometric Society.

Yock Y. Chong and David F. Hendry (1986) propose the concept of forecast encompassing--the lack of additional information in another model's forecasts. The corresponding test statistic is based on the regression of one model's forecast errors on the other model's forecasts. This paper generalizes Chong and Hendry's statistic to include sets of dynamic nonlinear models with uncertain estimated coefficients generating multistep forecasts with possibly systematic biases. Using stochastic simulation, the generalized statistic is applied to forecasts over 1985Q1-1987Q4 from six models of the U.S. merchandise trade balance, revealing misspecification in all models. Copyright 1993 by MIT Press.

This paper evaluates an empirical model of U.K. money demand developed by Milton Friedman and Anna J. Schwartz in Monetary Trends in the United States and the United Kingdom. Testing reveals misspecification and hence the potential for an improved model. Using recursive procedures on their annual data, we obtain a better-fitting, constant, dynamic error-correction (cointegration) model. Results on exogeneity and encompassing imply that our money demand model is interpretable as a model of money but not of prices, since its constancy holds only conditionally on contemporaneous prices.