This paper considers simulation-based procedures to compute the Wald encompassing and the Cox test statistics for non-nested models. These simulation estimation procedures are applied to both the encompassing contrast and its covariance matrix in the case of a Wald non-nested test statistic, and both the numerator and the denominator in the Cox test statistic. The proposed procedures are illustrated by the example of comparing a linear with a log-linear model. Monte Carlo studies are conducted for both examples and the results indicate that with simulated covariance matrices, the small sample behaviour of both test statistics is close to that of their asymptotic distributions.
In examining China's exchange rate policy in the reforming years, the study finds empirical evidence of its long-run inflationary consequences, but the effects appear not to be sizable. In the short run, while changes in the devaluation rate are positively correlated with the increase in the growth rate of inflation, the inflation inertia is also modest. The moderate inflationary cost of devaluations provides some explanation of the smooth transition of exchange rate policy regime in China and the authorities' ability to put more weight on external competitiveness.
The exponentially tilted family of densities is used to discuss the relationship between the encompassing principle and the M-test or conditional moment testing principle. It is shown that the two principles are capable of generating the same test statistics and in this sense equivalent. However, there are differences in motivation and emphasis underlying the principles that are important in econometric modeling. In addition, parsimonious encompassing interpretations for test statistics, including those of Cox (1961, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability I, pp. 105-123; 1962, Journal of the Royal Statistical Society, Series B 24, 406-424) and Atkinson (1970, Journal of the Royal Statistical Society, Series B 32, 323-344) are provided.
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