A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information

In order to better understand the economy and conduct policy analysis, both econometricians and decision makers are interested in effective inferences using econometric models. Because of the complexity of economic data, econometricians heavily rely on asymptotic theory when making statistical inferences. However, the use of asymptotic approximations to the distributions of test statistics and estimators is not always successful. This paper illustrates the use of the Kullback-Leibler information (KLI) measure to assess the relative quality of two asymptotic approximations to an unknown distribution from which we can obtain simple random drawings. The illustration involves comparing the large-sample and small-disturbance asymptotic distributions under the null hypothesis of a t statistic from the dynamic linear regression model. We find convincing evidence in favour of the use of p values and critical values from the small-disturbance Student's t distribution, rather than from the large-sample standard normal distribution, in this case. This simple KLI measure has considerable potential. For example, it can guide us to conditions under which asymptotic approximations are reasonable and to circumstances when it may be inappropriate to rely totally on asymptotic approximations.