Noise Ratio As a Non-Nested Model Selection Tool.

Abstract

In this dissertation, we analyze whether the noise ratio statistic of Durlauf and Hall (1989), NRT, can be used as a non-nested model selection tool in a similar fashion to the Rivers and Vuong (2002) framework. For this purpose, we first show that, when scaled by the sample size T, NRT is distributed as a mixture of chi-square random variables, under a null hypothesis of correct specification. Further, we study the asymptotic distribution of functionals of this statistic for model selection purposes, under different assumptions about: i)model specification and ii) the data generating processes of two non-nested RE models, whose parameter vector is estimated either by GMM, in Chapter 1, or by the continuous updating estimator in Chapter 2. In Chapter 3, we use Monte-Carlo simulations to compute the empirical size and empirical power of tests with statistics whose limiting distributions were studied in Chapters 1 and 2 of this dissertation. First, we use a simulation routine and compute the rejection frequency of the tests developed using these statistics, which represents empirical size under a null hypothesis and power under an alternative. Under our null hypothesis, both models are equally good from a goodness of fit perspective. Under the first alternative, the first model is better and under the second alternative hypothesis, the second model is better from a goodness of fit perspective, that. Under all scenarios covered in the first chapter, we use the limit of the noise ratio statistic evaluated at the probability limit of the GMM estimator as our goodness of fit measure. Finally, in Chapter 4, we use the model selection methodology used in Chapter 1 for comparing different formulations of the pure production smoothing model of inventories. The particular models compared are the production smoothing model of inventories and a variant of it covered in Durlauf and Maccini (1995). All statistics used for model comparison are evaluated at the GMM estimator for the corresponding model i = 1; 2.