Inference in the Presence of Redundant Moment Conditions and the Impact of Government Health Expenditure on Health Outcomes in England

In his 1999 paper with Breusch, Qian and Wyhowski in the Journal of Econometrics, Peter Schmidt introduced the concept of “redundant” moment conditions. Such conditions arise when estimation is based on moment conditions that are valid and can be divided into two sub-sets: one that identifies the parameters and another that provides no further information. Their framework highlights an important concept in the moment-based esti- mation literature namely, that not all valid moment conditions need be informative about the parameters of interest. In this paper, we demonstrate the empirical relevance of the concept in the context of the impact of government health expenditure on health outcomes in England. Using a simulation study calibrated to this data, we perform a comparative study of the finite performance of inference procedures based on Generalized Method of Moment (GMM) and info-metric (IM) estimators. The results indicate that the properties of GMM procedures deteriorate as the number of redundant moment conditions increases; in contrast the IM methods provide reliable point estimators but the performance of as- sociated inference techniques based on first order asymptotic theory, such as confidence intervals and overidentifying restriction tests, deteriorates as the number of redundant mo- ment conditions increases. However, for IM methods, it is shown that bootstrap procedures can provide reliable inferences; we illustrate such methods when analysing the impact of government health expenditure on health outcomes in England.