Inference in the presence of redundant moment conditions and the impact of government health expenditure on health outcomes in England

Abstract

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 estimation 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 associated inference techniques based on first order asymptotic theory, such as confidence intervals and overidentifying restriction tests, deteriorates as the number of redundant moment conditions increases. However, it is shown that bootstrap procedures can provide reliable inferences. We use IM and bootstrap methods to perform inference about the impact of government health expenditure on health outcomes in England.

The impact of NHS expenditure on health outcomes in England: Alternative approaches to identification in all‐cause and disease specific models of mortality

“…Andrews et al (, p. 31) note that each PCT's annual allocation of health expenditure could be expressed as where (a) the age index reflects the demographic profile of the local population; (b) the additional needs index reflects local deprivation and other factors likely to influence the need for health care; (c) the input price index reflects prices in the local health economy; and (d) the distance from target (DFT) index reflects how far each PCT's actual allocation is from its target allocation. The four index adjustments all take a mean value of one (Andrews et al, , p. 31).…”

“…The health outcome equation estimated by both Claxton et al (, ) and Andrews et al () is of the form where expenditure is likely to be endogenous, the controls reflect the need for health care expenditure, and e reflects everything not included elsewhere in the specification. As controls, Claxton et al (, ) use a small number census based indicators of deprivation (e.g., the proportion of lone parent households), whereas Andrews et al () use measures of education deprivation and income deprivation in older people. The use of different controls by the two research teams is considered to be of relatively little importance.…”

“…Andrews, Elamin, Hall, Kyriakoulis, and Sutton () use a very similar dataset but a rather different estimation approach. Rather than estimate disease‐specific elasticities, Andrews et al () directly estimate the all‐cause elasticity of mortality with respect to total health expenditure.…”

“…Andrews, Elamin, Hall, Kyriakoulis, and Sutton () use a very similar dataset but a rather different estimation approach. Rather than estimate disease‐specific elasticities, Andrews et al () directly estimate the all‐cause elasticity of mortality with respect to total health expenditure. The estimation of this (all programme) outcome elasticity is complicated by the fact that expenditure (both in total and for individual programmes) is likely to be endogenous and, therefore, should be instrumented.…”

Econometricians Have Their Moments: GMM at 32

“…See Andrews et al . () for further discussion and an empirical illustration of where these differences are important for estimation of a policy parameter.…”