Instrumental variable methods in structural equation models

Abstract

Instrumental variable regression (RegIV) provides a means for detecting and correcting parameter bias in causal models. Widely used in economics, recently several papers have highlighted its potential utility for ecological applications. Little attention has thus far been paid to the fact that IV methods can also be implemented within structural equation models (SEMIV). In this paper I present the motivations, requirements and basic procedures for using SEMIV. I first consider causal inference and IVs from the perspective of a randomized experiment with partial control of the cause of interest. I consider common sources of bias, the role of randomization and limits to its capacity to exclude bias. Sources of bias include omitted confounders, reciprocal causation, reverse causation and measurement error, all of which can all be seen as a single problem—endogeneity. The approach to estimating IV models most commonly used in econometric practice, two-stage least squares regression (2SLS), is explained, followed by a brief exposition of the covariance modelling approach used in SEM. Using data from an ecological field experiment, I illustrate the use of the treatment variable as an IV and then illustrate procedures for evaluating candidate variables that might serve as additional IVs. IV methods are shown to be useful for both detecting endogeneity and removing its influences. I illustrate some of the ways that bias can be generated, as well as diagnostic capabilities and means for remedy embedded within SEM. Procedures for screening and evaluating additional IVs reveal valuable lessons regarding the theoretical requirements and empirical standards for IVs. SEMIV provides a useful way to detect and control for bias. I suggest that the use of IVs within the SEM framework can support the simultaneous pursuit of causal inference and explanatory modelling, a common pair of aspirations for ecologists. Moving forward, there is a need for a better understanding of the capabilities of SEMIV and requirements for successful application.