  Multiple Indicators Multiple Causes (MIMIC) models are type of structural
equation models, a theory-based approach to confirm the influence of a set of
exogenous causal variables on the latent variable, and also the effect of the
latent variable on observed indicator variables. In a common MIMIC model,
multiple indicators reflect the underlying latent variables/factors, and the
multiple causes (observed predictors) affect latent variables/factors. Basic
assumptions of MIMIC are clearly violated in case of a variable being both an
indicator and a cause, i.e. in the presence of reverse causality. Furthermore,
the model is then unidentified. To resolve the situation, which can arise
frequently, and as MIMIC estimation lacks closed form solutions for parameters
we utilize a version of Bollen's (1996) 2SLS estimator for structural equation
models combined with J\"oreskog (1970)'s method of the analysis of covariance
structures to derive a new, 2SLS estimator for MIMIC models. Our 2SLS empirical
estimation is based on static MIMIC specification but we point also to
dynamic/error-correction MIMIC specification and 2SLS solution for it. We
derive basic asymptotic theory for static 2SLS-MIMIC, present a simulation
study and apply findings to an interesting empirical case of estimating
precarious status of older workers (using dataset of Survey of Health, Ageing
and Retirement in Europe) which solves an important issue of the definition of
precarious work as a multidimensional concept, not modelled adequately so far.
