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

MIMIC modelling with instrumental variables: A 2SLS-MIMIC approach