regression - Solving a system of equations by 2SLS method in econometrics using R

Question

My longitudinal clinical study focusses on the predictors of quality of life in patients. We know that when patients are given medicine, their symptoms improve and so does their quality of life. But, there may be other predictors that influence quality of life.

I was asked by my supervisor to perform a two-stage least squares (2SLS) as an estimation method for a simultaneous equation model. This would be for the equations for whether a patient is on medication (binary variable - yes or no; 1 or 0) and quality of life of the patient (continuous variable that is bound between 0 and 1; 0 is worst health and 1 is best health):

medicine (y) = a + bage + csex etc.

quality of life (z) = a + dmedicine + fage + gsex etc.

Here, the binary variable for medicine would be a function of clinical variables that determine if a patient is on treatment or not. This would be estimated first and a proxy would be obtained, which would then be put into the second estimation of quality of life (continuous variable). Note - according to literature, quality of life itself does not typically feed into the equation of whether or not a patient is on medicine. Because a doctor looks at other disease-related variables (rather than quality of life) to determine if a patient should be on medicine or not.

I know that usually 2SLS models are meant to solve the problem of endogeneity by using instrumental variables. However, in my dataset prior to performing any sort of analysis, I do not know which variables are endogenous, and for that matter which instrumental variable would be needed. Can I perform this 2SLS analysis without the use of instrumental variables? If so, would I then need to use the "ivreg" package (which is typical for 2SLS) or the "systemfit" package in R? Bear in mind, my dataset is longitudinal (multiple visits for the same patient) so maybe is there some other package out there?

I do not have a background in econometrics so I am a beginner. I apologize if this is a silly question. Thank you.

question from:https://stackoverflow.com/questions/65945046/solving-a-system-of-equations-by-2sls-method-in-econometrics-using-r

Answer 1

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