For the numerous use of IV regression in economics, Ii come across this question?
for example, if we take Y=bX+u(1), a possible causal relationship with possible endogeneity problem, and also an opposite possible causal relationship X=b*Y+u*(2). and to estimate b or b* we probably may use IV approach, for example, z1 in the model(1) and z2 in the model(2). and here is my question: what is the statistical analytical relationship between z1 and z2? is it causal ? do they come from an opposite base of eigenvectors (meaning orthogonal bases), whats the cov(z1,z2)? a common example of that in economics is the relationship between health and in income or health and education, many types of research used many instruments to prove both-ways causal effects.
that is my question I hope it was clear enough, please any related work or paper would be of great help? or any answer would be amazing. Thank you
I think you should see the pearson and spearman correlations, the causality refers a directed effect unlike the correlational analysis being one of the most known methods the linear regression, the essence of this analysis is extended through many tutorials on youtube.
Cristian Ramos-Vera thank you for your answer, I am actually looking what type of relationship of different instruments, it is of course important to study their correlation using spearman or Pearson's approach but the focus here is on the instrumental vraibales econometrics aspect nevertheless thank you
I think they should be orthogonal, but I also believe that one cannot prove it because you do not know the true data generating model...
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