Say I have 2 variables (x,y) that are associated, but the direction of association (=causality) is not known.
I model this causality by estimating 2 different models, where the dependent variables are x and y, respectively and the regressors include an instrument for y and x, respectively, due to the obvious simultaneity concerns.
I received feedback that my empirical results show an 'association', not a 'causality', because I use cross-sectional data.
I have 2 qustions to ask:
a) Is that true? The models are inappropriate for examining causality?
b) If yes, then given the data, what consists a correct way to examine teh direction/existence of causality?
Your results showed a simple association which is the base for any kind of causality, however it is not enough to determine anything beyond it's logical posibilities of development which are always the same, i believe a better model for causality analisis should require at least a third variable related to x and y
Thanks. In that case (when a third variable is present) how this may determin causality?
X and Y are diferent(sometimes contradictory), if X is true then Z is true, if Y is true then Z is false.
Thus X causes Z and Y causes -Z
It the basic logical form, but applies to anything that is affected by movement and by extension to anything affected by causality.
So, you regress: X on Z & Y on Z, and according to the signs of the Z coefficients you determine which causes what?
I'm not sure on the terms, but i believe you got it.
Maybe i'm wrong, please check the results in case we are understanding different terms
I think that you can also compare the estimates by using two different models. First, you should estimate an OLS model and then you will control for endogeneity by means of an instrumental variable approach.
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