1/ Summarizing our discussion of "demand" via "ceteris paribus" (CP), we've seen that, once formalized, CP amounts to comparing Y under two settings of X, say X=x and X=x', while leaving other variables in the structural equation for Y unchanged. The beauty of formal definitions
https://twitter.com/yudapearl/status/1439842754498949120
2/ is that they hold for all models and are independent on the meanings of X, Y,Z, etc,
or the procedure by which we estimate things. Leveraging these beauties, we come to realize that the resultant CP definition of "demand" is none other but the counterfactual definition of
or the procedure by which we estimate things. Leveraging these beauties, we come to realize that the resultant CP definition of "demand" is none other but the counterfactual definition of
3/ Causal Effect, namely {Y(x, Z),Y(x', Z)}, where Z is the set of other variables in the eq. of Y, both observed and unobserved. Thus, the analysis of "demand" can benefit directly from the literature on causal effects, presenting no peculiarities that demand special treatments.
4/ Of course, the cyclicity of the equations prevent us from leveraging d-separation and do-calculus. But the logic of counterfactuals can still be summoned to advantage, as is done here ucla.in/2NnfGPQ#page=59. From this point on, as they say in economics: Ceteris Paribus.
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