Be that as it may, perhaps the Sonnenschein-Mantel-Debreu results show that the Arrow-Debreu model has no empirical implications. That is, the theory imposes no restrictions on the directions of aggregate movements in prices and quantities in response to changes in the data. Kenneth Arrow, Alan Kirman, D. Saari, and S. Abu Turab Rizvi are some who have advanced this claim.
Some have challenged my understanding on this claim, pointing out some work done by Donald Brown and others. S. Abu Turab Rizvi has recently reviewed this recent work ("The Sonnenschein-Mantel-Debreu Results after Thirty Years", History of Political Economy, V. 38 (Annual Supplement): 228-245). He concludes that:
"...Brown and Matzkin do provide a restriction that can conceivably be refuted... Despite this ..., if the only data ... are at the aggregate level, general equilibrium theory does not generate refutable restrictions... [T]he Brown-Matzkin results require individual-level ... vectors.I continue to remain puzzled about what mainstream economists take the content of price theory to be.
Matters are even clearer on qualitative features ... such as local uniqueness, stability, and comparative statics. The equilibrium manifold approach ... does not allow us to refute statements on these features... [W]e cannot test to see if an economy is poorly behaved... [T]he intuition that general equilibrium theory is devoid of meaningfully general results remain true..."
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"That is, the theory imposes no restrictions on the directions of aggregate movements in prices and quantities in response to changes in the data."
Yes but in a way, wealth effects SHOULD make everything weird, else they're almost not even worth bothering with. So the difficulty of applying the theory empirically is the result of the realism of the theory. Life's tough and the world is under no obligation to make things easy for economists.
Well, nothing stops you from working, in empirical applications, with further restricted models. -- If you estimate the latest Gali-esque NK models you get marginally better forecasts than the large, old econometric models.
What I don't understand in your post is the claim that G.E. is "very short run". Models with infinite time are clearly not "very short run".
The requirements for the Ist Welfare Theorem are so loose these days that you can have much weirdness in your production set or preference relation.
In the Arrow-Debreu model of intertemporal equilibrium, the initial quantities of all commodities are among the given data. This includes the initial quantities of both fixed capital and circulating capital goods. Hence, the model is very short-run.
Actually there is research using empirical data on the individual level to get results about actual economies using a GE approach. Werner Hildenbrand does exactly that in his work on the law of demand.
The initial endowment is given. It doesn't follow that you can't produce more (capital). What am I missing?
I nowhere assert that more capital goods cannot be produced at future time periods in an Arrow-Debreu intertemporal equilibrium.
Consider long run models like the Harrod-Domar model, the Solow growth model, or the von Neumann growth model. In these models the initial quantities of capital goods are not given data. These quantities are solved for in solving the model.
The transition from given initial quantites to long run equilibrium paths is modeled by some sort of short run model.
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