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..."