smd
From The Representative Agent in Macroeconomics, Hartley, p190-191:
In a remarkable series of papers, Sonnenschein (1972, 1973, 1973), Mantel (1974, 1976), Debreu (1974), and Mas-Colell (1977) showed that in an economy in which every individual well-behaved excess demand function, there are only three restrictions on the aggregate excess demand function: (a) it satisfies Walras' law; (b) it is continuous; and (c) it is homogenous of degree zero in prices.
That is it. Nothing else can be inferred. Any completely arbitrary function satisfying these three properties can be an aggregate excess demand function for an economy of well-behaved individuals. Having an economy in which every single agent obeys standard microeconomic rules of behavior tells us virtually nothing about the aggregate economy.
[...]
These results are quite general, placing no restrictions on the distribution of agents' preferences or income distribution, and were initially met with skepticism. Deaton (1975, p. 237) argued that the results required "arbitrary manipulation of the income distribution and of preferences." (See also Grandmont, 1987, and Kirman's, 1989, discussion of it). However, Kirman and Koch (1986) show that restricting the distribution of agent's preferences or income distribution does not solve the matter. As Kirman summarises:
Put another way, given an arbitrary excess demand function, no matter how ill-behaved and difficult to work with, I can give you an economy in which people are as close as you like to being identical, i.e., they have the same preferences and almost the same income, which will generate this ugly aggregate excess demand function. (Kirman, 1992, p. 128)
I came across the SMD result in S4, but I had come to the same conclusion as Deaton mentioned in the quote; its removal is quite surprising.
I'll have to think about it after sitting through statistics past papers, I think...
In a remarkable series of papers, Sonnenschein (1972, 1973, 1973), Mantel (1974, 1976), Debreu (1974), and Mas-Colell (1977) showed that in an economy in which every individual well-behaved excess demand function, there are only three restrictions on the aggregate excess demand function: (a) it satisfies Walras' law; (b) it is continuous; and (c) it is homogenous of degree zero in prices.
That is it. Nothing else can be inferred. Any completely arbitrary function satisfying these three properties can be an aggregate excess demand function for an economy of well-behaved individuals. Having an economy in which every single agent obeys standard microeconomic rules of behavior tells us virtually nothing about the aggregate economy.
[...]
These results are quite general, placing no restrictions on the distribution of agents' preferences or income distribution, and were initially met with skepticism. Deaton (1975, p. 237) argued that the results required "arbitrary manipulation of the income distribution and of preferences." (See also Grandmont, 1987, and Kirman's, 1989, discussion of it). However, Kirman and Koch (1986) show that restricting the distribution of agent's preferences or income distribution does not solve the matter. As Kirman summarises:
Put another way, given an arbitrary excess demand function, no matter how ill-behaved and difficult to work with, I can give you an economy in which people are as close as you like to being identical, i.e., they have the same preferences and almost the same income, which will generate this ugly aggregate excess demand function. (Kirman, 1992, p. 128)
I came across the SMD result in S4, but I had come to the same conclusion as Deaton mentioned in the quote; its removal is quite surprising.
I'll have to think about it after sitting through statistics past papers, I think...