Download Aggregation in Economic Research: From Individual to Macro by J. van Daal PDF

By J. van Daal

Our curiosity in difficulties of aggregation originates from approximately seven years in the past once we grew to become thinking about examine within the box of utilized microeconomics. To our astonishment an enormous majority of researchers during this sector took it with no consideration that their, ordinarily completely derived, micro types may well meaningfully be faced with in keeping with capita information. Nany of them didn't even become aware of - at the least they gave no utterance to it - that utilising macro information in micro types increases significant difficulties. those that did point out the trouble, normally belittled its value. thankfully, there are noteworthy exceptions. puzzling over aggregation increases no less than questions: "Why or why now not aggregate?" and "How to mixture and, specifically, to what degree?" basic solutions to those questions can basically accept in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, due to the loss of (individual) info, to prevent or to lessen multicollineartiy, to save lots of levels of freedom; one abstains from aggregation to prevent lack of info, to prevent aggregation biases and one aggregates such and to such measure as to avoid or lessen the drawbacks pointed out above.

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Example text

The sufficiency is straightforward; the proof of the necessity requires quite a lot of effort. 1 with nonzero first derivatives. 5) it is necessary and sufficient that all the functions of the scheme be additively separable, the atomistic macro function H included, hence: y M H(x 11 , ••• ,x JM ) = ~{~ J ~ ¢. (x. )}. J. Green's (1964) book on aggregation. 3 Nataf's result on consisten~ aggregation Nataf's theorem is one of the theorems that establish the many impossibilities (or rather: very restricted possibilities) in the field of aggregation.

X.. )}. J". ~ )}. J m (1. 4. • )}. >j' I/I~. L L ~. >l and CPj~m with: M x. p . pj~m(Xj~m) }. £. ~ (Xj~ )}. 9) J •• J ~=l AGGREGATION WITHOUT SIDE CONDITIONS L L 37 ¢o. (Xo. 11) As there ar now more kinds of aggregates then before, the use of dots in the formulae above is necessary to avoid confusion. m)' border ele-1 ments Fo. (x o. <.. <.. m) m together with sums of these border elements on the edges and L L L¢0R. (x0R. ) in the vector opposite of the starting j R, m J m J m point. A trivial example of this extension to more dimensions is the aggregation over L countries or regions of the macro production functions obtained in the preceding sections.

In that case there may be elements x and i EX such that g(x) (GO -I( Gf(x». 5). g(x) and * Gf(x). 6) has in common with other very general results in economics that as such it is not useful CHAPTER I 48 in practical situations. It is doubtful, whether in specifying the relations, we can go far beyond the results obtained so far. To clarify the link with Nataf take X C RJxM, V C RJ, W C RM and Y C R. 5). 6 Consequences for empirical work If we want to do empirical research with macro relations and we want to obey Nataf's theorem we are put in an additive world, but we also meet an additional difficulty viz.

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