By J. van Daal
ISBN-10: 9400963343
ISBN-13: 9789400963344
ISBN-10: 940096336X
ISBN-13: 9789400963368
Our curiosity in difficulties of aggregation originates from approximately seven years in the past after we turned taken with learn within the box of utilized microeconomics. To our astonishment an unlimited majority of researchers during this quarter took it without any consideration that their, ordinarily completely derived, micro types may well meaningfully be faced with consistent with capita information. Nany of them didn't even discover - no less than they gave no utterance to it - that using macro info in micro versions increases substantial difficulties. those that did point out the trouble, mostly belittled its value. thankfully, there are noteworthy exceptions. pondering aggregation increases at the least questions: "Why or why now not aggregate?" and "How to combination and, particularly, to what degree?" basic solutions to those questions can basically receive in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, as a result loss of (individual) facts, to prevent or to lessen multicollineartiy, to avoid wasting 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 circumvent or decrease the drawbacks pointed out above.
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Additional resources for Aggregation in Economic Research: From Individual to Macro Relations
Sample text
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. A less obvious example is the application of three-stage aggregation to multi-product firms, the case considered by Nataf (1948). m the R. output of firm j that is obtained by the mth input. 2b) a function of the macro outputs of the L different products. The interpretation of the remaining equations is now straightforward.
3b) = i •• m(xl. m ) - ( x l , ••• ,x L ), • m • m •• m Xj~. ~m(xl~m,···,xJ~m)' 36 CHAPTER I J W := G{ l: f. (X . ) } j=l J.. )} M (X l: f m=l •• m )}. 5c) •• m L x J' •• _~. ~ )} J .. ~=l J . J . 6a) F. {Llf. (x. )}. ~)}_ •• •• j=l j~. J . ~m)}' x J := F {L f. (x. ~m)}· M where x J'.. • { L x. F. p.. (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.
By considering the intersection of row j with the union C of A' and column m'. 5) (~). The additive separability of the other functions. 6) where the primes attached to
jm denote differentia- tion. 6) by the relation that we get if we af. af. 6) yields that ___J_ / ~ ax. , Jm Jm '. ,(x. Jm ) / 1> Jm Jm x '. Consequently, all micro functions fj are on Xjm and jm additively separable. Similarly, we can prove that all aggregation functions ~ are additively separable. The additive separablility of F and G can be proved as follows.
Aggregation in Economic Research: From Individual to Macro Relations by J. van Daal
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