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 enthusiastic about examine within the box of utilized microeconomics. To our astonishment an enormous majority of researchers during this region took it with no consideration that their, normally completely derived, micro versions might meaningfully be faced with consistent with capita facts. Nany of them didn't even discover - at the least they gave no utterance to it - that employing macro information in micro versions increases enormous difficulties. those that did point out the trouble, mainly belittled its significance. thankfully, there are noteworthy exceptions. considering aggregation increases not less than questions: "Why or why no longer aggregate?" and "How to mixture and, particularly, to what degree?" normal solutions to those questions can in basic terms receive in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, as a result loss of (individual) information, to prevent or to lessen multicollineartiy, to save lots of levels of freedom; one abstains from aggregation to prevent lack of details, 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 info for Aggregation in Economic Research: From Individual to Macro Relations

Example text

1) E v. j=1 J (the arithmetic mean), G J .! 3) H(p) (the generalized harmonic mean). Note that A, log G and {H(p)}-P are unweighted averages of Vj' log Vj and v;p respectively. Usually we prefer such means to sums or products because these aggregates have roughly the same order of magnitude as the micro variables on which they are based. There is, however, another reason: by taking averages one avoids the introduction of a new macro variable, viz. the total number J of individuals (that may vary over time).

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. Using an argument that we owe to Green (1964, p. 37) we can say for all m, m' and any j: aF ax- m -a-F- = axm, _af. _J_ ax. Jm af. _ _J_ ax jm , agm / ax. 5) with respect to Xjm and x jm " respectively, and divide the results). This means that the ratio of aF/ax m and aF/axm, depends at most on all micro variables xlm, ••• ,x Jm and xlm" ••• ,x Jm '.

Definition Let $ be again a function of N variables that maps vectors of a certain domain D RN into the real line R. Let S = C {sl, ••• ,sK} be a subset of {l, ••• ,N} and let T = {t 1 , ••• ,t K,} be its complement in {l, ••• ,N}; hence K + K' = N. 2 The function $ is quasi-separable with respect to S if and only if for all sk and sk' depend only on vS1' ••• 'v sk • E S the ratios a~P sk / ~ sk' Proof: The original proof, using third-order derivatives, was given by Leontief (1947a). Green (1964, pp.

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

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