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

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 once we grew to become desirous about learn within the box of utilized microeconomics. To our astonishment an unlimited majority of researchers during this region took it without any consideration that their, normally completely derived, micro versions may meaningfully be faced with in keeping with capita information. Nany of them didn't even notice - a minimum of they gave no utterance to it - that using macro facts in micro types increases huge difficulties. those that did point out the trouble, in general belittled its value. thankfully, there are noteworthy exceptions. pondering aggregation increases not less than questions: "Why or why no longer aggregate?" and "How to combination and, specifically, to what degree?" normal solutions to those questions can in basic terms accept in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, end result of 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 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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12) a a ma a ra a Sa (where a = 1 ••••• A. the x. Ja the n. Ja are the outputs of firm a. the functions' arguments with respect to the different kinds of labour inputs and the zka that with respect to capital). ···. z sA) of output. labour and capital. respectively. Z) = o. 12) refers to m different outputs instead of one. this problem is more general than the problem of theorem 1. Moreover. 16). This reduction is an example of aggregation over the arguments of a function, generally referred to as aggregation over commodities.

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. 12-15) presented a proof where only the existence and continuity of non-zero first derivatives is required. In appendix B to this chapter a new, rather simple proof is given for the case that all functions considered have continuous second order derivatives.

Labour and capital. respectively. Z) = o. 12) refers to m different outputs instead of one. this problem is more general than the problem of theorem 1. Moreover. 16). This reduction is an example of aggregation over the arguments of a function, generally referred to as aggregation over commodities. This is not the topic of this book. although it appears now and then; some specific attention is paid to it in chapter 6. In his 1946 article Klein reduces the problem to a set of partial differential equations; Nataf has solved it by integration in his 1948 article.

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


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