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 curious about examine within the box of utilized microeconomics. To our astonishment an enormous majority of researchers during this quarter took it with no consideration that their, usually completely derived, micro types may meaningfully be faced with in keeping with capita facts. Nany of them didn't even become aware of - a minimum of they gave no utterance to it - that utilizing macro facts in micro types increases enormous difficulties. those that did point out the trouble, regularly belittled its value. thankfully, there are noteworthy exceptions. puzzling over aggregation increases at the least questions: "Why or why now not aggregate?" and "How to combination and, specifically, to what degree?" basic solutions to those questions can purely take delivery of in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, end result of the loss of (individual) information, 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 lessen the drawbacks pointed out above.

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Example text

14). 14), we have to prove that for each pair (x jm ' Xj'm') the ratio ~ / ~ depends on Xjm and xj'm' only. This will be xj'm' x jm done in three steps (cf. 4). :). With "row j" and "column m" we will denote the sets{x jl ,··· ,x jM } and {x lm ' ••• ,xJm }, respectively. For consistent aggregation to be possible H must be quasiseparable with respect to row j as well as with respect to column m' for all j and m'. 3 it follows then that H is quasi-separable with respect to the union A of row and column m' because their intersection is {xo ,} and is, Jm therefore, non-void.

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.

L If u = ~(vl, ••• ,vN) and if for each n (=I, ••• ,N; N ~ 3) the partial derivatives are different from zero: (B. 3) Proof: Let ~ * n: n' both {I, ••• ,N}. I), for each nand € ~' n -~-,- n' n n ~' n' (B. 2).

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

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