By Terry Barker (ed.), M. Hashem Pesaran (ed.)
Aggregation is an important challenge in a lot fiscal thought and in so much utilized paintings in fiscal modelling. a formal knowing of the matter and the equipment selected to unravel it are the most important to the layout and overview of utilized learn in economics. during this booklet, prime theorists and utilized economists deal with themselves to the major questions of aggregation: what point of aggregation can be selected in utilized research?; while is an mixture strategy justified?; is there an optimum point of disaggregation?; does disaggregation enhance predictive functionality? and why?; how can aggregation bias be detected?; how does aggregation vague informal relationships?; can macro-equations be derived from non-linear micro-equations?; what tools can be found for linking macro and micro types? and the way do they paintings? those matters are lined either theoretically and in wide-ranging functions.
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Extra info for Disaggregation in Econometric Modelling
Let us then restate condition (c 2 ). 4· ) Dynamic specification speci[ication of o[ aggregated models (remember that invertihility of Yi( y;( LL)) is included in assumption I). The condition is: (B) For any i and j, x,/ xj x/[ X,I is independent of t (compositional (H) stability of the x;/s), XiI'S), while aa;( )/y;( L) == a j( L )/Yj( L). i( L )/Yi( In case (A) aggregation is immediate. 4") one obtains a(L) Y =L _ß;(L) a(L) qf3i(L) X + + U y;(L) X[I V[, y(L) Y[, - L q,I Yi(L) Case (B) deserves so some me observations.
When N is the millions, the there are N independent eomponents. number of parameters will be unreasonably large. Clearly, a model with fewer parameters will provide an adequate approximation, perhaps because individual AR(1) models will have similar parameter values and because cancel for the beeause roots may (almost) eaneel AR and MA polynomials in B of the aggregate series. A different approach is to assume assurne that the AR( 1) l) parameters are drawn from some curious results ean can oeeur.
Tt) be the rank of the variance-covariance matrix of '11' t" Assuming 'tt 11 fc¥- 0 we hflve 1 :5: #(t,) #('11) :5: n. As regards the #(it), it is easily seen (see also appendix mathematical meaning of #(XI)' 3A, section 1) that, though having dimension n, it XI (and consequently XI) xt ) is driven by #(it) #(XI) white noises, while the others are Xi'! xiI Xit is exact linear combinations of the former. for instance, if X;/ independent of t for far any i and j, then #(Xt) #(xl) == 1, in which case all the xi,'s x;/s are driven by only one white noise.