Hi Kevin,

The aggregation problem refers to a, largely unresolved, issue over the conditions for the identification of an aggregate production function. The problem stems from the irreducibility of alternative forms of capital - the way i see it is that the production function fails to take into account heterogeneous PROCESSES and instead models them as homogenous. For example: the purchase of an expresso coffee machine for academics to freely use probably has a larger impact on productivity then the provision of computers which actually work as many academics use their own computers in the first place and sometimes overutilise the ritual of getting a coffee from the cafe as a method of procrastination. The functional representation of these two types of capital, aggregated as a single source of capital, fails to take into account their differential impacts on output as their prices are not reflective of their additions to value adding in the sense of academic output (the coffee machine's price is inflated by consumers' increasing love of good coffee whilst computer power has differential value adding capabilities for academics depending on whether they are doing lots of modelling or simply word processing and thus prices fail to reflect their value adding potential properly).

The problem was referred to historically as the 'Cambridge controversy" as the debate surrounding it was largely undertaken by economists from the UK Cambridge (asserting the problem) and economists from the US Cambridge (denying its existence and/or its relevance). Their has been no satisfactory resolution to my knowledge.

I am concerned over the problem from the perspective of applied production analysis for enterprise data - i.e. standard production functions. I feel that the standard general linear functional approach to modelling production is inadequate mainly because it does not restrict the dynamics inherent in many productive systems - particularly surrounding the investment in and depreciation of capital. That dynamical issues are one of the key aspects limiting identification has been shown in some of the literature on this debate.

If you are simply trying to measure the average value-added which could be expected to arise from the addition of some measure of aggregate capital i think there is probably no issue here. However, if you are trying to use statistical results from aggregate production functions to predict the net impact on output from the addition or deletion of a specific type of capital (e.g. a new railway or an optical fibre network) i think significant issues will arise. I am not sure that this topic deserves the attention it received as i think it mainly surrounds intelligent use of a clearly highly simplified model.

In terms of avoiding aggregation i suppose very good data, a lot of effort and a structural model would be something along the lines of what you need to allow for the simultaneous modelling of what could be conjectured to be separate production processes. For example if you have three process which feed in a linear way from one to the next to the last and additional labour and capital is used in each process you could try to create a structural model along the lines of:

P1=AK1^beta1*L1^beta2

P2=phi1P1*A2*K2^alpha1*L2^alpha2

P3=phi2P2*A3*K3^gamma1*L3^gamma2

And using a simultaneous equations model of some sort. You then have 3 labour and capital elasticies each, two process elasticities and three technical change coefficients. I wouldn't know if such a model would actually be estimable even if you had the data. However, three such levels might be identified as: (1) resource extraction industries; (2) value adding industries (processing), and; (3) marketing and consumption industries.

My two cents Patrick, i hope it is relevant. I have read a bit about it and have given it some thought but am more a micro-economist than a macro... Seeing as no one had contributed in the last several weeks i thought i'd give it a burl.

Cheers,

Daniel