The Cobb-Douglas exponent (CDALF) of the production function is known to change over long time periods, giving somewhat less weight to capital as an economy becomes more capital intensive (see, for instance, Thirlwall 1977: chapter 2). The GTAP project data again provided the basis for an estimation of this relationship.

That function, in combination with data from Thirlwall and others on sectoral differences in capital share, allow the computation of sectoral capital shares (CDAlfS), normalized so as to generate CDALF for the total economy. A parameter ( salpha ) represents a generic pattern of capital share variation across production sectors.