Consequently, the cost share of primary inputs attends to be a good approximation of the magnification factor, with an error of less than one per cent in magnitude in most industries.
Such results are comparable, provided that one knows the appropriate magnification factor.
Over longer periods of time, the real share of intermediate inputs can change enough that the growth factors of primary inputs and all inputs can begin to diverge significantly so that the general rule of the magnification factor being approximately equal to the cost share of primary inputs in the base year is less useful.
Chart 3 and Table 5 presents the magnification factor of each Australian industry as a per cent deviation from the (approximate) magnification factor of the construction industry for TFP growth between 2000 and 2012.
Since construction had the lowest magnification factor over the 2000-2012 period (0.
Over short time horizons, the share of primary inputs in total input use provides a very close approximation to the magnification factor relating gross output and value added TFP measures, so it can serve as a simple way to evaluate the sensitivity of results to the choice of TFP measure or to compare studies which use different output measures.
20) Since the latter term is approximately equal to one provided that the growth rates are similar or small, the Paasche magnification factor is:
The Paasche and Laspeyres magnification factors can be used to approximate the magnification factor in a Fisher framework as (Diewert 2015, equation 39):
where the weight given to the Laspeyres magnification factor is defined using the Paasche and Laspeyres gross output-based TFP growth rates as w [equivalent to] [[pi].
We will refer to this as the "complex" approximation of the Fisher magnification factor.
In most industries, the choice of a Laspeyres, Paasche, or Fisher index for aggregation has very little impact on the estimated magnification factor (Appendix Table 3).