heinz,
I find the uncertainty surrounding the productivity numbers quite unwarranted. What it measures and how the calculations are carried out is crystal clear, which should be obvious to anybody.
Here is the definition, just in case :
stats.bls.gov Procedures
Multifactor productivity
BLS aggregates inputs for its multifactor productivity measures using a Tornqvist chain index. Some of the basic properties of this index are: It is calculated as a weighted average of growth rates of the components; the weights are allowed to vary for each time period; and the weights are defined as the mean of the relative compensation shares of the components in two adjacent years. Hence, the growth rate of the index (I) for major sectors is the proportional change over time (the triangle (delta) refers to discrete change with respect to time), such that:
% D I = exp(D ln I) =
exp {1/2 * [sk(t) + sk(t-1)] D ln K
+ 1/2 * [sl(t) + sl(t-1)] D ln L}
where sl(t) = labor costs(t) / total costs(t)
and sk(t) = capital costs(t) / total costs(t)
Similarly, both capital, K, and labor, L are Tornqvist indexes. Each is a weighted average of the growth rates of detailed types of capital, ki, and labor inputs, li, respectively.
% D K = exp ( D ln K)
= exp{Si 1/2 * [ski(t) + ski(t-1)] D ln ki}
where ski(t) = cki(t) * ki(t)/ total capital costs
and where cki(t) is the rental price for capital asset ki.
% D L = exp ( D ln L)
= exp{Si 1/2 * [sli(t) + sli(t-1)] D ln li}
where sli(t) = wli(t) * li(t)/ total capital costs
and wli(t) is the hourly compensation for worker group li.
Changes in the index of labor composition, LC, are defined as the difference between changes in the aggregate labor input index, L, and the simple sum of the hours of all persons, H.
% D LC = exp (D ln LC) = exp (D ln L - D ln H)
The Tornqvist index for major sector multifactor productivity growth, A, is:
% D A = exp (D ln A) = exp(D ln Q - D ln I)
where Q is the Fisher-Ideal index of sector output as measured by BLS.
For manufacturing and the 20 industries which comprise manufacturing, aggregate input has a conceptually similar definition except that there are 5 inputs rather than just the 2 used in the major sector measures.
% D I = exp (D ln I) =
exp{1/2 * [sk(t) + sk(t-1)) D ln K
+ 1/2 * [sl(t) + sl(t-1)] D ln L
+ 1/2 * [se(t) + se(t-1)] D ln E
+ 1/2 * [sm(t) + sm(t-1)] D ln M
+ 1/2 * [ss(t) + ss(t-1)] D ln S}
where L = total hours at work
sl(t) = labor costs(t)/total costs(t)
sk(t) = capital costs(t) / total costs(t)
se(t) = energy costs(t)/total costs(t)
sm(t) = materials costs(t) / total costs(t)
ss(t) = purchased business services costs(t) / total costs(t)
and total costs are the current dollar value of shipments adjusted for inventory change.
Using this definition for aggregate input, multifactor productivity for manufacturing or any of the 20 industries which comprise manufacturing is identically defined as above.
% D A = exp (D ln A) = exp(D ln Q - D ln I)
where Q is a Tornqvist output index developed by BLS.
See, nothing to it!
Q=I explains why there was no increase in productivity for Nondurable Goods!
Regards
per s |
