Abstract
Recent theoretical advances in total factor productivity (TFP) measurement mean that TFP indexes can now be exhaustively decomposed into unambiguous measures of technical change and efficiency change. To date, all applications of this new methodology have involved decomposing indexes that have poor theoretical properties. This article shows how the methodology can be used to decompose a new TFP index that satisfies all economically-relevant axioms from index theory. The application is to state-level data from 1960 to 2004. In most states, the main drivers of agricultural TFP change are found to have been technical change and scale and mix efficiency change.
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Notes
- 1.
Local linearity means the frontier is formed by a number of intersecting hyperplanes. Thus, it may be more appropriate to refer to DEA as a semiparametric rather than a nonparametric approach.
- 2.
More precisely, reference prices should be representative of the relative importance (i.e., relative value) that decision-makers place on different outputs and inputs. Observed prices are not always the best measures of relative importance.
- 3.
For example, the prices in the larger sample could be used to test the joint null hypothesis that the population mean prices are equal to the reference prices. Such a test can be conducted in a regression framework using test commands available in standard econometrics software packages.
- 4.
Let q nit denote the nth element of \( {\boldsymbol{q}}_{it} \). The notation \( {\boldsymbol{q}}_{hs}\ge {\boldsymbol{q}}_{it} \) means that \( {q}_{nhs}\ge {q}_{nit} \) for n = 1, …, N and there exists at least one value \( n\in \left\{1,\dots, N\right\} \) where \( {q}_{nhs}>{q}_{nit} \).
- 5.
For this index, the identity axiom requires \( PI\left({\boldsymbol{q}}_{hs},{\boldsymbol{q}}_{it},{\boldsymbol{p}}_{it},{\boldsymbol{p}}_{it},{\boldsymbol{p}}_0\right)=1 \) while the proportionality axiom requires \( PI\left({\boldsymbol{q}}_{hs},{\boldsymbol{q}}_{it},{\boldsymbol{p}}_{hs},\lambda {\boldsymbol{p}}_{hs},{\boldsymbol{p}}_0\right)=\lambda \) for \( \lambda >0 \). Both axioms will be satisfied if \( {\boldsymbol{p}}_0\propto {\boldsymbol{p}}_{hs}\propto {\boldsymbol{p}}_{it} \) (e.g., if there is no price change in the dataset and \( {\boldsymbol{p}}_0=\overline{\boldsymbol{p}} \); or if \( {\boldsymbol{p}}_{hs}\propto {\boldsymbol{p}}_{it} \) for all \( h=1,\dots, I \) and \( s=1,\dots, T \) and \( {\boldsymbol{p}}_0=\overline{\boldsymbol{p}} \)).
- 6.
Version 4 of the InSTePP dataset covers the period 1949–2002 and can be downloaded from http://www.instepp.umn.edu/data/instepp-USAgProdAcct.html. All variables in this dataset take the value 100 in 1949, so it cannot be used to generate TFP indexes that are comparable with the indexes depicted in Fig. 17.3.
- 7.
Estimates of profitability change, TFP change, technical change, output-oriented technical efficiency change and output-oriented scale-mix efficiency change in each state in each period are available in a supplementary appendix online.
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O’Donnell, C.J. (2016). Nonparametric Estimates of the Components of Productivity and Profitability Change in U.S. Agriculture. In: Zhu, J. (eds) Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 238. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7684-0_17
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