Abstract
Decompositions of total factor productivity (TFP) shed light on the driving factors behind productivity change. We develop the first exact decomposition of the Fisher ideal TFP index which contains no debatable mixed-period components or residuals. We systematically isolate five effects of (1) technical change, (2) technical efficiency, (3) scale efficiency, (4) allocative efficiency, and (5) price effect. The three efficiency components (2–4) represent the efficiency of achieving a given target point. Components (1) and (5) capture the changes of the target point. While the technical change component is well-established, changes in the relative input–output prices can have real effects on the scale and scope of the target. Such changes are captured by the new price effect component (5). The new decomposition is compared with existing decompositions both in theory and by means of an empirical application to a panel data of 459 Finnish farms in years 1992–2000.
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Notes
However, if firms are assumed to operate with perfect allocative efficiency, then the quantity data suffices for estimating the Fisher index, as shown by Kuosmanen et al. (2004).
In the axiomatic approach, decompositions of the Fisher ideal price and quantity indices have been developed (see Balk 2003, for a review).
There is a good reason for resorting to the economic (dual) measures of scale efficiency. The conventional distance function based scale measure would be problematic here, because the decomposition would then depend on the order in which its components are calculated, as aptly pointed out by McDonald (1996). The measure of allocative efficiency tends to give different results depending on whether we define it relative to the VRS or CRS benchmark. The dual measures of scale efficiency circumvent this problem.
We are grateful to an anonymous reviewer of this journal for suggesting this alternative interpretation.
The results of the ZP decomposition depend on the weight assigned on the input and the output projections, and are thus not directly comparable.
Kuosmanen and Sipiläinen (2004) report sample averages based on farm-specific productivity indices. For the Fisher TFP index and its decomposition, these sample averages are very similar to those of the representative farm discussed here.
To make this critical profitability measure more robust to data errors and outliers, the 95 percentile of the profitability distribution was used as the empirical estimator for the profitability function. The clipping of the profitability distribution did not have a notable influence on the results to be presented.
The price effect index tracks very closely the observed patterns in the output prices (cf. Fig. 6 in Kuosmanen and Sipiläinen 2004).
References
Althin R, Färe R, Grosskopf S (1996) Profitability and productivity changes: an application to swedish pharmacies. Ann Oper Res 66:219–230. doi:10.1007/BF02187592
Balk B (1993) Malmquist productivity indexes and Fisher ideal indexes: comment. Econ J 103:680–682. doi:10.2307/2234540
Balk BM (1998) Industrial price, quantity, and productivity indices: the micro-economic theory and an application. Kluwer Academic Publishers, Boston, MA
Balk BM (2003) Decompositions of Fisher indexes. Econ Lett 82:107–113. doi:10.1016/j.econlet.2003.09.006
Bauer PW (1990) Decomposing TFP growth in the presence of cost inefficiency, nonconstant returns to scale, and technological progress. J Prod Anal 1:287–299. doi:10.1007/BF00160047
Bjurek H (1996) The malmquist total factor productivity index. Scand J Econ 98:303–313. doi:10.2307/3440861
Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output and productivity. Econometrica 50:1393–1414. doi:10.2307/1913388
Chavas J-P, Cox TM (1999) A generalized distance function and the analysis of production efficiency. South Econ J 66(2):295–318. doi:10.2307/1061144
Coelli TJ, Rao DSP, O’Donnell CJ, Battese GE (2005) An introduction to efficiency and productivity analysis, 2nd edn. Springer
Diewert WE (1992) Fisher ideal output, input and productivity indexes revisited. J Prod Anal 3(3):211–248. doi:10.1007/BF00158354
Diewert WE, Nakamura AO (2003) Index number concepts, measures and decompositions of productivity growth. J Prod Anal 19:127–159. doi:10.1023/A:1022897231521
Färe R, Grosskopf S (1992) Malmquist productivity indexes and Fisher ideal indexes. Econ J 102:158–160. doi:10.2307/2234861
Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer Academic Publishers
Färe R, Primont D (2003) Luenberger productivity indicators: aggregation across firms. J Prod Anal 20:425–435. doi:10.1023/A:1027360018763
Färe R, Grosskopf S, Norris M, Zhang Z (1994) Productivity growth, technical progress and efficiency change in industrialized countries. Am Econ Rev 84(1):66–83
Färe R, Grosskopf S, Norris M (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: reply. Am Econ Rev 87(5):1040–1044
Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc, Ser A (Gen) 120(3):253–282. doi:10.2307/2343100
Grifell-Tatjé E, Lovell CAK (1999) Profits and productivity. Manage Sci 45(9):1177–1193. doi:10.1287/mnsc.45.9.1177
Kuosmanen T, Sipiläinen T (2004) On the anatomy of productivity growth: a decomposition of the Fisher ideal TFP index, MTT Discussion Paper 2004/17. MTT Agrifood Research Finland, Helsinki
Kuosmanen T, Post T, Sipiläinen T (2004) Shadow price approach to total factor productivity measurement: with an application to finnish grass silage production. J Prod Anal 22(1–2):95–121. doi:10.1023/B:PROD.0000034693.38576.94
Lawrence D, Diewert WE, Fox KJ (2006) The contributions of productivity, price changes and firm size to profitability. J Prod Anal 26(1):1–13. doi:10.1007/s11123-006-0001-y
Lovell CAK (2003) The decomposition of malmquist productivity indexes. J Prod Anal 20:437–458. doi:10.1023/A:1027312102834
McDonald J (1996) Note: a problem with the decomposition of technical inefficiency into scale and congestion components. Manage Sci 42(3):473–474. doi:10.1287/mnsc.42.3.473
Nishimizu M, Page JM (1982) Total factor productivity growth, technological change and technical efficiency change. Econ J 92:920–936. doi:10.2307/2232675
Ray SC, Desli E (1997) Productivity growth, technical progress and efficiency change in industrialized countries: comment. Am Econ Rev 87(5):1033–1039
Ray SC, Mukherjee K (1996) Decomposition of the Fisher ideal index of productivity: a nonparametric dual analysis of us airline data. Econ J 106:1659–1678. doi:10.2307/2235206
Zofio JL, Prieto AM (2006) Return to dollar, generalized distance function and the Fisher productivity index. Span Econ Rev 8:113–138. doi:10.1007/s10108-006-9004-0
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We are grateful to two anonymous reviewers of this journal for their constructive comments that helped to improve this paper.
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Kuosmanen, T., Sipiläinen, T. Exact decomposition of the Fisher ideal total factor productivity index. J Prod Anal 31, 137–150 (2009). https://doi.org/10.1007/s11123-008-0129-z
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DOI: https://doi.org/10.1007/s11123-008-0129-z