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A decomposition of US business sector TFP growth into technical progress and cost efficiency components

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Abstract

A problem with index number methods for computing TFP growth is that during recessions these methods show declines in TFP. This is rather implausible since it implies technological regress. We develop a new method to decompose TFP growth into technical progress and inefficiency arising from the short run fixity of capital and labour, and apply this to new data on the US corporate nonfinancial sector and the noncorporate nonfinancial sector. The analysis sheds light on sources of the productivity growth slowdowns over the period 1960–2014.

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Notes

  1. See Jorgenson and Griliches (1967) or Balk (1998).

  2. Examples of technical regress in history include the loss of hydraulic mining techniques following the decline of the Roman Empire (Wilson 2002) and the loss of boat building technologies following societal collapse in Easter Island (Diamond 1995).

  3. Puzzling about their empirical results which seemed to show “technological degradation” for countries with very low capital-labour ratios, Kumar and Russell (2002) pithily ask the following: “Does knowledge decay? Were “blueprints” lost?”

  4. See Gordon (2016), Mokyr et al. (2015), Byrne et al. (2016), and Syverson (2016).

  5. The use of nonparametric methods for estimating technical progress can be traced back to Diewert (1980; 264); Diewert (1981); Diewert and Parkan (1983; 153–157) and Tulkens (1993; 201–206). Subsequent contributions to this “sequential” approach (where past observations on the production unit up to and including the current period are used to determine the best practice technology) include Färe et al. (1985), Tulkens and Eeckaut (1995), Suhariyanto and Thirtle (2001), Shestalova (2003) and Casu et al. (2013).

  6. We assume Ct > 0 for each t.

  7. The convexity assumption is not required in the one output case. If we assume that the best practice technology can be represented by the conical free disposal hull (FDH) of past observations, then the corresponding best practice unit cost function is still defined by (2). For references to the FDH approach to nonparametric production theory, see the pioneering contributions by Tulkens (1986, 1993) and his coauthors and the subsequent papers by Diewert and Fox (2014) (2017). Our approach can be viewed as applying cost data to Tulkens’ (1993; 201–206) sequential FDH measurement of efficiency and local technical progress approach.

  8. This approximation will become more adequate for the later observations in our sample.

  9. A reason for assuming constant returns to scale is that when we try to generalize our framework to a nonconstant returns to scale framework, we run into the problem that some of our linear programs may not have a feasible solution.

  10. This definition follows Balk (1998; 28). Note that e1 is equal to unity.

  11. Note that we are using cost efficiency rather than technical efficiency. Technical efficiency does not require price information and is therefore useful in many data constrained contexts, but prices do contain information. Ideally, such information should be always used when available.

  12. This type of cost based measure of technical progress can be traced back to Salter (1960). Balk (1998; 58) defined a family of indexes similar to that defined by (6) by using the best practice total cost function in place of the best practice unit cost function. The definitions (6)–(13) are specializations (to the case of one output) of the cost function based definitions used by Diewert (2011; 181–182) Diewert (2012; 223–225) to decompose total cost growth into explanatory factors using a reference best practice cost function. What is missing in Diewert’s decompositions is the change in cost efficiency term εt defined by (5).

  13. This will ensure that the resulting measure of technical progress satisfies the time reversal property; i.e., if we reverse the role of time and recalculate the measure of technical progress, we obtain the reciprocal of the original measure when we take the geometric average.

  14. Fisher (1922) defined his ideal index as the geometric mean of the corresponding Laspeyres and Paasche indexes and noted that the resulting index satisfied the time reversal test.

  15. If the number of outputs is equal to one, then the family of indexes defined by (10) reduces to a Konüs (1939) true cost of living index family in the case of homothetic preferences where c(w,t) is the consumer’s unit utility expenditure function using period t preferences and output is interpreted as a utility level. Shephard (1953) developed this theory of input price indexes for the case of a constant returns to scale production function.

  16. This implies that we are choosing a particular unit of measurement for aggregate output.

  17. Of course, Eq. (20) can be rearranged to give a decomposition of real output of the production unit in period t, yt, into the product of the period t input level Xt times the period t level of cost efficiency Et times the period t level of technology Tt. This is similar to Kohli’s (1990) decomposition of nominal GDP into the product of explanatory factors. See also Fox and Kohli (1998) for a similar decomposition.

  18. Diewert and Fox (2018b) also use these data to analyze factors that explain value added growth.

  19. The published data for this sector did not allow Diewert and Fox to decompose real value added into gross output and intermediate input components.

  20. A key difference between this data set and many national and international productivity data bases is the breadth of assets included. Specifically, we consider land, inventories and monetary balances as assets that generate services used in production, whereas data bases such as EUKLEMS and World KLEMS do not; see Jorgenson and Timmer (2016). We note that the Australian Bureau of Statistics produces an experimental KLEMS data base which includes land and inventories; see ABS (2015).

  21. The year t Fisher chain link input index is defined as γt* ≡ [(wt−1·xt wt·xt)/(wt−1·xt−1 wt·xt−1)]1/2.

  22. These percentages are actually percentage points. The corresponding geometric average rate of growth for our nonparametric rate of input growth γt was 1.881% per year while the corresponding Fisher index rate of input growth γt* was 1.886% per year.

  23. We thank John Fernald for suggesting taking averages over these sub-periods.

  24. For issues related to the explicit modelling of capacity utilization in the context of nonparametric frontiers, see e.g. Färe et al. (1989), De Borger et al. (2012) and references therein.

  25. Recall that the year t cost efficiency factors et are defined by (4), the year t change in cost efficiency factors εt defined by (5), the year t measures of technical progress τt defined by (9), the nonparametric input price index βt defined by (13), the nonparametric input quantity (or volume) index γt defined by (14) and the nonparametric total factor productivity growth factor for year t, TFPGt ≡ [yt/yt−1]/γt is defined by (15).

  26. The corresponding geometric average rates of growth for our nonparametric rate of input growth γt was 1.137% per year while the corresponding geometric average Fisher index rate of input growth γt* was 1.166% per year.

  27. Evidently it took the noncorporate sector some twenty years to fully recover from the effects of the first oil shock recession in 1973-74. Another possibility is that there is a considerable amount of measurement error in our data for this sector.

  28. Recall that Eqs. (17)–(19) in Section 2 converted the growth decomposition for TFP into the levels decomposition TFPt ≡ yt/Xt = EtTt defined by (20). Again define Xt* as the Fisher chained index level of input for year t and again define the Fisher index level of TFP in year t as TFPt* ≡ yt/Xt*. The Fisher input and productivity level series for the Noncorporate Nonfinancial Sector, Xt* and TFPt*, are also listed in Table 4 for comparison purposes.

  29. Note that yt, Xt and Xt* are measured in billions of constant 1960 dollars.

  30. The finding that cost inefficiency is so much bigger in the noncorporate sector can be at least partially explained by the fact that this sector uses land and structures much more intensively than the corporate sector, which uses machinery and equipment more intensively. Thus when there is a recession, due to the quasi-fixed nature of the land and structure inputs, the noncorporate sector cannot reduce their use of these inputs.

  31. This is the discussion paper version of the current paper.

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Acknowledgements

The authors thank three anonymous referees, John Fernald, Chad Syverson, and seminar participants at the Bureau of Economic Analysis, Society for Economic Measurement Conference 2016 (Thessaloniki) and the North American Productivity Workshop 2016 (Quebec City) for helpful comments. The first author gratefully acknowledges the financial support of the SSHRC of Canada, and both authors gratefully acknowledge the financial support of the Australian Research Council (DP150100830).

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  1. University of British Columbia and UNSW Sydney, Sydney, 2052, Australia

    W. Erwin Diewert

  2. School of Economics & Centre for Applied Economic Research, UNSW Sydney, Sydney, 2052, Australia

    Kevin J. Fox

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  1. W. Erwin Diewert
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Diewert, W.E., Fox, K.J. A decomposition of US business sector TFP growth into technical progress and cost efficiency components. J Prod Anal 50, 71–84 (2018). https://doi.org/10.1007/s11123-018-0535-9

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