Abstract
Productivity analysis is carried out at various levels of aggregation. In microdata studies the emphasis is on individual firms (or plants), whereas in sectoral studies it is on (groupings of) industries. Microdata researchers do not care too much about the interpretation of the weighted means of firm-specific productivities employed in their analyses. In this chapter the consequences of this attitude are explored, based on a review of the literature. However, a structurally similar phenomenon happens in sectoral studies, where the productivity change of industries is compared to each other and to the productivity change of some next-higher-level aggregate, which is usually the (measurable part of the) economy. Though there must be a relation between sectoral and economy-level measures, in most publications by statistical agencies and academic researchers this aspect is more or less neglected. The point of departure of this chapter is that aggregate productivity should be interpreted as productivity of the aggregate. It is shown that this implies restrictive relations between the productivity measure, the set of weights, and the type of mean employed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The relation between levels and indices was discussed in Sect. 5.4.
- 2.
PROD t can be considered as a 2-stage aggregation procedure: first PROD kt aggregates over basic inputs and outputs per production unit k, and then PROD t aggregates over all the units \(k \in \mathcal {K}^t\). \(\mathit {PROD}^{\mathcal {K}^{t}t}\) can be considered as a 1-stage aggregate of the same basic inputs and outputs. See Diewert (1980, 495–498) for a similar discussion in terms of variable profit (or, value added) functions and technological change (assuming continuous time and differentiability), and the PPI Manual (2004, Chapter 18) for the cases of revenue, intermediate-input-cost, and value-added based price indices. Notice the double role of the variable t in \(\mathit {PROD}^{\mathcal {K}^{t}t}\).
- 3.
- 4.
Notice that we are considering here additivity of production units, which is different from additivity of commodities as considered in Sect. 5.2.
- 5.
This is the model underlying the CSLS decomposition as implemented by Calver and Murray (2016).
- 6.
This reflects the denominator rule and the numerator rule of Fare and Karagiannis (2017), respectively.
- 7.
This measure was also considered by Foster et al. (2001). Actually, two variants were considered, one where the labour unit was an hour worked and one where it was a worker. The geometric alternative was employed by Hyytinen and Maliranta (2013) for plants; labour quantity was thereby measured in full-time equivalents.
- 8.
Actually, their multi-factor productivity index, discussed in Sect. 5.4.4.2, can be seen as a special case of \(\mathit {TFPROD}_{Y}^{k}(t,b)\).
- 9.
Essentially the same method was used by Figal Garone et al. (2020), except that \(\mathit {TFPROD}_{Y}^{k}(t,b)\) was replaced by revenue productivity.
References
Baily, M.N., E.J. Bartelsman, and J. Haltiwanger. 2001. Labor Productivity: Structural Change and Cyclical Dynamics. The Review of Economics and Statistics 83: 420–433.
Bartelsman, E.J., and Ph.J. Dhrymes. 1998. Productivity Dynamics: US Manufacturing Plants, 1972–1986. Journal of Productivity Analysis 9: 5–34.
Basu, S., and J.G. Fernald. 2002. Aggregate Productivity and Aggregate Technology. European Economic Review 46: 963–991.
Calver, M., and A. Murray. 2016. Decomposing Multifactor Productivity Growth in Canada by Industry and Province, 1997–2014. International Productivity Monitor 31: 88–112.
Collard-Wexler, A., and J. de Loecker. 2015. Reallocation and Technology: Evidence from the U. S. Steel Industry. American Economic Review 105: 131–171.
De Loecker, J., and J. Konings. 2006. Job Reallocation and Productivity Growth in a Post-Socialist Economy: Evidence from Slovenian Manufacturing. European Journal of Political Economy 22: 388–408.
Diewert, W.E. 1980. Aggregation Problems in the Measurement of Capital. In The Measurement of Capital, ed. Dan Usher (National Bureau of Economic Research, Cambridge MA; University of Chicago Press).
Eslava, M., J. Haltiwanger, A. Kugler, and M. Kugler. 2013. Trade and Market Selection: Evidence from Manufacturing Plants in Colombia. Review of Economic Dynamics 16: 135–158.
Färe, R., and G. Karagiannis. 2017. The Denominator Rule for Share-weighting Aggregation. European Journal of Operational Research 260: 1175–1180.
Figal Garone, L., P.A. López Villalba, A. Maffioli, and C.A. Ruzzier. 2020. Firm-level Productivity in Latin America and the Caribbean. Research in Economics 74: 186–192.
Foster, L., J. Haltiwanger and C.J. Krizan. 2001. Aggregate Productivity Growth: Lessons from Microeconomic Evidence. In New Developments in Productivity Analysis, ed. C.R. Hulten, E.R. Dean, and M.J. Harper. Studies in Income and Wealth, vol. 63. Chicago and London: The University of Chicago Press.
Hyytinen, A., and M. Maliranta. 2013. Firm Lifecycles and Evolution of Industry Productivity. Research Policy 42: 1080–1098.
Maliranta, M., and N. Määttänen. 2015. An Augmented Static Olley-Pakes Productivity Decomposition with Entry and Exit: Measurement and Interpretation. Economica 82: 1372–1416.
Melitz, M.J., and S. Polanec. 2015. Dynamic Olley-Pakes productivity decomposition with entry and exit. The RAND Journal of Economics 46: 362–375.
Olley, S., and A. Pakes. 1996. The Dynamics of Productivity in the Telecommunications Equipment Industry. Econometrica 64: 1263–1297.
PPI Manual. 2004. Producer Price Index Manual: Theory and Practice (Published for ILO, IMF, OECD, UN, Eurostat, The World Bank by IMF, Washington, DC).
van Biesebroeck, J. 2008. Aggregating and Decomposing Productivity. Review of Business and Economics LIII: 122–146.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Balk, B.M. (2021). Connecting the Two Approaches. In: Productivity. Contributions to Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-75448-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-75448-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-75447-1
Online ISBN: 978-3-030-75448-8
eBook Packages: Economics and FinanceEconomics and Finance (R0)