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. An industry is an ensemble of individual firms (decision making units) that may or may not interact with each other. In National Accounts terms this is symbolized by the fact that industry (aggregate) nominal value added is the simple sum of firm-specific nominal value added. From this viewpoint it is natural to expect there to be a relation between industry productivity and the firm-specific productivities. Yet, microdata researchers do not appear to pay much attention to the interpretation of the weighted means of firm-specific productivities they employ in their analyses. In this paper the consequences of this 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 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 paper 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. For instance, value-added based total factor productivities and output based weights require a harmonic mean, if additivity is assumed.
This paper draws from an extended version available at SSRN: http://ssrn.com/abstract=2585452. Presentations took place at the North American Productivity Workshop IX, 15–18 June 2016, Québec City, and the 34th General Conference of the International Association for Research in Income and Wealth, 21–27 August 2016, Dresden. Susanto Basu informed me that he had once written a paper with a virtually identical title. On inspection this turned out to be an embryonic version of Basu and Fernald (2002). Though related, my paper has a different focus.
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
Similar content being viewed by others
Notes
- 1.
This section has been copied from Balk (2016). Though the time dimension does not play an explicit role in the present paper, the notation is retained for consistency.
- 2.
“Consolidated” means that intra-unit deliveries are netted out. At the industry level, in some parts of the literature this is called “sectoral”. At the economy level, “sectoral” output reduces to GDP plus imports, and “sectoral” intermediate input to imports. In terms of variables to be defined below, consolidation means that \(C_{EMS}^{kkt} = R^{kkt} = 0\).
- 3.
See Balk (2015, footnote 2) for the treatment of net taxes on intermediates.
- 4.
On the relation between levels and indices, see Balk (2016, 21–28).
- 5.
de Loecker and Konings (2006) noted that there is no clear consensus on the appropriate weights (shares) that should be used. In their own work they used employment based shares L kt/∑ k L kt to weigh value-added based total factor productivity indices \(Q_{\mathit {VA}}^k(t,b)/Q_{KL}^k(t,b)\). We will return to this example.
- 6.
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 \(\mathit {PROD}^{\mathcal {K}^{t}t}\).
- 7.
Expression (18) is the model underlying GEAD-TFP as implemented by Calver and Murray (2016). Stated in our notation, instead of the right-hand side of expression (18) Basu and Fernald (2002) consider
$$\displaystyle \begin{aligned} \sum_{k \in \mathcal{K}^t}\frac{\mathit{VA}^{kt}}{\mathit{VA}^{\mathcal{K}^{t}t}}\mathit{TFPROD}_{VA}^{k}(t,b); \end{aligned}$$that is, mean value-added based total factor productivity where the weights are nominal value-added shares. This, then, cannot be interpreted as value-added based total factor productivity of the ensemble, unless special conditions apply.
- 8.
This paragraph has been inserted at the suggestion of a referee.
- 9.
Notice that we are considering here additivity of production units, which is different from additivity of commodities as considered in Balk (2016, Section 4.2).
- 10.
This is the model underlying the CSLS decomposition as implemented by Calver and Murray (2016).
- 11.
This measure was also considered by Foster et al. (2001). Actually, two variants were considered, one where the labour unit is an hour worked and one where it is a worker. The geometric alternative was employed by Hyytinen and Maliranta (2013) for plants; labour quantity was thereby measured in full time equivalents.
- 12.
Actually, their multi-factor productivity index, discussed in the extended version of this paper, can be seen as a special case of \(\mathit {TFPROD}_{Y}^{k}(t,b)\).
References
Baily, M. N., Bartelsman, E. J., & Haltiwanger, J. (2001). Labor productivity: Structural change and cyclical dynamics. The Review of Economics and Statistics, 83, 420–433.
Balk, B. M. (2010). An assumption-free framework for measuring productivity change. The Review of Income and Wealth, 56(Special Issue 1), S224–S256.
Balk, B. M. (2011). Measuring and decomposing capital input cost. The Review of Income and Wealth, 57, 490–512.
Balk, B. M. (2014). Dissecting aggregate output and labour productivity change. Journal of Productivity Analysis, 42, 35–43.
Balk, B. M. (2015). Measuring and relating aggregate and subaggregate total factor productivity change without neoclassical assumptions. Statistica Neerlandica, 69, 21–28.
Balk, B. M. (2016). The dynamics of productivity change: A review of the bottom-up approach. In W. H. Greene, L. Khalaf, R. C. Sickles, M. Veall, & M.-C. Voia (Eds.), Productivity and efficiency analysis. Proceedings in Business and Economics. Cham: Springer International Publishing.
Bartelsman, E. J., & Dhrymes, Ph. J. (1998). Productivity dynamics: US manufacturing plants, 1972–1986. Journal of Productivity Analysis, 9, 5–34.
Basu, S., & Fernald, J. G. (2002). Aggregate productivity and aggregate technology. European Economic Review, 46, 963–991.
Calver, M., & Murray, A. (2016). Decomposing multifactor productivity growth in Canada by industry and province, 1997–2014. International Productivity Monitor 31, 88–112.
Collard-Wexler, A., & de Loecker, J. (2015). Reallocation and technology: Evidence from the U. S. steel industry. American Economic Review, 105, 131–171.
de Loecker, J., & Konings, J. (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 D. Usher (Ed.), The measurement of capital. Cambridge, MA: National Bureau of Economic Research/University of Chicago Press.
Dumagan, J. C., & Balk, B. M. (2016). Dissecting aggregate output and labour productivity change: A postscript on the role of relative prices. Journal of Productivity Analysis, 45, 117–119.
Eslava, M., Haltiwanger, J., Kugler, A., & Kugler, M. (2013). Trade and market selection: Evidence from manufacturing plants in Colombia. Review of Economic Dynamics, 16, 135–158.
Foster, L., Haltiwanger, J., & Krizan, C. J. (2001). Aggregate productivity growth: Lessons from microeconomic evidence. In C. R. Hulten, E. R. Dean, & M. J. Harper (Eds.), New developments in productivity analysis (Studies in Income and Wealth, Vol. 63). Chicago/London: The University of Chicago Press.
Hyytinen, A., & Maliranta, M. (2013). Firm lifecycles and evolution of industry productivity. Research Policy, 42, 1080–1098.
Maliranta, M., & Määttänen, N. (2015). An augmented static Olley-Pakes productivity decomposition with entry and exit: Measurement and interpretation. Economica, 82, 1372–1416.
Melitz, M. J., & Polanec, S. (2015). Dynamic Olley-Pakes productivity decomposition with entry and exit. Rand Journal of Economics, 46, 362–375.
Olley, S., & Pakes, A. (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 Washington, DC: IMF).
van Biesebroeck, J. (2008). Aggregating and decomposing productivity. Review of Business and Economics, LIII, 122–146.
Vancauteren, M., Veldhuizen, E., & Balk, B. M. (2012). Measures of productivity change: Which outcome do you want? Paper presented at the 32nd General Conference of the IARIW, Boston, MA, August 5–11, 2012.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Balk, B.M. (2018). Aggregate Productivity and Productivity of the Aggregate: Connecting the Bottom-Up and Top-Down Approaches. In: Greene, W., Khalaf, L., Makdissi, P., Sickles, R., Veall, M., Voia, MC. (eds) Productivity and Inequality. NAPW 2016. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-68678-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-68678-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68677-6
Online ISBN: 978-3-319-68678-3
eBook Packages: Business and ManagementBusiness and Management (R0)