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Sectoral productivity trends: convergence islands in oceans of non-convergence

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Abstract

Growth theory argues that thresholds can lead to multiple growth regimes, which are reflected in heterogeneous patterns of cross-country convergence and divergence. We study sectoral convergence patterns by using a new longitudinal sectoral database for 65 developed and developing countries. We employ an econometric method, quantile smoothing splines, which explicitly allows for identification of parameter heterogeneity both with regard to initial conditions (X-heterogeneity) and growth performances (Y-heterogeneity). Findings suggest that convergence is rather the exception than the rule.

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Notes

  1. In what follows, we will use the term country-sectors to denote the observations in our samples (i.e. the Dutch agricultural sector, or the Indonesian manufacturing sector).

  2. See the theoretical models reviewed in section 2 of this paper.

  3. The 14 countries in BJ’s sample are Australia, Belgium, Canada, Denmark, Finland, France, Italy, Japan, the Netherlands, Norway, Sweden, the United Kingdom, the United States, and West Germany.

  4. For 49 countries, the series start in 1970; for many Eastern European countries, reliable data is only available from 1995 onwards.

  5. The main sectors are: Agriculture, Mining, Manufacturing, Utilities, Construction, Wholesale and retail trade, Transport, storage and communication, Financial services, and Non-market services (community social and personal services, and government services). The data are publicly available for free at www.ggdc.net and www.wiod.org.

  6. Details about the estimation of the sectoral PPPs for 2005 can be found in Inklaar and Timmer (2013).

  7. In a reply to Sørensen (2001), Bernard and Jones (2001) argued that this systematic finding is a consequence of the Balassa-Samuelson effect. In countries with high labor productivity growth in manufacturing, relative manufacturing prices tend to decline rapidly; hence, initial value added in manufacturing is underestimated in high productivity growth countries if GDP PPPs associated with a later base year are used to deflate its value added, leading to a tendency to find β-convergence.

  8. In a recent paper, Rodrik (2013) focused on the manufacturing sector, finding strong evidence for unconditional labor productivity convergence in a sample that contains even more non-OECD countries than ours. His analysis, however, is based on UNIDO industrial survey data, which typically only considers the formal economy, while our data also take informal economic activity into account.

  9. See Koenker (2005) for an extended exposition.

  10. In the period 1970–2009, labor productivity growth in Denmark’s agricultural sector grew on average by 7.3 % per year, while Venezuela’s corresponding figure amounted to a tiny 0.7 %. We borrowed the term ‘law of motion’ from Bernard and Durlauf (1996).

  11. The number of linearly interpolated y i s (p λ ) is at least 2 and at most the number of observations n. The number of linear segments in the fitted function associated with the smoothing parameter λ equals (n - p λ +1).

  12. We will consider sensitivity of the results to inclusion of country fixed effects, though, applying techniques introduced by Koenker (2004). See Holst Milton Bache et al. (2013) for more elaborate comparisons between methods to analyze panel data using quantile regression techniques.

  13. In view of the limited number of observations, we do not produce regressions for “extreme” quantiles (such as τ = 0.1 and 0.9). Programs for quantile regressions are available in R and Stata. Code to run quantile smoothing splines is currently only available in R (Ng and Maechler, 2011).

  14. Unconstrained linear quantile smoothing splines were estimated using the COBS package, version 1.1–3.5 (He and Ng, 1999).

  15. An all-encompassing approach to assessing the statistical significance of results of analyses based on quantile smoothing splines would also consider the stochastic nature of the existence and location of the kinks. Are the kinks statistically significant, and what are the confidence intervals for the initial productivity level where a kink is located? In principle, simultaneously testing for the existence of kinks and the significance of slopes should also be possible using a bootstrapping approach. However, we consider that developing such a testing framework and carefully assessing its statistical properties would be beyond the scope of this paper.

  16. Appendix B shows that the absence of kinks for manufacturing and services is not due to the value of the parameter λ that follows from the Schwarz Information Criterion (Eq. 7)

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Author information

Authors and Affiliations

  1. Centre for Technology, Innovation and Culture (TIK), University of Oslo, P.O. Box 1108, Blindern, 0317, Oslo, Norway

    Fulvio Castellacci

  2. Faculty of Economics/Groningen Growth and Development Center, University of Groningen, P.O. Box 800, NL-9700 AV, Groningen, The Netherlands

    Bart Los & Gaaitzen J. de Vries

Authors
  1. Fulvio Castellacci
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  2. Bart Los
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  3. Gaaitzen J. de Vries
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Corresponding author

Correspondence to Fulvio Castellacci.

Additional information

This paper benefitted comments from and discussions with participants at the DIME conference in Maastricht, the Globelics Conference in Mexico City, the North-American Productivity Workshop at New York University, a seminar at the University of Groningen, communication with Roger Koenker and Pin Ng, and detailed comments by two anonymous referees and the Editor of this journal.

Appendices

Appendix A

Table 5 Labor productivity growth rates, 1970-2009
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Appendix B

Section 4.2 explains the role of λ, which is a smoothing parameter for the estimated splines. In our empirical application of quantile smoothing splines, we choose the smoothing parameter λ such that the SIC criterion in Eq. 7 reaches its global minimum. The results indicate that X-heterogeneity appears to play a limited role in the convergence patterns in Agriculture, Manufacturing and Services. Here, we analyze the sensitivity of these results to the selection of lambda.

For Agriculture, we find that the SIC criterion leads us to choose λ = 1403, for all three quantiles. However, a plot of the SIC criterion against λ suggests that the value of SIC hardly increases if λ is stepwise reduced, until λ = 10. For values lower than 10, SIC is considerably higher. Hence, λ = 10 might serve as a lower bound to examine the absence of X-heterogeneity (note that if λ = 0, all observations for a quantile are linearly interpolated). The results for Agriculture obtained for λ = 10 are depicted in Fig. 2. A similar strategy was followed for Manufacturing and Services. All results clearly suggest that the absence or minor role of thresholds in the sectoral productivity dynamics is a result that is not sensitive to the choice of other reasonable values for the smoothing parameter λ.

Fig. 2
figure 2

Quantile smoothing splines for agriculture, manufacturing and services using lower values for the smoothing parameter λ

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Castellacci, F., Los, B. & de Vries, G.J. Sectoral productivity trends: convergence islands in oceans of non-convergence. J Evol Econ 24, 983–1007 (2014). https://doi.org/10.1007/s00191-014-0386-0

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