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Determinants of Wealth Disparities in the EU: A Multi-scale Development Accounting Investigation

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Abstract

This paper presents a development accounting framework in order to quantify the determinants of disparities in GDP per hour worked within the EU in 2016. Its originality is twofold insofar as, on the one hand, it theoretically extends the existing framework from 2 factors up to \(n\) explanatory factors and on the other, it numerically illustrates this same framework in case where \(n=3\) factors. This illustration is made macro-economically between 19 EU countries—representing 90% of its aggregate GDP—and sectorally between their market, state, and mixed sectors. The calibration data come from the latest EU-KLEMS and PWT versions. Examination of the results by decomposition shows a strong proximity of macroeconomic standard deviations ($ 13.74/h) and the market (13.38) and non-market (12.34) spheres. The differences between countries are fundamentally (around 90% according to each of the three spheres) explained by the disparities in labor quality (and around 10% by the disparities in capital deepening). The profile, however, is not at all the same in real estate activities (mixed sector) whose GDP per hour’ standard deviation reaches $ 570.28/h and is completely explained by the disparities in capital deepening.

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Fig. 1

Source: Author's calculations based on EU KLEMS database, 2019 release

Fig. 2

Source: Author's calculations based on EU KLEMS database, 2019 release

Fig. 3

Source: Author's calculations based on EU KLEMS database, 2019 release

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Notes

  1. We speak more precisely of “technical bias evolution” on the concerned production factor.

  2. A general and synthetic overview of the conceptual framework for growth accounting can be found for instance in the OECD manual (2001, section 2.4). Several works in the spirit of this framework can be evoked here: The works of Jorgenson (1995) for example, analyzing comparatively the differences in growth between industrialized countries post-World War II; of Young (1995) explaining that the “Asian miracle,” in particular an average annual growth around 5.5% in 8 countries in Southeast Asia between 1960 and 1995, could be explained by the growth of labor and capital and less by TFP; or Barro and Sala-i-Martin (2004) showing that the “augmented Solow model” was consistent with the speeds of convergence between countries and between states or regions of the same entity (USA, Japan, Europe).

    More recently, in France, we have for example the works of Cette et al. (2004, 2005a, b, 2014) and Daw (2019) ; in the USA, the works of Oliner and Sichel (2002) or Jorgenson et al. (2004, 2006 and 2008) ; Baier et al. (2006), show for 144 countries between 1990 and 2000, that only 14% of the evolution of the product per worker is due to the evolution of TFP (authors present a development accounting part that we describe in this section). The papers of Van Ark et al. (2008) for a comparison between the USA and the European Union or even Oulton (2002) and Marrano et al. (2009) for the UK, illustrate according to the authors or the year of publication, aggregated (macroeconomic) or more disaggregated frameworks of exogenous retrospective and prospective growth accounting without bias of technical progress (Except Daw 2019, where we retrieve these biases). In Japan, Sato and Tamaki (2009) illustrate an aggregated growth accounting exercise (exogenous long-term retrospective growth accounting with technical progress bias). The works of Madsen (2010a, b), Fernald and Jones (2014) and Bergeaud et al. (2017) for example can also be considered as variation but in which endogenous modeled mechanisms appear explaining the evolution of factors contributing to growth without, however, moving toward what is meant by general equilibrium modeling of economies that are measured.

    Indeed, today, alongside the more or less “standard” growth accounting frameworks mentioned above, there is a second approach of growth accounting, but which is carried out using general equilibrium modeling (à la Uzawa, 1963) of the economy to be measured (Greenwood et al. 1997; Cummins and Violante 2002; Whelan 2003; Fisher 2006; Ngai and Samaniego 2009; Oulton 2012; Byrne and Corrado 2017…).

  3. With regard to growth accounting, Klenow and Rodriguez-Clare (1997, p.79), Barro and Sala-i-Martin (2004, p.441-442), Caselli (2005, p.10) or even Baier et al. (2006, p.37) highlight the inconvenience of the econometric method linked, among other things, to endogeneity of TFP with GDP as well as to co-movements between explanatory variables. Hulten (2001) sees possible synergies when, for example, econometrics manages to shed light on the content of the growth residual (therefore “our ignorance”) which is previously determined by the growth accounting exercise. Although attributing merit to econometrics, OECD (2001, p.19) also highlights several limitations and indicates that the tool recommended in practice remains the usual growth accounting framework.

  4. That we have distinguished from the question of attribution to put forward more the solution adopted for the treatment of the problem than the problem itself.

  5. Even if the variable to be explained is not exactly the same: product per capita in Mankiw et al. (1992) and product per worker for Klenow and Rodriguez-Clare (1997).

  6. Please, see note 15 for the meaning of “correlated portion.”

  7. $$\mathrm{Y}={\mathrm{AK}}^{{\alpha }}{\left(\mathrm{Lh}\right)}^{1-{\alpha }}$$
  8. $$\begin{aligned} \text{var} ~\left( {aX + bY + cZ} \right) &=& E~\left( {\left( {\left[ {aX + bY + cZ} \right] - E\left[ {aX + bY + cZ} \right]} \right)^{2} } \right) = E~\left( {\left( {a\left[ {X - E\left[ X \right]} \right] + b\left[ {Y - E\left[ Y \right]} \right] + c\left[ {Z - E\left[ Z \right]} \right]} \right)^{2} } \right) \\ &=& E\left( {\left( {a^{2} \left( {X - E\left[ X \right]} \right)^{2} } \right)} \right) + \left( {b^{2} \left( {Y - E\left[ Y \right]} \right)^{2} } \right) + \left( {c^{2} \left( {Z - E\left[ Z \right]} \right)^{2} } \right) + 2ab\left( {X - E\left[ X \right]\left( {Y - E\left[ Y \right]} \right) + 2ac\left( {X - E\left[ X \right]} \right)\left( {Z - E\left[ Z \right]} \right) + 2bc\left( {Y - E\left[ Y \right]} \right)\left( {Z - E\left[ Z \right]} \right)} \right) \\ & =& a^{2} E(X - E\left[ X \right])^{2} + b^{2} E\left( {Y - E\left[ Y \right]} \right)^{2} + c^{2} E\left( {Z - E\left[ Z \right]} \right)^{2} + 2ab~E\left( {\left( {X - E\left[ X \right]} \right)\left( {Y - E\left[ Y \right]} \right)} \right) + 2ac~E\left( {\left( {X - E\left[ X \right]} \right)\left( {Z - E\left[ Z \right]} \right)} \right) + 2bc~E\left( {\left( {Y - E\left[ Y \right]} \right)\left( {Z - E\left[ Z \right]} \right)} \right) \\ \end{aligned}$$

    , and finally:

    $$\mathrm{var }\left(\mathrm{aX}+\mathrm{bY}+\mathrm{cZ}\right)={\mathrm{a}}^{2}\mathrm{varX}+{\mathrm{b}}^{2}\mathrm{varY}+{\mathrm{c}}^{2}\mathrm{varZ}+2\mathbf{a}\mathbf{b}\mathbf{c}\mathbf{o}\mathbf{v}\left(\mathbf{X},\mathbf{Y}\right)+2\mathbf{a}\mathbf{c}\mathbf{c}\mathbf{o}\mathbf{v}\left(\mathbf{X},\mathbf{Z}\right)+2\mathbf{b}\mathbf{c}\mathbf{c}\mathbf{o}\mathbf{v}\left(\mathbf{Y},\mathbf{Z}\right)$$

    If the interdependencies were zero: \(\mathrm{v}\mathrm{a}\mathrm{r}\left(\mathrm{a}\mathrm{X}+\mathrm{b}\mathrm{Y}+\mathrm{c}\mathrm{Z}\right)={\mathrm{a}}^{2}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{X}+{\mathrm{b}}^{2}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{Y}+{\mathrm{c}}^{2}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{Z}\).

  9. By analogy with the variance formula, set: \(\mathrm{X}=\mathrm{lnA };\mathrm{Y}=\mathrm{lnk };\mathrm{Z}=\mathrm{lna}\) ; \(\mathrm{a}=1\); \(\mathrm{b}={\alpha }\) and \(\mathrm{c}=\left(1-{\alpha }\right)\)

  10. Or what, except for the notations, is equivalent to (15) or (17).

  11. A negative variance (!) is synonymous with a negative explanatory power (!); a relative variance greater than unity (!) is synonymous with an explanatory power greater than 100% (!).

  12. By dividing on both sides, the equation 4 by \(var\mathrm{ln}{y}_{G}\), one can easily have an equivalent writing but with correlation coefficients, here represented in the expressions in bold:

    $$1=\frac{\mathrm{varlnA}}{{\mathrm{varlny}}_{\mathrm{G}}}+{{\alpha }}^{2}\frac{\mathrm{varlnk}}{{\mathrm{varlny}}_{\mathrm{G}}}+{\left(1-{\alpha }\right)}^{2}\frac{\mathrm{varlna}}{{\mathrm{varlny}}_{\mathrm{G}}}+2{\varvec{\alpha}}{{\varvec{\uprho}}}_{\mathbf{l}\mathbf{n}\mathbf{A},\mathbf{l}\mathbf{n}\mathbf{k}}\frac{{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{A}}{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{k}}}{\mathbf{v}\mathbf{a}\mathbf{r}\mathbf{ln}{\mathbf{y}}_{\mathbf{G}}}$$
    $$+2\left(1-{\varvec{\alpha}}\right){{\varvec{\uprho}}}_{\mathbf{l}\mathbf{n}\mathbf{A},\mathbf{l}\mathbf{n}\mathbf{a}}\frac{{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{A}}{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{a}}}{\mathbf{v}\mathbf{a}\mathbf{r}\mathbf{ln}{\mathbf{y}}_{\mathbf{G}}}+2{\varvec{\alpha}}\left(1-{\varvec{\alpha}}\right){{\varvec{\uprho}}}_{\mathbf{l}\mathbf{n}\mathbf{k},\mathbf{l}\mathbf{n}\mathbf{a}}\frac{{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{k}}{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{a}}}{\mathbf{v}\mathbf{a}\mathbf{r}\mathbf{ln}{\mathbf{y}}_{\mathbf{G}}}$$

    With: \({\uprho }_{\mathrm{lni},\mathrm{lnj}}=\frac{\mathrm{cov}\left(\mathrm{lni},\mathrm{lnj}\right)}{{\upsigma }_{\mathrm{lni}}{\upsigma }_{\mathrm{lnj}}}\) the correlation coefficient, and: \(\mathrm{i},\mathrm{j}=\mathrm{lnA},\mathrm{lnk orlna}\) and: \(-1\le {\uprho }_{\mathrm{lni},\mathrm{lnj}}\le 1\)

    The object of the game is to allocate the correlated portions of the last three expressions to the numerators of the first three in accordance with the principle of averaging. By correlated portion, we mean, for example between TFP and capital per hour worked, the value of: \(2{\varvec{\alpha}}{{\varvec{\uprho}}}_{\mathbf{l}\mathbf{n}\mathbf{A},\mathbf{l}\mathbf{n}\mathbf{k}}{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{A}}{{\varvec{\upsigma}}}_{\mathbf{l}\mathbf{n}\mathbf{k}}\). Furthermore, the “all or nothing” technique would consist in assigning all this value to the TFP variance and to that of capital/h in a symmetrical configuration.

  13. If we materialize the “all” of the correlated portion by “+” and the “nothing” by “-“, in the case of two factors, the only configuration and its perfect symmetry :\({\mathrm{x}}^{+}{\mathrm{y}}^{-}\) (the whole correlated portion goes to the variance in \(\mathrm{x}\) and nothing to the variance in \(\mathrm{y}\)) and \({\mathrm{x}}^{-}{\mathrm{y}}^{+}\) (the whole correlated portion goes to the variance in \(\mathrm{y}\) and nothing to the variance in \(\mathrm{x}\)) and then we take the mean covariance which comes back to variance x and that of y in the two situations. In the case of three factors, an example configuration is: \({\mathrm{x}}^{+}{\mathrm{y}}^{-} ; {\mathrm{x}}^{-}{\mathrm{z}}^{+};{\mathrm{y}}^{+}{\mathrm{z}}^{-}\) (and there are 5 others, playing on the signs). We have seen in the case of two factors that the “all” is understood by factor, which generates two perfectly symmetrical configurations, which is inapplicable here. In the example given (or among the other 5 combinations), what is the “all”? There is no “all” by configuration since each factor is involved in several configurations (three configurations and their three symmetrical) and there is therefore no “nothing” perfectly symmetrical in the sense of unique. Violation of this property of perfect symmetry of configurations invalidates the “all or nothing” technique when \(\mathrm{n}>2\).

  14. To be more precise, this solution would be satisfactory in the context of \(\mathrm{n}>2\) factors. With 2 factors for example, the satisfactory solution is that of Baier et al. (2006), Turner et al. (2013) or Tamura et al. (2019).

  15. The sections of NACE Rév. 2: O “Public administration,” P “Education” and Q “Human health and social action,” group together activities usually carried out on a non-profit basis.

  16. The mixed sphere—Section L “Real estate activities” includes the purchases, sales, rentals of private or public real estate, related activities such as the valuation and management-for own account or for others- of these goods.

  17. There is necessarily at least one, by definition of the developed formula of the variance.

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Authors and Affiliations

  1. Université Paris 8 Vincennes Saint-Denis (Laboratoire d’économie dionysien-LED, EA 3391), Saint-Denis, France

    Georges Daw

  2. ESSCA School of Management (UER Economics, Law & Society), Boulogne-Billancourt, France

    Georges Daw

  3. Université Paris 1 Panthéon–Sorbonne (Centre d’économie de la Sorbonne-CES, UMR 8174), Paris, France

    Georges Daw

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Daw, G. Determinants of Wealth Disparities in the EU: A Multi-scale Development Accounting Investigation. Comp Econ Stud 64, 211–254 (2022). https://doi.org/10.1057/s41294-021-00161-4

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