The role of production factor quality and technology diffusion in twentieth-century productivity growth


The twentieth century was a period of exceptional growth, driven mainly by the increase in total factor productivity (TFP). Using a database of 17 OECD countries over the 1890–2013 period, this paper integrates production factor quality into the measure of TFP, namely by factoring the level of education of the working-age population into the measure of labor and the age of equipment in the measure of capital stock. We then estimate how the diffusion of technology impacts the growth of this newly measured TFP through two emblematic general purpose technologies, electricity and information and communication technologies (ICT). Using growth decomposition methodology from instrumental variable estimates, this paper finds that education levels contribute most significantly to growth, while the age of capital makes a limited, although significant, contribution. Quality-adjusted production factors explain less than half of labor productivity growth in the largest countries except for Japan, where capital deepening posted a very large contribution. As a consequence, the “one big wave” of productivity growth (Gordon in Am Econ Rev 89(2):123–128, 1999), as well as the ICT productivity wave for the countries which experienced it, remains only partially explained by quality-adjusted factors, although education and technology diffusion contribute to explain the earlier wave in the USA in the 1930s–1940s. Finally, technology diffusion, as captured through our two general purpose technologies, leaves unexplained between 0.6 and 1 percentage point of yearly growth, as well as a large proportion of the two twentieth-century technology waves. These results both support a significant lag in the diffusion of general purpose technologies and raise further questions on a wider view on growth factors, including changes in the production process, management techniques and financing practices. Measurement problems may also contribute to the unexplained share of growth.

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Fig. 1

Source: van Leeuwen and van Leeuwen-Li (2014)

Fig. 2

Source: Authors’ calculations—see text. The depreciation rate is assumed to be equal to 10 % per year

Fig. 3

Source: See text (human capital has been computed with a value of 7 % for θ and age of capital with a value of 10 % for ε). α is set to 0.3

Fig. 4

Source: see text

Fig. 5

Source: Authors’ calculation based on Cette et al. (2015)

Fig. 6

Source: See text (human capital has been computed with a value of 7 % for θ and age of capital with a value of 10 % for ε). α is set to 0.3. The coefficients for electricity and ICT are 0.079 and 1.557, respectively


  1. 1.

    All these figures come from sources that will be detailed below and are used throughout the paper.

  2. 2.

    Basu and Fernald (2002) show that imperfections and frictions in output and factor markets matter in the relation between aggregate technology and aggregate productivity. For example, with heterogeneous firm markups, the same resources may be valued differently in different uses. Then, “reallocating resources toward more socially valued uses raises aggregate productivity, without necessarily reflecting changes in technology.” Citation from page 964 of Basu and Fernald (2002). Edquist (2001) raises the question of the role of innovation policy with respect to technology diffusion.

  3. 3.

    “[T]he rise of China, India and other emerging economy countries, [is] likely [to] impl[y] rapid growth in world researchers for at least several decades.” Citation from page 48 of Fernald and Jones (2014).

  4. 4.

    The calculation starts with primary school and does not include kindergarten or any other type of education received before 6.

  5. 5.

    In our model, depreciation of each element of capital follows a geometric distribution where the probability of depreciation is \(\delta\). This distribution is memoryless, that is, the probability of depreciation is independent of the age of capital, and the average life expectancy of capital is then equal to \(\frac{1}{\delta }\).

  6. 6.

    In practice, we compute G by taking the average of the growth rate of GDP over 10 years. This relationship makes a strong assumption, but the initial stock of capital is computed years before 1890, which is the first year in this study. The empirical impact of this simplification is then of minor importance in the age of capital evaluation.

  7. 7.

    As raised in Psacharopoulos (1994), this return can be higher in other regions of the world (12.4 % in Latin America, 13.4 % in sub-Saharan Africa and 9.6 % in Asia).

  8. 8.

    Over the long run, the ratio of capital to output is very stable, as seen in Madsen (2010a). Such stability is consistent with the idea that the saving rate results from aggregated individual preferences that are quite constant over time.

  9. 9.

    A reverse impact could come from a learning by doing effect: firms may manage to use a capital vintage better as it ages. Our estimates encompass this effect, which appears not to be predominant.

  10. 10.

    The effect of the age of the capital stock on productivity is of course negative. We will, however, present the effect in absolute value terms in the following paragraphs to better relate it to the value of ε, which is positive.

  11. 11.

    The dependent variable shows very strong autocorrelation of degree one which disappears when looking at longer lags. We thus check that our results are still valid when autocorrelation and heteroskedasticity robust standard errors using the Newey–West variance estimator are implemented (of course this does not affect the coefficients).

  12. 12.

    For these columns and for all the others, we include time and country fixed effects and remove war periods.

  13. 13.

    Capital stock is constructed from investment which is included in GDP, so any measurement error in investment would impact both labor productivity and capital intensity.

  14. 14.

    Periods in Table 3 are based on productivity breaks from Bergeaud et al. (2016).

  15. 15.

    The waves presented in Figs. 3 and 6 have been computed by removing the cyclical component of our time series using a HP filter with a coefficient of 500. The choice of this coefficient has been made to better capture 30-year-long business cycles, consistent with Norbert (2006). On these aspects, see Bergeaud et al. (2015).

  16. 16.

    When data were missing, we have interpolated them with the production of CO2 emissions from the Global Carbon Project.

  17. 17.

    When all countries are included (and when we only estimate the effect on electricity), the coefficients remain extremely stable.

  18. 18.

    Small variations in this starting date do not affect our results; we do, however, believe that 1905 is a good starting point at the end of the first industrial revolution since from Fig. 4 we can see that it is the beginning of the surge in electricity production in the USA. Results are also robust to starting the estimations in 1895 or 1913.


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The views expressed herein are the authors’ and do not necessarily reflect the views of the institutions they belong to. We wish to thank, without in any way holding responsible, Thierry Mayer for valuable advice concerning the construction of the instruments, Bas Van Leeuwen for advice on education data, and Nicholas Craft and John Fernald for their comments. We also thank two anonymous referees from the journal for their remarks.

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Correspondence to Rémy Lecat.

Appendix 1: Methodology for the evaluation of the contribution of ICT to labor productivity growth through capital deepening

Appendix 1: Methodology for the evaluation of the contribution of ICT to labor productivity growth through capital deepening

The evaluation of the contribution of ICT to hourly labor productivity growth, through capital deepening, is calculated by applying the growth-accounting methodology set out by Solow (1956, 1957). This contribution in year t, noted as \(CO_{t}^{ICT}\), is evaluated using the following relation:

$$CO_{t}^{\text{ICT}} = \alpha_{t}^{\text{ICT}} \times \left( {\Delta k_{t - 1}^{\text{ICT}} - \Delta n_{t} - \Delta h_{t} } \right)$$

where \(K_{t - 1}^{\text{ICT}}\) corresponds to the ICT capital installed at the end of year t − 1, \(N_{t}\) refers to total employment in year t and \(H_{t}\) designates the average annual hours worked per person per year t. The notation of the variables in lowercase corresponds to their natural log \(\left( {x = \ln \left( X \right)} \right)\), and the growth rate of a variable is approximated by the variation of its logarithm. The Δ symbol refers to the variation of a variable \(\left( {\Delta X_{t} = X_{t} - X_{t - 1} } \right)\).

The coefficient \(\alpha_{t, 2}^{\text{ICT}}\) is the Törnquist index of the coefficient \(\alpha_{t}\):

$$\alpha_{t,2}^{\text{ICT}} = \frac{1}{2}\times \left( {\alpha_{t}^{\text{ICT}} + \alpha_{t - 1}^{\text{ICT}} } \right)$$

The coefficient \(\alpha_{t}^{\text{ICT}}\) corresponds to the share of capital remuneration in GDP:

$$\alpha_{t}^{\text{ICT}} = \frac{{C_{t}^{\text{ICT}} \times K_{t - 1}^{\text{ICT}} }}{{P_{{Y_{t} }} \times Y_{t} }}$$

where \(C_{t}^{\text{ICT}}\) corresponds to the user cost of capital, \(P_{{Y_{t} }}\) corresponds to the GDP deflator and \(Y_{t}\) refers to GDP in volume.

The user cost of ICT capital C is calculated employing the relation proposed by Jorgenson (1963):

$$C_{t}^{\text{ICT}} = P_{t}^{\text{ICT}}\times \left( {i_{t} + \delta^{\text{ICT}} + \Delta p_{t}^{\text{ICT}} } \right)$$

where \(P^{\text{ICT}}\) corresponds to the investment price of ICT, i refers to the nominal interest rate and δ ICT designates the assumed invariant depreciation rate of ICT.

We have considered two alternative options for the nominal interest rate: 10-year government bond yields and a fixed rate of 10 %. The evaluation of both approaches is close to one another in the growth contribution calculation. In this study, we have used the 10-year government bond yields taken from the OECD’s main economic indicators.

The overall share of capital, α, is assumed to be invariant and the same for all countries, with α = 0.3. This means that to evaluate the overall capital deepening effect, we have assumed that \(\alpha_{t}^{\text{NICT}}\), the non-ICT capital share, is obtained, for each year t and country i observation, from the relation:

$$\alpha_{t} = \alpha_{t}^{\text{ICT}} + \alpha_{t}^{\text{NICT}} = 0.3\;{\text{and}}\;{\text{then}}\;\alpha_{t}^{\text{NICT}} = 0.3 - \alpha_{t}^{\text{ICT}}$$

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Bergeaud, A., Cette, G. & Lecat, R. The role of production factor quality and technology diffusion in twentieth-century productivity growth. Cliometrica 12, 61–97 (2018).

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  • Productivity
  • Total factor productivity
  • Education
  • Technological change
  • Technology diffusion
  • Global history

JEL Classification

  • N10
  • O47
  • E20