Total factor productivity, domestic knowledge accumulation, and international knowledge spillovers in the second half of the twentieth century


This paper analyses the relationship between total factor productivity (TFP) and innovation-related variables during the second half of the twentieth century. We perform this analysis for several European countries (France, Germany, UK, and Spain) and the USA, extending Coe and Helpman’s (Eur Econ Rev 39:859–887, 1995) empirical specification to include human capital. We use a new dataset of patents data for the past 150 years to calculate the stock of knowledge using the perpetual inventory method. Our time series empirical analysis confirms the heterogeneous relationship between innovation variables (domestic stock of knowledge, imports of knowledge, and human capital) and productivity. Our results reveal the extent to which observed differences in technology adoption patterns and the levels of endowment of such resources can explain differences in TFP dynamics across countries. The estimated coefficients confirm the considerable gap that still exists between the European countries and the USA in innovation-related variables. Furthermore, we obtain a finding that may have important implications for innovation policies: the higher the levels of human capital and domestic knowledge stocks, the higher will be the response of TFP to a 1 % increase in any of the aforementioned variables.

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  1. 1.

    These conditions were determined by a new international order, more favourable to trade liberalisation and cooperation between Europe and the USA. Trade liberalisation helped speed up technology transfers from the USA to Europe and contributed to reducing Europe’s technology gap with the USA (Badinger 2005; Madsen 2007). The USA’s pre-war advantages, based on its exceptional endowment of natural resources and vast market potential, became less obvious after the war because of trade liberalisation (Nelson and Wright 1992). Further, this process was reinforced as Europe took advantage of its “old social capabilities” such as high levels of education, and well-established political and market institutions (Abramovitz 1986), as well as the “new social capabilities”, based on the investment in human capital and R&D, and a favourable environment for investment supported by the new social set-up between firms, state, and workers (Eichengreen 2007). Additionally, Comin and Hobijn (2010a) show that countries that were able to catch-up most with the US were also those receiving more economic aid and technical assistance from America.

  2. 2.

    The increasing use of ICT equipment explains the acceleration in American productivity growth since 1995 (Oliner and Sichel 2000; Jorgenson and Stiroh 2001).

  3. 3.

    Khan and Luintel (2006) and Coe et al. (2009) point out that the estimated coefficients of the innovation variables seem to be robust to the incorporation of new variables not strictly linked to innovation.

  4. 4.

    Several studies have incorporated improved measures of human capital following Engelbrecht (1997). See, among others, Frantzen (2000) and Barrio-Castro et al. (2002).

  5. 5.

    Our study distinguishes between the innovation experiences of countries with different levels of income per capita.

  6. 6.

    For the period 1950–1979, we use the 1980 labour and capital input shares taken from the Groningen Growth Development Centre (GGDC) Total Economy Growth Accounting Database.

  7. 7.

    Using data of citation patents granted for in the USA, Caballero and Jaffe (1993) find that the average annual rate of knowledge or technological obsolescence rises from about 3 % at the beginning of the century to about 10–12 % in 1990. As we are using patent data since 1870 to calculate the initial stock of knowledge, we follow Madsen (2007) and apply an average depreciation rate of 5 % for the whole period. Nonetheless, the literature fails to settle on an appropriate depreciation rate. For example, Pakes and Schankerman (1984) advocate a 20 % depreciation rate. Madsen (2007), on the other hand, tests both depreciation rates and finds no significant differences.

  8. 8.

    Coe and Helpman (1995) and Lichtenberg and Van Pottelsberghe de la Potterie (1998) use total imports as the channel for international technology spillovers.

  9. 9.

    Data on bilateral imports of highly technological products are drawn from Feenstra et al. (2005) for 1962–2000. We use the United Nations publication “Yearbook of International Trade Statistics” for years before 1962 (United Nations 1951–1965).

  10. 10.

    We also estimate our model using the average years of schooling as a measure of human capital. These results are available from the authors upon request.

  11. 11.

    Kortum and Lerner (1999) related this upsurge in patenting both to changes in firms’ management of research and in the US patent policy. In particular, these authors argue that the rise in patenting does not reflect a widening set of technological opportunities but a higher propensity of firms to protect their investment in R&D by means of patenting in advance.

  12. 12.

    To test for the order of integration of the series, we use a modified version of the Dickey–Fuller and Phillips–Perron tests, proposed by Ng and Perron (2001), who solve the three main problems facing the conventional tests for unit roots. These modified tests are \(\bar{M}Z_{\alpha }^{\text{GLS}}\), \(\bar{M}SB^{GLS}\), and \(\bar{M}Z_{t}^{GLS}\). A modified Akaike information criteria (MAIC) is used to select the autoregressive truncation lag, k, as proposed in Perron and Ng (1996). See Ng and Perron (2001) and Perron and Ng (1996) for a detailed description of these tests and the MAIC information criteria.

  13. 13.

    The results of these tests are available from the authors upon request.

  14. 14.

    In order to provide further evidence on the degree of integration of the domestic stock of patents, we also apply the Perron–Rodriguez test (Perron and Rodriguez 2003) for a unit root in the presence of a one-time change in the trend function, where a change in the trend function is allowed to occur at an unknown time, T B . To apply these tests, we select the break maximising the absolute value of the t-statistic on the coefficient of the slope change.

  15. 15.

    The results of these tests are available from the authors upon request.

  16. 16.

    In the empirical model, we test for deterministic cointegration using Shin’s (1994) test. This test is based on the calculation of an LM statistic from the DOLS residuals, namely C μ , to test for deterministic cointegration (when α 1 = 0). If cointegration is present in the demeaned specification given in (2), this occurs when α 1 = 0, corresponding to deterministic cointegration, which implies that the same cointegrating vector eliminates deterministic trends as well as stochastic trends. See Ogaki and Park (1997) and Campbell and Perron (1991) for an extensive treatment of deterministic and stochastic cointegration. We check for the presence of deterministic cointegration using the demeaned specification and obtain that the null hypothesis of deterministic cointegration is not rejected at the 1 % level in all cases. These results are available from the authors upon request.

  17. 17.

    The coefficient for the human capital variable, although positive in Model 2, is only significant at the 17.5 % level.

  18. 18.

    Further, our results give support to the idea that productivity relationships are heterogeneous across countries, depending on their accumulated stocks of knowledge and human capital, a result reported in previous panel data studies (see for example, Khan et al. 2010; Coe et al. 2009).

  19. 19.

    See, among others, Freeman (1987), Lundvall (1985), and Nelson (1993). A more recent perspective can be found in Fagerberg et al. (2005).

  20. 20.

    We compare our results with those of Coe et al. (2009), who use R&D panel data for 1970–2004, and with those of Madsen (2007), who uses patent data for the period 1870–2004.

  21. 21.

    For example, the results undergo no significant change when we include the interaction of knowledge imports with the propensity to import and when we use alternative measures of human capital. Even the different measures of human capital are statistically significant and positive.

  22. 22.

    See, among others, Schmookler (1966), Griliches (1984, 1990) Griliches et al. (1987), Schankerman and Pakes (1986), Jaffe et al. (2000), and Dernis et al. (2001).

  23. 23.

    Data have been drawn from WIPO Statistics Database. We particularly use patent grants and applications series by patent office, broken down by resident and non-resident (1883–2010).

  24. 24.

    We would like to thank an anonymous referee for pointing us this relevant issue.

  25. 25.

    Coe and Helpman (1995) and Madsen (2007) show that the estimation results are robust to different depreciation rates.

  26. 26.

    Other authors explore alternative channels, using different weights to build the foreign knowledge stocks. The channels that scholars habitually consider are as follows: imports of capital goods (Xu and Wang 1999; Luintel and Khan 2009), inward and forward FDI stocks (Van Pottelsberghe de la Potterie and Litchtenberg 2001; Lee 2006; Zhu and Jeon 2007), and the pattern of international patenting (Guellec and van Pottelsberghe de la Potterie 2004; Hafner 2008). Although most of these channels are significant for the transmission of foreign knowledge across borders, significant differences between channels are non-existent (Luintel and Khan 2009).

  27. 27.

    It is important to note that imports of highly technological products come mainly (around 50 % or more) from the biggest seven countries (France, Germany, Japan, Italy, Sweden, UK, and USA); however, we use 15 countries to construct the stock of imports of technology for two reasons. First, because in some cases, imports coming from countries not belonging to this group of seven countries are more important, such is the case of the USA with regard to imports coming from Canada. And second, because this is the procedure followed in other empirical researches (for example, Coe and Helpman 1995; Xu and Wang 1999; Lumenga-Neso et al. 2005; Madsen 2007).


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Financial support from the Instituto Valenciano de Investigaciones Económicas, the Ministerio de Ciencia y Tecnología (Projects ECO2011-25033; ECO2011-30323-C03-02; and ECO2012-39169-C03-02), MINECO (Ministerio de Economía y Competitividad, Project ECO2011-30260-CO3-01), Fundación Seneca-Regional Agency of the Regional Government of Murcia (Project 15363/PHCS/10), the Generalitat Valenciana (Project GVPROMETEO2009-098), the Department of Education and Science of the Regional Government of Castilla-La Mancha (Project PEII09-0072-7392), and the Generalitat Valenciana (Project GVPROMETEO2009-098 and PROMETEO/2009/068), and the GLOBALEURONET program from the European Science Foundation is gratefully acknowledged. We would also like to thank participants for comments and suggestions in the workshop “Patents in Economic History” (Eindhoven, 2009), in the European Historical Economics Society Conference (Geneva, 2009), in the VI Jornadas sobre Integración Económica (Valencia, 2009), and III Encuentro AEHE (Barcelona, 2012) and participants in a seminar at the University of Groningen (2009).

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Correspondence to Teresa Sanchis.



In what follows, we describe the procedure to calculate the variables used to estimate our model.

Measurement of total factor productivity

The construction of TFP uses a homogeneous Cobb–Douglas technology function with factor shares that vary over time and across countries:

$${\text{TFP}}_{it} = \frac{{Y_{it} }}{{K_{it}^{{\beta_{it} }} \cdot L_{it}^{{(1 - \beta_{it} )}} }}$$

where Y it is real GDP, K it is capital stock, L it is employment, and β it is the share of capital in total income. We use estimates of GDP, labour employed, physical capital stock, and labour share in the economy drawn from the Total Economy Growth Accounting Database (Groningen Growth Development Centre, GGDC), which covers the period 1980 to 2000. GDP and capital stock are in millions of 2000 US dollars.

For the years previous to 1980, TFP has been calculated using value added, labour employed, capital, and labour shares in the economy drawn from the Total Economy Database from the same institution. Capital and labour shares corresponding to 1980 are used for the period 1950–1979. Capital has been obtained using the homogenous capital stock series from O’Mahony (1996) for the UK, France, and Germany. In these series, the capital stock is computed as machinery and equipment capital stock plus non-residential buildings and structures capital stock. For Spain, we take the capital stock series calculated by Prados de la Escosura and Rosés (2010).

All the above estimates are used to measure TFP under the assumptions that production technology exhibits constant returns to scale and perfectly competitive product markets. These assumptions are widely used in the existing literature. Under these assumptions, the output elasticity of labour services is calculated through the share of labour input in the manufacturing sector.

Domestic knowledge stock

A novelty of this paper is that we use data of patents as an indicator of knowledge accumulation. Patents data come from the World Intellectual Property Organization (WIPO) Statistics Database. We use patents applied by residents instead of patents granted. For international comparisons, the number of patents applications is probably a better measure of the innovative activity of a country than the number of patents granted because the granting frequency varies across countries (Griliches 1990). For each country, we have calculated the domestic stock of patents and a weighted foreign stock of patents (or imports of knowledge). Patents are widely accepted as a reliable indicator for the innovative activity, especially when there are not appropriate data on R&D.Footnote 22

However, when using patent statistics as an indicator of the inventive activity, a number of issues should be considered, as put forward by Dernis et al. (2001) and Griliches (1990). First, not all inventions are patented. This is so as there are other alternatives to patenting that inventors may use to protect their inventions, such as trade secrecy or technical know-how. Second, a small number of patents account for most of the value of all patents. This means that simple patent counts could bias the measure of technology output. Third, patent systems for protecting inventions vary across countries and industries. Fourth, applicants’ different filling in strategies or preferences may make direct comparisons of patent statistics difficult across countries. A large set of innovations is not ever patented. Fifth, differences in patent systems may influence the applicant’s patent filling decisions in different countries. Sixth, due to the increase in the internationalisation of R&D activities, R&D may be conducted in one location but the protection for the invention is done in a different one. And, finally, cross-border patent fillings depend on various factors, such as trade flows, foreign direct investment, and market size of a country. Relative to other measures of technology, patents have the advantage that data have been collected for a long period of time (more than 150 years) and for a vast number of countries.

However, one of the main drawbacks in using patent statistics is that different countries have different standards of patentability. According to Lerner’s work (2000 and 2002), on the differences in international patent protection, there are important differences among countries analysed: concerning to patent fees, structure of patent renewals, patent office practices, etc. This means that the same invention can be patented in one country and not patented in another country. This is a common and well-known problem with patent data that affects both the number of patents granted and the number of patent applications.

One way of correcting for differences in the propensity to patent is to calculate a scaling factor. For this reason, we explore the correction made by Madsen (2007, p. 467) and other authors in relation to this issue. In particular, Madsen (2007) scales down Japanese patent applications by a factor of 4.9 following Eaton and Kortum (1999). This correcting factor compares the different propensity to patent (applications over granted) of any particular country with regard to the propensity to patent in the USA. Proceeding in similar way, we have calculated country-specific scaling factors following Okada (1992).Footnote 23 Eaton and Kortum (1999) and Madsen (2007) scaled down only the Japanese patents, the most outstanding case. Madsen (2007) argued that not scaling the other countries should not introduce major biases in the empirical work, given the efforts for patent harmonisation after the Paris convention. However, we have implemented the correcting scale factors to all countries, as we detect significant differences across countries, especially due to the length of the period analysed.Footnote 24 This correction is made as follows:

$$p_{it} = \frac{{{\text{pa}}_{it} }}{{s_{it} }}$$

where p it is the number of new patents in country i in year t, pa it is the number of patents applications of country i in year t in its national office (see below), and s it is the scaling factor calculated as the ratio between the rate of patents applications over granted for country i in the USA in year t over the same rate for the USA.

An additional issue related to patent series is related to the opening of the European Patent Office (EPO) in 1977. Since then, European inventors may decide to apply for patents at the EPO instead of using national patent offices. Therefore, patents applied in the national offices, which are also registered at the WIPO, do not represent anymore the total number of patents applied by residents in a particular country. To avoid this measurement problem and following a standard procedure, we add EPO patents to those applied at the national patent offices (or national patents at WIPO) to build the patent stocks.

Once we correct for the two issues raised above, the domestic stock of patents has been calculated from the accumulation of annual patent data based on the perpetual inventory method. The formula of the stock is:

$$S_{it}^{\text{d}} = (1 - \delta )S_{it - 1}^{\text{d}} + p_{it}$$

where \(S_{it}^{\text{d}}\) is the patent stock for country i in year t, p it is the number of new patents in country i in year t, and δ is the depreciation or obsolescence rate, assumed to be 5 %.Footnote 25 The initial value for the stock of patents was calculated using the perpetual inventory method.

To measure the technology spillovers embodied in trade flows, we follow Coe and Helpman (1995) to aggregate foreign stocks of patents as:

$$S_{it}^{{{\text{f}},{\text{CH}}}} = \sum\limits_{j} {\frac{{m_{ijt} }}{{m_{it} }}} S_{jt}^{\text{d}}$$

where m ijt is the flow country i imports of goods and services from country j in period t, and m it is country i total imports from its trading partners in t. This formulation assumes that a country will catch, ceteris paribus, more international knowledge spillovers if the country imports more from countries with a relatively high domestic capital stock.Footnote 26 To construct these measures, we use 15 exporter countries: USA, France, Germany, UK, Japan, Italy, Spain, Switzerland, Sweden, the Netherlands, Norway, Denmark, Greece, Portugal, and Belgium.Footnote 27

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Sanchis, T., Sanchis-Llopis, J.A., Esteve, V. et al. Total factor productivity, domestic knowledge accumulation, and international knowledge spillovers in the second half of the twentieth century. Cliometrica 9, 209–233 (2015).

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  • Innovation
  • International technology transfer
  • Patents
  • Productivity
  • Cointegration techniques
  • Second half XXth century

JEL Classification

  • N14
  • O33
  • O47
  • O22