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

Abstract

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.

Appendix

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

1.1 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:

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

(3)

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.

1.2 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.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).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.²⁴ This correction is made as follows:

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

(4)

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:

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

(5)

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 %.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:

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

(6)

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.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.²⁷