To take a simple example, consider the production of the latest bestselling novel, the hottest-selling computer game, or the new Volkswagen Beetle. To produce the first unit of these items requires a large amount of effort: the novel must be written, the computer game must be created, and the Beetle must be (re)designed. But clearly these are one-time costs. The “idea” underlying each product only needs to be created once. Afterwards, subsequent units might plausibly be described as being produced with a constant returns to scale production function, following the standard replication argument. The idea is non-rivalrous in the sense that it can be used for each unit simultaneously. Total production of novels, computer games, and automobiles is then characterized by increasing returns once the fixed cost of creating the idea is taken into account. It is this fundamental link between ideas and returns to scale that gives rise to a basic scale effect in idea-based growth models.

Charles I. Jones (1998)

*This working paper is accessible in a PDF version at the end of this post.*

**Abstract.** According to the Schumpeterian endogenous growth theory, the efficacy of R&D is lowered by the proliferation of products. To be consistent with empirical data, the ratio between innovative activity and product variety (also called R&D intensity) must be stationary. In this perspective, our contribution investigates whether the R&D intensity series are stationary when structural breaks are considered. Our sample of G7 countries is examined over the period spanning from 1870 to 2016. Our results indicate that traditional unit root tests (ADF, DF-GLS and KPSS) conclude that the R&D intensity series are non-stationary in contradiction with the Schumpeterian endogenous growth theory. The conclusions of these traditional unit root tests may be misleading, as they ignore the presence of structural breaks. Indeed, we use several types of Fourier Dickey-Fuller tests to consider the presence of structural breaks. In the Fourier Dickey-Fuller unit root tests using double frequency and fractional frequency, the R&D intensity is significantly stationary at least at the 5% level for Canada, France, Germany, Italy, Japan and the U.K. when a deterministic trend is included in the tests. Nevertheless, the R&D intensity is non-stationary for the US, even when we consider structural breaks. Indeed, the integration analyses aimed at discriminating between competing theories of endogenous growth should be careful of the presence of structural breaks. Especially when historical data are used, traditional unit root tests may lead to erroneous economic interpretations. These findings may help to understand the true nature of long-run economic growth and may help to formulate sound policy recommendations.

Feel free to download, share or comment the following working paper:

**Yifei Cai, Jamel Saadaoui.** Fourier DF unit root test for R&D intensity of G7 countries. BETA Working Paper (2021). Available at SSRN: https://dx.doi.org/10.2139/ssrn.3885026

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