Working Paper BETA #2021-34

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Title : Fourier DF unit root test for R&D intensity of G7 countries

Author(s) : Yifei Cai, Jamel Saadaoui

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 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.

Key-words : R&D intensity; Schumpeterian growth model; Double frequency; Fourier DickeyFuller unit root test

JEL Classification : C12; C22; O30; O40