Rolling regressions and conditional correlations of foreign patents in the USA

Patent registrations have often been used as a proxy of innovation as they reflect a country's technological capability. Recently, some studies have found that the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model and an asymmetric extension, namely Glosten, Jagannathan and Runkle's (GJR) model, are useful to model the time-varying volatility of the patent ratio, namely the ratio of foreign patents registered in the USA to total patents in the USA. However, this approach assumes that the conditional variance is independent across countries. Furthermore, the time series properties of the patent growth rate, namely the rate of change of foreign patents registered in the USA, have not previously been analysed. This paper examines the conditional variance of the patent growth rate from the leading four foreign countries, namely Canada, France, Germany and Japan, using the Constant Conditional Correlation – Multivariate GARCH (CCC-MGARCH), Vector Autoregressive Moving Average – GARCH (VARMA-GARCH) and VARMA – Asymmetric GARCH (VARMA-AGARCH) models. The results reveal the existence of cross-countries effects in the patent growth rate among the leading four countries, as well as asymmetric effects using monthly data from January 1975 to December 1998. Rolling estimates show that the restrictive assumption of constant conditional correlation is unlikely to hold, and models that accommodate dynamic conditional correlations may provide greater insights for investigating the effects of global factors on changes in innovation for the four leading foreign countries