Shadow price of patent stock as knowledge stock: Time and country heterogeneity

This study compares the shadow price (marginal cost) and shadow value (total cost) of patent stock (as knowledge stock) in each of 92 countries between 1992 and 2010. Two specifications are considered in the data envelopment analysis approach. One specification considers population, capital, patent stock, energy use (four inputs), greenhouse gas (undesirable output), and gross domestic product (desirable output). The other uses human capital and natural capital instead of population and energy use. Under these two specifications, respectively, the shadow price of the patent stock (on weighted average) for the whole period is −0.106 and −0.054 million US dollars per patent in the entire sample. Similarly, the shadow value of the patent stock (by the ratio of gross domestic product) in the entire sample is −5.8% and −2.9%, respectively. As the standing position of patent stock, the patent stock is less valuable than human capital and (produced) capital but more valuable than population, energy use, and natural capital. The patent stock also is likely to be valuable in developing countries. In addition, the shadow value of the patent stock is relatively high in certain large countries and nearly flat in most of the countries.