Scale Effects, An Error of Aggregation Not Specification: Empirical Evidence

Abstract

In a set of influential papers, Charles Jones (1995a, 1995b, 1999) argued that R&D based endogenous growth models are inconsistent with the data. He showed, in a very striking manner, that the scale effects prediction of early endogenous growth models (e.g. Romer, 1986 and 1990, Grossman and Helpman, 1991, and Aghion and Howitt, 1992) is not borne out in the data. Standard endogenous growth models attribute constant or increasing returns in the stock of knowledge or technology to the aggregate level of resources. This assumption leads to the counterfactual prediction that the rate of productivity growth should be increasing in the aggregate amount of resources devoted to accumulating knowledge. This paper presents empirical evidence in support of R&D based endogenous growth models without scale effects (e.g. Young, 1998, Howitt, 1999, Thompson, 2001, and Peretto and Smulders, 2002). In these models the average level of workers or R&D workers per firm drives growth as opposed to the aggregate level and do not share the scale effects property in the limit. Using data for the US covering 1964-2001, we show that when the number of employees or scientists/engineers are scaled down on a per establishment basis, the empirics support the latter version of endogenous growth models. Specifically, the long-run size of establishments is stable, neither declining or growing in the long-run, where size is measured in two ways: by workers per establishment and R&D workers per establishment. Second, we demonstrate a positive effect running from average establishment size to productivity growth as predicted by the theories.