Stepping on toes in the production of knowledge: a meta-regression analysis

ABSTRACT

Decreasing returns to scale in physical resources in the knowledge production function have been widely considered in the economic growth literature. However, given the heterogeneity of empirical results, it is difficult to assess its magnitude. We provide a meta-analysis of the value of the decreasing returns to physical resources in the knowledge production function (stepping-on-toes effect). This has important policy implications regarding the subsidization of R&D activities and policy measures to enable the diffusion of knowledge. We conclude that there is some evidence of publication bias. Moreover, the average effect size is quite small, around 0.2, which implies a high stepping-on-toes effect. This value tends to be higher when variables related to international linkages are present, resources allocated to R&D are measured by labour, the knowledge pool is proxied by population, and instrumental variable estimation techniques are employed. On the contrary, the average returns to scale estimate decreases when resources allocated to R&D are measured by population and when only rich countries are included in the sample.

KEYWORDS:

• Knowledge production function
• R&D
• meta-analysis
• stepping-on-toes
• duplication effect

JEL CLASSIFICATION:

• O10
• O30

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Although most of these contributions include resources allocated to the knowledge production, they usually neglect the pool of knowledge as a determinant of its production. Although Crepon, Duguet, and Mairessec (1998) also have estimations for equations of patents flows, they never regress them on the stock of patents, nor did they include alternative pools of knowledge.

² For a detailed analysis and taxonomy of the different branches of the literature estimating a k.p.f. we refer the reader to Neves and Sequeira (2018).

³ In a companion paper, Neves and Sequeira (2018) apply a meta-regression analysis to the standing-on-the-shoulders effect or spillover parameter ($\varphi$). In that paper, the authors conclude for a high standing-on-the-shoulders effect (but lower than one, implying that economic growth may be semi-endogenous, depending on population growth).

⁴ There are diminishing returns to scale if $0<\lambda <1.$ The lower the value of $\lambda$, the lower the amount of new knowledge that is created by additional inputs, hence the higher the duplication/stepping-on-toes effect. If $\lambda =1$, there are constant returns to scale and there is no duplication/stepping-on-toes effect.

⁵ The Cochrane’s Q and the $I^2$ index are two indicators of the degree of heterogeneity in meta-analyses. The former is the weighted sum squares of the differences between study estimates and the fixed-effects average estimate, while the latter measures the proportion of total variation in the reported estimates that is due to heterogeneity between studies (Higgins and Thompson 2002; Higgins et al. 2003).

⁶ Strong outliers in the t-statistics are above $Q_3+3(Q_3-Q_1)$ and below $Q_1-3(Q_3-Q_1)$, where $Q_i$ is the $i^{th}$ quartile.

⁷ Note that the dependent variable of Equation (2) is an estimated coefficient drawn from the primary studies, which has its own variance. Therefore, the disturbances $u_i$ are heteroskedastic.

⁸ Additional LR tests reject the hypothesis of the variance of ${\alpha }_0$ being equal to zero, but do not reject the hypothesis of the variance of ${\alpha }_1$ being equal to zero. Results available upon request.

⁹ For example, in Jones and Williams (2000: Table 2), a value of $\lambda =0.25$ – thus higher than our average estimate, and representing a very high value of the standing-on-the-shoulders effect – consistent with the average value found in our companion paper (Neves and Sequeira 2018) and overinvestment in R&D is obtained. This implies that knowledge production should be taxed and not subsidized, as it is in the majority of countries.

¹⁰ Or, in a more general view, openness to international trade or external financial dependence.

¹¹ Using time dummies, time-trend variables, or year-fixed effects.

¹² For most of the estimations of the multivariate meta-regression presented in this section, LR tests reveal that the hierarchical models are not preferred to OLS models.

¹³ The estimation results of the complete model are presented in Table A3 of the Appendix.

¹⁴ Note that governments usually subsidize knowledge production (or R&D) through tax credits on R&D expenditures. However, to be definite about a policy recommendation, one should take into account the different externalities affecting the market equilibrium.

Additional information

Funding

This paper is financed by National Funds of the FCT - Portuguese Foundation for Science and Technology within the project UID/ECO/04007/2019.