Sectoral R&D Activities and Knowledge Production Functions: A Study Using International Data ^†

Abstract

This study explores the relationship between the stock of knowledge generated by sectoral groups of the economy, calculated using Research and Development (R&D) expenditure, and knowledge output as measured by official patent applications. Using sector-specific R&D expenditure data published by the OECD, we calculate the total domestic R&D spending across the manufacturing, non-manufacturing, government, and educational sectors. Constructing a consistent 15-year panel dataset for the 17 most significant countries in R&D, we employ econometric subsampling, various estimators, and consider different rates of knowledge depreciation. Our findings reveal that the stock of knowledge in the private manufacturing, government, and educational sectors has a robust positive effect on patent generation.

1. Introduction

This study uses OECD statistical datasets on research and development (R&D) expenditure and input–output tables. It classifies research data by economic sector across countries and harmonizes the sectors of the R&D expenditure dataset with those of the OECD input–output tables. Subsequently, based on the primary sources of R&D expenditure, it calculates and allocates these expenditures to four distinct groups of sectors within the domestic economy. This research aims to estimate the influence of the knowledge stock generated by each of these four domestic aggregate sectors through their R&D expenditures on domestic knowledge production, as measured by patents.

Our study intends to make a significant contribution to the relevant literature, where studies in knowledge production and diffusion considering sectoral inputs, e.g., sectoral R&D activity, are rather limited. Previous studies have predominantly focused on sampled firms within specific geographic areas, limiting the comprehensive and broadly applicable assessment of the impact of sectoral expenditure. In contrast, our study involves the total sectoral data from multiple countries over a time period. Additionally, the existing literature often attributes patent data to specific firms and sectors, overlooking the collaborative efforts among different firms that have led to patent production. The issue extends beyond sectoral studies, where patents stemming from collaborative efforts across regions are assigned to multiple entities, leading to an overestimation of knowledge production as the same patent is credited to different firms or sectors, meaning that they are counted repeatedly in observations. Our data and approach ascribe fractional values to patent applications based on the nationality of the contributing researchers. Distributing each patent application to the calculated fractional values according to the contributing researchers of each country enables the produced knowledge to be measured more accurately at the country level. Sectoral R&D expenditures, which are our independent variables, are used to measure the “stock of knowledge”. For this reason, they are calculated accumulatively for each sector, in each country, for every year, over the examined period. This straightforward accumulation assumes no “knowledge depreciation”. However, all calculations and accumulation take place by assuming also 5%, 10%, 15%, and 20% knowledge depreciation rates, as suggested by findings in the literature [1]. Depending on each scenario, the sectoral R&D expenditures of each year are transformed by the appropriate factors before they are added to yield the stock of knowledge in a certain year. This process is applied over all panel data observations. Econometric analysis takes place for all depreciation scenarios. Our exact dependent variable observation, affected by the stock of knowledge accumulated by each sector annually and per country throughout the examined period, is measured by the number of research patent applications originating from triadic patent families. We consider the priority day for each unique country–year pair and the residence of each researcher (inventor), enabling the assignment of fractional, non-integer patent numbers to different countries.

2. Materials and Methods

Following the aforementioned processing and calculations of our data, we constructed a panel data set, encompassing a span of 15 years and comprising the 17 preeminent countries engaged in R&D activities. This comprehensive dataset was crafted to encompass four distinct categories of domestic R&D expenditure stocks. For the purposes of our econometric analysis, we employed a Knowledge Production Function (KPF) adhering to the Cobb–Douglas framework, as originally articulated by Griliches in 1979. Drawing upon a review of the existing literature and the various econometric models utilized in the domain of R&D, the KPF framework was modified to align with the contemporary literature [2,3,4,5].

While the general framework of production functions traditionally construes inputs as being solely attributable to the agent under examination, without accounting for external sources (e.g., foreign countries, other firms, etc.), the landscape of R&D economics uniquely accommodates the inclusion of inputs from external entities, particularly in the context of capturing the influence of knowledge spillovers. While the R&D literature does not customarily bifurcate R&D expenditures by industry, a recurrent issue that emerges is that of multicollinearity; this is a phenomenon that is well documented in the pertinent literature [1,6,7] and is driven by linear correlations between independent variables. Scholarly discourse does not extensively engage with this predicament. Conversely, it is a common practice to introduce “foreign” R&D expenditure multiple times into the model, each instance weighted differently. This practice is employed to discern the impact of knowledge spillovers through distinct conduits. We posit that the utilization of varying weighting factors serves to mitigate the multicollinearity challenge. In our model, the inclusion of additional effects beyond our designated variables is achieved through the integration of pseudo-variables that are representative of spatial and temporal dimensions. Moreover, the calculation of such weighting factors proves impractical when applied to aggregated industry and country-level data sets, such as those characteristic of the OECD, owing to the unavailability of requisite statistical data.

3. Results and Discussion

Subsequent to the refinement of our Knowledge Production Function (KPF) framework, a series of tests was conducted to ascertain the selection of an appropriate econometric model. Both the Hausman test and the Breusch–Pagan Lagrange Multiplier test [8] were employed, concurring in their determination that the most suitable model was the fixed-effects model [9,10]. Next, the examination extended to encompass the identification of groupwise heteroscedasticity and autocorrelation phenomena. To assess the presence of these characteristics, we applied a modified Wald test and the Wooldridge test, respectively [11]. The outcomes of these tests yielded confirmation of groupwise heteroscedasticity and autocorrelation. In response, various estimators were considered in accordance with the established literature guidelines [12,13,14]. Additionally, the Newey–West estimator was deployed for estimation purposes, yielding outcomes consistent with those obtained through the previously mentioned estimators [15,16].

Nevertheless, it is crucial to acknowledge a limitation in the aforementioned estimators. While they demonstrate robustness in estimating specific parameters, they fail to adequately account for correlation between clusters. These estimators solely assume the existence of residual correlation within clusters. In light of this limitation, the Generalized Least Squares (GLS) estimator emerged as an alternative choice. Although the GLS estimator is traditionally applied in scenarios where the sample size (N) is less than the number of time periods (T), it remains an acceptable recourse in cases where the disparity between N and T is minimal, as is the case here (N = 17, T = 15). It should be noted that this situation, where N is approximately equal to 15, straddles a nuanced territory, and researchers adopt varying approaches to address it [17]. Additionally, we incorporated the Panel-Corrected Standard Error (PCSE) estimator, as posited by Beck et al. (1995). This estimator’s appeal lies in its capacity to exhibit standard error estimates that are resilient to heteroskedastic disturbances, while simultaneously accounting for inter-cluster correlation and AR (1)-type autocorrelation. Lastly, we employed the Driscoll–Kraay methodology. This approach is lauded for its ability to adjust standard errors, ensuring the consistency of the estimator’s covariance matrix irrespective of the stratified dimension represented by N. Furthermore, it effectively addresses the challenges of heteroscedasticity and autocorrelation within the analytical framework.

4. Conclusions

In our analysis, we applied our approach across different depreciation rates, ranging from 0% to 20%. A consistent observation emerged: the outcomes remained consistent across all depreciation rates, with no significant divergence, even with the utilization of various estimators. Our empirical analysis sheds light on the substantial and affirmative impact of Research and Development (R&D) expenditures on patent production. Specifically, our findings reveal that R&D spending within the private manufacturing sector, the educational sector, and the government sector have a significant impact on patent output. The estimated coefficients, reflecting the magnitudes of these effects, underscore the role of R&D spending in private manufacturing, surpassing the influence of R&D expenditure in other economic sectors. This outcome aligns with expectations, given the sectors’ substantial allocation of resources and patent production. Additionally, our analysis underscores the role of R&D expenditure within the educational sector in driving patent production, surpassing the influence of the government sector; this is supported by the concentration of researchers and extensive research activities within educational institutions. Conversely, our results indicate that the impact of R&D expenditure on patent production in the private non-manufacturing sector is negligible and statistically insignificant.

Notably, while our focus centers on the sectors of private manufacturing, education, and government, it is important to highlight the indirect contributions of sectors closely aligned with agriculture, such as food processing and related manufacturing sectors. These sectors actively engage in R&D activities, investing in innovation and generating patents. The resulting knowledge diffusion from these sectors into agriculture underscores the interconnected nature of R&D efforts across the broader economic landscape, enhancing the agricultural sector’s capacity for innovation and growth. Our findings emphasize the crucial role of strategic R&D investments in driving patent production, especially in the private manufacturing sector, and advocate for policies fostering educational–private sector collaboration that recognize the educational sector’s significant influence on knowledge spillovers and innovation, while also highlighting the need to address sectoral R&D disparities for a balanced and sustainable distribution of innovation. Incorporating spatial and temporal dimensions with dummy variables in our analytical model yielded statistically significant results, confirmed by F-tests. Future research endeavors should construct indicators that aim to assess the disparities in the allocation of R&D expenditure among various sectors and countries. Analyzing sector interactions within countries unveils R&D concentration levels, enhances the comprehension of patent geographical distribution, and identifies nations’ knowledge production specialization.