Returns to scale in research

When universities or university departments produce research outputs—such as published papers—they sometimes experience increasing returns to scale, sometimes constant returns to scale, and sometimes decreasing returns to scale. At the level of nations however, R&D tends to see increasing returns to scale. These results are preliminary.


“Returns to scale” refers to the responsiveness of a process’ outputs when all inputs (e.g. researcher hours, equipment) are increased by a certain proportion. If all outputs (e.g. published papers, citations, patents) increase by that same proportion, the process is said to exhibit constant returns to scale. Increasing returns to scale and decreasing returns to scale refer to situations where outputs still increase, but by a higher or lower proportion, respectively.

Assessing returns to scale in research may be useful in predicting certain aspects of the development of artificial intelligence, in particular the dynamics of an intelligence explosion.


The conclusions in this article are drawn from an incomplete review of academic literature assessing research efficiency, presented in Table 1. These papers assess research in terms of its direct outputs such as published papers, citations, and patents. The broader effects of the research are not considered.

Most of the papers listed below use the Data Envelopment Analysis (DEA) technique, which is a quantitative technique commonly used to assess the efficiency of universities and research activities. It is capable of isolating the scale efficiency of the individual departments, universities or countries being studied.

Paper Level of comparison Activities assessed Results pertaining to returns to scale
Wang & Huang 2007 Countries’ overall R&D activities Research Increasing returns to scale in research are exhibited by more than two-thirds of the sample
Kocher, Luptacik & Sutter 2006 Countries’ R&D in economics Research Increasing returns to scale are found in all countries in the sample except the US
Cherchye & Abeele 2005 Dutch universities’ research in Economics and Business Management Research Returns to scale vary between decreasing, constant and increasing depending on each university’s specialization
Johnes & Johnes 1993 UK universities’ research in economics Research Constant returns to scale are found in the sample as a whole
Avkiran 2001 Australian universities Research, education Constant returns to scale found in most sampled universities
Ahn 1988 US universities Research, education Decreasing returns to scale on average
Johnes 2006 English universities Research, education Close to constant returns to scale exhibited by most universities sampled
Kao & Hung 2008 Departments of a Taiwanese university Research, education Increasing returns to scale exhibited by the five most scale-inefficient departments. However, no aggregate measure of returns to scale within the sample is presented.

Table 1: Sample of studies of research efficiency that assess returns to scale
Note: This table only identifies increasing/constant/decreasing returns to scale, rather than the size of this effect. Although DEA can measure the relative size of the effect for individual departments/universities/countries within a sample, such results cannot be readily compared between samples/studies.

Discussion of results

Of the studies listed in Table 1, the first four are the most relevant to this article, since they focus solely on research inputs and outputs. While the remaining four include educational inputs and outputs, they can still yield worthwhile insights.

Table 1 implies a difference between country-level and university-level returns to scale in research.

  • The two studies assessing R&D efficiency at the country level, Wang & Huang (2007) and Kocher, Luptacik & Sutter (2006), both identify increasing returns to scale.
  • The two university-level studies that assessed the scale efficiency of research alone found mixed results. Concretely, Johnes & Johnes (1993) concluded that returns to scale are constant among UK universities, and Cherchye & Abeele (2005) concluded that returns to scale vary among Dutch universities. This ambiguity is echoed by the remainder of the studies listed above, which assess education and research simultaneously and which find evidence of constant, decreasing and increasing returns to scale in different contexts.

Such differences are consistent with the possibility that scale efficiency may be influenced by scale (size) itself. In this framework, as an organisation increases its size, it may experience increasing returns to scale initially, resulting in increased efficiency. However, the efficiency gains from growth may not continue indefinitely; after passing a certain threshold the organisation may experience decreasing returns to scale. The threshold would represent the point of scale efficiency, at which returns to scale are constant and efficiency is maximized with respect to size.

Under this framework, size will influence whether increasing, constant or decreasing returns to scale are experienced. Applying this to research activities, the observation of different returns to scale between country-level and university-level research may mean that the size of a country’s overall research effort and the typical size of its universities are not determined by similar factors. For example, if increasing returns to scale at the country level and decreasing returns to scale at the university level are observed, this may indicate that the overall number of universities is smaller than needed to achieve scale efficiency, but that most of these universities are individually too large to be scale efficient.

Other factors may also contribute to the differences between university-level and country-level observations.

  • The country level studies use relatively aggregated data, capturing some of the non-university research and development activities in the countries sampled.
  • Country level research effort is not necessarily subject to some of the constraints which may cause decreasing returns to scale in large universities, such as excessive bureaucracy.
  • Results may be arbitrarily influenced by differences in the available input and output metrics at the university versus country level.

Limitations to conclusions drawn

One limitation of this article is the small scope of the literature review. A more comprehensive review may reveal a different range of conclusions.

Another limitation is that the research outputs studied—published papers, citations, and patents, inter alia—cannot be assumed to correspond directly to incremental knowledge or productivity. This point is expanded upon under “Topics for further investigation” below.

Further limitations arise due to the DEA technique used by most of the studies in Table 1.

  • DEA is sensitive to the choice of inputs and outputs, and to measurement errors.
  • Statistical hypothesis tests are difficult within the DEA framework, making it more difficult to separate signal from noise in interpreting results.
  • DEA identifies relative efficiency (composed of scale efficiency and also “pure technical efficiency”) within the sample, meaning that at least one country, university, or department is always identified as fully efficient (including exhibiting full scale efficiency or constant returns to scale). Of course, in practice, no university, organisation or production process is perfectly efficient. Therefore, conclusions drawn from DEA analysis are likely to be more informative for countries, universities, or departments that are not identified as fully efficient.
  • It may be questionable whether such a framework—where an optimal scale of production exists, past which decreasing returns to scale are experienced—is a good reflection of the dynamics of research activities. However, the frequent use of the DEA framework in assessing research activities would suggest that it is appropriate.

Topics for further investigation

The scope of this article is limited to direct research outputs (such as published papers, citations, and patents). While this is valuable, stronger conclusions could be drawn if this analysis were combined with further work investigating the following:

  • The impact of other sources of new knowledge apart from universities or official R&D expenditure. For example, innovations in company management discovered through “learning by doing” rather than through formal research may be an important source of improvement in economic productivity.
  • The translation of research outputs (such as published papers, citations, and patents) into incremental knowledge, and the translation of incremental knowledge into extra productive capacity. Assessment of this may be achievable through consideration of the economic returns to research, or of the value of patents generated by research.

Implications for AI

The scope for an intelligence explosion is likely to be greater if the returns to scale in research are greater. In particular, an AI system capable of conducting research into the improvement of AI may be able to be scaled up faster and more cheaply than the training of human researchers, for example through deployment on additional hardware. In addition, in the period before any intelligence explosion, a scaling-up of AI research may be observed, especially if the resultant technology were seen to have commercial applications.

This review is one component of a larger project to quantitatively model an intelligence explosion. This project, in addition to drawing upon the conclusions in this article, will also consider inter alia the effect of intelligence on research productivity, and actual increases in artificial intelligence that are plausible from research efforts.

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