Operationalizing opportunities in entrepreneurship research: use of data envelopment analysis

We believe that failure to account for pure arbitrage opportunities—which are still an important predictor of entrepreneurial activity—is unlikely to challenge prior results that link innovative opportunities and entrepreneurship because their emergence is most likely explained by random events and fluctuations. If necessary, one may account for their emergence by creating a series of dummy variables reflecting major changes in the market—such as natural disasters, terrorist attacks, elections, etc.—or simply considering temporal effects to account for consumer preferences changes and fashion shifts. At the same time, because technological arbitrage opportunities directly depend on innovation (discovery of new ways to bundle resources that could be profitably imitated), it is important to find a robust operationalization for them.

It is important to note that our arguments need to be considered at the level of analysis we adopt in this paper. At the country level of aggregation we may only talk about the situation in general. At the individual level it is easy to imagine a situation when a particular technology developed, for instance, by a star scientist in one of the lesser effective Eastern European countries may be imitated in the US profitably. However, when we look at the country level of analysis, such instances are likely to be relatively few and far between.

Here, we plot one frontier for all country-year observations (the so-called intertemporal frontier). It is also possible to plot a series of frontiers for each year. We chose to depict the intertemporal frontier for illustration purposes to demonstrate the movement (catching-up) of some countries like China towards the frontier established by the benchmark countries like the US. Because we assess countries’ efficiencies against relevant comparison group and do not attempt to produce the absolute value of technical and efficiency change, we adopt the ‘frontier for all countries’ and not the ‘frontier for the single countries’ approach.

Importantly, to obtain unit invariance, DEA utilizes radial efficiency measures.

With DEA both input-oriented and output-oriented measures could be calculated. In the former case, the idea is to minimize the inputs required to produce a given amount of outputs; in the latter it is to maximize the outputs obtainable from a set amount of inputs. The same units will be declared efficient/non-efficient regardless of the orientation one chooses.

As different countries have different patent laws and intellectual property (IP) protection systems, relying on patents as a proxy for innovation in the cross-country context may be problematic. First, in a number of countries where IP protection is weak, individuals and firms may not file patent application because the proprietary information will be disclosed but the protection will not be provided. Second, globally patents are often sought to establish a favorable market position. Thus, a company in the US may apply for a patent in Japan to foreclose certain opportunities for its competitors there. Such patents will not reflect Japanese innovations. Third, in most countries patents are awarded on a first-to-file, not first-to-invent basis. The international TRIPS system follows this principle as well. Thus, patents filed in a country may reflect one’s attempt to secure a market based on someone else’s innovation.

With R&D expenses the problems are twofold. First, the nature of the innovation is ill-defined such that R&D investments may not result in commercializable discoveries. Second, as suggested by Zahra (1996), high R&D expenditures may be a result of agency problem and not innovation.

Thus, it is important to keep in mind the limitations of the measures when using them for testing substantive theories.

There may be certain exceptions that the technique is not sensitive to—such as the already mentioned discovery by a star scientist of an innovative technology that could be profitably imitated in the benchmark countries.

With DEA it is possible to use different combinations of inputs and outputs. For instance, it could have been possible to account for arable land, number of universities, patents, etc., as inputs. We believe that the choice of inputs and outputs should be determined by the theory one intends to test with the proposed measures. While we simply intended to illustrate the technique and suggest its use in the entrepreneurship research, to us using inputs like patents was not acceptable because they themselves serve as a proxy for technological development and thus would have ‘contaminated’ our estimates of innovation and technical change.

While we could have estimated the model using variable returns to scale assumptions, it was not necessary in this case. Variable returns to scale assumptions could theoretically further decompose efficiency change into pure efficiency change and scale efficiency gains. However, as extant research has suggested, in the variable returns to scale case, the Malmquist index does not accurately measure the productivity change (Grifell-Tatjé and Lovell 1995; Ray and Desli 1997).

Because our estimates of opportunities are relative and not absolute, it may be that by having the ever increasing ‘innovation pie’ grow at declining rates, the absolute value of innovative opportunities remains rather stable across years. To fully understand the reasons behind the declining opportunities growth rates, more research is needed.

Because DEA is a non-parametric technique, we also considered using non-parametric correlation coefficients. The results are consistent with the one reported above: Spearman’s ρ = 0.21 (p < 0.05) and 0.36 (p < 0.01) for the relationship between total entrepreneurial activity and innovative and arbitrage opportunities, respectively. For Kendall’s τ the respective coefficients are 0.15 (p < 0.05) and 0.26 (p < 0.01).

Although we have not discussed it in detail, with panel data it is possible to use DEA without resorting to model extensions such as the Malmquist productivity index decomposition to operationalize individual countries’ total factor productivity change by employing the intertemporal production frontier technique and to estimate arbitrage opportunities by calculating a series of production frontiers for every year for which data are available.