Often, economic policies are set to encourage entrepreneurship, with the idea that entrepreneurs are the ones that drive economic growth. But not everyone is a good entrepreneur, and encouraging this too much leads some people to become entrepreneurs while they would have been more productive as employees. In other words, there is an optimal number of entrepreneurs, and it is not 100%.
André van Stel and Mirjam van Praag are set out to find this optimal number using cross-national data. They see one of their contribution in adding a little bit of microeconomic reasoning in macroeconomics. I quote: "We think it is important, per sé [sic], to inspire a macroeconomic study on insights from microeconomics, thereby providing a link between macro and microeconomics that is often missing, but may provide valuable insights." Really? What has macroeconomics done for the last thirty years? Only run cross-country regressions?
Anyway, they estimate a Cobb-Douglas production function with the following factors: labor, physical capital, knowledge capital, and the number of business owners. That is not how I would have imagined a microfoundation. It would have included a model where entrepreneurs hire workers, something along the lines of what Vincenzo Quadrini has published. But no, van Stel and van Praag prefer the good old reduced form way. Maybe that will at least inform us about some features of the data. The problem is that they measure knowledge capital, a stock, with R&D expenditures, a flow. To obtain an optimal business ownership rate, a squared rate is added to the regression. Is there a microeconomic justification for this? Is there evidence that the elasticity of substitution between the business ownership rate and the other factors is different form one and variable? You cannot just throw something into a regression because it then yields a maximum.
Too bad this is so poorly implemented, it was an interesting question.