Why Tobit models are overused

In my field of research we’re often running regressions with innovation expenditures or sales with new products aon the left-hand side. Usually we observe many zeros for these variables because firms do not invest at all in R&D and therefore also do not come up with new products. Many researchers then feel inclined to use Tobit models. But frankly, I never understood why. In an earlier version of one of my papers I’ve commented on this:

Authors in previous studies (Laursen and Salter, 2006; Leiponen and Helfat, 2010, 2011; Klingebiel and Rammer, 2014) often rely on limited dependent variable models, namely a Tobit type I regression (Tobin, 1958; Amemiya, 1985), because they recognize the non-negativity of sales with new products. In agreement with Angrist and Pischke (2009), we break with this tradition as we do not make sense of a latent variable interpretation with a separate censoring mechanism that forces negative sales to be zero. Rather we think that zeros occur naturally in this setting. Another justification for the Tobit model is sometimes provided by a hurdle model interpretation (Cragg, 1971). Here, the censoring point is thought as a threshold of “participation” which is modeled by a separate probabilistic process. Excess zeros (e.g., relative to the likelihood of a normal distribution) occur because a part of the sample is simply reluctant to engage in any innovation activities. We think that such a two-part approach is not appropriate for our application either as some form of innovation activity is a necessary condition to appear in our sample. In addition, we do not require fitted values to satisfy boundary conditions at the lower ends of the distribution, since we are not interested in effects that appear in certain distributional ranges of the dependent variable. Estimation by ordinary least squares, in contrast, conveniently allows to incorporate cluster-robust standard errors (clustered at the firm level) which is advisable when analyzing survey data considering that some firms appear in both survey waves.
A couple of (reiterating) points:
  • Cases of firms with no innovation expenditures (or sales with new products) are natural zeros. There is no censoring or truncation mechanism that forces negative expenditures to appear as zeros in the data. The actual value is zero, period.
  • Some people worry that with lots of zeros in the data the distribution of the outcome variable, Y, becomes very skewed. First of all, OLS can handle that as it doesn’t require normal errors for consistency. And secondly, if you worry about skewness there are other models you could use, such as Poisson, which are more robust to distributional misspecifications than Tobit.
  • Most importantly, if you introduce a latent variable (as in Tobit) you better have a good structural interpretation for it (like Heckman in his female labor supply example).  If you, e.g., argue that zero innovation expenditures are the result of a firm’s profit maximization problem—in which expected future cash flows are traded-off against project costs—then you should model this decision explicitly and tell me why you’re specifically interested in the effects on the latent rather than the observed variable. Everything else is too handwavy for my taste. In other words, if you’re doing reduced-form econometrics, do it properly (or switch to fully-fledged structural otherwise)!
  • A Heckman selection model “is equivalent to a Tobit model with stochastic threshold” (Cameron & Trivedi 2005, ch. 16.5.2) and therefore relies on a similar set of strong distributional assumptions. So if you’re worried about endogeneity as a result of sample selection I would usually advise you to go with two-stage least squares instead.



Networking For Innovation

Olav Sorenson from Yale published a new NBER working paper called “Innovation Policy in a Networked World”. The essay is quite interesting because it reviews insights we got from social network theory (no, not Facebook, although you could analyze Facebook with the same tools) and puts them into context for designing effective policy measures to stimulate innovation. Continue reading Networking For Innovation

Innovation on (government) demand?

Next week we will organize the 7th ZEW/MaCCI Conference on the Economics of Innovation and Patenting in Mannheim and the program will be great. We will have Bronwyn Hall from Berkeley and Pierre Azoulay from MIT as keynote speakers. I’m definitely looking forward to hear them speak.

Myself, I will present a new project on the relationship between public procurement and innovation. In brief the research question is the following. Continue reading Innovation on (government) demand?

Cardwell’s Law

While reading Joel Mokyr’s newest book I came across an older paper of him, which I found very interesting. It is about what Mokyr calls Cardwell’s law*— the empirical regularity that “most societies that have been technologically creative have been so for relatively short periods”. Throughout economic history successful countries in terms of innovation and economic growth have usually lost their competitive edge pretty soon again and were overtaken by others. Continue reading Cardwell’s Law

Do Most Companies Even Try to Innovate Anymore?

This post first appeared on hbr.org (Harvard Business Review, 14 April 2017).

We are living in the age of the superstar firm. Companies like Samsung, Google, or BMW—the top players in their respective industries—are prospering. Yet economic growth remains sluggish in many parts of the world. The reason for that paradox, as the OECD has warned, is that the productivity gap between firms at the global frontier and those lagging behind has widened. Continue reading Do Most Companies Even Try to Innovate Anymore?

How effective are patents really?

Today, an interesting NBER working paper by Deepak Hegde from NYU Stern and coauthors got published:

We provide evidence on the value of patents to startups by leveraging the random assignment of applications to examiners with different propensities to grant patents. Using unique data on all first-time applications filed at the U.S. Patent Office since 2001, we find that startups that win the patent “lottery” by drawing lenient examiners have, on average, 55% higher employment growth and 80% higher sales growth five years later. Patent winners also pursue more, and higher quality, follow-on innovation. Winning a first patent boosts a startup’s subsequent growth and innovation by facilitating access to funding from VCs, banks, and public investors.

Continue reading How effective are patents really?

Innovation activity in Germany is becoming more concentrated

This is an English translation of a column I published together with my colleague Christian Rammer from ZEW on oekonomenstimme.org. A pdf version can be downloaded here.

For years investments in research and development (R&D) have shown a rising trend in Germany. In 2015 they have reached a record high of 157.4 billion euro. At the same time, however, R&D expenditures are becoming concentrated within a smaller number of actors. The share of companies that invest in innovation falls steadily. As a result, innovation activities in the economy are more unevenly distributed. This column discusses possible causes for this development. Continue reading Innovation activity in Germany is becoming more concentrated