Maximum Likelihood Estimation of Court Errors
2008 Ford Scholars Project Description
| Project Director: | Alan C. Marco |
| Department: | Economics |
| Dates: | 8 weeks to be completed between May 26 – August 1, 2008 |
| Location: | Vassar College, Poughkeepsie, NY |
| Number of Students: | 1 |
Description of the Project:
My research investigates uncertainty in patent rights. By “uncertainty”, I mean the legal uncertainty over the property right that is embodied in the patent. Both the validity of a patent and the infringement of competing technologies are uncertain: validity can be revoked by the courts and patent scope depends on interpretation by the courts. Further—and importantly for this project—courts can make mistakes. [1] If each party is relatively optimistic about its chance of success at trial (i.e., they both think they’re going to win), they will go to court more frequently.
The current project aims to create an estimable structural model of patent litigation based on three sets of unknowns: The respective beliefs about winning for each party[1], the probability that the court will err[2], and the degree of stake asymmetry[3]. These unknown parameters are to be estimated using maximum-likelihood estimation.
Consider for a moment the seemingly impossible task: how can one measure the rate at which courts make mistakes? If they knew they were making mistakes, they would correct them! The error rate is inherently unobservable.
The intuition lies in “black holes.” Black holes are inherently unobservable. Their gravitational pull is so strong that even light cannot escape. How then can astronomers “observe” them? They can’t! But, they can observe the effects of black holes. Black holes affect nearby stars and thus reveal their existence. In the same way, we cannot observe court errors, but we can observe the effects of those errors on litigating parties. Court errors will affect win rates and the willingness of parties to litigate and to appeal lower court decisions. Econometrically, one can estimate the underlying court error based on observed behavior.
My previous and ongoing research has made some headway in this area. This is the crux of the matter: since error rates have been considered unknowable, policy makers have been ill-equipped to handle judicial policy. I hope to inform the debate on---among other things---tort reform by providing quantitative analysis of court errors.
Two components of the project are complete. First, the data involving about four thousand cases has been collected (Ford grant, summer 2004). And, a theoretical model has been built (Ford grant, summer 2005). The first grant produced the data for one empirical working paper, and the second grant produced two theoretical papers (one published and one under review).
The working paper has not been submitted for publication because a new estimation algorithm must be developed to deal with the data. Without belaboring the econometric details, in its current form the estimation exploits only the observed win rates at trial conditional on the observed litigation history of the patents. However, the model needs to be expanded to incorporate the observation that some cases are appealed, and some are not.
This piece of evidence probably seems like empirical minutiae. However, it is a very important component for the estimation: it directly connects outcomes at lower court trials with outcomes at the appellate level. And, because of this, a much more complicated estimation routine is necessary. Developing this maximum likelihood estimator is a well-defined—yet still challenging—endeavor. It’s perfect for a well-qualified Ford Scholar.
Anticipated Summer Activities:
The student will be involved directly in three stages of the project. First, s/he will develop the maximum likelihood estimation routine based in part on previous theoretical results. Going from a purely theoretical model to an estimable econometric equation is no small task in this instance. This is the “pencil and paper” part of the summer.
Second, the student will program the algorithm using Stata (statistical software). This application of maximum likelihood estimation has no “canned” routine in Stata (because it estimates a unique structural model), so a significant amount of programming is required.
Finally, the student will bring the algorithm to the data. This is the “fun” part, because we get results. (Except that in reality, several iterations of the second and third stages will probably be required in order to get robust results.)
Preferred Student Qualifications/Skills:
Because of the econometric nature of the work, some advanced mathematics and economics is required. The ideal candidate would have a sound background in econometrics (at least Econ 210) and also probability models (Math 241). Additional upper division courses should include linear algebra (Math 221). Mathematical Statistics (Math 341) or Advanced Econometrics (Econ 310) would be a plus.
The student should have an interest in patents, law, and econometrics. Some experience with Stata, Excel, and basic programming (any language) is necessary. Law & Economics (Econ 238) and Patent Law & Policy (STS 136) would be useful, but not required.
Anticipated Follow-up Teaching/Professional Activity for the Student:
The student will contribute substantially to a publishable research paper, and will learn research methodology, from the design stage to the results. This particular project is an unusual opportunity for a student to engage in advanced econometric work – work typically inaccessible to undergrads.
Additionally, I would help the student prepare for the Ford symposium presentation and discuss the possibility of extending the research for use as a thesis topic (at the student’s discretion).
Depending on the interest of the student, possible additional activities would include: presentation at a conference, such as the annual meetings of the American Law and Economics Association, or presentations during freshman week or during a Law & Economics (Econ 238) or Econometrics (Econ 210) lecture.
[2] When courts are prone to make mistakes, the litigants’ payoffs from going to court are changed. How does this impact selection and win rates?
[3] Patent cases are known to have higher stakes for patent holders than for (alleged) infringers. This is because the patent holder can have its entire patent invalidated in the course of a trial (thus, trials have a high opportunity cost for patent holders).