Empirical Legal Studies

Modeling Rates/Fractions/Percentages

While I probably should have mentioned this when Stata's (relatively) new and quite helpful "fracreg" command was released, a recent surge of student questions about how to best model a rate (or fractional) dependent variable motivates this post.

Periodically ELS scholars will need (or want) to model a defendant variable that is bounded between zero and one (e.g., rates, fractions, percentages, etc.). Until recently few satisfactory options (at least "off-the-shelf" ones) existed as the various standard "reg" commands are inapt given the rate/fractional/percentage dependent variable's bounded structure. The "fracreg" command in Stata, however, is designed for dependent variables that range from zero to one (inclusive). Anyone intrigued should consult the user manual (here) and watch a brief introductory tutorial video (here).

Descriptive Analyses of Hidden Legal "Corners": Lone Pine Orders

While an increasingly important mass tort litigation mainstay since their creation in 1986, "Lone Pine" orders remain in relative scholarly obscurity. In Lone Pine Orders: A Critical Examination and Empirical Analysis, Nora F. Engstrom (Stanford) and Amos Espeland (Stanford-grad student) set out to "pull back the curtain." They do just that as it relates to Lone Pine orders in a brief essay and, in so doing, their paper demonstrates, once again, how the creation of new original data sets, combined with basic descriptive analyses, can add helpful information. The paper's abstract follows.

"Invented in 1986 and now a prominent feature of the mass tort landscape, Lone Pine orders require plaintiffs to provide to the court prima facie evidence of injury, exposure, and specific causation — sometimes early, and usually on pain of dismissal. Though they’ve taken root in a hazy space outside of the Federal Rules of Civil Procedure, these case management orders are frequently issued, and they play an important role in the contemporary litigation and resolution of mass torts. But although Lone Pine orders are common, potent, and increasingly controversial, they have mostly fallen under the academic radar. Even their key features are described inconsistently by commentators and courts. This Essay pulls back the curtain. Drawing on a unique hand-coded data set, this Essay describes the origin and evolution of Lone Pine orders, sketches poles of the debate surrounding their use, and offers empirical evidence regarding their entry, content, timing, and effect."

Comparing "predicted probabilities" and "odds ratios"

Those who use the logistic as well as the margin commands (and both are quite common in ELS) sometimes confront the question of whether to report out odds ratios (from the logistic command) or the predicted probabilities (from the margin command). As one commentator notes in this Stata list discussion (here), "An odds [ratio] is related but not the same as a probability. They are related in the sense that both are ways of quantifying how likely an event (success) is. They differ in that the "odds [ratio] is the average number of success per failure. The probability is the average number of successes per trial." What is the more intuitive of the two will, of course, vary across people.

Referees, "Home Field" Advantages, and "Empty" Stadiums: An Empirical Perspective

If current events continue as presently trajected we are likely to see a slew of professional (and D1 college) athletic games played in "empty" stadiums for some unknown period of time. For gamblers (and fans), one immediate question is how playing in an empty stadium may impact the outcome. One piece of emerging conventional wisdom--fueled by little more than intuition--is that the putative "home field advantage" attributable to (assumed) systematic referee "bias" favoring home teams may vanish in empty stadiums.

It turns out that the "empty" stadium "experiment" has happened before--in Italian professional soccer flowing from a tragic soccer "hooligan" incident in 2007. Consequently, some data--albeit limited--exist. Perhaps unsurprisingly, two economists, Per Pettersson-Lidbom (Stockholm Univ.) and Mikael Priks' (CESifo, Germany), exploited these data, construed the temporary "empty stadium" policy as an exogenous shock to the number of spectators, and leveraged it to test the "referees may be biased due to social pressure" hypothesis.

Findings from their 2010 paper, Behavior under social pressure: Empty Italian stadiums and referee bias, generally comport with the received wisdom. Specifically, and as summarized in a recent Sports Illustrated article (here), in "full" stadiums home teams won the majority of matches. And they did so, in part, because the home teams received fewer red cards and yellow cards, and fewer penalty and foul calls. As well, when home teams were trailing, they received more injury time, the minutes that officials discretionarily tack onto the end of games, increasing their odds of catching up. When home teams were leading, injury time dwindled." However, for games played in "empty" stadiums the home team advantage effectively vanished and teams didn’t win at home any more than on the road. Contributing to this was that when no fans were in the stands the "home/away penalty differential shriveled. The favorable calls conferred on the home team dropped by 23%–70%, depending on the type of calls. Subjective close calls no longer favored the home team. Injury time favoring the home team declined as well."

While it remains difficult to conclusively rule out concurrent effects of an "empty" stadium on the athletes, the paper addresses such confounds to the extent that their research design allows. To be clear, however, the paper focuses on observing "the same referees overseeing the same two teams in the same stadium" and notes that they "behaved dramatically differently when spectators were present, versus when no one was watching." On the interpretative front the authors are generous to the referees: "It is not because officials are biased, much less because they are corrupt. It is because they are human. As such, they are susceptible to the powerful force that is social influence."