Empirical Legal Studies

Count data, Logging Zeros, and Poisson

A persistent issue confounding many empirical legal studies using count data involves the "zeros problem," especially when the count data require a log transformation. Contests on how to best deal with this problem persist. Popular approaches include standard OLS regression models that add a "plus one" to each count data so to not lose all cases with a zero count in the log transformation and Poisson regressions models.

While empirical assessments of these two approaches are relatively rare, a recent paper compares these two approaches drawing on replication analyses of five recent corporate patenting papers. In Count Data in Finance, Jonathan Cohn (Texas--Business) et al., find that one OLS regression approach (LOG1PLUS) "using log-transformed outcomes can produce biased and incorrectly signed estimates of economic relationships and provide guidance for future research in finance-related applications involving zero-bounded count data." By comparison, while the Poisson model estimates may "lose efficiency if the model’s conditional mean-variance equality restriction is not satisfied in the data, they remain unbiased and consistent as long as the standard conditional mean independence assumption holds." The paper's abstract follows.

"This paper examines the use of count data-based outcome variables such as corporate patents in empirical corporate finance research. We demonstrate that the common practice of regressing the log of one plus the count on covariates (“LOG1PLUS” regression) produces biased and inconsistent estimates of objects of interest and lacks meaningful interpretation. Poisson regressions have simple interpretations and produce unbiased and consistent estimates under standard exogeneity assumptions, though they lose efficiency if the count data is overdispersed. Replicating several recent papers on corporate patenting, we find that LOG1PLUS and Poisson regressions frequently produce meaningfully different estimates and that bias in LOG1PLUS regressions is likely large."

Life Sentences "With" or "Without"

While significant public and scholarly attention rightly dwells on capital punishment, comparatively under-explored is a steady surge of life sentences without the possibility of parole ("LWOP"). While the Furman Court's "death is different" doctrine retains obvious salience and moral force, it should not obscure LWOPs from much-needed empirical inquiry.

To this end, in a recent paper, Life 'With' or 'Without'?: An Empirical Study of Homicide Sentencing, forthcoming in JELS, Michael O'Hear (Marquette) and Darren Wheelock (Marquette--Dept. Social and Cultural Sciences) do just that. While the paper's data set is limited to Wisconsin homicides, the authors do a deep data dive into 450 individuals convicted of first-degree intentional homicide between the start of 2001 and about mid-2018. The core findings are mixed. On the one hand, "intentional-homicide defendants who have more serious criminal histories are more likely to receive LWOP." On the other hand, "sentencing outcomes are influenced by the identity of the judge and prosecutor." The paper's abstract follows.

"The number of Americans serving sentences of life without the possibility of parole (“LWOP”) has grown rapidly over the past generation and now exceeds 50,000. Yet, little empirical research has been conducted on the determinants of LWOP sentences. The dearth of research on LWOP sentencing stands in sharp contrast to the many dozens of studies that have been conducted on the determinants of death sentences—studies that have consistently found that race, gender, and other questionable factors may influence sentencing outcomes. The present study is the first to employ a similar methodology to identify both case- and county-level variables that are correlated with the imposition of discretionary LWOP sentences.

More specifically, we have assessed the relationship between fifty different variables and LWOP decisions in 450 homicide cases in Wisconsin between 2001 and 2018. In our final model, we find seven variables that are correlated with sentencing outcomes. Of particular note, we find that judge and prosecutor personal characteristics are statistically significant correlates of LWOP decisions. We also find a significantly greater likelihood that LWOP sentences will be imposed in counties that are more Republican. We conclude with a proposal for a new LWOP sentencing process that may help to ensure that this very severe sentence is reserved for the most serious crimes committed by the most dangerous defendants."

"Results-to-Table" in Stata

While Stata--to my mind, anyway--still has not "fixed" the "unnecessary" degree of complexity in its graphics capabilities, it's nice to see it attend to the critical and often-challenging "results-to-table" migration task in v.17. While some may simply "hand-transcribe" results from the computer screen onto a table created for or embedded into Word documents, the more adventurous likely play with various "outreg" and related commands (e.g., "outreg2"). Stata has recently turned its attention to an alternative (or complementary) approach with updated commands that facilitate users "customizing" table presentations derived from various results. Unlike most efforts thus far, coding for this approach is "native" to Stata. Again, while I'm not entirely sure whether Stata has, once again, made the process unduly complicated, for anyone interested an introductory (and explanatory) video is here.

"Judging" Autonomous Vehicle Liability

Conventional wisdom implies that, on balance, judges, as a group and in their professional capacity, tend to disfavor new technologies. This judicial lurch towards disfavoring can present important policy implications as, especially in common law systems, judges can play a critical role in the regulation of new technologies. One example that will likely play out soon in real-time involves autonomous cars.

Dominating the experimental judicial decisionmmkaing literature are studies that rely on "mock" judges deciding "experimental" case hypotheticals. All too often, however, these "mock" judges involve either undergraduate students or a non-random collection of MTurk respondents. By contrast, findings from a recent paper, Judging Autonomous Vehicles, by Jeff Rachlinski (Cornell) and Judge Andrew Wistrich (Ca Central Dist. Ct), both valued Cornell colleagues, reflect an important advancement insofar as they derive from actual, real-live sitting judges (N=933).

In their studies, the authors presented hypothetical cases in which judges had to assess fault or determine damages for either an accident caused by an autonomous vehicle or by a human driver. What the paper finds is that "judges will treat automated vehicles with skepticism. In the related experiments we conducted, judges treated an autonomous vehicle that had been involved in a car accident more harshly than a human-driven vehicle involved in an essentially identical accident.” As these results comport with others prior research focusing on other technologies, larger policy implications loom. As the authors note, "at least when an innovation is artificial, non-human, and a dramatic departure from existing practices, judges act as a brake, delaying and hindering its adoption." The paper's abstract follows.

“The introduction of any new technology challenges judges to determine how it into existing liability schemes. If judges choose poorly, they can unleash novel injuries on society without redress or stifle progress by overburdening a technological breakthrough. The emergence of self-driving, or autonomous, vehicles will present an enormous challenge of this sort to judges, as this technology will alter the foundation of the largest source of civil liability in the United States. Although regulatory agencies will determine when and how autonomous cars may be placed into service, judges will likely play a central role in defining the standards for liability for them. How will judges treat this new technology? People commonly exhibit biases against innovations such as a naturalness bias, in which people disfavor injuries arising from artificial sources. In this paper we present data from 933 trial judges showing that judges exhibit bias against selfdriving vehicles. They both assigned more liability to a self-driving vehicle than they would to a human-driven vehicle and treated injuries caused by a self-driving vehicle as more serious than injuries caused by a human-driven vehicle.”

Diff-in-Diff

Owing to the steadily increasing popularity of Diff-in-Diff models across an array of fields, including law, Stata's newest version (v.17) builds out its Diff-in-Diff modeling capacities (a brief summary tutorial video is here). While Stata's brief video provides a quick introduction, Brady Neal's more detailed Diff-in-Diff modeling video (here) might assist those seeking more comprehensive information. Obviously, Diff-in-Diff models are not without important limitations, including the all-important parallel trends assumption. That such modeling limitations exist, however, do not distinguish Diff-in-Diff specifications from other competing empirical strategies.