Empirical Legal Studies

"Heatplots" for Correlation Coefficients Graphs

While I've never used one myself, I detect an upward trend in "heatplots" (example below) for basic descriptive correlation coefficient graphs.

A helpful discussion (along with coding suggestions) on what is possible with Stata's heatplot command is found here.

Importing Non-Stata Data Sets Into Stata

While perhaps old-hat for some (many), a quick new Stata tutorial video (click here) walks viewers through some of the basics incident to data importation. For old-time users (including those who may reflexively turn to StatTransfer programs for conversions), increasingly easy--and a wider array of--data transfer options remain much-welcome news.

A Quick Refresher on T- vs. F-Tests

While I haven't thought about this since grad school, a recent discussion on the StataList (here) provides a helpful, quick refresher on when F- and T-Tests converge and when they do not (and why).

An Online Resource of Note

For those new to ELS, and even those with more sophisticated questions, UCLA's statistical consulting site, festooned with an array of resource links (here), remains quite helpful. While the site continues to evolve over time, some well-organized and useful links will help orient and guide those engaged in ELS-related work. Examples include a quick reference chart on "choosing the correct statistical test" (which includes command syntax for SAS, Stata, SPSS, & R), illustrated examples of how to interpret annotated output for standard commands, and robust "FAQ" links that are, again, program-specific (complemented by a "general FAQ" link (here)).

Interpreting DID Output

While one may quibble about how the questioner designed her DID estimation, the question itself--how to understand and interpret standard DID output (in Stata)--elicited some helpful replies in a recent StataList discussion (here).

Poisson Tutorial Videos

The good folks at Stata recently posted a series of video tutorials focusing on how to fit various Poisson regression models which assist when modeling count data. The various videos take up a Poisson model with: a) continuous predictors (here); b) categorical predictors (here); and c) Poisson models that include both continuous and categorical variables (here).

A Small--But Important--Logistical Matter Incident to Dataset Merging

Those who have merged (or appended or crossed) datasets may have inadvertently bumped into a not uncommon problem--where the two separate datasets share a variable with the identical variable label name. For relatively smaller datasets, and where the researcher is aware of this hurdle ex ante, one can always, by hand, rename variables prior to combining the datasets. For larger datasets with many more variables, however, while this may not be practical it nevertheless remains critical.

A recent discussion of how to manage this nettlesome problem is found here. The comments' leading suggestion references Daniel Klein's -elabel- package, available from SSC (as it involves user-written code). Put briefly, the elable command allows a user to add a suffix (e.g., "_1") to every variable name in "dataset1." An analogous manipulation to datast2 can add another unique suffix (e.g., "_2") to every variable name in dataset2. And so forth. The end result includes datasets with distinct variable label names that can then be combined.

Helpful Statistics Resources

On the better late than never front, I just stumbled across a wonderfully rich "one-stop" resource for statistics novices. Germán Rodríguez (Princeton) hosts a site (here) that includes tutorials for both Stata and R. As to the tutorials' scope, the Stata tutorial, e.g., ranges from a "gentle introduction" to coding examples for customizable tables. Many--especially students--may find this resource helpful.

Law School Curriculum: Reform, Assessment, and Research Design

While age-old complaints persist about the basic structure of the first-year law school curriculum, few law schools have dared to experiment with meaningful reforms. Fewer still study these reforms coherently. The "Curriculum B" experiment at Georgetown Law School, as well as a recent paper by David Hyman et al. (Georgetown), Does the 1L Curriculum Make a Difference?, are important and interesting exceptions.

Since 1991, Georgetown Law School has offered an "alternative" Curriculum B along side a standard, more traditional first-year curriculum. Curriculum B was designed to provide “critical” perspectives on the law and respond to important changes in legal practice and theory in the years since the standard 1L curriculum was first developed decades earlier. At Georgetown, students elect into Curriculum B and, when demand exceeds supply, student assignment to Curriculum B is determined by lottery.

For assessment purposes, the quasi-randomized control trial aspect of student assignment to Curriculum B provides a way to overcome selection bias. That is, Hyman et al. compare student outcomes for those who opted into Curriculum B (the treatment group) with student outcomes from those students who wanted to receive the "treatment" (Curriculum B) but, due to excess demand and random selection (lottery), were instead assigned the "placebo" (that is, to the standard, traditional first-year curriculum).

Aside from careful attention to research design, a few of the paper's warrant note. When it comes to students' overall law school academic performances, for example, the authors find that "Curriculum B leads to a mean preserving contraction in students’ overall grades. At the same time, we find that it leads to diminished performance in two key business law electives (Corporations and Securities Regulation)."

Everything You Wanted to Know About Tables (in Stata)

Throughout the second-half of 2021, the Stata Blog ran a 7-part series on generating various tables. A single link to the 7-part series is here.

A "Guide" on how to Interpret Empirical Corporate Governance Scholarship

While empirical work continues to proliferate across an growing array of legal "silos," lawyers (and some law professors) increasingly need to engage with these studies to understand their implications for legal practice and policy implications. This is especially true for corporate governance scholars (and practitioners). As empirical corporate governance work reaches a wider audience, the work intersects with an ever-increasing number of individuals "not trained in econometrics and statistical methods."

This is a problem, and a recent paper endeavors to contribute to a solution. In A Lawyer's Guide to Empirical Corporate Governance, Ofer Eldar (Duke) sets out to provide a general guide that overviews "key empirical strategies for evaluating the relationship between governance and shareholder value, and to demonstrate to lawyers how they can engage with their weaknesses." Critically, the paper identifies a set of three key comparisons that dominate empirical corporate governance scholarship: "(1) comparing firms with and without the governance provisions, (2) evaluating the value of firms before and after adoptions or removals of governance provisions, and (3) evaluating what happens to shareholder value after a legal change."

While papers like these may not be standard empirical legal scholarship, they nonetheless contribute to the field more generally by helping to make empirical scholarship a bit more accessible to those lacking formal empirical training. The abstract follows.

"Empirical studies in corporate law have proliferated in the last two decades, and have had a major impact on legal practice and policy relating to corporate governance. As a result, lawyers increasingly engage with these studies in order to understand their implications for legal practice and policy. This is often challenging because most lawyers are not trained in econometrics and statistical methods, and thus, there is a risk that they misinterpret these studies and their implications. These studies, while critical for evaluating different corporate governance regimes, suffer from well-known weaknesses. The purposes of this guide are to provide an overview of the key empirical strategies for evaluating the relationship between governance and shareholder value, and to demonstrate to lawyers how they can engage with their weaknesses. The main theme of the guide is that largely all empirical strategies are based on three key intuitive comparisons: (1) comparing firms with and without the governance provisions, (2) evaluating the value of firms before and after adoptions or removals of governance provisions, and (3) evaluating what happens to shareholder value after a legal change. By identifying these basic comparisons and the roles they play in the key methodologies for evaluating shareholder value, lawyers will be better positioned to assess empirical studies and evaluate their implications for legal policy."

Graphics, Options, and Color

While Stata's graphics options (and related coding) have always struck me as unnecessarily complex, others seem to be inspired by them. While in the past "color options" involved monochromatic versus gray-scale, journals increasingly permit actual "color" options. Thus, to this end, I want to pass along a pair of related, though distinct, StataList discussions describing (with helpful coding)  various basic color options for box-plots and histograms.

Marginal Effects

While journals have traditionally focused on a key variable's direction and statistical significance, over time an increasing number of journal editors (and reviewers) ask for explications of a variable's substantive and "practical" influence. This trend is unlikely to abate anytime soon. And this is precisely where marginal effects (and Stata's margins command) come into play.

While no longer a new topic, I want to pass along the following resource, Using Stata’s Margins Command to Estimate and Interpret Adjusted Predictions and Marginal Effects, by Richard Williams (Notre Dame--sociology). The document is, at once, accessible, thorough, and yet not over-bearing as it walks readers through the basics of the  margins command. The presentation is greatly enhanced by step-by-step illustrations and the necessary coding. In all, quite a helpful resource for those seeking a quick tutorial.

Visual Displays of Uncertainty

A recent post on Gelman's Stats blog (by Jessica Hullman) nicely merges a few critical threads. One involves Tufte's classic push to display data in creative and informative ways (see, e.g., Tufte's classic). Another relates to a detectable nudge towards emphasizing results' "uncertainty" rather than a "false" sense of "precision" through, say, point estimates. While Jessica's discussion dwells on election forecast uncertainty--and interesting ways to visually convey it--the basic point includes obvious spill-over implications. As well, even if one is persuaded that visually conveying uncertainty is a worthwhile objective, the question about whether withholding point estimates a good idea is not easily answered.

Ways to Approach (and "Interpret") Null Results

"Null" results are a species of output that remains comparatively under-explored. Or, more accurately, how much analytic weight null results can plausibly bear (and/or how to "interpret" null findings) quickly invite complex questions that frequently derail into other, related lines of inquiry (the very concept of "yes/no" statistical "significance", power testing, etc.) As is often the case, at bottom some level of judgment and discernment is required. This general topic was the subject of a recent StataList discussion (here).