Empirical Legal Studies

Transforming "Vertical" Regression Output Into a "Horizontal" Table Format

A recent Statalist discussion (here) walks readers through the coding necessary to transform the following (traditionally "vertical") regression output:

-----------------------------------------
                               mpg       
-----------------------------------------
Weight (lbs.)                      -0.006
                       [-0.009    -0.003]
                                     0.00
Displacement (cu. in.)              0.006
                       [-0.014     0.025]
                                     0.57
Turn circle (ft.)                  -0.139
                       [-0.496     0.219]
                                     0.44
Intercept                          43.588
                       [33.688    53.489]
                                     0.00
Number of observations                 74
-----------------------------------------

into a "horizontal" output format:

-------------------------------------------------------------
                       Coefficient       95% CI       p-value
-------------------------------------------------------------
Weight (lbs.)               -0.006 [-0.009    -0.003]    0.00
Displacement (cu. in.)       0.006 [-0.014     0.025]    0.57
Turn circle (ft.)           -0.139 [-0.496     0.219]    0.44
Intercept                   43.588 [33.688    53.489]    0.00
-------------------------------------------------------------

Anticipated and Unanticipated Costs and Benefits of Mandatory Insider Trading "Blackout" Requirements--Evidence From the EU

Many countries, including the U.S., impose closed periods (a.k.a. "blackouts") on corporate insider trading for a period of time preceding earnings announcements. Such regulations on insiders' trading activity are typically justified due to insiders' unique role and position in capital markets. Whether these regulations achieve their stated goals remains relatively understudied.

In July 2016, all E.U.-listed firms were required to impose a 30-day blackout period on corporate insider trading prior to interim or fiscal year-end earnings announcements. The variation across firms prior to the July 2016 rule created a quasi-natural experiment to assess the new (2016) rule's impact on "insider trading activity, profitability, and market consequences."

In The Impact of Mandatory Closed Periods on Corporate Insider Trading, Francois Brochet (BU—Accounting) et al. report results from a difference-in-differences strategy that compares 30 compare countries that adopted mandated closed periods after July 2016 (treatment group) with companies that already had such policies (control group) in place prior to 2016. Notably, what the authors report is that their results highlight that uniform closed periods "deter informed trading but may unintentionally harm market liquidity and information quality." The abstract follows.

"The Market Abuse Regulation (MAR), implemented in July 2016 across the EU, mandates uniform closed periods, prohibiting insider trading 30 days before earnings announcements. We find a significant reduction in insider trading during these periods in treated countries without prior mandates. Although some trades still occur, they do not appear to be driven by private information. However, treated insiders experience an increase in compensation. Furthermore, information asymmetry rises before earnings announcements, and treated firms experience a decline in institutional ownership. Overall, the study suggests that mandated closed periods do not lead to a wealth transfer from insiders to outsiders, nor do they enhance the information environment. These results underscore the limitations of regulatory one-size-fits-all measures in curbing corporate insider trading."

Empirical Evidence, Courts, and the 4th Amendment

Over time, and since Katz (1954), Justice Harlan's two-part approach has largely guided how courts construe privacy protections in the 4th Amendment context. As the second part of Harlan's approach involves what many consider to be amenable to empirical social science, a growing body of scholarship sets out to mark the boundaries of where, as Christine Scott-Hayward (CSU-Long Beach--criminology) et al., note, "society [reasonably] expects privacy." Increasingly, defense attorneys increasing turn to such research findings in their briefs and pleadings to courts.

While entirely descriptive, The Role of Empirical Scholarship in Fourth Amendment Privacy Jurisprudence levers 13 leading empirical papers in the 4th Amendment space and then identifies and dives deeply into the relatively (and absolutely) small number of judicial opinions that cite to the leading empirical work. The authors' main takeaway is one of frustration with the courts' reluctance to engage with empirical legal scholarship relevant to the question of societal expectations of privacy in the search and seizure context. (To be sure, any judicial reluctance to engage with empirical legal research is merely a sub-set of, for better or worse, courts' collective benign neglect of legal scholarship generally.)

In the end, the paper's findings (and the authors' frustration) both bump into and provide indirect support for a larger point that my Cornell colleague (and friend) Jeff Rachlinski described years ago (2011): “Empirical legal scholarship . . . is not the same as evidence-based law. Empirical legal scholarship resides primarily in the academy.” That relevant empirical legal scholarship will migrate from the academy and into judicial opinions is not a given. Moreover, any such migration will likely continue to vary across legal doctrines and case types.

Options for Small and Unbalanced ("Rare Events") Data Sets

While relogit is a standard "go-to" Stata command when a data set includes "rare events," a threat of bias is enhanced if rare events derive from a "small sample." While bootstraping may be an option for some, a recent Stata listserv discussion (here) emphasizes a pair of commands -- firthlogit and exlogit -- that might make sense for others. Relatedly, Prof. Williams (ND-sociology) helpfully delves into the challenge a bit more comprehensively (here).

George L. Priest (1947-2024)

When my former mentor, Ted Eisenberg (1947-2014), periodically reminded me that "it is difficult to overestimate the influence of selection effects in litigation," his point of reference was a seminal 1984 article, The Selection of Disputes for Litigation. Sadly, one-half of the "Priest-Klein" hypothesis, George L. Priest, the Edward J. Phelps Professor of Law and Economics at Yale Law School, passed away recently.

Yale Law School's memorial notice echoes what Ted emphasized for decades, "[Priest's] 1984 article (with UCLA economist Benjamin Klein) “The Selection of Disputes for Litigation,” revolutionized theories of the common law and engendered decades of inquiry regarding the probability of litigation outcomes. The article presented what became known as the ‘Priest-Klein hypothesis’ and introduced the concept of selection bias into legal literature.” Empirical scholars, and many others, mourn Prof. Priest's passing.

Job Opportunity of Note (& ELS' Expanding Footprint)

While my proverbial "gaze" typically fixes on scholarship, "ELS-adjacent" issues periodically catch my eye as well. In this spirit, I recently came across a "real-world" (that is, non-academic) job opportunity that might interest statistics-savvy post-docs (and others). The job posting also implies the possibility that ELS is expanding beyond its traditional academic "silo."

What I learned from the job posting includes that: 1) an "Quantitative Research Unit" operates within (and services) the New Jersey judiciary, and 2) this Unit is actively hiring a "Research Analyst Manager" (click here for a direct link to the job posting). According to the [NJ] Judiciary Research Manager, the Unit is looking to hire "an individual to lead the team doing research across the Civil Court and Family Court practice areas. This is a great opportunity to lead applied work in the Law and Courts arena that has near-immediate impact."

"T-Testing" Group Differences at Various Percentiles

While the standard t-test compares means, somewhat less clear is what to do if one wants to test, e.g., whether group differences at various percentiles achieve statistical significance. In a recent Statalist discussion (click here), the specific question posed involves an effort to determine whether “Black-White wealth differences at p10 (10^th percentile) and p90 (90^th percentile)” systematically vary.

Possible options, described in the responses, range from using the qreg and ttest commands.

Taxing Autonomy and Budget Volatility

While complaints from public entities about the policy challenges and harms incident to fiscal uncertainty attributable to budget volatility emerge on an almost annual basis, factors that inform budget volatility remain understudied. Moreover, the particular role that a public entity's taxing autonomy might play remains especially obscure in the empirical literature. However, a recent paper, Does Taxing Authority Help School Districts in Managing Revenue Volatility?, by Laiyang Ke (Ark. St. Univ.--Poli Sci), makes a helpful contribution.

The paper defines taxing autonomy in terms of the degree to which a subnational government (here, public school districts) controls their tax revenues. "Budget volatility" is understood as a function of a school district's "fluctuations and uncertainty in revenue streams and expenditure patterns." Notably, both concepts have particular traction in the US public school district context. First, school districts vary in terms of their taxing autonomy. Second, "previous research has shown that state and local government revenue volatility could lead to expenditure volatility, and uncertain spending fluctuations in school districts may impair education outcomes."

One of the paper's key contributions includes its proposed measure of school district taxing autonomy which draws from school district financial data from the 1998/1999 to 2018/2019 school years. The paper's two-pronged empirical execution features a correlated random effects model as well as D-I-D estimations. The paper's findings emphasize that "school districts with a higher degree of tax autonomy—specifically, those able to change tax rates—experience less current expenditure volatility than districts with lower degrees of tax autonomy." The abstract follows.

"This study examines the impact of tax autonomy on school district expenditure volatility in the U.S., where school districts differ in their ability to levy and adjust taxes, with some having full taxing authority and others relying on fixed appropriations or lacking control over tax rates. This research introduces a comprehensive index to measure taxing autonomy across districts and develops an ordinal classification based on this framework. Using finance data from 1998/1999 to 2018/2019 and difference-in-differences, the study investigates whether districts with higher tax autonomy experience lower expenditure volatility compared to those with limited or no tax authority. The findings reveal that districts with greater tax autonomy, particularly those able to adjust tax rates, exhibit less volatility in current expenditures. Additionally, during the Great Recession, districts with higher autonomy faced smaller cuts in current expenditures by increasing tax revenues, which helped protect educational inputs like pupil-teacher ratios."

With Apologies...

Now that some nettlesome technical web domain hosting/forwarding issues have finally been resolved, regularly blog posting will resume.

Serial Correlation Testing for Panel Data

When working with panel data, testing for serial correlation is common—if not expected—diagnostic. To this end, a new user-created command (v.1.0.3) – xtdpdserial – functions as a postestimation command for many (though not all) standard commands (e.g., regress, xtreg, etc.).

For those interested, installation download sites include: ssc install xtdpdserial as well as: net install xtdpdserial, from(http://www.kripfganz.de/stata/)

On a distinct, though related, point, Prof. Kripfganz's (Exeter Business School--Econ. Dept.) website includes a very helpful array of related Stata user-commands (click here).

SCOTUS Database--Updates

The Supreme Court Database, motivated in part by Prof. Harold Spaeth (1930-2017), remains a leading source for Court and judicial decisionmaking scholars. Indeed, "virtually all systematic analyses of the contemporary Supreme Court and its members have relied on it." Given the Database's scholarly prominence, I wanted to pass along a few, brief updates.

First, the Database, which includes information (247 variables) on every SCOTUS decision since the "beginning" (1791), has now been updated to include information on all SCOTUS cases through the 2023 Term. Second, the Database's "home" has migrated from Washington University and, starting with the current (Oct. Term 2024), will be archived at Penn State University (click here).

RSAs & Chapt. 11

While relatively uncommon prior to the mid-2000s, as Figure 1 (below) illustrates, restructuring support agreements ("RSAs") "have become a regular fixture in Chapter 11 proceedings." RSAs typically lay out a pre-agreed reorganization plan and are usually in place prior to a formal Chapter 11 filing.

Figure 1: RSAs in Cases with Over $100M Assets

While RSAs and their rise in Chapter 11 proceedings remain the subject of sustained debate in normative and theoretical literatures, in a recent paper, Restructuring Support Agreements: An Empirical Analysis, the authors, Katherine Waldock (Columbia), Anthony Casey (Chicago) & Frederick Tung (BU), assess RSAs from an empirical lens. In their effort to "study how RSA contracts evolve over time," the authors lever PACER data archives and focus on more than 400 non-financial Chapter 11 filings that involved more than $100M in declared assets during just over the past two decades. While the analyses are entirely descriptive, key trends are identified in the abstract (below).

"Restructuring support agreements (RSAs), or contracts that commit bankruptcy parties to supporting a plan of reorganization that will conform to certain requirements, are now a common feature of Chapter 11. Parties utilize these agreements in nearly half of all large cases. While prior literature has debated the normative value of RSAs, we take an empirical approach to look at what provisions the parties include in these agreements and how those provisions have changed over time.

Our analysis looks at all RSAs associated with large bankruptcies through the end of 2020. We characterize the types of firms with RSAs, the parties involved, and the language contained within their key sections. A significant majority of RSAs are entered into on or before the petition date. Common provisions relate to the bargaining process during the case and often commit the parties in advance to certain elements of the restructuring plan. Provisions related to control such as debtor milestones have become more frequent in the last ten years of the sample."