Empirical Legal Studies

Impacts on Firms From Joining the S&P 500 Index

For those whose financial portfolios include investments in low-cost index funds, most assume that companies benefit from inclusion in the leading indexes, such as the S&P 500. As a recent paper, Does Joining the S&P 500 Index Hurt Firms?, by Benjamin Bennett (Tulane) et al., notes, being added to the index is like "joining a prestigious club. A firm gains prestige by joining the club, but at the cost of becoming compared to other firms in the club."

To better assess the costs and benefits, the paper executes "difference-in-differences (DiD) analyses based on S&P 500 index addition. Specifically, we first identify all S&P 500 additions in our sample period. Added firms are our treated firms. For each treated firm, we search for a control firm that is never a member of the S&P 500 index in our sample period and use a propensity-score match on total assets, Tobin’s q, stock return, and 2-digit SIC industry (exact match) in the year before a treated firm is added to the index, so that the matching process is not affected by index additions." The main findings are summarized in the paper's abstract.

“We investigate the impact on firms of joining the S&P 500 index from 1997 to 2017. We find that the positive announcement effect on the stock price of index inclusion has disappeared and the long-run impact of index inclusion has become negative. Inclusion worsens stock price informativeness and some aspects of governance. Compensation, investment, and financial policies change with index inclusion. For instance, payout policies of firms joining the index become more similar to the policies of their index peers. ROA falls following inclusion. There is no evidence of an impact of inclusion on competition.”

Testing a "Ratio Problem" in Finance Scholarship

On the heels of a recent post (here) describing a Stata regression command tailored to the unique needs of a dependent variable that takes the form of a ratio/percentage/fraction, comes a recent paper that explores potential problems with finance papers that model ratios. Potentially compounding the problem is that ratios as dependents variables are certainly not uncommon in the finance literature (see, e.g., papers featuring Tobin's Q). In The Ratio Problem, Robert Bartlett (Berkeley) and Frank Partnoy (Berkeley) frame the ratio "problem" in terms of two challenges–omitted variable and measurement error bias–"that arise anytime a researcher uses linear regression to estimate a production function that has a ratio as an output." As the paper notes, "In theory, the [ratio] denominator is not necessarily problematic; in practice, however, there are statistical concerns whenever the output of a production function is a ratio." The paper's abstract follows.

“We use the term ‘ratio problem’ to describe the omitted variable and measurement error bias that can arise when a ratio is the dependent variable in an economic model. First, we show how bias can arise from the omission of two classes of variables based on a ratio’s denominator. As an example, we demonstrate that the widely-cited ‘inverse U’ relationship between managerial ownership and Tobin’s Q is reversed when these variables are included. Second, we show how measurement error in the ratio’s denominator can produce bias. We provide empirical tests and solutions, and urge caution about ratios as dependent variables.”

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."

Can Technology Reduce Group-Level Litigation Disparities?

While perhaps aspirational, the court room is one context where we at the very least expect judicial proceedings to unfold in an impartial manner. Insofar as judges are humans, they, too, are vulnerable to various implicit biases. While the "digital-divide" is frequently framed in terms of how technology enhances the distance separating the proverbial "haves, and have nots," this may not be inevitable. For example, and setting aside arguments moored in economy and access, migrating judicial proceedings from the current, in-person, "bricks-and-mortar" context to online platforms that may not require "face-to-face" interactions may also, paradoxically, enhance impartiality by reducing "the salience of group identity traits."

Avital Mentovich (Haifa), J.J. Prescott (Mich.), and Orna Rabinovich-Einy (Haifa), explore this argument in Are Litigation Outcome Disparities Inevitable? Courts, Technology, and the Future of Impartiality. The authors submit their implicit bias hypotheses to "case-level data [N=5,232 cases: 2,713 face to-face; 2,519 online] using a quasi-natural experiment—the plausible exogenous adoption and implementation of online dispute resolution (ODR) procedures in two U.S. state district courts. Our data allow us to compare differences in litigation outcomes reached in face-to-face procedures relative to ODR-style hearings for civil infractions by party age, gender, and race." What they find, in part, is "evidence that is consistent with the existence of implicit or other structural biases in face-to-face proceedings; all else equal, legal outcomes appear to vary by litigant age and race but not by gender. These disparities fade with the change in medium, possibly by reducing implicit bias."

To be sure, and as the authors note, important aspects limit the force of the paper's findings. For example, the findings "emerge from a particular court system, a narrow range of case types [traffic violations], and from a specific ODR platform technology." As well, selection effects lurk as "litigants actively choose whether to pursue a traditional face-to-face proceeding, an online hearing, or nothing at all." Limitations notwithstanding, this is an important emerging trend that warrants sustained scholarly attention.

An Empirical Analysis of Entrepreneurs and Corporate Form Selection

Over the last few decades the LLC displaced the C corporation as the corporate form "of choice" for many entrepreneurs and closely-held corporations. According to many, while the C corporation benefited from comparative simplicity it was encumbered by tax disadvantages and governance "inflexibility." Despite a migration away from the C corporation among entrepreneurs, there has been quite little empirical work that directly engages with the "anti-C corporation" thesis or explores how C corporation selections distribute across entrepreneurs.

A recent paper, published in JELS, begins to fill this scholarly void. In Entrepreneurs' Legal Status Choices and the C Corporation Survival Penalty, Emily Satterthwaite (Toronto) explores whether "C corporations underperformed as compared to similarly situated businesses with alternative legal statuses." To do so the paper exploits "a large panel dataset that contains legal status, owner, business, financing, and other firm‐specific information collected from an eight‐year survey of nearly 5,000 enterprises that were formed in 2004." A summary of the paper's four key findings follow in the excerpted abstract.

"First, C corporation status is associated with firm failure rates that are 38 percent higher (significant at 0.1 percent) than those of non‐C corporations with similar characteristics. Second, this C corporation survival penalty persists at nearly the same magnitude and significance even after a subset of “anticipated cash‐exit” C corporations with (a) venture capital investors or (b) employee stock option plans are separated out. Third, nonwhite and foreign‐born entrepreneurs have a significantly higher likelihood of choosing C corporation status. Fourth, within the subset of firms that appear eligible to elect out of the default (subchapter C) corporate tax classification and into the tax‐advantaged subchapter S classification, nonwhite and older entrepreneurs are significantly more likely to remain in C corporation status. These findings suggest that increasing legal status complexity is unlikely to be neutral from a distributive perspective, and may be disproportionately burdensome for marginalized entrepreneurs."

Some of COVID-19's "Lockdown" Costs

Insofar as the COVID-19 crisis continues to unfold, in real time, scholarly efforts to study various aspects of this crisis may be somewhat premature. That said, the “floodgates” of “COVID-19” studies have already opened and are unlikely close anytime soon.

In response to the coronavirus pandemic, nearly all U.S. states issued stay-at-home orders designed to restrict the movement of people and help realize public-health dividends. The orders triggered an array of “considerable” costs, however. In The Impact of the Coronavirus Lockdown on Domestic Violence, Sarath Sanga (Northwestern) & Justin McCray (Columbia) explore one such potential cost: An increase in domestic violence. The authors exploit a database of “approximately 50 million 911 call records from 14 large U.S. cities. We also obtain mobile device location data from these same cities.” The paper’s key results are summarized in the abstract.

We use 911 call records and mobile device location data to study the impact of the coronavirus lockdown on domestic violence. The percent of people at home sharply increased at all hours, and nearly doubled during regular working hours, from 45 to 85 percent. Domestic violence increased 12 percent on average and 20 percent during working hours. Using neighborhood-level identifiers, we show that the rate of first-time abuse likely increased even more: 16 percent on average and 23 percent during working hours. Our results contribute to an urgent need to quantify the physical and psychological burdens of prolonged lockdown polices"

More "Replication" (or Data "Integrity") Problems--Medical Sciences

Just a stunning situation unfolding at The Lancet, one of medical sciences' leading scholarly journals. Setting aside the ambient politics surrounding Hydroxychloroquine's potential role as a possible treatment for COVID-19, the recent retraction of a peer-reviewed paper that received considerable public (and scientific) attention, in a matter of weeks following its publication, itself has garnered attention. Three of the paper's four authors, according to The Lancet, have concluded that they “can no longer vouch for the veracity of the primary data sources.” A helpful summary of this unfolding situation appears on Gelman's blog (here and here).

Re-Scheduled CELS--From 2020 to 2021

It is with a heavy heart that I pass along the following CELS update from the Society for Empirical Legal Studies' Board of Directors:

Empirical Efforts to Assess Recidivism Risk--Is There a Role For Algorithms?

In assessing recidivism risk, policymakers increasingly turn to algorithms. This turn remains contested. Many of these contests pivot on claims that algorithms themselves incorporate various biases. More specifically, "some critics oppose the use of risk assessment instruments to scaffold criminal justice reform efforts, based on concerns that algorithms are racially biased and could result in inequitable outcomes for already disadvantaged groups."

Of course, and as made clear in a recent paper by Jennifer Skeem (Berkeley--public policy) and Christopher Lowenkamp (AO, US Courts), Using Algorithms to Address Trade-Offs Inherent in Predicting Recidivism, "concerns about the legitimacy of specific risk factors and the potential discriminatory effects of using risk assessment instruments are not new—and can be examined empirically." This paper takes up the challenge by comparing "how alternative strategies for 'debiasing' risk assessment algorithms affect these tradeoffs, based on a large sample of Black and White federal probationers assessed with the Post Conviction Risk Assessment [PCRA]." The abstract follows.

"Although risk assessment has increasingly been used as a tool to help reform the criminal justice system, some stakeholders are adamantly opposed to using algorithms. The principal concern is that any benefits achieved by safely reducing rates of incarceration will be offset by costs to racial justice claimed to be inherent in the algorithms themselves. But fairness tradeoffs are inherent to the task of predicting recidivism, whether the prediction is made by an algorithm or human. Based on a matched sample of 67,784 Black and White federal supervisees assessed with the Post Conviction Risk Assessment (PCRA), we compare how three alternative strategies for “debiasing” algorithms affect these tradeoffs, using arrest for a violent crime as the criterion. These candidate algorithms all strongly predict violent re-offending (AUCs=.71-72), but vary in their association with race (r= .00-.21) and shift tradeoffs between balance in positive predictive value and false positive rates. Providing algorithms with access to race (rather than omitting race or ‘blinding’ its effects) can maximize calibration and minimize imbalanced error rates. Implications for policymakers with value preferences for efficiency vs. equity are discussed."

All About Multilevel Modelling Resources

With an admitted bias for "one-stop" resource sites, I recently came across a very thorough (and thoroughly helpful) site sponsored by the University of Bristol's (UK) Centre for Multilevel Modeling (here). Multilevel modelling's usefulness for many ELS research projects is as acute as it is obvious. The site teems with an array of focused resources, including a deep pool of useful online instructional videos (here). For anyone interested in a brief overview of multilevel modelling, this quick explanatory video (here) might be one place to start; a series of PowerPoint presentations (found here) is another.

Interrupted Time Series Regression

I note this recent discussion in Statalist (click here) only because an interrupted time series research design is not infrequently helpful in empirical legal studies. Note also comment No.7's point about the assumption that the external shock (the "interruption") applying equally across all the firms in the panel.

Local Prosecutor Elections, Prosecutorial Reforms, and Geography

A growing movement of local prosecutor candidates running for office with clear "reform" agendas (e.g., decriminalization of various drug laws through express non-enforcement, deincarceration, etc.) assumes the efficacy of the ballot box as an instrument of policy reform. Such a movement, however, risks a collision with received academic wisdom that local prosecutor elections are little more than "empty exercises" owing to an enormous "incumbency advantage." In a recent paper, Picking Prosecutors, Carissa Hessick (UNC) and Michael Morse (Harvard--Govt.) submit the received academic assumption to data. The data include prosecutor election results drawn from 2,314 separate districts across 45 states during the 2014 (or 2016) election cycle.

While largely descriptive, what they find includes the expected as well as the unexpected. Consistent with the "received wisdom," Hessick and Morse find that "incumbent prosecutors rarely face challengers and almost always win." One complicating wrinkle, however, is that the "degree of [prosecutor] incumbent entrenchment" is a function of an incumbent's time in office. Finally, one surprise is the salience of geography: or, more specifically, "a stark divide between rural and urban prosecution." A summary of this point is described in the excerpted abstract (below).

"Urban areas are more likely to hold a contested election than rural areas. Rural areas, in which very few lawyers live, rarely hold contested elections and sometimes are not able to field even a single candidate for a prosecutor election. The results suggest that the nascent movement to use prosecutor elections as a source of criminal justice reform may have success, at least in the short term. But elections are, as of now, not a likely source of reform in rural areas—the very areas where incarceration rates continue to rise."