Empirical Legal Studies

Approaches Toward Missing Data

Missing data vex researchers, and there's no single "correct" way to deal with this not-infrequent real-world problem. A recent question posted on the StataList (here) visually illustrates what this can look like (in terms of N variation) across alternative specifications of a multilevel regression model drawing from a data set that contains missing data in some variables.

As this output illustrates, as one proceeds across models 1-4 what is clear is that the addition (and subtraction) of variables introduce missing data. How to approach this and what to do about it motivated the initial query. And in the discussion that follows identifies (some of the) various "standard" approaches.

Data on Life Insurance Markets and Racial Discrimination

A recent paper, Racial Discrimination in Life Insurance, explores the impact of modern anti-racial discrimination statutes on life insurance coverage differences across racial groups. To do so, the paper's authors, William Gale (Brookings Inst.) et al., exploit data from the 2014 panel of the Survey of Income and Program Participation (SIPP) and then merge it with Avraham, Logue and Schwarcz's (2014) ordinal rankings of "how restrictive a political jurisdiction (each of the 50 states and Washington, DC) is in limiting the use of race as a determinant of life insurance premiums and payouts (as of 2012)." The data sample is restricted to "white and Black adults aged 25-64 in order to focus on the working age population most likely to purchase life insurance. We limit our analysis to data for white and Black individuals in the interest of simplicity and in order to focus on the type of racial discrimination that has been most prevalent historically in the life insurance market."

The paper's core findings include: 1) individuals in states with strong anti-discrimination laws tend to have lower life insurance coverage rates than those living in other states; and 2) Black individuals are somewhat more likely than white individuals to hold life insurance, controlling for observable factors.

While hardly the final word, this paper identifies a fruitful path forward for future research. For example, this paper considers only whether a life insurance policy exits at all, and not the amount (or the face value) of such policies. It remains possible that racial discrimination "could conceivably impact the level [amount] of life insurance even if it does not influence the choice of whether to purchase a policy at all." The paper's abstract follows.

“We examine the historical and statistical relationship between race and life insurance. Life insurance can play a central role in households’ financial security. Race has played an important and changing role in the provision of life insurance in the U.S. from slave insurance before the Civil War, to ‘Scientific Racism’ continuing into the 20th century, to policies that do not explicitly mention race in recent decades. In empirical work using new data, we confirm earlier work showing that Black individuals have higher life insurance coverage rates than white individuals, controlling for observable characteristics. We find no difference in the likelihood of purchasing coverage—for Black individuals versus white individuals—in states with strong versus weak anti-discrimination laws. We also find that the presence of strong antidiscrimination laws tends to reduce overall life insurance coverage – by about 3 percentage points. We present some evidence that this finding is due to a generally stronger regulatory stance in the state rather than the specific impact of the anti-discrimination life insurance law. This analysis bears on the presence of discrimination in the current life insurance industry as well as related issues like the financial status of minority households.”

Save The Dates--16th Annual CELS (In-Person)

 

 

The Society for Empirical Legal Studies’

16th Annual Meeting

will be held on

November 4th and 5th, 2022 (Friday and Saturday) at the

University of Virginia School of Law

More information here (https://www.cels2022.com/)

A call for papers will be coming soon, but please mark your calendars now.

Federal Courts and "Certification" of State Law Questions

When federal courts need to apply state law and no clear articular of state law exists, federal judges have few options. While generating an Erie "guess" remains one option, another involves certifying the legal question to the state's highest court. Proponents suggest that state certification promotes federal-state cooperation, reduces forum shopping incentives, and, on net, reduces costs and increases efficiencies. Critics, by contrast, emphasize the unidirectional federal-state cooperation, the persistence of forum shopping, and the associated costs and delay.

While the SCOTUS and Judicial Conference have expressed growing interest in the state certification alternative of late, helpful data are scant. A recent paper by Jason Cantone (George Mason--criminology) and Carly Griffin (Univ. Ill.--ag.), Certified Questions of State Law: An Empirical Examination of Use in Three U.S. Courts of Appeals, seeks to contribute by presenting results drawn from three federal courts of appeals. While the analyses are purely descriptive, temporally bound (from 2010 through 2018), and limited to three federal circuits, they nonetheless cast some helpful initial empirical light on some of the basic contours of the certification process.

Drawing on a sample (N=218) of certified question events across three federal circuits from 2010-2018, the paper explores: "how often the certified question procedure is utilized in three U.S. Courts of Appeals, how often the circuits certify a question, how often states grant the certified question, and how long the process takes." Notably, the paper finds important variation across the three circuits when it came to state certification rates and duration. The paper's abstract follows.

"Federal courts routinely need to apply state law, but this task becomes complicated when no definitive state law exists. In these instances, federal judges have a few options, including making an Erie guess, or certifying the question of state law to the highest state court. During the U.S. Supreme Court’s October 2020 term, two opinions endorsed the certification of questions of state law procedure. However, despite recent interest by the U.S. Supreme Court and the U.S. Judicial Conference Committee on Federal-State Jurisdiction, little empirical research has examined the perceived benefits and burdens of the procedure. This Article provides new empirical data to help fill that gap.

Using a sample of 218 certified-question events across the U.S. Courts of Appeals for the Ninth, Third, and Sixth Circuits from 2010 to 2018, we examine how certified questions originate, in what types of cases, how often U.S. courts of appeal certify the questions of state law, and whether the corresponding state supreme courts grant or deny the question. Further, to address the perceived time burden associated with certification, we examine how long each part of the process takes in the appellate court, from filing to certification to termination. We found significant variation between the three U.S. courts of appeals in certification rates and timing. While we encourage future studies regarding certification of state law questions, our data can be readily used to inform courts and academic debates regarding the benefits and burdens of the procedure."

ABF Fellowship

A long-time Els blog reader, Elizabeth Mertz (Wisc./ABF), asked me to pass along the following information about an ABF Fellowship opportunity (sponsored jointly with AccessLex Institute). I am happy to do so.

"We are writing to spread the word about a special opportunity at the American Bar Foundation, offered jointly with the AccessLex Institute.  We have funding for a researcher who is currently a candidate for an LLM, SJD, or PhD -- and who is doing empirical, interdisciplinary research on legal education or on legal aspects of higher education.  The baseline funding is for a fellowship of $35,000 a year, extendable up to 2 years, to be held in residence at the ABF in Chicago.  (Additional funding for relocation to Chicago, and for research and travel to conferences is available as well.) Please circulate this to any colleagues who might be interested -- or who might have students who could apply."

Anyone interested in further information should directly contact: Jothie Rajah (jrajah@abfn.org), Laura Beth Nielsen (lnielsen@abfn.org), or Elizabeth Mertz (emertz@abfn.org).

CELS 2022--Toronto: Registration and More Information

Registration and related logistical information follow for the 15th Annual Conference on Empirical Legal Studies (online), 18-19 March 2022, organized by the Univ. Toronto Faculty of Law:

Registration: We invite you to register for CELS using the link (click here). Given that the conference is remote, the registration fees $50 for faculty and $20 for students. We ask that you kindly register at your earliest convenience. For participants, we ask that you register by March 13, 2022.

Keynote Speaker: This year's keynote speaker will be Prof. David Card, the Class of 1950 Professor of Economics at the University of California, Berkeley. In 2021, Prof. Card was awarded the Nobel Memorial Prize in Economic Sciences. A native of Guelph, Ontario, Prof. Card keynote talk is titled, ""Affirmative Action for Racial and Gender Diversity." The talk will take place on Friday, March 18, 2022 from 12:30pm - 1:30pm EST.

Training: We will be using the VVC conference platform. To avoid technical snafus on the day of the conference, VVC will be providing participants with an opportunity to try out the platform in advance of the conference. The training session will be on Wednesday, March 16, 2022, at 1pm. We specifically ask that the chair for each session (i.e., see below) join. We will circulate a link in the upcoming days.

Presentation Length: Each paper is scheduled for 30 minutes. That 30 minutes will be divided into three parts: 15 minutes for the presenter’s presentation, 8 minutes for the discussant’s discussion, and 7 minutes for general Q&A.

We ask presenters and discussants to respect these times to the best of their ability. The Chair of each session (described below) will be asked to keep time, but it is the responsibility of each speaker to abide by the time limits.

Session Chairs:The presenter of the last paper in each session is the Chair of that session, as designated by an asterisk on the program. The Chair’s only responsibility is timekeeping.

For additional conference information (click here).

Judicial Outcomes, "Industry Peer" Stock Ownership, and Recusal

While research on "outside" influences on judicial decisions is relatively well-developed, much of that research dwells on various political influences (judge political ideology, etc.). Comparatively less well-developed is the possibility that judges' stock holdings influence their decisions in cases that involve corporate parties from "industry-peer" firms. While recusal doctrine (and practices and norms) are designed to guard against direct judicial financial conflicts of interests, indirect financial conflicts, by contrast, fall outside of formal recusal boundaries. And one example of an "indirect" financial conflict includes when a presiding judge has a financial stake in a litigant's "industry peer."

Barriers to data access are among the reasons that account for a deficit in research on this topic. In Stock Ownership of Federal Judges and its Impact on Corporations, April Knill (Fl. St.--Business) et al., explore this question after cobbling together data from an array of sources. The key move on the data front involved matching, at the individual case-level, presiding judges and their financial holdings. The authors "manually download 21,044 individual financial disclosures from JudicialWatch.org file by file... . This process results in a sample comprising 11,447 unique reports for federal judges in the years 2007 – 2012.” And within their sample, the authors report that the sample contains "observations from 69,060 federal district court cases.… Judges own industry peer stock in 8.6% of the cases in our sample.”

It is worth underscoring that in these instances the presiding judges did not violate any formal recusal obligations as the possible conflicts of interests flowing from their "industry peer" stock holdings are indirect. That said, the paper's core results imply that judges are "being influenced by their stock ownership in industry peer firms of litigants – a practice that is completely legitimate – in cases over which they preside." The paper's abstract follows.

“This paper investigates whether and how litigant peer stock ownership by federal district judges affects characteristics of case outcomes for large corporate litigants. We find that industry-peer stock ownership by district judges is associated with the following outcomes for corporate litigants named in their assigned cases: 1) an increased likelihood of judgments for the corporate litigants, 2) a decrease in the amount received by the parties suing these corporate litigants, and 3) a decrease in the length of the litigation proceedings. The random assignment of district judges to cases provides exogenous variation in the judge stock ownership. We further identify the association outlined in our base results by examining appellate court reversals of district judgments, a triple difference analysis isolating large-stake investments, and outcomes in case types that should impact industries either cooperatively or competitively. Our results survive a falsification test as well as a battery of robustness tests. Our findings underscore the importance of mandates governing judge stock ownership, and more broadly, judge conflicts of interest.”

Mistaking Correlation for Causation

Economists--and econometrics--have been involved in empirical legal studies for generations. This is particularly true for anti-trust doctrine, both its development and current application. Legal challenges to proposed mergers, and questions relating to anti-competitive spill-over effects, including market concentration, remain a staple for empirical analyses.

In the anti-trust context, one intuitive move involves assessing whether "prices are positively related to measures of concentration, such as the Herfindahl-Hirschman Index (HHI), comparing across different geographic markets or time periods." Pursuing such a question can involve (and frequently does involve) something as simple (and potentially powerful) as regressing price on the HHI.

Despite whatever intuitive appeal such a move holds, in a recent brief essay--co-signed by many leading law and economics scholars (including, and I add in interest of full disclosure, my Cornell colleague George Hay), On the Misuse of Regressions of Price on the HHI in Merger Review, the authors caution against such a move as it invites one basic fundamental problem: Mistaking correlation for causation. And it is for the essay's description of just how such a basic mistake can arise (rather than it's specific application in the anti-trust context) that I recommend this essay, especially to younger, developing empirical legal scholars.

As it relates to the specific anti-trust point developed in the essay, the authors' argue that: "The underlying problem with regressions of price on the HHI is that the relationship between price and the HHI is not causal. Instead, both are equilibrium outcomes that are determined by demand, supply, and the factors that drive them. Thus, a regression of price on the HHI does not show the sort of causal effect that would be helpful in predicting the competitive effects of a merger." More specifically, as the "HHI can take values ranging from 0 to 10,000, with the former corresponding to a fragmented market with infinitesimal firms, and the latter to monopoly. All else equal, a decrease in the number of firms leads to a higher HHI. However, the HHI can increase if, for a given number of firms, the market shares of the larger firms increase."

The root problem, of course, flows from challenges posed by “endogeneity” or “simultaneity.” Such problems lurk "when a clear causal path between two variables is posited by the relevant economic theory but the causal factor (on the right side of the regression equation) is either correlated with unobserved factors or, more subtly, is simultaneously determined by the variables (in this case, price) on the left side of the regression. A famous example of simultaneity involves price and quantity, which are simultaneously determined in the classic economic model of supply and demand." The problems posed by "endogeneity” or “simultaneity," of course, are not limited to the anti-trust realm. An excerpted abstract follows.

"It might seem natural to determine whether prices are positively related to measures of concentration, such as the Herfindahl-Hirschman Index (HHI), comparing across different geographic markets or time periods. This might be implemented by using a simple regression of price on the HHI. However, for reasons that we describe, regressions of price on the HHI should not be interpreted as establishing causation. That is, they do not inform how a change in concentration from a merger would affect prices. Courts and other policy-makers should not rely on regressions of price on the HHI for the purposes of antitrust merger review."

An Empirical Assessment of What "Substantial Similiarity" Means to Courts in Copyright Litigation

Judicial assessments of copyright infringement claims remain dominated by the two-prong "substantial similarity" test. Despite this test's centrality to copyright doctrine, very little is known about how courts operationalize and apply it. In a recent paper, An Empirical Study of Copyright's Substantial Similarity Test, Clark Asay (BYU) seeks to sketch some of the test's general empirical contours. To do so, the paper, drawing from the universe of substantial similarity opinions (found on WestLaw), exploits a random sample of 1,005 opinions (district and appellate) between 1978 and 2020.

The study's key findings intrigue. First, and unsurprising to most practitioners in this space, the Second and Ninth Circuits dominate this litigation. Second, judicial analyses on the substantial similarity test tend to dwell on the second prong with comparably less judicial attention to the first. Third, judicial analyses focusing on prong two--assessing whether the defendant’s copying amounts to improper appropriation--evidence a wide diversity of approaches. As Asay notes, "[n]o dominant means exists for resolving this question, and, in any given opinion, a court typically uses multiple subtests and copyright limitations to decide this inquiry."

The paper concludes by recommending: "First, courts should maintain the two traditional prongs of the substantial similarity test as distinct and reinvigorate their assessments of similarity under the first prong of the substantial similarity test. Second, courts should make discussing and applying any relevant copyright limitations the heart of their prong two analyses to ensure that copyright law serves its constitutional purposes."

Defendant-Prosecutor Gender "Pairings" and Leniency

While various pockets on criminal law are increasingly subject to empirical analyses, one particular pocket--how prosecutors distribute discretion--is comparatively under-studied. This is so, partly, due to a comparative paucity of relevant data on the prosecutors themselves (and matching them to individual cases and dispositions). A recent paper, Gender Favoritism Among Criminal Prosecutors, by Stephanie Holmes Didwania (Wisc.), tries move the scholarly needle a bit by exploiting data on over 130,000 federal criminal defendants sentenced in 2002 through 2016 to assess possible "gender-based differences in how prosecutors exercise critical discretion."

The paper matches Sentencing Commission data and data from the Executive Office for United States Attorneys (EOUSA) which regularly publishes case data from the 93 USAOs located throughout the United States. Critically, the breadth of the LIONS data "is substantial—the data covers all cases in which a USAO was involved, including those cases that are the primary responsibility of another agency and those the USAO declines to prosecute." Despite its breath, the LIONS data set is not without important limitations including a comparatively non-trivial amount of missing data. After matching, the resultant data set data includes "131,207 federal criminal defendants sentenced between 2001 and 2016 in 63 of the 94 federal district courts."

Data set limitations aside, the paper's core finding intrigues: "That defendants receive more lenient charges when they match with their prosecutor on gender relative to when they are assigned a prosecutor of the opposite gender. Through this charging channel, prosecutor-defendant pairs that match on gender produce lower sentences relative to prosecutor-defendant pairs that mismatch." More specifically, "the leniency associated with gender-matching ultimately translates into significantly lower sentences: a defendant can expect to earn a roughly five-month shorter sentence when their prosecutor is their own gender compared to when their prosecutor is the opposite gender, which represents a roughly eight percent reduction in sentence length at the mean." The paper's abstract follows.

"Prosecutors enjoy wide discretion in the decisions they make but are largely unstudied by quantitative empirical scholars. This paper explores gender bias in prosecutorial decision-making. I find that male and female prosecutors exhibit small and statistically insignificant differences in their treatment of defendants overall but demonstrate relative leniency towards defendants of their own gender. Such favoritism at charging translates into a sentencing gap of roughly five months of incarceration for defendants who are paired with an own-gender prosecutor versus an opposite-gender prosecutor, which represents a roughly eight percent reduction in sentence length at the mean. The estimates do not appear to be driven by differences in case assignments for male and female prosecutors."

Judge Ideology and Pleadings Decisions in the Circuits

While the Twombly and Iqbal decisions separately and collectively helped galvanize empirical work in civil procedure in terms of access to federal courts, now that we're well into a post-Twombly and Iqbal world sufficient data exist to begin to test various normative claims regarding whether the two procedure decisions amplify the potential impact of judge ideology. And in a new paper, Politics, Identity, and Pleadings Decisions on the U.S. Courts of Appeals, Stephen Burbank (Penn) and Sean Farhang (Berkeley) set out to do just that.

To do so, the authors drew a random sample of 700 cases from the universe of cases post-Iqbal through 2019 that involved a Court of Appeals review of a district court decision on whether to dismiss for failure to state a claim under Rule 12(b)(6). The paper focuses on "the extent to which the party (of appointing president), gender, and racial composition of panels are associated with their disposition of 12(b)(6) appeals." Key findings include "that panels with women and non-white judges are substantially more likely to rule in favor of a plaintiff reaching discovery in other civil rights claims, an important and cross-cutting civil rights category amounting to a quarter of 12(b)(6) appeals in our data, but that race and gender are insignificant outside that substantive area. Party is insignificant across the board in the random sample."

CELS (Toronto)--Some Very Good News and Some Sub-Optimal News

I begin with the good news: CELS (Toronto), scheduled for March 18-19, 2022, will go forward. The sub-optimal wrinkle, however, is that organizers were forced to move the event to an on-line (remote) platform and format. As the organizers note: "Unfortunately, the surge in Omicron has led to travel restrictions into Canada, as well as restrictions on gatherings in the province of Ontario. Events at the University of Toronto are not permitted. It is likely that many of these restrictions will still be in force in March."

For more information about the conference click here.

Writing Up Results From a Logit Model Using the Odds Ratio Option

A fairly innocuous question -- how best to interpret odds ratio results from a xtlogit model estimation -- unleashed a torrent of commentary on the StataList (click here). As this is a not uncommon model used in many ELS papers, I thought others may benefit from the (extended) discussion.

One of the (many) points that garners attention includes the numeric range for odds ratios: "There is no reason an odds ratio can't be greater than 2. On the other hand, an odds ratio can never be less than 0. The possible values for an odds ratio range from 0 to + infinity. And the interpretation does not depend on the size of the odds ratio. In your case, assuming the predictor is dichotomous, it means that the odds of a positive outcome when the predictor is 1 is 2.46 times the odds of a positive outcome when the predictor is 0. If the predictor is continuous, it means that a unit difference in the value of the predictor is associated with the odds of a positive outcome increasing by a factor of 2.46."

The Empirics of Post-Conviction Plea Bargains

As a prosecutorial tool, the plea bargain exists in uncomfortable space. Any discomfort aside, however, the criminal justice system, as currently constituted, necessarily relies on it. As research on how prosecutors exercise their discretion--including how they deploy plea bargains--continues to develop, greater empirical clarity surrounding plea bargains will hopefully emerge.

While virtually all (of the small number of) plea bargaining studies typically focus on how prosecutors wield plea bargains after a defendants has been charged and prior to the defendant entering a formal plea, a recent paper explores plea bargaining at an entirely different moment in time. Specifically, in Plea Bargaining in the Shadow of a Retrial: Bargaining Away Innocence, Keith Findley (Wisc.) et al. set out to re-focus plea bargaining research by exploring what it looks like in the post-conviction appeals stage. And by exploiting only those post-conviction appeals brought by U.S.-based innocence organizations from 2010 through 2020, the authors try to focus on plea bargains for those defendants who have not-implausible claims of actual innocence.

To be sure, a dataset filtered by innocence organizations' case selections does not by any means insure that all of the (convicted) defendants are actually (or legally) innocent. Indeed, the authors admit as much when they note that "it is a virtual certainty that not all of the defendants in these cases are actually innocent." Over-inclusiveness aside, the authors feel that their dataset is "about as good as one can get for studying plea bargaining with innocent defendants."

Even after adjusting for an imprecise dataset, what the authors find intrigues. "In post-conviction litigation involving defendants with a high likelihood of being actually innocent and wrongly convicted, prosecutors offered plea bargains in 23 percent of the cases. Moreover, when prosecutors made plea offers, the plea concessions they offered were uniformly steep." If nothing else, this paper helps point the way for future research. An excerpted abstract follows.

"Critics of plea bargaining have long contended that it has an innocence problem—that the imbalanced and coercive nature of plea negotiations can induce even innocent defendants to plead guilty. While laboratory studies confirm that innocent individuals can indeed be induced to plead guilty, little real-world empirical evidence exists about the nature and extent of plea bargaining’s innocence problem.

Utilizing original empirical data, this article begins to fill that void. Looking at cases in a post-conviction context, we study the extent to which prosecutors in real cases utilize their plea-bargaining power to preserve convictions, even when the convictions appear to be deeply flawed and the chances the defendants are innocent are high. We also examine the degree to which innocence-claiming defendants succumb to those pressures and accept the deals. To address these questions, we collected a wide-range of data from U.S.-based member organizations of the Innocence Network about the cases they litigated from 2010-2020."

Data on Prosecutorial Discretion By Gender

While a robust judicial outcomes research literature continues to mature and evolve, a critical pre-judicial outcome stage--the exercise of prosecutorial discretion--remains relatively understudied. Understanding the prosecutor's role is crucial as they "exercise unfettered decision-making authority throughout criminal cases by selecting whom to charge, which charges to bring, and what plea bargains to accept." While prosecturial discretion increasingly garners critical public attention, scholarly attention remains hamstrung by a paucity of helpful, systematic data.

In a recent paper, Gender Favoritism Among Criminal Prosecutors, Stephanie Holmes Didwania (Wisconsin) makes some intriguing headway by exploring individualized evidence about prosecutorial decision-making with the benefit of data from more than 130,000 federal criminal defendants sentenced from 2002 through 2016.

The paper's individualized line prosecutor-level data are, of course, key, and the data set is the product of two separate data sources: U.S. Sentencing Commission data (for the defendants) and the Executive Office for United States Attorneys (EOUSA) that regularly publishes case-level data from the 93 USAOs located throughout the United States. These data originate from the Legal Information Office Network System (LIONS), which is the computer program that the EOUSA uses to track and manage case loads. After employing various filters, what emerged includes data on "131,207 defendants sentenced in 63 of the 94 federal district courts in the United States, comprising 172 unique courthouses, 1,498 unique prosecutors, and 1,589 unique courthouse-prosecutor combinations."

Despite the granular data, the paper's empirical execution is not without important limitations. One limiting factor is that line prosecutors are not randomly assigned to cases. Another is that the defendant's underlying criminal conduct is not observable to the researcher. As this paper explores gender-based in-group favoritism, the non-random case assignment is important as "cases in which prosecutors and defendants match on gender are systematically different from those in which prosecutor and defendant mismatch."

Limitations aside, the paper's key findings include some intriguing gender-based differences. While the paper finds that male and female prosecutors exhibit small and statistically insignificant differences in their treatment of defendants overall, evidence of relative leniency towards defendants of their own gender exists. And for the defendants, such gender-based in-group favoritism is not inconsequential. "The leniency associated with gender-matching ultimately translates into significantly lower sentences: a defendant can expect to earn a roughly five-month shorter sentence when their prosecutor is their own gender compared to when their prosecutor is the opposite gender, which represents a roughly eight percent reduction in sentence length at the mean." The paper's abstract follows.

"Prosecutors enjoy wide discretion in the decisions they make but are largely unstudied by quantitative empirical scholars. This paper explores gender bias in prosecutorial decision-making. I find that male and female prosecutors exhibit small and statistically insignificant differences in their treatment of defendants overall but demonstrate relative leniency towards defendants of their own gender. Such favoritism at charging translates into a sentencing gap of roughly five months of incarceration for defendants who are paired with an own-gender prosecutor versus an opposite-gender prosecutor, which represents a roughly eight percent reduction in sentence length at the mean. The estimates do not appear to be driven by differences in case assignments for male and female prosecutors."