Inferences from Litigated Cases

2. Inferences from Litigated Cases Dan Klerman & Yoon-Ho Alex Lee Law and Economic Theory Conference December 7, 2013

3. MOTIVATING QUESTION • Take an area of private law. • Suppose in State A, the legal standard governing liability is f. In State B, the standard is g, more plaintiff-friendly.What should we expect to observe in terms of the rate of plaintiff’s trial victory among litigated cases, all else equal? • Alternatively, suppose we observe a higher rate of plaintiff’s trial victory among litigated cases in State B with g, as compared to State A, with f. Can we validly make an inference that g is more plaintiff-friendly than f, all else equal?

4. Theoretical Literature on Settlement and Litigation “50%!” “Any deviation from 50% is from noise/errors or asymmetric stakes!” - Priest & Klein (1984) “No inferences regarding the legal standard are possible!” - Wittman (1985)(interpreting Priest & Klein) “Any frequency of plaintiff win is possible!” - Shavell (1996)

5. Standard Models of Settlement and Litigation • Divergent Expectations (Priest & Klein (1984)) • Asymmetric Information • Screening (P’ng (1983), Bebchuk (1984), Shavell (1996)) • Defendant has informational advantage • Plaintiff has informational advantage • Signaling (Reinganum & Wilde (1986)) • Defendant has informational advantage • Plaintiff has informational advantage OUR AIM: Across all standard classes of models of settlement/ litigation, valid inferences are possible under plausible assumptions about the distributions of disputes.

6. Theoretical Literature on Settlement and Litigation “50%!” “Any deviation from 50% is from noise/errors or asymmetric stakes!” - Priest & Klein (1984) “No inferences regarding the legal standard are possible!” - Wittman (1985)(interpreting Priest & Klein) “Any frequency of plaintiff win is possible!” - Shavell (1996)

7. Asymmetric Information:The Screening Model

8. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer • A legal standard is, f(p), a PDF over [0,1], distributing potential Ds in terms of type p = p’s probability of win. High p for low-quality D. • Damage = d, respective cost of litigating: CD,Cp> 0. • D’s p private info, p makes a “take-or-leave” settlement offer at x. • D’s strategy: Accept if x < pd + CD, reject otherwise. • p offers x to maximize expected recovery: p’s payoff from Litigating Ds p’s payoff from Settling Ds

9. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer • A legal standard is, f(p), a PDF over [0,1], distributing potential Ds in terms of type p = p’s probability of win. High p for low-quality D. • Liability = d, respective cost of litigating: CD,Cp> 0. • D’s p private info, p makes a “take-or-leave” settlement offer at x. • D’s strategy: Accept if x < pd + CD, reject otherwise. • p offers x to maximize expected recovery: “Any frequency of p win is possible!” – Shavell (1996) Translated: “Give me any probability, and I can construct a PDF producing that probability as p’s win rate.” Empirical Relevance?: We can’t choose the PDF. Relevant Question: Given a PDF representing a legal standard, what condition must a new PDF satisfy in relation to the original PDF to permit valid natural inferences? p’s payoff from Litigating Ds p’s payoff from Settling Ds

10. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer • How should we understand the “more pro-p” standard? • Given 2 PDFs, f(p) and g(p), what relation describes “more pro-p”? • Stochastic Dominance: not sufficient • Monotone Likelihood Ratio Property: sufficient

11. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer Exp. Payoff: • FOC over x: • Let , k = : . Hazard rate of fhf(p) Threshold D type

12. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer • As long as hg(p) < hf(p), under f(p) < under f(p) • But if MLRP (), we have hg(p) < hf(p).

13. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer • So MLRP implies under f(p) < under g(p), with which we can show p’s win-rate is higher under g(p).

14. Screening Model (Bebchuk, Shavell): Overview D has private info, p makes a “take-it-or-leave-it” offer Proposition 1 (Inferences Under the Screening Model). When p is screening, the probability that pwill prevail in litigated cases is strictly higher under a “more pro-plaintiff” legal standard, as characterized by monotone likelihood ratio property. Proposition 1A (Inferences Under the Screening Model). Same result when D is screening. PDF Families over [0,1] Exhibiting MLRP: Over [0,1]: uniform, beta, rising triangle, falling triangle Truncated: normal, exponential, binomial, Poisson

15. Asymmetric Information:The Signaling Model

16. Signaling Model (Reinganum & Wilde): Overview p has private info, p makes a “take-it-or-leave-it” offer • p knows type. Type is probability that plaintiff will prevail at trial • p makes a “take-it-or-leave-it” offer, s(p), that increases with type • D rejects offer with probability, p(s), that increases with the offer and is largely independent of the distribution of disputes • So high probability plaintiffs are disproportionately represented among litigated cases • Pro-plaintiff shift in law • increases proportion of high probability plaintiffs in population (e.g. in pool of litigated + settled cases) • increases proportion of high probability plaintiffs in litigated subset • increases observed probability of plaintiff success

17. Signaling Model (Reinganum & Wilde): Overview p has private info, p makes a “take-it-or-leave-it” offer Proposition 2 (Inferences Under the Signaling Model). When p has the informational advantage, the probability that pwill prevail in litigated cases is strictly higher under a more pro-plaintiff legal standard, as characterized by monotone likelihood ratio property. Proposition 2A (Inferences Under the Signaling Model). Same result when D has the informational advantage.

18. The Priest-Klein Model

19. Priest-Klein Model: Overview DISTRIBUTION OF ALL DISPUTES (SETTLED OR LITIGATED) p WINS (BLUE) p WINS (BLUE) DEGREE OF D FAULT DEGREE OF D FAULT Distributions of litigated disputes if parties make moderate errors Distributions of litigated disputes if parties make small errors PRO-D STANDARD PRO-p STANDARD

20. Priest-Klein Model: Overview Proposition 3 (Inferences Under the Priest-Klein Model). Under the Priest-Klein model, if the distribution of disputes has a log concave CDF, then p’s win-rate among litigated cases increasesas the decision standard becomes more pro-p. PDFs with Log-Concave CDFs: normal, generalized normal, skew normal, exponential, logistic, Laplace, chi, beta, gamma, log-normal, Weibull…

21. Priest-Klein Model • As legal standard becomes morepro-D, p’s win-rate decreases • Effect varies with standard deviation of prediction error • Paper presents evidence that standard deviation is large

22. Why We Disagree with P&K I • Priest & Klein understood that plaintiff trial win rates would vary with the legal standard unless prediction errors were very small (e.g. σ=0.1) • They estimated prediction errors from trial rates based on simulations • Lower prediction errors produce lower trial rates • Exact effect depends on (C-S)/J = (cost of trial – cost of settlement)/judgment • If (C-S)/J = 0.33, then 2% trial rate implies very small prediction errors (σ=0.1) • If (C-S)/J ≥ 0.66, then 2% trial rate implies prediction errors large enough to make plaintiff trial win rates vary significantly with legal standard

23. Why We Disagree with P&K II • Priest & Klein assumed (C-S)/J=0.33, because 33% is standard contingent fee percentage • That is wrong for two reasons • 1) (C-S)/J = (Cπ-S π)/J + (CΔ-SΔ)/J • So, at best, contingent fee measures (Cπ-S π)/J • (C-S)/J ≈ 2 (Cπ-S π)/J = 0.66 • 2) Under simple contingent fee, lawyer gets paid same percentage whether case settles or goes to trial • C/J = S/J which implies (C-S)/J = 0 • Can’t estimate (C-S)/J from contingent fee • RAND (1986) estimates (C-S)/J = 0.75

24. Extensions • Effect of different decisionmakers • Republican versus Democratic judges • Male versus female judges • 6 or 12 person jury • Whether factor affects trial outcome • Race or gender of plaintiff • In-state or out-of-state defendant • Law firm quality • Effect of change in composition of cases • Business cycle induces stronger or weaker plaintiffs to sue (Siegelman & Donohue 1995)

25. Caveats • Assumes that distribution of underlying behavior doesn’t change • Not usually true • Exceptions • Retroactive legal change • Uninformed defendants • Analysis of judicial biases or case factors, when cases randomly assigned • Advice to empiricists • Worry less about settlement selection • Worry more about changes in behavior • Distribution of disputes (litigated & settled) • Monotone likelihood ratio property for asymmetric information • Logconcave for Priest-Klein

26. Conclusions • Selection effects are real • But, under all standard settlement models, change in legal standard, under plausible assumptions, will lead to predictable changes in plaintiff trial win rate • Bebchuk screening model • Reinganum-Wilde signaling model • Priest-Klein divergent expectations model • Pro-plaintiff change in law will lead to increase in plaintiff trial win rate • So may be able to draw valid inferences from litigated cases • Measure legal change • Measure biases of decision makers • Identify factors affecting outcomes • Good news for empiricists