Relative performance of liability rules: experimental evidence

Abstract

We compare the performance of liability rules for managing environmental disasters when third parties are harmed and cannot always be compensated. A firm can invest in safety to reduce the likelihood of accidents. The firm’s investment is unobservable to authorities. The presence of externalities and asymmetric information call for public intervention in order to define rules aimed at increasing prevention. We determine the investments in safety under No Liability, Strict Liability, and Negligence rules, and compare these to the first best. Additionally, we investigate how the (dis)ability of the firm to fully cover potential damage affects the firm’s behavior. An experiment tests the theoretical predictions. In line with theory, Strict Liability and Negligence are equally effective; both perform better than No Liability; investment in safety is not sensitive to the ability of the firm to compensate potential victims. In contrast with theory, however, prevention rates absent liability are much higher and liability is much less effective.

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Notes

  1. 1.

    See Posner (1992) or Shavell (2004) for a textbook description of liability rules.

  2. 2.

    Under CERCLA, liability is strict and (at least presumptively), it is joint and several. “A potentially responsible party (PRP) cannot simply say that it was not negligent or that it was operating according to industry standards. If a PRP sent some amount of the hazardous waste found at the site, that party is liable” (http://www.epa.gov/compliance/cleanup/superfund/liability.html). Such liability is said to be strict because exercise of due care is not a defense. Although CERCLA does not explicitly provide for joint and several liability, Congress confirmed that when passing the Superfund Amendments and Reauthorization Act (SARA) amendments in 1986 that it was its intention. Accordingly, all the responsible parties at a cleanup site are said to be jointly and severally liable for the response costs at the site. “Any one potentially responsible party may be held liable for the entire cleanup of the site (when the harm caused by multiple parties cannot be separated).” In practical terms, if five out of twenty responsible parties are meaningfully solvent at the time that response costs are sought under Section 107 of CERCLA, these five may be liable for the entire cost of the cleanup (see Ashford and Caldart 2008, p. 761). CERCLA is a good illustration for our analysis, excluding the case of harm with multiple responsible parties where the contribution of each cannot be distinguished.

  3. 3.

    When oil is discharged from a vessel or facility into the navigable waters of the United States, adjacent shorelines, or the exclusive economic zone, the Oil Pollution Act makes each “responsible party” liable for “removal costs” and “damages.” The Oil Pollution Act explicitly adopts the standard of liability of section 311 of the Clean Water Act, knowing that courts have consistently construed section 311 to establish Strict Liability (see Murchison 2011).

  4. 4.

    Directive 2004/35/CE on environmental liability regarding the prevention and compensation of environmental damage, adopted by the European Parliament and Board of Ministers on April 21, 2004.

  5. 5.

    Other limits include the low probability of a suit, the difficulty of proving causality between the decisions of injurers and harm, the time required, scientific ignorance, and uncertainty about court judgments stemming from mistakes or judges’ subjectivity (Shavell 1984b). Furthermore, liability may change the contractual or market relationships in risky sectors, which may lead to under-investment (Hiriart and Martimort 2006b). On the other hand, liability is a very natural way to align private and public interests; there is, therefore, a strong tendency to introduce it as a part of traditional regulation all over the world.

  6. 6.

    Since we are talking about the firm and third parties, the reader may ask who the second party is: the second party is the public authority.

  7. 7.

    See Shavell (2004) for unilateral accidents in the Law and Economics literature.

  8. 8.

    Although grammatically incorrect, when talking about the firm we will use the pronouns “her” and “she” in order to be consistent with the literature.

  9. 9.

    See Pitchford (1995), Newman and Wright (1990), or Hiriart and Martimort (2006a), although all these papers study essentially extended liability.

  10. 10.

    This model is an adaptation of Shavell (1984a).

  11. 11.

    See Shavell (2004).

  12. 12.

    An injurer firm is held liable for losses if her level of care is less than a level called “due care” specified by the courts. See Posner (1992).

  13. 13.

    This means that the firm’s choice \(e=1\) will be induced by a Ne rule for a larger set of parameters, i.e., also for \(w_{t}\in \left[ \frac{c}{ p_{0}},\frac{c}{\Delta p}\right) \).

  14. 14.

    All data and instructions are available upon request.

    Table 1 Treatments
  15. 15.

    Phase 1 was independent from phase 2 in both the random draw of roles, and the random assignment to pairs.

  16. 16.

    To keep a neutral frame, we never used the terms “injurer” and “victim” in the instructions.

  17. 17.

    Instead of an “accident” we referred to an “event” in the instructions, to maintain the neutral frame.

  18. 18.

    Recall that until the end of the phase subjects did not know their role in the pair. Therefore, receiving information about an accident occurring to a subject potentially paired with oneself would unnaturally influence one’s decision path.

  19. 19.

    An accident introduces an asymmetry in the decision situation. Before the accident, A holds her endowment less the cost for investment in safety. After the accident, depending on the liability rule, A may not have any more resources to invest in safety, even if she wants to.

  20. 20.

    Since A was protected by limited liability, A was not asked to give to B more than what A owned.

  21. 21.

    The translation from German read: (1) How do you judge yourself: are you generally a risk loving person, or do you try to avoid risks? (2) Would you say that most of the time people try to help others or only follow their own interests? (3) Would you say that most of the time you try to help others or only follow your own interests? The answer to (1) was on a scale from 0 (very risk-averse) to 10 (very risk-loving). Answers to (2) and (3) were on a scale from 0 (help others) to 6 (follow own interests).

  22. 22.

    In reality information about major environmental disasters is usually provided in the form of statistics in the news and may lead to a change in the behavior of potential injurers.

  23. 23.

    The two phases were chosen to be not too long (only 5 periods), in order to avoid noise in the decisions caused by boredom or fatigue.

  24. 24.

    For example, two fallacies that may apply here are the gambler’s fallacy and the hot hand fallacy. Given a fair coin, after a sequence of heads, people suffering from the former would expect tails while people suffering from the latter would expect heads (see, e.g., Slovic 2000). For our experiment this would mean, respectively, that a person who was hit by an accident in phase 1 would not expect to be hit in phase 2, or would expect to be hit once again in phase 2.

  25. 25.

    These terms are borrowed from Cox et al. (2012).

  26. 26.

    See, e.g., Cox and Epstein (1989) and Cox and Grether (1996).

  27. 27.

    In an individual choice experiment with five lottery pairs, Cox et al. (2012) have compared the performance of several payment mechanisms, among those are POR, PAS, and a one-task (henceforth OT) design. They find that POR data are biased toward significantly more risk aversion compared to OT data, while PAS data show less risk aversion than OT data. This result seems to support the insensitivity to risk attitudes of our payment protocol, if we interpret it as a mixture of PAS and POR.

  28. 28.

    We acknowledge that the risk attitude of an individual cannot directly be translated to the risk attitude of a company. It is debatable whether firms are risk-averse, like individuals, or not. The attitude toward risk of companies is certainly related to their size and to their financial constraints. The framework of our experiment is by far too simple to take into account such parameters. The argument that firms are not necessarily risk-neutral and that, as a result, their decisions can look like the decisions of individuals, has been stressed by Leland and Pyle (1977). These authors show that the assumption of risk aversion has traction for small companies that suffer from restricted access to financial markets. However, in order to convince investors that their project is worthwhile, these risk-averse small firms accept to bear some risk and, finally, seem to behave like risk-neutral big companies.

  29. 29.

    To be precise, the only difference in predictions with respect to the CRRA case is that a risk-averse subject with a (constant absolute) degree of risk aversion \(r>9.65\) should not invest under SL. However, such extremely risk-averse subjects are quite rare in the real world (see, e.g., Binswanger 1980). For instance, such subjects would prefer a sure amount of 1 euro to a lottery giving them 1,000 euros with probability 0.99 and 0 euro otherwise.

  30. 30.

    Obviously, any expected utility maximizing subject should not invest under NoL, whatever her attitude toward risk.

  31. 31.

    For example, both Holt and Laury (2002) and Harrison et al. (2005) find that only 8 % of subjects in their pool of undergraduate students are risk-loving in the same “low real payoff” individual decision under risk. Both studies provide evidence that this percentage decreases as long as payoffs are scaled up. Also, notice that participants in our study are undergraduate students and that the expected payoff in our safety investment game is around three times as much as in Holt and Laury’s (2002) “low real payoff” task.

  32. 32.

    Our experimental design includes a question aimed at eliciting risk attitude (see footnote 21). However, this risk-elicitation instrument—based on a hypothetical question—is hardly adequate for our analysis. First of all, the measure that it provides is self reported. Moreover, it can hardly be incorporated into the CARA and CRRA analysis in Appendix.

  33. 33.

    In both treatments NoL-high and NoL-low, the subject pays 1 ECU if she invests in safety and nothing if she does not invest. The occurrence of an accident does not lead to any cost for this subject. Hence, the subject should not invest, regardless of her attitude toward risk.

  34. 34.

    In treatment SL-low, \(\min \{h,w_{t}\}=h=30\); \(c=1\) is smaller than \(0.04*30=1.2\). In treatment SL-high, \(\min \{h,w_{t}\}=w_{t}\); \( c=1\) is smaller than \((0.04*w_{t})\in [1.4;1.6]\). Condition (2) is thus satisfied in all SL treatments, meaning that a risk-neutral subject should invest in safety in each period. From the Appendix, it is easy to see that the same result holds for CRRA subjects, and for CARA subjects when their degree of risk aversion is not extreme.

  35. 35.

    In treatment Ne-low, \(\min \{h,w_{t}\}=h=30\); \(c=1\) is smaller than \(p_{0}*30=1.5\). In treatment Ne-high, \(\min \{h,w_{t}\}=w_{t}\); \(c=1\) is smaller than \((p_{0}*w_{t})\in [1.75;2]\). Condition (3) is thus satisfied in all Ne treatments, meaning that a risk-neutral subject should invest in safety in each period. From the Appendix, it is easy to see that the same result holds for both CARA and CRRA subjects, for any positive degree of risk aversion.

  36. 36.

    Recall that the number of times a subject had to decide whether or not to invest in safety is lower than ten when a subject was hit by an accident.

  37. 37.

    We estimate similar treatment effects if we allow the error rate \( \varepsilon \) to differ across treatments.

  38. 38.

    The standard of due care is also set at its optimal level \(e=1\) in our experiment, so the difference in results cannot come from this specification.

  39. 39.

    The distribution of investment ratios under NoL-low is significantly below the distribution of investment ratios under both SL-low (Mann–Whitney test \(p=0.028\)) and Ne-low (Mann–Whitney test \(p=0.021\)). The same is true when comparing NoL-high to SL-high, and NoL-high to Ne-high, with \(p=0.081\) and \(p=0.048\), respectively, from a Mann–Whitney test.

  40. 40.

    E.g., Phase 1 dummy * period takes the value of one if we are in phase 1, period 1. The same variable takes the value of two if we are in phase 1, period 2, and so on until phase 1, period 5. Phase 1 dummy * period takes the value zero if we are in phase 2.

  41. 41.

    See Segerson (2002) for informal arguments and Shavell (1980) for formal ones.

  42. 42.

    See Pitchford (1995) or Hiriart and Martimort (2006a) and the references therein.

  43. 43.

    See Shavell (1984a), Kolstad et al. (1990), or Hiriart et al. (2008); Hiriart et al. (2010).

  44. 44.

    In the case where \(\gamma =1\), \(u(x)=\ln x\).

  45. 45.

    Hence, \(u(w_{t}-h-c)\simeq u(w_{t}-h)-cu^{\prime }(w_{t}-h)\) and \( u(w_{t}-h)\simeq u(w_{t})-cu^{\prime }(w_{t})\) for \(c\) small enough.

  46. 46.

    This is because \(u^{\prime }(w_{t})<p_{1}u^{\prime }(w_{t}-\min \{h,w_{t}\})+(1-p_{1})u^{\prime }(w_{t})\) and \(p_{0}\ge p_{0}-p_{1}\).

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Acknowledgments

We thank David Alary; Marie Obidzinski; participants at the 15th Conference on the Foundations and Applications of Utility, Risk and Decision Theory (FUR) in Atlanta, the 10th Annual Conference of the German Law and Economics Association in Magdeburg, 19th Annual Conference of the European Association of Environmental and Resource Economists (EAERE) in Prague, the French Experimental Economics Association Annual Meeting (ASFEE) in Montpellier, the LAMETA Seminar (University of Montpellier), the CREM Seminar (University of Rennes), the CES-ifo Conference on Law and Economics in Munich, the ESREL Annual Conference in Troyes, the 20th SRA-Europe Meeting in Stuttgart, and the International Workshop on Economic and Financial Risks in Niort; as well as two anonymous referees for their useful comments and suggestions. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) Grant Agreement No. 230589. Financial support from the Foundation for an Industrial Safety Culture (FONCSI) and from the French Agence Nationale pour la Recherche (ANR) for the project Environmental Regulation and Market Imperfections is also acknowledged, together with CESifo sponsorship.

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Correspondence to Vera Angelova.

Appendix

Appendix

  • Risk aversion with a CARA utility function. Assume that the firm is risk-averse and her preferences are captured by a CARA utility function: \(u(x)=\frac{1-e^{-rx}}{r}\), where the parameter \(r>0\) measures the absolute risk aversion and \(x\) is a monetary payoff. Social optimum Prevention is socially optimal as long as:

    $$\begin{aligned} p_{1}u(w_{t}-h-c)+(1-p_{1})u(w_{t}-c)\ge p_{0}u(w_{t}-h)+(1-p_{0})u(w_{t}),\quad \end{aligned}$$
    (4)

    which can be rewritten:

    $$\begin{aligned} c\le \frac{1}{r}*\ln \left( \frac{1-p_{0}+p_{0}e^{rh}}{ 1-p_{1}+p_{1}e^{rh}}\right) . \end{aligned}$$
    (5)

    No liability The firm chooses to invest in prevention as long as:

    $$\begin{aligned} p_{1}u(w_{t}-c)+(1-p_{1})u(w_{t}-c)\ge p_{0}u(w_{t})+(1-p_{0})u(w_{t}), \end{aligned}$$
    (6)

    a condition that reduces to \(u(w_{t}-c)\ge u(w_{t})\) and that, obviously, never holds. Hence, the firm never invests in safety in the absence of liability. Strict liability The firm chooses to invest in prevention as long as:

    $$\begin{aligned}&p_{1}u(w_{t}-\min \{h,w_{t}\}-c)+(1-p_{1})u(w_{t}-c)\nonumber \\&\quad \ge p_{0}u(w_{t}-\min \{h,w_{t}\})+(1-p_{0})u(w_{t}), \end{aligned}$$
    (7)

    which can be rewritten:

    $$\begin{aligned} c\le \frac{1}{r}*\ln \left( \frac{1-p_{0}+p_{0}e^{r\min \{h,w_{t}\}}}{ 1-p_{1}+p_{1}e^{r\min \{h,w_{t}\}}}\right) . \end{aligned}$$
    (8)

    Comparing (5) and (8), it is straightforward to see that the firm will make the socially optimal decision if she is wealthy enough, i.e., if her wealth \(w_{t}\) is sufficient to cover harm \(h\). Negligence The firm chooses to invest in prevention as long as:

    $$\begin{aligned} p_{1}u(w_{t}-c)+(1-p_{1})u(w_{t}-c)\ge p_{0}u(w_{t}-\min \{h,w_{t}\})+(1-p_{0})u(w_{t}),\nonumber \\ \end{aligned}$$
    (9)

    a condition that can be rewritten:

    $$\begin{aligned} c\le \frac{1}{r}*\ln \left( 1-p_{0}+p_{0}e^{r\min \{h,w_{t}\}}\right) . \end{aligned}$$
    (10)

    Comparing (8) and (10), we can easily show that the former is more demanding than the latter: the firm is induced to exercise care for a larger set of parameters when submitted to Negligence rather than Strict Liability. The qualitative theoretical results obtained with a risk-neutral firm, therefore, do not change when moving to a CARA case. In particular, for the set of parameters \((c,w_{t},h,p_{0},p_{1})\) that characterize our experimental setting, a risk-averse firm should behave as a risk-neutral one both under No Liability and under Negligence: for every \(r>0\), she should not invest in safety in the former regime and invest in the latter. Under Strict Liability, a risk-averse firm should invest in safety for each \(r\in \{0,9.65\}\), i.e., so long as she is not extremely risk-averse.

  • Risk aversion with a CRRA utility function. Assume that the firm is risk-averse and her preferences are captured by a CRRA utility function: \(u(x)=\frac{x^{1-\gamma }}{1-\gamma }\), where the parameter \(\gamma >0\) (\(\gamma \ne 1\)) measures the relative risk aversion and \(x\) is a monetary payoff.Footnote 44 Social optimum Prevention is socially optimal when condition (4) is satisfied. Using the fact that \( f(x+y)=f(x)+yf^{\prime }(x)\) when \(y\) is small,Footnote 45 this condition can be rewritten as:

    $$\begin{aligned} c\le \frac{\Delta p\left[ u(w_{t})-u(w_{t}-h)\right] }{p_{1}u^{\prime }(w_{t}-h)+(1-p_{1})u^{\prime }(w_{t})}. \end{aligned}$$
    (11)

    No liability The firm chooses to invest in prevention when condition (6) is satisfied, a condition that, again, reduces to \(u(w_{t}-c)\ge u(w_{t})\), which never holds. Hence, the firm never invests in safety in the absence of liability. Strict liability The firm chooses to invest in prevention when condition (7) is satisfied. This condition can be rewritten as:

    $$\begin{aligned} c\le \frac{\Delta p\left[ u(w_{t})-u(w_{t}-\min \{h,w_{t}\})\right] }{ p_{1}u^{\prime }(w_{t}-\min \{h,w_{t}\})+(1-p_{1})u^{\prime }(w_{t})}. \end{aligned}$$
    (12)

    Hence, (12) coincides with (11) when the firm is wealthy enough, i.e., she takes the socially optimal decision if her wealth \(w_{t}\) is sufficient to cover harm \(h\). Negligence The firm chooses to invest in prevention when (9) is satisfied. This condition can be rewritten as:

    $$\begin{aligned} c\le \frac{p_{0}\left[ u(w_{t})-u(w_{t}-\min \{h,w_{t}\})\right] }{ u^{\prime }(w_{t})}. \end{aligned}$$
    (13)

    Comparing (13) and (12), we see that the former is less demanding than the latter:Footnote 46 regardless her wealth, the firm is induced to exercise care for a larger set of parameters when submitted to Negligence rather than Strict Liability. Using the same arguments, in the case where \(\min \{h,w_{t}\}=h\), we also see that (13) is less demanding than (11). The set of parameters for which wealthy firms with CRRA preferences invest in prevention is larger under Negligence than at the social optimum. For the values of parameters \((c,w_{t},h,p_{0},p_{1})\) adopted in our experiment, a firm presenting CRRA preferences should behave as a risk-neutral one under any liability regime and for any positive degree of relative risk aversion \(\gamma \): she should not invest in safety under No Liability and invest under Strict Liability and Negligence. Indeed, the term on the right-hand side in (12) is equal to 1.206 when \(w_{t}=40\) and \(\gamma =0.01\), and strictly increases with a lower wealth level \(w_{t}\) or a higher degree of relative risk aversion. Since \(c=1\), condition (12) is satisfied for all possible values taken by the parameters in our experiment: the subjects should always invest under Strict Liability. The same happens under Negligence since the lowest value obtained on the right-hand side of (13) is also 1.206.

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Angelova, V., Armantier, O., Attanasi, G. et al. Relative performance of liability rules: experimental evidence. Theory Decis 77, 531–556 (2014). https://doi.org/10.1007/s11238-013-9405-0

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Keywords

  • Risk regulation
  • Liability rules
  • Incentives
  • Insolvency
  • Experiment

JEL Classification

  • D82
  • K13
  • K32
  • Q58