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1. ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

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Page 1 of 36

ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

ARTICLE: The Incentive Effects of No-Fault Automobile Insurance *

October, 2001

Reporter 44 J. Law & Econ. 427 *

Length: 17781 words

Author: J. David Cummins, University of Pennsylvania, Richard D. Phillips, Georgia State University and Mary A. Weiss, Temple University

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ABSTRACT

This paper presents a theoretical and empirical analysis of the effects of no-fault automobile insurance on fatal accident rates. As a mechanism for compensating the victims of automobile accidents, no-fault insurance has several important advantages over the tort system. However, by restricting access to tort, no-fault may weaken incentives for careful driving and lead to higher accident rates. We conduct an empirical analysis of automobile accident fatality rates in all U.S. states over the period 1968-94, controlling for the potential endogeneity of no-fault laws. The results support the hypothesis that no-fault is significantly associated with higher fatal accident rates than tort.

Text

[*427] I. INTRODUCTION

No-fault automobile insurance has been adopted by several jurisdictions in the United States, Canada, Australia, and New Zealand as a mechanism for controlling automobile insurance costs and improving the efficiency and timeliness of accident compensation. 1 No-fault has two primary characteristics--compulsory first-party insurance for personal injuries and restrictions on the right to sue for automobile accidents. As a compensation system, no- fault [*428] has a number of advantages over tort. 2 However, by restricting the right to sue, no-fault may weaken

* The authors thank Richard A. Derrig, Francis X. Diebold, Alan O. Sykes, and two anonymous referees for comments on earlier drafts of this paper. Financial support from the Wharton Financial Institutions Center (Cummins) and the Research Program Council at Georgia State University (Phillips) is gratefully acknowledged.

1 No-fault has been proposed frequently as a measure for reforming the tort liability system both for automobile and medical malpractice claims. See, for example, Frank A. Sloan et al., The Road from Medical Injury to Claims Resolution: How No-Fault and Tort Differ, 60 Law & Contemp. Probs. 35 (1997). In addition, a national no-fault automobile insurance program has recently been considered by Congress (Steven Brostoff, Rep Armey Reintroduces "Auto Choice" Bill, at 5, 6 (Nat'l Underwriter/Prop. & Casualty/Risk & Benefits ed., May 3, 1999)).

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

the deterrent effect of tort law and therefore lead to an increase in automobile accidents. The purpose of the present paper is to provide a theoretical and empirical analysis of the incentive effects of no-fault by analyzing the relationship between no-fault and fatal accident rates. Our database consists of all U.S. states over the period 1968-94. 3

Researchers who have analyzed the pure no-fault systems adopted in Canada, Australia, and New Zealand, namely, R. Ian McEwin and Rose Anne Devlin, have found a positive association with automobile accident fatality rates. 4 However, whereas pure no-fault systems substantially eliminate tort liability for automobile accidents, the partial no-fault laws adopted in the United States retain the right to sue for death and serious injuries and thus are likely to have a weaker effect on deterrence. The prior empirical evidence on the relationship between no-fault and fatalities in the United States has been mixed. Elizabeth Landes found a positive relationship between no-fault and fatal accident rates in the United States, but other U.S. researchers, Paul Kochanowski and Madelyn Young, and Paul Zador and Adrian Lund, have not confirmed this relationship. 5 A possible explanation for the mixed U.S. [*429] results is that prior researchers have not controlled for the potential endogeneity of no-fault, an issue addressed in this paper.

The present paper provides new empirical evidence on the relationship between no-fault and fatalities in the United States to help resolve the conflicting findings in the prior literature. 6 We innovate by using estimation

2 In comparison with tort, a higher proportion of premiums under no-fault represents loss payments as opposed to legal and administrative expenses. See Henry Grabowski, W. Kip Viscusi, & William Evans, Price and Availability Tradeoffs of Automobile Insurance Regulation, 56 J. Risk & Ins. 275 (1989); and Stephen J. Carroll, No-Fault Approaches to Compensating People Injured in Automobile Accidents (1991). No-fault is also superior to tort in promptness of claims payment (Rand Corporation, Automobile Accident Compensation (1985)) and can reduce insurance fraud by removing relatively small bodily injury liability claims from the tort system; Herbert I. Weisberg & Richard A. Derrig, Fraud and Automobile Insurance: A Report on Bodily Injury Liability Claims in Massachusetts, 9 J. Ins. Reg. 497 (1991). Finally, no-fault reduces the proportion of claimants who receive compensation in excess of their economic losses and increases the proportion of claimants who are fully compensated for their economic losses. Carroll, supra.

3 Thirteen U.S. states now have some form of no-fault law. No-fault states are defined as those that require motorists to purchase first-party medical expense coverage and place some restrictions on lawsuits. See Insurance Information Institute, Insurance Facts: 1999 (1999). Twelve additional jurisdictions have enacted so-called add-on laws, which provide first-party medical expense coverage but place no restrictions on tort.

4 Pure no-fault has been adopted in the Canadian province of Quebec, in Australia's Northern Territory, and in New Zealand. More details on the Australasian and Canadian laws are provided in R. Ian McEwin, No-Fault and Road Accidents: Some Australasian Evidence, 9 Int'l Econ. Rev. 13 (1989); Rose Anne Devlin, Some Welfare Implications of No-Fault Automobile Insurance, 10 Int'l Econ. Rev. 193 (1990); and Rose Anne Devlin, Liability versus No-Fault Automobile Insurance Regimes: An Analysis of the Experience in Quebec, in Contributions to Insurance Economics 499 (Georges Dionne ed. 1992).

5 Elizabeth M. Landes, Insurance Liability, and Accidents: A Theoretical and Empirical Investigation of the Effect of No-Fault Accidents, 25 J. Law & Econ. 49 (1982); Paul S. Kochanowski & Madelyn V. Young, Deterrent Aspects of No-Fault Automobile Insurance: Some Empirical Findings, 52 J. Risk & Ins. 269 (1985); Paul Zador & Adrian Lund, Reanalyses of the Effects of No- Fault Auto Insurance on Fatal Crashes, 53 J. Risk & Ins. 226 (1986).

6 We focus on fatality rates rather than injury rates for two reasons: (1) Focusing on fatalities facilitates comparison of our results with the prior literature, which also emphasizes fatality rates. (2) Reported injury rates are affected by fraud and moral hazard, making it difficult to isolate the effects of no-fault on driving behavior as opposed to claiming behavior in an accident injury rate analysis. Drivers have a stronger incentive to report accidents in tort states than in no-fault states because they are eligible to sue for pain-and-suffering awards, even for relatively minor injuries. The availability of potential pain-and-suffering awards leads some drivers to file claims for difficult-to-verify injuries such as whiplash and other types of strains and sprains even though the injury may not exist or may be less severe than claimed (see, for example, Weisberg & Derrig, supra note 2). No-fault reduces this moral hazard effect by eliminating pain-and-suffering awards for relatively small accidents. Thus, any positive effect of no- fault on injury accident rates is likely to be offset by claims reporting moral hazard. Evidence of significant moral hazard in auto insurance claiming is provided in J. David Cummins & Sharon Tennyson, Controlling Automobile Insurance Costs, 6 J. Econ. Persp. 95 (1992); J. David Cummins & Sharon Tennyson, Moral Hazard in Insurance Claiming: Evidence from Automobile Insurance, 12 J. Risk & Uncertainty 29 (1996); Weisberg & Derrig, supra note 2; Richard A. Derrig, Herbert I. Weisberg, & Xiu

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

methodologies that take into account the possibility that the type of automobile compensation regime (tort versus no-fault) that exists in a state may be endogenous; that is, the compensation regimes adopted by the states may be systematically related to accident rates or other state characteristics. Two techniques are used to correct for this potential endogeneity--instrumental variables and inverse Mill's ratios. Our analysis also includes a more complete set of explanatory variables than has been used in prior U.S. studies. Finally, in addition to using the conventional approach of measuring the presence of no-fault with a dummy variable, we also utilize estimates of the proportion of automobile bodily injury claims ineligible for tort because of no-fault thresholds to control for differences in threshold stringency across states.

The remainder of the paper is organized as follows: Section II provides a theoretical investigation of the effects of no-fault on care incentives. The theory yields a number of useful implications about the incentive effects of compensation systems. Section III describes our database, specifies the variables used in our analysis, and discusses the estimation methodology. The results of the analysis are presented in Section IV, and Section V concludes the paper.

[*430] II. NO-FAULT AND OPTIMAL CARE LEVELS: A THEORETICAL ANALYSIS

In this section, we model the effects of tort restrictions on accident rates. Prior researchers typically have argued that no-fault weakens incentives, which leads to lower care levels and higher accident rates. Our model extends prior work on no-fault insurance by providing a more precise discussion of the effects of care levels on accident rates and negligence probabilities, analyzing the effects of expense loadings, and focusing attention on experience rating as an incentive device.

A. The Model

We model the negligence rule by introducing a parameter [delta], where 0 </= [delta] </= 1. When [delta] = 0, no liability rule is in effect. This configuration can be considered "pure no-fault." Choosing [delta] = 1 indicates the presence of a negligence rule ("full tort"). When 0 < [delta] < 1, accident victims can bring suit for some but not all accident losses. These systems are called "partial no-fault" or "limited tort." Thus, [delta] can be thought of as the probability that a given claim will qualify for tort, that is, the probability of satisfying the tort threshold. The negligence rule under full or limited tort is assumed to apply only to general damages; economic losses are assumed to be covered by first-party insurance. 7

Accidents are assumed to be bilateral; that is, they involve two drivers, both of whom are assumed to sustain injuries. The accident losses of each driver consist of economic losses, for example, medical bills and lost earnings, in amount l, and general damages (pain and suffering losses) in amount g. Both l and g are assumed to be nonstochastic. The accident probability [lambda] is assumed to be a function of the care expenditures of both drivers; that is, [lambda] = [lambda] (x, y), where x and y denote the care expenditures of drivers 1 and 2, respectively. Each driver is assumed to take the other driver's decisions as given when choosing his or her own care level, so [lambda] (x, y) is written as [lambda] (x) or, more simply, as [lambda]. We assume that [See formula in printed version] and [See formula in printed version].

To model the effects of care expenditures on negligence, we introduce the probability functions p[i](x, y), i = 1, 2, where p[1] is the probability that driver 1 is found to be negligent and driver 2 is found not to be negligent, while p[2] is the probability that driver 1 is not negligent and driver 2 is negligent. If driver 1 is negligent but driver 2 is not, then

Chen, Behavioral Factors and Lotteries under No-Fault with a Monetary Threshold: A Study of Massachusetts Automobile Claims, 61 J. Risk & Ins. 245 (1994); and Insurance Research Council, Auto Injuries: Claiming Behavior and Its Impact on Insurance Cost (1994). Herbert I. Weisberg & Richard A. Derrig, Massachusetts Automobile Bodily Injury Tort Reform, 10 J. Ins. Reg. 384 (1992), shows that a change in the Massachusetts no-fault threshold in 1988 led to dramatic changes in claims reporting. Landes, supra note 5, also reports that injury accident rates are sensitive to differences across states and over time in insurance requirements.

7 The theoretical predictions are similar if the analysis is conducted under the assumption that the victim does not have first- party insurance for economic losses but can sue to recover economic losses.

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

driver 1 pays driver 2's general damages, while the reverse is true if driver 2 is negligent and driver 1 is not. If neither or both are negligent, each driver bears his or her own [*431] general damages. 8 Thus, p[1] + p[2] </= 1. Again focusing on the decision making of driver 1, it is assumed that [See formulas in printed version], and [See formula in printed version].

Modeling negligence assignment as a probabilistic process implies that there is no threshold level of care beyond which a driver cannot be found negligent. For example, the legal system and/or drivers can make mistakes. Drivers who choose relatively high care levels (x) can still commit negligent acts or be erroneously judged negligent by the legal system. Thus, taking care does not reduce the negligence probability to zero.

To focus on the effects of the negligence rule on care incentives, we assume that the decision about the level of first-party insurance coverage has already been made; that is, l is not a decision variable. 9 We also assume that drivers have liability insurance to cover their potential liability to other drivers resulting from an accident. First-party general damage insurance (that is, insurance where the driver's own insurer pays his or her general damages) is assumed not to be available. Thus, drivers who cannot establish the negligence of the other driver bear their general damage losses directly. The insurance premium for driver 1 is [pi] = (1 + e) [lambda] (l + [delta] gp[1]), where l represents economic losses, g represents general damages, and e represents insurer expenses as a proportion of expected losses. Thus, the premium equals expected losses, [lambda] (l + [delta] gp[1]), times a proportional expense charge. The first component of expected loss ([lambda] l) represents the driver's own expected economic losses, while the second component ([lambda] [delta] gp[1]) equals the driver's expected liability losses, where [lambda] (x) has been written as [lambda] to simplify the notation. 10

B. No-Fault and Incentives

Drivers are assumed to be identical risk-averse expected utility maximizers with nonstochastic initial wealth W and utility function U(W), where U' > 0 and U" < 0. All drivers are assumed to purchase both first-party coverage in amount l and general damage coverage in amount g. Thus, the sole decision variable is the level of care, x.

[*432] There are two states of the world--the loss state, where wealth is reduced by the amount of general damages and the insurance premium, so wealth equals W - g - [pi]; and the no-loss state, where wealth is W - [pi], either because no accident occurs or because an accident occurs for which the driver is fully compensated. The wealth in the loss and no-loss states reflects the assumption that drivers are compensated by their own insurers for economic losses. The probability of the loss state is [lambda][L] = [lambda] (1 - [delta] p[2]) (that is, the probability that an accident occurs times the probability of not collecting from the other driver), and the probability of the no- loss state is 1 - [lambda][L] = [1 - [lambda] (1 - [delta] p[2])]. Thus, as the probability that the claim qualifies for tort ([delta]) increases, the probability of being in the loss state declines because of the higher probability of collecting general damages from the other driver. The parameter [delta] is the primary policy instrument used to define the compensation regime, with pure no-fault ([delta] = 0) and pure tort ([delta] = 1) as limiting cases.

The utility function is initially assumed to be separable in premiums and care expenditures, so the driver's expected utility is

8 Conducting the analysis under the assumption that drivers can obtain partial payment if both are negligent (comparative negligence) yields similar predictions.

9 This could represent a situation where first-party coverage is mandated by law, as in no-fault and some add-on jurisdictions or a situation where the coverage decision is made prior to the care decision. Endogenizing the coverage decision would not change the predictions of the model with respect to the effects of no-fault on care levels. The theoretical predictions also are unchanged if injured parties can sue to recover both economic losses and general damages.

10 That is, the expected liability losses equal the probability that driver 1 is required to pay driver 2's general damages times the amount of the general damages (g). The probability that driver 1 is required to pay ([lambda] [delta] p[1]) equals the probability of an accident ([lambda]) times the probability that the loss exceeds the threshold ([delta]) times the probability that driver 1 is found to be negligent (p[1]).

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

EU = [1 - [lambda] (1 - [delta] p[2])]U(W) + [lambda] (1 - [delta] p[2])U(W - g) - [pi] (x) - x, (1)

where [pi] (x) is the insurance premium, which equals (1 + e) [lambda] (l + p[1] [delta] g). The driver chooses x, the level of care expenditures, to maximize expected utility. The first-order condition for optimization with respect to x is

EU[x] = -[[lambda][x] (1 - [delta] p[2]) - [lambda] [delta] p[2x]] x [U(W) - U(W - g)] - [pi][x] - 1 = 0, (2)

where

U(W) = utility in the no-loss state,

U(W - g) = utility in the loss state, and

[pi][x] = the derivative of the premium with respect to care expenditures, equal to (1 + e)[[lambda][x] l + [delta] g(p[1] [lambda][x] + [lambda] p[1x])].

We also define the following symbols that are used to facilitate the discussion:

[lambda][L] = the probability of the loss state, equal to [lambda] (1 - [delta] p[2]); and

[lambda][Lx] = [lambda][Lx] = [lambda][x](1 - [delta] p[2] - [lambda] [delta] p[2x] = the derivative with respect to x of the probability of being in the loss state.

Notice that [pi][x] < 0 and [lambda][Lx] < 0, so increased care reduces both the premium and the probability of being in the loss state.

The first two terms in (2) are the marginal benefits of additional care expenditures. The first is equal to (-1 times) the derivative of the probability of being in the loss state [[lambda][x](1 - [delta] p[2]) - [lambda] [delta] p[2x]] times the difference in utility between the no-loss and loss states [U(W) - U(W - g)], and the second is [*433] (-1 times) the derivative of premiums with respect to x. The third term (-1) represents the marginal cost of additional care expenditures, that is, the cost of an additional unit of care. 11

The derivative of x with respect to an arbitrary parameter k is

dx/dk = -EU[xk]/EU[xx], (3)

where [See formula in printed version]. Because [See formula in printed version] (the second-order sufficient condition) is less than 0, the sign of dx/dk is the same as the sign of EU[xk].

It is easily shown that dx/de > 0 (see Appendix A). Thus, the reduction in administrative expenses under no-fault exacerbates any incentive problems caused by weaker negligence rules.

The marginal effect of changes in the negligence rule on care expenditures, dx/d [delta], is ambiguous. To see why, consider [See formula in printed version]:

EU[x [delta]] = ([lambda][x] p[2] + p[2x] [lambda])[U(W) - U(W - g)] - (1 + e)g([lambda][x] p[1] + [lambda] p[1x]). (4)

The second term in (4) is unambiguously positive, while the first depends on the sign of ([lambda][x] p[2] + p[2x] [lambda]), because [lambda][x] < 0 and p[2x] > 0. A nonnegative value for this factor provides a sufficient condition for dx/d [delta] > 0, that is, for no-fault to reduce care levels.

Intuitively, the ambiguity in dx/d [delta] can be easily explained in terms of the sufficient condition for dx/d [delta] > 0; that is, ([lambda][x] p[2] + p[2x] [lambda]) >/= 0. The sufficient condition is (-1 times) the derivative of [lambda][Lx] with respect to [delta]; that is, [See formula in printed version]. The ambiguity arises because stricter negligence

11 Notice that (1 + [pi][x]) must be greater than zero at the optimum in order to avoid corner solutions, because drivers would continue to increase care if the marginal premium reduction exceeded the cost of care.

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

rules have offsetting effects on incentives. A stricter rule (higher [delta]) increases the incentive to take more care in order to be successful in collecting from the other driver (the [lambda] p[2x] term in -[lambda][Lx [delta]]) but reduces incentives by lowering the probability of being in the loss state (the [lambda][x] p[2] term).

Additional insight can be gained by writing the sufficient condition as

p[2x]/p[2] >/= -[lambda][x]/[lambda]. (5)

Thus, no-fault unambiguously reduces care levels if the elasticity with respect to x of the probability of collecting from the other driver is larger than (-1 times) the elasticity of the accident rate with respect to x. If negligence assignment is not very responsive to care expenditures, for example, if the legal system makes significant errors in assigning fault, condition (5) is less likely to hold. The extreme case would be where p[2] is not a function of x, [*434] that is, where negligence assignment is random so that p[2x] = 0. In this case, the sufficient condition [lambda][x] p[2] + p[2x] [lambda] >/= 0 cannot hold. The first term in equation (4) then becomes unambiguously negative, and the sign of dx/d [delta] is determined by the relative magnitude of the unambiguously negative first term in (4) and the unambiguously positive second term. However, if negligence assignment is reasonably responsive to care expenditures, then the sufficient condition is more likely to be satisfied and no-fault is likely to lead to reductions in care levels. And, of course, even if the sufficient condition does not hold, no-fault will reduce care levels if the absolute value of the second term in (4) exceeds the absolute value of the first term.

Finally, we investigate the effects of experience rating on incentives by changing the premium formula to [See formula in printed version], where [pi]<z> is the experience-rated premium and Z is the credibility factor, where 0 </= Z </= 1. The experience-rated premium is a weighted average of the driver's premium, [pi], and the average premium for all drivers in the market, [SEE ILLUSTRATION IN ORIGINAL]. The degree of experience rating is captured by the credibility factor Z. Experience rating is almost always less than complete (that is, Z < 1) because of sampling error (an individual's driving record reveals some but not all information about his or her accident and negligence probabilities), imperfections in reporting systems, and so on. In Appendix A, we show that dx/dZ is unambiguously greater than zero; that is, more responsive experience rating increases care levels. Thus, policy makers concerned about the potential adverse effects of no-fault on accident rates could compensate for a weaker tort deterrent by more accurate or more stringent experience-rating plans.

Removing the assumption that the driver's decision problem is separable in premiums and care expenditures introduces another source of ambiguity in dx/d [delta]--an income effect arising from the impact of higher care expenditures on the second derivative of the utility function (see Appendix A). The presence of this term requires adding another condition in order for dx/d [delta] to be unambiguously greater than zero. Intuitively, the second condition requires that risk aversion be below a specified level. This leads to the intuitively reasonable conclusion that no-fault does not necessarily reduce care levels if drivers are highly risk averse. However, as risk aversion declines, a level of risk aversion is reached below which only condition (5) is required for dx/d [delta] > 0. The limiting case is risk neutrality, where neither condition is required (although p[1x] must be less than zero). With identical drivers, dx/dZ remains unambiguously greater than zero in the nonseparability case. 12

[*435] C. Summary: Theoretical Results

The principal difference between no-fault and tort in our model is that no-fault restricts the ability of motorists to sue. The effect of these tort restrictions on incentives is ambiguous. However, if negligence assignment and premium rates are relatively responsive to care levels, then no-fault is likely to lead to an increase in accidents. Such a result could be mitigated by improvements in experience-rating plans.

12 Drivers are assumed to make care decisions as if their decisions have no effect on [SEE ILLUSTRATION IN ORIGINAL]. Thus, increasing the experience-rating parameter Z leads to a one-time reduction in accident rates, with the new average applying to all drivers (in the identical-drivers case). With two classes of drivers, good drivers ([See formula in printed version]) and bad drivers ([See formula in printed version]), dx/dZ is unambiguous for either good drivers or bad drivers but ambiguous for the other group (see Appendix A).

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

III. DATA, METHODOLOGY, AND HYPOTHESES

We now turn to an empirical examination of the effects of no-fault on fatal accident rates. In addition to the standard approach of using dummy variables to represent the presence of no-fault in a state, we are able to obtain an estimate of the proportion of automobile bodily injury claims that are eligible for tort in no-fault states, that is, an estimate of [delta], and then test the hypothesis that the fatal accident rate is inversely related to [delta].

A. Data and Hypotheses

The sample for our study consists of pooled cross-section, time-series data on all 50 states over the period 1968- 94. Our sample period includes the year of adoption and at least 3 preceding years for each no-fault state (see Appendix B). 13 The sample includes 312 no-fault state observations and 1,038 tort state observations.

The dependent variable in our analysis is the fatal accident rate by state and year, defined as fatal accidents per 10 million vehicle miles. 14 The first part of our analysis uses dummy variables to represent the presence in a state of a no-fault law, consistent with the prior literature on automobile insurance. 15 We then turn to an examination of the relationship between fatality rates and the stringency of no-fault thresholds.

No-Fault Variables. The first no-fault variable tested in the study is an indicator variable set equal to 1 if a state has a no-fault law and to 0 otherwise. We next consider indicator variables representing the type of tort threshold present in the no-fault states. There are two types of thresholds--"monetary thresholds," where a claim qualifies for tort if the medical expenses resulting from the accident exceed a specified dollar amount, and "verbal thresholds," where claims qualify for tort if the injury satisfies a verbal definition of [*436] severity. 16 Because verbal no-fault thresholds are generally considered more restrictive or at least qualitatively different from monetary thresholds, we specify two indicator variables, the first equal to 1 if a state has a monetary threshold and equal to 0 otherwise, and the second equal to 1 if a state has a verbal threshold and equal to 0 otherwise. If no-fault significantly weakens incentives, these variables are expected to be positively related to fatal accident rates.

As a measure of [delta], the proportion of bodily injury claims eligible for tort, we obtained data from a series of studies conducted by the All-Industry Research Advisory Committee (AIRAC) and the Insurance Research Council (IRC) involving the analysis of thousands of automobile bodily injury claims. 17 The studies, based on claims settled in 1977, 1987, 1992, and 1997, provide estimates of the proportion of personal injury protection (PIP) claimants eligible to file a tort claim under the thresholds in effect in no-fault states, essentially a measure of [delta] from our theoretical model. 18 If tort provides an effective deterrent against hazardous driving, [delta] should be inversely related to fatal accident rates. To facilitate comparisons with the no-fault indicator variables, which would be positively related to fatalities if no-fault weakens incentives, our regression analysis uses the complement of the eligibility ratio (one minus the ratio) as a measure of the stringency of the threshold in a state, that is, the proportion

13 The first state to adopt no-fault was Massachusetts, in 1971, and the median year of adoption was 1974 (see Appendix B).

14 See U.S. Department of Transportation, Federal Highway Administration, Highway Statistics: 1994 (1994).

15 Grabowski, Viscusi, & Evans, supra note 2.

16 For example, Michigan's no-fault law specifies that general damages are recoverable only if the injury results in death, serious impairment of bodily function, or permanent serious disfigurement (American Insurance Association, 1999 Automobile Insurance Laws (1999)).

17 All-Industry Research Advisory Committee, Automobile Injuries and Their Compensation in the United States (1979); Insurance Research Council, Compensation for Automobile Injuries in the United States (1989); and Insurance Research Council, Injuries in Auto Accidents: An Analysis of Auto Insurance Claims (1999). The Insurance Research Council is the successor organization of the All-Industry Research Advisory Committee.

18 The first-party economic loss coverage provided under no-fault laws is known as personal injury protection.

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

of claims that are ineligible for tort because of the threshold. If no-fault significantly weakens incentives, the sign of this variable will be positive in our fatality rate regressions. 19 [*437]

TABLE 1

PERCENT OF PIP CLAIMS INELIGIBLE FOR TORT CLAIM UNDER

STATE NO-FAULT THRESHOLDS

1977 1987 1992 1997 Threshold a

State (%) (%) (%) (%) (]

Colorado 84 74 66 70 500

Connecticut 59 400

Florida 69 68 63 66 Verbal

Georgia 51 500

Hawaii 97 81 64 79 6,000

Kansas 87 71 83 78 2,000

Kentucky 90 75 67 58 1,000

Massachusetts 74 47 37 48 2,000

Michigan 94 88 81 85 Verbal

Minnesota 90 78 66 71 4,000

New Jersey 37 1,700 b

New York 73 71 69 78 Verbal

North Dakota 87 2,500

Utah 81 81 77 76 3,000

Average 84 69 67 71

NOTE.--PIP = personal injury protection (first-party economic loss

coverage).

SOURCES.--The estimates of claims ineligible for tort were derived from

All-Industry Research Advisory Council, Automobile Injuries and Their

Compensation in the United States (1979); Insurance Research Council,

Compensation for Automobile Injuries in the United States (1989); and

19 Landes, supra note 5, also used a threshold stringency variable based on the 1979 AIRAC study (All-Industry Research Advisory Committee, supra note 17). Whereas our variable is the percentage of PIP claimants judged ineligible for tort claims under a state's threshold, hers is an estimate of the proportion of tort claims eliminated by the threshold. The variables differ because some claims would not qualify for tort even in the absence of a no-fault law. The latter group includes claims such as those resulting from single-vehicle accidents and those barred from tort because of the negligence of the injured party. Landes's variable measures the stringency of thresholds after netting out claims that would be ineligible in the absence of no-fault, while our variable does not net out this group of claims. Although which of the two variables is more appropriate may be arguable, we were not able to use Landes's variable in most of our analysis in any event because the IRC does not provide all of the data needed to define her variable in its 1992 and 1997 study samples. However, for the 1977 and 1987 samples, the Landes variable and our variable are highly correlated (correlation > 90 percent). Moreover, sensitivity tests based on the 1987 IRC data show that the two variables produce similar results and lead to the same conclusions.

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

TABLE 1

PERCENT OF PIP CLAIMS INELIGIBLE FOR TORT CLAIM UNDER

STATE NO-FAULT THRESHOLDS

1977 1987 1992 1997 Threshold a

State (%) (%) (%) (%) (]

Insurance Research Council, Injuries in Auto Accidents: An Analysis of Auto

Insurance Claims (1999). The data for threshold were taken from American

Insurance Association, Summary of State Laws and Regulations Relating to

Automobile Insurance (various years).

a In 1989, approximately the midpoint of our sample period.

b Insured has a choice of a lower threshold ($ 200) for a higher premium.

Summary statistics on the proportion of claims ineligible for tort because of thresholds, that is, (1 - [delta]), are presented in Table 1. The results presented in Table 1 have the following important implications for our study: (1) A significant proportion of automobile bodily injury claims are ineligible for tort under the no-fault thresholds in effect in the United States, on the basis of the IRC estimates. The proportion of ineligible claims in 1987 (the year with the most complete data), for example, ranged from 88 percent under Michigan's verbal threshold to 37 percent under New Jersey's monetary threshold. The average proportion of ineligible claims in the 1987, 1992, and 1997 study years has remained consistent at about 70 percent. Thus, the ineligibility proportions are sufficiently high that no- fault could indeed have a significant effect on incentives for careful driving. (2) Contrary to the conventional wisdom, verbal thresholds are not necessarily more stringent than monetary thresholds. Although Michigan's verbal threshold is associated with the largest proportion of ineligible claims, several of the state monetary thresholds lead to a higher proportion of ineligible claims than the Florida and New York verbal thresholds. (3) Finally, the dollar value of monetary thresholds is imperfectly correlated with the proportion of ineligible claims. This reflects some differences in the types of expenses that can be used to [*438] satisfy thresholds as well as differences in the economic and social environments of the states. For example, in 1997, 78 percent of claims were ineligible because of the $ 2,000 threshold in Kansas, but only 48 percent were ineligible because of a $ 2,000 threshold in Massachusetts. We consider the IRC estimates to convey more information about stringency than the dollar value of monetary thresholds and accordingly rely on the IRC estimates in the empirical tests of threshold stringency presented below.

Other Explanatory Variables. In addition to no-fault, other differences among states are expected to affect accident rates. Driving under the influence of alcohol has been shown to be an important factor in many fatal accidents. 20 To test the hypothesis that alcohol is positively related to fatality rates, we use alcohol consumption in gallons per capita as an explanatory variable. Another driving behavior variable that we test is speed variance, defined as the difference between the 85th percentile of vehicle speeds in miles per hour in a state minus the average vehicle speed in the state. Speed variance has been shown to be an important determinant of accident rates. 21 The expected sign of this variable is positive. Average speed is also included and is expected to have a positive sign.

The driving environment is proxied by two variables--annual snowfall in inches and rural interstate miles driven as a proportion of total vehicle miles driven. Snowfall is expected to be inversely related to fatal accident rates because adverse weather conditions tend to reduce driving speeds and the number of miles driven. Rural interstate miles driven is used to measure rural driving intensity. Rural mileage is important because fatality rates are higher on

20 Christopher J. Bruce, The Deterrent Effects of Automobile Insurance and Tort Law, 6 Law & Pol'y 67 (1984). 21 Charles A. Lave, Speeding, Coordination, and the 55 MPH Limit, 75 Am. Econ. Rev. 1159 (1985).

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rural highways. 22 The availability of emergency medical care services also is likely to have an impact on the proportion of injury accidents that result in fatalities. To proxy for emergency medical services, we use the ratio of the number of hospitals in a state to the number of square miles of land area. A higher value of this variable should be associated with lower fatality rates.

The stringency of experience rating is expected to be inversely related to fatality rates. Experience rating is measured by a dummy variable equal to 1 for states that assess driver's license points for accidents in which the driver is less than 50 percent negligent and equal to 0 otherwise. This is an appropriate experience-rating variable because insurers use state motor vehicle [*439] records to verify self-reported accident and conviction histories of policy-holders. Accident histories are less complete in states that are less rigorous in assigning driver's license points, thus increasing information asymmetries between insurers and drivers and weakening experience rating. Less stringency in assigning points also implies lower incentives for careful driving arising out of the potential loss of one's driver's license. The expected sign of this variable is negative.

Three variables are used as controls for the characteristics of the driving population. The percentage of the population aged 18-24 is included to control for the tendency of young, relatively inexperienced drivers to have higher accident rates. This variable is expected to be positively related to fatalities. Theoretical and empirical research has shown that education tends to be related to behavior with a positive effect on health and safety. 23 To proxy for the potential effects of education on driving safety, we include the proportion of the population with a bachelor's degree. This variable is predicted to be inversely related to fatalities. Various hypotheses have been proposed regarding the relationship between income and driving behavior. On the one hand, income tends to be positively correlated with education, which implies an inverse relationship between this variable and the fatality rate. However, higher income also implies higher costs of time, possibly leading to more risk taking by relatively affluent drivers. 24 The latter reasoning implies a positive relationship between income and fatalities. 25

Year dummy variables are included in the regressions to capture differences in accident rates across years. Among other effects, the year dummies capture the downward secular trend in fatality rates resulting from safer automobiles, better roadway design, and the aging of the driver population. 26 In most of the regressions, we also include state dummy variables to account for unmeasured differences among states not captured by the explanatory variables. 27 Thus, our most fully specified models are full fixed-effects panel data regressions. Definitions and sources of variables are provided in Appendix C.

Summary statistics on the explanatory variables for no-fault and tort states [*440]

TABLE 2

STATISTICAL PROFILE OF STATES BY COMPENSATION SYSTEM SAMPLE MEANS, 1968-94

Variable No-Fault Tort

Fatal accident rate (per 10 million vehicle miles) 24.11 34.10 **

22 For example, in 1992, the fatal accident rate on rural highways was 2.58 per 100 million vehicle miles, whereas the fatality rate on urban highways was 1.21 per 100 million vehicle miles. Interstate highways are safer than other types of highways, but the fatal accident rate is higher on rural interstates (1.20 per 100 million miles) than on urban interstates (.62 per 100 million miles). See U.S. Department of Transportation, supra note 14. 23 See, for example, Phillip Farrell & Victor R. Fuchs, Schooling and Health: The Cigarette Connection, 1 J. Health Econ. 217 (1982). 24 Sam Peltzman, The Effects of Automobile Safety Regulation, 83 J. Pol. Econ. 677 (1975). 25 A number of other potential explanatory variables relating to state characteristics also were tested, including traffic violations, the proportion of new cars in the state (because newer cars have more safety features), the presence of comparative negligence, the presence of a seat belt law, and so on. These variables proved to be statistically insignificant. Their inclusion in the regressions did not affect the findings with respect to the no-fault variable. 26 The use of a linear time trend variable in place of the year dummies produced similar results. However, we consider the year dummies to be superior to the time trend because they do not force the differences between consecutive years to be constant. 27 The results were qualitatively unchanged when the state fixed effects are replaced by dummy variables for eight of the nine U.S. regions defined by the U.S. Bureau of the Census, with one region omitted to avoid singularity.

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TABLE 2

STATISTICAL PROFILE OF STATES BY COMPENSATION SYSTEM SAMPLE MEANS, 1968-94

Variable No-Fault Tort

Injury accident rate (per 10 million vehicle miles) 191.29 176.77 +

Alcohol consumption (gallons per capita) 26.15 25.79 **

Annual snowfall (inches) 37.37 27.89 **

Miles driven: rural interstates (%) 8.44 12.17 **

Real income per capita (1982 ] 13,187 11,491 **

% of population with bachelor's degree 19.41 15.62

Average speed (mph) 56.75 57.63

speed variance (85th percentile - average speed) 6.32 7.04 +

% of population aged 18-24 11.74 11.83

Hospitals per square mile of land area 63.64 36.67 **

Points assigned if <50% at fault .86 .71 **

Number of observations 312 1,038

NOTE.--Significance tests are for differences between no-fault and tort

state means.

+ Significant at the 10% level.

** Significant at the 1% level.

are presented in Table 2. The mean values for most of the variables differ significantly between the two groups of states. The fatal accident rate is lower in no-fault states than in tort states, reflecting differences in the driving environment, demographics, and other factors; and the injury accident rate is higher in no-fault states than in tort states, reflecting similar interstate differences. Rural interstate mileage accounts for 8.4 percent of miles driven in no-fault states compared to 12.2 percent in tort states, and no-fault states have higher annual snowfall and lower speed variance than tort states. Alcohol consumption is higher in no-fault states. No-fault states also have higher per capita income and more hospitals per square mile than tort states. These significant differences between tort and no-fault states emphasize the importance of controlling for state characteristics when studying accident rates; that is, estimating the effect of no-fault is inherently a multivariate problem.

B. Estimation Methodology

The regression equations were estimated initially using ordinary least squares (OLS), the same estimation approach used by prior researchers. Ordinary least squares is potentially problematical because the presence of no-fault in a state is likely to be endogenous, which leads to selectivity bias. Endogeneity will be present if states tend to adopt no-fault in response to high auto insurance costs or if there are other systematic differences in the types of states that adopt no-fault. High costs tend to occur in states with high injury accident rates, but such states have relatively low fatality rates, [*441] on average (see Table 2). 28 Thus, it is important to test for endogeneity and to make adjustments to the estimation methodology if endogeneity appears to be present.

28 See Cummins & Tennyson, Controlling Automobile Insurance Costs, supra note 6, for a discussion regarding the correlations between the cost of automobile insurance and nonfatal and fatal automobile accident rates.

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We employ two standard methods to test for endogeneity--(1) the Hausman test for endogeneity 29 and (2) the inverse Mill's ratio technique 30 as developed and applied in similar circumstances by Lung-Fei Lee and Chris Robinson. Both tests led to the rejection of the hypothesis that compensation systems are exogenous. 31 Accordingly, we estimate our fatal accident rate equations using estimation techniques that control for endogeneity. The techniques differ depending on which variable(s) are included in the equation to represent no-fault. To simplify the discussion, we first discuss estimation for the case in which a single indicator variable is used to represent no- fault and then more briefly discuss estimation for the cases in which monetary and verbal indicators and claims ineligibility ratios are used to represent no-fault.

When no-fault is represented by a single indicator variable equal to 1 in no-fault states and 0 otherwise, we utilize two estimation techniques to control for endogeneity, based on instrumental variables (IV) and inverse Mill's ratios (IM). We specify the following two-equation model:

q[it] = [alpha]' X<q>[it] + [nu][it], (6)

A[it] = [beta]' X<A>[it] + [gamma] I[it] + I[it] [epsilon][nit] + (1 - I[it]) [epsilon][fit] + [omega][it], (7)

where

q[it] = "sentiment" for or political support for no-fault in state i and year t,

[*442] I[it] = indicator variable equal to 1 if state i has a no-fault law in year t, and equal to 0 otherwise,

[alpha], [beta] = parameter vectors,

X<q>[it], X<A>[it] = vectors of exogenous variables for state i, year t, applicable to equations (6) and (7), respectively,

A[it] = the fatal accident rate in state i in year t,

[nu][it] = a random error term for equation (6),

[epsilon][nit], [epsilon][fit] = random error terms for no-fault states and tort states, respectively, in equation (7), and

[omega][it] = the overall random error term for equation (7).

The specification allows for different error terms in tort and no-fault states.

The variable q[it] is an unobserved latent variable. The observed realization of q[it] is a dichotomous variable (I[i]) representing the state's auto insurance compensation system. If q[it] > 0, I[i] is equal to 1, which means that the state has a no-fault law, whereas if q[it] </= 0, I[i] is equal to 0, which indicates that the state has retained the tort system. An endogeneity problem arises if [nu][it] is correlated with [epsilon][nit] or [epsilon][fit]. In that case, OLS estimates of (7) are inconsistent. This problem often arises when the units of observation (in this case, states) choose or are assigned to categories (for example, no-fault or tort) in some systematic way rather than being randomly assigned. The problem could arise in state automobile accident compensation systems if, for example, states with relatively high injury accident rates and relatively low fatality rates have a tendency to choose no-fault.

29 William H. Greene, Econometric Analysis 763 (1997), provides a discussion of the Hausman test applied here. 30 Lung-Fei Lee, Unionism and Wage Rates: A Simultaneous Equations Model with Qualitative and Limited Dependent Variables, 19 Int'l Econ. Rev. 415 (1978); Chris Robinson, The Joint Determination of Union Status and Union Wage Effects: Some Tests of Alternative Models, 97 J. Pol. Econ. 639 (1989). 31 The F-test statistic for the Hausman test is 5.84, with 1 and 1,262 degrees of freedom. The critical values at the 1 and 5 percent levels are 6.63 and 3.84, leading to rejection of the hypothesis of exogeneity at the 5 percent level. This test utilized the model with a no-fault indicator variable and full state and year fixed effects, because we believe the full fixed-effects approach to be the most accurate way to measure the effects of no-fault. The inverse Mill's ratio test of the null hypothesis of the exogeneity of the compensation systems is equivalent to testing the hypothesis that the coefficients of the inverse Mill's ratio terms in equation (7') are not jointly statistically different from zero. The F-statistic for the joint significance test of the inverse Mill's ratios in equation (7') was 5.49, with 2 and 1,261 degrees of freedom. The critical values at the 1 and 5 percent levels are 4.61 and 3.00, leading to rejection of the hypothesis of exogeneity at the 1 percent level of significance. This test was based on the IM model with the no-fault indicator variable and full fixed effects.

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ARTICLE: The Incentive Effects of No-Fault Automobile Insurance , 44 J. Law & Econ. 427

This is likely to occur because auto insurance premiums are highest in states with high injury accident rates and low fatal accident rates, and reducing premium costs is a primary motivation for modifying auto accident compensation systems. 32

In the IV estimation methodology, we use as an instrument for no-fault the predicted probability that state i has a no-fault law, F([alpha]' X<q>[it]), based on a reduced-form probit equation (equation (6)), where F(.) is the standard normal distribution function applicable to the error term [nu][it]. The IM approach involves the introduction of inverse Mill's ratios as additional regressors in (7), which yields

[See formula in printed version], (7')

where f(.) and F(.) are standard normal density and distribution functions. 33 [*443] The addition of the inverse Mill's ratios to the set of regressors is designed to adjust for the inconsistency that arises if the error term in equation (6) is correlated with the error terms in (7). 34

In models where no-fault is represented by monetary and verbal indicators, we control for endogeneity using an IV estimation technique analogous to the methodology described above. However, in this case, we use as the instruments for monetary and verbal no-fault the predicted values from a reduced-form multinomial logit model with the dependent variable consisting of three categories--tort, monetary-threshold no-fault, and verbal-threshold no- fault. The explanatory variables for the reduced-form multinomial logit model are the same as for the binary model used in IV estimation when no-fault is represented by a single indicator variable. The multinomial logit model is shown in Appendix D.

We also use IV estimation when no-fault is represented by the claims ineligibility ratio. In this case, the instrument for the no-fault variable is the predicted value from a reduced-form Tobit regression with the proportion of ineligible claims as the dependent variable. Both tort states and no-fault states are included in the Tobit regression, with the dependent variable set equal to zero for the tort states, which reflects the absence of no-fault restrictions on the right to sue and is equal to the proportion of ineligible claims in no-fault states. The Tobit regressions are also shown in Appendix D.

As mentioned above, time effects are accounted for in our models using year dummy variables. State dummy variables also are included in most of the regressions to absorb other differences among states not captured by the explanatory variables in the regressions. 35 Ordinary least squares results are shown for comparison with the instrumental variables and inverse Mill's regressions.

[*444] IV. ESTIMATION RESULTS

32 Cummins & Tennyson, Controlling Automobile Insurance Costs, supra note 6. 33 The probit equation is presented in Appendix D. The parameter vector [SEE ILLUSTRATION IN ORIGINAL] for the reduced-form probit equation (6) is estimated using maximum likelihood. We also tested a binary logit model and obtained similar results. The standard errors in the IV fatality rate regression (7') are calculated following the methodology presented in G. S. Maddala, Limited Dependent and Qualitative Variables in Econometrics (1983). The probit equation included the regressors in X<A> as well as five additional exogenous variables hypothesized to be related to the political sentiment for no-fault (see Appendix D). The five variables are the cost of 1 day of hospitalization, the percentage of state legislators who are Democrats, a dummy variable equal to 1 if the state has a Democratic governor and 0 otherwise, population density (population per square mile), and the percentage of a state's population residing in urban areas. The two Democratic party variables are designed to proxy for political factors relating to the existence of no-fault in a state. Population density and the urban population percentage provide proxies for urbanization, while hospital costs are a key factor related to personal injury insurance costs. The coefficients [sigma][vn] and [sigma][vf] are, respectively, covariances between the error term of the reduced-form probit equation (6) and the error terms [epsilon][nit] and [epsilon][fit] from equation (7). 34 If this type of correlation is present, the conditional means E([epsilon][nit] I[i] = 1) and E([epsilon][fit] I[i] = 0) are not equal to 0, where I[i] is the no-fault indicator variable, equal to 1 for no-fault and 0 for tort. Estimating the augmented equation (7') by OLS provides consistent estimates of the other parameters in this equation, as long as the assumption of multivariate normality of the error terms in (6) and (7) is satisfied. The terms [sigma][vn] [-f(.)/F(.)] and [sigma] [f(.)/[1 - F(.)]] are, in fact, the conditional means E([epsilon][nit] I[i] = 1) and E([epsilon][fit] I[i] = 0). One reason for also conducting the Hausman (IV) test is that this test is viewed as nonparametric and thus does not depend upon the multivariate normality of the residuals in (6) and (7). See John T. Addison & Pedro Portugal, The Endogeneity of Union Status and the Application of the Hausman Test, 10 J. Lab. Res. 437 (1989). 35 As a robustness check, models also were estimated with regional and time random effects. The results were similar and therefore not reported.

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This section presents the results of our tests of the relationship between no-fault and fatal accident rates. We first present the results using a single indicator variable to represent no-fault and then present results based on monetary and verbal indicator variables and the proportion of claims ineligible for tort.

A. The No-Fault Indicator Variable

The regression models that include a single indicator variable for no-fault are presented in Table 3. In the IM equations, the inverse Mill's ratio for no-fault states is interacted with the no-fault dummy variable, while the inverse Mill's ratio for tort states is interacted with 1 minus the no-fault dummy variable.

The no-fault indicator variable is positive and significant in all of the models presented in Table 3, which supports the hypothesis that no-fault weakens the deterrent effect of tort and is positively associated with higher fatal accident rates. When the endogeneity of no-fault is taken into account in the IV and IM regressions, the coefficient of the no-fault variable is larger than in the OLS runs, as expected if states with relatively high injury accident rates and relatively low fatality rates are more likely to adopt no-fault.

We computed the implied increases in fatality rates associated with no-fault on the basis of the regressions in Table 3. The implied increase was calculated as the ratio of the no-fault indicator coefficients in the nine models shown in Table 3 to the mean fatality rate in tort states. The results suggest that no-fault is associated with fatality rates from 2.7 to 17.3 percent higher than tort, with a median predicted increase of 13.8 percent. These results are generally consistent with the findings of Landes, Devlin, and McEwin. 36 Landes found estimated increases in fatalities ranging from 2 to 14 percent, depending on threshold stringency, while Devlin estimated a 9 percent increase in fatalities in Quebec. McEwin estimated that fatalities were 16 percent higher under no-fault in Australia and New Zealand.

The coefficients of most of the other variables are consistent with expectations. The experience-rating variable (license points assessed for an accident even if the driver is less than 50 percent at fault) is negative and significant as predicted by our theory and thus reinforces the view that more rigorous experience rating can be used to blunt the adverse incentive effects of no-fault. However, because this variable changes little over time, we could not include it in the equations with state dummy variables because of multicolinearity [*445] problems. Consequently, some caution is in order in interpreting the results based on this variable. 37

The alcohol consumption variable is positive and significant in the models that do not include state effects but is negative and usually insignificant in the state effects models, which suggests that the state dummy variables tend to absorb the impact of this variable. The driving environment variables, annual snowfall and rural interstate mileage, are both significant with the expected signs (negative and positive, respectively), which implies that adverse weather conditions tend to reduce the number of serious accidents and that fatality rates are higher on rural interstates. The number of hospitals per square mile is inversely related to the fatality rate, as predicted if the proximity of emergency medical services tends to reduce fatality rates.

Speed variance is positive and statistically significant in all of the equations shown in Table 3, consistent with prior research. 38 The average speed variable also is positive and statistically significant, with coefficients that are smaller than the corresponding coefficients of the speed variance. This is consistent with Lave's argument that "speed variance has more effect on fatalities than speed, per se--'coordinating' the traffic flow is more important than 'limiting' it." 39 Recalling that speed variance is defined as the 85th percentile speed minus average speed, the equations imply a net negative effect of average speed on fatalities, also consistent with Lave's findings. Thus, our results support his hypothesis that speed variance is more important than average speed in determining traffic fatalities.

36 Landes, supra note 5; Devlin, Liability versus No Fault, supra note 4; and McEwin, supra note 4. 37 However, the variable was also negative and statistically significant in models that include dummy variables for eight of the nine U.S. Census Bureau regions. 38 Lave, supra note 21. 39 Id. at 1163.

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The results also provide some evidence that educational attainment is related to the fatal accident rate. The proportion of the population with bachelor's degrees is statistically significant and inversely related to fatality rates in the equations that do not include state fixed effects, consistent with greater demand for safety among better- educated drivers. However, this variable becomes insignificant when state fixed effects are included in the model. The proportion of drivers aged 18-24 is positive and statistically significant in all equations shown in Table 3, consistent with the view that youthful drivers have higher accident rates. Real income per capita is positive and statistically significant in the fatality rate equations that include state fixed effects, consistent with the hypothesis that the costs of time are higher for drivers with higher incomes.

B. Monetary and Verbal Threshold Indicators

In the next set of tests, we use two indicator variables--representing monetary- and verbal-threshold no-fault states, respectively--in place of the single [*446] [*447]

TABLE 3

REGRESSION RESULTS USING SINGLE NO-FAULT INDICATOR VARIABLE

(Dependent Variable: Fatal Accident Rate)

OLS I OLS II OLS State Effects

Intercept + -8.469 -3.763 ** -17.559

No-fault indicator * .932 ** 1.407 ** 1.688

Alcohol consumption a + .065 .048 + -.132

Annual snowfall

(inches) ** -.078 ** -.075 ** -.034

Miles driven: rural

interstates (%) ** 64.311 ** 65.538 ** 27.481

Real income per

capita .137 .112 ** 2.030

% of population with

bachelor's degree ** -24.845 ** -24.818 6.575

Average speed ** .241 ** .179 ** .327

Speed variance b ** .748 ** .670 ** .412

% of population aged

18-24 ** 55.845 ** 47.414 ** 39.377

Hospitals per square

mile ** -.038 ** -.040 ** -.028

Points assigned if

< 50% at fault ** -2.565

Inverse Mill's ratio:

No-fault

Tort

Adjusted R<2> (%) 85.4 86.0 92.3

NOTE.--Regressions are based on 50 states for the period 1968-94. All

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TABLE 3

REGRESSION RESULTS USING SINGLE NO-FAULT INDICATOR VARIABLE

(Dependent Variable: Fatal Accident Rate)

OLS I OLS II OLS State Effects

models include dummy variables (not shown) for each year (1994 omitted to

avoid singularity). The state effects models include dummy variables for each

state, with one state omitted to avoid singularity. The inverse Mill's

variable for no-fault is interacted with the no-fault dummy variable, and the

inverse Mill's variable for tort is interacted with 1 minus the no-fault

dummy variable. Variables are defined in Appendix C. OLS = ordinary least

squares; IV = instrumental variables; IM = inverse Mill's ratios.

a Alcohol consumption is in gallons per capita.

b Speed variance = 85th percentile - average speed.

+ Significant at the 10% level.

* Significant at the 5% level.

** Significant at the 1% level.

TABLE 3

REGRESSION RESULTS USING SINGLE NO-FAULT INDICATOR VARIABLE

(Dependent Variable: Fatal Accident Rate)

IV I IV II IV State Effects

Intercept ** -11.796 + -7.727 ** -22.358

No-fault indicator ** 5.033 ** 5.450 ** 4.348

Alcohol consumption a ** .108 * .089 -.107

Annual snowfall

(inches) ** -.084 ** -.081 ** -.042

Miles driven: rural

interstates (%) ** 70.196 ** 71.214 ** 29.715

Real income per

capita .035 .010 ** 1.916

% of population with

bachelor's degree ** -37.880 ** -38.122 -.309

Average speed ** .300 ** .250 ** .401

Speed variance b ** .859 ** .799 ** .538

% of population aged

18-24 ** 62.460 ** 54.342 ** 45.478

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TABLE 3

REGRESSION RESULTS USING SINGLE NO-FAULT INDICATOR VARIABLE

(Dependent Variable: Fatal Accident Rate)

IV I IV II IV State Effects

Hospitals per square

mile ** -.038 ** -.040 * -.023

Points assigned if

< 50% at fault ** -2.454

Inverse Mill's ratio:

No-fault

Tort

Adjusted R<2> (%) 85.5 86.1 92.3