Adverse incentives from improved technology: traffic safety regulation in Norway.

• Author: Risa, Alf Erling

1. Introduction

   Much of the literature on safety regulation by economists have pointed out adverse incentive effects. It does, however, seem misguided to believe that effects like these were unknown to regulators before they were pointed out by economists. One example of a popular regulatory measure that takes incentive effects explicitly into consideration, is the use of road-bumps in residential areas. In this case the regulator incurs a positive cost to make the technological environment worse for drivers. If speed were unchanged after the regulation, accident probabilities would go up due to reduced control of the cars. The regulators believe, however, that the physical deterioration of the driver environment will reduce speed to the extent that accident rates go down. It might be a disturbing feature of this line of thought that the same regulators may advocate a technical improvement of a stretch of highway (better surface, wider road etc.) in the interest of accident prevention. In this case the regulator must believe that the ceteris paribus technical improvement of the driving environment will dominate a possible adverse incentive effect.

   It may well happen that the technological nature of these two types of regulation--or the behaviorable responses--differs to such an extent that it is not illogical to advocate both the measures cited above. The example illustrates that for purposes of optimal regulation, it is not only necessary to establish that adverse incentive effects may occur, but also to say something about when they are likely to occur--and when not. The theoretical contribution of the present analysis is to provide one step in this direction, within a unified framework that captures some earlier considerations made in the literature as special cases.(1) The theoretical analysis provides an apparatus for evaluating the effects of regulation in different circumstances with different predictions concerning incentive effects. These theoretical categories have identifiable empirical counterparts. The predictions are tested against a Norwegian data set. The data consist of a pooled cross section and yearly time series of automobile drivers, motorcyclists, and pedestrians that have been killed or injured in Norwegian counties, 1980-1986.

   The next section contains a theoretical discussion of the behavioral responses to regulation. It is shown how the interaction between prevention technologies and attitudes toward risk determines behavior. Individual accident prevention varies greatly--and not always monotonically--with different attitudes towards risk. The impact of changing risk attitudes on prevention is also sensitive to the type of risky situation that is considered. In spite of the great variability in individuals' incentives to take precautions, it is, however, possible to identify simple properties of the prevention technology that makes us able to predict the direction of the incentive effects regardless of the underlying preferences.

   The empirical analysis in section III is embedded in the reduced form of the theoretical model. Although the data set is quite aggregated, it has interesting features that makes it better suited to reveal potential external effects and moral hazard than in much of the earlier literature. One such feature is unique information on actual seat-belt use compiled by the national police task-force for traffic control in Norway. The empirical analysis suggests the presence of adverse incentive effects to technical and legal regulation. One of several results in this category is that increased use of seat-belts by drivers has a significant adverse effect on other road users.

2. The Agents' Response to Regulation

   The starting point of the analysis is a simple model of self-protection as introduced by Ehrlich and Becker |7~. The probability that an agent will experience a well-defined accident is a function of the level of care taken by the agent (c), and a vector describing the physical and technological environment (x). This relationship is modelled as a decreasing, convex prevention function

   p = p(c,x), p |is an element of~ (0,1~. (1)

   The agent's efforts to prevent accidents might also have an impact on the severity of the accidents should they occur. In the case of automobile accidents, taking care by reducing speed will reduce the probability of a collision, and also reduce the damage should such a collision occur. On the other hand, if the potential accident considered is driving over a cliff and falling down, reduced speed will only reduce the probability of the accident. The height of the cliff will determine the potential damage, regardless of the speed of the car as it started to fall. This shows that also the physical environment (x), might affect the loss from an accident for the agent. These considerations give rise to a nonegative, nonincreasing, convex loss function of the form

   L = L(c,x). (2)

   Losses are measured in monetary terms. This has the advantage that attitudes towards risk are easily defined when only monetary elements enter the utility functions additively. A potential problem is that an analysis of traffic accidents should accommodate the possibility of health losses. Viscusi and Evans |20~ have argued forcefully against use of the monetary equivalent of ill health formulation to analyze health losses. Their argument is directed against formulations with a fixed monetary equivalent. The monetary equivalent can, however, be derived from more primitive concepts in the vein of Cook and Graham |5~. It follows from the analysis in Risa |15~ that such derivations implies that the loss function should be decreasing in prevention costs (c), given that the Viscusi and Evans |20~ assumptions regarding the health state dependent utility functions hold. The loss function in the present formulation can therefore also be interpreted to contain elements of monetized health losses.

   Risa |16~ contains a discussion of how a principal can regulate accident risks among multiple agents with external effects in prevention activities. That analysis motivates investigation of incentive effects from regulation. Here, optimal regulation will not be discussed. The focus is limited to a positive investigation of the expected incentive effects from regulation. The main analytical departure from Risa |16~ is the introduction of the endogenous loss function. Different technical assumptions on this function will identify different risk-taking regimes, and different regulation schemes, that correspond to empirical counterparts in traffic safety regulation.

   A (representative) individual has a gross wealth of Y. Disposable wealth without an accident, but with accident prevention, is |y.sup.0~ = (Y - c). In the accident state, disposable wealth equals |y.sup.1~ = (Y - c - L(c, x)). Superscripts 0 and 1 denote the favorable and unfavorable state of the world, respectively, throughout the paper. The optimization problem for the individual facing a well defined potential accident is to choose a level of care that maximizes expected utility, given a physical environment.

   |Mathematical Expression Omitted~

   The first order necessary condition for a maximum is:

   |Mathematical Expression Omitted~,

   where subscripts denote (partial) derivatives with respect to care (c), and disposable wealth. The second order sufficient condition for a maximum is:

   |Mathematical Expression Omitted~.

   The properties and predictions of this model depend to a large extent on the limiting assumptions that are made concerning the partial derivatives of the p and L functions. We consider three regimes that are special cases of the model above.

   Regime 1: Technical assumption: |p.sub.c~ |is less than~ 0, |L.sub.c~ = 0.

   Individual precautions influence accident probabilities, but not the loss.(2) Empirical counterparts to this regime:

   Care and attention by pedestrians to prevent being hit by a car.

   Reduced speed by drivers, if the potential accident is driving over a cliff.

   Regime 2: Technical assumption: |p.sub.c~ |is less than~ 0, (1 + |L.sub.c~) |is less than~ 0.

   Individual precautions influence both the size of the loss and the probability of the accident. The marginal loss reduction in case of...