Globalization in road safety: explaining the downward trend in road accident rates in a single country (Israel)

Accident Analysis and Prevention 32 (2000) 71 – 84 www.elsevier.com/locate/aap

Globalization in road safety: explaining the downward trend in road accident rates in a single country (Israel) Michael Beenstock *, Dalit Gafni Department of Economics, The Hebrew Uni6ersity of Jerusalem, Mount Scopus, 91905 Jerusalem, Israel Received 16 July 1998; received in revised form 29 April 1999; accepted 18 May 1999

Abstract A theoretical model is proposed in which road safety in a single country depends upon parochial considerations, such as police enforcement, and upon global considerations, such as international road safety technology. We show that there is a non-spurious relationship between the downward trend in the rate of road accidents in Israel and the road accident rate abroad. We suggest that this reflects the international propagation of road safety technology as it is embodied in motor vehicles and road design, rather than parochial road safety policy. Recent developments in the econometric analysis of time series are used to estimate the model using data for Israel. We make no direct attempt to explain the downward trend in the rate of road accidents outside Israel. © 1999 Published by Elsevier Science Ltd. All rights reserved. Keywords: Globalization in road safety; Downward trend; Econometric analysis of time series

1. Introduction Road accident rates and fatality rates in the industrialized countries have tended to exhibit pronounced negative time trends. Table 1 and Figs. 1 and 2 summarize some relevant data. Fig. 1 shows that the accident rate in Israel was ten times higher in 1960 than in 1995. The fatality rate was also seven times higher. Fig. 2 shows that for five industrialized countries the average accident rate was almost three times greater in 1964 than in 1994, while Table 1 indicates that the fatality rate fell even faster. Some scholars, e.g. Oppe (1991) interpret the downward trend as evidence of exponential learning, while others e.g. Peltzman (1975), Harvey and Durbin (1986) and Broughton (1991) treat it as a nuisance parameter that happens to be essential for model fitting. In this paper we focus upon the determinants of the trend itself. This is important because it is arguably the dominant factor in the determination of road safety. By contrast, the effects of various road safety interventions, which have been the legitimate focus of so much * Corresponding author. Tel.: +972-2-5883120; fax: + 972-25816071. E-mail address: [email protected] (M. Beenstock)

research, are of secondary importance. For example, in Peltzman’s model for the US, the time trend accounts for a secular decline in the fatality rate of 712% per year. By contrast, other effects pale in importance. We propose a model in which road safety results from both global and parochial considerations. The former are common to all countries, and reflect the globalization of the automobile market and road technology. The latter are country-specific, and reflect the separate initiatives taken in individual countries. It may be, however, that some of these initiatives, such as seat-belt laws, are more global than parochial since they have been applied more or less universally. In terms of Hakim and co-workers’ characterization of so-called ‘macro-models’ estimated from time series, ours is structural in nature, and is based upon solid micro-foundations (Hakim et al., 1991). We propose a theoretical framework in which drivers are assumed to trade-off safety against time; faster (less safe) driving saves time at the expense of safety. We use this framework to develop hypotheses about the secular trend in road safety rates. It should be noted that we are concerned with the trend rather than the level of road safety. An intervention such as a seat-belt law, or a speed limit, being discrete in nature, can be expected to

0001-4575/99/$ - see front matter © 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 1 - 4 5 7 5 ( 9 9 ) 0 0 0 5 3 - 6

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

72

affect the level of the accident rate without necessarily affecting its trend. By contrast, technical change in road safety technology, being of a continuous nature, can be expected to affect the trend in road safety, and not just its level. The analytical difference between levels effects and trend effects shall be central to our thesis. In this context we use econometric techniques, developed in the last decade, for handling non-stationary time series such as accident rates. These techniques are collectively known as ‘unit root econometrics’ since, as we shall explain, non-stationary data contain a unit root. Trending variables such as the data featured in Figs. 1 and 2 are necessarily non-stationary, in which case conventional econometric techniques will not be appropriate, and may even mislead. For example, two trending time series, which in reality are unrelated, may be spuriously correlated with high R 2. The high correlation arises, either because both variables are related to time, or because they are related to third variables that happen to be time-trended. Unit root econometrics, which distinguishes between genuine and spurious correlation, has transformed the way in which users of time series conduct their research, and has been applied in a wide variety of settings. However, to our best knowledge it has not been applied in the road safety literature. We shall argue that it is especially suitable for investigating the determination of trend-like behavior in data such as the rate or number of accidents. Indeed, one of our objectives is to introduce these research methods to road safety scholars. The specific focus in the present paper is upon the accident rate rather than the fatality rate. In Israel, as noted above, the accident and fatality rates have had similar trends. In 1960 the severity rate (the ratio of fatalities to accidents) was 0.02, and 0.022 in 1995. However, it rose in the interim and peaked at 0.04 in 1974. Data obtained from the International Road Federation indicate that between 1975 and 1994 severity rates rose in some countries, such as Holland and Denmark, fell in other countries, such as the UK and US, and remained the same elsewhere, such as Belgium and Italy. The simultaneous determination of fatality and accident rates goes beyond our present, more modest, terms of reference.

The remainder of the paper is organized as follows. In Section 2 we set out the theoretical framework which underpins our empirical investigation of road accident rates in Israel. In Section 3 we summarize unit root econometrics insofar as they are relevant to the present application. The data are presented in Section 4. Results are discussed in Section 5, while policy implications and suggestions for further research are discussed in Section 6. Our main conclusion is that the downward trend in the accident rate in Israel is largely, but not entirely, unrelated to parochial developments in Israel. We show instead that the downward trend in Israel is an integral part of a world trend. We suggest, by way of explanation, that the common denominator to the two trends is improving safety standards in vehicles and road technologies. We refer to this as the ‘globalization model’ of road safety because it emphasizes international rather than parochial factors in the continuing decline in accident rates. If road accident rates in otherwise diverse settings happen to have a common stochastic trend, this is unlikely to be the coincidental result of country-specific policies. On the contrary, despite heterogeneous developments across countries, the common stochastic trend in accident rates emphasizes the importance of technology transfer in the propagation of road safety. We wish to emphasize that the mere fact that national accident rates happen to exhibit downward trends does not in itself automatically imply globalization. It is possible for accident rates to trend downwards without them being related. As mentioned, an important methodological component of the paper is the distinction between spurious and genuine relationships between trending time series. Globalization requires accident rates to have common stochastic trends, a formal statistical test for which is supplied in Section 3 and implemented in Section 5. The globalization thesis does not necessarily mean that country-specific road safety initiatives have achieved nothing. As discussed in Section 6, they might have influenced the level, but not the trend, in the accident rate. It is also conceivable that a succession of such initiatives might induce a downward trend in the

Table 1 Trends in international fatality rates (OECD median)a

1970 1975 1980 1985 1990 1994 a

Fatalities per 100 million km

Fatalities per 10 000 vehicles

Fatalities per 100 000 population

5.6 3.6 2.9 2.2 1.7 1.3

10.5 6.6 4.4 3.2 2.8 2.3

23.4 18.8 17.1 15.1 14.0 11.4

Source: International Road Traffic and Accident Database.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84

73

Fig. 1. Accidents per million km in Israel (S).

accident rate. It is yet further conceivable that the succession of initiatives taken in different countries just happened to have produced a common stochastic trend in international accident rates. We cannot prove that this is not the case. We feel that our globalization thesis provides a more intuitive explanation for the common stochastic trends in international accident rates. In this paper we do not go beyond the confines of Israel; we do not try to explain the internationally observed downward trend in road accident rates. We focus instead on the more modest objective of establishing that the dominant determinant of the downward trend in the rate of road accidents in Israel is the road accident rate abroad. Nor do we claim that the globalization model, which seems to be empirically valid in Israel, has broader empirical validity. In Section 6 we discuss how our approach may be generalized to include other countries.

2. Theoretical framework The theoretical framework upon which the econometric analysis is based is drawn from Lave and Weber (1970) and Peltzman (1975), who argued that driving behavior is likely to be adaptive with respect to the legal and traffic environment. In what follows we present a behavioral model in which the value of time, road and vehicle quality, and traffic-law enforcement play an integrated role in the determination of road safety. We begin by considering the behavior of a single driver given the behavior of other drivers. Thereafter, we consider the joint determination of driving behavior by single drivers and the class of all drivers. The model assumes that drivers are heterogeneous, both observed

(e.g. age, experience, gender) and unobserved (e.g. impatience). The theoretical model serves to clarify the role of global and parochial factors in the determination of road safety. Specifically, it establishes the theoretical relationship between the domestic (Israel in our case) and global accident rates. While data for some of the variables in the model are not available in our case, e.g. speed, we nevertheless present it as an integral whole because it motivates the empirical analysis presented in Section 5. In any case ‘speed’ in the present context serves as a metaphor for ‘care’ in the sense that more careful driving demands more effort and is more time consuming. We certainly do not intend that ‘speed’ be interpreted literally, indeed, we do not investigate empirically the relationship between speed and road safety. Nor do we wish to enter the empirical debate concerning the effect of speed on road accidents and their severity. The safety (S) experienced by the representative driver depends upon his own behavior (V) as well as that of other drivers (V( ). V may be thought of as a variable that indexes bad driving behavior; it is increasing in ‘speed’ and decreasing in ‘care’. We assume that safety is determined as in Eq. (1): S= S



(−)

(−)

(+)



(+)

V , V( , C , R

(1)

where C and R denote vehicle and road quality, respectively, and where the signs of partial derivatives are indicated above the respective variables. The assumptions in Eq. (1) are quite standard. The positive effect of speed upon accidents (both fatal and non-fatal) has been found by a large number of investigators, e.g. Loeb (1987) and Johanssen (1996), however, some in-

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

74

vestigators, e.g. Lave (1985) and Rodriguez (1991), have argued that it is the variance that matters rather than the mean. The effects of road quality (Garbacs and Kelly, 1987; Loeb, 1987) and vehicle quality (Peltzman, 1975) have also been widely investigated. Better vehicles and roads enable drivers to avoid accidents, for given driving behavior. They may also reduce accident severity. We show below that speed and careful driving are choice decisions that are not independent of car and road quality. An improvement in the latter may induce drivers to drive less carefully or at greater speed. Since bad driving practice is increasingly dangerous we assume SVV B0 and SV( V( B0. Although, as indicated in Eq. (1), safety varies directly, ceteris paribus, with car and road quality, we assume that the marginal contribution of investment in road and vehicle quality is likely to diminish, hence SRR B0 and SCC B0. The schedule cj in Fig. 3 (where positive values are measured away from the origin) plots the inverse relationship between S and V that is implied by Eq. (1). The schedule will shrink toward the origin as either V( rises or as R and C fall. Vehicle quality (C) is assumed to vary directly with income (W), since richer people can afford better cars, and with a technological parameter tC, i.e.:



(+)

(+)

C =C W , tc



(2)

Since vehicle technology tends to improve over time, Eq. (2) implies that a given outlay on a vehicle bought more safety in 1999 than it did in 1989. We assume that road quality (R) is set exogenously by the relevant authority. As in the case of vehicles, it depends on investment and technology. A given road development budget most probably bought more safety in 1999 than it did in 1989.

The opportunity cost per trip is equal to W/V since unit trip time is 1/Vand the opportunity cost of time is assumed to be proportional to W. Trip time cost is represented in Fig. 3 by the horizontal distance subtended by schedule TT%, which has a natural lower asymptote. An increase in income (W) will shift this schedule to the left since time becomes more expensive. There is a risk of punishment (p) by traffic police, which is increasing in V and policing P but, because if everybody is driving fast there is less danger of being marked out from the crowd, it is decreasing in V( . We denote the fine, if caught, by F, hence the expected value of the fine due to apprehension may be written as: A= F · p



(+)

(+)



(−)

P , V , V(

(3)

where we assume that AVV \ 0, i.e. the risk of apprehension is increasing in V. In the model V is a choice variable, hence if enforcement is increased due to changes in P, F and p, driving behavior will alter. Schedule OA in Fig. 3 plots the relationship between V and the expected value of the fine that is implied by Eq. (3). OA, which has a natural upper asymptote, will tend to rotate anti-clockwise as V( increases and as enforcement decreases. Although the specification of Eq. (3) assumes that enforcement policy improves road safety, we note that the evidence on this issue is mixed. For example, Carr et al. (1980) found no effect of police enforcement in Nashville, TN, whereas Cameron et al. (1995) report a powerful effect in Victoria, Australia. Schedule GG%, which plots the horizontal sums subtended by schedules TT% and OA, measures the relationship between the total expected trip cost and V. It has a natural asymptote, but it is not necessarily monotonic. It may have a minimum at g. The upper left

Fig. 2. Accident rate (S*): average accident rate per 100 000 vehicles in France, Germany, Japan, Norway and Spain.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84

75

Fig. 3. Optimal driving behavior — micro.

quadrant of Fig. 3 simply converts travel costs into savings (G) due to increasing V; the smaller the cost the greater is the saving subtended by the inverted 45° line. Finally, schedule mbc plots the ‘transformation frontier’ between safety and saving that is implied by schedules cj and GG%. It is non-monotonic if GG% is not monotone; the turning point at b corresponds to the turning point at g as indicated. The efficient part of the ‘transformation frontier’ is of course bc. The individual driver’s utility function is assumed to be: U =U



(+)



(+)

S, G

(4)

i.e. he prefers more safety to less, and he prefers lower expected unit travel costs. The family of indifference curves (of which u0 is a member) implied by Eq. (4) fans outwards from the origin in the upper right quadrant in Fig. 3. Utility is maximized at a implying that the optimal driving behavior is i as indicated. This implies that in equilibrium apprehension risk is r, trip time cost is l, and total trip cost is n. If income (W) increases two offsetting effects occur simultaneously. Insofar as car quality increases (C), schedules cj and cb move to the right thereby raising the equilibrium value of S. Insofar as the value of time increases, schedule TT% will shift to the right thereby creating an incentive to trade-off safety for gains. It is in this way that the model takes into account induced driving behavior, as suggested by Peltzman. If indeed income is responsible for the downward trend in acci-

dent rates it would have to be because the former effect dominates the latter; people drive faster but in safer cars. If police enforcement is increased schedule OA rotates clockwise, the expected gain from ‘speeding’ is reduced, schedule cb rotates anti-clockwise from c, and the equilibrium value of V should fall, although this is not unambiguous. If road quality improves schedules cj and bc shift to the right. Peltzman (1975) has pointed out that the equilibrium value of S may decline. However, this will not happen if the indifference map is homothetic. Similar considerations apply to exogenous increases in car quality (tC ). Thus far the model determines the driving behavior of the individual given the behavior of other drivers. We now turn from the micro to the macro in which aggregate driving behavior is determined, i.e. where V and V( are jointly determined. If V( increases, schedule cj contracts towards the origin thereby shifting schedule cb to the left. If the indifference curve map is homothetic the equilibrium value of V will decrease, but safety and saving on trip costs are likely to decrease too. This implies that there is negative correlation between V and V( . These negative spillover effects tend to steepen schedule cj, which steepens schedule cb, so that both S and G increase in equilibrium at a higher than otherwise level of V. Some of this negative dependence will be offset, insofar as there is less risk of apprehension if others drive faster, i.e. if schedule OA rotates anticlockwise.

76

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

The principle of conjectural variations implies that if each driver optimizes his behavior in terms of the model in Fig. 3 given the behavior of other drivers, and if each driver thinks that his fellow drivers optimize in a similar way, then we may summarize the joint determination of V and V( as in Fig. 4. Schedule I plots the negative effect of V( upon V, while schedule II plots the negative effect of V upon V( . Schedule I is naturally flatter than schedule II. The conjectural variations equilibrium occurs at the intersection of the two schedules. An intervention, or a change in one of the parameters of the model, which induces drivers as a whole to drive more slowly or carefully (i in Fig. 3 falls), will be represented by a contraction in both schedules. It is obvious that the negative spillover effects will reduce the aggregate efficacy of the intervention (so that i falls by less). The whole is less than the sum of its parts. In summary, the theoretical model implies that trending variables such as GDP per head have an ambiguous effect on road safety, even when preferences are homothetic. By contrast road quality and car quality will tend to increase road safety under homothetic preferences. More generally, as in Peltzman (1975), changes in the regulatory and technological environment, which shift the transformation frontier cb, have an ambiguous effect on road safety. The model implies that in equilibrium V depends upon V( , W, tC R, P etc. while V( depends upon W( etc. By the principle of conjectural variations V and V( will be jointly determined implying that the aggregate, or macro-solution for S is: S = S(V(W, tC, R, P); C(W, tC ); R)

(5)

We may classify the variables in Eq. (5) into global and parochial variables. The latter include the indicators of police enforcement (P, F, and p), income (W), seat-belt legislation etc. The former are embodied in the technological parameters iC and iR. In Section 3 we discuss how Eq. (5) may be estimated econometrically when the data are non-stationary. Empirical macro-representations of the variables that feature in Eq. (5) are the accident rate as plotted, for example, in Fig. 1, GDP or consumption per capita

Fig. 4. Optimal driving behavior — macro.

(W), road capital per kilometer (R), and traffic-police per car (P). In the absence of an obvious way of proxying vehicle quality (tC ) we assume that this information is embodied in the accident rate abroad (S *) since the latter depends, according to Eq. (5) upon W *, t*C etc. Because the vehicle fleet in Israel is entirely imported it is reasonable to assume that tC = t*, C which implies that tC may be proxied by S*, W * etc. In practice we proxy it by S* and the age of the fleet (A) since the latter is expected to vary inversely with W/ W *. In summary we estimate models of the type: St = a + b1 Wt + b2 Rt + b3 Pt + b4 S*t + b5 At + g t + ut

(6)

where u denotes a stationary error term and t denotes time. If g= 0 there is no autonomous time trend in the accident rate; the time trend is entirely captured by the other variables in the model.

3. Unit root econometrics Since the variables featuring in Eq. (6) have time trends, they are non-stationary, and spurious correlation may exist between S and the right hand side variables. For example, there may be a high degree of correlation between the accident rate in Israel (S) and the accident rate abroad (S*), when in fact these two variables are unrelated, i.e. the observed correlation is spurious. Engle and Granger (1987) were the first to argue that if u in Eq. (6) is stationary (defined below) the estimated model is not spurious. They referred to such variables as being ‘co-integrated’. Co-integration occurs when a weighted combination of two or more non-stationary variables creates a new variable (u) which happens to be stationary. See Enders (1995) for a useful survey of unit root econometrics. We illustrate these ideas by using Israeli data to estimate Smeed’s original model (Smeed, 1949). According to Smeed the fatality rate varies inversely with the rate of motorization: ln(D/N)t = a+b ln(N/POP)t + ut

(7)

where D denotes road fatalities, N the number of vehicles and POP the population. Smeed’s estimate for b was − 0.66. Since the fatality rate trends downward and the motorization rate trends upwards, it is possible that the two trends are negatively related in a spurious fashion. The test for this consists of determining whether the residuals from the model (u) are stationary, i.e. that the two variables are co-integrated. A less restricted test of Smeed’s model would be to test whether ln D, ln N and ln POP are co-integrated. If these variables are not co-integrated, Smeed’s model would be spurious, despite a possibly high value for R 2.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84 Table 2 Unit root tests for ln (D/N)a Dickey–Fuller (ADF)

Phillips–Perron (PP)

p=0

p=3

p= 3

−0.71 (−2.95) −1.95 (−3.54)

−0.25 (−2.95) −2.13 (−3.54)

−2.48 (−2.95) −2.43 (−3.54)

−5.19 (−2.95) −5.1 (−3.54)

Levels DS −0.2 (−2.95) TS −1.89 (−3.54) First differences DS −5.19 (−2.95) TS −5.1 (−3.54) a

Note: critical values in parentheses for significant level of 0.05.

For example, Gharaybeh (1994) reports R 2’s that range from 0.16 to 0.95 for Smeed models estimated in a variety of countries. If the results we report below (R 2 =0.87) are anything to go by, many of these correlations would be spurious. We first need to determine whether the variables in Smeed’s model are non-stationary, and if so, the type of non-stationarity. If their first differences are stationary we shall refer to this as difference stationarity (DS), and if their deviations from a fixed time trend are stationary we shall refer to this as trend stationarity (TS). The Dickey–Fuller test suggested in Fuller (1976) consists of running the following regression: p

DXt =a +(r −1)Xt − 1 +g t + % di DXt − i +ot

(8)

i=1

If r \ 1 and g= 0 the series is DS, otherwise it is TS. Dickey and Fuller (1981) have suggested a test to determine which model is superior in the event that Eq. (8) does not discriminate between DS and TS. The p augmentations that appear in Eq. (8) are specified to ensure that o is iid. Phillips and Perron (1988) have suggested a non-parametric alternative for correcting for serial correlation in o when p =0. We illustrate the application of Eq. (8) with respect to the dependent variable in Smeed’s model, i.e. the logarithm of the fatality rate. The numbers reported in Table 2 are the t-values for r −1 in Eq. (8) and their critical values, as computed by Dickey and Fuller, are reported in parentheses. The Dickey – Fuller (DF, or ADF if Eq. (8) includes augmentations, i.e. p\ 0) statistics indicate that the levels of the variable are not stationary even as deviations from trend, i.e. the variable is not TS. However, the variable is stationary in first differences (since 5.19 is larger than 2.95 in absolute value), which leads us to conclude that the variable is DS, i.e. the first difference in logarithms of the fatality rate is stationary and trend-free. Notice that the DF statistic may be sensitive to the number of augmentations as in the case of the DS model. The Phillips– Perron test leads to similar conclusions as the DF test;

77

that the series is DS. We also assume that ln (N/POP) is DS. Having concluded that the variables in Eq. (7) are non-stationary, the next step is to estimate b while testing for spuriousness. Several different approaches have been suggested in the literature. Case 1 in Table 3 refers to the Engle–Granger methodology in which ln (D/N) is regressed by ordinary least squares (OLS) upon ln (N/POP) without lags. R 2 is quite impressive at 0.87 and b. = − 1.14. The DW statistic of 0.189 indicates the presence of severe serial correlation. However, what matters is not whether r\ 0, but whether rB1, since the latter would imply that the residuals are stationary, in which event the model is co-integrated and the high correlation is not spurious. To test for this, Eq. (8) is estimated with X replaced by the estimated OLS residuals obtained from Eq. (7). Engle and Yoo (1987) have calculated appropriate critical values for the t-statistic of r− 1 and MacKinnon (1991) calculated its response surface. In case 1 in Table 3 ADF = − 2.1 whereas the critical value at p=0.05 is − 3.55. This implies that the residuals are non-stationary, the variables are not co-integrated, and that the high correlation is spurious. The fatality and motorization rates happen to be both correlated with time, but there is no genuine statistical relationship between them. A similar conclusion is implied by the Phillips– Perron statistic. Note that we do not report parameter standard errors because, as already mentioned, the parameter estimates generally have non-standard distributions when the data are non-stationary. The only relevant test here is the co-integration test as expressed by ADF. Johansen (1995) has suggested an entirely different approach to test for co-integration. It is based on maximum likelihood (ML), and it involves two steps. First, the data are filtered using a vector autoregression (VAR). Subsequently, the filtered data are applied in a reduced-rank regression. Details may be found in Enders (1995) and the procedure features in several software packages (e.g. Eviews, Microfit, Give). Model 2 in Table 3 reports Johansen’s co-integration test and assoTable 3 Co-integration tests for Smeed’s modela Model

b.

Co-integration test

1 Engle– Granger 2a Johansen (DS) 2b Johansen (TS) 3 DRM

−1.14

ADF =−2.1

−2.16 (0.40)

Rank= 1

−2.04 (0.32)

Rank =1

a

−0.916

Standard errors in parentheses.

PP=−2.2

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

78 Table 4 Unit root tests

Dickey–Fullera

Phillips–Perronb

Level

LnS (Fig. 1) LnP (Fig. 5) LnR (Fig. 6) LnS* (Fig. 2) LnA (Fig. 7)

First difference

Level

First difference

DS

TS

DS

TS

DS

TS

DS

TS

−2.45 −2.18 −2.54 −2.05 −3.03

−2.06 −1.96 −2.19 −0.9 −3.41

−3.01* −2.33 −1.37 −2.23 −2.64

−4.23* −2.43 −1.94 −3.35* −2.84

−1.91 −2.96* −1.45 −2.20 −2.46

−1.58 −2.7 −1.04 −0.92 −2.33

−4.74* −6.79* −3.93* −4.37* −6.19*

−4.95* −6.72* −4.24* −4.82* −6.34*

a

Three augmentations. Third order lag truncation. * Denotes significant at 0.05. Critical values are reported in Table 2.

b

ciated parameter estimates. It has been estimated using a second order VAR in the data. We report two sets of estimates: model 2a in which the data are assumed to be DS and model 2b in which they are assumed to be TS. In both cases Smeed’s model turns out to be co-integrated with b. = −2.04 in the case of model 2b. It turns out that the estimates are not sensitive to the choice of DS vs. TS. In short, the ML estimates contradict the OLS estimates both in terms of the estimate of b and the co-integration of Smeed’s model. The third approach is the dynamic regression model (DRM) as proposed by Hendry (1995). It involves regressing the dependent variable on lags of itself as well as on current and lagged values of the explanatory variable. Insignificant lag terms are dropped until a restricted DRM is obtained. Suppose that the DRM is: m

n

1

0

Yt = %gi Yt − i +%8i Xt − i +et i.e. with m lags on the dependent variable (Y) and n on the independent variable (X), such that e is iid. The estimate of b that is implied is obtained by collapsing the lag structure, and solving for the long-run relationship between Y and X as: n

%8i b=

0 m

1 − %gi 1

We set m =n= 5 to obtain model 3 in Table 3. The long-run estimate of b that this generates is −0.916 which is closer to the Engle – Granger estimate than the Johansen estimate. We wish to stress that the analysis of Smeed’s model merely serves to illustrate the technique of co-integration; we do not propose it as a serious contender to the models that we present in Section 5.

4. Data The underlying phenomenon we seek to explain has already been presented in Fig. 1. We stress that since there is no trend in annual mileage per vehicle, a similar picture is obtained if accidents are normalized by the number of vehicles instead of by mileage. Nor, as already noted in Section 1, is there a trend in the ratio of fatalities to accidents. Therefore, we would have obtained a broadly similar picture had Fig. 1 been expressed in terms of fatality rates. A closer inspection of the data in Fig. 1 reveals that between 1960 and 1985 the accident rate declined at an exponential rate of about 7.2% per year. Between 1975 and 1978 the accident rate stabilized but continued to fall once more in 1979 at a relatively faster rate. Between 1986 and 1992 the accident rate stabilized once more after which it fell at a more rapid rate between 1993 and 1997. The downward trend may stall for a while, but this tends to be temporary. It is obvious that the accident rate has a natural lower bound, in which case it is reasonable to expect that sooner or later the trend will slow down. In this case a logistical trend might fit the data better than an exponential trend. However, it turns out that the data in Fig. 1 do not suggest this. If the accident rate is DS, it implies that random changes in it, both adverse and beneficial, can be expected to persist. However, the opposite applies if the accident rate is TS. For example, a discrete intervention to lower the accident rate will have a permanent effect if it is DS but not if it is TS. It turns out (Table 4) that the logarithm of the accident rate (S) is DS rather than TS, and that while its level is clearly non-stationary in Fig. 1, it is stationary in first differences. The Dickey–Fuller t-statistic (ADF) is − 3.01 which exceeds its critical value of − 2.95, while the Phillips–Perron statistic is −4.74. Removing a time trend from the level of the logarithm of the accident rate does not stationarize the variable

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84

since the Dickey–Fuller statistic is only − 2.06, which is well below its critical value of −3.54. Since the accident rate is a stochastically trending variable we need to identify other stochastically trending variables to serve as covariates. Some candidates are plotted in Figs. 5 – 7 and their associated ADF and PP statistics are reported in Table 4. These include road quality (R), as measured by the capital stock invested in roads (at constant 1990 prices) per kilometer of road. This index, which is constructed by the Bank of Israel, calculates the average cumulative investment in a kilometer of road by dividing the total capital stock invested in roads by the total number of road kilometers. The total capital stock captures road quality because it includes investment in road improvements on existing highways, as well as the cost of building to a higher standard on new highways. For example, the investment cost of a fly-over, which is considerably greater than that of a conventional intersection, and the investment cost of safety features (such as crash barriers, lighting, and shoulders) are all included in the statistical definition of R. It is arguably a better measure of road quality than that used by Garbacs and Kelly (1987), and Loeb (1987) who use road length alone as a measure of quality. We assume that the greater is this investment, the greater is the quality of the road. According to Fig. 5 capital invested per kilometer of road averaged about 370 000 shekels (at 1990 prices, about $176 000) in 1960, whereas by 1994 it had more than tripled to 1 150 000 shekels (about $548 000), implying an underlying rate of growth of 3.3% per year. This suggests that road quality improved on average at an annual rate of 3.3% during the observation period. Police enforcement (P) is approximated by the ratio of police reports for driving offenses to the number of

79

vehicles. This will tend to decrease if the rate of growth of the traffic police does not keep up with the rate of growth of the fleet. If this happens, the enforcement rate per vehicle will fall. Fig. 6 indicates that the enforcement rate, thus measured, was relatively high in the early 1960s; on average each vehicle was involved in about two apprehensions per year. Since 1970, however, the enforcement rate has been substantially lower with each vehicle being involved in about 0.7 apprehensions per year. Finally, in Fig. 7 we plot the proportion of the fleet aged in excess of 10 years (A). In the early 1960s close to half the fleet was older than 10 years. This exceptional situation resulted from the economic austerity in force since Israel achieved independence in 1948. With the relaxation of austerity in the 1960s the proportion of old vehicles fell rapidly to about 20% before rising to close to 30%. It should be mentioned that vehicles are heavily taxed in Israel. Currently they are taxed at 100%. Prior to 1990 vehicle tax rates were even higher. Such high tax rates reduce the economic incentive to rejuvenate the fleet, for even an old vehicle, which elsewhere would have long since been scrapped, is artificially expensive as a result of the tax rate. No doubt this policy goes a long way to explaining why the fleet in Israel is relatively old. It turns out, especially according to the Phillips–Perron statistic, that the variables in Figs. 5–7 are difference stationary time series, and so are potentially co-integrating variables with the accident rate. We shall see in Section 5 that the downward trend in the age structure of the fleet in the 1960s and 1970s contributes to the explanation of the downward trend in the accident rate. We shall also see that, in some of the models, the upward trend in road quality contributes to the

Fig. 5. Road quality (R): capital investment per kilometer of road.

80

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

Fig. 6. Police enforcement (P): the ratio of police reports for driving offenses to the number of vehicles.

downward trend in the accident rate. Moreover, once these trending variables have been taken into consideration, it turns out that despite the negative trend in Fig. 6, the fall in the accident rate would have been even greater had police enforcement not been reduced. As seen in Fig. 2, we have formed a variable that represents the ‘world accident rate’, which is a weighted average of the accident rates in five countries, as reported by the International Road Federation (IRF). Gaps in the IRF data (e.g. US from 1971 to 1973 and Britain in 1972 and 1976) prevented us from including a larger group of countries. However, accident rates for key omitted countries also have pronounced negative time trends falling from 2510 per 100 000 vehicles in Britain in 1964 to 982 in 1994. In Belgium the rate fell from 3580 to 1095, in Italy from 1830 to 446 (in 1991), in Sweden from 700 to 322 (in 1993), and the US from 1220 (in 1965) to 1150 (in 1992). The weakest trend occurs in the US. While no doubt other global indices may be constructed, we feel that the expression for S* in Fig. 2 is quite representative.

5. Results We have already seen that the Smeed model does not co-integrate, except according to Johansen’s method. Indeed, there are many models which do not co-integrate in which the covariates include various macroeconomic and demographic variables, and where R 2 is high. In this section we concentrate on two non-nested models which do co-integrate, irrespective of the method of estimation, with the logarithm of the accident rate (in Tables 5 and 6, respectively). In the first, the co-integrating vector consists of the logarithms of

the accident rate (S), the accident rate abroad (S*), and the proportion of old vehicles (A). In the second, the co-integrating vector consists of the logarithms of the accident rate, the enforcement rate (P), the proportion of old vehicles (A) and road quality (R). These models are non-nested because neither model is a special case of its rival. However, they are both special cases of Eq. (6). We refer to these models as the global and parochial models because the former attaches importance to the international transmission of road safety technology via S*, whereas the latter comprises parochial variables. A more general model would combine the two, as suggested by Eq. (6). Indeed, this was our point of departure for estimation purposes. To save space, however, we limit the discussion to the two models since these turned out to be the main serious empirical contenders. Results for the global model are presented in Table 5, while Table 6 presents results for the parochial model. The results in Table 5 indicate that the stochastic trend in the accident rate in Israel is explained by two variables, the world safety trend (S*) and the proportion of old vehicles in the fleet. Estimates of b4 in Eq. (6) range from 1.213 to 1.465, implying that the downward secular trend in Israel is more pronounced than in the countries included in S*. However, the older the fleet the higher is the accident rate in Israel implying that older vehicles do not embody the latest in road safety technology. Here the elasticities range for the most part between 0.358 and 0.66. It is conceivable, as suggested by the theoretical model in Section 2, that older cars are driven more slowly. However, this effect is not sufficiently strong to compensate for their lower safety standard relative to the latest models.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84

The latter result shows that even in the so-called global model, local factors such as the age of the fleet, are important. Hence the dichotomy between global and parochial must not be over-stretched; indeed, they even share a common parochial variable (A). Nevertheless, the co-integration tests reported in Table 5 show that the relationship between the downward trends in the accident rate in Israel and the accident rate abroad is substantive and not spurious. To emphasize this globalization phenomenon, we refer to the model in Table 5 as we do. By contrast, in Table 6 all the variables are parochial; road quality (R), police enforcement (P), and the proportion of old vehicles (A). All the models reported in Table 6 imply that the accident rate varies inversely with road quality and police enforcement, and that it varies directly with the proportion of old vehicles. The estimated elasticity of the accident rate with respect to road quality ranges between −1.87 and − 2.3, while the elasticity with respect to the police enforcement rate ranges between − 0.28 and − 0.78. The elasticity for vehicle age structure ranges between 0.23 and 0.66. All the models show that the elasticity of the accident rate to road quality is relatively high, implying that if road quality is improved by 1%, the accident rate can be expected to fall by about 2% in the long-run. The elasticities in the case of police enforcement are smaller. The estimates of b5 in Table 6 turns out to be similar to its counterpart in Table 5. In both Tables 5 and 6 we report four versions of the Johansen estimates since they may be sensitive to the specification of the VAR (see Section 3). The results in both tables indicate that they are not sensitive to the specification of the trend (stochastic or deterministic), but they are sensitive to the VAR’s lag order. In Table

81

6 a second order VAR induces non-uniqueness in the co-integrating vector and substantially increases the estimate of b5. The evidence in favor of co-integration in Table 6 for the parochial model is less strong than it is for its global rival in Table 5. The ADF statistic is below its critical value at conventional p-values in Table 6 and the Johansen estimates indicate that co-integration depends upon the order of the VAR. On the other hand, the EG and DRM estimates indicate error correcting behavior (not reported) suggesting that the variables in the model are most probably co-integrated after all. Both in Tables 5 and 6 the Engle–Granger and DRM estimates tend to be similar. There is no intrinsic reason for this. Asymptotically the parameter estimates should be similar, however, in finite samples they may differ depending upon the effects of stationary shocks which will vanish asymptotically but which may persist in given samples. We experimented with a number of other parochial variables, including macro-economic variables (such as unemployment), demographic variables (such as the proportion of women and young drivers), and logistical variables (such as the proportion of motorcycles and taxis in the fleet, and the proportion of inter-urban kilometrage). We do not report these experiments in Table 6 because their co-integration properties were not robust. Nevertheless, they suggested that taxi drivers, motorcyclists, young drivers, and inter-urban driving are more accident prone, while women drivers are less accident prone. Also, unemployment has a positive effect on the rate of accidents. However, we are naturally less confident about these findings, than those featuring in Tables 5 and 6, because they are not statistically robust.

Fig. 7. (A): the proportion of the fleet aged in excess of 10 years.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

82 Table 5 Global model (1964–1994)a,b

Method of estimation Engle–Granger

aˆ b. 4 b. 5 Test

−7.512 1.213 0.358 ADF1 = −4.67 DF=−4.04 PP3 =−3.62

Johansen (VAR)

DRM

TS1

DS1

TS2

DS2

−7.848 1.32 0.658 r= 1

−7.817 1.312 0.66 r= 1

−7.902 1.485 1.457 r =2

−7.93 1.465 1.481 r= 2

−6.085 1.212 0.456 –

ln S= a+b4 ln S*+b5 ln A. DF, critical value for Dickey–Fuller statistic (MacKinnon, 1991) without augmentations; ADFp, augmented Dickey–Fuller statistic with p augmentation; PPp, Phillips–Perron statistic with p order lag truncation. The numerical suffix to DS and TS refers to the order of the VAR. The number of co-integrating vectors is denoted by r. a

b

6. Concluding remarks Our main finding is that the downward trend in the road accident rate in Israel is part of a global phenomenon. This is endorsed by the statistical significance of the age distribution of the vehicle fleet, which acts as an intervening variable between the domestic and ‘world’ accident rates. The more up-to-date the fleet, the lower is the domestic accident rate likely to be. This implies that policies which encourage the rejuvenation of the fleet, such as lower car taxes (in Israel the tax rate is 100%), should lower the accident rate because there will be safer cars on the roads. In 1995 27% of the fleet was older than 10 years, whereas in 1960 the proportion was 52%. If almost all the old vehicles were scrapped the annual accident rate would fall by 0.7 per million km driven to about 0.37. The implications of the parochial model regarding the age of the fleet are the same as in the global model. However, the parochial model has some additional implications, apart from the need to rejuvenate the fleet. Fig. 5 shows that between 1960 and 1995 road quality tripled; the capital invested per kilometer rose from about 350 000 shekels at 1990 prices (about $175 000) to 1.15 million shekels. The trend rate of increase in road quality is 3.3% per annum, which is currently equal to an investment of 37 950 shekels per year in each kilometer of road. According to the parochial model this investment in road quality achieves a 6.6% reduction in the accident rate, which is equal to a reduction in the accident rate from about 0.7 accidents per million kilometers driven to 0.657 accidents. A further implication of the parochial model is that the rate of police enforcement reduces the rate of road

accidents. In 1995 there were on average 0.6 vehicle apprehensions per year (see Fig. 6). Suppose that this rate were restored to unity, as a result of a policy to restore police enforcement to its peak in the 1970s and 1980s. The parochial model implies that the accident rate would fall from 0.7 per million kilometers driven to about 0.6. The global model does not attach importance to road quality and police enforcement. Instead it implies that as long as road safety technology continues to manifest itself in lower accident rates globally, the accident rate in Israel is likely to continue to fall. We do not try to explain the downward trend in the global accident rate, which remains a separate research topic. In this context it would be interesting to learn whether accident rates in the leading industrialized countries share a common stochastic trend. If so, it would lend additional support to the global model. A related extension of the globalization thesis is whether accident rates are converging from above. Suppose, for example, we take Norway as the technological leaders because it has the lowest accident rate. Is it the case, that other countries are closing the gap on Norway? Is it also the case that the most laggard countries relative to Norway are experiencing more negative time trends in their accident rates? If so, evidence such as this would be consistent with the globalization thesis. It would be of further interest to investigate whether the road accident rate in countries which do not import western vehicles and road technologies (such as the former Soviet bloc countries, Cuba and developing countries such as India) do not share a common stochastic trend. Such evidence would also be consistent with the globalization thesis.

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (2000) 71–84

83

Table 6 Parochial model (1960–1994)a,b Method of estimation Engle–Granger

aˆ b. 2 b. 3 b. 5 Test

a b

13.13 −1.87 −0.277 0.331 ADF= −3.52 DF = −4.43 PP3 =−3.58

Johansen (VAR)

DRM

TS1

DS1

TS2

DS2

19.143 −2.739 −1.380 0.729 r=0

20.959 −2.973 −1.620 0.746 r= 0

16.314 −2.308 −0.884 0.659 r= 1

15.659 −2.208 −0.780 0.662 r =1

8.938 −1.869 −0.358 0.228 –

ln S= a+b2 ln R+b3 ln P+b5 ln A . See notes to Table 5.

We have focussed exclusively on the accident rate. The analysis may be extended to fatality rates, and severity. Certain variables may have differential effects on accident and fatality rates. For example, seat-belt legislation might be expected to reduce severity without necessarily affecting the accident rate. Nevertheless, we do not consider that our preoccupation with accident rates undermines the basis of our globalization thesis. We hope that we have demonstrated the usefulness of unit root econometrics as a statistical tool for hypothesis testing when the data, as in the case of accident rates, happen to be non-stationary. Moreover, these techniques also extend to the statistical testing of the effects of discrete policy interventions upon accident rates when the data are non-stationary. For example, a new seat-belt law can be expected to induce a gradual, once-and-for-all lowering of the fatality rate without necessarily affecting its trend. The same applies to vehicle inspection policy (Loeb, 1987). In terms of Eq. (6) this may be represented by a discrete fall in a. The standard practice is to apply a dummy variable before and after the intervention. However, this practice is only appropriate if the data are stationary. If they are not stationary, inferences may be spurious (Perron and Vogelsang, 1992). For example, the fall in the accident rate that occurred in Victoria, Australia in the early 1990s following an intervention package introduced in 1989 (Cameron et al., 1995) may simply have been the renewal of a downward trend in the accident rate that would have occurred without the interventions. For a discussion of appropriate unit root methodologies for avoiding the estimation of spurious intervention effects see Gregory et al. (1996), Gregory and Hansen (1996) and Campos et al. (1996).

Acknowledgements We wish to thank the Editor and four referees for their helpful remarks.

References Broughton, J., 1991. Forecasting road accident casualties in Great Britain. Accident Analysis and Prevention 23, 353 – 362. Campos, J., Ericsson, N.R., Hendry, D.F., 1996. Co-integration tests in the presence of structural breaks. Journal of Econometrics 30, 187 – 220. Cameron, M., Newstead, S., Gantzer, S., Vulcan, P., 1995. Modelling of some major factors influencing road trauma trends in Victoria 1989 – 1993. Monash University, Accident Research Center, Report no. 74. Carr, A.F., Schnelle, J.F., Kirchner, R.E., 1980. Police crackdowns and slowdowns: a naturalistic evaluation of changes in police traffic. Behavioral Assessment 2, 33 – 41. Dickey, D.A., Fuller, W.A., 1981. Likelihood ratio statistics for autoregressive time series with unit roots. Econometrica 49, 1057 – 1972. Enders, W., 1995. Applied Econometric Time Series. John Wiley, New York. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation and testing. Econometrica 55, 251 – 276. Fuller, W., 1976. Introduction to Statistical Time Series. John Wiley, New York. Garbacs, C., Kelly, G., 1987. Automobile safety inspection: new econometric and benefit/cost estimates. Applied Economics 19, 763 – 771. Gharaybeh, F.A., 1994. Application of Smeed’s formula to assess development of traffic safety in Jordan. Accident Analysis and Prevention 26, 113 – 120. Gregory, A.W., Nason, J.M., Watt, D.G., 1996. Testing for structural breaks in co-integrated relationships. Journal of Econometrics 30, 321 – 341. Gregory, A.W., Hansen, B.E., 1996. Residual-based tests for co-integration in models with regime shifts. Journal of Econometrics 30, 99 – 126.

84

M. Beenstock, D. Gafni / Accident Analysis and Pre6ention 32 (1999) 71–84

Hakim, S., Shefer, D., Hakkert, A.S., Hocherman, I., 1991. A critical review of macro models for road accidents. Accident Analysis and Prevention 23, 379 – 400. Harvey, A.C., Durbin, J., 1986. The effects of seat belt legislation on british road casualties: a case study in structural time series modelling. Journal of Royal Statistical Society 149, 187–227. Hendry, D.F., 1995. Dynamic Econometrics. Oxford University Press. Johansen, S., 1995. Likelihood-Based Inference in Co-integrated Vector Auto-regressive Models. Oxford University Press. Johanssen, P., 1996. Speed limitation and motorway casualties: a time series count data regression approach. Accident Analysis and Prevention 28, 73 – 87. Lave, C.A., 1985. Speeding, coordination, and the 55 mph limit. American Economic Review 75, 1159–1164. Lave, L.B., Weber, W.E., 1970. A benefit–cost analysis of auto safety features. Applied Economics 2, 265–275. Loeb, P.D., 1987. The determinants of automobile fatalities with special

.

consideration to policy variables. Journal of Transport Economics and Policy 21, 279 – 287. MacKinnon, J.G., 1991. Critical Values for Co-integration Tests. In: Engle, R.F., Granger, C.W.J. (Eds.), Long-run Economic Relationships: Readings in Co-integration. Oxford University Press, Oxford, pp. 267 – 276. Oppe, S., 1991. The development of traffic and traffic safety in six developed countries. Accident Analysis and Prevention 23, 401– 412. Peltzman, S., 1975. The effects of automobile safety regulation. Journal of Political Economy 83, 677 – 725. Perron, P., Vogelsang, T.J., 1992. Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics 10, 301 – 320. Phillips, P.C.B., Perron, P., 1988. Testing for a unit root in time series regression. Biometrica 75, 435 – 452. Smeed, R.J., 1949. Some statistical aspects of road safety research. Journal of Royal Statistical Society A, 1 – 34.