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With such a large number of models and configurations, even within models based on the same level of data, it is difficult to summarise the results without completely reproducing the many tables from the study. To simplify matters here, models from each level of data will be discussed, in turn, with possible limitations. Then, the overall nature of the findings across the models and criticisms will be discussed.

2.9.2. 1 The 29 Year Annual Models

The 29 year annual models consisted of estimates for the following variables :

• Trend

• Unemployment Rate

• (OIL) Dummy variable for the 1973 Oil crisis

• (D 1973) Dummy variable for 1973 speed limit change

• (D1985) Dummy variable for 1985 speed limit change

• New car registrations

• Compulsory breath tests (CBTs) • (SHindex) Enforcement

• (ADindex) Advertising

• (SHindex * ADindex) Enforcement and advertising interaction

• (SRSP _* SHindex) SRSP and enforcement interaction • (SRSP * ADindex) SRSP and advertising interaction

The OIL variable was statistically non-significant across Fatalities, Non-motorcycle fatalities and fatal crashes so models were run with and without OIL. Otherwise all variables were significant when derived from the PCA analysis while very few were significant when using OlS. Guria and leung claim that this would be due to the problems of multicollinearity among the independent variables. Unfortunately, no measures are provided about the correlations among the independent variables.

The D1985 estimates are negative when an increase in the speed limit would be expected to result in an increase in fatalities. Guria and leung claim that the negative val ue for the D1985 estimates estimate are due to the increased vigilance of the Police when the limit was increased. However, they fail to provide any evidence to support this claim or any reasoning why this effect is not simply accounted for by the enforcement variable SHindex.

Both u nemployment and new cars a re negative and significant in the PCA models but non­ significant in the OLS models. Both of these variables are effectively measuring the same concept, the economy, and it is rather unusual to find them together in the same model for this reason a lone. As a result, it is very likely that they are highly correlated with one another and therefore it is no surprise that they are non-significant in the OLS models. Furthermore, Guria a nd Leung do not explain why an economic indicator is required in the model when the dependent variables are normalized by the traffic volume index (TV!). The TV! would be expected to be highly correlated to the economy however without access to the analysis data this can not be verified. Inclusion in the model of any economic indicators would lead to an upward bias of their impact on the dependent variable. Therefore, the decision to include both the TV!, through normalization of the dependent variables and not one but two measures of the economy, raises questions about the validity of the model's estimates. Furthermore, Guria and Leung claim that the unexpected negative estimate for new cars points to the greater safety of increased imported cars. However, the 29 year period ( 1971 to 2000) covered by Guria and Leung's models stretches beyond the period import

restrictions were relaxed in New Zealand in 1989. To a pply this one micro-event to the overall measure of new car registrations is inappropriate and would be better represented by the inclusion of a specific indicator variable.

All the intervention coefficients in the PCA models are negative and significant which is what would be expected if the interventions were effective in reducing road fatalities. However, this is not the case with the OLS estimates and, again, Guria and Leung claim that this is simply due to multicollinearity. From the PCA regression results Guria and Leung claim that the advertising and enforcement have significantly reduced road trauma. Furthermore, because the interactions between the SRSP and the advertising and enforcement a re significant, the change in these interventions by the SRSP has resulted in g reater benefits than were achieved beforehand. Finally, the interaction between the advertising and enforcement indicates that there is a complementary effect over and a bove their individual impact on road trauma.

However, there is a question mark over how far the results can be generalised from these models. With only 29 data points for each variable and 12 independent variables, the models easily exceed the recommended ratio of five observations for each independent variable with a ratio of 2.4: 1 and is likely to result in the over fitting of the variate to the sample (Hair et al., 1998). It is difficult to extend the results further without validation against another time series. On the other hand, this problem may be reduced by collaborating results from the other models.

2.9.2.2 The 10 Year Annual Models

Clearly, a model with only 10 data points is of limited a pplication but Guria and Leung repeatedly claim that while there are problems with the individual models, consistent results across the models will overcome any shortfalls with the individual models. Despite these claims, the number of independent variables almost exceeds the number of data pOints at

nine to ten or a ratio of 1 . 1 : 1 and clearly the variate is again being over fitted to the sample making the results potentially too specific to the sample.

The 10 year annual models used the following independent variables:

• Trend

• Unemployment Rate

• Compulsory breath tests (CBTs) • (SHindex) Enforcement

• (ADindex) Advertising

• (SHindex * ADindex) Enforcement and advertising interaction

• (SRSP * SHindex) SRSP and enforcement interaction

• (SRSP _* ADindex) SRSP and advertising interaction

The trend was significant in all the 10 year annua l models suggesting that variables not included in the model have been contributing to a downward trend on road fatalities and crashes. However, unemployment was non-significant except for the model using fatal crashes. Furthermore, in this model, half the intervention variables had signs opposite to what was expected by Guria and Leung. When unemployment was removed, the affected variable's sign reversed and increased in magnitude. On the other hand, when the previously non-significant intervention variables were removed a nd unemployment retained,

unemployment continued to be significant and the other intervention variables became positive. Guria and Leung suggest that there is a possibility that unemployment captured the effects of the other variables it is highly correlated with and therefore should not be included . Without access to the data set it is difficult to say whether this action is based on

convenience or good theory. As alluded to before in the discussion of the 29 year models, one would expect that estimates for economic indicators, such as unemployment, would be upwardly biased as a result of the normalization of the dependent variables by the 1VI. Unfortunately, further analysis is required before the validity of Guria and Leung's actions and subsequent claims can be more fully assessed.

are consistent in direction and significance for the PCA regressions. Once again, the OLS results vary in terms of direction, magnitude and significance. Nonetheless, the interplay between the small sample size and the ratio of the number of independent variables, relative to the sample size, may be playing a part in the failure to obtain significant estimates using standard OLS regression.

2.9.2.3 The 10 Year Quarterly Models

The 10 year Quarterly models contained estimates for the following variables:

• Dummy variable for 4th Quarter (54) • Trend

• Unemployment Rate

• Compulsory breath tests (CBTs)

• Dummy variable for both the CBT and Speed programmes (CBTSPD)

• Enforcement (SHindex) • Advertising (ADindex)

• Enforcement and advertising interaction (SHindex * ADindex)

• SRSP and enforcement interaction (SRSP * SHindex) • SRSP and advertising interaction (SRSP * ADindex)

The seasonal dummy variable for the 4th quarter was significant and positive across all the PCA and OLS regressions, indicating higher levels of risk than other quarters. However, no estimates were provided for the other quarters. The trend was again significant and negative across all the PCA and OLS regression models which are consistent with the previous models. Once again, the estimates for enforcement and advertising are significant in the PCA

regressions but inconsistent and varied in the OLS regression models. In contrast, the interaction term for the SRSP and enforcement is positive and significant rather than

negative. Guria and Leung claim that this could be d ue to poor data quality as they assumed the SHindex and ADindex were the same across all quarters when they were not in reality. One can only assume that the claim of poor data quality was not extended to the other estimates for advertising and enforcement because the estimates were consistent with previous results and claims.

Therefore, it would appear that Guria and Leung are stating the quarterly estimates merely played a confirmatory role to the smaller and possibly i nferior 10 year annual and 29 year annual model estimates. The sample size relative to the number of independent variables is

higher for the q uarterly models at 4: 1 than the other two model series so one would assume that the quarterly models wou ld play a leading role in the formation of conclusion as opposed to a supporting role. Guria a nd Leung did not provide any reasoning for this unusual

viewpoint. Furthermore, if Guria and Leung were aware that the assumption of the quarterly advertising and enforcement was incorrect, why did they not simply re-estimate the quarterly numbers to better reflect the actual situation? They acknowledged the use of adstock to represent advertising in their introduction, yet for some unknown reason chose to disregard the measure in favor of estimated expenditure. This decision would appear to undermine the validity of their models and their subsequent claims.

There does not appear to be any obviously apparent reason why Guria a nd Leung did not chose to use monthly level data for their models. Using their model specifications, the data would be either obtainable or able to be constructed at the lower level but more importantly it would have possibly reduced the issue of multicollinearity and the subsequent complexity in the use of PCA regression. Monthly level data would have provided g reater levels of

variability, reduced collinearity and greater degrees of freedom.

2.9.3 Conclusions and Implications of Guria and Leung's (2004) Models

At the beginning of the study, Guria and Leung claim that because of data limitations, no single model would be a ble to provide sufficient confidence, but if the estimates were

consistent across the models, confidence would be improved. The study contains constructed data for all the key intervention variables and the quality of the assumptions underlying the development of the data has even been questioned by the authors themselves. They also claim that they were unable to derive the benefits for the advertising and enforcement components as the estimated savings were inconsistent across the models. Guria and Leung eventually concede that no conclusions can be drawn a bout the advertising or enforcement effects due to problems with multicollinearity and the claimed complementary effects of these two interventions.

Despite these substantive limitations, Guria and Leung (2004) still claim that the results across the models are (p.904) "mostly consistent" and that this somehow suggests "strong validity". What's more, they then claim that the SRSP contributed to an estimated saving of

333 lives and that the package has made a substantial impact on road safety. The conclusions of this study do not match at all well the u nderlying self-acknowledged reservations and limitations of the study. Without further validation one cannot have confidence in Guria and Leung's (2004) claims.