In order to better understand the various contributors, the Ministry of Transport commissioned an econometric analysis of the 2011 number of road deaths. The objective was to assess the degree to which the drop in 2011 could be attributed to any particular causes, rather than to random variation.
The econometric analysis was extended in 2013 to include 2012 road deaths data
An explanation of the methodology for econometric modelling
The method adopted was two stage. Firstly a long-term model was used to capture the downward trend in fatalities, and secondly a short-term model was developed to explain the remaining variation.
The underlying trend from 2000 to December 2010 was established to be 10.4 fewer deaths each year. Ongoing safety interventions and technology improvements have contributed to this ongoing improvement.
The graph below compares the actual road deaths with that predicted by the long term model. Quarter three is typically lower than the other quarters, so the model includes a seasonal effect for that quarter. That is why the predicted quarter three numbers are lower than the trend for the other quarters.
The long-term trend model predicts a number of road deaths of 355 for 2011, a decrease of 20 on 2010. The actual toll was 284, which was a decrease of 91 on 2010. That means the long-term trend explains 20 of the decrease of 91.
The short-term model was developed to explain the reduction in 2011, over and above the underlying trend. It was formulated using the data from 2000 to 2010, and provided the best predictor of the variation from the long term model that was seen in those years.
Among the factors considered were travel, advertising, enforcement, short-term changes in vehicle quality, weather, real GDP, terms of trade (possibly affecting rural travel), light vehicle prices, interest rates, alcohol consumption, Waitangi day and ANZAC day falling on weekends, unemployment, real wages, fuel prices, motorcycle registrations, real private consumption and vehicle speeds.
Many combinations of those data items were tested, and the best explanatory variables were determined to be petrol prices, real wages and motorcycle registrations. The short-term model was then applied to 2011.
There was a drop of 91 road deaths from 2010 to 2011. The short-term model (petrol prices, wage levels and motorcycle registrations) explained 21 of these deaths, the long-run trend explained 20 deaths. The remaining 50 deaths cannot yet be explained by trends and models, and could be random variation, but with the passage of time and further work, contributing factors may become more apparent.
In the graph below what the model predicts is shown by the red line and the actual number of road deaths is shown by the blue line. The model predicts the toll road well for the period it was fitted to (2000-2010) but does not predict all the drop experienced in 2011.