- Email: [email protected]
The effects of seat belt legislation on British road casualities: A case study in structural modelling
J. Scott Armstrong, Research on forecasting: a quarter-century Znterfuces 16 : 1 (1986) 89-109.
review, 1960-1984,
with comment,
Armstrong summaries the state of forecasting in 1960 by offering eight guidelines (1960’s style). He then comments on how they have stood up to the last 25 years of research. The guidelines are concerned with: (1) decomposition of a forecasting problem, (2) extrapolation, (3) expert opinion, (4) intentions surveys, (5) the accuracy of econometric models, (6) combining forecasts, (7) prediction intervals, and (8) implementation. Armstrong argues that the areas that have seen the highest payoff have been research on expertise, and on the combination of forecasts. For the future he forecasts that decomposition, expertise (again), prediction intervals and implementation will come into their own. The commentators, Makridakis, Gardner, Schultz and Fischhoff, differ in their emphasis from Armstrong. Like them, I would question the small print of Armstrong’s conclusions. Where all contributors agree, is that the thrust of research into questions of the empirical accuracy of different forecasting approaches have proved productive, and in Fischhoff’s words, have moved forecasting from a quasi-science, to a situation where vigorous peer review and self-criticism have led to the professionalisation of forecasting. There’s still plenty of productive research to be done though, and the controversies this interesting review highlight are good places to start. - Robert Fildes [Professor J. Scott Armstrong, Department vania, Philadelphia, PA 19104, USA]
of Marketing,
Wharton
School, University
of Pennsyl-
A.C. Harvey and J. Durbin, The effects of seat belt legislation on British road casualities: A case study in structural modelling (with discussion), Journal of the Royal Statistical Society, Series A 149 (1986) (in press). The class of structural models is reviewed by Harvey (1984). Structural models are related to various other classes of model, including state-space models and the dynamic linear model of Harrison and Stevens (1976) - see, for example, Abraham and Ledolter (1986). The Kalman filter provides a convenient way of updating the model when a new observation becomes available. The basic structural model (BSM) assumes additive trend and seasonal terms which are themselves locally updated. The resulting procedure is related to the Holt-Winters exponential smoothing approach, but has the added advantages that prediction MSE’s can be calculated, that data irregularities can be handled more easily, and that it can be extended to incorporate explanatory variables. This case study applies the BSM, with explanatory variables, to British road accident data showing numbers killed and seriously injured (KSI) for various categories of road user from 1969 to 1984. Seat belt legislation was introduced at the end of January, 1983, and forecasts were computed from that date for comparison with the actual numbers. There is a drop of about 10% in the number of car drivers KSI. The results for front-seat passengers are even better, but there are worrying increases in numbers killed for rear-seat passengers, cyclists, and pedestrians. The paper also makes some controversial remarks about ARIMA modelling. In particular the authors say they ‘have become disenchanted with the notion that the appropriate way to deal with trend and seasonal components is to eliminate them by differencing’. They also say that they are ‘sceptical about the emphasis on stationarity of the differenced series’. The authors also point out that ARIMA modelling began after the advent of Kalman -filtering, and clearly believe that, with
hindsight, the structural-approach route would have been better. As this paper was read to the Royal Statistical Society, a complete record of the ensuing discussion is also published. As often happens, the discussion is arguably as interesting as the paper itself. The paper was generally well received, and there was wide approval for adding structural models to the set of models available to the time-series analyst. Inevitably there were some remarks of caution or of disagreement, and it is not yet obvious that structural modelling should occupy as important a place in time-series modelling as the authors appear to suggest. Dr. G. Tunnicliffe-Wilson rose to the ARIMA challenge by demonstrating that ARIMA forecasts can be found which are nearly identical to the structural forecasts. My own contribution to the discussion produced Holt-Winters forecasts which are also very similar. A completely different viewpoint was taken by J.G.U. Adams, who is the leading proponent of the theory of risk compensation. Adams suggested that factors other than seat-belt legislation may account for the apparent reduction in numbers KS1 since January 1983. Several discussants also pointed out that it is not easy in practice to say exactly who is ‘seriously injured’ and so the data thereon should be viewed with caution. Other aspects of the data or of structural modelling were also discussed, after which the authors replied to the points raised. Many readers should find it rewarding to study the entire discussion. - Chris Chatfield References Abraham, B. and J. Ledolter, 1986, Forecast functions implied by autoregressive integrated moving average related forecast procedures, International Statistical Review 54, 51-66. Harrison, P.J. and C.F. Stevens, 1976, Bayesian forecasting (with discussion), Journal of the Royal Statistical
models
and other
Society,
Series B,
School of Economics, Houghton
Street,
38,205-247. Harvey,
A.C.,
1984, A unified
view
of statistical
forecasting
procedures,
[Professor A.C. Harvey, Department London WC2A 2AE, UK]
of Statistics, London
Robert B. Litterman, A statistical Economic Statistics 4 (1986) l-4.
approach
Journal
to economic
of Forecasting
forecasting,
3, 245-275.
Journal of Business and
Stephen K. McNees, Forecasting accuracy of alternative techniques: A comparison of US macroeconomic forecasts, with comment, Journal of Business and Economic Statistics 4 (1986) 5-23. Robert B. Litterman, Forecasting with Bayesian Vector Autoregressions Journal of Business and Economic Statistics 4 (1986) 25-38.
- Five years of experience,
These three articles describe the Litterman-Sims approach to macroeconomic forecasting with McNees offering an evaluation of the historical record of the Litterman forecasts. Litterman’s model is unusual in that only limited information is presumed known about the economic structure of the system being modelled The core model does not define any variables as exogenous to the system, modelling all variables in the form Y(t)=D(t)+xB,Y(t-j)+e(t), nX1
nX1
nXnnX1
nXl
review, 1960-1984,
with comment,
Armstrong summaries the state of forecasting in 1960 by offering eight guidelines (1960’s style). He then comments on how they have stood up to the last 25 years of research. The guidelines are concerned with: (1) decomposition of a forecasting problem, (2) extrapolation, (3) expert opinion, (4) intentions surveys, (5) the accuracy of econometric models, (6) combining forecasts, (7) prediction intervals, and (8) implementation. Armstrong argues that the areas that have seen the highest payoff have been research on expertise, and on the combination of forecasts. For the future he forecasts that decomposition, expertise (again), prediction intervals and implementation will come into their own. The commentators, Makridakis, Gardner, Schultz and Fischhoff, differ in their emphasis from Armstrong. Like them, I would question the small print of Armstrong’s conclusions. Where all contributors agree, is that the thrust of research into questions of the empirical accuracy of different forecasting approaches have proved productive, and in Fischhoff’s words, have moved forecasting from a quasi-science, to a situation where vigorous peer review and self-criticism have led to the professionalisation of forecasting. There’s still plenty of productive research to be done though, and the controversies this interesting review highlight are good places to start. - Robert Fildes [Professor J. Scott Armstrong, Department vania, Philadelphia, PA 19104, USA]
of Marketing,
Wharton
School, University
of Pennsyl-
A.C. Harvey and J. Durbin, The effects of seat belt legislation on British road casualities: A case study in structural modelling (with discussion), Journal of the Royal Statistical Society, Series A 149 (1986) (in press). The class of structural models is reviewed by Harvey (1984). Structural models are related to various other classes of model, including state-space models and the dynamic linear model of Harrison and Stevens (1976) - see, for example, Abraham and Ledolter (1986). The Kalman filter provides a convenient way of updating the model when a new observation becomes available. The basic structural model (BSM) assumes additive trend and seasonal terms which are themselves locally updated. The resulting procedure is related to the Holt-Winters exponential smoothing approach, but has the added advantages that prediction MSE’s can be calculated, that data irregularities can be handled more easily, and that it can be extended to incorporate explanatory variables. This case study applies the BSM, with explanatory variables, to British road accident data showing numbers killed and seriously injured (KSI) for various categories of road user from 1969 to 1984. Seat belt legislation was introduced at the end of January, 1983, and forecasts were computed from that date for comparison with the actual numbers. There is a drop of about 10% in the number of car drivers KSI. The results for front-seat passengers are even better, but there are worrying increases in numbers killed for rear-seat passengers, cyclists, and pedestrians. The paper also makes some controversial remarks about ARIMA modelling. In particular the authors say they ‘have become disenchanted with the notion that the appropriate way to deal with trend and seasonal components is to eliminate them by differencing’. They also say that they are ‘sceptical about the emphasis on stationarity of the differenced series’. The authors also point out that ARIMA modelling began after the advent of Kalman -filtering, and clearly believe that, with
hindsight, the structural-approach route would have been better. As this paper was read to the Royal Statistical Society, a complete record of the ensuing discussion is also published. As often happens, the discussion is arguably as interesting as the paper itself. The paper was generally well received, and there was wide approval for adding structural models to the set of models available to the time-series analyst. Inevitably there were some remarks of caution or of disagreement, and it is not yet obvious that structural modelling should occupy as important a place in time-series modelling as the authors appear to suggest. Dr. G. Tunnicliffe-Wilson rose to the ARIMA challenge by demonstrating that ARIMA forecasts can be found which are nearly identical to the structural forecasts. My own contribution to the discussion produced Holt-Winters forecasts which are also very similar. A completely different viewpoint was taken by J.G.U. Adams, who is the leading proponent of the theory of risk compensation. Adams suggested that factors other than seat-belt legislation may account for the apparent reduction in numbers KS1 since January 1983. Several discussants also pointed out that it is not easy in practice to say exactly who is ‘seriously injured’ and so the data thereon should be viewed with caution. Other aspects of the data or of structural modelling were also discussed, after which the authors replied to the points raised. Many readers should find it rewarding to study the entire discussion. - Chris Chatfield References Abraham, B. and J. Ledolter, 1986, Forecast functions implied by autoregressive integrated moving average related forecast procedures, International Statistical Review 54, 51-66. Harrison, P.J. and C.F. Stevens, 1976, Bayesian forecasting (with discussion), Journal of the Royal Statistical
models
and other
Society,
Series B,
School of Economics, Houghton
Street,
38,205-247. Harvey,
A.C.,
1984, A unified
view
of statistical
forecasting
procedures,
[Professor A.C. Harvey, Department London WC2A 2AE, UK]
of Statistics, London
Robert B. Litterman, A statistical Economic Statistics 4 (1986) l-4.
approach
Journal
to economic
of Forecasting
forecasting,
3, 245-275.
Journal of Business and
Stephen K. McNees, Forecasting accuracy of alternative techniques: A comparison of US macroeconomic forecasts, with comment, Journal of Business and Economic Statistics 4 (1986) 5-23. Robert B. Litterman, Forecasting with Bayesian Vector Autoregressions Journal of Business and Economic Statistics 4 (1986) 25-38.
- Five years of experience,
These three articles describe the Litterman-Sims approach to macroeconomic forecasting with McNees offering an evaluation of the historical record of the Litterman forecasts. Litterman’s model is unusual in that only limited information is presumed known about the economic structure of the system being modelled The core model does not define any variables as exogenous to the system, modelling all variables in the form Y(t)=D(t)+xB,Y(t-j)+e(t), nX1
nX1
nXnnX1
nXl