Improvements in medical care and technology and reductions in traffic-related fatalities in Great Britain

The BHHH estimator can be used to estimate â (Greene, 2000).

We also use a simple ordinary least squares regression with fixed effects to analyze
models with ratios as dependent variables. This model is defined simply as,

y_lt = a + X_ita + Vi + £i_t      i = 1,........, N ; t = 1,........, T₁                          (5)

where y_it is the ratio of fatalities to injuries (explained further in the next section) in an
observation unit i in a given time period t, V_l is the unit specific residual; it differs between
units but, for any particular unit its value is constant, ε_it is the usual residual with the
properties of mean 0, uncorrelated with itself, uncorrelated with X_lt, uncorrelated with V
and homoskedastic. Other terms are as previously defined.

We also estimate a cross-sectional time series regression model when the disturbance
term is first-order autoregressive to correct for serial correlation in the data. We choose the
fixed-effects version of the linear model with an AR(1) disturbance that is defined simply as
equation (5) where

£it = p£i, t-ɪ + Vit                                                                               (6)

and where ∣p∣ < ɪ and η_it is independent and identically distributed with zero mean and
variance ση2, V_i are assumed to be fixed parameters and may be correlated with the
covarites Xit .

Results

Several models were developed to test the hypothesis of whether various proxies for
medical technology improvements are associated with reductions in traffic-related fatalities.
Table 2 has results for estimates using a fixed effects negative binomial model. The
dependent variables were total fatalities (model A and B), serious injuries (model C and D) ,
and slight injuries (model E and F). We include dummy variables for each year as opposed to
a year time trend variable which was correlated with some of our independent variables, but

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