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,
ylt = a + Xita + Vi + £it i = 1,........, N ; t = 1,........, T1 (5)
where yit is the ratio of fatalities to injuries (explained further in the next section) in an
observation unit i in a given time period t, Vl is the unit specific residual; it differs between
units but, for any particular unit its value is constant, εit is the usual residual with the
properties of mean 0, uncorrelated with itself, uncorrelated with Xlt, 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 ηit is independent and identically distributed with zero mean and
variance ση2, Vi 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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