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Further tests were also conducted on the
equations estimated to determine whether the
explanatory variables themselves (number of EGMs,
etc) are affected by the dependent
variable (regional gaming expenditure). This
“exogeneity” or feedback can be tested for
using the Generalised Method of Moments (GMM)
estimator. The model comprises four
simultaneous equations regressing gaming
expenditure at different time periods on current
and lagged values of the explanatory variable,
or regressor, with all variables in logarithms.
The stages involved in GMM estimation can be
summarised as follows:
reduced form equations are used to generate
predicted values for all current endogenous
variables, as in the first stage of 2-stage
least squares (2SLS);
two-stage least squares is applied to each
structural equation in turn, to obtain 2SLS
residuals. These residuals are then used to
estimate the elements of the contemporaneous
covariance matrix ?;
the GMM estimator is applied to the entire
system, with current endogenous variable
observations replaced by predicted values, and
with elements of the unknown matrix ?
replaced by estimates obtained in stage (2).
The GMM estimation procedure is equivalent to
3-stage least squares if the errors are serially
independent and the same variables are used for
each equation.
Tests were used to ascertain whether the
explanatory variables were fully or partially
exogenous:
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