variables. The C-statistics indicate that the instrument sets used for the three endogenous
variables are neither correlated to UNE rates nor endogenous.
Tests of Instrument Relevance
In addition to being orthogonal to the error term, instruments also must be
sufficiently correlated with the endogenous explanatory variables. To test for this, each
endogenous explanatory variable is regressed on all of the exogenous and instrumental
variables in the model. The coefficients on the instruments are then tested for whether
they are jointly equal to zero. To be valid, the coefficients should not jointly equal zero.
This test is complicated by the use of the system GMM estimator. By definition,
the system GMM estimator estimates two equations simultaneously, one in levels and the
other in first differences. The equation in levels is estimated along with the equation in
first differences because estimations in first differences with highly persistent dependent
variables result in weak instruments (Bond, 2002, p 154).
Table A-3 reports the results of the tests of instrument relevance for each of the
three endogenous explanatory variables for the equations in both levels and first
differences. The chi-square values suggest that the instruments easily pass the threshold
test for relevance except for the form of retail rate regulation variable in the first
differences equation. As noted above, this result is not worrisome as it is addressed by the
system GMM estimation.
Test of the Exogeneity of the Lagged Average Retail Rate
One may be concerned that the average retail rate variable is endogenous, even
though it is lagged one year. To test for this the C statistic can be used where the J
statistic from the model assuming the variable is endogenous is subtracted from the J