Tests of Instrument Validity and the Exogeneity of the Average Retail Rate Variable
This section outlines how the validity of the instruments used in the UNE rates
regressions is tested. The first sub-section describes the tests performed to determine if
the instruments are not correlated with the error term, while the second sub-section
details the test used to determine if the instruments are sufficiently correlated with the
endogenous explanatory variables.
The third sub-section explains the econometric test used to confirm that the lagged
average retail rate is exogenous to the determination of UNE rates.
(This section borrows heavily from Baum, Schaffer, and Stillman (2004).)
Tests of Instruments' Orthogonality to the Error Process
When there are more instruments than endogenous variables (i.e., the model is
overidentified), one can test whether all of the instruments are orthogonal to the error
term. In GMM estimation the overidentifying restrictions can be tested with Hansen's J
statistic, which if found to be greater than a threshold value indicates that the instruments
are not exogenous or that they should be included as explanatory (rather than
instrumental) variables in the regression. The J statistics are reported in Table A-2. The J
statistics for the base model suggest that the instrument set as a whole is orthogonal to the
error term.
One can also test whether subsets of instruments are orthogonal to the error
process. The test statistic (referred to as the C statistic) is the difference in J statistics
between the specification that includes all the instruments and the specification that
excludes the instruments to be tested. If the C statistics exceeds a threshold value, there is
cause for concern that the tested instruments are not valid. Table A-2 also details the C
statistics for the instrument sets used for each of the three endogenous explanatory