Does Black's output variability hypothesis hold for Mexico?

We study, using two data series, namely GDP and the index of industrial production, the relationship between output variability and the growth rate of output for Mexico. Ng-Perron unit root test shows that the growth rate of GDP is non-stationary but the growth rate of industrial output is stationary. Therefore, we use the ARCH-M model for the monthly data of industrial output. A number of specifications (with and without a dummy variable) are used. In all cases, the results show that output variability for Mexico has a negative but insignificant effect on the growth rate of output.