Table 7.

Random Generated Samples and Statistical significance, with and without refinement. Share of simulations

	p-value(Fstat${}_z$) $<$p-value(Fstat Data)
	Without refinement	With refinement
Random iid data	0.1%	0.1%
Random correlated data	0.0%	0.0%

Note: this table displays the share of simulations (out of 1000), in percent, for which the p-value of the F-statistics (null hypothesis: $H_0:$$\tilde{\beta }=0$, in model 2) is less than the one found in the data. The first row displays the results when the regressors are assumed to be iid. The second row displays the results when the regressors are assumed to have the same covariance matrix as the regressors in the data. The first column presents the results without the refinement, while the second column presents the results with the refinement.