The claim that MGTOW makes is a bit different than the more widely made claim that women "control" 80% of spending. Drive means something different than control, but I'll answer this question based on the widely known claim about women controlling 80% of spending.
From Who Makes the Call at the Mall, Men or Women? (Carl Bialik - Wall Street Journal):
Several recent surveys suggest that men have nearly equal say on spending, and that when men and women live together, both participate in spending decisions.
The 80% figure is often repeated and is "ubiquitous", but it lacks a source.
Many marketing gurus who rely on the 80% figure cite the work of Marti Barletta. [...] Ms. Barletta concedes that she has no specific source for the figure.
One survey asked women the percentage of household spending they control or influence. The average answer was 73%. When men were asked what percentage of household spending they (men) control or influence, the average answer was 61%.