Actually this does NOT hint at an answer the counterfactual. Because spending is unchanged as a result of lower taxes from the government. Government spends as much as it did before cutting taxes (this is because the federal government doesn't spend taxes, but spends regardless of tax income. This is what is called the deficit).

If a study was done to answer the counterfactual, my bet is that the result of higher taxes would actually increase GDP because the rich will do everything possible not to pay for those taxes. So they will do things like spend more on R&D, or increase wages, or buy equipment. In other words reduce their tax burden. If given the choice between the government burning profits via taxes, or spending more on wages and investment, they will choose the latter.