Basically, US postwar economic history falls into two parts: an era of high taxes on the rich and extensive regulation, during which living standards experienced extraordinary growth; and an era of low taxes on the rich and deregulation, during which living standards for most Americans rose fitfully at best.
From Down The Memory Hole - Paul Krugman Blog - NYTimes.com

While this doesn’t show causation; it does show that the claims on the right about the New Deal causing economic stagnation and Reaganomics creating a boom are unsupported.