A Free-Market is based upon an institutional framework, voluntary exchange, property rights, the rule of law, etc. If you change the way that the institutions operate, you will change the outcome of events. The problem we face with our analysis of economic phenomena is that it is hard to observe counter-factual outcome. An example: policymakers often argued in 2008 that if the government had not intervened that the economic outcome that would have transpired would have been much worse. Critics of the intervention imagine a different counter-factual, one where the intervention actualy made things worse than they otherwise would have been. Because neither side can provide an undisputable empirical analysis, neither side can win the argument. All the economist can do is make an estimate based on certain assumptions.
However, proponents of the free-market do have some very large natural experiments and empirical data that they can point to on institutional analysis in other areas. The 20th century was defined, in economic circles, by the debate between the free-market (an 18th century idea) and the socialist state (a 19th century idea). From around 1920-1990, a very large natural experiment took place between the two competing institutions. Half the world adopted an approach that more closely resembled a free-market and the other half adopted the socialist state. The results were overwhelmingly favorable for the countries who adopted the free-market over the coercive power of the state in guiding economic life.
Our analysis of these results can be fogged by the issue of time and place. Americans became rich and prosperous in 20th century but they had advantages in natural resources, military power, a dominate currency, etc. In order to develop a deeper understanding of how institutions affect outcomes we need to look at the same people over a relatively short time frame.
The transformation of West Germany after World War II and the economic boom that followed the destruction that had occurred there was remarkable. East Germany had roughly the same demographics but were under the control of a very different institutional framework. The East Germans did not fare as well as the West Germans. In 1990, the two separate German states reunified. Our natural experiment gains a new dimension. We know how the East Germans fared under communism. How did they fare under the free market? Here is a photo gallery of the results since 1990.
Change the institutions, change the outcomes.