New Keynesian dynamic stochastic general equilibrium models are the principal paradigm currently employed for central bank policymaking. In this paper, we construct experimental economies, populated with human subjects, with the structure of a New Keynesian DSGE model. We give individuals monetary incentives to maximize the objective functions in the model, but allow scope for agents' boundedly rational behavior and expectations to influence outcomes. Subjects participate in the roles of consumer/workers, producers, or central bankers. Our objective is twofold. The first objective is general, and is to create an experimental environment for the analysis of macroeconomic policy questions. The second objective is more focused and is to consider several specific research questions relating to the persistence of shocks, the behavior of human central bankers, and the pricing behavior of firms, using our methodology. We find that the presence of menu costs is not necessary to generate persistence of output shocks, but rather that monopolistic competition in the output market is sufficient. Interest rate policies of human discretionary central bankers are characterized by persistence in interest rate shocks, the use of the Taylor principle, and lower output and welfare than under an automated instrumental rule. Pattens in price changes conform closely to stylized empirical facts.