In recent years, New Keynesian dynamic stochastic general equilibrium (NK DSGE) models have become increasingly popular in the academic literature and in policy analysis. However, the success of these models in reproducing the dynamic behavior of an economy following structural shocks is still disputed. This paper attempts to shed light on this issue. We use a VAR with sign restrictions that are robust to model and parameter uncertainty to estimate the effects of monetary policy, preference, government spending, investment, price markup, technology, and labor supply shocks on macroeconomic variables in the United States and the euro area. In contrast to the NK DSGE models, the empirical results indicate that technology shocks have a positive effect on hours worked, and investment and preference shocks have a positive impact on consumption and investment, respectively. While the former is in line with the predictions of Real Business Cycle models, the latter indicates the relevance of accelerator effects, as described by earlier Keynesian models. We also show that NK DSGE models might overemphasize the contribution of cost-push shocks to business cycle fluctuations while, at the same time, underestimating the importance of other shocks such as changes to technology and investment adjustment costs.