TANK Models with Amplification and no Puzzles: the Magic of Output Stabilization and Capital
We show that the standard two-agent new Keynesian (TANK) model without capital is able to produce monetary policy amplification and no forward guidance puzzle. This finding contrasts with the previous literature that argued that both results cannot be achieved simultaneously. Our key ingredient is output stabilization in the Taylor rule, and we do not rely on the presence of idiosyncratic uncertainty. For both deterministic and stochastic versions, we derive novel closed form solutions for all conceivable cases of eigenvalues and analyze the effects of redistribution between participants and non-participants in asset markets. A stochastic version of the model predicts that positive productivity shocks always worsens consumption inequality, which is counterfactual. Finally, we built a version of the model with capital which realistically predicts that consumption inequality can either increase or decrease in response to shocks. Moreover, the forward guidance puzzle is resolved even without output stabilization in the Taylor rule.