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This dissertation investigates non-linear macroeconomic dynamics within the New Keynesian model during periods with zero short-term nominal interest rates. I implement modern quantitative tools to solve and analyze Dynamic Stochastic General Equilibrium (DSGE) models where the feedback rule that defines monetary policy is subject to the Zero Lower Bound (ZLB) constraint. The revived attention about the importance of the ZLB constraint followed the extreme events that took place in the United States after the financial crisis of 2008.

The first chapter studies aggregate dynamics near the ZLB of nominal interest rates in a medium-scale New Keynesian model with capital. I use Sequential Monte Carlo methods to uncover the shocks that pushed the U.S. economy to the ZLB during the Great Recession and investigate the interaction between shocks and frictions in generating the contraction of output, consumption and investment during 2008:Q3-2013:Q4. I find that a combination of shocks to the marginal efficiency of investment and to households’ discount factor generated the prolonged liquidity trap observed in this period. A comparison between these two sources suggests that investment shocks played a more important role in accounting for the contraction of economic activity. Fiscal and monetary policy stimulus helped the U.S. economy avoid deflation and accelerated the recovery.

The second chapter studies a New-Keynesian model with Markov sunspot shocks that move the economy between a targeted-inflation regime and a deflation regime and fit it to data from the U.S. and Japan. For the U.S. we find that adverse demand shocks have moved the economy to the zero lower bound (ZLB) in 2009 and an expansive monetary policy has kept it there subsequently. In contrast, Japan has experienced a switch to the deflation regime in 1999 and remained there since then, except for a short period. The two scenarios have drastically different implications for macroeconomic policies. Fiscal multipliers are about 20% smaller in the deflationary regime, despite the economy remaining at the ZLB. While a commitment by the central bank to keep rates near the ZLB doubles the fiscal multipliers in the targeted-inflation regime (U.S.), it has no effect in the deflation regime (Japan).