This dissertation consists of four essays that study topics in macroeconomics, finance and their interplay using nonlinear quantitative equilibrium models and state of the art econometric techniques. Chapter 1 proposes a general equilibrium model with financial intermediation and sovereign default risk to study the macroeconomic consequences of news regarding a future sovereign default. The model, estimated on Italian data, is used to measure the output losses of the 2010-2012 sovereign debt crisis, and to evaluate the effects of credit policies implemented by European authorities. Chapter 2 proposes a new class of time series model that can be used to measure nonlinearities in the data and to evaluate the fit of Dynamic Stochastic General Equilibrium (DSGE) models solved with high order perturbation. We first characterize this class, the Quadratic Autoregressive (QAR) model. We then show how the QAR model can be used as a diagnostic tool to assess whether a DSGE model is able to replicate the nonlinear behavior of a set of U.S. aggregate time series. Chapter 3 studies the determinants of medium term movements in the market value of U.S. corporations. We find that secular movements in the mean and volatility of TFP growth are strongly associated with these medium term fluctuations in asset prices. These empirical findings are then interpreted within a production based asset pricing model where the mean and volatility of aggregate productivity growth varies over time. We show that the model can rationalize a sizable elasticity of asset prices to the drivers of aggregate productivity. Chapter 4 proposes a method to identify Harrod-neutral technology shocks in the data in presence of input heterogeneity in the aggregate production function. We prove that, in a wide class of models, Harrod-neutral technology shocks are the only one consistent with a certain form of balanced growth. We then use this property to identify Harrod-neutral shocks using a state-space model. Monte Carlo simulations show that the proposed method performs very well in small samples
