Essays in financial economics

Abstract

This thesis consists of three chapters on asset pricing, dynamic stochastic general equilibrium and structural estimation of dynamic models. Chapter 1 introduces a global, nonlinear numerical method to solve a large class of continuous-time models in economics and finance. Using modern tools from Machine Learning, I show that the problem of solving the corresponding nonlinear partial differential equations (PDEs) can be recast as a sequence of supervised learning problems. Furthermore, I propose a setting to test and evaluate solution methods. In the context of a Neoclassical Growth Model, given any value function, the productivity function can be reverse engineered so that the Hamilton-Jacobi-Bellman (HJB) equation corresponding to the dynamic optimization problem is identically zero. This provides a testing ground for solution methods. Chapter 2 leverages the algorithm developed in chapter 1 to do structural estimation of stochastic dynamic models in economics. By extending the state space to include all model parameters, I show that we need to solve the model only once to do structural estimation. Parameters are then estimated by minimizing the distance between key empirical moments and the model-implied ones. Unlike the Simulated Method of Moments, the model-implied moments are estimated without the computation of a single moment. Instead, a neural network learns the corresponding moments using raw simulated observations. In chapter 3 I study a multi-sector production-based economy where countercyclical risk premia and capital reallocation lengthens recessions. In the model, risk-aversion increases after negative productivity shocks, and the ensuing capital reallocation propagates the reduction in aggregate productivity and aggregate consumption. The decrease in consumption keeps the risk aversion high, preventing a quick recovery to the balanced growth path.