Agent-Level Adaptive Learning

Adaptive learning is a boundedly rational alternative to rational expectations that is increasingly used in macroeconomics, monetary economics, and financial economics. The agent-level approach can be used to provide microfoundations for adaptive learning in macroeconomics. Two central issues of bounded rationality are simultaneously addressed at the agent level: replacing fully rational expectations of key variables with econometric forecasts and boundedly optimal decisions-making based on those forecasts. The real business cycle (RBC) model provides a useful laboratory for exhibiting alternative implementations of the agent-level approach. Specific implementations include shadow-price learning (and its anticipated-utility counterpart, iterated shadow-price learning), Euler-equation learning, and long-horizon learning. For each implementation the path of the economy is obtained by aggregating the boundedly rational agent-level decisions. A linearized RBC can be used to illustrate the effects of fiscal policy. For example, simulations can be used to illustrate the impact of a permanent increase in government spending and highlight the similarities and differences among the various implements of agent-level learning. These results also can be used to expose the differences among agent-level learning, reduced-form learning, and rational expectations. The different implementations of agent-level adaptive learning have differing advantages. A major advantage of shadow-price learning is its ease of implementation within the nonlinear RBC model. Compared to reduced-form learning, which is widely use because of its ease of application, agent-level learning both provides microfoundations, which ensure robustness to the Lucas critique, and provides the natural framework for applications of adaptive learning in heterogeneous-agent models.

Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

Bayesian Estimation of Economic Simulation Models Using Neural Networks

Recent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly agent-based models, are able to replicate a number of empirically-observed stylised facts not easily recovered by more traditional alternatives, such models remain notoriously difficult to estimate due to their lack of tractable likelihood functions. While the estimation literature continues to grow, existing attempts have approached the problem primarily from a frequentist perspective, with the Bayesian estimation literature remaining comparatively less developed. For this reason, we introduce a widely-applicable Bayesian estimation protocol that makes use of deep neural networks to construct an approximation to the likelihood, which we then benchmark against a prominent alternative from the existing literature. Overall, we find that our proposed methodology consistently results in more accurate estimates in a variety of settings, including the estimation of financial heterogeneous agent models and the identification of changes in dynamics occurring in models incorporating structural breaks.