Research

This paper introduces a computationally efficient method for full-information estimation of nonlinear Dynamic Stochastic General Equilibrium (DSGE) models. In contrast to the traditional approach of treating model solution and filtering as two separate and potentially computationally intensive steps, we integrate the solution into the filtering procedure. The method computes a sequence of local linear solutions at the best forecast of the current state, yielding a time-varying linear state-space system for likelihood evaluation via the Kalman filter. The method captures nonlinear dynamics with high accuracy while avoiding global solution methods and nonlinear filtering, resulting in computational gains of several orders of magnitude. We benchmark the approach on canonical labor search and New Keynesian (NK) models. Applied to an NK model with labor market frictions, the method shows that these frictions generate state-dependent monetary policy transmission consistent with empirical evidence from local projections. The framework extends to models with stochastic volatility, regime switching, and heterogeneous agents.

Without regularization, vector autoregressions (VARs) with many variables suffer from large standard errors and poor out-of-sample forecasting performance. Regularization is typically associated with a bias-variance trade-off; however, we show that in finite samples, imposing parameter equality restrictions — akin to clustering parameters along both rows and columns of the coefficient matrix — can reduce bias and variance by mitigating second-order bias, even when the restrictions are mildly misspecified. We introduce the Matrix Dirichlet Process (MDP) prior for VARs, which remains agnostic ex ante about the appropriate restrictions by jointly sampling the clustering structure and parameter values within a computationally efficient Gibbs sampling framework. Simulations and three applications — forecasting personal income growth across U.S. states, estimating an 18-variable proxy SVAR to identify the effects of monetary policy, and analyzing price spillovers across 24 industries in response to uncertainty shocks — demonstrate that the MDP prior recovers intuitive economic relationships and improves forecasting accuracy.

This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and transition probability matrix. The method can be used for multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made arbitrarily small if enough grid points are used. We compare our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find our method leads to more parsimonious discretizations and more accurate solutions, and the discretization matters for the welfare costs of risk, the marginal propensities to consume, and the amount of wealth inequality a life-cycle model can generate.

Many macroeconomic models, including heterogeneous agent models, have a block structure that allows for multi-step estimation, where a subset of its parameters can be identified and estimated using a subset of moment conditions, independent from the other model parameters. Multi-step estimators, while less efficient in the absence of misspecification, can isolate subsets of parameters from misspecification in other parts of the model, and efficiency losses are therefore directly rewarded by robustness gains. I illustrate this in the workhorse heterogeneous household model of Aiyagari (1994) by establishing its block structure and showing how the firm-side parameters can be isolated from misspecification in the earnings process of the households. Similarly, in the workhorse heterogeneous firm model of Khan and Thomas (2008), I show that a one-step estimation procedure can overestimate the adjustment cost of capital by as much as 90 percent when omitting investment shocks from the aggregate shock process, while its two-step estimator is unaffected.

This paper provides a novel characterization of time-varying heterogeneous earnings risk through a Markov process with heterogeneous transition probabilities. The resulting earnings process allows for a richer notion of earnings risk heterogeneity than previously studied by the literature. Assumptions are derived under which a combination of savings and earnings data can be used to identify the earnings process parameters. Alternatively, a narrower interpretation of earnings risk can be adopted, limiting risk heterogeneity to heterogeneous variances of earnings shocks, such that the earnings process is identifiable from earnings data only. This gives rise to two identification strategies. Applying both strategies to the Survey of Income and Program Participation dataset shows that individuals face considerable inequality of earnings risk. High-risk states are found to be temporary, while low-risk states are persistent. Comparing both strategies shows that only allowing for variance heterogeneity is too restrictive, and a rich notion of risk is required to capture the joint dynamics of individuals' savings and earnings.