美联储-有限状态马尔可夫链逼近：一种隐马尔可夫方法（英）-2023.6-62页_1mb

Key Contributions and Methodology

Objective: This paper introduces a novel approach to finite-state Markov-chain approximations for continuous-state Markov processes by employing a Hidden Markov Model (HMM) minimization framework based on Kullback-Leibler (KL) divergence to minimize information loss. It provides both optimal grid selection and transition probability matrices, applicable to univariate, multivariate, and non-stationary processes like those with life-cycle dynamics.

Methodology: The method minimizes the KL divergence between the true continuous process and an approximating HMM, where the latent states are discrete Markov chains embedded via Gaussian or general distributions. Under sufficient use of grid points, the method ensures the approximation converges to the true process. Theoretical proof establishes the universal approximation capability for stationary Markov processes with bounded conditional densities, leveraging Lipschitz continuity and ergodicity assumptions.

Applications: The paper evaluates the method in asset pricing (stochastic volatility model) and life-cycle consumption-saving models. It demonstrates superior performance in capturing higher-order moments like excess skewness and kurtosis, leading to more accurate model solutions. For example, in an asset-pricing model, KL divergence is significantly lower compared to binning-based methods, and in life-cycle models, discretization impacts welfare costs of risk, wealth inequality, and marginal propensities to consume.

Economic Implications: Discretization errors have substantial effects on key economic predictions. The approach yields parsimonious grids that reduce computational burden while maintaining accuracy, and differences in discretization methods quantitatively change outcomes in welfare and inequality indices. The method allows for consistent comparison across stochastic processes, such as those with persistent states versus mixture distributions.

Significance: This approach bridges econometric discretization techniques with machine learning insights, offering enhanced numerical methods for solving dynamic stochastic models. It underscores the importance of discretization quality in capturing risk and dynamics, with implications for policy analysis and applied economics.