2023-07-05-美联储-有限状态马尔可夫链逼近_一种隐马尔可夫方法_62页_1mb

报告摘要

Methodology:

Proposes a novel finite-state Markov-chain approximation by minimizing Kullback-Leibler (KL) divergence between a misspecified Hidden Markov Model (HMM) and the true continuous process, using a full-information approach.
The HMM embeds a discrete Markov chain into a continuous process via Gaussian measurement errors, enabling quasi-maximum likelihood estimation with simulated data.
Proves that under certain conditions (Assumptions A1-A5), increasing grid points reduces KL divergence, making the approximation arbitrarily accurate for stationary, first-order Markov processes.

Key Contributions:

Provides both optimal grid points and transition probabilities, avoiding tensor grids to mitigate the curse of dimensionality.
Offers computational advantages (parsimonious discretization) and theoretical insights into how process persistence (e.g., AR(1) processes) affects required grid size.

Applications:

Asset Pricing Model: Better captures dividend growth moments (e.g., skewness, kurtosis) and yields solutions closer to the closed-form benchmark than competing methods (e.g., Farmer-Toda, binning).
Life-Cycle Model: Discretization affects welfare costs, wealth inequality, and marginal propensities to consume. For example:
- Non-employment risks in Guvenen et al. (2021) increase welfare costs by 23 pp relative to binning.
- Captures excess skewness/kurtosis in earnings processes, affecting wealth distribution (Gini index, top 1% shares).

Comparisons:

Outperforms tensor-grid-based methods (e.g., Tauchen, Rouwenhorst) in accuracy for multivariate processes.
Matches or exceeds binning methods in higher-order moments and economic quantities.

Conclusion:

HMM-based discretization offers a universal approximation tool for stochastic processes, improving accuracy in asset pricing and life-cycle models while being computationally efficient.
Highlights the sensitivity of economic outcomes to discretization choice, emphasizing the need for richer representations.

Keywords: Finite-state Markov chains, Hidden Markov Models, Kullback-Leibler divergence, Numerical methods, Economic applications.

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