間接變分推斷：應用於收入動態

摘要

潛變數模型在經濟學中至關重要，但往往涉及難以處理的積分。變分推論（VI）廣泛應用於機器學習，透過以變分目標取代似然函數，將此積分轉化為可處理且可微分的優化問題。然而，當變分族靈活度不足時，恢復真實參數的保證仍然有限——這是將VI應用於經濟學的主要障礙。我們首先在收入動態模型中評估VI，並顯示變分後驗的選擇至關重要。接著我們引入間接變分推論（IVI），將VI視為輔助模型，並修正由變分近似所引發的偏差。IVI保留了VI的諸多可處理性，因為它無需計算似然函數。我們將這些方法應用於允許非線性持續性、非高斯且序列相關的暫時性衝擊，以及潛在異質性的模型。在模擬與實證應用中，靈活的變分族結合IVI能夠提供可靠的估計值。

English

Latent-variable models are central to economics but often entail intractable integration. Variational inference (VI), widely used in machine learning, turns this integration into tractable, differentiable optimization by replacing the likelihood with a variational objective. However, guarantees of recovering the true parameters remain limited when the variational family is insufficiently flexible -- a key obstacle to the adoption of VI in economics. We first evaluate VI in models of earnings dynamics and show that the choice of variational posterior is crucial. We then introduce indirect variational inference (IVI), which treats VI as an auxiliary model and corrects the bias induced by the variational approximation. IVI retains much of VI's tractability because it does not require computing the likelihood. We apply these methods to models allowing for nonlinear persistence, non-Gaussian and serially correlated transitory shocks, and latent heterogeneity. Across simulated and empirical applications, flexible variational families combined with IVI deliver reliable estimates.

間接變分推斷：應用於收入動態

Indirect Variational Inference: Applications to Earnings Dynamics

摘要

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