Full‐information estimation of heterogeneous agent models using macro and micro data

Abstract

We develop a generally applicable full‐information inference method for heterogeneous agent models, combining aggregate time series data and repeated cross‐sections of micro data. To handle unobserved aggregate state variables that affect cross‐sectional distributions, we compute a numerically unbiased estimate of the model‐implied likelihood function. Employing the likelihood estimate in a Markov Chain Monte Carlo algorithm, we obtain fully efficient and valid Bayesian inference. Evaluation of the micro part of the likelihood lends itself naturally to parallel computing. Numerical illustrations in models with heterogeneous households or firms demonstrate that the proposed full‐information method substantially sharpens inference relative to using only macro data, and for some parameters micro data is essential for identification.

Estimation of Heterogeneous Agent Models: A Likelihood Approach

“…A potential way to overcome this difficulties is to use some dimensionality‐reduction technique similar to those introduced in the recent HANK literature (see e.g., Bayer and Luetticke, 2020, Papp and Reiter (2020), Auclert et al . (2021), Liu and Plagborg‐Møller, 2023, among others). This will help to extend the information set used in the estimation process, e.g.…”

“…On the other hand, the biases on the discount rate, ρ, the capital share in production, α, and on the depreciation rate, δ, are within reasonable ranges, even in small samples 7 . on income could improve the estimation of the income parameters (see, e.g., Papp andReiter, 2020 andLiu andPlagborg-Møller, 2023). 7 We do not propose to estimate the capital share and/or the depreciation rate from the wealth data alone rather than from NIPA data.…”

“…In contrast, in this paper we use of the information available in the entire cross‐sectional distribution of microeconomic data to estimate parameters that enter directly in the computation of the steady state of the economy. Closer to our approach is the work by Papp and Reiter (2020) and Liu and Plagborg‐Møller (2023). They develop likelihood‐based methods to estimate the parameters of HA models using simultaneously macroeconomic time series and microeconomic data in the form of snapshots (moments) of either repeated cross‐sections or panel data.…”