Dynamic local linear solutions for efficient nonlinear DSGE estimation
This paper by Eva F. Janssens and Sean McCrary presents a new computational method for full-information estimation of nonlinear Dynamic Stochastic General Equilibrium (DSGE) models that achieves dramatic efficiency gains while maintaining accuracy. The core methodological innovation integrates the model solution directly into the filtering procedure, departing from traditional approaches that treat these as separate steps. The method constructs a dynamic sequence of local linear solutions around the best forecast of the current state, yielding a time-varying linear state-space system for likelihood evaluation via the Kalman filter. There are three key technical components:
- Local linear solutions: The approach approximates nonlinear policy functions and laws of motion using Taylor projections that are recomputed at each forecasted state. This captures nonlinear dynamics by allowing model coefficients to vary across the state space while maintaining computational tractability.
- Time-varying Kalman filter: Rather than solving the model once and applying a filter, the solution is constructed dynamically within the filtering procedure at each forecasted state. This eliminates the need for costly global solution methods and nonlinear filtering procedures.
- Analytical expectations: When policies are linear in logs and shocks are Gaussian, expectations in the equilibrium conditions can be computed analytically rather than through numerical integration, providing exact solutions and significant speed improvements.
Key findings
- Computational performance: The method achieves computational gains of several orders of magnitude compared to traditional nonlinear approaches while maintaining high accuracy. For the New Keynesian model, 100,000 posterior draws take under eight minutes—less than twice the time for linearized estimation.
- State-dependent monetary policy: The framework reveals that monetary policy effects vary significantly with economic conditions. Policy shocks affect vacancies and unemployment differently across states, with effects varying by as much as a factor of two.
- Phillips multiplier dynamics: The inflation-unemployment trade-off exhibits substantial time variation, averaging 0.15 but ranging from 0.08 in recessions to 0.18 in expansions—consistent with empirical evidence from local projections.
- Methodological innovation: Unlike traditional approaches that solve models once and then apply filters, this method integrates solution directly into filtering by computing local linear approximations at each forecasted state, enabling dynamic capture of nonlinear behavior.
- Extensions: The framework successfully accommodates stochastic volatility, regime switching, and heterogeneous agent models while preserving computational efficiency and capturing state-dependent dynamics that perturbation methods miss.
Efficient Estimation of Nonlinear DSGE Models
Authors: Eva F. Janssens, Sean McCrary
From: University of Michigan, The Ohio State University
Neural network solutions for computationally intractable HANK models
This BIS working paper by Hanno Kase, Leonardo Melosi, and Matthias Rottner introduces a methodological advancement in macroeconomic modeling by developing an integrated neural network-based approach to solve and estimate nonlinear heterogeneous agent New Keynesian (HANK) models. The framework addresses three critical computational challenges:
- Extended policy functions
The key innovation involves treating model parameters as pseudo-state variables when approximating policy functions. Instead of repeatedly solving the model at different parameter values during estimation, the neural networks are trained once across the entire parameter space. This approach uses two separate neural networks to approximate individual and aggregate policy functions, where parameters become inputs alongside traditional state variables. - Neural network particle filter
To handle likelihood evaluation for nonlinear models, the authors train a specialized neural network to approximate the likelihood function. This “NN particle filter” is trained through three steps: generating thousands of quasi-random parameter draws, evaluating likelihood at each draw using standard particle filters, and training the neural network to predict these likelihood values. This eliminates the need for repeated computationally expensive Monte Carlo filter evaluations. - Deterministic steady state approximation
A separate auxiliary neural network approximates the deterministic steady state equilibrium, which is essential for heterogeneous agent models but computationally intensive to solve repeatedly. This enables estimation of parameters that affect the model’s steady state – something typically avoided in previous HANK estimation studies due to computational constraints.
Key findings
- Methodological validation
The neural network approach successfully replicates analytical solutions with extreme precision and accurately recovers true parameter values in simulated data tests. - Empirical results from US Data (1990-2019)
When estimated on US macroeconomic data, the nonlinear HANK model reveals that idiosyncratic income risk emerges as a key driver of aggregate volatility through its interaction with zero lower bound constraints. Higher idiosyncratic risk increases precautionary savings, lowering interest rates and raising the probability of hitting the zero lower bound. - Economic insights
The framework identifies a deflationary bias of approximately 30 basis points due to occasionally binding zero lower bound constraints and demonstrates that microeconomic heterogeneity can be identified from aggregate data alone through its effects on macroeconomic nonlinearities.
Estimating Nonlinear Heterogeneous Agent Models with Neural Networks
Authors: Hanno Kase, Leonardo Melosi, Matthias Rottner
From: European Central Bank, University of Warwick, BIS
