Dynamic Stochastic General Equilibrium Models.

dsge

Dynamic Stochastic General Equilibrium Models for R.

Overview

The dsge package provides tools for specifying, solving, and estimating DSGE models by maximum likelihood and Bayesian methods. It supports:

• Linear models via a formula-based interface (obs(), unobs(), state())
• Nonlinear models via string-based equations with first-order perturbation around steady state (dsgenl_model())
• Bayesian estimation of linear models via adaptive MCMC (bayes_dsge())

Postestimation tools include policy and transition matrix extraction, stability diagnostics, impulse-response functions with confidence/credible bands, and forecasting with fan charts.

Installation

# Install from source
install.packages("path/to/dsge", repos = NULL, type = "source")

# Or using devtools
devtools::install("path/to/dsge")

Quick Start: Maximum Likelihood

library(dsge)

# Define a simple New Keynesian model
nk <- dsge_model(
  obs(p   ~ beta * lead(p) + kappa * x),
  unobs(x ~ lead(x) - (r - lead(p) - g)),
  obs(r   ~ psi * p + u),
  state(u ~ rhou * u),
  state(g ~ rhog * g),
  fixed = list(beta = 0.96),
  start = list(kappa = 0.1, psi = 1.5, rhou = 0.7, rhog = 0.9)
)

# Estimate the model
fit <- estimate(nk, data = your_data)
summary(fit)

# Postestimation
policy_matrix(fit)
transition_matrix(fit)
stability(fit)

# Impulse-response functions (with plot)
irfs <- irf(fit, periods = 20)
plot(irfs)

# Forecast (with plot)
fc <- forecast(fit, horizon = 12)
plot(fc)

Bayesian Estimation

Bayesian estimation is available for linear DSGE models via adaptive Random-Walk Metropolis-Hastings (RWMH).

library(dsge)

# Define the model (same syntax as ML)
nk <- dsge_model(
  obs(p   ~ beta * lead(p) + kappa * x),
  unobs(x ~ lead(x) - (r - lead(p) - g)),
  obs(r   ~ psi * p + u),
  state(u ~ rhou * u),
  state(g ~ rhog * g),
  start = list(beta = 0.95, kappa = 0.15, psi = 1.5, rhou = 0.7, rhog = 0.9)
)

# Specify priors
my_priors <- list(
  beta  = prior("beta", shape1 = 95, shape2 = 5),
  kappa = prior("beta", shape1 = 30, shape2 = 70),
  psi   = prior("gamma", shape = 184, rate = 122.7),
  rhou  = prior("beta", shape1 = 70, shape2 = 20),
  rhog  = prior("beta", shape1 = 70, shape2 = 20)
  # shock SDs default to inv_gamma(0.01, 0.01)
)

# Run MCMC
fit <- bayes_dsge(nk, data = your_data, priors = my_priors,
                  chains = 2, iter = 10000, warmup = 5000)

# Results
summary(fit)                        # posterior table with ESS, R-hat

# MCMC diagnostics
plot(fit, type = "trace")            # trace plots (all chains)
plot(fit, type = "density")          # posterior density + prior overlay
plot(fit, type = "prior_posterior")   # dedicated prior-vs-posterior
plot(fit, type = "running_mean")     # cumulative mean convergence
plot(fit, type = "acf")              # autocorrelation diagnostics
plot(fit, type = "pairs")            # pairwise scatter + correlations
plot(fit, type = "all")              # combined trace + density panel

# Parameter selection (works with all diagnostic types)
plot(fit, type = "trace", pars = c("kappa", "psi"))

# Posterior IRFs with credible bands
plot(fit, type = "irf", periods = 12)

Supported prior distributions: normal, beta, gamma, uniform, inv_gamma.

Plotting: All plot types support a pars argument for parameter selection (e.g., pars = c("kappa", "psi")). Pagination handles any number of parameters. Forecast plotting is not yet available for Bayesian fits.

Nonlinear DSGE Example

library(dsge)

# Define a nonlinear RBC model
rbc <- dsgenl_model(
  "1/C = beta / C(+1) * (alpha * exp(Z) * K^(alpha-1) + 1 - delta)",
  "K(+1) = exp(Z) * K^alpha - C + (1 - delta) * K",
  "Z(+1) = rho * Z",
  observed = "C",
  endo_state = "K",
  exo_state = "Z",
  fixed = list(alpha = 0.33, beta = 0.99, delta = 0.025),
  start = list(rho = 0.9),
  ss_guess = c(C = 2, K = 30, Z = 0)
)

# Compute steady state
ss <- steady_state(rbc, params = c(alpha = 0.33, beta = 0.99,
                                    delta = 0.025, rho = 0.9))

# Solve (linearize + Klein solver)
sol <- solve_dsge(rbc, params = c(alpha = 0.33, beta = 0.99,
                                   delta = 0.025, rho = 0.9))

# IRFs and postestimation work identically to linear models
irfs <- irf(sol, periods = 40, se = FALSE)
plot(irfs)

Try It Yourself in RStudio

The package ships with self-contained demo scripts. After installing:

library(dsge)

# AR(1) model demo (simplest case)
source(system.file("examples", "demo_ar1.R", package = "dsge"))

# New Keynesian model demo (multivariate)
source(system.file("examples", "demo_nk.R", package = "dsge"))

# Nonlinear RBC model demo (first-order perturbation)
source(system.file("examples", "demo_rbc.R", package = "dsge"))

# Bayesian NK with real FRED data (requires internet; ~10 min)
source(system.file("examples", "bayesian_nk_fred.R", package = "dsge"))

# Bayesian nonlinear NK model (~15-25 min)
source(system.file("examples", "bayesian_nk_nonlinear.R", package = "dsge"))

# Bayesian nonlinear RBC with capital — quick demo (~2.5 min)
source(system.file("examples", "bayesian_rbc_capital_demo.R", package = "dsge"))

What This Package Currently Supports

Included in v0.4.0:

• Linear DSGE models with rational expectations
• Nonlinear DSGE models via first-order perturbation (linearization around deterministic steady state)
• Bayesian estimation of both linear and nonlinear DSGE models via adaptive RWMH
• For nonlinear models, the steady state is re-solved and the model re-linearized at each candidate parameter vector
• Prior specification: normal, beta, gamma, uniform, inverse-gamma
• MCMC diagnostics: ESS, R-hat, MCSE, acceptance rates
• Posterior impulse-response functions with credible bands
• Formula-based specification for linear models (obs(), unobs(), state())
• String-based specification for nonlinear models (dsgenl_model())
• Deterministic steady-state solver (Newton-Raphson or user-supplied)
• Method of undetermined coefficients solver (Klein 2000)
• Maximum likelihood estimation via the Kalman filter
• Delta-method standard errors for all structural parameters
• Impulse-response functions with confidence bands
• Multi-step forecasting with fan charts
• Policy matrix, transition matrix, and Blanchard-Kahn stability diagnostics
• Predictions (fitted values) and residuals

Not yet supported (planned for future releases):

• Higher-order perturbation (second-order, third-order)
• Nonlinear filtering (particle filter)
• Model-implied covariance matrices
• Variance decomposition
• Historical shock decomposition

Validation

The package has been validated on:

• Synthetic data: parameter recovery tests for AR(1), NK, and RBC models (both linear and nonlinear)
• Real data: Bayesian NK estimation on US macroeconomic data from FRED (1955Q1–2015Q4), producing economically plausible posteriors and IRFs
• Nonlinear Bayesian: parameter recovery on nonlinear RBC and NK models with all true parameters within 95% credible intervals
• Solver accuracy: policy and transition matrices verified against analytical solutions and published benchmark results

Key Features

• Formula-based model specification with obs(), unobs(), and state() equation wrappers
• Forward expectations via lead(x) or E(x) operators
• Klein (2000) solution method via undetermined coefficients
• Maximum likelihood and Bayesian estimation via Kalman filter
• Prior specification with prior() constructor
• MCMC diagnostics: ESS, R-hat, MCSE, acceptance rates
• Postestimation tools: policy matrix, transition matrix, stability check, predictions, impulse-response functions, forecasting
• Built-in plotting: IRF plots, forecast fan charts, trace plots, posterior density plots, prior-vs-posterior, running mean, ACF, pairs
• CRAN-compatible design with minimal dependencies

Model Syntax

Variables are declared by their role in the model:

References

• Klein, P. (2000). "Using the generalized Schur form to solve a multivariate linear rational expectations model." Journal of Economic Dynamics and Control, 24(10), 1405-1423.
• Iskrev, N. (2010). "Local identification in DSGE models." Journal of Monetary Economics, 57(2), 189-202.

License

MIT.