HANS: A Heterogeneous-Agent model Nonlinear Solver

HANS is an open-source toolbox designed to solve nonlinear solutions in discrete-time heterogeneous-agent (HA) models with a continuum of individual decision makers. It excels in scenarios where large deviations from stationary equilibrium values demand highly nonlinear solutions. HANS provides a useful addition to the existing suite of excellent HA modeling toolboxes, especially for researchers addressing highly nonlinear problems.

HANS offers flexibility by accommodating:

Multiple endogenous individual state and choice variables
Discrete individual decision variables
Linearized equilibrium solutions with perfect foresight or with aggregate shocks via the Sequence-Space Jacobian method (Auclert, Bardczy, Rognlie and Straub, 2021)
Nonlinear deterministic transition path solutions through our specialized nonlinear equation solvers

To explore HANS’s capabilities in greater depth, refer to the examples listed below.

HANS takes intuitive model script files as input for automatic code generation (similar to Dynare and GDSGE), compiles C++ binaries for high-performance computations, and offers user-friendly MATLAB interfaces. For example, the model of Krusell and Smith (1998) can be represented with the following toolbox script:

parameters beta w r;
beta = 0.99;

var_shock e;
shock_trans = [0.600000, 0.400000;
               0.044445, 0.955555];
e = [0.00, 1.00];

var_state k;
k = exp(linspace(log(0.25), log(500 + 0.25), 500)) - 0.25;

% allow multiple choice variables
var_policy c kp;
initial c 1.0;
initial kp 0.0;

vfi;
    budget = (1+r)*k + w*e;
    u = log(c);
    % decision problem stated following the Bellman equation
    Tv = u + beta*EXPECT(v(kp));
    % allow arbitrary equality/inequality constraints
    c + kp == budget;
    kp >= 0.0;
end;

var_agg K;
K = 40.0;       % initial guess
L = 1.0;        % constant labor
z = 1.0;        % TFP
alpha = 0.36;   % capital share
delta = 0.025;  % depreciation

var_agg_shock z;

model;
    % aggregate conditions stated like Dynare
    r = z*alpha*(K(-1)^(alpha-1))*(L^(1-alpha)) - delta;
    w = z*(1-alpha)*(K(-1)^alpha)*(L^(-alpha));
    K == kp;    % asset demand = asset supply
    % allow box constraints for aggregate variables
    K >= 38.0;  % make sure VFI converges
end;