2. First model

A three-equation New Keynesian model, end to end, in fewer than twenty lines.

2.1. The model file

Save the following as nk.rs:

@endogenous x pi i

@exogenous eps_m

@parameters beta sigma kappa phi_pi phi_y rho_m std_eps_m

@model
    x{t}  = x{t+1} - (1/sigma)*(i{t} - pi{t+1});
    pi{t} = beta*pi{t+1} + kappa*x{t};
    i{t}  = phi_pi*pi{t} + phi_y*x{t} + std_eps_m*eps_m{t};

2.2. Build and solve

In MATLAB:

p = struct( ...
    'beta',      0.99,  ...
    'sigma',     1.0,   ...
    'kappa',     0.30,  ...
    'phi_pi',    1.50,  ...
    'phi_y',     0.125, ...
    'std_eps_m', 0.0025);

m = dsge_model('nk.rs');
m = set(m, parameters = p);
[m, retcode] = solve(m);
assert(retcode == 0, decipher(retcode));

2.3. Inspect

print_solution(m);
myirfs = irf(m, irf_periods = 20);
plot(myirfs.eps_m.pi, LineWidth = 2);

2.4. What just happened

• dsge_model(...) parsed nk.rs into a model object describing the state-space, with no class-specific metadata stashed away. dsge_model is the DSGE-shape factory; the VAR family has its own (rfvar_model, svar_model, proxy_svar_model, prfvar_model, dsge_var_model).

• set(m, parameters = ...) bound numerical values to the declared parameters. The model file declared the model; this call parameterized it. See the Modern architecture chapter for why these are kept separate.

• solve(m) ran the perturbation engine and returned the model with the solution attached. The retcode is always captured and checked.

• irf returned a struct of time series objects (one per shock, one per variable). plot is overloaded for the time series type – no need to extract the underlying numeric array.

2.5. Next steps

• Modeling -> Model file language for the full .rs grammar.

• Modeling -> Solving for the solver options exposed on solve.

• Modeling -> Estimation for taking the model to data.