First model
============

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

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};

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));

Inspect
--------

::

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

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.

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.