DSGE Modeling
=============

A Markov-switching DSGE in the modern toolbox is a forward-looking
nonlinear system

.. math::

    E_t f(y_{t+1}, y_t, y_{t-1}, \varepsilon_t, p(r_t)) = 0,

with :math:`r_t = 1, 2, \dots, h` a Markov-chain regime, transition
matrix :math:`Q_{i,j}(I_t)` that can be constant or endogenous, and a
parameter vector :math:`p(r_t)` that can switch on one or more
chains. The constant-parameter case is the trivial :math:`h = 1`
special case of the same engine; there is no separate
constant-parameter code path.

The modern toolbox builds a DSGE via the ``dsge_model`` factory.
Once you have the object, ``solve``, ``filter``, ``estimate``,
``forecast``, ``simulate``, ``irf`` and the decompositions operate
on it directly. The rest of this chapter covers the DSGE-specific
machinery, one section at a time:

.. toctree::
   :maxdepth: 2

   Model file language
   Steady state and balanced-growth path
   First order perturbation
   Higher order perturbation
   Solving
   Optimal policy
   Optimized simple rules
   Occasionally-binding constraints
   Deterministic and quasi-deterministic solutions
   Heterogeneous agents
   Very large models
   Automatic translation of files