Model Design

DSGE.jl is an object-oriented approach to solving the New York Fed DSGE model that takes advantage of Julia's type system, multiple dispatch, package-handling mechanism, and other features. A single model object centralizes all information about the model's parameters, states, equilibrium conditions, and settings in a single data structure. The model object also keeps track of file locations for all I/O operations.

The following objects define a model:

• Parameters: Have values, bounds, fixed-or-not status, priors. An instance of the AbstractParameter type houses all information about a given parameter in a single data structure. See The AbstractParameter Type.
• Model Indices: Mappings of state, shock, observable, and pseudo-observable names to indices (e.g. y_t -> 1). See Defining Indices.
• Observables and PseudoObservables: Mapping of names to indices, as well as information necessary for transformations. See The Observable and PseudoObservable Types.
• Equilibrium Conditions: A function that takes parameters and model indices, then returns Γ0, Γ1, C, Ψ, and Π (which fully describe the model in canonical form).
• Measurement Equation: A function mapping states to observables.
• Pseudo-Measurement Equation: A function mapping states to what we call "pseudo-observables", i.e. linear combinations of existing states which are not observed. (Note that this is not strictly required to implement a model, but we often use the pseudo-measurement equation instead of adding new states in order to achieve a more parsimonious model.)

These are enough to define the model structure. Everything else is essentially a function of these basics, and we can solve the model and forecast observables via the following chain:

• Parameters + Model Indices + Equilibrium conditions -> Transition matrices in state-space form
• Transition matrices + Data -> Estimated parameter values
• Estimated parameters + Transition matrices + Data -> Forecast