Writing RECS model files

Structure of a rational expectation models

Before starting to write the model file, you need to organize your equations as described in Definition of a stochastic rational expectations problem. This means that you need to identify and separate in your model the following three group of equations:

Equilibrium equations

$\underline{x}(s) \le x \le \overline{x}(s) \perp f(s,x,z).$

Expectations definition

$z = \mathrm{E} \left[h(s,x,e_{+},s_{+},x_{+})\right].$

Transition equations

$s = g(s_{-},x_{-},e).$

When defining your model, it is important to try to minimize the number of state variables. Currently, RECS relies for interpolation on grids constructed with tensor products, so the dimension of the problem increases exponentially with the number of state variables. This implies that RECS should be used only to solve small-scale models: more than three or four state variables may make the problems too large to handle. One way of reducing the problem size is, whenever possible, to sum together the predetermined variables that can be summed. You can see in the demonstrations files (e.g., CS1 or STO1) that states variables are occasionaly defined as sums of other predetermined variables.

Structure of RECS model files

An RECS model can be written in a way that is quite similar to the original mathematical notations (as is proposed in most algebraic modeling languages). The model file that must be created is called a Yaml file (because it is written in YAML and has the .yaml extension). A Yaml file is easily readable by human, but not by MATLAB. So the file needs to be processed for MATLAB to be able to read it. This is done by the function recsmodel, which uses a Python preprocessor, dolo-recs, to do the job.

RECS Yaml files require three basic components, written successively:

Yaml file structure

To illustrate a complete Yaml file let us consider how to write a standard stochastic growth model in Yaml (see GRO1 for the complete example):

declarations:

  states: [K, Z]

  controls: [C]

  expectations: [E]

  shocks: [Epsilon]

  parameters: [a, tau, delta, beta, rho, alpha]

equations:

  arbitrage:

    - C^(-tau)-beta*E=0 | -inf <= C <= inf

  transition:

    - K = a*exp(Z(-1))*K(-1)^alpha+(1-delta)*K(-1)-C(-1)
    - Z = rho*Z(-1)+Epsilon

  expectation:

    - E = C(1)^(-tau)*(1-delta+a*alpha*exp(Z(1))*K(1)^(alpha-1))

calibration:

  parameters:

    tau   : 2
    delta : 0.0196
    beta  : 0.95
    rho   : 0.9
    alpha : 0.33
    a     : (1/beta-1+delta)/alpha

  steady_state:

    Z : 0
    K : 1
    C : a-delta
    E : C^(-tau)/beta

See Demos for other examples of complete yaml files.

Yaml files can be written with any text editor, including MATLAB editor.

Yaml syntax conventions

For the file to be readable, it is necessary to respect some syntax conventions: