Define the interpolation structure

Following the previous two steps (Writing RECS model files and Defining the model object) to completely define the problem, it remains only to define the domain over which it will be approximated and the precision of the approximation.

Create the interpolation structure

This task is done by the function recsinterpinit, which requires at least three inputs: the number of points on the grid of approximation, the lower bounds and the upper bounds of the grid.

The structure of the call to recsinterpinit is then

[interp,s] = recsinterpinit(n,smin,smax,method);

The inputs are as follows: n designates the order of approximation (if it is a scalar, the same order is applied for all dimensions), smin and smax are size-d vectors of left and right endpoints of the state space, and the (optional) string method defines the interpolation method, either spline ('spli', default), or Chebyshev polynomials ('cheb').

This function call returns two variables: the structure interp, which defines the interpolation structure, and the matrix s, which represents the state variables on the grid.

An example

We now define the interpolation structure for the stochastic growth model example (GRO1). Using the model object defined in the preceding step, we choose bounds for capital 15% below and above the steady-state value (model.sss(1)), and for productivity, which follows an AR(1), we choose 4 times below minimum and 4 times above maximum discretized shocks (model.shocks.e):

smin          = [0.85*model.sss(1) min(model.shocks.e)*4];
smax          = [1.15*model.sss(1) max(model.shocks.e)*4];

Using 10 nodes for each dimension and Chebyshev polynomials, the function call is:

[interp,s] = recsinterpinit(10,smin,smax,'cheb');

The interpolation structure has the following fields:

disp(interp)

    fspace: [1×1 struct]
       Phi: [1×1 struct]
         s: [100×2 double]

Choice Spline/Chebyshev polynomials

To be completed

Notes on functions used

For interpolation, RECS relies entirely on the tools programmed in the CompEcon toolbox. So, to know more about the underlying functions, see CompEcon documentation and Miranda and Fackler (2002).

References

Miranda, M. J. and Fackler, P. L. (2002). Applied Computational Economics and Finance. Cambridge: MIT Press.