dsolve 0.0.3

Solver of dynamic equations with forward looking variables

dsolve

A package to solve systems of dynamic equations with Python. It understands Latex syntax and it requires minimum specifications from the user end. It implements the Klein (2000) algorithm, which allows for static equations.

The main usage of the package is the following (check the notebook for further examples)

from solvers import Klein

# Your latex equations here as a list of strings
eq=[
    '\pi_{t}=\beta*E\pi_{t+1}+\kappa*y_{t}+u_{t}',
    'y_{t}=Ey_{t+1}+(1-\phi)*E[\pi_{t+1}]+\epsilon_{t}',
    '\epsilon_{t} = \rho_v*\epsilon_{t-1}+v_{t}'
]

# Your calibration here as a dictionary
calibration = {'\beta':0.98,'\kappa':0.1,'\phi':1.1,'\rho_v':0.8}

# Define pre-determined variables, forward looking variables, and shocks as strings separated by commas or a list of strings.

x = '\epsilon_{t-1}'
p = '\pi_t, y_t'
z = 'v_t, u_t'

system = Klein(eq = eq, x=x, p=p, z=z, calibration=calibration)

Flexible input reading

The standarized way to write a variable is E_{t}[x_{s}] to represent the expectation of x_{s} at time t. but dsolve understands other formats. Ex_{s}, E[x_s] and Ex_s are quivalents to E_{t}[x_{s}], and the subscript t is assumed.

Greek symbols can be writen as \rho or just rho. ´

dsolve understands fractions and sums. \sum_{i=0}^{2}{x_{i,t}} produces x_{0,t}+x_{1,t}+x_{2,t}