def find_steady_state(model, m=None):
n_s = len(model.calibration["states"])
n_x = len(model.calibration["controls"])
if m is None:
m = model.calibration["exogenous"]
p = model.calibration["parameters"]
def fobj(v):
s = v[:n_s]
x = v[n_s:]
d = dict(states=s, controls=x, exogenous=m, parameters=p)
res = residuals(model, d)
return np.concatenate([res["transition"], res["arbitrage"]])
calib = model.calibration
x0 = np.concatenate([calib["states"], calib["controls"]])
import scipy.optimize
sol = scipy.optimize.root(fobj, x0)
res = sol.x
d = dict(exogenous=m, states=res[:n_s], controls=res[n_s:], parameters=p)
return CalibrationDict(model.symbols, d)
def __update_from_symbolic__(self):
import numpy
# updates calibration according to the symbolic definitions
system = self.symbolic.calibration_dict
from dolo.compiler.triangular_solver import solve_triangular_system
self.calibration_dict = solve_triangular_system( system )
from dolo.compiler.misc import CalibrationDict, calibration_to_vector
calib = calibration_to_vector(self.symbols, self.calibration_dict)
self.calibration = CalibrationDict(self.symbols, calib)
from .symbolic_eval import NumericEval
evaluator = NumericEval(self.calibration_dict)
# read symbolic structure
self.options = evaluator.eval(self.symbolic.options)
distribution = evaluator.eval(self.symbolic.distribution)
discrete_transition = evaluator.eval(self.symbolic.discrete_transition)
covariances = distribution
if distribution is None:
self.covariances = None
else:
self.covariances = numpy.atleast_2d(numpy.array(covariances, dtype=float))
markov_chain = discrete_transition
if markov_chain is None:
self.markov_chain = None
else:
self.markov_chain = [numpy.atleast_2d(numpy.array(tab, dtype=float)) for tab in markov_chain]
def calibration(self):
if self.__calibration__ is None:
calibration_dict = super(self.__class__, self).get_calibration()
from dolo.compiler.misc import CalibrationDict, calibration_to_vector
calib = calibration_to_vector(self.symbols, calibration_dict)
self.__calibration__ = CalibrationDict(self.symbols, calib) #
return self.__calibration__
def __update_from_symbolic__(self):
import numpy
# updates calibration according to the symbolic definitions
system = self.symbolic.calibration_dict
from dolo.compiler.triangular_solver import solve_triangular_system
self.calibration_dict = solve_triangular_system(system)
from dolo.compiler.misc import CalibrationDict, calibration_to_vector
calib = calibration_to_vector(self.symbols, self.calibration_dict)
self.calibration = CalibrationDict(self.symbols, calib)
from .symbolic_eval import NumericEval
evaluator = NumericEval(self.calibration_dict)
# read symbolic structure
self.options = evaluator.eval(self.symbolic.options)
self.exogenous = self.get_exogenous()
self.domain = self.get_domain()
def find_steady_state(model):
n_s = len(model.calibration['states'])
n_x = len(model.calibration['controls'])
m = model.calibration['exogenous']
p = model.calibration['parameters']
def fobj(v):
s = v[:n_s]
x = v[n_s:]
d = dict(states=s, controls=x, exogenous=m, parameters=p)
res = residuals(model,d)
return np.concatenate([res['transition'],res['arbitrage']])
calib = model.calibration
x0 = np.concatenate([calib['states'],calib['controls']])
import scipy.optimize
sol = scipy.optimize.root(fobj, x0)
res = sol.x
d = dict(exogenous=m, states=res[:n_s],controls=res[n_s:],parameters=p)
return CalibrationDict(model.symbols, d)
def calibration(self):
if self.__calibration__ is None:
calibration_dict = self.__get_calibration__()
calib = calibration_to_vector(self.symbols, calibration_dict)
self.__calibration__ = CalibrationDict(self.symbols, calib) #
return self.__calibration__
rk="1/β-1+δ",
w="(1-α)*exp(z)*(k/n)**(α)",
k="n/(rk/α)**(1/(1-α))",
y="exp(z)*k**α*n**(1-α)",
i="δ*k",
c="y - i",
V="log(c)/(1-β)",
u="c**(1-σ)/(1-σ) - χ*n**(1+η)/(1+η)",
m="β/c**σ*(1-δ+rk)")
from dolang.triangular_solver import solve_triangular_system
calibration_dict = solve_triangular_system(calibration_strings)
calibration_vector = calibration_to_vector(symbols, calibration_dict)
calibration = CalibrationDict(symbols, calibration_vector)
calibration
###
### Define functions
###
# the basic formulation of the functions (aka kernel)
# take and return "tuples" of floats because tuples are supposed
# to be easy to be optimzed away by the compiler
# after the definition of the function, there is some boilerplate
# to translate these functions into broadcastable ones, with
# optional numerical differentiation capabilities
from numba import jit
def find_deterministic_equilibrium(model,
constraints=None,
return_jacobian=False):
'''
Finds the steady state calibration.
Taking the value of parameters as given, finds the values for endogenous
variables consistent with the deterministic steady-state.
This function requires the specification of the first order equations.
Parameters
----------
model: NumericModel
an `(f,g)` compliant model
constraints: dict
a dictionaries with forced values.
Use it to set shocks to non-zero values or to add additional
constraints in order to avoid unit roots.
Returns:
--------
OrderedDict:
calibration dictionary (i.e. endogenous variables and parameters by
type)
'''
f = model.functions['arbitrage']
g = model.functions['transition']
s0 = model.calibration['states']
x0 = model.calibration['controls']
p = model.calibration['parameters']
if 'shocks' in model.calibration:
e0 = model.calibration['shocks'].copy()
else:
e0 = numpy.zeros(len(model.symbols['shocks']))
n_e = len(e0)
z = numpy.concatenate([s0, x0, e0])
symbs = model.symbols['states'] + model.symbols['controls']
addcons_ind = []
addcons_val = []
if constraints is None:
constraints = dict()
for k in constraints:
if k in symbs:
i = symbs.index(k)
addcons_ind.append(i)
addcons_val.append(constraints[k])
elif k in model.symbols['shocks']:
i = model.symbols['shocks'].index(k)
e0[i] = constraints[k]
else:
raise Exception(
"Invalid symbol '{}' for steady_state constraint".format(k))
def fobj(z):
s = z[:len(s0)]
x = z[len(s0):-n_e]
e = z[-n_e:]
S = g(s, x, e, p)
r = f(s, x, e, s, x, p)
d_e = e - e0
d_sx = z[addcons_ind] - addcons_val
res = numpy.concatenate([S - s, r, d_e, d_sx])
return res
jac = MyJacobian(fobj)(z)
if return_jacobian:
return jac
rank = numpy.linalg.matrix_rank(jac)
if rank < len(z):
msg = """\
There are {} equilibrium variables to find, but the jacobian \
matrix is only of rank {}. The solution is indeterminate."""
warnings.warn(msg.format(len(z), rank))
sol = root(fobj, z, method='lm')
steady_state = sol.x
s = steady_state[:len(s0)]
x = steady_state[len(s0):-n_e]
e = steady_state[-n_e:]
calib = OrderedDict(states=s, controls=x, shocks=e, parameters=p.copy())
if 'auxiliary' in model.functions:
a = model.functions['auxiliary'](s, x, p)
calib['auxiliaries'] = a
from dolo.compiler.misc import CalibrationDict
return CalibrationDict(model.symbols, calib)