def solve_time1_bellman(self):
'''
Solve the time 1 Bellman equation for calibration Para and initial grid mugrid0
'''
Para, mugrid0 = self.Para, self.mugrid
Pi = Para.Pi
S = len(Para.Pi)
#First get initial fit from lucas stockey solution.
#Need to change things to be ex_ante
PP = LS.Planners_Allocation_Sequential(Para)
interp = utilities.interpolator_factory(2, None)
def incomplete_allocation(mu_, s_):
c, n, x, V = PP.time1_value(mu_)
return c, n, Pi[s_].dot(x), Pi[s_].dot(V)
cf, nf, xgrid, Vf, xprimef = [], [], [], [], []
for s_ in range(S):
c, n, x, V = zip(
*map(lambda mu: incomplete_allocation(mu, s_), mugrid0))
c, n = np.vstack(c).T, np.vstack(n).T
x, V = np.hstack(x), np.hstack(V)
xprimes = np.vstack([x] * S)
cf.append(interp(x, c))
nf.append(interp(x, n))
Vf.append(interp(x, V))
xgrid.append(x)
xprimef.append(interp(x, xprimes))
cf, nf, xprimef = utilities.fun_vstack(cf), utilities.fun_vstack(
nf), utilities.fun_vstack(xprimef)
Vf = utilities.fun_hstack(Vf)
policies = [cf, nf, xprimef]
#create xgrid
x = np.vstack(xgrid).T
xbar = [x.min(0).max(), x.max(0).min()]
xgrid = np.linspace(xbar[0], xbar[1], len(mugrid0))
self.xgrid = xgrid
#Now iterate on Bellman equation
T = BellmanEquation(Para, xgrid, policies)
diff = 1.
while diff > 1e-6:
PF = T(Vf)
Vfnew, policies = self.fit_policy_function(PF)
diff = np.abs((Vf(xgrid) - Vfnew(xgrid)) / Vf(xgrid)).max()
print diff
Vf = Vfnew
#store value function policies and Bellman Equations
self.Vf = Vf
self.policies = policies
self.T = T
def solve_time1_bellman(self):
'''
Solve the time 1 Bellman equation for calibration Para and initial grid mugrid0
'''
Para,mugrid0 = self.Para,self.mugrid
Pi = Para.Pi
S = len(Para.Pi)
#First get initial fit from lucas stockey solution.
#Need to change things to be ex_ante
PP = LS.Planners_Allocation_Sequential(Para)
interp = utilities.interpolator_factory(2,None)
def incomplete_allocation(mu_,s_):
c,n,x,V = PP.time1_value(mu_)
return c,n,Pi[s_].dot(x),Pi[s_].dot(V)
cf,nf,xgrid,Vf,xprimef = [],[],[],[],[]
for s_ in range(S):
c,n,x,V = zip(*map(lambda mu: incomplete_allocation(mu,s_),mugrid0))
c,n = np.vstack(c).T,np.vstack(n).T
x,V = np.hstack(x),np.hstack(V)
xprimes = np.vstack([x]*S)
cf.append(interp(x,c))
nf.append(interp(x,n))
Vf.append(interp(x,V))
xgrid.append(x)
xprimef.append(interp(x,xprimes))
cf,nf,xprimef = utilities.fun_vstack(cf), utilities.fun_vstack(nf),utilities.fun_vstack(xprimef)
Vf = utilities.fun_hstack(Vf)
policies = [cf,nf,xprimef]
#create xgrid
x = np.vstack(xgrid).T
xbar = [x.min(0).max(),x.max(0).min()]
xgrid = np.linspace(xbar[0],xbar[1],len(mugrid0))
self.xgrid = xgrid
#Now iterate on Bellman equation
T = BellmanEquation(Para,xgrid,policies)
diff = 1.
while diff > 1e-6:
PF = T(Vf)
Vfnew,policies = self.fit_policy_function(PF)
diff = np.abs((Vf(xgrid)-Vfnew(xgrid))/Vf(xgrid)).max()
print diff
Vf = Vfnew
#store value function policies and Bellman Equations
self.Vf = Vf
self.policies = policies
self.T = T
def fit_policy_function(self,PF):
'''
Fits the policy functions
'''
S,xgrid = len(self.Pi),self.xgrid
interp = utilities.interpolator_factory(3,0)
cf,nf,xprimef,Tf,Vf = [],[],[],[],[]
for s_ in range(S):
PFvec = np.vstack([PF(x,s_) for x in self.xgrid]).T
Vf.append(interp(xgrid,PFvec[0,:]))
cf.append(interp(xgrid,PFvec[1:1+S]))
nf.append(interp(xgrid,PFvec[1+S:1+2*S]))
xprimef.append(interp(xgrid,PFvec[1+2*S:1+3*S]))
Tf.append(interp(xgrid,PFvec[1+3*S:]))
policies = utilities.fun_vstack(cf), utilities.fun_vstack(nf),utilities.fun_vstack(xprimef),utilities.fun_vstack(Tf)
Vf = utilities.fun_hstack(Vf)
return Vf,policies
def fit_policy_function(self,PF):
'''
Fits the policy functions
'''
S,xgrid = len(self.Pi),self.xgrid
interp = utilities.interpolator_factory(3,0)
cf,nf,xprimef,Tf,Vf = [],[],[],[],[]
for s_ in range(S):
PFvec = np.vstack([PF(x,s_) for x in self.xgrid]).T
Vf.append(interp(xgrid,PFvec[0,:]))
cf.append(interp(xgrid,PFvec[1:1+S]))
nf.append(interp(xgrid,PFvec[1+S:1+2*S]))
xprimef.append(interp(xgrid,PFvec[1+2*S:1+3*S]))
Tf.append(interp(xgrid,PFvec[1+3*S:]))
policies = utilities.fun_vstack(cf), utilities.fun_vstack(nf),utilities.fun_vstack(xprimef),utilities.fun_vstack(Tf)
Vf = utilities.fun_hstack(Vf)
return Vf,policies