Ejemplo n.º 1
0
    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
Ejemplo n.º 2
0
 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
Ejemplo n.º 3
0
 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
Ejemplo n.º 4
0
 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