class testAggShockMarkovConsumerType(unittest.TestCase): def setUp(self): # Make one agent type and an economy for it to live in self.agent = AggShockMarkovConsumerType() self.agent.cycles = 0 self.agent.AgentCount = 1000 # Low number of simulated agents self.agent.IncomeDstn[0] = 2 * [self.agent.IncomeDstn[0]] ## see #557 self.economy = CobbDouglasMarkovEconomy(agents=[self.agent]) def test_agent(self): # Have one consumer type inherit relevant objects from the economy, # then solve their microeconomic problem self.agent.getEconomyData(self.economy) self.agent.solve() self.assertAlmostEqual( self.agent.solution[0].cFunc[0](10.0, self.economy.MSS), 2.5635896520991377) def test_economy(self): # Adjust the economy so that it (fake) solves quickly self.economy.act_T = 500 # Short simulation history self.economy.max_loops = 3 # Just quiet solving early self.economy.verbose = False # Turn off printed messages self.agent.getEconomyData(self.economy) self.economy.makeAggShkHist( ) # Make a simulated history of aggregate shocks self.economy.solve( ) # Solve for the general equilibrium of the economy self.economy.AFunc = self.economy.dynamics.AFunc self.assertAlmostEqual(self.economy.AFunc[0].slope, 1.0904698841958917) self.assertAlmostEqual(self.economy.history["AaggNow"][5], 9.467758924955897)
class testAggShockMarkovConsumerType(unittest.TestCase): def setUp(self): self.agent = AggShockMarkovConsumerType() self.agent.IncomeDstn[0] = 2*[self.agent.IncomeDstn[0]] ## see #557 self.economy = CobbDouglasMarkovEconomy( agents = [self.agent]) def test_economy(self): self.agent.getEconomyData(self.economy) # Makes attributes of the economy, attributes of the agent self.economy.makeAggShkHist() # Make a simulated history of the economy # Set tolerance level. self.economy.tolerance = 0.5
# $\forall \{s,s'\}=\{g,b\}\times\{g,b\}$, the following two conditions hold: # # $$\underbrace{\pi_{ss'01}}_{p(s \rightarrow s',u \rightarrow e)}+\underbrace{\pi_{ss'00}}_{p(s \rightarrow s', u \rightarrow u)} = \underbrace{\pi_{ss'11}}_{p(s\rightarrow s', e \rightarrow e) } + \underbrace{\pi_{ss'10}}_{p(s \rightarrow s', e \rightarrow u)} = \underbrace{\pi_{ss'}}_{p(s\rightarrow s')}$$ # # $$u_s \frac{\pi_{ss'00}}{\pi_{ss'}}+ (1-u_s) \frac{\pi_{ss'10}}{\pi_{ss'}} = u_{s'}$$ # %% [markdown] # ### Solving the Model # Now, we have fully defined all of the elements of the macroeconomy, and we are in postion to construct an object that represents the economy and to construct a rational expectations equilibrium. # %% {"code_folding": []} # Construct the economy, make an initial history, then solve KSAgent.getEconomyData(KSEconomy) # Makes attributes of the economy, attributes of the agent KSEconomy.makeAggShkHist() # Make a simulated history of the economy # Set tolerance level. KSEconomy.tolerance = 0.01 # Solve macro problem by finding a fixed point for beliefs KSEconomy.solve() # Solve the economy using the market method. # i.e. guess the saving function, and iterate until a fixed point # %% [markdown] # The last line above is the converged aggregate saving rule for good and bad times, respectively. # %% {"code_folding": []} # Plot some key results
plt.plot(m_grid + mMin, c_at_this_M) plt.ylim(0.0, None) plt.show() # ### Example Implementations of AggShockMarkovConsumerType if solve_markov_micro or solve_markov_market or solve_krusell_smith: # Make a Markov aggregate shocks consumer type AggShockMrkvExample = AggShockMarkovConsumerType() AggShockMrkvExample.IncomeDstn[0] = 2 * [AggShockMrkvExample.IncomeDstn[0]] AggShockMrkvExample.cycles = 0 # Make a Cobb-Douglas economy for the agents MrkvEconomyExample = CobbDouglasMarkovEconomy(agents=[AggShockMrkvExample]) MrkvEconomyExample.DampingFac = 0.2 # Turn down damping MrkvEconomyExample.makeAggShkHist( ) # Simulate a history of aggregate shocks AggShockMrkvExample.getEconomyData( MrkvEconomyExample ) # Have the consumers inherit relevant objects from the economy if solve_markov_micro: # Solve the microeconomic model for the Markov aggregate shocks example type (and display results) t_start = process_time() AggShockMrkvExample.solve() t_end = process_time() print("Solving an aggregate shocks Markov consumer took " + mystr(t_end - t_start) + " seconds.") print("Consumption function at each aggregate market \ resources-to-labor ratio gridpoint (for each macro state):") m_grid = np.linspace(0, 10, 200)
def consExample(filename): KSAgentDictionary = { "CRRA" : 3.0, # Coefficient of relative risk aversion "DiscFac" : 0.99, # Intertemporal discount factor "LivPrb" : [1.0], # Survival probability "AgentCount" : 1000, # Number of agents of this type (only matters for simulation) "aNrmInitMean" : 0.0, # Mean of log initial assets (only matters for simulation) "aNrmInitStd" : 0.0, # Standard deviation of log initial assets (only for simulation) "pLvlInitMean" : 0.0, # Mean of log initial permanent income (only matters for simulation) "pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income (only matters for simulation) "PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor (only matters for simulation) "T_age" : None, # Age after which simulated agents are automatically killed "T_cycle" : 1, # Number of periods in the cycle for this agent type # # Parameters for constructing the "assets above minimum" grid "aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value "aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value "aXtraExtra" : [None], # Some other value of "assets above minimum" to add to the grid "aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid "aXtraCount" : 24, # Number of points in the grid of "assets above minimum" # # Parameters describing the income process "PermShkCount" : 1, # Number of points in discrete approximation to permanent income shocks - no shocks of this kind! "TranShkCount" : 1, # Number of points in discrete approximation to transitory income shocks - no shocks of this kind! "PermShkStd" : [0.], # Standard deviation of log permanent income shocks - no shocks of this kind! "TranShkStd" : [0.], # Standard deviation of log transitory income shocks - no shocks of this kind! "UnempPrb" : 0.0, # Probability of unemployment while working - no shocks of this kind! "UnempPrbRet" : 0.0, # Probability of "unemployment" while retired - no shocks of this kind! "IncUnemp" : 0.0, # Unemployment benefits replacement rate "IncUnempRet" : 0.0, # "Unemployment" benefits when retired "tax_rate" : 0.0, # Flat income tax rate "T_retire" : 0, # Period of retirement (0 --> no retirement) "BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets "cycles" : 0, # Consumer is infinitely lived "PermGroFac" : [1.0], # Permanent income growth factor # # New Parameters that we need now 'MgridBase': np.array([0.1, 0.3, 0.6, 0.8, 0.9, 0.98, 1.0, 1.02, 1.1, 1.2, 1.6, 2.0, 3.0]), # Grid of capital-to-labor-ratios (factors) 'MrkvArray': np.array([[0.875, 0.125], [0.125, 0.875]]),# Transition probabilities for macroecon. [i,j] is probability of being in state j next # period conditional on being in state i this period. 'PermShkAggStd' : [0.0, 0.0], # Standard deviation of log aggregate permanent shocks by state. No continous shocks in a state. 'TranShkAggStd' : [0.0, 0.0], # Standard deviation of log aggregate transitory shocks by state. No continuous shocks in a state. 'PermGroFacAgg' : 1.0 } # Economy Dictionary KSEconomyDictionary = { 'PermShkAggCount': 1, 'TranShkAggCount': 1, 'PermShkAggStd' : [0.0, 0.0], 'TranShkAggStd' : [0.0, 0.0], 'DeprFac' : 0.025, # Depreciation factor 'CapShare' : 0.36, # Share of capital income in cobb-douglas production function 'DiscFac' : 0.99, 'CRRA' : 3.0, 'PermGroFacAgg' : [1.0, 1.0], 'AggregateL' : 1.0, # Fix aggregate labor supply at 1.0 - makes interpretation of z easier 'act_T' : 1200, # Number of periods for economy to run in simulation 'intercept_prev' : [0.0, 0.0], # Make some initial guesses at linear savings rule intercepts for each state 'slope_prev' : [1.0, 1.0], # Make some initial guesses at linear savings rule slopes for each state 'MrkvArray' : np.array([ [0.875, 0.125], [0.125, 0.875]]), # Transition probabilities 'MrkvNow_init' : 0 # Pick a state to start in (we pick the first state) } ### Representative Agent # Create the Krusell-Smith agent as an instance of AggShockMarkovConsumerType KSAgent = AggShockMarkovConsumerType(**KSAgentDictionary) # Construct the income distribution for the Krusell-Smith agent prb_eg = 0.96 # Probability of employment in the good state prb_ug = 1 - prb_eg # Probability of unemployment in the good state prb_eb = 0.90 # Probability of employment in the bad state prb_ub = 1 - prb_eb # Probability of unemployment in the bad state p_ind = 1 # Persistent component of income is always 1 ell_ug = ell_ub = 0 # Labor supply is zero for unemployed consumers in either agg state ell_eg = 1.0/prb_eg # Labor supply for employed consumer in good state ell_eb = 1.0/prb_eb # 1=pe_g*ell_ge+pu_b*ell_gu=pe_b*ell_be+pu_b*ell_gu # IncomeDstn is a list of lists, one for each aggregate Markov state # Each contains three arrays of floats, representing a discrete approximation to the income process. # Order: # state probabilities # idiosyncratic persistent income level by state (KS have no persistent shocks p_ind is always 1.0) # idiosyncratic transitory income level by state KSAgent.IncomeDstn[0] = [ [np.array([prb_eg,prb_ug]), np.array([p_ind,p_ind]), np.array([ell_eg,ell_ug])], # Agg state good [np.array([prb_eb,prb_ub]), np.array([p_ind,p_ind]), np.array([ell_eb,ell_ub])] # Agg state bad ] KSEconomy = CobbDouglasMarkovEconomy(agents = [KSAgent], **KSEconomyDictionary) # Combine production and consumption sides into an "Economy" # Calibrate the magnitude of the aggregate shocks Tran_g = 1.01 # Productivity z in the good aggregate state Tran_b = 0.99 # and the bad state # Aggregate productivity shock distribution by state. # First element is probabilities of different outcomes, given the state you are in. # Second element is agg permanent shocks (here we don't have any, so just they are just 1.). # Third element is agg transitory shocks, which are calibrated the same as in Krusell Smith. KSAggShkDstn = [ [np.array([1.0]),np.array([1.0]),np.array([Tran_g])], # Aggregate good [np.array([1.0]),np.array([1.0]),np.array([Tran_b])] # Aggregate bad ] KSEconomy.AggShkDstn = KSAggShkDstn # Construct the economy, make an initial history, then solve KSAgent.getEconomyData(KSEconomy) # Makes attributes of the economy, attributes of the agent KSEconomy.makeAggShkHist() # Make a simulated history of the economy # Tolerance level KSEconomy.tolerance = 0.01 # Solve the economy using the market method. KSEconomy.solve() ### Plots print('Consumption function at each aggregate market resources gridpoint (in general equilibrium):') m_grid = np.linspace(0,20,200) c_m = KSAgent.solution[0].cFunc[0](m_grid,10.0*np.ones_like(m_grid)) f = plt.figure() plt.plot(m_grid,c_m, color = '#4a69bd', linewidth = 2.5) plt.ylabel(r'$c(y)$', labelpad = 15, rotation = 0) plt.ylim([-0.15, 2.15]) plt.yticks([0 + 0.25 * k for k in range(9)], [r'${:.1f}$'.format(0 + 0.25 * k) if k % 2 == 0 else '' for k in range(9)]) plt.xlabel(r'$y$') plt.xlim([-1, 21]) plt.xticks([0 + 2.5 * k for k in range(9)], [r'${:.0f}$'.format(0 + 2.5 * k) if k % 2 == 0 else '' for k in range(9)]) plt.show() f.savefig(filename, bbox_inches='tight')