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[wip] Uncertainty-and-the-Saving-Rate #120

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238 changes: 144 additions & 94 deletions notebooks/Uncertainty-and-the-Saving-Rate.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,7 @@
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Expand Down Expand Up @@ -115,7 +115,7 @@
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Expand All @@ -126,41 +126,47 @@
"# Import HARK tools and cstwMPC parameter values\n",
"from HARK.utilities import plotFuncsDer, plotFuncs\n",
"from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType\n",
"import HARK.cstwMPC.cstwMPC as cstwMPC\n",
"import HARK.cstwMPC.SetupParamsCSTW as Params\n",
"from HARK.ConsumptionSaving.ConsAggShockModel import AggShockConsumerType, CobbDouglasEconomy\n",
"from HARK.datasets import load_SCF_wealth_weights\n",
"from HARK.utilities import getLorenzShares\n",
"\n",
"#import HARK.cstwMPC.cstwMPC as cstwMPC\n",
"\n",
"SCF_wealth, SCF_weights = load_SCF_wealth_weights()\n",
"# Which points of the Lorenz curve to match in beta-dist (must be in (0,1))\n",
"percentiles_to_match = [0.2, 0.4, 0.6, 0.8] \n",
"\n",
"# Double the default value of variance\n",
"# Params.init_infinite['PermShkStd'] = [i*2 for i in Params.init_infinite['PermShkStd']]"
]
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"# Setup stuff for general equilibrium version\n",
"\n",
"# Set targets for K/Y and the Lorenz curve\n",
"lorenz_target = cstwMPC.getLorenzShares(Params.SCF_wealth,weights=\n",
" Params.SCF_weights,percentiles=\n",
" Params.percentiles_to_match)\n",
"lorenz_target = getLorenzShares(SCF_wealth,\n",
" weights= SCF_weights,\n",
" percentiles= percentiles_to_match)\n",
"\n",
"lorenz_long_data = np.hstack((np.array(0.0),\\\n",
" cstwMPC.getLorenzShares(Params.SCF_wealth,weights=\\\n",
" Params.SCF_weights,percentiles=\\\n",
" np.arange(0.01,1.0,0.01).tolist()),np.array(1.0)))\n",
" getLorenzShares(SCF_wealth,\n",
" weights=SCF_weights,\n",
" percentiles=np.arange(0.01,1.0,0.01).tolist()),np.array(1.0)))\n",
"KY_target = 10.26"
]
},
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Expand All @@ -170,33 +176,70 @@
"source": [
"# Setup and calibration of the agent types\n",
"\n",
"# Define a dictionary with calibrated parameters\n",
"cstwMPC_init_infinite = {\n",
" \"CRRA\":1.0, # Coefficient of relative risk aversion \n",
" \"Rfree\":1.01/(1.0 - 1.0/160.0), # Survival probability,\n",
" \"PermGroFac\":[1.000**0.25], # Permanent income growth factor (no perm growth),\n",
" \"PermGroFacAgg\":1.0,\n",
" \"BoroCnstArt\":0.0,\n",
" \"CubicBool\":False,\n",
" \"vFuncBool\":False,\n",
" \"PermShkStd\":[(0.01*4/11)**0.5], # Standard deviation of permanent shocks to income\n",
" \"PermShkCount\":5, # Number of points in permanent income shock grid\n",
" \"TranShkStd\":[(0.01*4)**0.5], # Standard deviation of transitory shocks to income,\n",
" \"TranShkCount\":5, # Number of points in transitory income shock grid\n",
" \"UnempPrb\":0.07, # Probability of unemployment while working\n",
" \"IncUnemp\":0.15, # Unemployment benefit replacement rate\n",
" \"UnempPrbRet\":None,\n",
" \"IncUnempRet\":None,\n",
" \"aXtraMin\":0.00001, # Minimum end-of-period assets in grid\n",
" \"aXtraMax\":40, # Maximum end-of-period assets in grid\n",
" \"aXtraCount\":32, # Number of points in assets grid\n",
" \"aXtraExtra\":[None],\n",
" \"aXtraNestFac\":3, # Number of times to 'exponentially nest' when constructing assets grid\n",
" \"LivPrb\":[1.0 - 1.0/160.0], # Survival probability\n",
" \"DiscFac\":0.97, # Default intertemporal discount factor; dummy value, will be overwritten\n",
" \"cycles\":0,\n",
" \"T_cycle\":1,\n",
" \"T_retire\":0,\n",
" 'T_sim':1200, # Number of periods to simulate (idiosyncratic shocks model, perpetual youth)\n",
" 'T_age': 400,\n",
" 'IndL': 10.0/9.0, # Labor supply per individual (constant),\n",
" 'aNrmInitMean':np.log(0.00001),\n",
" 'aNrmInitStd':0.0,\n",
" 'pLvlInitMean':0.0,\n",
" 'pLvlInitStd':0.0,\n",
" 'AgentCount':10000,\n",
"}\n",
"\n",
"# The parameter values below are taken from\n",
"# http://econ.jhu.edu/people/ccarroll/papers/cjSOE/#calibration\n",
"\n",
"Params.init_cjSOE = Params.init_infinite # Get default values of all parameters\n",
"init_cjSOE = cstwMPC_init_infinite # Get default values of all parameters\n",
"# Now change some of the parameters for the individual's problem to those of cjSOE\n",
"Params.init_cjSOE['CRRA'] = 2\n",
"Params.init_cjSOE['Rfree'] = 1.04**0.25\n",
"Params.init_cjSOE['PermGroFac'] = [1.01**0.25] # Indiviual-specific income growth (from experience, e.g.)\n",
"Params.init_cjSOE['PermGroFacAgg'] = 1.04**0.25 # Aggregate productivity growth \n",
"Params.init_cjSOE['LivPrb'] = [0.95**0.25] # Matches a short working life \n",
"init_cjSOE['CRRA'] = 2\n",
"init_cjSOE['Rfree'] = 1.04**0.25\n",
"init_cjSOE['PermGroFac'] = [1.01**0.25] # Indiviual-specific income growth (from experience, e.g.)\n",
"init_cjSOE['PermGroFacAgg'] = 1.04**0.25 # Aggregate productivity growth \n",
"init_cjSOE['LivPrb'] = [0.95**0.25] # Matches a short working life \n",
"\n",
"PopGroFac_cjSOE = [1.01**0.25] # Irrelevant to the individual's choice; attach later to \"market\" economy object\n",
"\n",
"# Instantiate the baseline agent type with the parameters defined above\n",
"BaselineType = cstwMPC.cstwMPCagent(**Params.init_cjSOE)\n",
"BaselineType = AggShockConsumerType(**init_cjSOE)\n",
"BaselineType.AgeDstn = np.array(1.0) # Fix the age distribution of agents\n",
"\n",
"# Make desired number of agent types (to capture ex-ante heterogeneity)\n",
"EstimationAgentList = []\n",
"for n in range(Params.pref_type_count):\n",
"for n in range(1):\n",
" EstimationAgentList.append(deepcopy(BaselineType))\n",
" EstimationAgentList[n].seed = n # Give every instance a different seed"
]
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Expand All @@ -206,16 +249,30 @@
"source": [
"# Make an economy for the consumers to live in\n",
"\n",
"EstimationEconomy = cstwMPC.cstwMPCmarket(**Params.init_market)\n",
"init_market = {'LorenzBool': False,\n",
" 'ManyStatsBool': False,\n",
" 'ignore_periods':0, # Will get overwritten\n",
" 'PopGroFac':0.0, # Will get overwritten\n",
" 'T_retire':0, # Will get overwritten\n",
" 'TypeWeights':[], # Will get overwritten\n",
" 'Population': 10000,\n",
" 'act_T':0, # Will get overwritten\n",
" 'IncUnemp':0.15,\n",
" 'cutoffs':[(0.99,1),(0.9,1),(0.8,1),(0.6,0.8),(0.4,0.6),(0.2,0.4),(0.0,0.2)],\n",
" 'LorenzPercentiles':percentiles_to_match,\n",
" 'AggShockBool':False\n",
" }\n",
"\n",
"EstimationEconomy = CobbDouglasEconomy(init_market)\n",
"EstimationEconomy.print_parallel_error_once = True # Avoids a bug in the code\n",
"\n",
"EstimationEconomy.agents = EstimationAgentList\n",
"EstimationEconomy.act_T = Params.T_sim_PY # How many periods of history are good enough for \"steady state\""
"EstimationEconomy.act_T = 1200 # How many periods of history are good enough for \"steady state\""
]
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Expand All @@ -228,7 +285,7 @@
"EstimationEconomy.LorenzTarget = lorenz_target\n",
"EstimationEconomy.LorenzData = lorenz_long_data\n",
"EstimationEconomy.PopGroFac = PopGroFac_cjSOE # Population growth characterizes the entire economy\n",
"EstimationEconomy.ignore_periods = Params.ignore_periods_PY # Presample periods\n",
"EstimationEconomy.ignore_periods = 400 # Presample periods\n",
"\n",
"#Display statistics about the estimated model (or not)\n",
"EstimationEconomy.LorenzBool = False\n",
Expand All @@ -238,86 +295,80 @@
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"# construct spread_estimate and center_estimate if true, otherwise use the default values\n",
"Params.do_param_dist=True # Whether to use a distribution of ex-ante heterogeneity\n",
"\n",
"# Discount factors assumed to be uniformly distributed around center_pre for spread_pre on either side\n",
"\n",
"spread_pre=0.0019501105739768 #result under the default calibration of cjSOE\n",
"center_pre=1.0065863855906343 #result under the default calibration of cjSOE\n",
"\n",
"do_optimizing=False # Set to True to reestimate the distribution of time preference rates\n",
"\n",
"if do_optimizing: # If you want to rerun the cstwMPC estimation, change do_optimizing to True\n",
" # Finite value requires discount factor from combined pure and mortality-induced\n",
" # discounting to be less than one, so maximum DiscFac is 1/LivPrb\n",
" DiscFacMax = 1/Params.init_cjSOE['LivPrb'][0] # \n",
" param_range = [0.995,-0.0001+DiscFacMax] \n",
" spread_range = [0.00195,0.0205] # \n",
"\n",
" if Params.do_param_dist: # If configured to estimate the distribution\n",
" LorenzBool = True\n",
" # Run the param-dist estimation\n",
" paramDistObjective = lambda spread : cstwMPC.findLorenzDistanceAtTargetKY(\n",
" Economy = EstimationEconomy,\n",
" param_name = Params.param_name,\n",
" param_count = Params.pref_type_count,\n",
" center_range = param_range,\n",
" spread = spread,\n",
" dist_type = Params.dist_type) # Distribution of DiscFac\n",
" t_start = time()\n",
" \n",
" spread_estimate = golden(paramDistObjective \n",
" ,brack=spread_range\n",
" ,tol=1e-4) \n",
" center_estimate = EstimationEconomy.center_save\n",
" t_end = time()\n",
" else: # Run the param-point estimation only\n",
" paramPointObjective = lambda center : cstwMPC.getKYratioDifference(Economy = EstimationEconomy,\n",
" param_name = Params.param_name,\n",
" param_count = Params.pref_type_count,\n",
" center = center,\n",
" spread = 0.0,\n",
" dist_type = Params.dist_type)\n",
" t_start = time()\n",
" center_estimate = brentq(paramPointObjective # Find best point estimate \n",
" ,param_range[0]\n",
" ,param_range[1],xtol=1e-6)\n",
" spread_estimate = 0.0\n",
" t_end = time()\n",
" \n",
" print(spread_estimate)\n",
" print('****************')\n",
" print(center_estimate)\n",
" print('****************')\n",
"else: # Just use the hard-wired numbers from cstwMPC\n",
" center_estimate=center_pre\n",
" spread_estimate=spread_pre"
"def distributeParams(self,param_name,param_count,center,spread,dist_type):\n",
" '''\n",
" Distributes heterogeneous values of one parameter to the AgentTypes in self.agents.\n",
" Parameters\n",
" ----------\n",
" param_name : string\n",
" Name of the parameter to be assigned.\n",
" param_count : int\n",
" Number of different values the parameter will take on.\n",
" center : float\n",
" A measure of centrality for the distribution of the parameter.\n",
" spread : float\n",
" A measure of spread or diffusion for the distribution of the parameter.\n",
" dist_type : string\n",
" The type of distribution to be used. Can be \"lognormal\" or \"uniform\" (can expand).\n",
" Returns\n",
" -------\n",
" None\n",
" '''\n",
" # Get a list of discrete values for the parameter\n",
" if dist_type == 'uniform':\n",
" # If uniform, center is middle of distribution, spread is distance to either edge\n",
" param_dist = approxUniform(N=param_count,bot=center-spread,top=center+spread)\n",
" elif dist_type == 'lognormal':\n",
" # If lognormal, center is the mean and spread is the standard deviation (in log)\n",
" tail_N = 3\n",
" param_dist = approxLognormal(N=param_count-tail_N,mu=np.log(center)-0.5*spread**2,sigma=spread,tail_N=tail_N,tail_bound=[0.0,0.9], tail_order=np.e)\n",
"\n",
" # Distribute the parameters to the various types, assigning consecutive types the same\n",
" # value if there are more types than values\n",
" replication_factor = len(self.agents) // param_count \n",
" # Note: the double division is intenger division in Python 3 and 2.7, this makes it explicit\n",
" j = 0\n",
" b = 0\n",
" while j < len(self.agents):\n",
" for n in range(replication_factor):\n",
" self.agents[j](AgentCount = int(self.Population*param_dist[0][b]*self.TypeWeight[n]))\n",
" exec('self.agents[j](' + param_name + '= param_dist[1][b])')\n",
" j += 1\n",
" b += 1\n",
" \n",
"EstimationEconomy.distributeParams = distributeParams"
]
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{
"ename": "NameError",
"evalue": "name 'center_estimate' is not defined",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-23-7d280b67d178>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;34m'DiscFac'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;36m7\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m# How many different types of consumer are there\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mcenter_estimate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;31m# Increase patience slightly vs cstwMPC so that maximum saving rate is higher\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mspread_estimate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;31m# How much difference is there across consumers\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m Params.dist_type) # Default is for a uniform distribution\n",
"\u001b[0;31mNameError\u001b[0m: name 'center_estimate' is not defined"
]
}
],
"source": [
"# Construct the economy at date 0\n",
"EstimationEconomy.distributeParams( # Construct consumer types whose heterogeneity is in the given parameter\n",
" 'DiscFac',\n",
" Params.pref_type_count,# How many different types of consumer are there \n",
" 7,# How many different types of consumer are there \n",
" center_estimate, # Increase patience slightly vs cstwMPC so that maximum saving rate is higher\n",
" spread_estimate, # How much difference is there across consumers\n",
" Params.dist_type) # Default is for a uniform distribution"
Expand Down Expand Up @@ -563,8 +614,7 @@
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Expand Down
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