class testPerfForesightConsumerType(unittest.TestCase):
def setUp(self):
self.agent = PerfForesightConsumerType()
self.agent_infinite = PerfForesightConsumerType(cycles=0)
PF_dictionary = {
"CRRA": 2.5,
"DiscFac": 0.96,
"Rfree": 1.03,
"LivPrb": [0.98],
"PermGroFac": [1.01],
"T_cycle": 1,
"cycles": 0,
"AgentCount": 10000,
}
self.agent_alt = PerfForesightConsumerType(**PF_dictionary)
def test_default_solution(self):
self.agent.solve()
c = self.agent.solution[0].cFunc
self.assertEqual(c.x_list[0], -0.9805825242718447)
self.assertEqual(c.x_list[1], 0.01941747572815533)
self.assertEqual(c.y_list[0], 0)
self.assertEqual(c.y_list[1], 0.511321002804608)
self.assertEqual(c.decay_extrap, False)
def test_another_solution(self):
self.agent_alt.DiscFac = 0.90
self.agent_alt.solve()
self.assertAlmostEqual(self.agent_alt.solution[0].cFunc(10).tolist(),
3.9750093524820787)
def test_check_conditions(self):
self.agent_infinite.check_conditions()
self.assertTrue(self.agent_infinite.conditions["AIC"])
self.assertTrue(self.agent_infinite.conditions["GICRaw"])
self.assertTrue(self.agent_infinite.conditions["RIC"])
self.assertTrue(self.agent_infinite.conditions["FHWC"])
def test_simulation(self):
self.agent_infinite.solve()
# Create parameter values necessary for simulation
SimulationParams = {
"AgentCount": 10000, # Number of agents of this type
"T_sim": 120, # Number of periods to simulate
"aNrmInitMean": -6.0, # Mean of log initial assets
"aNrmInitStd": 1.0, # Standard deviation of log initial assets
"pLvlInitMean": 0.0, # Mean of log initial permanent income
"pLvlInitStd":
0.0, # Standard deviation of log initial permanent income
"PermGroFacAgg": 1.0, # Aggregate permanent income growth factor
"T_age":
None, # Age after which simulated agents are automatically killed
}
self.agent_infinite.assign_parameters(
**SimulationParams
) # This implicitly uses the assign_parameters method of AgentType
# Create PFexample object
self.agent_infinite.track_vars = ["mNrm"]
self.agent_infinite.initialize_sim()
self.agent_infinite.simulate()
self.assertAlmostEqual(
np.mean(self.agent_infinite.history["mNrm"], axis=1)[40],
-23.008063500363942,
)
self.assertAlmostEqual(
np.mean(self.agent_infinite.history["mNrm"], axis=1)[100],
-27.164608851546927,
)
## Try now with the manipulation at time step 80
self.agent_infinite.initialize_sim()
self.agent_infinite.simulate(80)
# This actually does nothing because aNrmNow is
# epiphenomenal. Probably should change mNrmNow instead
self.agent_infinite.state_now['aNrm'] += (-5.0)
self.agent_infinite.simulate(40)
self.assertAlmostEqual(
np.mean(self.agent_infinite.history["mNrm"], axis=1)[40],
-23.008063500363942,
)
self.assertAlmostEqual(
np.mean(self.agent_infinite.history["mNrm"], axis=1)[100],
-29.140261331951606,
)
def test_stable_points(self):
# Solve the constrained agent. Stable points exists only with a
# borrowing constraint.
constrained_agent = PerfForesightConsumerType(cycles=0,
BoroCnstArt=0.0)
constrained_agent.solve()
# Check against pre-computed values.
self.assertEqual(constrained_agent.solution[0].mNrmStE, 1.0)
# Check that they are both the same, since the problem is deterministic
self.assertEqual(constrained_agent.solution[0].mNrmStE,
constrained_agent.solution[0].mNrmTrg)
PFexample.assign_parameters(**SimulationParams)
# %% [markdown] {"incorrectly_encoded_metadata": "pycharm= [markdown] {\"name\": \"#%% md\\n\"}"}
# To generate simulated data, we need to specify which variables we want to track the "history" of for this instance. To do so, we set the `track_vars` attribute of our `PerfForesightConsumerType` instance to be a list of strings with the simulation variables we want to track.
#
# In this model, valid arguments to `track_vars` include $\texttt{mNrm}$, $\texttt{cNrm}$, $\texttt{aNrm}$, and $\texttt{pLvl}$. Because this model has no idiosyncratic shocks, our simulated data will be quite boring.
#
# ### Generating simulated data
#
# Before simulating, the `initialize_sim` method must be invoked. This resets our instance back to its initial state, drawing a set of initial $\texttt{aNrm}$ and $\texttt{pLvl}$ values from the specified distributions and storing them in the attributes $\texttt{aNrmNow_init}$ and $\texttt{pLvlNow_init}$. It also resets this instance's internal random number generator, so that the same initial states will be set every time `initialize_sim` is called. In models with non-trivial shocks, this also ensures that the same sequence of shocks will be generated on every simulation run.
#
# Finally, the `simulate` method can be called.
# %% {"pycharm": {"name": "#%%\n"}}
PFexample.track_vars = ['mNrm']
PFexample.initialize_sim()
PFexample.simulate()
# %% {"incorrectly_encoded_metadata": "pycharm= [markdown] {\"name\": \"#%% md\\n\"}"}
# Each simulation variable $\texttt{X}$ named in $\texttt{track_vars}$ will have the *history* of that variable for each agent stored in the attribute $\texttt{X_hist}$ as an array of shape $(\texttt{T_sim},\texttt{AgentCount})$. To see that the simulation worked as intended, we can plot the mean of $m_t$ in each simulated period:
# %% {"pycharm": {"name": "#%%\n"}}
plt.plot(np.mean(PFexample.history['mNrm'], axis=1))
plt.xlabel("Time")
plt.ylabel("Mean normalized market resources")
plt.show()
# %% [markdown] {"incorrectly_encoded_metadata": "pycharm= [markdown] {\"name\": \"#%% md\\n\"}"}
# A perfect foresight consumer can borrow against the PDV of his future income-- his human wealth-- and thus as time goes on, our simulated agents approach the (very negative) steady state level of $m_t$ while being steadily replaced with consumers with roughly $m_t=1$.
#
# The slight wiggles in the plotted curve are due to consumers randomly dying and being replaced; their replacement will have an initial state drawn from the distributions specified by the user. To see the current distribution of ages, we can look at the attribute $\texttt{t_age}$.