def plotQmodel(model, exog, returnDF = False):
# Simpulate the optimal response
dr = pf.deterministic_solve(model = model,shocks = exog,verbose=True)
# Plot exogenous variables
ex = ['R','tau','itc_1','psi']
fig, axes = plt.subplots(1,len(ex), figsize = (10,3))
axes = axes.flatten()
for i in range(len(ex)):
ax = axes[i]
ax.plot(dr[ex[i]],'.')
ax.set_xlabel('Time')
ax.set_ylabel(ex[i])
fig.tight_layout(rect=[0, 0.03, 1, 0.95])
fig.suptitle('Exogenous variables', fontsize=16)
# Plot optimal response variables
fig, axes = plt.subplots(2,2, figsize = (10,6))
axes = axes.flatten()
opt = ['k','i','lambda_1','q_1']
for i in range(len(opt)):
ax = axes[i]
ax.plot(dr[opt[i]],'.')
ax.set_xlabel('Time')
ax.set_ylabel(opt[i])
fig.tight_layout(rect=[0, 0.03, 1, 0.95])
fig.suptitle('Endogenous response', fontsize=16)
if returnDF:
return(dr)
def simul_change_dolo(model, k0, exog0, exog1, t_change, T_sim):
# The first step is to create time series for the exogenous variables
exog = np.array([
exog1,
] * (T_sim - t_change))
if t_change > 0:
exog = np.concatenate(
(
np.array([
exog0,
] * (t_change)),
exog,
),
axis=0,
)
exog = pd.DataFrame(exog, columns=["R", "tau", "itc_1", "psi"])
# Simpulate the optimal response
dr = pf.deterministic_solve(model=model,
shocks=exog,
T=T_sim,
verbose=True,
s1=k0)
# Dolo uses the first period to report the steady state
# so we ommit it.
return dr[1:]
def plotQmodel(model, exog, returnDF=False):
# Simpulate the optimal response
dr = pf.deterministic_solve(model=model, shocks=exog, verbose=True)
# Plot exogenous variables
ex = ["R", "tau", "itc_1", "psi"]
fig, axes = plt.subplots(1, len(ex), figsize=(10, 3))
axes = axes.flatten()
for i in range(len(ex)):
ax = axes[i]
ax.plot(dr[ex[i]], ".")
ax.set_xlabel("Time")
ax.set_ylabel(ex[i])
fig.tight_layout(rect=[0, 0.03, 1, 0.95])
fig.suptitle("Exogenous variables", fontsize=16)
# Plot optimal response variables
fig, axes = plt.subplots(2, 2, figsize=(10, 6))
axes = axes.flatten()
opt = ["k", "i", "lambda_1", "q_1"]
for i in range(len(opt)):
ax = axes[i]
ax.plot(dr[opt[i]], ".")
ax.set_xlabel("Time")
ax.set_ylabel(opt[i])
fig.tight_layout(rect=[0, 0.03, 1, 0.95])
fig.suptitle("Endogenous response", fontsize=16)
if returnDF:
return dr
# Dolo receives a DataFrame with the full future paths for ALL exogenous
# variables. So we create one:
Exog = pd.DataFrame({'R':[R]*T,
'tau':[tau]*T,
'itc_1':[zeta]*T,
'psi':Psi_sequence})
# Examine the first few entries.
Exog.head()
# Note all other variables are left constant.
# %%
# Now use the "perfect foresight" dolo solver
response = pf.deterministic_solve(model = QDolo, # Model we are using (in dolo)
shocks = Exog, # Paths for exog. variables
T=T, # Total simulation time
s1 = [k0], # Initial state
verbose=True)
# Response is a DataFrame with the paths of every variable over time.
# It adds information we don't need on the first row. So we delete it
response = response[1:]
# Inspect the first few elements.
response.head()
# %% [markdown]
# # IMPORTANT
#
# Because of the way the model is implemented, it does not keep track of $\lambda_t$ or $ITC_t$, but $\lambda_{t+1}$ and $ITC_{t+1}$ instead.
#