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Computing Heterogenous Agent Jacobians in HARK

By William Du

This notebook illustrates how to compute Heterogenous Agent Jacobian matrices in HARK.

These matrices are a fundamental building building block to solving Heterogenous Agent New Keynesian Models with the sequence space jacobian methodology. For more information, see Auclert, Rognlie, Bardoszy, and Straub (2021)

For the IndShockConsumerType, Jacobians of Consumption and Saving can be computed with respect to the following parameters: LivPrb, PermShkStd,TranShkStd,UnempPrb, Rfree, IncUnemp.

import time

import matplotlib.pyplot as plt

from HARK.ConsumptionSaving.ConsNewKeynesianModel import (
    NewKeynesianConsumerType,
)

Create Agent

# Dictionary for Agent
Dict = {
    # Solving Parameters
    "aXtraMax": 1000,
    "aXtraCount": 200,
    # Transition Matrix Simulations Parameters
    "mMax": 10000,
    "mMin": 1e-6,
    "mCount": 300,
    "mFac": 3,
}

Agent = NewKeynesianConsumerType(**Dict)

Compute Steady State

start = time.time()
Agent.compute_steady_state()
print("Seconds to compute steady state", time.time() - start)

Seconds to compute steady state 21.450182676315308

Compute Jacobians

Shocks possible: LivPrb, PermShkStd,TranShkStd, DiscFac,UnempPrb, Rfree, IncUnemp

Shock to Standard Deviation to Permanent Income Shocks

start = time.time()

CJAC_Perm, AJAC_Perm = Agent.calc_jacobian("PermShkStd", 300)

print("Seconds to calculate Jacobian", time.time() - start)

Seconds to calculate Jacobian 12.027279376983643

Consumption Jacobians

plt.plot(CJAC_Perm.T[0])
plt.plot(CJAC_Perm.T[10])
plt.plot(CJAC_Perm.T[30])
plt.show()

Asset Jacobians

plt.plot(AJAC_Perm.T[0])
plt.plot(AJAC_Perm.T[10])
plt.plot(AJAC_Perm.T[30])
plt.plot(AJAC_Perm.T[60])
plt.show()

Shock to Real Interest Rate

CJAC_Rfree, AJAC_Rfree = Agent.calc_jacobian("Rfree", 300)

Consumption Jacobians

plt.plot(CJAC_Rfree.T[0])
plt.plot(CJAC_Rfree.T[10])
plt.plot(CJAC_Rfree.T[30])
plt.plot(CJAC_Rfree.T[60])
plt.show()

Asset Jacobians

plt.plot(AJAC_Rfree.T[0])
plt.plot(AJAC_Rfree.T[10])
plt.plot(AJAC_Rfree.T[30])
plt.plot(AJAC_Rfree.T[60])
plt.show()

Shock to Unemployment Probability

CJAC_UnempPrb, AJAC_UnempPrb = Agent.calc_jacobian("UnempPrb", 300)

plt.plot(CJAC_UnempPrb.T[0])
plt.plot(CJAC_UnempPrb.T[10])
plt.plot(CJAC_UnempPrb.T[30])
plt.plot(CJAC_UnempPrb.T[60])
plt.show()

plt.plot(AJAC_UnempPrb.T[0])
plt.plot(AJAC_UnempPrb.T[10])
plt.plot(AJAC_UnempPrb.T[30])
plt.plot(AJAC_UnempPrb.T[60])
plt.show()