def calcNatlSavingRate(PrmShkVar_multiplier, RNG_seed=0):
"""
This function actually performs the experiment we want.
Remember this experiment is: get consumers into the steady-state associated with the low-growth
regime. Then, give them an unanticipated shock that increases the income growth rate
and permanent income uncertainty at the same time. What happens to the path for
the national saving rate? Can an increase in permanent income uncertainty
explain the high Chinese saving rate since economic reforms began?
The inputs are:
* PrmShkVar_multiplier, the number by which we want to multiply the variance
of the permanent shock in the low-growth state to get the variance of the
permanent shock in the high-growth state
* RNG_seed, an integer to seed the random number generator for simulations. This useful
because we are going to run this function for different values of PrmShkVar_multiplier,
and we may not necessarily want the simulated agents in each run to experience
the same (normalized) shocks.
"""
# First, make a deepcopy of the ChineseConsumerTypes (each with their own discount factor),
# because we are going to alter them
ChineseConsumerTypesNew = deepcopy(ChineseConsumerTypes)
# Set the uncertainty in the high-growth state to the desired amount, keeping in mind
# that PermShkStd is a list of length 1
PrmShkStd_multiplier = PrmShkVar_multiplier**.5
IncomeParams.PermShkStd = [LowGrowth_PermShkStd[0] * PrmShkStd_multiplier]
# Construct the appropriate income distributions
HighGrowthIncomeDstn = constructLognormalIncomeProcessUnemployment(
IncomeParams)[0][0]
# To calculate the national saving rate, we need national income and national consumption
# To get those, we are going to start national income and consumption at 0, and then
# loop through each agent type and see how much they contribute to income and consumption.
NatlIncome = 0.
NatlCons = 0.
for ChineseConsumerTypeNew in ChineseConsumerTypesNew:
### For each consumer type (i.e. each discount factor), calculate total income
### and consumption
# First give each ConsumerType their own random number seed
RNG_seed += 19
ChineseConsumerTypeNew.seed = RNG_seed
# Set the income distribution in each Markov state appropriately
ChineseConsumerTypeNew.IncomeDstn = [[
LowGrowthIncomeDstn, HighGrowthIncomeDstn
]]
# Solve the problem for this ChineseConsumerTypeNew
ChineseConsumerTypeNew.solve()
"""
Now we are ready to simulate.
This case will be a bit different than most, because agents' *perceptions* of the probability
of changes in the Chinese economy will differ from the actual probability of changes.
Specifically, agents think there is a 0% chance of moving out of the low-growth state, and
that there is a (1./160) chance of moving out of the high-growth state. In reality, we
want the Chinese economy to reach the low growth steady state, and then move into the
high growth state with probability 1. Then we want it to persist in the high growth
state for 40 years.
"""
## Now, simulate 500 quarters to get to steady state, then 40 years of high growth
ChineseConsumerTypeNew.T_sim = 660
# Ordinarily, the simulate method for a MarkovConsumerType randomly draws Markov states
# according to the transition probabilities in MrkvArray *independently* for each simulated
# agent. In this case, however, we want the discrete state to be *perfectly coordinated*
# across agents-- it represents a macroeconomic state, not a microeconomic one! In fact,
# we don't want a random history at all, but rather a specific, predetermined history: 125
# years of low growth, followed by 40 years of high growth.
# To do this, we're going to "hack" our consumer type a bit. First, we set the attribute
# MrkvPrbsInit so that all of the initial Markov states are in the low growth state. Then
# we initialize the simulation and run it for 500 quarters. However, as we do not
# want the Markov state to change during this time, we change its MrkvArray to always be in
# the low growth state with probability 1.
ChineseConsumerTypeNew.MrkvPrbsInit = np.array(
[1.0, 0.0]) # All consumers born in low growth state
ChineseConsumerTypeNew.MrkvArray[0] = np.array(
[[1.0, 0.0], [1.0, 0.0]]) # Stay in low growth state
ChineseConsumerTypeNew.initializeSim(
) # Clear the history and make all newborn agents
ChineseConsumerTypeNew.simulate(500) # Simulate 500 quarders of data
# Now we want the high growth state to occur for the next 160 periods. We change the initial
# Markov probabilities so that any agents born during this time (to replace an agent who
# died) is born in the high growth state. Moreover, we change the MrkvArray to *always* be
# in the high growth state with probability 1. Then we simulate 160 more quarters.
ChineseConsumerTypeNew.MrkvPrbsInit = np.array(
[0.0, 1.0]) # All consumers born in low growth state
ChineseConsumerTypeNew.MrkvArray[0] = np.array(
[[0.0, 1.0], [0.0, 1.0]]) # Stay in low growth state
ChineseConsumerTypeNew.simulate(160) # Simulate 160 quarders of data
# Now, get the aggregate income and consumption of this ConsumerType over time
IncomeOfThisConsumerType = np.sum(
(ChineseConsumerTypeNew.aNrmNow_hist *
ChineseConsumerTypeNew.pLvlNow_hist *
(ChineseConsumerTypeNew.Rfree[0] - 1.)) +
ChineseConsumerTypeNew.pLvlNow_hist,
axis=1)
ConsOfThisConsumerType = np.sum(ChineseConsumerTypeNew.cNrmNow_hist *
ChineseConsumerTypeNew.pLvlNow_hist,
axis=1)
# Add the income and consumption of this ConsumerType to national income and consumption
NatlIncome += IncomeOfThisConsumerType
NatlCons += ConsOfThisConsumerType
# After looping through all the ConsumerTypes, calculate and return the path of the national
# saving rate
NatlSavingRate = (NatlIncome - NatlCons) / NatlIncome
return NatlSavingRate
"""
Now, write the function to perform the experiment.
Recall that all parameters have been assigned appropriately, except for the income process.
This is because we want to see how much uncertainty needs to accompany the high-growth state
to generate the desired high savings rate.
Therefore, among other things, this function will have to initialize and assign
the appropriate income process.
"""
# First create the income distribution in the low-growth state, which we will not change
from ConsIndShockModel import constructLognormalIncomeProcessUnemployment
import ConsumerParameters as IncomeParams
LowGrowthIncomeDstn = constructLognormalIncomeProcessUnemployment(
IncomeParams)[0][0]
# Remember the standard deviation of the permanent income shock in the low-growth state for later
LowGrowth_PermShkStd = IncomeParams.PermShkStd
def calcNatlSavingRate(PrmShkVar_multiplier, RNG_seed=0):
"""
This function actually performs the experiment we want.
Remember this experiment is: get consumers into the steady-state associated with the low-growth
regime. Then, give them an unanticipated shock that increases the income growth rate
and permanent income uncertainty at the same time. What happens to the path for
the national saving rate? Can an increase in permanent income uncertainty
explain the high Chinese saving rate since economic reforms began?
Recall that all parameters have been assigned appropriately, except for the income process.
This is because we want to see how much uncertainty needs to accompany the high-growth state
to generate the desired high savings rate.
Therefore, among other things, this function will have to initialize and assign
the appropriate income process.
"""
# First create the income distribution in the low-growth state, which we will not change
from ConsIndShockModel import constructLognormalIncomeProcessUnemployment
import ConsumerParameters as IncomeParams
LowGrowthIncomeDstn = constructLognormalIncomeProcessUnemployment(IncomeParams)[0][0]
# Remember the standard deviation of the permanent income shock in the low-growth state for later
LowGrowth_PermShkStd = IncomeParams.PermShkStd
def calcNatlSavingRate(PrmShkVar_multiplier,RNG_seed = 0):
"""
This function actually performs the experiment we want.
Remember this experiment is: get consumers into the steady-state associated with the low-growth
regime. Then, give them an unanticipated shock that increases the income growth rate
and permanent income uncertainty at the same time. What happens to the path for
the national saving rate? Can an increase in permanent income uncertainty
explain the high Chinese saving rate since economic reforms began?
def calcNatlSavingRate(PrmShkVar_multiplier,RNG_seed = 0):
"""
This function actually performs the experiment we want.
Remember this experiment is: get consumers into the steady-state associated with the low-growth
regime. Then, give them an unanticipated shock that increases the income growth rate
and permanent income uncertainty at the same time. What happens to the path for
the national saving rate? Can an increase in permanent income uncertainty
explain the high Chinese saving rate since economic reforms began?
The inputs are:
* PrmShkVar_multiplier, the number by which we want to multiply the variance
of the permanent shock in the low-growth state to get the variance of the
permanent shock in the high-growth state
* RNG_seed, an integer to seed the random number generator for simulations. This useful
because we are going to run this function for different values of PrmShkVar_multiplier,
and we may not necessarily want the simulated agents in each run to experience
the same (normalized) shocks.
"""
# First, make a deepcopy of the ChineseConsumerTypes (each with their own discount factor),
# because we are going to alter them
ChineseConsumerTypesNew = deepcopy(ChineseConsumerTypes)
# Set the uncertainty in the high-growth state to the desired amount, keeping in mind
# that PermShkStd is a list of length 1
PrmShkStd_multiplier = PrmShkVar_multiplier ** .5
IncomeParams.PermShkStd = [LowGrowth_PermShkStd[0] * PrmShkStd_multiplier]
# Construct the appropriate income distributions
HighGrowthIncomeDstn = constructLognormalIncomeProcessUnemployment(IncomeParams)[0][0]
# To calculate the national saving rate, we need national income and national consumption
# To get those, we are going to start national income and consumption at 0, and then
# loop through each agent type and see how much they contribute to income and consumption.
NatlIncome = 0.
NatlCons = 0.
for ChineseConsumerTypeNew in ChineseConsumerTypesNew:
### For each consumer type (i.e. each discount factor), calculate total income
### and consumption
# First give each ConsumerType their own random number seed
RNG_seed += 19
ChineseConsumerTypeNew.seed = RNG_seed
# Set the income distribution in each Markov state appropriately
ChineseConsumerTypeNew.IncomeDstn = [[LowGrowthIncomeDstn,HighGrowthIncomeDstn]]
# Solve the problem for this ChineseConsumerTypeNew
ChineseConsumerTypeNew.solve()
"""
Now we are ready to simulate.
This case will be a bit different than most, because agents' *perceptions* of the probability
of changes in the Chinese economy will differ from the actual probability of changes.
Specifically, agents think there is a 0% chance of moving out of the low-growth state, and
that there is a (1./160) chance of moving out of the high-growth state. In reality, we
want the Chinese economy to reach the low growth steady state, and then move into the
high growth state with probability 1. Then we want it to persist in the high growth
state for 40 years.
"""
## Now, simulate 500 quarters to get to steady state, then 40 years of high growth
ChineseConsumerTypeNew.sim_periods = 660
## If we wanted to *simulate* the Markov states according to agents' perceived
## probabilities, this is how we would do it
#ChinaExample.Mrkv_init = np.zeros(ChinaExample.Nagents,dtype=int) #everyone starts off in low-growth state
#ChinaExample.makeMrkvHist()
## We actually want to CHOOSE the Markov states, rather than simulate them.
## To do that, first set the history for China that we are interested in
# Initialize an array of 0s, to reflect the long low-growth period before the reforms
ChineseHistory = np.zeros((ChineseConsumerTypeNew.sim_periods,
ChineseConsumerTypeNew.Nagents),dtype=int)
# Set values of 1 to reflect the high-growth period following reforms
ChineseHistory[-160:,:] = 1
# Finally, assign our radically simplified version of ChineseHistory as the history
# of Markov states experienced by our simulated consumers
ChineseConsumerTypeNew.MrkvHist = ChineseHistory
# Finish the rest of the simulation
ChineseConsumerTypeNew.makeIncShkHist() #create the history of income shocks, conditional on the Markov state
ChineseConsumerTypeNew.initializeSim() #get ready to simulate everything else
ChineseConsumerTypeNew.simConsHistory() #simulate everything else
# Now, get the aggregate income and consumption of this ConsumerType
IncomeOfThisConsumerType = np.sum((ChineseConsumerTypeNew.aHist * ChineseConsumerTypeNew.pHist*
(ChineseConsumerTypeNew.Rfree[0] - 1.)) +
ChineseConsumerTypeNew.pHist, axis=1)
ConsOfThisConsumerType = np.sum(ChineseConsumerTypeNew.cHist * ChineseConsumerTypeNew.pHist,
axis=1)
# Add the income and consumption of this ConsumerType to national income and consumption
NatlIncome += IncomeOfThisConsumerType
NatlCons += ConsOfThisConsumerType
# After looping through all the ConsumerTypes, calculate and return the path of the national
# saving rate
NatlSavingRate = (NatlIncome - NatlCons)/NatlIncome
return NatlSavingRate
def calcNatlSavingRate(PrmShkVar_multiplier,RNG_seed = 0):
"""
This function actually performs the experiment we want.
Remember this experiment is: get consumers into the steady-state associated with the low-growth
regime. Then, give them an unanticipated shock that increases the income growth rate
and permanent income uncertainty at the same time. What happens to the path for
the national saving rate? Can an increase in permanent income uncertainty
explain the high Chinese saving rate since economic reforms began?
The inputs are:
* PrmShkVar_multiplier, the number by which we want to multiply the variance
of the permanent shock in the low-growth state to get the variance of the
permanent shock in the high-growth state
* RNG_seed, an integer to seed the random number generator for simulations. This useful
because we are going to run this function for different values of PrmShkVar_multiplier,
and we may not necessarily want the simulated agents in each run to experience
the same (normalized) shocks.
"""
# First, make a deepcopy of the ChineseConsumerTypes (each with their own discount factor),
# because we are going to alter them
ChineseConsumerTypesNew = deepcopy(ChineseConsumerTypes)
# Set the uncertainty in the high-growth state to the desired amount, keeping in mind
# that PermShkStd is a list of length 1
PrmShkStd_multiplier = PrmShkVar_multiplier ** .5
IncomeParams.PermShkStd = [LowGrowth_PermShkStd[0] * PrmShkStd_multiplier]
# Construct the appropriate income distributions
HighGrowthIncomeDstn = constructLognormalIncomeProcessUnemployment(IncomeParams)[0][0]
# To calculate the national saving rate, we need national income and national consumption
# To get those, we are going to start national income and consumption at 0, and then
# loop through each agent type and see how much they contribute to income and consumption.
NatlIncome = 0.
NatlCons = 0.
for ChineseConsumerTypeNew in ChineseConsumerTypesNew:
### For each consumer type (i.e. each discount factor), calculate total income
### and consumption
# First give each ConsumerType their own random number seed
RNG_seed += 19
ChineseConsumerTypeNew.seed = RNG_seed
# Set the income distribution in each Markov state appropriately
ChineseConsumerTypeNew.IncomeDstn = [[LowGrowthIncomeDstn,HighGrowthIncomeDstn]]
# Solve the problem for this ChineseConsumerTypeNew
ChineseConsumerTypeNew.solve()
"""
Now we are ready to simulate.
This case will be a bit different than most, because agents' *perceptions* of the probability
of changes in the Chinese economy will differ from the actual probability of changes.
Specifically, agents think there is a 0% chance of moving out of the low-growth state, and
that there is a (1./160) chance of moving out of the high-growth state. In reality, we
want the Chinese economy to reach the low growth steady state, and then move into the
high growth state with probability 1. Then we want it to persist in the high growth
state for 40 years.
"""
## Now, simulate 500 quarters to get to steady state, then 40 years of high growth
ChineseConsumerTypeNew.T_sim = 660
# Ordinarily, the simulate method for a MarkovConsumerType randomly draws Markov states
# according to the transition probabilities in MrkvArray *independently* for each simulated
# agent. In this case, however, we want the discrete state to be *perfectly coordinated*
# across agents-- it represents a macroeconomic state, not a microeconomic one! In fact,
# we don't want a random history at all, but rather a specific, predetermined history: 125
# years of low growth, followed by 40 years of high growth.
# To do this, we're going to "hack" our consumer type a bit. First, we set the attribute
# MrkvPrbsInit so that all of the initial Markov states are in the low growth state. Then
# we initialize the simulation and run it for 500 quarters. However, as we do not
# want the Markov state to change during this time, we change its MrkvArray to always be in
# the low growth state with probability 1.
ChineseConsumerTypeNew.MrkvPrbsInit = np.array([1.0,0.0]) # All consumers born in low growth state
ChineseConsumerTypeNew.MrkvArray[0] = np.array([[1.0,0.0],[1.0,0.0]]) # Stay in low growth state
ChineseConsumerTypeNew.initializeSim() # Clear the history and make all newborn agents
ChineseConsumerTypeNew.simulate(500) # Simulate 500 quarders of data
# Now we want the high growth state to occur for the next 160 periods. We change the initial
# Markov probabilities so that any agents born during this time (to replace an agent who
# died) is born in the high growth state. Moreover, we change the MrkvArray to *always* be
# in the high growth state with probability 1. Then we simulate 160 more quarters.
ChineseConsumerTypeNew.MrkvPrbsInit = np.array([0.0,1.0]) # All consumers born in low growth state
ChineseConsumerTypeNew.MrkvArray[0] = np.array([[0.0,1.0],[0.0,1.0]]) # Stay in low growth state
ChineseConsumerTypeNew.simulate(160) # Simulate 160 quarders of data
# Now, get the aggregate income and consumption of this ConsumerType over time
IncomeOfThisConsumerType = np.sum((ChineseConsumerTypeNew.aNrmNow_hist*ChineseConsumerTypeNew.pLvlNow_hist*
(ChineseConsumerTypeNew.Rfree[0] - 1.)) +
ChineseConsumerTypeNew.pLvlNow_hist, axis=1)
ConsOfThisConsumerType = np.sum(ChineseConsumerTypeNew.cNrmNow_hist*ChineseConsumerTypeNew.pLvlNow_hist,axis=1)
# Add the income and consumption of this ConsumerType to national income and consumption
NatlIncome += IncomeOfThisConsumerType
NatlCons += ConsOfThisConsumerType
# After looping through all the ConsumerTypes, calculate and return the path of the national
# saving rate
NatlSavingRate = (NatlIncome - NatlCons)/NatlIncome
return NatlSavingRate
