Part 2.1 Use Fred to estimate changes to the model parameters during the Covid-19 economic crisis. You did this already in the Should Do (Ch12) assignment. Update or upgrade your calculations as necessary. Include graphs as needed.
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Part 2.2 Set the model to a total timeframe of 50 years and use the changes you estimated in part 2.1 to simulate the economy during 2020 and 2021. Set 2020 to be equal to period 5 in the model. Justify your choices and describe the outcome under the three different policy rules.
The plots below are from the IS curve calibration and the first row is the actual share of output for C, I, and G. The last plot is the actual output compare to potential output during 01/01/2019 - 10/01/2024. The second set of plots are the same but it represents the percent change for each variable during thr same time period. In this scenario we can see how Covid impacted the economy, but we can also see an increase in Government spending which helped bring consumption, investments, and output back form the economic doomday path they where in. In the 2.1 scenario other economic stimulation will need to be done apart from just lowering rates.
from macrofunctions import plot_m_vs_period_Q
# CH 11 Should do Calibration
plot_m_vs_period_Q("C://Users//User//OneDrive - BYU-Idaho//Desktop//Coding//Macro//Should Do's//macrodata.xlsx", ['C/Y_Q', 'I/Y_Q', 'G/Y_Q', 'Y_actual_Q','C/Y_Q%', 'I/Y_Q%', 'G/Y_Q%', 'Y_actual_Q%'], '01/01/2019', '10/01/2022')
Has both models for CH13 & 12 model combined
# Has both models for CH13 & 12 model combined
import pandas as pd
from macrofunctions import calculate_inflation_stabilization_inflation, calculate_inflation_stabilization_sroutput, calculate_output_stabilization, calculate_taylor_rule_sroutput, calculate_taylor_rule_inflation, update_excel_df, calculate_y_tilde, calculate_c_inflation, calculate_inflation, calculate_inflation1, calculate_SRY, calculate_Rt, plot_m_vs_period, plot_m_vs_period_Q, CH13_Short_Run_Output
parameters = {
'Simulation Period (yrs)': 20,
'a': 0.0,
'a(%)': 0.0,
'b': 0.68,
'r(%)': 2.0,
'R(%)': 2.0,
'v': 0.076,
'o(%)': 0.0,
'm': 0.5,
'n': 0.5,
'pi_bar': 2,
'fed_target_initial_inflation': 2.0
}
# 2020 =5, 2025 = 10, 2030 = 15, 2035 = 20.
quantitative_experiments = {
'a(%)': [
{'new_value': -8, 'time_period': 5, 'length': 1},
{'new_value': 8, 'time_period': 6, 'length': 1},
{'new_value': 4, 'time_period': 7, 'length': 1},
{'new_value': 1, 'time_period': 8, 'length': 1},
{'new_value': 1.5, 'time_period': 9, 'length': 1},
{'new_value': 2.5, 'time_period': 10, 'length': 1},
{'new_value': 0, 'time_period': 11, 'length': 1},
{'new_value': .35, 'time_period': 12, 'length': 1},
{'new_value': -1.5, 'time_period': 13, 'length': 1},
{'new_value': -1, 'time_period': 14, 'length': 1}
],
'R(%)': [
{'new_value': .4, 'time_period': 1, 'length': 1},
{'new_value': 1, 'time_period': 2, 'length': 1},
{'new_value': 1.83, 'time_period': 3, 'length': 1},
{'new_value': 2.16, 'time_period': 4, 'length': 1},
{'new_value': .038, 'time_period': 5, 'length': 1},
{'new_value': 0.08, 'time_period': 6, 'length': 1},
{'new_value': 1.68, 'time_period': 7, 'length': 1},
{'new_value': 5.02, 'time_period': 8, 'length': 2},
{'new_value': 4.65, 'time_period': 10, 'length': 1},
{'new_value': 4, 'time_period': 11, 'length': 1},
{'new_value': 2.0, 'time_period': 12, 'length': 1},
]
} # to add just use the same format & change parameter
# Initialize the DataFrame
num_periods = parameters['Simulation Period (yrs)'] + 1
df = pd.DataFrame({
'Period': range(num_periods),
'a': [parameters['a']] * num_periods,
'a(%)': [parameters['a(%)']] * num_periods,
'b': [parameters['b']] * num_periods,
'r(%)': [parameters['r(%)']] * num_periods,
'R(%)': [parameters['R(%)']] * num_periods,
'v': [parameters['v']] * num_periods,
'o(%)': [parameters['o(%)']] * num_periods,
'm': [parameters['m']] * num_periods,
'n': [parameters['n']] * num_periods,
'pi_bar': [parameters['pi_bar']] * num_periods,
'Inflation Stabilization sroutput': [0.0] * num_periods,
'Inflation Stabilization inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Output Stabilization sroutput': [0.0] * num_periods,
'Output Stabilization inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Taylor Rule sroutput': [0.0] * num_periods,
'Taylor Rule inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Y_tilde': [0.0] * num_periods,
'c_inflation': [0.0] * num_periods,
'inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'inflation_13CH': [0.0] * num_periods,
'SRY': [0.0] * num_periods,
'Rt': [0.0] * num_periods
})
# Convert columns to numeric type explicitly
numeric_columns = ['a(%)', 'b', 'r(%)', 'R(%)', 'v', 'o(%)', 'm', 'n', 'Inflation Stabilization sroutput', 'Inflation Stabilization inflation', 'Output Stabilization sroutput', 'Output Stabilization inflation', 'Taylor Rule sroutput', 'Taylor Rule inflation', 'Y_tilde', 'c_inflation', 'inflation', 'inflation_13CH', 'SRY', 'Rt']
df[numeric_columns] = df[numeric_columns].apply(pd.to_numeric)
date_columns = []
for col in date_columns:
df[col] = pd.to_datetime(df[col]).dt.date
# Apply Quantitative Experiments
for param, changes_list in quantitative_experiments.items():
for changes in changes_list:
for period in range(changes['time_period'], changes['time_period'] + changes['length']):
if period < num_periods:
df.at[period, param] = changes['new_value']
# Apply the calculations to each row in the DataFrame
for i in range(len(df)):
inflation = calculate_inflation_stabilization_inflation(df, i, parameters['fed_target_initial_inflation']) # inflation stabilization inflation
df.at[i, 'Inflation Stabilization inflation'] = inflation
sroutput = calculate_inflation_stabilization_sroutput(df, i, parameters['fed_target_initial_inflation']) # inflation stabilization sroutput
df.at[i, 'Inflation Stabilization sroutput'] = sroutput
sroutput, inflation = calculate_output_stabilization(df, i, parameters['fed_target_initial_inflation']) # Output Stabilization
df.at[i, 'Output Stabilization sroutput'] = sroutput
df.at[i, 'Output Stabilization inflation'] = inflation
sroutput = calculate_taylor_rule_sroutput(df, i, parameters['fed_target_initial_inflation']) # Taylor Rule sroutput
df.at[i, 'Taylor Rule sroutput'] = sroutput
inflation = calculate_taylor_rule_inflation(df, i, parameters['fed_target_initial_inflation']) # Taylor Rule inflation
df.at[i, 'Taylor Rule inflation'] = inflation
# Calculate Y_tilde
Y_tilde = calculate_y_tilde(df, i)
df.at[i, 'Y_tilde'] = Y_tilde
# Calculate c_inflation
c_inflation = calculate_c_inflation(df, i)
df.at[i, 'c_inflation'] = c_inflation
# Calculate inflation
inflation = calculate_inflation(df, i, parameters['fed_target_initial_inflation'])
df.at[i, 'inflation'] = inflation
# 13 class example
inflation = calculate_inflation1(df, i, parameters['b'], parameters['m'], parameters['v'], parameters['pi_bar'])
df.at[i, 'inflation_13CH'] = inflation
# 13 class example
SRY = calculate_SRY(df, i, parameters['b'], parameters['m'], parameters['v'], parameters['pi_bar'])
df.at[i, 'SRY'] = SRY
# 13 class example
Rt = calculate_Rt(df, i, parameters['m'])
df.at[i, 'Rt'] = Rt
# update_excel_df("C://Users//eduar//OneDrive - BYU-Idaho//Desktop//Coding//Macro//macrodata.xlsx", df)
# display
# display(df.head(20))
plot_m_vs_period(df, ['a(%)', 'R(%)', 'Y_tilde', 'inflation']) # , x_tick_interval=2
# Example usage of the function
CH13_Short_Run_Output(df, 0, 20, ['Inflation Stabilization sroutput', 'Output Stabilization sroutput', 'Taylor Rule sroutput'])
# Example usage of the function
CH13_Short_Run_Output(df, 0, 20, ['Inflation Stabilization inflation', 'Output Stabilization inflation', 'Taylor Rule inflation'])
The situation approach was to take a more aggresive approach to inflation in the economy. The Fisacal policy cause output and inflation to sky rocket in 2021 so I started rasing rates in 2021 and it 2023 my rates where at 5.68 and kept them there for the next 3 years or till 2025. In 2027 rates where back to 2. In 2027 or period 12 output was just above potential, but the recent high rates still had effects for the next two periods (28-29) output shot below potential which can be the recession that was anticipated at the beginning of covid. In the year 2030 the recession is no more, inflation is back at the fed target of 2, output is stabilize or at zero, real interest rates are at 12 and no more crazy shocks with a. I tried to simulate the current situation in the economy by using part 3.1 plots to generate the first set of plots for part 3.2. I got them to be very similar during covid, and in that simulation in the year 2030 things seem to be back to normal but inflation was still above the fed target rate. By taking a more agressive approach to the interest rate, I was able to nring down inflation, to its target and everything else normal by 2030, but it did cost a lot of jobs. Has both models for CH13 & 12 model combined
# Has both models for CH13 & 12 model combined
import pandas as pd
from macrofunctions import calculate_inflation_stabilization_inflation, calculate_inflation_stabilization_sroutput, calculate_output_stabilization, calculate_taylor_rule_sroutput, calculate_taylor_rule_inflation, update_excel_df, calculate_y_tilde, calculate_c_inflation, calculate_inflation, calculate_inflation1, calculate_SRY, calculate_Rt, plot_m_vs_period, plot_m_vs_period_Q, CH13_Short_Run_Output
parameters = {
'Simulation Period (yrs)': 20,
'a': 0.0,
'a(%)': 0.0,
'b': 0.68,
'r(%)': 2.0,
'R(%)': 2.0,
'v': 0.076,
'o(%)': 0.0,
'm': 0.5,
'n': 0.5,
'pi_bar': 2,
'fed_target_initial_inflation': 2.0
}
# 2020 =5, 2025 = 10, 2030 = 15, 2035 = 20.
quantitative_experiments = {
'a(%)': [
{'new_value': -8, 'time_period': 5, 'length': 1},
{'new_value': 8, 'time_period': 6, 'length': 1},
{'new_value': 4, 'time_period': 7, 'length': 1},
{'new_value': 1, 'time_period': 8, 'length': 1},
{'new_value': 1.5, 'time_period': 9, 'length': 1},
{'new_value': 2.5, 'time_period': 10, 'length': 1},
{'new_value': 0, 'time_period': 11, 'length': 1},
{'new_value': .35, 'time_period': 12, 'length': 1},
{'new_value': -1.5, 'time_period': 13, 'length': 1},
{'new_value': -1, 'time_period': 14, 'length': 1}
],
'R(%)': [
{'new_value': .4, 'time_period': 1, 'length': 1},
{'new_value': 1, 'time_period': 2, 'length': 1},
{'new_value': 1.83, 'time_period': 3, 'length': 1},
{'new_value': 2.16, 'time_period': 4, 'length': 1},
{'new_value': .038, 'time_period': 5, 'length': 1},
{'new_value': 2, 'time_period': 6, 'length': 1},
{'new_value': 4, 'time_period': 7, 'length': 1},
{'new_value': 5.68, 'time_period': 8, 'length': 3},
{'new_value': 3.6045, 'time_period': 11, 'length': 1}
]
} # to add just use the same format & change parameter
# Initialize the DataFrame
num_periods = parameters['Simulation Period (yrs)'] + 1
df = pd.DataFrame({
'Period': range(num_periods),
'a': [parameters['a']] * num_periods,
'a(%)': [parameters['a(%)']] * num_periods,
'b': [parameters['b']] * num_periods,
'r(%)': [parameters['r(%)']] * num_periods,
'R(%)': [parameters['R(%)']] * num_periods,
'v': [parameters['v']] * num_periods,
'o(%)': [parameters['o(%)']] * num_periods,
'm': [parameters['m']] * num_periods,
'n': [parameters['n']] * num_periods,
'pi_bar': [parameters['pi_bar']] * num_periods,
'Inflation Stabilization sroutput': [0.0] * num_periods,
'Inflation Stabilization inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Output Stabilization sroutput': [0.0] * num_periods,
'Output Stabilization inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Taylor Rule sroutput': [0.0] * num_periods,
'Taylor Rule inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'Y_tilde': [0.0] * num_periods,
'c_inflation': [0.0] * num_periods,
'inflation': [parameters['fed_target_initial_inflation']] * num_periods,
'inflation_13CH': [0.0] * num_periods,
'SRY': [0.0] * num_periods,
'Rt': [0.0] * num_periods
})
# Convert columns to numeric type explicitly
numeric_columns = ['a(%)', 'b', 'r(%)', 'R(%)', 'v', 'o(%)', 'm', 'n', 'Inflation Stabilization sroutput', 'Inflation Stabilization inflation', 'Output Stabilization sroutput', 'Output Stabilization inflation', 'Taylor Rule sroutput', 'Taylor Rule inflation', 'Y_tilde', 'c_inflation', 'inflation', 'inflation_13CH', 'SRY', 'Rt']
df[numeric_columns] = df[numeric_columns].apply(pd.to_numeric)
date_columns = []
for col in date_columns:
df[col] = pd.to_datetime(df[col]).dt.date
# Apply Quantitative Experiments
for param, changes_list in quantitative_experiments.items():
for changes in changes_list:
for period in range(changes['time_period'], changes['time_period'] + changes['length']):
if period < num_periods:
df.at[period, param] = changes['new_value']
# Apply the calculations to each row in the DataFrame
for i in range(len(df)):
inflation = calculate_inflation_stabilization_inflation(df, i, parameters['fed_target_initial_inflation']) # inflation stabilization inflation
df.at[i, 'Inflation Stabilization inflation'] = inflation
sroutput = calculate_inflation_stabilization_sroutput(df, i, parameters['fed_target_initial_inflation']) # inflation stabilization sroutput
df.at[i, 'Inflation Stabilization sroutput'] = sroutput
sroutput, inflation = calculate_output_stabilization(df, i, parameters['fed_target_initial_inflation']) # Output Stabilization
df.at[i, 'Output Stabilization sroutput'] = sroutput
df.at[i, 'Output Stabilization inflation'] = inflation
sroutput = calculate_taylor_rule_sroutput(df, i, parameters['fed_target_initial_inflation']) # Taylor Rule sroutput
df.at[i, 'Taylor Rule sroutput'] = sroutput
inflation = calculate_taylor_rule_inflation(df, i, parameters['fed_target_initial_inflation']) # Taylor Rule inflation
df.at[i, 'Taylor Rule inflation'] = inflation
# Calculate Y_tilde
Y_tilde = calculate_y_tilde(df, i)
df.at[i, 'Y_tilde'] = Y_tilde
# Calculate c_inflation
c_inflation = calculate_c_inflation(df, i)
df.at[i, 'c_inflation'] = c_inflation
# Calculate inflation
inflation = calculate_inflation(df, i, parameters['fed_target_initial_inflation'])
df.at[i, 'inflation'] = inflation
# 13 class example
inflation = calculate_inflation1(df, i, parameters['b'], parameters['m'], parameters['v'], parameters['pi_bar'])
df.at[i, 'inflation_13CH'] = inflation
# 13 class example
SRY = calculate_SRY(df, i, parameters['b'], parameters['m'], parameters['v'], parameters['pi_bar'])
df.at[i, 'SRY'] = SRY
# 13 class example
Rt = calculate_Rt(df, i, parameters['m'])
df.at[i, 'Rt'] = Rt
# update_excel_df("C://Users//eduar//OneDrive - BYU-Idaho//Desktop//Coding//Macro//macrodata.xlsx", df)
# display
# display(df.head(20))
plot_m_vs_period(df, ['a(%)', 'R(%)', 'Y_tilde', 'inflation'], x_tick_interval=1) # , x_tick_interval=2
In response to the crisis, the Fed has gotten creative in its approach to monetary policy. Below are excerpts of their stance on interest rates now and in the near future. Translate these into parameter values n and m. How does changing the parameters of the policy rules affect the behavior of short-run output and inflation? Explain
Federal funds rate: The Fed has cut its target for the federal funds rate, the rate banks pay to borrow from each other overnight, by a total of 1.5 percentage points since March 3, 2020, bringing it down to a range of 0% to 0.25%. The federal funds rate is a benchmark for other short-term rates and also affects longer-term rates, so this move is aimed at lowering the cost of borrowing on mortgages, auto loans, home equity loans, and other loans, but it will also reduce the interest income paid to savers.
Forward guidance: Using a tool honed during the Great Recession of 2007-2009, the Fed has offered forward guidance on the future path of its key interest rate, saying that rates will remain low “until labor market conditions have reached levels consistent with the Committee’s assessments of maximum employment and inflation has risen to 2 percent and is on track to moderately exceed 2 percent for some time.” This forward guidance on the overnight rate, updated in September 2020 to reflect the Fed’s new monetary policy framework, puts downward pressure on longer-term rates.