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local_projections.py
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local_projections.py
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from typing import Any, Union
import pandas as pd
import numpy as np
import statsmodels.regression.linear_model as linear_model
import statsmodels.api as sm
import statsmodels.formula.api as smf
import matplotlib.pyplot as plt
import warnings
class LocalProjections:
"""
Local projections model (Jorda 2004).
Estimates the impact of an exogenous variable on
the endogenous variable using local projections
as in Jorda (2004):
.. math::
y_{t+h} = \beta exog_t + \gamma controls_{t} + e_t
where control variables can also include lagged values
of the endogenous and exogenous variables. One regression
is estimated for each horizon h in [0,1,..,H].
Parameters
----------
dta : pd.DataFrame
DataFrame containg the data
endog_name : str
Name of the endogenous variable (must be stored in a column of dta)
exog_name : str
Name of the exogenous variable (must be stored in a column of dta)
controls_names : list, default []
Name of all the control variables (must be stored in columns of dta)
Examples
--------
Estimating the response of real GDP following a rise in the
nominal interest rate.
Import dataset
>>> import statsmodels.api as sm
>>> import numpy as np
>>> dta = sm.datasets.macrodata.load_pandas().data
Create nominal interest rate and logs
>>> dta["i"] = dta["realint"] + dta["infl"]
>>> for var in ["realgdp", "cpi"]:
>>> dta[f"{var}_log"] = np.log(dta[var])
Set endogenous, exogenous and control variables
>>> endog = "realgdp_log"
>>> exog = "i"
>>> controls = ["cpi_log", "unemp"]
Estimate results
>>> lp = LocalProjections(dta, endog, exog, controls)
>>> irf = lp.fit(
>>> H=16,
>>> contemporaneous_control=1,
>>> scale=100,
>>> lags_exog=2,
>>> ylabel="Percent of real GDP",
>>> displaylag=True,
>>> )
References
----------
Jorda (2005). Estimation and Inference of Impulse Responses
by Local Projections. American Economic Review. 95(1). pp. 161-182
"""
def __init__(
self,
dta: pd.DataFrame,
endog_name: str,
exog_name: str,
controls_names: list = [],
) -> None:
self.dta = self._is_valid_dta(dta)
self.endog = self._is_valid_endog(endog_name)
self.controls = self._is_valid_controls(controls_names)
self.exog = self._is_valid_exog(exog_name)
def _is_valid_dta(self, dta):
if type(dta) is not pd.DataFrame:
raise TypeError(f"'dta' is not a Pandas DataFrame")
return dta
def _is_valid_endog(self, endog):
if endog not in self.dta:
raise ValueError(f"'{endog}' is not a column of dta")
return endog
def _is_valid_controls(self, controls):
for var in controls:
if var not in self.dta:
raise ValueError(f"'{var}' is not a column of dta")
return controls
def _is_valid_exog(self, exog):
if exog not in self.dta:
raise ValueError(f"'{exog}' is not a column of dta")
# remove exog if it is also in list of controls to avoid duplication
if exog in self.controls:
self.controls.remove(exog)
warnings.warn(f"'{exog}' in the list of controls was ignored")
return exog
def fit(
self,
contemporaneous_control: int = 0,
lag_selection: Union[str, None] = "AIC",
h_selectlag: int = 0,
maxlagselect: int = 12,
displaylag: bool = False,
lags_control: int = 1,
lags_endog: int = 1,
lags_exog: int = 1,
H: int = 12,
alpha: list = [.01, .05, .1],
cov_type: str = 'HAC',
cov_kwds: Union[dict[str, Any], None] = {'maxlags': 6, 'kernel': 'bartlett', 'use_correction': True},
scale: float = 1.0,
show_plot: bool = True,
xlabel: str = r"h",
ylabel: str = "",
) -> pd.DataFrame:
"""
Estimates local projections at all horizons h=0,1,..,H and store results.
Parameters
----------
contemporaneous_control: int
Whether to include contemporaneous values of the control
variables (set to 1) or not (set to 0).
lag_selection: Union[str, None], default "AIC"
Desired criterion for lag selection ("AIC", "BIC" or "R2_adj"), if
None no lag selction is performed.
h_selectlag: int, default 0
Horizon of the regression for lag selection.
maxlagselect: int, default 12
Maximum number of lags to consider.
displaylag: bool, default False
Display selected number of lags or not.
lags_control: int
Number of lags of control variables to include.
lags_endog: int
Number of lags of endogenous variable to include.
lags_exog: int
Number of lags of exogenous variable to include.
H: int
Maximum horizon to which estimate projections.
alpha: list, default [.01, .05, .1]
Significance level for confidence intervals.
cov_type: str, default "HAC"
Covariance estimator to use. Default is set to Heteroskedasticity-
autocorrelation robust covariance ("HAC") to account for serial
auto-correlation in residuals. Can also use "nonrobust" or "HC0/1/2/3".
cov_kwds: Union[dict[str, Any], None], default {'maxlags':6, 'kernel': 'bartlett', 'use_correction': True}
Keyword arguments for the covariance estimator. "nonrobust" and
"HC#" do not support cov_kwds.
scale: float, default 1.0
Scaling of the results.
show_plot: bool, default True
Draw plot of impulse response function or not.
xlabel: str, default "h"
x-axis label.
ylabel: str, default ""
y-axis label.
Returns
-------
irf: pd.DataFrame (H x (1 + 2*len(alpha)))
DataFrame containing the point estimates, upper, and lower confidence
"""
# add necessary lags and leads
self.regdta = self.make_leads_lags(
max(lags_control, maxlagselect),
max(lags_endog, maxlagselect),
lags_exog,
H
)
# perform lag selection
if lag_selection:
self.n_lags = self.select_lags(
contemporaneous_control,
lags_exog,
h_selectlag=h_selectlag,
criterion=lag_selection,
maxlagselect=maxlagselect,
displaylag=displaylag,
)
lags_endog, lags_control = self.n_lags, self.n_lags
# initialize DataFrame to store results
irf = pd.DataFrame(
index=range(H + 1),
columns=["IRF"] + [f"IRF_u{alf}" for alf in alpha] + [f"IRF_l{alf}" for alf in alpha]
)
# run regressions for each horizon and store results
for h in range(H + 1):
reg = self.fit_h(
h,
contemporaneous_control,
lags_control,
lags_endog,
lags_exog,
cov_type=cov_type,
cov_kwds=cov_kwds,
)
irf.loc[h]["IRF"] = reg.params[self.exog] * scale
for alf in alpha:
irf.loc[h][f"IRF_l{alf}"] = reg.conf_int(alpha=alf)[0][self.exog] * scale
irf.loc[h][f"IRF_u{alf}"] = reg.conf_int(alpha=alf)[1][self.exog] * scale
# draw plot of impulse response function
if show_plot:
self.plot_irf(
irf,
alpha,
xlabel=xlabel,
ylabel=ylabel,
)
return irf
def make_leads_lags(
self,
lags_control: int,
lags_endog: int,
lags_exog: int,
H: int,
) -> pd.DataFrame:
"""Constructs the lags and leads of necessary variables."""
self.dta = self.make_lags(lags_control, lags_endog, lags_exog)
self.dta = self.make_leads(H)
return self.dta
def make_lags(
self,
lags_control: int,
lags_endog: int,
lags_exog: int,
) -> pd.DataFrame:
"""
Constructs the lags of the endngeous, exogenous and
control variables and store in dta DataFrame.
Parameters
----------
lags_control: int
Number of lags of the control variables to create
lags_endog: int
Number of lags of the endogenous variables to create
lags_exog: int
Number of lags of the exogenous variables to create
Returns
-------
pd.DataFrame
dta DataFrame including lagged variables
"""
for lag in range(lags_control + 1):
for var in self.controls:
self.dta[f"{var}_L{lag}"] = self.dta[var].shift(lag)
for lag in range(lags_endog + 1):
self.dta[f"{self.endog}_L{lag}"] = self.dta[self.endog].shift(lag)
for lag in range(lags_exog + 1):
self.dta[f"{self.exog}_L{lag}"] = self.dta[self.exog].shift(lag)
return self.dta
def make_leads(self, H: int) -> pd.DataFrame:
"""
Constructs the lead values of the endngeous and store in dta DataFrame.
Parameters
----------
H: int
Maximum horizon to which estimate projections.
Returns
-------
pd.DataFrame
dta DataFrame including lead values of endogenous variable
"""
for lead in range(H + 1):
self.dta[f"{self.endog}_h{lead}"] = self.dta[self.endog].shift(-lead)
return self.dta
def select_lags(
self,
contemporaneous_control: int,
lags_exog: int,
h_selectlag: int = 0,
criterion: str = "AIC",
maxlagselect: int = 12,
displaylag: bool = False,
) -> int:
"""
Selects the number of lags of control variables and
endogenous variables using criterion AIC, BIC or R2
from regression for a given horizon `h`.
Parameters
----------
contemporaneous_control: int
Whether to include contemporaneous values of the control
variables (set to 1) or not (set to 0).
lags_exog: int
Number of lags of exogenous variable to include.
h_selectlag: int, default 0
Horizon of the regression
criterion: str, default "AIC"
Desired criterion of the selection ("AIC", "BIC" or "R2_adj")
maxlagselect: int, default 12
Maximum number of lags to consider.
displaylag: bool, default False
Display selected number of lags or not.
Returns
-------
n_lags: int
Best number of lags ot include according to desired criterion.
Raises
------
ValueError
If criterion is not "AIC", "BIC" or "R2_adj"
"""
crit = np.inf
for lag in range(maxlagselect):
reg = self.fit_h(
h_selectlag,
contemporaneous_control,
lag,
lag,
lags_exog,
)
if criterion == "BIC":
if reg.bic <= crit:
crit = reg.bic
n_lags = lag
elif criterion == "AIC":
if reg.aic <= crit:
crit = reg.aic
n_lags = lag
elif criterion == "R2_adj":
if reg.rsquared_adj <= crit:
crit = reg.rsquared_adj
n_lags = lag
else:
raise ValueError('criterion must be set to "AIC", "BIC" or "R2_adj"')
if displaylag:
print(f"{n_lags} lags selected using the {criterion} criterion")
return n_lags
def fit_h(
self,
h: int,
contemporaneous_control: int,
lags_control: int,
lags_endog: int,
lags_exog: int,
cov_type: str = 'HAC',
cov_kwds: Union[dict[str, Any], None] = {'maxlags': 6, 'kernel': 'bartlett', 'use_correction': True},
) -> linear_model.RegressionResults:
"""
Estimates regression at horizon `h` and returns statsmodel regression results.
Parameters
----------
h: int
Horizon of regression to estimate.
contemporaneous_control: int
Whether to include contemporaneous values of the control
variables (set to 1) or not (set to 0).
lags_control: int
Number of lags of control variables to include.
lags_endog: int
Number of lags of endogenous variable to include.
lags_exog: int
Number of lags of exogenous variable to include.
cov_type: str, default "HAC"
Covariance estimator to use. Default is set to Heteroskedasticity-
autocorrelation robust covariance ("HAC") to account for serial
auto-correlation in residuals. Can also use "nonrobust" or "HC0/1/2/3".
cov_kwds: Union[dict[str, Any], None], default {'maxlags':6, 'kernel': 'bartlett', 'use_correction': True}
Keyword arguments for the covariance estimator. "nonrobust" and
"HC#" do not support cov_kwds.
Returns
-------
reg: sm.regression.linear_model.RegressionResults
Regression results.
"""
eqtn = self.make_equation(
h,
contemporaneous_control,
lags_control,
lags_endog,
lags_exog,
)
reg = (
smf.ols(eqtn, data=self.regdta)
.fit(cov_type=cov_type, cov_kwds=cov_kwds)
)
return reg
def make_equation(
self,
h: int,
contemporaneous_control: int,
lags_control: int,
lags_endog: int,
lags_exog: int,
) -> str:
"""
Creates the string regression equation to be used using
the statsmodels api for a given horizon `h`.
Parameters
----------
h: int
Horizon of the regression
contemporaneous_control: int
Whether to include contemporaneous values of the control
variables (set to 1) or not (set to 0).
lags_control: int
Number of lags of control variables to include.
lags_endog: int
Number of lags of endogenous variable to include.
lags_exog: int
Number of lags of exogenous variable to include.
Returns
-------
eqtn, str
Equation in string format to be read by statsmodels api.
Raises
------
ValueError
If contemporaneous_control is not 0 or 1.
"""
if not ((contemporaneous_control == 1) | (contemporaneous_control == 0)):
raise ValueError("'contemporaneous_control' must be either 0 or 1")
lagcontrols = "".join([
f" + {var}_L{lag}"
for var in self.controls
for lag in range((1 - contemporaneous_control), lags_control + 1)
])
lagendog = "".join([
f" + {self.endog}_L{lag}" for lag in range(1, lags_endog + 1)
])
lags_exog = f"{self.exog}" + "".join([
f" + {self.exog}_L{lag}" for lag in range(1, lags_exog + 1)
])
eqtn = f"{self.endog}_h{h} ~ {lags_exog} {lagcontrols} {lagendog}"
return eqtn
def plot_irf(
self,
irf: pd.DataFrame,
alpha: list,
xlabel: str = r"h",
ylabel: str = "",
) -> None:
"""
Draws impulse response function plot from results.
Parameters
----------
irf: pd.DataFrame
DataFrame of results.
alpha: list
List of significance levels for confidence intervals in `irf`.
xlabel: str, default "h"
x-axis label.
ylabel: str, default ""
y-axis label.
"""
for alf in alpha:
plt.fill_between(
irf.index,
irf[f"IRF_l{alf}"].astype(float),
irf[f"IRF_u{alf}"].astype(float),
alpha=0.1,
color="k",
)
plt.plot(
irf["IRF"],
c="k",
)
plt.axhline(0, c='k', linewidth=1)
plt.ylabel(ylabel), plt.xlabel(xlabel)
plt.tight_layout()
plt.show()