localprojections

This module implements the local projections models for single entity time series, and panel / longitudinal data settings, due to Jorda (2005), and based on codes available here.

Installation

pip install localprojections

Implementation

Panel Local Projections Model

Documentation

localprojections.PanelLP(data, Y, response, horizon, lags, varcov, ci_width)

Parameters

data :
Pandas MultiIndex dataframe with entity as the outer index, and time as the inner index.

Y :
List of column labels in data to be used in the model estimation

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

varcov :
Variance-covariance estimator to be used in estimating standard errors; refer to the linearmodels package.

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function returns a pandas dataframe of 6 columns:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Example

from statsmodels.datasets import grunfeld
import localprojections as lp

df = grunfeld.load_pandas().data # import the Grunfeld investment data set
df = df.set_index(['firm', 'year']) # set entity-year indices (as per requirements in bashtage's linearmodels)

endog = ['invest', 'value', 'capital'] # cholesky ordering: invest --> value --> capital
response = endog.copy() # estimate the responses of all variables to shocks from all variables
irf_horizon = 8 # estimate IRFs up to 8 periods ahead
opt_lags = 2 # include 2 lags in the local projections model
opt_cov = 'robust' # HAC standard errors
opt_ci = 0.95 # 95% confidence intervals

irf = lp.PanelLP(data=df, # input dataframe
                 Y=endog, # variables in the model
                 response=response, # variables whose IRFs should be estimated
                 horizon=irf_horizon, # estimation horizon of IRFs
                 lags=opt_lags, # lags in the model
                 varcov=opt_cov, # type of standard errors
                 ci_width=opt_ci # width of confidence band
                 )
irfplot = lp.IRFPlot(irf=irf, # take output from the estimated model
                     response=['invest'], # plot only response of invest ...
                     shock=endog, # ... to shocks from all variables
                     n_columns=2, # max 2 columns in the figure
                     n_rows=2, # max 2 rows in the figure
                     maintitle='Panel LP: IRFs of Investment', # self-defined title of the IRF plot
                     show_fig=True, # display figure (from plotly)
                     save_pic=False # don't save any figures on local drive
                     )

Panel Local Projections Model with Exogenous Variables (Panel LPX)

Documentation

localprojections.PanelLPX(data, Y, X, response, horizon, lags, varcov, ci_width)

Parameters

data :
Pandas MultiIndex dataframe with entity as the outer index, and time as the inner index.

Y :
List of column labels in data to be used in the model estimation as endogenous variables

X :
List of column labels in data to be used in the model estimation as exogenous variables

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

varcov :
Variance-covariance estimator to be used in estimating standard errors; refer to the linearmodels package.

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function returns a pandas dataframe of 6 columns:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Example

from statsmodels.datasets import grunfeld
import localprojections as lp

df = grunfeld.load_pandas().data # import the Grunfeld investment data set
df = df.set_index(['firm', 'year']) # set entity-year indices (as per requirements in bashtage's linearmodels)

endog = ['invest', 'value', 'capital'] # cholesky ordering: invest --> value --> capital
response = endog.copy() # estimate the responses of all variables to shocks from all variables
irf_horizon = 8 # estimate IRFs up to 8 periods ahead
opt_lags = 2 # include 2 lags in the local projections model
opt_cov = 'robust' # HAC standard errors
opt_ci = 0.95 # 95% confidence intervals

irf = lp.PanelLP(data=df, # input dataframe
                 Y=endog, # variables in the model
                 response=response, # variables whose IRFs should be estimated
                 horizon=irf_horizon, # estimation horizon of IRFs
                 lags=opt_lags, # lags in the model
                 varcov=opt_cov, # type of standard errors
                 ci_width=opt_ci # width of confidence band
                 )
irfplot = lp.IRFPlot(irf=irf, # take output from the estimated model
                     response=['invest'], # plot only response of invest ...
                     shock=endog, # ... to shocks from all variables
                     n_columns=2, # max 2 columns in the figure
                     n_rows=2, # max 2 rows in the figure
                     maintitle='Panel LP: IRFs of Investment', # self-defined title of the IRF plot
                     show_fig=True, # display figure (from plotly)
                     save_pic=False # don't save any figures on local drive
                     )

Threshold Panel Local Projections Model with Exogenous Variables (Threshold Panel LPX)

Documentation

localprojections.ThresholdPanelLPX(data, Y, X, threshold_var, response, horizon, lags, varcov, ci_width)

Parameters

data :
Pandas MultiIndex dataframe with entity as the outer index, and time as the inner index.

Y :
List of column labels in data to be used in the model estimation as endogenous variables

X :
List of column labels in data to be used in the model estimation as exogenous variables

threshold_var :
String indicating column in data to be used as the threshold variable; must take values 0 or 1 for technically correct implementation

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

varcov :
Variance-covariance estimator to be used in estimating standard errors; refer to the linearmodels package.

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function returns two pandas dataframes of 6 columns each, with the first output corresponding to when threshold_var takes value 1, and the second when ```threshold_var`` takes value 0:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Example

from statsmodels.datasets import grunfeld
import localprojections as lp

df = grunfeld.load_pandas().data  # import the Grunfeld investment data set
df = df.set_index(['firm', 'year'])  # set entity-year indices (as per requirements in bashtage's linearmodels)
df["state"] = np.random.randint(0, 1, size=len(df))  # creates the state dummy variable (random numbers for illustration)
df["exog"] = np.random.normal(loc=5,scale=1,size=n)  # new column of floats as exogenous variable (random numbers for illustration)

endog = ['invest', 'value', 'capital']  # cholesky ordering: invest --> value --> capital
exog = ["exog"]
threshold = ["state"]
response = endog.copy()  # estimate the responses of all variables to shocks from all variables
irf_horizon = 8  # estimate IRFs up to 8 periods ahead
opt_lags = 2  # include 2 lags in the local projections model
opt_cov = 'kernel'  # HAC standard errors
opt_ci = 0.95  # 95% confidence intervals

irf_on, irf_off = lp.ThresholdPanelLPX(
    data=df,  # input dataframe
    Y=endog,  # endogenous variables in the model
    X=exog,  # exogenous variables in the model
    threshold_var=threshold,  # the threshold dummy variable
    response=response,  # variables whose IRFs should be estimated
    horizon=irf_horizon,  # estimation horizon of IRFs
    lags=opt_lags,  # lags in the model
    varcov=opt_cov,  # type of standard errors
     ci_width=opt_ci  # width of confidence band
     )
irfplot = lp.ThresholdIRFPlot(
    irf_threshold_on=irf_on,  # IRF for when the threshold variable takes value 1
    irf_threshold_off=irf_off,  # IRF for when the threshold variable takes value 0
    response=['invest'],  # plot only response of invest ...
    shock=endog,  # ... to shocks from all variables
    n_columns=2,  # max 2 columns in the figure
    n_rows=2,  # max 2 rows in the figure
    maintitle='Panel LP: IRFs of Investment',  # self-defined title of the IRF plot
    show_fig=True,  # display figure (from plotly)
    save_pic=False  # don't save any figures on local drive
    )

Threshold Single Entity Time Series Local Projectiosn Model with Exogenous Variables (Threshold LPX)

Documentation

ThresholdTimeSeriesLPX(data, Y, X, threshold_var, response, horizon, lags, newey_lags=4, ci_width=0.95)

Parameters

data :
Pandas dataframe

Y :
List of column labels in data to be used in the model estimation as endogenous variables

X :
List of column labels in data to be used in the model estimation as exogenous variables

threshold_var :
String indicating column in data to be used as the threshold variable; must take values 0 or 1 for technically correct implementation

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

newey_lags :
Maximum number of lags to be used when estimating the Newey-West standard errors

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function returns two pandas dataframes of 6 columns each, with the first output corresponding to when threshold_var takes value 1, and the second when ```threshold_var`` takes value 0:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Single Entity Time Series Local Projections Model (LP)

Documentation

localprojections.TimeSeriesLP(data, Y, response, horizon, lags, newey_lags, ci_width)

Parameters

data :
Pandas dataframe

Y :
List of column labels in data to be used in the model estimation as endogenous variables

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

newey_lags :
Maximum number of lags to be used when estimating the Newey-West standard errors

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function also returns a pandas dataframe of 6 columns:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Example

from statsmodels.datasets import grunfeld
import localprojections as lp

df = grunfeld.load_pandas().data # import the Grunfeld investment data set
df = df[df['firm'] == 'General Motors'] # keep only one entity (as an example of a single entity time series setting)
df = df.set_index(['year']) # set time variable as index

endog = ['invest', 'value', 'capital'] # cholesky ordering: invest --> value --> capital
response = endog.copy() # estimate the responses of all variables to shocks from all variables
irf_horizon = 8 # estimate IRFs up to 8 periods ahead
opt_lags = 2 # include 2 lags in the local projections model
opt_cov = 'robust' # HAC standard errors
opt_ci = 0.95 # 95% confidence intervals

# Use TimeSeriesLP for the single entity case
irf = lp.TimeSeriesLP(data=df, # input dataframe
                      Y=endog, # variables in the model
                      response=response, # variables whose IRFs should be estimated
                      horizon=irf_horizon, # estimation horizon of IRFs
                      lags=opt_lags, # lags in the model
                      newey_lags=2, # maximum lags when estimating Newey-West standard errors
                      ci_width=opt_ci # width of confidence band
                      )
irfplot = lp.IRFPlot(irf=irf, # take output from the estimated model
                     response=['invest'], # plot only response of invest ...
                     shock=endog, # ... to shocks from all variables
                     n_columns=2, # max 2 columns in the figure
                     n_rows=2, # max 2 rows in the figure
                     maintitle='Single Entity Time Series LP: IRFs of Investment', # self-defined title of the IRF plot
                     show_fig=True, # display figure (from plotly)
                     save_pic=False # don't save any figures on local drive
                     )

Single Entity Time Series Local Projections Model with Exogenous Variables (LPX)

Documentation

localprojections.TimeSeriesLPX(data, Y, X, response, horizon, lags, newey_lags=4, ci_width=0.95)

Parameters

data :
Pandas dataframe

Y :
List of column labels in data to be used in the model estimation as endogenous variables

X :
List of column labels in data to be used in the model estimation as exogenous variables response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

newey_lags :
Maximum number of lags to be used when estimating the Newey-West standard errors

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

Output

This function also returns a pandas dataframe of 6 columns:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Panel Quantile Local Projections Model with Exogenous Variables (Panel Quantile LPX)

Documentation

Note: This function implements the panel quantile LPX using statsmodel's panel quantile regression and entity dummies, rather than "de-meaned" fixed effects as would PanelOLS.

PanelQuantileLPX(data, Y, X, Entity, response, horizon, lags, varcov="robust", kernel="epa", bandwidth="hsheather", ci_width=0.95, quantile=0.5)

Parameters

data :
Pandas dataframe

Y :
List of column labels in data to be used in the model estimation as endogenous variables

X :
List of column labels in data to be used in the model estimation as exogenous variables

Entity :
Column label corresponding to the entity identifiers, which will be used to construct dummy fixed effects.

response :
List of column labels in Y to be used as response variables when estimating the impulse response functions (IRFs)

horizon :
Integer indicating the estimation horizon of the IRFs

lags :
Integer indicating the number of lags to be included in the model estimation

varcov :
Variance-covariance estimator to be used in estimating standard errors; refer to the statsmodels package.

kernel :
Asymptotic kernel matrix; refer to the statsmodels package.

bandwidth :
Bandwidth selection method for asymptotic covariance estimate; refer to the statsmodels package.

ci_width :
Float higher than 0 and less than 1, i.e., (0, 1), indicating the width of the confidence intervals of the IRFs; ci_width=0.95 indicates a 95% confidence interval

quantile :
Float between 0 and 1 indicating the quantile of interest. E.g., 0.05 corresponds to the 5th percentile and 0.95 corresponds to the 95th percentile.

Output

This function also returns a pandas dataframe of 6 columns:

Shock indicates the shock variable
Response indicates the response variable
Horizon indicates the response horizon of the IRF
Mean indicates the point estimate of the IRF
LB indicates the lower bound of the confidence interval of the IRF
LB indicates the upper bound of the confidence interval of the IRF

For instance, the estimates of the 6-period ahead IRF of y from a shock in x, can be found in the row with Shock=x, Response=y, and Horizon=6.

Plotting Impulse Response Functions

Documentation

localprojections.IRFPlot(irf, response, shock, n_columns, n_rows, maintitle, show_fig, save_pic, out_path, out_name, annot_size, font_size)

Parameters

irf :
pd.Dataframe containing 6 columns, labelled as Shock, Response, Horizon, Mean, LB, UB

response :
List of variables contained in irf's Response column whose IRFs is to be plotted

shock :
List of variables contained in irf's Shock column whose IRFs is to be plotted

n_columns :
Integer indicating the number of IRF figures per row in the overall figure

n_rows :
Integer indicating the number of IRF figures per column in the overall figure

maintitle :
Strings to be used as the title of the overall figure; default is ''Local Projections Model: Impulse Response Functions'

show_fig :
Boolean indicating whether to render the overall figure

save_pic :
Boolean indicating whether to save the overall figure in the local directory; if True, a html file and a png file will be saved

out_path :
Strings indicating the directory at which the overall figure should be saved in; only used if save_pic is True

out_name :
Strings indicating the name of the file in which the overall figure should be saved as; only used if save_pic is True, and default is IRFPlot

annot_size :
Integer indicating the font size of titles of each subplot in the figure; defaults to 6

font_size :
Integer indicating the font size of the title, and axes labels; defaults to 9

Output

This function returns a plotly graph objects figure with n_columns (columns) x n_rows (rows) subplots. Depending on arguments passed, the figure may be rendered during implementation and / or saved in the local directory.

Example

See above.

Requirements

Python Packages

pandas>=1.4.3
numpy>=1.23.0
linearmodels>=4.27
plotly>=5.9.0
statsmodels>=0.13.2

Plotting Impulse Response Functions of a Threshold Local Projections Model

Documentation

This function plots IRFs estimated from ThresholdPanelLPX and ThresholdTimeSeriesLPX.

localprojections.ThresholdIRFPlot(irf_threshold_on, irf_threshold_off, response, shock, n_columns, n_rows, maintitle, show_fig, save_pic, out_path, out_name, annot_size, font_size)

Parameters

irf_threshold_on :
pd.Dataframe containing 6 columns, labelled as Shock, Response, Horizon, Mean, LB, UB, correspoinding to when the threshold variable is switched on; the first output from ThresholdPanelLPX and ThresholdTimeSeriesLPX

irf_threshold_off :
pd.Dataframe containing 6 columns, labelled as Shock, Response, Horizon, Mean, LB, UB, correspoinding to when the threshold variable is switched on; the second output from ThresholdPanelLPX and ThresholdTimeSeriesLPX