Welcome to localprojections’s documentation!

class localprojections.LP(df, maxlags=1, sample=None, endogvars=None, responsevars=None, shocks=None, ci=0.9, use_t=True, use_correction=True, interaction=None, timelevel=None, cluster=None, identification='cholesky', trend=0)

Bases: object

The LP class implements the local projections methodology of Jorda (2005) and the R package lpirfs.

dfpandas.DataFrame: DataFrame containing the time series or panel data to be used in the estimation.
maxlagsint, optional: Maximum number of lags to include in the model. The default is 1.
samplefunction, optional: Function that takes a pandas.DataFrame and returns a boolean array of the same length indicating whether to include that observation in the estimation. The default is True for all. Reason for this is that the user may want to exclude observations after lags are computed.
endogvarsdict or list, optional: Lagged variables to include in the model. The default is None, in which case all variables are included. If a dict is supplied, the keys are the names of the variables and the values are the lags to include. Lags can be an integer n, in which case lags will be 1,...,n. Lags can also be a tuple (n,m), in which case lags will be n,...,m. Or they can be an exact list of lags. If a list is supplied, maxlags is used to determine the lags.
responsevarslist or string, optional: List of variables to use as response variables. The default is None, in which case all endogvars are used.
shockslist or string, optional: List of variables to use as shocks. The default is None, in which case endogvars are used. If shocks are not supplied, identification must be supplied to indicate how reduced-form innovations in endogvars are transformed into structural shocks.
cifloat, optional: Confidence interval to use for the impulse response plots. The default is 90%.
use_tbool, optional: In the case of time series data, whether to use t-statistics instead of z-statistics. The default is True. This is ignored for panel data, which always uses t-statistics.
use_correctionbool, optional: In the case of time series data, whether to use small sample correction for the standard errors. The default is True. This is ignored for panel data, which always uses small sample correction.
interactionstring, optional: Name of the variable to use for interaction terms. The default is None, in which case no interaction terms are used. If a categorical variable is supplied, a separate IRF path is computed for each level. If a continuous variable is supplied, the base effect and interaction effect are computed.
timelevelstring, optional: Name of the time index in the DataFrame. The default is None, in which case the last index is assumed to be the time index.
clusterbool or string, optional: Whether to use clustered standard errors in panel estimation. If True, all index levels other than the time index are used for clustering. If a string, that variable is used. If None, Driscoll-Kraay standard errors with Bartlett Kernel are used with a bandwidth of horizon + 1. cluster is ignored for time series data, which always uses Newey-West standard errors with a bandwidth of horizon + 1.
identificationstring or 2D ndarray, optional: Method to use for identification if no shocks are supplied. The default is 'cholesky', in which case the Cholesky decomposition of the reduced-form covariance matrix is used using the ordering in endogvars. If a 2D ndarray is supplied, it is used as the identification matrix.
trendint, optional: Order of polynomial trend to include in the model. The default is 0, in which case no trend is included. If 1, a linear trend is included. If 2, a quadratic trend is included, etc.

Jorda (2005) defines local projections as a series of separately estimated regressions where a shock at time \(t\) is used to predict the response variable at time \(t+h\) for \(h=0,1,...,H\).

Without exogenously identified shocks, the model is written as:

\[y_{t+h} = \alpha_{h} + \sum_{s=1}^p \beta_{h,s}' x_{t-s} + \epsilon_{t+h}, \qquad h=0,1,...,H \]

where \(y_{t+h}\) is the response variable at time \(t+h\), \(x_{t-s}\) is the vector of endogenous variables at time \(t-s\) (potentially including \(y_{t}\)). The impulse response to the reduced-form shock is \(\hat{beta}_{h,1}\). It is transformed into a structural shock using the identification matrix \(B\) such that

\[I(h) = B \hat{\beta}_{h,1}\]

\(B\) is computed separately. By default, it will be estimated using the Cholesky decomposition of the equivalent VAR(p) model. Alternatively, the user can supply an identification matrix.

With exogenously identified shocks, the model is written as:

\[y_{t+h} = \alpha_{h} + \beta_h' z_t + \sum_{s=1}^p \gamma_{h,s}' x_{t-s} + \epsilon_{t+h}, \qquad h=0,1,...,H \]

A panel version estimates effect \(\beta_h\) of \(x_{i,t-1}\) on \(y_{i,t+h}\) using fixed effects \(\alpha_{i,h}\).

design_matrices(rhs, responsevar)

This function generates the design matrices for the regression. It is used internally by the estimate and orthogonalize methods. It will always return the design matrices for a contemporaneous regression. Subsequent lags are handled by the shift_lhs method. This is done for efficiency, since creating the design matrices can be quite slow.

rhsstring: Right-hand side of the regression.
responsevarstring: Response variable of the regression (LHS)

This function uses the patsy package to generate the design matrices. Maybe in the future we will switch to formulaic which is faster.

dflhsDataFrame: LHS design matrix
dfrhsDataFrame: RHS design matrix

estimate(max_horizon, shock_size=None)

This method estimates the impulse response functions using local projections.

max_horizonint: Maximum horizon to compute the impulse response functions.
shock_sizefloat, optional: Size of the shock. The default is 1 for identified shocks and standard deviation for orthogonalized shocks.

coefsDataFrame

DataFrame containing the impulse response functions. The indices are:

response: response variable
impulse: impulse variable
horizon: horizon
interaction: interaction variable (if applicable)

The columns are:

coef: impulse response function
lb: lower bound of the confidence interval
ub: upper bound of the confidence interval

regresultsdict

Nested dictionary containing the regression results. The keys are the horizons and the values are dictionaries containing the regression results for each spec.

estimate_var()

This function estimates a VAR model. It is used internally by the orthogonalize method to estimate the covariance matrix of the residuals, which is used to orthogonalize the shocks.

constDataFrame

DataFrame containing the constant term of the VAR model.

outcoefsdict

Dictionary containing the coefficients of the VAR model. The keys are:

coef: coefficients
lb: lower bound of the confidence interval
ub: upper bound of the confidence interval

Each dictionary value is a DataFrame with a row for each response variable and a column for each impulse variable and lag. df[y,(x,s)] represents (y,x) th element of the s th lag of the VAR.

SigmaDataFrame

DataFrame containing the covariance matrix of the residuals.

gen_rhs(endogvars=None, shocks=None, responsevars=None, use_interaction=True)

This function generates the right-hand side of the model. It is used internally by the estimate and orthogonalize methods.

endogvarsdict, optional: Lagged variables to include in the model. The default is None, in which the object instance’s endogvars attribute is used.
shockslist, optional: List of variables to use as shocks. The default is None, in which case the object instance’s shocks attribute is used.
responsevarslist, optional: List of variables to use as response variables. The default is None, in which case the object instance’s responsevars attribute is used.
use_interactionbool, optional: Whether to include interaction terms. The default is True, which means the instance’s interaction attribute is used. False means no interaction terms are used, whatever the instance’s interaction attribute is. This is useful for the orthogonalize method, which estimates a VAR model and isnt’ compatible with interaction terms.

rhs : string

orthogonalize(identification)

This function orthogonalizes the shocks using the supplied identification strategy.

identificationstring or ndarray

If identification is a string, it must be one of the following:

'cholesky': use the Cholesky decomposition of the covariance matrix of the residuals.

Otherwise, identification must be a square matrix with the same number of rows as endogenous variables. The matrix must be invertible.

orthofunction: Function that takes a vector of shocks and returns a vector of orthogonalized shocks.

run_regression(dflhs, dfrhs, nwlags=0)

This function runs the regression for a given horizon. It is used internally by the estimate and orthogonalize methods.

dflhsDataFrame: LHS design matrix
dfrhsDataFrame: RHS design matrix
nwlagsint, optional: Number of Newey-West lags to use. The default is 0, which means no Newey-West correction.

outDataFrame

DataFrame containing the regression results. The columns are:

params: regression coefficients
lb: lower bound of the confidence interval
ub: upper bound of the confidence interval

residsSeries

Series containing the regression residuals.

fit : RegressionResults from OLS or PanelOLSResults from PanelOLS

shift_lhs(dflhs, dfrhs, horizon=0)

This function shifts the LHS design matrix by the horizon. It is used internally by the estimate and orthogonalize methods to compute the impulse response functions at different horizons. After shifting, the resulting missing rows are removed.

dflhsDataFrame: LHS design matrix
dfrhsDataFrame: RHS design matrix
horizonint, optional: Horizon to shift the LHS design matrix. The default is 0, which means no shift.

This function creates copies of the design matrices because the caller may need to use the original matrices for other horizons. We can refactor this later to avoid the copies if we can be sure that horizons are always incremented sequentially.

dflhsDataFrame: LHS design matrix shifted by the horizon.
dfrhsDataFrame: RHS design matrix shifted by the horizon.

localprojections.drop_singletons(df, level): Find levels of a MultiIndex that have only one value and drop them.

localprojections.fill_index_level(df, level=0)

Fill in missing values in a dataframe index. For MultiIndexes, this doesn’t necessarily generate a balanced panel. It just fills in missing times within the entity-specific range of times.

dfDataFrame: DataFrame with a MultiIndex to fill.
levelint or str, optional: Level of the index to fill. The default is 0.

dfDataFrame: DataFrame with filled index.

localprojections.flatten(nested_list): Recursively flatten a nested list

localprojections.lag(x, n=0, cxlevel=None)

Lag by n periods. If cxlevel is supplied, lag within each cross-section.

xSeries, DataFrame, or ndarray: Object to lag.
nint, optional: Number of periods to lag. The default is 0. Negative numbers shift forward.
cxlevelstr or list, optional: Name of the cross-section level(s) of the index. The default is None.

localprojections.make_iterable(x, n=1)

Make an object iterable. If x is already iterable, return it. Otherwise, if

n is an integer, return a list of length n with each element equal to x

n is a list, return a dictionary with keys n and values x

localprojections.make_polynomial(var, n, pre='', post=''): Create a formula for a polynominal of degree n in var, prepending or postpending additional strings if needed.

localprojections.plot_irf(dftmp, impulse=None, response=None, interaction=None, colorlevel='interaction', colorvalues=None, ax=None, colormap=None, legend_here=True, title_fcn=None)

Plot a single impulse response function. This function can be called directly by the user or by the plot_irfs function that plots a grid of IRFs.

dftmpDataFrame

DataFrame containing the impulse responses. The expected contents of the DataFrame depend on how the function is called.

If impulse and response are both supplied, then dftmp can contain multiple
IRFs, but its indices must be, in order, impulse, response, horizon.

If impulse and response are not supplied, then dftmp must contain a
single IRF.

In either case, the DataFrame must contain the following columns:

coef: impulse response function
lb: lower bound of the confidence interval
ub: upper bound of the confidence interval

If colorlevel is supplied, then the DataFrame must also contain a column with the name colorlevel.

impulsestr, optional

Name of the impulse variable. The default is None, in which case the DataFrame must contain a single IRF.

responsestr, optional

Name of the response variable. The default is None, in which case the DataFrame must contain a single IRF.

interactionstr, optional

Name of the interaction variable. The default is None.

colorlevelstr, optional

Name of the column in dftmp that indexes the dimension that will be represented by color. The default is ‘interaction’.

colorvalueslist, optional

List of values of colorlevel to plot. The default is None, in which case all values of the colorlevel column are plotted.

axmatplotlib Axes, optional

Axes on which to plot. The default is None, in which case a new figure and axes are created.

colormaplist, optional

List of colors to use for each value of colorvalues. The default is None, in which case the default matplotlib color cycle is used.

legend_herebool, optional

Whether to plot the legend on the axes. The default is True.

title_fcnfunction, optional

Function that takes impulse, response, and interaction as arguments and returns a string to use as the title. The default is None, in which case the title is impulse on response.

localprojections.plot_irfs(dfirf, impulses=None, responses=None, interactions=None, rows='impulse', columns='response', color='interaction', colormap=None, styles=None)

Plot a grid of impulse response functions.

dfirfDataFrame

DataFrame containing the impulse responses. It must contain the following indices:

impulse: name of the impulse variable
response: name of the response variable
horizon: forecast horizon
interaction: optional, name of the interaction variable

It must also contain the following columns:

coef: impulse response function
lb: lower bound of the confidence interval
ub: upper bound of the confidence interval

The first argument returned by estimate() is a suitable DataFrame.

impulseslist, optional

List of impulse variables to plot. The default is None, in which case all impulse variables in dfirf are plotted.

responseslist, optional

List of response variables to plot. The default is None, in which case all response variables in dfirf are plotted.

interactionslist, optional

List of interaction variables to plot. The default is None, in which case all interaction variables in dfirf are plotted.

rowsstr, optional

Name of the index level to use for the rows of the grid. The default is ‘impulse’.

columnsstr, optional

Name of the index level to use for the columns of the grid. The default is ‘response’.

colorstr, optional

Name of the index level to use for the color of the lines. The default is ‘interaction’.

colormaplist, optional

List of colors to use for each value of colorvalues. The default is None, in which case the default matplotlib color cycle is used.

styleslist, optional

NOT IMPLEMENTED YET: List of line styles to use for each value of colorvalues. The default is None, in which case the default matplotlib line styles are used.

localprojections.set_lags(endogvars_list, maxlags): Assign the same max lags for each endogenous variable. Returns a dict with the same keys as endogvars_list and the same value for all keys.

Welcome to localprojections’s documentation!

Indices and tables