svarFit#
Purpose#
Estimate structural vector autoregressive models.
Format#
- rslt = svarFit(Y[, maxlags, const, ctl])#
- Parameters:
Y (matrix) – NxM data.
maxlags (scalar) – Optional, maximum number of lags to consider for VAR model.
const (scalar) –
Optional, specifying deterministic components of model.
0
No constant or trend.
1
Constant. (Default)
2
Constant and trend.
ctl (struct) – Optional, an instance of the
svarControlstructure containing the following members.
- Return:
An instance of an
svarOutstructure containing the following members.- rtype:
struct
Examples#
Example One: Short-run restrictions#
This example demonstrates the use of short-run restrictions to identify the structural model. It uses the cholesky identification method to determine the structural model.
This is the default identification method so no svarControl structure is necessary.
// Load library
new;
library tsmt;
/*
** Data import
*/
lutkepohl2 = loadd(getGAUSShome("pkgs/tsmt/examples/lutkepohl2.dta"));
// Filter data
lutkepohl2 = selif(lutkepohl2, lutkepohl2[., "qtr"] .<= "1978-12-30");
// Set Y
y = packr(lutkepohl2[., "qtr" "dln_inv" "dln_inc" "dln_consump"]);
// Set up output structures
struct svarOut sout;
// Compute structural VAR model
sout = svarFit(Y);
This prints the estimates for the reduced for coefficients:
=====================================================================================================
Model: SVAR(2) Number of Eqs.: 3
Time Span: 1960-04-01: Valid cases: 73
1978-10-01
Log Likelihood: 606.307 AIC: -24.632
SBC: -24.067
=====================================================================================================
Equation R-sq DW SSE RMSE
dln_inv 0.12856 2.01020 0.14056 0.04615
dln_inc 0.11419 1.75766 0.00906 0.01172
dln_consump 0.25128 -1.84234 0.00589 0.00944
=====================================================================================================
Results for reduced form equation dln_inv
=====================================================================================================
Coefficient Estimate Std. Err. T-Ratio Prob |>| t
-----------------------------------------------------------------------------------------------------
Constant -0.01672 0.01723 -0.97073 0.33523
dln_inv L(1) -0.31963 0.12546 -2.54775 0.01318
dln_inc L(1) 0.14599 0.54567 0.26754 0.78989
dln_consump L(1) 0.96123 0.66431 1.44696 0.15264
dln_inv L(2) -0.16055 0.12491 -1.28537 0.20316
dln_inc L(2) 0.11460 0.53457 0.21438 0.83091
dln_consump L(2) 0.93440 0.66509 1.40491 0.16474
=====================================================================================================
Results for reduced form equation dln_inc
=====================================================================================================
Coefficient Estimate Std. Err. T-Ratio Prob |>| t
-----------------------------------------------------------------------------------------------------
Constant 0.01577 0.00437 3.60427 0.00060
dln_inv L(1) 0.04393 0.03186 1.37891 0.17258
dln_inc L(1) -0.15273 0.13857 -1.10219 0.27438
dln_consump L(1) 0.28850 0.16870 1.71014 0.09194
dln_inv L(2) 0.05003 0.03172 1.57726 0.11952
dln_inc L(2) 0.01916 0.13575 0.14116 0.88817
dln_consump L(2) -0.01020 0.16890 -0.06039 0.95203
=====================================================================================================
Results for reduced form equation dln_consump
=====================================================================================================
Coefficient Estimate Std. Err. T-Ratio Prob |>| t
-----------------------------------------------------------------------------------------------------
Constant 0.01293 0.00353 3.66626 0.00049
dln_inv L(1) -0.00242 0.02568 -0.09437 0.92510
dln_inc L(1) 0.22481 0.11168 2.01305 0.04819
dln_consump L(1) -0.26397 0.13596 -1.94153 0.05646
dln_inv L(2) 0.03388 0.02556 1.32534 0.18963
dln_inc L(2) 0.35491 0.10941 3.24398 0.00185
dln_consump L(2) -0.02223 0.13612 -0.16329 0.87079
=====================================================================================================
The IRFs for the model are stored in the irf member of the svarOut output structure. This member is 3-dimensional array, with each plane containing the response to shocks to a different endogenous variable. The planes house a MxH matrix of responses with each row containg the responses from different response variable, and each column representing a different horizon.
For example, let’s preview the response of our three endogenous variables to, dln_inv, dln_inc, and dln_consump, to a shock in the first variable, dln_inv.
// Index of shock variable
shk_indx = 1;
// Get matrix of responses to dln_inv
res_to_dln_inv = getMatrix(sout.irf, shk_indx);
// Print first five responses
res_to_dln_inv[., 1:3];
0.046147884 -0.011956777 -0.0009900109
0.001551898 0.002560746 0.0012599300
0.002670542 -0.000467869 0.0027831146
Example Two: Long-run restrictions#
This example demonstrates the use of long-run restrictions to identify the structural model. This is done using the ctl.irf.ident member of the svarControl structure.
// Load library
new;
library tsmt;
/*
** Data import
*/
lutkepohl2 = loadd(getGAUSShome("pkgs/tsmt/examples/lutkepohl2.dta"));
// Filter data
lutkepohl2 = selif(lutkepohl2, lutkepohl2[., "qtr"] .<= "1978-12-30");
// Set up output structures
struct svarOut sout;
// Declare controls structure
// Fill with defaults
struct svarControl ctl;
ctl = svarControlCreate();
// Use long-run restrictions for
// structural identification
ctl.irf.ident = "long";
// Set Y
y = packr(lutkepohl2[., "qtr" "dln_inv" "dln_inc" "dln_consump"]);
// Run model
maxlags = 8;
const = 1;
// Check structural VAR model
sout = svarFit(Y, maxlags, const, ctl);
The reduced for estimates for this model are the same as the first model, because identification restrictions have no impact on the reduced form estimates.
However, if we look at the IRFS using these restrictions:
// Index of shock variable
shk_indx = 1;
// Get matrix of responses to dln_inv
res_to_dln_inv = getMatrix(sout.irf, shk_indx);
// Print first five responses
res_to_dln_inv[., 1:3];
0.041667833 -0.0067978789 0.0016807041
0.0056614147 0.0026748073 0.0013125032
0.0059236730 -0.00039186770 0.0040106258
Example Three: Sign restrictions#
The sign-restrictions option implements identification based on the theoretically anticipated direction of the IRFs. For example, consider a VAR model which includes real (GDP), the personal consumption expenditure price index (PCEPI), and the federal funds rate (FFR).
We can use sign-restricted IRFs to model the theory that real GDP and the PCEPI should initially respond with negatively to a monetary policy shock.
To start we import and transform the data:
new;
rndseed 908098;
library tsmt;
// Data files
fname = getGAUSSHome("pkgs/tsmt/examples/sign_restrictions_data.csv");
// Load data from .csv file
// and take ln of GDPC1 and PCEp1
data = loadd(__FILE_DIR $+ fname, "ln(GDPC1) + ln(PCEPI) + FEDFUNDS");
// Renaming columns
data = asDF(data, "l_gdp"$|"l_pce"$|"ffr");
// Remove missing values
reg_data = packr(data);
Next we implement the sign restrictions using the svarControl structure. This requires specifying:
* The use of sign-restrictions for identification by setting the svarControl structure member ctl.irf.ident to "sign".
* Which shocks to restrict using the ctl.irf.restrictedShock control structure member.
* The horizons whose responses are restricted using the ctl.irf.restrictionHorizon control structure member.
* The direction of the restrictions using the ctl.irf.signrestrictions control structure member. This matrix should have a row for each restricted shock and a column for each response variable. A value of -1 restricts a shock to be negative, a value of 1 restricts a shock to be positive, and a value of 0 indicates no restrictions.
// Declare controls structure
// Fill with defaults
struct svarControl ctl;
ctl = svarControlCreate();
// Specify to use sign restrictions
ctl.irf.ident = "sign";
// Specify which shock variable is restricted
ctl.irf.restrictedShock = 3;
// Set up restrictions horizon
ctl.irf.restrictionHorizon = 1;
/* Specify sign restrictions
** GDP response to monetary shock must < 0 (-1)
** PCE response to monetary shock must < 0 (-1)
** FFR response to monetary shock must > 0 (1)
*/
ctl.irf.signRestrictions = { -1 -1 1 };
Finally, we run the model using svarFit().
/*
** Setup VAR estimation
*/
// Maximum lags
maxlags = 8;
// Use constant in model
const = 1;
// Check structural VAR model
struct svarOut sOut;
sout = svarFit(reg_data, maxlags, const, ctl);
Remarks#
The procedure svarFit() is designed to provide flexibility in estimating SVAR models by allowing users to specify various options for the deterministic components, number of lags, and control settings for model estimation and impulse response analysis. The inclusion of bootstrapping methods and sign restrictions further enhances the robustness and interpretability of the resulting SVAR model.
See also
Functions arimaFit(), plotIRF(), svarControlCreate(), plotFEVD()