System Regression ModelsΒΆ
System regression estimates multiple regressions simultaneously. There are three reasons to consider system estimation instead of equation by equation estimation
Joint inference on parameters across models
Efficiency gains in some circumstances using cross-model GLS
Imposing restrictions on parameters across models
The main model is the Seemingly Unrelated Regression (SUR
) Estimator. This estimator uses a modified syntax since the class allow multiple models to be specified, each with it own dependent and exogenous variables. The more structured syntax uses a dict
or preferably an OrderedDict
, which ensures that the order of the equations in the results is preserved, where each entry is a complete model with a dependent and exogenous (stored as a dict
with keys dependent
and exog
.
from collections import OrderedDict
import statsmodels.api as sm
from linearmodels.datasets import fringe
from linearmodels.system import SUR
data = sm.add_constant(fringe.load())
equations = OrderedDict()
equations['earnings'] = {'dependent': data.hrearn,
'exog': data[['const', 'exper', 'tenure']]}
equations['benefits'] = {'dependent': data.hrbens,
'exog': data[['const', 'exper', 'tenure']]}
mod = SUR(equations)
mod.fit(cov_type='unadjusted')
System GLS Estimation Summary
==============================================================================
Estimator: GLS Overall R-squared: 0.0757
No. Equations.: 2 Cov. Estimator: unadjusted
No. Observations: 616 Num. Constraints: None
Date: Sat, Jun 17 2017
Time: 23:21:18
Equation: earnings, Dependent Variable: hrearn
==============================================================================
Parameter Std. Err. T-stat P-value Lower CI Upper CI
------------------------------------------------------------------------------
const 4.2839 0.3407 12.573 0.0000 3.6161 4.9517
exper 0.1163 0.0186 6.2478 0.0000 0.0798 0.1528
tenure -0.0283 0.0295 -0.9598 0.3372 -0.0862 0.0295
Equation: benefits, Dependent Variable: hrbens
==============================================================================
Parameter Std. Err. T-stat P-value Lower CI Upper CI
------------------------------------------------------------------------------
const 0.6390 0.0449 14.220 0.0000 0.5509 0.7270
exper 0.0014 0.0025 0.5617 0.5743 -0.0034 0.0062
tenure 0.0316 0.0039 8.1254 0.0000 0.0240 0.0393
==============================================================================
SystemResults, id: 0x282ca8f7b70
In addition to SUR, the system module also contain an estimator for the Three-stage Least Squares (IV3SLS
) Estimator. 3SLS is a generalization of SUR which allows variables to be either exogenous or endogenous, and when there are endogenous variables, for instruments to be used. SUR is a special case of 3SLS where there are no endogenous variables or instruments. 3SLS allows systems of IV equations to be jointly estimated.
- Examples
- Using formulas to specify models
- Three-stage Least Squares (3SLS)
- Module Reference
- Seemingly Unrelated Regression (SUR/SURE)
- Covariance Estimation
- Memory efficient calculations
- Three Stage Least Squares (3SLS)
- System Generalized Method of Moments (GMM)
- Testing Covariance and Correlations
- System Measures of Fit (\(R^{2}\))