classmethod IVSystemGMM.from_formula(formula: str | dict[str, str], data: pandas.DataFrame, *, weights: dict[str, ndarray | DataArray | DataFrame | Series] | None = None, weight_type: str = 'robust', **weight_config: bool | str | float) linearmodels.system.model.IVSystemGMM[source]

Specify a 3SLS using the formula interface

formula: str | dict[str, str]

Either a string or a dictionary of strings where each value in the dictionary represents a single equation. See Notes for a description of the accepted syntax

data: pandas.DataFrame

Frame containing named variables

weights: dict[str, ndarray | DataArray | DataFrame | Series] | None = None

Dictionary like object (e.g. a DataFrame) containing variable weights. Each entry must have the same number of observations as data. If an equation label is not a key weights, the weights will be set to unity

weight_type: str = 'robust'

Name of moment condition weight function to use in the GMM estimation. Valid options are:

  • ”unadjusted”, “homoskedastic” - Assume moments are homoskedastic

  • ”robust”, “heteroskedastic” - Allow for heteroskedasticity


Additional keyword arguments to pass to the moment condition weight function


model – Model instance

Return type:



Models can be specified in one of two ways. The first uses curly braces to encapsulate equations. The second uses a dictionary where each key is an equation name.


The simplest format uses standard formulas for each equation in a dictionary. Best practice is to use an Ordered Dictionary

>>> import pandas as pd
>>> import numpy as np
>>> cols = ["y1", "x1_1", "x1_2", "z1", "y2", "x2_1", "x2_2", "z2"]
>>> data = pd.DataFrame(np.random.randn(500, 8), columns=cols)
>>> from linearmodels.system import IVSystemGMM
>>> formula = {"eq1": "y1 ~ 1 + x1_1 + [x1_2 ~ z1]",
...            "eq2": "y2 ~ 1 + x2_1 + [x2_2 ~ z2]"}
>>> mod = IVSystemGMM.from_formula(formula, data)

The second format uses curly braces {} to surround distinct equations

>>> formula = "{y1 ~ 1 + x1_1 + [x1_2 ~ z1]} {y2 ~ 1 + x2_1 + [x2_2 ~ z2]}"
>>> mod = IVSystemGMM.from_formula(formula, data)

It is also possible to include equation labels when using curly braces

>>> formula = "{eq1: y1 ~ x1_1 + [x1_2 ~ z1]} {eq2: y2 ~ 1 + [x2_2 ~ z2]}"
>>> mod = IVSystemGMM.from_formula(formula, data)