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Omitted Variable Bias: Wald Test in Python

Last Update: February 21, 2022

Omitted Variable Bias: Wald Test in Python can be done using statsmodels package wald_test function found within statsmodels.formula.api module for evaluating whether linear regression omitted independent variables explain dependent variable. Main parameters within wald_test function are r_matrix with omitted independent variables null hypothesis string and use_f with logical value on whether an F-test or chi-square test should be done.

As example, we can do number of bathrooms omitted variable Wald test from unrestricted multiple linear regression of house price explained by its lot size, number of bedrooms and bathrooms using data included within AER R package HousePrices object [1].

First, we import statsmodels package for data downloading, multiple linear regression fitting and Wald test [2].

In [1]:
import statsmodels.api as sm
import statsmodels.formula.api as smf

Second, we create houseprices data object using get_rdataset function and display first five rows and four columns of data using print function and head data frame method to view its structure.

In [2]:
houseprices = sm.datasets.get_rdataset(dataname="HousePrices", package="AER", cache=True).data
print(houseprices.iloc[:, 0:4].head())
Out [2]:
     price  lotsize  bedrooms  bathrooms
0  42000.0     5850         3          1
1  38500.0     4000         2          1
2  49500.0     3060         3          1
3  60500.0     6650         3          1
4  61000.0     6360         2          1

Third, we fit unrestricted multiple linear regression with ols function using variables within houseprices data object and store results within mlr object. Within ols function, parameter formula="price ~ lotsize + bedrooms + bathrooms" fits unrestricted model where house price is explained by its lot size, number of bedrooms and bathrooms.

In [3]:
mlr = smf.ols(formula="price ~ lotsize + bedrooms + bathrooms", data=houseprices).fit()

Fourth, as example again, we do Wald test using wald_test function, store results within waldtest object and print its results. Within wald_test function, parameters r_matrix="bathrooms = 0" includes number of bathrooms omitted independent variable null hypothesis string and use_f=True does F-test. Notice that unrestricted mlr model results and wald_test function parameter use_f=True were only included as educational examples which can be modified according to your needs.

In [4]:
waldtest = mlr.wald_test(r_matrix="bathrooms = 0", use_f=True)
Out [4]:
<F test: F=array([[122.41268574]]), p=8.544987755751257e-26, df_denom=542, df_num=1>


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[1] Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.

Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.

[2] statsmodels Python package: Seabold, Skipper, and Josef Perktold. (2010). “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference.

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