linearmodels.iv.results.IVResults.wooldridge_score

property IVResults.wooldridge_score: WaldTestStatistic[source]

Wooldridge’s score test of exogeneity

Returns:
WaldTestStatistic

Object containing test statistic, p-value, distribution and null

Notes

Wooldridge’s test examines whether there is correlation between the errors produced when the endogenous variable are treated as exogenous so that the model can be fit by OLS, and the component of the endogenous variables that cannot be explained by the instruments.

The test is implemented using a regression,

\[1 = \gamma_1 \hat{\epsilon}_1 \hat{v}_{1,i} + \ldots + \gamma_p \hat{\epsilon}_1 \hat{v}_{p,i} + \eta_i\]

where \(\hat{v}_{j,i}\) is the residual from regressing endogenous variable \(x_j\) on the exogenous variables and instruments.

The test is a \(n\times R^2 \sim \chi^2_{p}\).

Implemented using the expression in Wooldridge (2002), Eq. 6.19