linearmodels.iv.results.IVResults.wooldridge_overid

property IVResults.wooldridge_overid: InvalidTestStatistic | WaldTestStatistic[source]

Wooldridge’s score test of overidentification

Returns:
WaldTestStatistic

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

Notes

Wooldridge’s test examines whether there is correlation between the model residuals and the component of the instruments that is orthogonal to the endogenous variables. Define \(\tilde{z}\) to be the residuals of the instruments regressed on the exogenous variables and the first-stage fitted values of the endogenous variables. The test is computed as a regression

\[1 = \gamma_1 \hat{\epsilon}_i \tilde{z}_{i,1} + \ldots + \gamma_q \hat{\epsilon}_i \tilde{z}_{i,q}\]

where \(q = n_{instr} - n_{endog}\). The test is a \(n\times R^2 \sim \chi^2_{q}\).

The order of the instruments does not affect this test.