When the model is over-identified (more instruments than endogenous exposures), the Sargan (1958) J-statistic tests the null hypothesis that all instruments are valid (i.e., the exclusion restriction holds). The statistic is
Arguments
- data
A data frame.
- exposure
Character; name of the endogenous exposure column.
- outcome
Character; name of the outcome column.
- instruments
Character vector; names of instrument columns. More instruments than exposures gives an over-identified model on which the Sargan test is applicable.
- covariates
Optional character vector of exogenous-control column names included in both first and second stage.
Details
$$J = n \cdot R^2_{uu}$$
where R^2_uu is the R-squared of regressing the 2SLS residuals
on all instruments (and controls). Under H0, J ~ chi-sq(L - K)
where L is the number of instruments and K is the number of
endogenous regressors. Rejection (p < 0.05) is evidence that at
least one instrument is invalid.