As yet, the theory of instrumental variables (IV) estimation is not applicable to data from a stratified cross section (e.g., census data) since the moment matrices need not converge. This study provides general conditions for the consistency and asymptotic normality of the IV estimator in this case. Homoskedastic errors are not assumed, and a new, more general asymptotic parameter covariance matrix estimator is given which is consistent regardless of the presence of heteroskedasticity. A new estimator, two-stage instrumental variables, is proposed which is asymptotically efficient relative to two-stage least squares. Tests for model misspecification are also discussed.