An identified model is not necessary for statistical inference, but ambiguities can arise. This paper examines some simple examples and proposes a framework that distinguishes between the “refutation” and “confirmation” aspects of testing in an unidentified model. One particular problem is the interpretation given to overidentifying restrictions: a common view is that these are somehow not properly testable.

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems such as those advanced recently by Granger and Engle and quite general linear simultaneous equations systems with contemporaneous regressor error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate regressions with integrated processes are also studied. It is shown that the asympotic theory for conventional tests involves major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting distribution theory.