The Zero-Information-Limit Condition and Spurious Inference

The fact that weak instruments lead to spurious inference is now widely recognized. In this paper we ask whether spurious inference occurs more generally in weakly identified models. To distinguish between models where spurious inference will occur from those where it does not, we introduce the Zero-Information-Limit-Condition (ZILC). When ZILC holds, the information or precision of parameter estimates is overestimated. Further, the numerator and denominator of the t-statistic will under certain circumstances be functionally related, not independent. We discuss how ZILC applies to models encountered in practice and show that spurious inference does occur when ZILC holds