Conditional bimodality in a structural equations model

We investigate the conditional density of the MLE in a simple structural Keynesian model as in Phillips (2006). The marginal distribution is known to be bimodal but the cause has been dis- puted. We give a clear geometric explanation for the bimodality of the MLE. We further show that the degree of bimodality depends heavily on the value of appropriate ancillary statistics, as well as on the relevance and strength of the instrument in the observed sample. The relevant conditional distribution is still bimodal and we show that the saddlepoint approximation captures the relevant conditional distribution and its bimodality extremely well.
JEL: C01, C10, C30
Keywords: Saddlepoint Approximation, Weak Instruments