Significance test in nonstationary multinomial logit model

- The asymptotic distribution of a LM test in a nonstationary multinomial logit model when the qualitative response is serially correlated is derived.
- Significance test ignoring the serial correlation in qualitative response in a nonstationary multinomial logit model can result in spurious logit link.

We derive the asymptotic distribution of the overall significance/LM test in a multinomial logit model with nonstationary covariates when the qualitative response is serially correlated and show that conventional significance tests can result in spurious logit link due to its wrong test size.