Summary. We consider the problem of examining the extent of (partial) similarity in the dynamics of a panel of independent threshold autoregressive processes. We develop some tests for common structure via Wald's approach and by checking whether the parameter estimates of the unconstrained threshold models satisfy the constraints defining the common structure. One test concerns the equality of independent ratios of normal means, which is shown to have nonstandard asymptotic null distribution. These tests are illustrated with a modern panel of Canadian lynx data; our analysis suggests that the lynx data over Canada share similar dynamics in the decrease phase, but they appear to be different in the increase phase.