A few previous works also consider **data** combination for long-term causal inference, but they impose strong restrictions on the unmeasured confounders. Athey et al. [2019] rely on a surrogate criterion first proposed by Prentice [1989]. This surrogate criterion precludes any unobserved variable that can simultaneously affect the short-term and long-term outcomes (see Section 3.2). Athey et al. [2020] assume a latent confoundedness condition, requiring unobserved confounders to have no direct effects on the long-term outcome but only indirect effects through the short-term outcomes. Neither of these works can handle persistent confounders. By permitting the existence of persistent confounders, our setup is substantially more general than these existing literature.