Two-stage regression methods are typically used for handling endogeneity in the simultaneous equations models in economics and other social sciences. However, the problem is challenging in the presence of incomplete response and/or incomplete endogenous covariate(s). We propose a Bayesian approach for the joint modelling of incomplete longitudinal continuous response and an incomplete count endogenous covariate, where the incompleteness is caused by the censorship through a selection mechanism. We define latent continuous variables which are left-censored at zero and develop a Gibbs sampling algorithm for the simultaneous estimation of the model parameters. We consider partially varying coefficients regression models containing covariates with fixed and time-varying effects on the response. Our work is motivated by a sample dataset from the Health and Retirement Study (HRS) for modelling the out-of-pocket medical cost, where the number of hospital admissions is considered as an endogenous covariate. Our analysis addresses some of the previously unanswered questions on the physical and financial health of the older population based on HRS data. Simulation studies are performed for assessing the usefulness of the proposed method compared to its competitors.