The Current Population Survey (CPS) conducts reinterviews (RI) to measure the reliability of labor force (LBFR) status. Whether or not latent class analysis (LCA) can be used instead of RI, these models are able to identify sources and causes of unreliability as well as errors in its estimation. LCA uses substantially increasing the sample size without conducting RI. Agreed with RI results, we have been using LCA in parallel with RI to estimate the LBFR response error in CPS. We began with a first-order latent Markov model, but the challenge is it assumes unobserved homogeneity that is not always true. Mover-Stayer (MS) model solves the homogeneity problem, and outperformed the first-order model in estimating CPS response error, but if the dependency (second-order) goes beyond the previous state, we may be missing information. This paper presents different error models with second-order.