Mendelian Randomization (MR) has become an important tool for causal inference in the health sciences. It takes advantage of the random segregation of alleles to control for background confounding factors. In brief, the method works by using genetic variants as instrumental variables, but it depends on the assumption of exclusion restriction, i.e., that the variants affect the outcome exclusively via the exposure variable. Equivalently, the assumption states that there is no horizontal pleiotropy from the variant to the outcome. This assumption is unlikely to hold in nature, so several extensions to MR have been developed to increase its robustness against horizontal pleiotropy, though not eliminating the problem entirely (Sanderson et al. 2022). The Direction of Causation (DoC) model, which affords information from the cross-twin cross-trait correlations to estimate causal paths, was extended with polygenic scores to explicitly model horizontal pleiotropy and a causal path (MR-DoC, Minică et al 2018). MR-DoC was further extended to accommodate bidirectional causation (MR-DoC2 ; Castro-de-Araujo et al. 2023). In the present paper, we compared the power of the DoC model, MR-DoC, and MR-DoC2. We investigated the effect of phenotypic measurement error and the effect of misspecification of unshared (individual-specific) environmental factors on the parameter estimates., Competing Interests: Declarations Conflicts of interest Authors report no conflicts of interest