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We use molecular dynamics simulations for a first-principles-based effective Hamiltonian to calculate two important quantities characterizing the electrocaloric effect in BaTiO₃, the adiabatic temperature change ΔT and the isothermal entropy change ΔS, for different electric field strengths. We compare direct and indirect methods to obtain ΔT and ΔS, and we confirm that both methods indeed lead to an identical result provided that the system does not actually undergo a first order phase transition. We also show that a large electrocaloric response is obtained for electric fields beyond the critical field strength for the first order phase transition. Furthermore, our work fills several gaps regarding the application of the first-principles-based effective Hamiltonian approach, which represents a very attractive and powerful method for the quantitative prediction of electrocaloric properties. In particular, we consider the full temperature and field dependence of the calculated specific heat for the indirect calculation of ΔT, and we discuss the importance of maintaining thermal equilibrium during the field ramping when calculating ΔT using the direct method within a molecular dynamics approach.