Caloric cooling relies on reversible temperature changes in solids driven by an externally applied field, such as a magnetic field, electric field, uniaxial stress or hydrostatic pressure. Materials exhibiting such a solid-state caloric effect may provide the basis for an alternative to conventional vapor compression technologies. First-order phase transition materials are promising caloric materials, as they yield large reported adiabatic temperature changes compared to second-order phase transition materials, but exhibit hysteresis behavior that leads to possible degradation in the cooling performance. This work quantifies numerically the impact of hysteresis on the performance of a cooling cycle using different modeled caloric materials and a regenerator with a fixed geometry. A previously developed 1D active regenerator model has been used with an additional hysteresis term to predict how modeled materials with a range of realistic hysteresis values affect the cooling performance. The performance is quantified in terms of cooling power, coefficient of performance (COP), and second-law efficiency for a range of operating conditions. The model shows that hysteresis reduces efficiency, with COP falling by up to 50% as the hysteresis entropy generation (qhys) increases from 0.5% to 1%. At higher working frequencies, the cooling performance decreases further due to increased internal heating of the material. Regenerator beds using materials with lower specific heat and higher isothermal entropy change are less affected by hysteresis. Low specific heat materials show positive COP and cooling power up to 2% of qhys whereas high specific heat materials cannot tolerate more than 0.04% of qhys.