Demand Response is capable of reducing the total amount of generation capacity investment required to ensure electricity system security. We utilise this fact to devise a novel methodology to estimate the contribution of a load-shifting demand response resource to system adequacy. We then simulate an electricity market using mixed complementarity models to determine how the participation of demand response in capacity markets impacts on market outcomes. Demand response primarily affects the equilibrium outcome through the energy market, however demand response also reduces both equilibrium prices and consumer costs through its capacity market contribution. The effect is particularly pronounced when there is a high level of variable renewable generation and initial undercapacity. In the absence of demand response, increased wind generation leads to higher capacity prices as generators seek to offset depressed energy prices. However, we find that demand response's participation in the capacity market can combat these increased capacity prices. These results suggest that demand response participation in capacity markets can mitigate some of the market challenges of renewable integration, particularly that of the "missing money" problem.