We introduce inventories into an otherwise standard New Keynesian model and study the implications for inflation dynamics. Inventory holdings are motivated as a means to generate sales for demand-constrained firms. We derive various representations of the New Keynesian Phillips curve with inventories and show that one of these specifications is observationally equivalent to the standard model with respect to the behavior of inflation when the model's cross-equation restrictions are imposed. However, the driving variable in the New Keynesian Phillips curve - real marginal cost - is unobservable and has to be proxied by, for instance, unit labor costs. An alternative approach is to impute marginal cost by using the model's optimality conditions. We show that the stock-sales ratio is linked to marginal cost. We also estimate these various specifications of the New Keynesian Phillips curve using GMM. We find that predictive power of the inventory-specification at best approaches that of the standard model, but does not improve upon it. We conclude that inventories do not play a role in explaining inflation dynamics within our New Keynesian Phillips curve framework.