Inventory inaccuracy is the mismatch between the recorded inventory and the physical inventory, which is severe and widespread in industry. A few studies have investigated the bullwhip effect with the existence of inventory inaccuracy. The development of information technologies has provided companies with access to accurate inventory information in real time. This will surely affect the bullwhip effect and supply chain costs. The aim of this paper is to build an analytical model to systematically investigate these effects. We consider a retailer–manufacturer supply chain in which the retailer faces inventory shrinkage, which is the main cause of inventory inaccuracy. Both the situations with accurate real-time inventory information, i.e., high-quality information, and the situation with statistical inventory information, i.e., low-quality information are studied. We examine the relationships between the bullwhip effect, information distortion and supply chain costs with different levels of information quality. The results of our analysis enrich the existing literature on the bullwhip effect. First, we show that the bullwhip effect is magnified along the chain when higher-quality information on inventory shrinkage – specifically real-time rather than statistical data – is obtained. Second, we show that the magnification of the bullwhip effect does not necessarily result in higher costs. Third, we demonstrate that higher-quality information increases the benefits of information sharing. Our paper provides new insights into the causes, extent and economic dynamics of order variability in the presence of inventory inaccuracy, and may thus suggest ways of more effectively managing the bullwhip effect and inventory.