This paper develops and estimates a rational expectations storage model with rich dynamic features. The model incorporates elastic supply, long-run demand and cost trends, and four structural shocks. It is estimated by indirect inference using a linear supply and demand model as an auxiliary model. This approach deviates from the common practice of estimating storage models only on prices and allows all parameters to be estimated. The estimation is carried out on a market representing the caloric aggregate of four basic staples: maize, rice, soybean, and wheat. The results show that our extended storage model is consistent with most of the moments in the data, including the high price autocorrelation which is the subject of longstanding debate. However, it fails to replicate the strength of the negative correlation between consumption and price.