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We study the identification of a dynamic consumer stockpiling model. Previously, it has been common for researchers to assume that storage cost is a continuous function of inventory. We point out that this seemingly innocuous simplifying assumption rules out exclusion restrictions which naturally arise from the institutional features of the stockpiling problem.  The lack of exclusion restrictions in earlier models requires researchers to fix the discount factor, instead of estimating it. We argue that by properly modeling storage cost as a step function of inventory (because storage cost depends on the number of packages stored, instead of the actual amount of inventory), the key state variable of this model, inventory, provides natural exclusion restrictions that can help identify the model’s parameters, including the discount factor. We demonstrate the feasibility of our identification strategy with an empirical exercise, where we estimate a stockpiling model using scanner data on laundry detergents. Our estimates suggest that consumers are not as forward-looking as most papers in the literature assume; our estimates of weekly discount factors average at about 0.73, which is significantly lower than the value used in previous research (it is typically set at 0.99, using the market interest rate). We also find significant unobserved heterogeneity in discount factors across individuals.