We present a Maximum Likelihood estimator for the standard commodity storage model with stockouts, based on prices only. While it imposes no additional assumptions on the model, the Maximum Likelihood estimator has small sample properties superior to those of the Pseudo Maximum Likelihood approach. We provide a proof that is crucial for applying our estimator to the model with normal harvests and possibly unbounded prices, thereby eliminating an inconsistency in the empirical storage model literature. Applying our Maximum Likelihood estimator to a series of annual sugar prices from 1921 to 2009 provides new evidence for the empirical relevance of the standard storage model. Our results imply a cutoff price at which discretionary stocks go to zero, which is higher than the price obtained by applying the Pseudo Maximum Likelihood estimator to the same data. The implied frequency of stockouts is lower, and price correlations, skewness, and kurtosis implied by the model closely match those seen in the annual sugar price data. We find the price of sugar to be highly responsive to small changes in consumption. When inventories are not available to buffer the effects of negative supply shocks on consumption, prices must increase sharply to induce the consumption changes needed to clear the market. Our results show why production shocks are not necessarily aligned with price spikes; the same production shock can give rise to very different price responses, depending on whether or not there are sufficient stocks to buffer its impact.