Before revision:  As a demonstration of its capabilities , the method provides informative nonparametric bounds on household expenditures under the sole assumption that expenditure is continuous , showing that partial identification approaches can yield informative bounds under minimal assumptions. Moreover, it shows that additional monotonicity assumptions lead to considerably tighter bounds, which constitutes a novel assessment of the identificatory strength of such nonparametric assumptions in a unified framework .
After revision:  As a demonstration of its capabilities , the method provides informative nonparametric bounds on household expenditures under the sole assumption that expenditure is continuous . The mathematical contribution is an approach to approximately solving infinite dimensional linear programs on path spaces via sampling .