We present a method for consistently estimating nonparametric functions and distributions in simultaneous equations models. This method is used to identify and estimate a random utility model of consumer demand. Our identiﬁcation conditions for this particular model extend the results of Houthakker (1950), Uzawa (1971) and Mas-Colell (1977), where a deterministic utility function is uniquely recovered from its deterministic demand function.
Brown, Donald J. and Matzkin, Rosa L., "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand" (1998). Cowles Foundation Discussion Papers. 1423.