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Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze its finite sample behavior. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages and the difficulties of an approach that leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between endogenous nonparametric regression models and the recently emphasized issue of unobserved heterogeneity in structural models.<\/jats:p>","DOI":"10.1017\/s0266466610000423","type":"journal-article","created":{"date-parts":[[2010,11,4]],"date-time":"2010-11-04T09:55:36Z","timestamp":1288864536000},"page":"609-638","source":"Crossref","is-referenced-by-count":11,"title":["DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION"],"prefix":"10.1017","volume":"27","author":[{"given":"Stefan","family":"Hoderlein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hajo","family":"Holzmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,11,4]]},"reference":[{"key":"S0266466610000423_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060117"},{"key":"S0266466610000423_ref27","first-page":"169","article-title":"A statistical perspective on ill-posed inverse problems","volume":"4","author":"O\u2019Sullivan","year":"1986","journal-title":"Statistical Science"},{"key":"S0266466610000423_ref25","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347125"},{"key":"S0266466610000423_ref24","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00459"},{"key":"S0266466610000423_ref23","doi-asserted-by":"publisher","DOI":"10.1080\/02331889708802572"},{"key":"S0266466610000423_ref19","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347500"},{"key":"S0266466610000423_ref17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00801.x"},{"key":"S0266466610000423_ref14","volume-title":"Market Demand: Theory and Empirical Evidence","author":"Hildenbrand","year":"1993"},{"key":"S0266466610000423_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176349403"},{"key":"S0266466610000423_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000714"},{"key":"S0266466610000423_ref11","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1992.10476255"},{"key":"S0266466610000423_ref7","unstructured":"Darolles S. , Florens J.-P. , & Renault E. 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