The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian–Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

The aim of the present study was to evaluate the effect of flaxseed on choroid–sclera complex thickness and on LDL oxidation in the sclera, choroid and retina of diet-induced hypercholesterolaemic rabbits. New Zealand male albino rabbits (n 21) were divided into two groups: group 1 (G1; n 11), fed a hypercholesterolaemic diet, and group 2 (G2; n 10), fed a hypercholesterolaemic diet enriched with flaxseed flour. The serum concentrations of total cholesterol (TC), LDL-cholesterol (LDL-C), HDL-cholesterol, TAG and fasting blood glucose were determined at the start of the experiment and on the day of killing (8th week). Choroid and sclera samples were subjected to haematoxylin–eosin (HE) staining and histomorphometric and immunohistochemical analyses with the anti-oxidised LDL antibody. Sensory retina samples were subjected to an immunohistochemical analysis with the primary monoclonal nitrotyrosine antibody. At the end of the experiment, a significant increase was observed in TC and LDL-C concentrations in G1 rabbits when compared with G2 rabbits (P= 0·008 and P= 0·02, respectively). HE staining revealed a significant increase in choroid–sclera complex thickness in G1 rabbits when compared with G2 rabbits (P< 0·001). Immunohistochemical analysis of choroid and sclera samples with the anti-oxidised LDL marker revealed a significant increase in immunoreactivity in G1 rabbits when compared with G2 rabbits (P< 0·001). Immunohistochemical analysis of sensory retina samples with the anti-nitrotyrosine marker revealed a significant increase in immunoreactivity in G1 rabbits when compared with G2 rabbits (P= 0·002). Flaxseed reduced the choroid–sclera complex thickness of diet-induced hypercholesterolaemic rabbits and the expression of oxidised LDL in the choroid–sclera complex as well as the expression of nitrotyrosine in the sensory retina.

This paper is concerned with the problem of combining a data set that identifies the conditional distribution P(y|x) with one that identifies the conditional distribution P(z|x) to identify the regressions E(y|x,·) ≡ [E(y|x,z = j),j ∈ Z] when the conditional distribution P(y|x,z) is unknown. Cross and Manski (2002, Econometrica 70, 357–368) studied this problem and showed that the identification region of E(y|x,·) can be precisely calculated when y has finite support. Here we generalize the result of Cross and Manski, showing that the identification region can be precisely calculated also in the case in which y has infinite support.We are grateful to the co-editor Paolo Paruolo, an anonymous referee, Maria Goltsman, Nick Kiefer, Tymon Tatur, and Tim Vogelsang for useful comments. Any remaining errors are our own responsibility.Financial support from Northwestern University's Dissertation Year Fellowship is gratefully acknowledged.