# Inference on Regressions with Interval Data on a Regressor or Outcome

 Title Inference on Regressions with Interval Data on a Regressor or Outcome Publication Type Journal Article Year of Publication 2002 Authors Manski, CF, Tamer, E Journal Econometrica Volume 70 Issue 2 Pagination 519-46 Call Number pubs_2002_Manski_CEcmetrica.pdf Keywords Identification, interval data, Regression Analysis Abstract This paper examines inference on regressions when interval data are available on one variable, the other variables being measured precisely. Let a population be characterized by a distribution P(y, x, v, v0, v1), where y ε R1, x ε Rk, and the real variables (v, v0, v1) satisfy v0 ≤ v ≤ v1. Let a random sample be drawn from P and the realizations of (y, x, v0, v1) be observed, but not those of v. The problem of interest may be to infer E(y|x, v) or E(v|x). This analysis maintains Interval (I), Monotonicity (M), and Mean Independence (MI) assumptions: (I) P(v0 ≤ v ≤ v1) = 1; (M)E(y|x, v) is monotone in v; (MI) E(y|x, v, v0, v1) = E(y|x, v). No restrictions are imposed on the distribution of the unobserved values of v within the observed intervals [v0, v1]. It is found that the IMMI Assumptions alone imply simple nonparametric bounds on E(y|x, v) and E(v|x). These assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score (MMS) method. The IMMI assumptions combined with a parametric model for E(y|x, v) or E(v|x) yield an identification region that may be estimated consistently by a modified minimum-distance (MMD) method. Monte Carlo methods are used to characterize the finite-sample performance of these estimators. Empirical case studies are performed using interval wealth data in the Health and Retirement Study and interval income data in the Current Population Survey. Notes ProCite field 3 : Northwestern U; Princeton U DOI 10.1111/1468-0262.00294 Endnote Keywords Econometric Methods: Single Equation Models: General/Regression Endnote ID 1068 Citation Key 6785