Shift Restrictions and Semiparametric Estimation in Ordered Response Models

• Published in: Econometrica Vol. 70; no. 2; pp. 663 - 691
• Main Authors: Klein, Roger W., Sherman, Robert P.
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 01.03.2002; Econometric Society; Blackwell; Blackwell Publishing Ltd
• Subjects: Applications; Bias; Density; Density estimation; Distribution; Econometrics; Economic models; Economic theory; Error; Estimate reliability; Estimating techniques; Estimation; Estimation bias; Estimators; Exact sciences and technology; Independence; Insurance, economics, finance; Mathematical transformations; Mathematics; Nonparametric inference; ordered response model; Parametric inference; Parametric models; Probability; Probability and statistics; Probability distributions; Sciences and techniques of general use; semiparametric estimation; shift restrictions; Statistics; Studies; Survey data; Telecommunications; threshold points; transformation model; Error estimation; Transformation model; Order statistic; Response model; Semiparametric method; Statistical method; Regression coefficient; Survey; Asymptotic normality; Threshold point; Shift restriction; Econometrics; Telecommunication services
• ISSN: 0012-9682; 1468-0262
• DOI: 10.1111/1468-0262.00299

We develop a $\sqrt{n}\text{-}\text{consistent}$ and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various applications, particularly in new product demand forecasting from survey data subject to systematic misreporting. We apply the estimator to assess exaggeration bias in survey data on demand for a new telecommunications service.