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This paper proposes an estimation procedure for the partial linear regression models, when the explanatory variable of the non parametric component is supported on , and the covariates in the parametric part are contaminated by the measurement errors. Bias corrected estimators for the regression parameters and the non parametric components are constructed when the model errors are homoscedastic and heteroscedastic. Under some regularity conditions, large sample properties, including the consistency and asymptotic normality of the proposed estimators, are discussed. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed estimation procedure. [ABSTRACT FROM AUTHOR]

The article examines the problems arising in the testing for the rank of a system of Engel curves in the presence of preference heterogeneity using individual household data. The nonparametric analysis suggests that, when ignored, preference heterogeneity can bias the estimated rank. In particular, when preference heterogeneity is removed by projecting off the influence of demographic and other household characteristics on budget shares, a rank-3 system of Engel curves can be an adequate empirical specification. To illustrate the implications of this result for modeling consumer behavior, the article investigates the impact on rank tests from excluding important household characteristics from systems of Engel curves that belong to the quadratic logarithmic family. The results confirm that this can result in a dramatic increase in the significance of higher-order log-expenditure effects. At the same time, however, our results suggest that in parametric demand analysis the log-expenditure effects may be of higher order than that suggested by the rank established by nonparametric tests.