Correcting for measurement error when estimating pay distributions from household survey data

Abstract

The aim of this thesis is to develop and to evaluate different methods for estimating distributions in the presence of measurement error and missing data with a primary focus on a specific application concerning pay. Different methods for correcting for measurement error in a fully observed variable are considered by taking into account information on the accurately measured variable observed on a non-random subsample. To compensate for nonresponse in the correct variable and to effectively correct for measurement error in the erroneously observed variable several imputation methods are proposed treating the problem of measurement error as a missing data problem. Based on the assumption that the data are missing at random (MAR) hot deck imputation within classes as a form of predictive mean matching imputation is evaluated theoretically and empirically. This method provides approximately unbiased estimates of the parameter of interest, the proportion below a given threshold. The problem of estimating the variance of the estimator under this imputation method is investigated. A variance estimator is proposed which allows for uncertainty due to imputation. It is shown that this estimator is approximately unbiased under certain conditions.

Since some evidence is found that the results under hot deck imputation within classes may depend on the choice of imputation classes other forms of predictive mean matching imputation are evaluated theoretically and empirically under the assumption of MAR. The imputation methods are also compared to propensity score weighing. The use of repeated imputation shows gains in efficacy in comparison to single value imputation. It is found that nearest neighbour imputation using repeated imputation shows advantages in terms of bias robustness and efficiency of the point estimator. It is therefore recommended for practical use.

Several estimation methods under nonignorable nonresponse are considered making an alternative assumption of common measurement error (CME). An imputation method using data augmentation based on the assumption of CME rather than MAR is derived, which shows desirable properties of the point estimator of interest. The use of hot deck imputation in the data augmentation procedure is proposed. Data augmentation using nearest neighbour imputation under the assumption of CME is found to have desirable properties for the pay application.

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