Measurement error and imputation of consumption in survey data

We study how estimators used to impute consumption in survey data are inconsistent due to measurement error in consumption. Previous research suggests instrumenting consumption to overcome this problem. We show that, if additional regressors are present in the estimation, then instrumenting consumption may still produce inconsistent estimators. This inconsistency arises from the likely correlation between those additional regressors and the measurement error, a correlation not directly observable. We propose an additional condition to be satisfied by the instrument that reduces and even eliminates measurement error bias in the presence of additional regressors. This condition is directly observable in the data.