Measurement error and imputation of consumption in survey data

Abstract

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, then instrumenting consumption may still produce inconsistent estimators. This inconsistency arises from the correlation between additional regressors and measurement error. We propose an additional condition to be satisfied by the instrument that reduces measurement error bias. This condition is directly observable in the data. We apply our findings by revisiting recent research that imputes consumption data from the CEX to the PSID.