Bootstrapping Mean Squared Errors of Robust Small-Area Estimators: Application to the Method-of-Payments Data

This paper proposes a new bootstrap procedure for mean squared errors of robust small-area estimators. We formally prove the asymptotic validity of the proposed bootstrap method and examine its finite sample performance through Monte Carlo simulations. The results show that our procedure performs well and outperforms existing ones. We also apply our procedure to the estimation of the total volume and value of cash, debit card and credit card transactions in Canada as well as in its provinces and subgroups of households. In particular, we find that there is a significant average annual decline rate of 3.1 percent in the volume of cash transactions, and that this decline is relatively higher among high-income households living in heavily populated provinces. Our bootstrap estimator also provides indicators of quality useful in selecting the best small-area predictors from among several alternatives in practice.