Improved Estimation of Poisson Rate Distributions through a Multi-Mode Survey Design

Marcin Hitczenko
Working Paper 2021-10
February 2021

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Abstract: Researchers interested in studying the frequency of events or behaviors among a population must rely on count data provided by sampled individuals. Often, this involves a decision between live event counting, such as a behavioral diary, and recalled aggregate counts. Diaries are generally more accurate, but their greater cost and respondent burden generally yield less data. The choice of survey mode, therefore, involves a potential tradeoff between bias and variance of estimators. I use a case study comparing inferences about payment instrument use based on different survey designs to illustrate this dilemma. I then use a simulation study to show how and under what conditions a hybrid survey design can improve efficiency of estimation, in terms of mean-squared error. Overall, this work suggests that such a hybrid design can have considerable benefits as long as there is nontrivial overlap in the diary and recall samples.

JEL classification: C15, C81, C83

Key words: recall surveys, diaries, bias, mean-squared error, multi-level models

The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the author's responsibility.

Please address questions regarding content to Marcin Hitczenko, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street NE, Atlanta, GA 30309.

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