Optimal Cutoff Sampling for the Annual Survey of Public 

Employment and Payroll

Brian Dumbacher1, Carma Hogue1 

1U.S. Census Bureau

4600 Silver Hill Road, Washington, DC 20233

Brian.Dumbacher@census.gov, Carma.Ray.Hogue@census.gov

Proceedings of the 2013 Federal Committee on Statistical Methodology (FCSM) Research Conference

Abstract

The goal of cutoff sampling is to save cost, reduce respondent burden, and maintain accuracy of estimates by 

reducing the number of small units in sample. For the Annual Survey of Public Employment and Payroll, the 

Governments Division of the U.S. Census Bureau uses a modified version of cutoff sampling in which a subsample 

of units below the cutoff is selected. In this paper, we examine a numerical method based on minimizing the 

average of mean squared errors from linear regression models to find an optimal combination of cutoff and 

subsampling rate given a specified cost. Data from the 2002 and 2007 Censuses of Governments: Employment are 

used for this study.

Key Words: Cutoff sampling; Decision-based estimation; Linear regression; Mean squared error

1. Introduction

1.1 Survey Overview

The Annual Survey of Public Employment and Payroll (ASPEP) is conducted by the Governments Division of the 

U.S. Census Bureau to collect data on federal, state, and local government civilian employees and their gross 

payrolls. Key study variables for ASPEP include the total number of employees, total pay, and the number of fulltime equivalent employees. Small area composite methodology is used to estimate local government totals for each 

combination of state and government function. Government functions are identified by item code, and a complete 

list of item codes is provided in Appendix A. 

1.2 Sample Design

The sampling frame for ASPEP is a list of the 89,476 local governments identified during the 2007 Census of 

Governments and is updated annually with births (newly discovered governments), deaths (disincorporated 

governments), and mergers. Initial certainties are determined based on population size, school enrollment, and 

government function, and then a first-stage, stratified, probability-proportional-to-size sample (Särndal, Swensson, 

& Wretman, 1992, p. 90) is selected from the remaining local governments, where the strata are determined by the 

cross-classification of state and government type and the measure of size is total pay in 2007. 

___________________________________

This report is released to inform interested parties of ongoing research and to encourage discussion of work in 

progress. Any views expressed on statistical, methodological, technical, or operational issues are those of the 

authors and not necessarily those of the U.S. Census Bureau.
The different types of local government are counties, cities, townships, special districts, and independent school 

districts, but cities and townships are deemed similar enough to group together and are known collectively as 

subcounty governments. Counties and subcounties are known as general-purpose governments, and they tend to 

perform several of the functions listed in Appendix A. Special districts and school districts, on the other hand, are

known as single-purpose governments and tend to perform one or a very limited number of functions. The purpose 

of school districts is education, while special districts may be cemetery districts, public utilities, transit authorities, 

etc. As such, their contribution to a single function like air transportation may be great, but they would have no 

contribution to other functions. Table 1 gives a breakdown of the local governments in 2007 by type. As you can 

see, there are many subcounties and special districts, but these units’ shares of total employees and total pay are 

disproportionately small.

Table 1: Local governments in 2007

Government type Number % Total employees % Total pay ($) % 

County 3,033 3.39 2,928,244 20.64 10,093,125,772 21.77

Subcounty 36,011 40.25 3,510,995 24.75 12,717,946,464 27.43

Special district 37,381 41.78 821,369 5.79 2,651,730,327 5.72

Independent school district 13,051 14.59 6,925,014 48.82 20,904,942,336 45.09

Total 89,476 100.00 14,185,622 100.00 46,367,744,899 100.00

Source: U.S. Census Bureau, 2007 Census of Governments: Employment

To reduce the number of non-contributory units in sample, the Governments Division uses cutoff sampling in the 

subcounty and special district strata to divide each first-stage sample into a small cutoff stratum and a large cutoff 

stratum (Barth, Cheng, & Hogue, 2009). For the 2009 sample design, the cutoffs were determined by the 

cumulative square root of the frequency method (Dalenius & Hodges, 1959). [See Cochran (1977, p. 130) for an

overview and Appendix B for an illustration of this method.] Instead of completely ignoring the sample units in the 

small cutoff strata as is done in standard cutoff sampling, the Governments Division selects a subsample of them. 

This helps protect against bias that could result from small units becoming large units during intercensal years. A 

subsampling rate equal to 0.56 was used in all small cutoff strata, which resulted in a target reduction of 800 

subcounty and special district units. This target was based on a rough cost-benefit analysis, and we have planned 

more optimal methods for the future when a new ASPEP sample based on the 2012 Census of Governments is 

selected. 

1.3 Small Area Estimation Methodology

Estimates of local government totals are calculated for each combination of state and item code using small area 

composite methodology (Tran & Cheng, 2012). Each composite estimate is a weighted average of the direct 

Horvitz-Thompson estimate and a synthetic estimate. This synthetic estimate equals the product of a decision-based 

regression estimate of the state total and a proportion for the item code within the state. The term “decision-based” 

refers to statistical hypothesis tests that are carried out to determine whether the regression relationships in the small 

and large cutoff strata are similar enough that the strata can be combined for estimation purposes.

Figure 2 is a scatterplot of total pay in a survey year versus total pay in the most recent Census year for a

hypothetical sample after the cutoff is determined and subsampling is performed. Separate linear regressions are 

fitted in the small and large cutoff strata using sample data, and then a statistical hypothesis test of the equality of 

the regression slopes is carried out. If the null hypothesis is rejected, then the cutoff strata are kept separate. If the 

null hypothesis is not rejected, then the cutoff strata are combined and a new regression is fitted to all the units. 

Whichever regression is decided on is then applied to Census data to estimate the state total. This is a simplified 

description of the process as robust regression and auxiliary data are used to handle outliers and to strengthen poor 

fitting models. Also, the variable total pay is used in this example, but in production, the decision-based 

methodology would be applied to full-time pay and part-time pay separately. For a much more detailed description 

of decision-based estimation, see Cheng, Corcoran, Barth, and Hogue (2009).