Census Undercount Adjustment and the Quality of Geographic Population Distributions

Abstract

We develop a simulation procedure to measure the effects of synthetic adjustment for census undercounts on the quality of estimated proportionate geographic population distributions. Analyzing the influences of both interstate variations in census coverage and measurement errors in national undercount estimates, we find that, over a wide range of environments, nearly two out of every three simulated applications of synthetic adjustment improve the state proportions for a majority of the national population. There is always, however, a substantial probability that adjustment will produce a much poorer geographic distribution in any particular application. We derive analytical expressions showing as precisely as possible the conditions on which improvements from census adjustment depend.

Our simulation model considers two population groups, blacks and nonblacks, and 51 geographic areas, the 50 states plus the District of Columbia. We assume that both census counting errors and undercount measurement errors are lognormally distributed. From 1980 census counts, we generate true population counts according to our model and obtain, by the synthetic method, adjusted population counts. We consider several measures of adjustment success and find that whether policymakers decide to adjust may depend on which loss function they select.

To assess the effects of national group undercount measurement errors, we propose four scenarios. In one there are no such errors; in another national black and white undercounts are persistently underestimated by 1% and 2.75%. Errors like the latter may arise if many illegal aliens reside in the United States. We simulate stochastic measurement errors in two alternative scenarios. National undercounts are estimated correctly on average in one, in contrast to the other where black and white undercounts are underestimated typically by .5% and 1.4%. We study the effects of interstate variations in census coverage by considering, within scenarios, alternative cases distinguished by their variances, across states, in black or white undercounts. The highest and lowest values considered are .0064 and .0007 for blacks and .0007 and .0001 for whites. with respect to both undercount measurement errors and undercount variances, simulated parameter ranges are very wide and almost surely contain the true values. Despite the highly differing circumstances represented, however, we find a startling lack of sensitivity of adjustment success to changing parameter values. The extreme values for a measure giving the mean proportion of the national population residing in states whose population proportions are improved by adjustment, for example, are .508 and .566. Conditions more favorable to adjustment do produce slightly greater success.

Our principal analytical result shows that a necessary but not sufficient condition for adjustment to fail to improve the quality of the geographic distribution is that either blacks are most heavily undercounted where they are least prevalent or whites are most heavily undercounted where they are most prevalent. According to the best available empirical evidence, such patterns of covariation do not prevail. To derive the result, we assume that national undercounts are measured perfectly, although simulation results suggest that this is not critical.

Key Words:

• Simulation
• Synthetic adjustment
• Lognormal distribution
• Illegal aliens