system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why do people claim to know how many illegal immigrants are in the United States?

If someone is illegal, there's no documentation on them, right?  I realize the numbers are estimates, but I can't imagine how these estimations are even close if there isn't any hard data.
gpt
There are multiple ways to estimate the illegal population. These include economic impact, public service usage, population samples, the census, and migration tracking.

Economic impact looks at levels of spending and the flow of money to determine the population involved in the economy. We can compare this to the documentation we do have to find who is missing. We can also use this method to determine the black market size and under the table economy sizes, these are how illegal immigrants are paid.

We can also use data on public service usage to estimate size. Hospital visits, public school enrollment, and arrests all alow use to sample the population.

Population samples, the census, and migration tracking are forms of mass and local data collection taken on by the government. The data collected can be compared to know populations and communities to adjust for errors such as non-reporting by the population themselves.