Can the Employment Rate ever be over 100%? I am an MBA student taking courses in statistics.
Our statistics professor was telling us a story about statistics being used to estimate the employment rate in some country. According to the professor, some researchers in this country conducted a census survey across the country. The people in this country were sampled using "stratified weighted sampling" (i.e. people had to say whether they were employed or not employed).  If I understood this correctly, it means that certain people from certain regions were sampled more than other people from other regions - this was done apparently to "balance things out". However, there was still inevitable "over-coverage" and "under-coverage". So far, everything makes sense to me.
The professor said that the census had good overall coverage (over 95%) in the general population - however, some remote areas with small populations had worse coverage. The employment rate in any individual area of the country (e.g. province level, county level) is calculated using information obtained from other areas as well as the area itself.  This also makes sense to me.
The next part is the part that I didn't understand: The prof mentioned that because of this (i.e. the regions with small populations with lower coverage), the employment rate estimates in some of these regions with smaller populations and less coverage turned out to be greater than 100%!
When he said this, the whole class erupted in laughter! I also laughed, but at the same time, I was curious in knowing how and why this could happen. I spent all day thinking about this, and then tried to search for "statistical paradoxes" online. I found some interesting paradoxes such as Simpson's Paradox - where the overall career average of one baseball player can be better than a second baseball player, even if the second baseball player's individual averages are better. But I couldn't find any indication of a statistical paradox that suggests "employement rate can be estimated at over 100% if a certain minority group in the population has poor coverage compared to the overall coverage".
Can someone please point me in the right direction and help me understand what my professor was talking about? Or am I completely "out to lunch" and misunderstood the prof's story?

It is likely to be poor modelling.  Here is an oversimplified example:
Suppose in the rest of the country you find out 1% work in agriculture, 20% in manufacturing, and 60% in services, so you conclude their employment rate is 81%.
In this small area suppose you know 25% work in agriculture but you do not have any information about local manufacturing or services so you assume those figures are the same as other places (20% and 60%) and this leads you to think the local employment rate is 105%.
