Cities overemphasize population as a measure of economic health and overall vitality. If the population is stable or growing, the logic goes, then certainly there must be enough amenities and jobs to explain why people are moving or at least staying. Population loss certainly is a bad sign, one difficult to explain away. But growing or stable population is not necessarily what it seems. If you want to get a sense of the direction an urban area is trending, look at changes over time in population density.
Why does that statistic matter more? Let's look at one of my favorite Rust Belt punching bags. Peoria, IL is a good example, but honestly you could choose from the lengthy list of declining Midwestern and Northeastern industrial cities and prove the same point.
In 1950 the Census recorded 111,856 people in the city proper; 2015 Census estimates were 115,070. If it seems surprising that a city often cited as an example of decline actually grew (slightly) since the often-cited base year of 1950, it is. A closer look at how it managed the feat reveals a serious underlying problem. In 1950 the city covered 12.9 square miles. In 2015, that figure exploded to 50.3 square miles. Population density, then, fell from 8671 per sq. mile to 2288.
That's staggering, but so what? The main problem is that urban infrastructure is expensive, and the more a city spreads out in an effort create the appearance of population growth or stability the more of that infrastructure it needs to provide. Roads, police and fire, utilities, sanitation, and any other costly function of modern urban governing become more difficult to provide over an ever expanding area with a declining number of taxpayers – individuals and businesses – to support them. Leaving aside the fact that economic opportunities in such cities almost inevitably are shrinking, each taxpayer becomes "responsible" for more and more infrastructure. That's not a great formula. Add in the fact that populations in these places almost inevitably become older and more impoverished over time and it's a disaster. Add in the current anti-government hysteria that makes even modest attempts to raise revenue a pitched battle and you have a place where you really don't want to live unless you can't afford to get out.
What happens next is predictable. Services get worse, costs are piled onto the remaining population that is least likely to be able to afford it, and lowest-bidder privatization farms out many essential tasks. The few remaining large employers in the area get to write their own ticket after threatening to leave, which often results in further reduced local tax revenues (through various breaks, loopholes, and handouts) and environmental degradation that no one dares try to make them clean up. Eventually the sense of decline becomes pervasive. Signs of crime and urban decay become widespread. Garbage piles up. Streets look like the Luftwaffe just bombed them. Aging water and sewerage systems fail. 9-1-1 calls go unanswered and fewer police are asked to deal with more crime spread over a greater area. Businesses shutter, and people with marketable skills take them to other places where things are not quite as bleak.
Despite the cottage industry of urban renewal and revitalization schemes, there's very little cities can do to reverse the slide into urban blight once the population density takes an appreciable drop. More accurately, there are some things they can do but hundreds of other dying and shrinking places trying to do those exact same things. Offering tax incentives to lure new businesses there? Great. So is everyone else. The end result is a sort of community-wide torpor, a "who gives a shit" mentality that sinks in after a couple years or decades of looking at empty buildings, driving over crumbling streets, and seeing visible poverty everywhere. Expectations fall and anger rises among people being asked to pay more for public services that seem to get worse every year. They seem to because they are.
If you're curious about where your favorite city is heading over the next 20 or 30 years, look at the historical trend in population density. If it declines consistently there's a good chance that great things are not on the horizon.