As you’ve surely heard—and perhaps experienced firsthand—American jobs aren’t what they used to be. Corporations long ago stopped being a source of secure employment. Workers have responded by jumping from job to job and reinventing their careers. Loyalty is out the window. Before long the very idea of a “job” itself may be history, too, with fleeting gigs as independent free agents, or maybe just robots, taking its place.

At least, that’s the frequently told story. So why is it that so much of the data seems to contradict it? To wit:

The median number of years that wage and salary workers in the U.S. have been with their current employer was 4.2 when the Bureau of Labor Statistics last checked in January 2016. That’s higher than at any time in the 1980s or ’90s.

The percentage of Americans switching employers or shifting in and out of the workforce has been declining since the 1980s, economists at the Federal Reserve Board and University of Notre Dame documented last year.

Moves across state lines, which are often made by people searching for new job opportunities, have become much less common.Only 1.5 percent of Americans made such moves from early 2015 to early 2016, reports the U.S. Census Bureau, down from 3.6 percent from 1969 to 1970. Moves across county lines within the same state have also declined.

Self-employment has fallen slightly as a percentage of overall employment over the past decade, according to the BLS, and is far below the levels of the 1950s.

Some of these results become less surprising when you dig into the demographic details. For example, men aged 45 through 54 saw their median job tenure drop from 12.8 years in 1983 to 8.4 years in 2016, which fits the standard narrative of declining job security. A 2013 study by sociologists Matissa Hollister and Kristin Smith found that most of the rise in median tenure from 1983 to 2008 was a result of women becoming less likely to leave their jobs when they had kids.

Still, over the past decade even middle-aged men have seen median job tenure rise. And in general, since the early 2000s the statistical evidence of reduced job-market dynamism has become more pronounced and harder to explain away with demographics.

Another possibility is mismeasurement. Perhaps the government’s standard jobs questionnaires are too moored in an old model of work to capture the changes going on. Even as self-employment as measured by BLS surveys has declined, for example, the Internal Revenue Service has seen big increases in the number of 1099-MISC forms reporting nonemployee income. The Census Bureau’s count of what it calls “nonemployer businesses” (also based on tax data) rose almost 60 percent from 1997 to 2015. And a study released last year by economists Lawrence Katz and Alan Krueger found that those in “alternative work arrangements” such as independent contracting and on-call jobs had jumped to 15.8 percent of the workforce in 2015, from 10.1 percent in 2005.

These developments may well point to a very different job-market future. But when I asked Krueger whether there was a contradiction between his findings and the broad evidence of declining job turnover, he wrote back that “alternative jobs are still only 15 percent of the workforce, and some last a long time (e.g., being an independent contractor or contract employee). They are not necessarily less permanent.”

So that leaves us … pretty much back where we started. “It just doesn’t seem to square with people’s perceptions that job turnover would be declining,” says Notre Dame economist Abigail Wozniak, who co-authored the job-switching study cited above and has conducted related research. One partial explanation, she says, is a sharp drop since the late 1990s in the number of jobs lasting only a few months. This has driven job turnover down and median tenure up, but it doesn’t mean a lot to long-term jobholders. “People feel uncertain because they know that these longer-term jobs are less stable,” Wozniak says. Short-duration jobs becoming less common just isn’t “an experience that’s as salient.”

The decline in short-duration jobs seems to be part of a general trend of decreasing economic dynamism in the U.S. since about 2000. Startups have become rarer, turnover in the ranks of the Fortune 500 and S&P 500 is down, and more industries have come to be dominated by just a few companies. For all the talk of disruption, the past decade and a half has actually been great for incumbent businesses, which would seem to be compatible with reduced job turnover. Public perception may still be lagging this new reality.

Then again, the public perception that jobs aren’t what they used to be is backed up by ample evidence that workers have lost ground since the late 1970s. Real wages (after inflation) have risen only modestly since then (they’ve fallen for men), and labor’s share of gross domestic product has dropped while corporations’ share has soared. Company pension plans have given way to 401(k)s, which don’t guarantee steady retirement income. Maybe the rational reaction to this reduced status and increased risk is to hold on to your job as long as you can.

“People actually shifted jobs a lot in the 1950s,” says Rick Wartzman, author of the new history . “It wasn’t uncommon for a male worker to have 10 to 15 jobs over a career. What’s different is that’s what the worker chose. They moved in search of opportunity.”

This may have begun to happen again as the job market has strengthened over the past few years. That 4.2-year median job tenure in 2016 was actually down from 4.6 years in 2014 (it’s measured every other year). It was the first such drop since 2000—and an indication that job hopping can be a consequence of prosperity rather than insecurity.

    BOTTOM LINE – Statistics say the labor force is more stable now than in the past. But workers have good reasons to be concerned about their prospects.

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