From the department of unintended consequences come fresh confirmations that changing human behavior is a devilishly tricky business.

It's predictable that people will respond when confronted with altered incentives or tightened restrictions. But the particular way they will respond is harder to predict — except that it often will frustrate the best-laid plans of social policymakers.

Consider three new studies concerning timely issues. First, an essentially good news report from the Pew Research Center says the number of illegal immigrants living in the United States had declined by 2016 to its lowest level in more than a decade — to something under 11 million. (Other noted studies find larger numbers, but the same trends.)

Despite the decline, of course, political tensions over illegal immigration have never been higher. But it's hardly unknown for the reaction to a problem to keep intensifying well after the problem itself has begun to recede. We can hope that if the wave of illegal immigration that swelled the unauthorized population all through the 1990s and 2000s is playing itself out, the political strife it causes will in time wane, as well.

On his "Conversable Economist" blog (which noted all the new studies discussed here), Macalester College economist Timothy Taylor observes that a declining flow of Mexicans into America has been visible for some years. Likely causes, Taylor says, include better economic times and a falling birthrate south of the border, along with the Great Recession and its aftermath in the U.S.

Meanwhile, Pew notes that the U.S. population of unauthorized Central Americans from Honduras, Guatemala, etc. is still increasing — as reflected by the recent "caravan" excitement. But that trend is more than canceled out by the drop in the unauthorized Mexican population.

What's most intriguing is this: While the total unauthorized immigrant population has been modestly falling, a stark transformation has occurred in the nature of these newcomers' residence in America. Basically, illegal immigrants seldom leave anymore.

Back in 2007, Pew reports, fewer than 40 percent of illegal immigrants had been living in America for 10 years or more; by 2016, fully 66 percent were such long-term residents.

Meanwhile, by 2016 fewer than one in five among the unauthorized had been in the country less than five years — half the figure of a decade earlier.

This new permanence among illegal immigrants may confirm an intriguing theory Princeton sociologist Douglas S. Massey described last year in "The Counterproductive Consequences of Border Enforcement," in the Cato Journal.

Massey contended that the primary effect of toughening border security over the years has been, not to prevent illegal entry into the United States, but to discourage those who do enter from ever wanting to go back and face having to make such a crossing again.

Massey showed that before illegal border crossings became more costly, unpleasant and frightening, illegal immigration from Mexico was largely "a circular flow of male workers" who would enjoy higher earnings in America for a year or two, return to Mexico for a time and later come north once again — a kind of do-it-yourself guest worker program. But as the "militarization" of the border advanced from the late 1980s forward, powerful economic incentives still inspired illegal crossings — but once was often enough for even the most intrepid. Illegal immigration started producing "a large and growing population ..." in America to stay.

The new Pew report suggests that even though the forces propelling Mexicans northward may have eased, the roots put down by now are mainly keeping that large unauthorized population in place.

Paid leave for new parents is a social policy gaining enthusiastic support among progressives, who note that America is far behind much of the rich world in providing this kind of aid to new families. But from researchers at Sweden's Upsalla University, in a paper published by the American Economic Association, comes a reminder that even in trailblazing Scandinavia, "deviating from social norms is costly."

It seems that back in 1995, officials in Sweden became concerned that traditional gender roles were persisting among Swedish parents. Both fathers and mothers had for decades been eligible for paid leave but were free to transfer leave between one another. Overwhelmingly, Swedish fathers surrendered their ration of leave to mothers.

Eager to modernize this primitive practice, policymakers altered the rules to create a "daddy month" of leave that only fathers could use. Faced with a use-it-or-lose-it proposition, many more Swedish men took leave.

But economists Arizo Karimi and Daniel Avdic report a few additional results — namely, more divorce and less income.

Apparently, rather than relying on their husbands' new fatherly exertions, many Swedish mothers started taking more unpaid leave to compensate for the transferred paid leave they'd effectively lost, reducing household income.

And something else about the resulting experiences — "more information about their spouses," speculates Karimi — led to an 8 percent increase in the probability of divorce for affected couples.

These researchers hope that the policy reform has had, on balance, a positive effect changing social norms. But Karimi cautions that "there may be trade-off[s] ..."

America's heartbreaking heroin overdose epidemic may be a kind of trade-off, according to a study from researchers at the University of Pennsylvania and the RAND Corp. They report that about a decade ago, as abuse of prescription painkillers reached crisis proportions, pharmaceutical firms responded to policymakers' pressure and reformulated opioid medications to make them harder to misuse. In particular, OxyContin was made less easily crushed and dissolved in 2010, making it less "abusable."

The result, say Abby Alpert, David Powell and Rosalie Liccardo Pacula, was the heroin (and later fentanyl) epidemics that have blazed so destructively in recent years — as users found even more dangerous replacements.

"Our results imply that the recent heroin epidemic is largely due to the reformulation of OxyContin," the scholars write.

Here again, the researchers note that the long-run results of reformulation may prove beneficial, by closing off a gateway into the abuse of opioids.

Still, the message in each of these case studies is that social policy can have potent and unexpected side effects. Caution is always in order.

D.J. Tice is at Doug.Tice@startribune.com.