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Buy shares of Carter’s, a children’s clothing chain, reiterated analysts at Bank of America Merrill Lynch this past week. The reasons were straightforward, except for one.

Solid July sales and favorable Labor Day weather bode well for third-quarter results later this month. Fine. The bankruptcy of Gymboree puts market share up for grabs. Makes sense. Millennials could drive a baby boom.

Um, what?

I’ve had an Accumulate recommendation on offspring for years, but the group is out of favor. U.S. births fell to a 32-year low last year. A millennial baby bust, some called it. Theories abound to explain it. Child-rearing is expensive. Career opportunities for women have improved. Student loans are a drain. House prices are high.

Given the combination of falling fertility, widespread weight gain, and a recent pickup in fresh-produce demand, I’m not ruling out the possibility that we’re gradually becoming pandas.

Change is afoot, however. BofA points out that births have declined in nine out of the past 10 years, at an average rate of 1.1%, but that this has been led by a 7.6% yearly plunge in teenage births—a good thing, surely. Among women ages 35 to 39, meanwhile, births have increased by a modest 0.9% a year. In other words, couples are waiting to have kids, but they haven’t quite forgotten how.

We’re talking now about millennials, born from 1981 to 1994—or, using a Harrison Ford–based calendar, from Raiders of the Lost Ark to Clear and Present Danger. The oldest among them are about 38. As a generation, millennials slightly outnumber baby boomers, which means that the 30-something population will grow nicely in the years ahead.

America hasn’t quite hit bottom in the production of new American bottoms, but things are looking up. Last year, the decline in births slowed to 1.7% from 2.3% the year before. Euromonitor, a research group, predicts it will continue slowing from here, to just a 0.2% decline by 2021. An alternate measure of fertility, the number of children ever born to women now ages 40 to 44, has been rising in recent years.

We could even get an upside surprise in baby-making. Back in 2014, births increased 1.4%, an outlier in the data that hasn’t yet been explained. Recall that 2013 was the year that Netflix (ticker: NFLX) came into its own with home streaming. Well, Walt Disney (DIS) and Apple (AAPL) launch streaming services next month. All that couch time could drive a year-over-year expansion in funny business. That’s just science.

Either way, one byproduct of older parenting is higher disposable income to spend on children. That’s good news indeed for the likes of Carter’s (CRI). Mall-based store shares make me nervous, but earnings per share for this one are seen growing 5% to 8% a year over the next several years, and BofA sees 21% upside for investors. Shares trade at 14 times this year’s earnings forecast.

Other kids’ chains include Children’s Place (PLCE) and the buybuy Baby unit of Bed Bath & Beyond (BBBY). Bed Bath is struggling, but Wedbush Securities analyst Seth Basham upgraded the stock to Outperform from Neutral at the end of September. He predicted that the company would soon name a capable new CEO and argued that, with the stock then under $10, noncore assets are worth more than $13 a share, including $5.62 for buybuy Baby. This past week, the company announced the new chief: Target merchandising maven Mark Tritton. Shares rose 29% for the week.

There are more important things at stake in fertility than stock-picking. The number of workers per Social Security recipient has fallen to 2.8 last year from five in 1960. Population gains help drive economic growth. Immigration can make up for falling births, but last year, that hit its slowest pace in the U.S. since 2008. Want an explanation for meager bond yields in the U.S., and negative ones in Japan and Europe? You could do worse than citing the low fertility rate here, and even lower ones there.

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So make use of what momentum the U.S. enjoys. Let’s start pressing millennials to have more kids. Don’t be afraid to tap strangers on the shoulder on line at Chipotle. Also, Congress should expand the Federal Reserve’s mandate to include spicing up national romance. Don’t laugh: Chairman Jerome Powell is one of six kids, and he has three of his own. That guy knows a thing or two about getting the economy going.

Want shelter from falling earnings estimates next year? Reach for real estate investment trusts, say analysts at J.P. Morgan. Last year at this time, earnings growth for the S&P 500 index was pegged at 11%, they point out. Now, 3% looks more likely. But for REITs, which hold property and pass the income to shareholders as dividends, the forecast started at 4% and has stuck there.

The setup now is identical—11% growth forecast for the index and 4% for REITs. Only the REIT forecast is believable. Health care and tech REITs look better than office and retail ones, says JPM, which has some favorites. Welltower (WELL) focuses on senior housing and outpatient medical services and yields 3.8%. Equinix (EQIX) is a data-center giant favored for its growth more than its income. It pays 1.7%. The analysts recently upgraded HCP (HCP), a diversified health-care player, to Overweight from Equal Weight. It pays 4.1%.

As a group, REITs are fully priced relative to funds from operations, a measure of profitability. But falling interest rates flatter the dividend payments, and make capital for expansion cheap.

Write to Jack Hough at jack.hough@barrons.com