Homeownership does tend to be a local issue, Fleming said. "While the national homeownership rate declined modestly in 2016, homeownership rates varied significantly at the market level. Small changes in potential homeownership demand hide the large amount of variation in markets across the country. The underlying factors that the Homeownership Progress Index accounts for can vary substantially by region of the country and market. Regions or markets with stronger local economies that can attract increasingly educated millennial households will have stronger homeownership demand in the future."

In addition, he said, half of the top-10 markets for year-over-year growth in potential homeownership demand are in either California or Texas, while eight of the bottom 10 markets are on the East Coast or in the Midwest.

Fleming discussed the next generation following the millennials and what their tendency to own homes might be.

We know millennials are predicted to increase their homeownership rate as they age, but what about the generation behind them?

Fleming: Homeownership begets homeownership. One of the strongest indications of likely homeownership is if others in the family, particularly parents, are homeowners. Given Generation X has a high homeownership rate and Generation Y is expected to as well, I would expect nothing different from the youngest generation.

In which markets are millennials preferring to buy homes now?

Fleming: Demand is where the jobs are. Big cities on the coasts, but also some more affordable cities, like Charlotte, N.C., are popular for their higher degree of affordability.

What size, type and characteristics of homes are they seeking?

Fleming: Small is more affordable – not the McMansion. Smaller and older homes tend to be more affordable. As with generations past, the first home for many is not the dream home, but a start nonetheless.

What else should our readers know about future homeownership demand?

Fleming: The housing crisis could have tarnished the dream of homeownership in America, but instead homeownership remains a strong beacon for Americans and enduring symbol of success.

Single-Family Vs. Multifamily Home Demand

We often hear about the push and pull relationship between single-family and multifamily home activity that has hit pre-recession highs, interest ebbing or flowing from one to the other as consumers opt either for affordability and proximity to work or for the traditional American dream of lawns and picket fences. However, according to the Institutional Property Advisors August Research Brief, current market dynamics indicate a robust demand for both.

In fact, Jeffery Daniels, SVP and national director of Institutional Property Advisors' multifamily division, noted that single-family sales activity is at the highest level since the Great Recession, fueling the ongoing trend of potential buyers closed out of that market and turning to multifamily.

"As household formation strengthens and for-sale inventory remains limited, a large share of housing demand is filtering into apartments," he said.

In fact, the Brief reported a home price increase of 5.8% year-over-year, clear evidence of the demand. "The increase pushed the median to a record high, largely driven by strong buyer competition and limited inventory across the country," it said.

Meanwhile, "In the second quarter, apartment developers completed more than 86,400 units, a 30-year record, but absorption also reached a new peak as over 175,600 rentals were filled."

The ever-rising price of single-family homes as well as the competition is expected to continue to have an upward impact on the multifamily outlook, Daniels said.

Those prices and that competition "for existing single-family homes, as well as a lack of entry-level home construction, will continue to restrict first-time home buyers. As a result, current renters and newly forming households will both favor apartment living and sustain rental housing demand," he noted.

But, also playing into this dynamic is the expectation that Fannie Mae will raise the debt-to-income ratio (from 45% to 50%) which would ease lending criteria, good news for "first-time homebuyers and millennials riddled with student loan debt," he said. Obviously, the specific impact of this shift on purchasing remains to be seen.