One problem afflicting the Bay Area and other regions is that a growing percentage of people are “over-housed” or living in homes with unused bedrooms. This is largely because Baby Boomers make up a growing portion of the population and, like generations before them, can’t bear the stress of leaving a home full of memories and stuff.

“They’ll carry me out of here in a box,” is the answer many seniors give when asked about selling, said Justine Francis, an East Bay real estate agent who specializes in senior relocation.

If empty nesters living in three- and four-bedroom homes would downsize or take in tenants, they could get a better return on what is often their biggest asset and perhaps put a dent in the region’s dire housing shortage.

The California Association of Realtors is sponsoring a ballot initiative that, it says, would nudge older homeowners to sell their underutilized homes by vastly expanding the ways they could transfer their existing property tax assessment to a new place. The association said last week it has close to 1 million signatures, more than the 585,407 required to qualify for the November statewide ballot.

In California, your annual property tax bill is based on the assessed value of your home. The tax rate is 1 percent statewide, plus voter-approved local taxes, bringing the average to around 1.1 percent. Under Proposition 13, property is generally assessed at its purchase price when it is sold. In between sales, the assessed value can go up by no more than 2 percent per year, plus the value of additions or major improvements.

As a result, many longtime homeowners are paying a fraction of what they would pay if they sold their house and bought another, even if the new one cost less. Prop. 13, passed by voters in 1978, has helped people on fixed incomes stay in their homes, but it also has discouraged them from selling homes that no longer suit their needs.

To loosen this lock-in effect, two subsequent propositions — 60 and 90 — gave California homeowners 55 and older a once-in-a-lifetime chance to sell their primary residence and transfer their property tax assessment to a replacement home of equal or lesser value. However, the replacement home must be in the same county as the old one, or in one of 11 that accept incoming transfers. Those counties are Alameda, El Dorado, Los Angeles, Orange, Riverside, San Bernardino, San Diego, San Mateo, Santa Clara, Tuolumne, and Ventura, but El Dorado is dropping out after Nov. 7. Homeowners must buy the replacement home within two years of selling the existing one, or vice versa.

Under the proposed Property Tax Fairness Initiative, homeowners 55 and older could transfer their tax assessment to a replacement home in any county an unlimited number of times. They could also transfer it to a more expensive home, although the difference in price between their old and new homes would be added to their existing assessment. For example, if their existing home is assessed at $500,000 and they sell it for $1 million then buy another for $1.2 million, their new assessment would be $700,000.

In another twist, if they bought a less expensive home, their assessed value would be proportionately reduced. Suppose again that the old house had an assessed value of $500,000 and sells for $1 million, but in this case the homeowner purchased a replacement home for $800,000. Because the assessed value of the old house was one-half its market value, the replacement home would be assessed at one-half its value, or $400,000. In this case the homeowner’s assessed value would drop by $100,000. Under current law, it would remain at $500,000.

“Right now there is no incentive to buy down,” said Alex Creel, the association’s lobbyist. By creating a tax incentive to downsize, “we think there will be an incentive for builders to build new housing to accommodate this new demand.”

Leigh Anne Varney, 57, lives in a three-bedroom, 3,100-square-foot home in San Francisco’s Outer Richmond District. Since her two daughters and ex-husband moved out, it’s just her, two dogs and two cats. Making better use of her biggest asset “is something I think about literally every day in some fashion,” she said.

Varney has considered renting rooms on Airbnb, but as a single woman is concerned about having strangers in the house. She has thought about renting to students through a foreign-exchange program, like some friends have done. But she is leery of having a full-time renter, “unless it’s a connection with someone in my network.”

Another idea is selling her home and buying a smaller place in Sonoma County or Mendocino County, but neither accepts property tax assessments from other counties.

Her home is assessed at roughly $700,000 and worth at least $2.1 million. Under current law, she could buy a home in the counties of Sonoma or Mendocino for $700,000 or less without a tax increase because the new home would be assessed at its purchase price. But if she paid more, her taxes would go up.

The initiative would give her more options. Assuming she sold her home for $2.1 million, she could buy one in Sonoma or Mendocino for up to $2.1 million without a tax increase. If she bought one for $600,000, her assessed value would drop to $200,000. That’s because her current home is assessed at one-third its market value, so the new one would be assessed at one-third of $600,000.

The idea “definitely gives me something to ponder,” Varney says. “If I just think about selfish me, I would consider it.” But “property taxes do play into a city’s infrastructure. I think it might be a negative impact for a community.”

The Legislative Analyst’s Office said the initiative could increase the annual number of home sales statewide by “as much as tens of thousands per year” but result in a net loss of property taxes. The office estimated that in the first few years, California schools would lose about $150 million annually, as would local governments (cities, counties and special districts). Over time, these losses would probably reach $1 billion to a few billion dollars per year, split between schools and local governments. It added that most school losses would be offset by increased state funding.

“The impact on state and local funding would just be extraordinary,” said Carroll Wills, a spokesman for California Professional Firefighters. “The revenue losses would impact firefighters, police officers. We are already facing kind of a crossroad in our state with the disaster risk continuing to go up.”

David Garcia, policy director for the Terner Center for Housing Innovation at UC Berkeley, said the initiative “could be part of a solution” to the empty-room phenomenon. In 1970, the average four-bedroom, owner-occupied home had an average of 4.5 occupants; in 2014, it had only 3.2 people. Over the same period, the percentage of homes with empty rooms grew from one-quarter to 60 percent, a Terner report said.

Making it easier for homeowners to create additional dwelling units on their property would be another solution, Garcia said. Meanwhile, some nonprofit groups and for-profit companies, such as Nesterly and Silvernest are trying to match empty nesters with seniors or Millennials who need rooms.

The property tax initiative could encourage some seniors to downsize, but “I don’t know if this is going to be the make-or-break policy for a significant number of households,” Garcia said.

The main reason older homeowners are afraid to sell “is that they won’t be able to find a replacement property,” because of the inventory shortage, Francis said.

Kathy Kottom, 68, lives in a four-bedroom, 2,000-square-foot townhome in Alameda with her 21-year-old granddaughter. “This is just too big even for the two of us. It’s too much to take care of and maintain,” she said. Kottom would like to see her home be put to better use. “It’s a great family size — that’s what moved in next door.” Another unit in the complex is rented to eight college students.

But Kottom would like to stay in Alameda and can’t find any two-bedroom condos that match the quality and environment of her current place. She has considered moving to Rossmoor, an over-55 community in Walnut Creek, but her granddaughter couldn’t live there unless she was declared Kottom’s caregiver.

“Many people in their 80s, 90s just plain don’t want to move. They will give their adult children, families, Realtor any excuse,” said Millie Anderson, a real estate agent and senior relocation specialist in Marin.

Taxes, including capital gains tax on a highly appreciated house, are just one excuse. The underlying problem is that “they have a houseful of stuff. The thought of getting rid of that, making all those decisions, is overwhelming,” Anderson said.

While some adult children encourage their over-housed parents to move into something more manageable, others discourage them because they see the house as an inheritance or source of funds if the parent needs to enter a nursing home, Francis said.

Many seniors focus on the financial and emotional cost of moving without calculating what they would save over 10 or 15 years in decreased utility, maintenance and other expenses, said Jim Firman, chief executive officer of the National Council on Aging. “We think it’s a blind spot,” he said. “Their largest asset is not being optimized.”

If the Realtors’ initiative qualifies for the ballot and passes with a simple majority, it will take effect Jan. 1. Homeowners who qualify for the transfer and either sell their home or buy a replacement this year would have two years to complete the other side of the transaction, the association said.

Varney said the initiative could be to her generation what property tax law Prop. 13 was to the previous one. “When Prop. 13 passed, it was like, ‘Hallelujah, I can stay in my house,’” she said. “If this passed, it would be like, ‘Hallelujah, I can move.’”