Many economists worry that as more people get stuck renting, or borrow more than they can afford, it could contribute to greater inequality in major cities that could take years to unwind and add to political polarization.

It could also lead to more pushback from first-home buyers and affordable housing advocates that forces governments to take more aggressive action. In Berlin, voters on Sunday backed a nonbinding referendum to nationalize large real estate groups with more than 3,000 apartments.

But many policy makers are wary of doing too much to control prices, for fear of harming existing owners who benefit from higher values. They also don’t want to undermine an economic recovery that is being driven in part by confidence among owners of homes and other assets.

Price increases have been a boon for many families. Rising home values typically spur more spending on furniture and other goods, benefiting the economy at large.

Recent events in China are a reminder of how tricky it can be to try to tame the market. Chinese leaders, worried that rising housing costs could trigger unrest and add risks to the financial system, have moved to curtail price increases and rein in borrowing.

Now,

China Evergrande Group,

a leading developer, is on the brink of collapse, and home sales are weakening, triggering fears of wider economic damage.

The affordability problem, however, isn’t going away in many economies. A combination of low interest rates, pandemic-era stimulus and changes in buying patterns as people work remotely are pushing prices higher.

That has prompted buyers’ complaints across North America, Europe and parts of Asia. Australian lawmakers recently opened an inquiry into housing affordability.

“It really shouldn’t be this hard,” said Herlander Pinto, a 32-year-old software engineer, who recently bought a house with his partner in a Toronto suburb farther from the city than they wanted. “We just had to hope that somebody with deep pockets didn’t come along and put in an outrageous bid.”

In Canada, New Zealand and Norway, the home price-to-income ratio—a measure of affordability that is house prices divided by disposable income—is at its highest level ever, according to data from the Organization for Economic Cooperation and Development. Elsewhere, including the U.S. and France, price-to-income ratios are climbing.

“In Auckland, anyone who’s owned a house for the last seven or eight years is now a millionaire,” said Ben Hickey, chief executive at mortgage broker HomeBoost Mortgages NZ, referring to New Zealand’s biggest city. “Then you’ve got the other half of Auckland who don’t own a house and are really wondering what they’re going to do.”

There are few worries about a 2008-style housing crash. Lending standards have tightened since then and many households have increased their savings during the pandemic.

Still, studies have shown that homeownership is key to building wealth. Affordability issues could hurt some families to move farther from work and impact educational opportunities for their children.

“We were worried about the affordability situation for many households before the last wave of house price increases, and this wave is really enormous,” said Boris Cournède, a senior economist at the OECD. “All the problems that were there before have essentially become more exacerbated.”

In the U.S., the Biden administration is working to boost new-home construction. Canada’s government pledged to spend billions of dollars to build 100,000 new homes for urban middle-class families. Netherlands cities will soon be able to designate neighborhoods where investors are no longer allowed to buy and rent out cheaper homes.

Other approaches include so-called macroprudential tools, like limiting the value of mortgage loans to more targeted measures such as financial assistance for first-time home buyers. Some countries have tried to make it harder for investors to buy multiple properties or limit the influence of foreign buyers.

But many policy makers say such tools, which can be costly, do little to hold back prices amid a tide of easy money. Some programs to boost homeownership can encourage buyers to take unnecessary risks that could harm them later, especially if home prices fall.

Other efforts, like changing land-use regulations to build higher-density housing in desirable neighborhoods, can be politically contentious given that homeowners often oppose developments that could lower their home values.

Some economists think it is best to leave the market alone, and that prices will level out. There are signs this may be happening in the U.S., where existing-home sales posted a 2% decline in August from July, in part because high prices are squeezing out some buyers.

Still, prices aren’t expected to fall significantly. Interest-rate increases over the next year could make mortgages more expensive.

The debate is especially fraught with central banks, whose decisions to keep interest rates low during the pandemic helped fuel the global boom. Many central banks want to avoid using interest rate policy to address housing costs. Doing so could slow economic growth and lead to fewer jobs and weaker wage gains.

Australia’s central bank, for example, has resisted raising rates despite surging home prices.

“Central banks’ primary objective should be the integrity of money and controlling inflation, and the more goals you give them, the greater the likelihood they get distracted from the central one,” said Neil Shearing, group chief economist at Capital Economics.

But when South Korea lifted its benchmark interest rate recently, policy makers said they were worried about property prices. New Zealand’s government earlier this year directed its central bank to consider housing prices in monetary-policy decisions.

Norway’s central bank increased its benchmark interest rate on Sept. 23 to 0.25%, and signaled more rate increases to come, saying the actions would counter financial imbalances by curbing house price inflation and credit growth.

Central bank

Gov. Oystein Olsen

said in an interview he had been surprised by the rate of house price growth during the pandemic, even though interest-rate cuts were expected to spur asset prices, and wanted to lean against rising household indebtedness.

Klaas Knot,

who sits on the European Central Bank’s rate-setting committee as governor of the Dutch central bank, says higher home prices are creating major problems, particularly among younger generations, and potentially leading to more intergenerational wealth inequality.

“This is a serious side effect of our policy and it should be taken into account when assessing the proportionality of our actions,” he said.

Annualized price gains in the Netherlands are likely to peak at around 15% later this year, according to Oxford Economics. In Amsterdam, real-estate broker Jerry Wijnen said agents are receiving up to 10 offers per property.

Canada’s prices rose over 21% from a year ago, according to August data from the Canadian Real Estate Association. Polling showed housing affordability was a top voter concern in the recent election, which returned Prime Minister

Justin Trudeau’s

Liberals to power, though without a majority.

In Adelaide, Australia’s fifth-biggest city, 47-year-old Jo Alldis, who works in disability services for a government agency, and her partner searched for a house earlier this year. She says they probably could have bought something earlier, but waited to save more for their deposit.

Then prices started soaring. Looking to spend up to $360,000, Ms. Alldis and her partner put in offers on five properties but were outbid, with as many as 100 people at some open houses.

Now, Ms. Alldis plans to wait a year before resuming the search, hoping prices fall. She and her partner moved to a new rental property that is more expensive because rents have increased.

“The heartbreaking thing is, we were ready to go and that is when things just shifted,” she said. “We’re both on fairly good incomes, but even still, trying to get a decent house now is really out of the question for us.”

—Paul Vieira in Ottawa contributed to this article.

Write to Mike Cherney at mike.cherney@wsj.com and Tom Fairless at tom.fairless@wsj.com