When it was reported in 2017 that the tech billionaire Peter Thiel had bought a 477-acre farm in New Zealand two years earlier for around $10 million under his New Zealand-registered company, Second Star, the deal rankled locals and politicians alike. Many wondered whether Mr. Thiel, a German-born naturalized American, had received special treatment so he could avoid the Overseas Investment Act of 2005, which required foreign buyers to seek official permission to buy “sensitive land” in New Zealand.

As it turned out, Mr. Thiel had quietly obtained New Zealand citizenship in 2011, spurring widespread belief that he had not fulfilled the necessary prerequisites for naturalization. The controversy made him the face of a growing worry in the country: that wealthy foreign investors were inflating home prices and pushing native, first-time buyers out of the market.

According to the Real Estate Institute of New Zealand, housing prices there rose by nearly 65 percent between December 2008 and December 2018, with the median home price in the country’s largest city, Auckland, almost doubling in that period. At the beginning of 2017, Statistics NZ, New Zealand’s official data agency, reported that just 63.2 percent of New Zealanders lived in their own homes — the lowest rate since 1951.

So last August, prime minister Jacinda Ardern, made good on her Labour Party campaign promise to amend the Overseas Investment Act by designating all existing residential land “sensitive” — effectively banning foreigners from buying any existing homes in the country.

New Zealand became the latest in a wave of governments placing restrictions on foreign investors, joining countries like Denmark and Switzerland, which have long restricted real estate investment by noncitizens.

Other countries taking similar measures in recent years include Australia, which four years ago began requiring nonresidents to not only receive purchase approval from its Foreign Investment Review Board, but also to use the existing homes they bought as their primary residences, in an effort to soften prices for domestic buyers as foreign money flooded the market.

In 2017, the Canadian province of Ontario instituted a 15 percent nonresident speculation tax on home purchases. Last year, Singapore and another Canadian province, British Columbia, increased their already hefty taxes on foreign real estate investment to 20 percent. Britain is considering adding a 1 percent tax on home purchases made by nonresidents, on top of its 3 percent tax on second-home and rental property purchases, and Malaysia is also eyeing new levies.

Restrictions like these have led to slower growth in many of the areas that have adopted them. After years of big gains, some investors have seen profit margins shrink. According to the annual Prime Cities Index produced by the London-based real estate agency Knight Frank, which tracks the movement of home prices across 43 cities worldwide, prices are rising at the slowest rate since 2012.

The “proliferation of property market regulations” is one of the biggest risks to prime real estate markets globally, the report concluded.

In New Zealand, the new law, known as the Overseas Investment Amendment Act 2018, has met with a mixed response. Some, like David Parker, the country’s trade and export growth minister, see it as essential. Last August, Mr. Parker described it to Parliament as “a key part of the Government’s plan to improve housing affordability.” Others have scoffed at its restrictions on the free market and its air of xenophobia, claiming it is an effort to deter Chinese buyers, among the most active investors in New Zealand, from living there.

At the center of the debate is how much, if at all, the new law will succeed in bringing prices down and homeownership up.

Bindi Norwell, the chief executive of the Real Estate Institute, said that across the country, the growth in demand for housing from locals as well as foreigners is largely responsible for driving up prices. Tourism has increased the number of people moving to New Zealand, while a stable economy has discouraged natives from seeking opportunities elsewhere.

“You’ve got more people wanting to move here, less people leaving, and so we’ve had a very strong migration over the last few years,” Ms. Norwell said. “That’s put huge pressure on the market. On the flip side, it’s really expensive for land, it’s expensive for construction, and that really limits the ability to develop a lot of houses and meet that demand.”

As for the influence of foreign investors, Pene Milne, a sales associate at New Zealand Sotheby’s International Realty, said the data have been overstated. “The perception to the reality is a little incongruous,” Ms. Milne said. “The perception is that prices are forced up by nonresident buyers, but in reality, they only make up about 3 percent of the market.”

Supporters of the law argue that the percentage doesn’t include properties bought through a trust or a corporation, and that the rate is higher in popular areas like central Auckland. But Ms. Milne said that because many overseas buyers are seeking high-end properties, the luxury market is more affected than the midlevel market, which is suffering from a shortage of homes.

There are also several ways for foreign investors to get around the ban, said Shamubeel Eaqub, an economist at Sense Partners, a consultancy in Auckland. Because of pre-existing trade agreements, Australians, who make up the largest portion of foreign buyers in New Zealand, are exempt, as are citizens of Singapore. And the law doesn’t apply to new homes.

In the four months since it was enacted, Mr. Eaqub said, “essentially what we’ve seen is the share of house sales going to foreigners and corporations has fallen a little bit, by 1 or 2 percentage points. I don’t think that will change, because fundamentally the policy can be worked around.”

He regards the law as a political move. “This is part and parcel of that nativist pitch that we’ve seen around the world,” he said. “There’s this sort of general distrust of foreigners and outsiders and, from the political perspective, I think this gives them some credit. But in terms of whether it actually has an effect, it doesn’t look like it.”

The ban has affected the number of sales, at least in the short term, Ms. Norwell said, noting that December saw a 12.9 percent drop in sales volume, making it the least active December in seven years. January was more on par with the past, with sales of residential properties down just 2.5 percent year-over-year, according to data from the Real Estate Institute.

The summer months are typically slow in New Zealand, Ms. Norwell said, so it is too early to see any real effects of the law: “We really need another quarter’s data. But prices have continued to increase, particularly driven by the regional growth across New Zealand.”

The high housing prices and limited supply in Auckland have driven New Zealanders into more affordable areas, she said, and demand is now pushing up prices in those areas. In Auckland, home to about 1.6 million people, the median price fell 2.4 percent in January 2019, to $800,000, the lowest median price since February 2016. Elsewhere, prices increased by 10.1 percent, to a median price of $473,300.

The lack of inventory remains one of the biggest issues facing the New Zealand housing market. In 2018, about 33,000 permits for new homes or apartments were approved, up from the typical number of about 20,000, Mr. Eaqub said. The country would have to keep up that level of building for some time to catch up to its growing population, he added, but that isn’t likely, mostly because of increased construction costs and lower profit margins — unless the government steps in with some creative solutions.

“They spent a lot of time and effort on banning foreign buyers, but it was never really well established how big a problem they were, and whether by bringing in the policy there would be a substantial effect on reducing house prices and making it more affordable for New Zealanders,” Mr. Eaqub said. “From what we have seen to date, there hasn’t been much of an impact.”