The effects of higher rates might be visible in markets. Higher interest rates tend to eventually lower stock prices — in part because it costs businesses more to operate when money is expensive to borrow, and in part because Fed rate increases have a track record of touching off recessions, which are terrible for stocks. Pricier borrowing costs also tend to weigh on the value of other assets, like houses, as would-be buyers shy away from the market.

The Fed is also preparing to shrink its balance sheet of bond holdings, and many economists expect Fed officials to release a plan to do so as soon as May. That could push up longer-term rates and will probably further pull down stock, bond and house prices.

You might wonder why the Fed would want to slow down the economy and hurt the stock market. The central bank wants a strong economy, but sustainability is the name of the game: A little pain today could mean less pain tomorrow.

The Fed is trying to get inflation down to a level where price increases do not influence people’s spending choices or daily lives. Officials hope that if they can slow the economy enough to reduce inflation, without damaging it so much that it tips into a recession, they can set the stage for a long and steady expansion.

“I think it’s more likely than not that we can achieve what we call a soft landing,” Mr. Powell said during recent testimony before lawmakers.

The Fed has let the economy down easy before: In the early 1990s it raised rates without sending unemployment higher, and it appeared to be in the process of achieving a soft landing before the pandemic struck, having raised rates between 2015 and 2018.

But economists have warned that it could be a tough act to pull off this time around.

“I wouldn’t rule it out,” Donald Kohn, a former Fed vice chair, said of a soft landing. But he said a clampdown on demand that pushed unemployment higher was also possible.

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Live Updates: Russian Strikes Continue With Peace Talks Underway

LVIV, Ukraine — Hundreds of people escaped the besieged Ukrainian city of Mariupol by car on Monday, according to the local government, even as a convoy of vehicles carrying food, water and medicine slowly tried to find a safe path through the battle raging around the city.

Relatives of those still living in Mariupol said fleeing seems to offer the best, and perhaps only, chance for survival.

“I do not believe the humanitarian convoy will be a big help,” said Oleksandr Kryvoshapro, a humanitarian activist whose parents are in Mariupol. “Too many people are still there. And this once beautiful, big and constantly developing city is now completely destroyed. It is not possible to live there anymore. All people need to be evacuated.”

An estimated 400,000 people are trapped in the city, which is entering its second week without heat, food or clean water. Attempts to reach the city and evacuate people have failed day after day amid heavy fighting. The convoy on its way Monday was carrying 100 tons of relief supplies, officials said.

Russia has been laying siege to the city, a major industrial hub on the Azov Sea, creating a humanitarian catastrophe that led the International Committee of the Red Cross to issue an urgent appeal for a cease-fire to assist the hundreds of thousands of people with no access to clean water, food or heat.

“Dead bodies, of civilians and combatants, remain trapped under the rubble or lying in the open where they fell,” the I.C.R.C. said.

The Ukrainian government estimated on Sunday that more than 2,000 people have died — nearly double the estimate from just a day earlier.

The hundreds who managed to get out on Monday morning left the city in 160 cars and their escape was kept secret until they were deemed a safe distance away, according to Ukrainian officials. They were still on the move Monday afternoon, its exact location and route a guarded secret.

The group was expected to reach the city of Zaporizhzhia, where they will be given access to first aid and accommodations. If they do get there, it would offer a glimmer of hope.

With mass graves now being used to bury the dead in Mariupol and international aid groups warning that large numbers of people are on the verge of starvation, it remains exceedingly difficult to get an accurate picture of what was happening there as nearly all communication has been severed.

Mr. Kryvoshapro, the activist, said his contact with people inside lasts a few seconds each day when they “go out into a dangerous location where they can find a signal.”

This morning, he got some positive news.

“My friends were able to bring my parents some bread today,” he said. “So as of 10 a.m., I know they were alive.”

In that way, he said, he was fortunate. “So many people now cannot get in touch with their relatives,” he said.

Halyna Odnoroh, who is from Mariupol but is now in Zaporizhzhia, said she had gotten word from one of the people who escaped on Monday.

“My colleague has a friend who is one of the drivers there, and all he could say is that they keep moving and keep trying,” she said.

The hardest part to comprehend, she added, is that there are so many people struggling to survive. Even if the convoy arrives, hundreds of thousands will still be in urgent need of help.

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Frustrated With Utilities, Some Californians Are Leaving the Grid

The appeal of off-grid homes has grown in part because utilities have become less reliable. As natural disasters linked to climate change have increased, there have been more extended blackouts in California, Texas, Louisiana and other states.

Californians are also upset that electricity rates keep rising and state policymakers have proposed reducing incentives for installing solar panels on homes connected to the grid. Installing off-grid solar and battery systems is expensive, but once the systems are up and running, they typically require modest maintenance and homeowners no longer have an electric bill.

RMI, a research organization formerly known as the Rocky Mountain Institute, has projected that by 2031 most California homeowners will save money by going off the grid as solar and battery costs fall and utility rates increase. That phenomenon will increasingly play out in less sunny regions like the Northeast over the following decades, the group forecasts.

David Hochschild, chairman of the California Energy Commission, a regulatory agency, said the state’s residents tend to be early adopters, noting that even a former governor, Jerry Brown, lives in an off-grid home. But Mr. Hochschild added that he was not convinced that such an approach made sense for most people. “We build 100,000 new homes a year in California, and I would guess 99.99 percent of them are connected to the grid,” he said.

Some energy experts worry that people who are going off the grid could unwittingly hurt efforts to reduce greenhouse gas emissions. That is because the excess electricity that rooftop solar panels produce will no longer reach the grid, where it can replace power from coal or natural gas plants. “We don’t need everybody to cut the cord and go it alone,” said Mark Dyson, senior principal with the carbon-free electricity unit of RMI.

Pepe Cancino moved from Santa Monica to Nevada County in 2020 after he and his wife, Diane, lost their jobs during the pandemic. They bought five acres with spectacular views of snow-capped mountains. Mr. Cancino, 42, a former home health care worker, picked up a chain saw and an ax and began learning how to build a house and generate his own power.

When they finish their two-bedroom, two-and-a-half-bathroom home this fall, the family, including their 15-year-old daughter, will generate electricity and use a well for water.

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Ukraine Live Updates: U.S. to Send More Arms to Kyiv as Russia Flattens Parts of Cities

LVIV, Ukraine — Russian forces stepped up their campaign of bombardments aimed at devastating Ukraine’s cities and towns on Saturday, as the White House announced it was sending an additional $200 million in arms and equipment to help Ukraine, defying Moscow.

Soldiers fought street-by-street battles in a leafy suburb of Kyiv, the nation’s capital, and some residents wept as they dragged belongings across a destroyed bridge, trying to escape the violence. Russian forces detained the mayor of a captured city, an act that prompted hundreds of outraged residents to pour into the streets in protest.

President Volodymyr Zelensky of Ukraine accused Moscow of terrorizing the country in an attempt to break the will of the people. “A war of annihilation,” he called it.

He said an estimated 1,300 Ukrainian soldiers had been killed in the war, the first time the government had offered the number of its own soldiers killed.

Mr. Zelensky denounced what he called the kidnapping of the mayor — who had refused to cooperate with Russian troops after they seized his city — as “a new stage of terror, when they are trying to physically eliminate representatives of the legitimate local Ukrainian authorities.”

Russian forces have not achieved a major military victory since the first days of the invasion more than two weeks ago, and the assaults reinforced Moscow’s strategic turn toward increasingly indiscriminate shelling of civilian targets.

The American announcement of more arms for Ukraine’s military, including missiles for taking out warplanes and tanks, came just hours after Russia warned that convoys used for the “thoughtless transfer” of weapons to Ukraine would be “legitimate targets” for Russian forces.

Unable to mount a quick takeover of the country by air, land and sea, Russian troops have deployed missiles, rockets and bombs to destroy apartment buildings, schools, factories and hospitals, increasing civilian carnage and suffering, and leading more than 2.5 million people to flee the country.

Credit…Lynsey Addario for The New York Times

The suffering has been particularly devastating in the besieged city of Mariupol, which is experiencing “the worst humanitarian catastrophe on the planet,” according to Ukraine’s foreign minister, Dmytro Kuleba.

At least 1,582 civilians have died since the Russian siege of Mariupol began 12 days ago, he said, and residents are struggling to survive and have been forced to bury the dead in mass graves.

“There is no drinking water and any medication for more than one week, maybe even 10 days,” a staff member who works for Doctors Without Borders in Mariupol said in an audio recording released by the organization on Saturday.

“We saw people who died because of lack of medication, and there are a lot of such people inside Mariupol,” the staff member said.

During a 90-minute call with President Vladimir V. Putin of Russia, Chancellor Olaf Scholz of Germany and President Emmanuel Macron of France urged Mr. Putin to accept an immediate cease-fire, according to the French government, which described the talks as “frank” and “difficult.”

France said that Mr. Putin showed no willingness to stop the war, and said he “placed the responsibility for the conflict on Ukraine” and sounded “determined to attain his objectives.”

Credit…Maciek Nabrdalik for The New York Times

In its summary of the call, the Kremlin said Mr. Putin had discussed “several matters relating to agreements being drafted to meet the well-known Russian demands,” but did not specify those demands.

In the coming weeks, NATO, which has vowed to defend allied countries from any incursion by Russian forces, plans to gather 30,000 troops from 25 countries in Europe and North America in Norway to conduct live-fire drills and other cold-weather military exercises.

The exercises, which Norway hosts biannually, were announced more than eight months ago, NATO said, and are not linked to Russia’s invasion of Ukraine, which NATO said it was responding to with “preventive, proportionate and non-escalatory measures.”

But the training has taken on greater significance as Russia steps up its bombardment of Ukrainian population centers.

Around Kyiv, the capital, Russian forces have advanced into the suburbs but have been slowed by Ukrainian troops that have counterattacked with ambushes on armored columns. On Saturday, artillery fire intensified around Kyiv, with a low rumble heard in most parts of the city.

By Saturday, there were no indications of further efforts by the Russian army to move armored columns closer to the capital. Instead, soldiers appeared to be fighting for control of the towns along the highways that encircle it.

In Irpin, about three miles from Kyiv city limits, Ukrainian and Russian soldiers were fighting a street-by-street battle on Saturday, turning what was a quiet suburb just two weeks ago into a suburban battleground.

Credit…Lynsey Addario for The New York Times

“We are trying to push them back but we don’t control the town,” said Vitaly, a Ukrainian soldier who asked that his last name not be published for security reasons.

He had taken up a position outside what would once have been an unlikely spot for combat: a gas station mini-market, its windows blown out by shelling, on the city’s western edge. Irpin is his hometown, and he joined the volunteer forces called the Territorial Defense Forces to try to protect it just two weeks ago.

He described Irpin’s Unity Street as Ukrainian-controlled; Central Street as a no-man’s land, exposed to both Ukrainian and Russian forces; and University Street as taken by Russian forces.

But the situation was fluid. Ukrainian soldiers had a “little island” around a shopping center near the city center, he said, but otherwise it wasn’t always clear who was where.

In the southern city of Mykolaiv, residents awoke on Saturday morning to the sounds of a fierce battle hours after Russian shells hit several civilian areas, damaging a cancer hospital and sending residents fleeing into bomb shelters.

The early-morning fight was concentrated in the north of the city, said Col. Sviatoslav Stetsenko of the Ukrainian Army’s 59th Brigade, who was stationed near the front lines.

“They are changing their tactics,” Vitaliy Kim, the governor of the Mykolaiv region, said. “They are deploying in the villages and lodging in village schools and homes. We cannot shoot back. There are no rules now. We will have to be more brutal with them.”

For nearly two weeks, Russian forces have been trying to surround Mykolaiv and cross the Southern Buh River, which flows through the city and is a natural defense against a Russian push toward the west and Odessa, the Black Sea port that appears to be a prime Russian objective.

Russian forces had not crossed the river as of Saturday morning, Colonel Stetsenko said, but “they are continuing to shell Mykolaiv.”

Credit…Tyler Hicks/The New York Times

In Melitopol, Russian troops on Friday forced a hood over the mayor’s head and dragged him from a government building, according to Ukrainian officials, prompting hundreds of residents to demonstrate in the streets.

“Return the mayor!” the protesters shouted, according to witnesses and videos. “Free the mayor!”

But nearly as soon as the demonstrators gathered, Russian military personnel moved to shut them down, arresting a woman who they said had organized the protest, according to two witnesses and the woman’s Facebook account.

The episode was part of what Ukrainian officials said was an escalating pattern of intimidation and repression. It also illustrated a problem that Russia is likely to face even if it manages to pummel cities and towns into submission: In at least some of the few cities and towns that Russia has managed to seize — mostly in the south and east — they are facing popular unrest and revolt.

Mr. Zelensky sought to tap into public rage in an address to the nation overnight.

Credit…Tyler Hicks/The New York Times

“The whole country saw that Melitopol did not surrender to the invaders,” he said. “Just as Kherson, Berdyansk and other cities where Russian troops managed to enter didn’t.” He said that popular resistance “will not be changed by putting pressure on mayors or kidnapping mayors.”

Melitopol’s mayor, Ivan Fyodorov, had remained stubbornly defiant even after Russian soldiers took over the city after a fierce assault on the first day of the invasion. “We are not cooperating with the Russians in any way,” he had said.

Last weekend, with Mr. Fyodorov’s encouragement, people waving Ukrainian flags took to the streets of Melitopol and other occupied cities. For the most part, Russian soldiers stood aside, even as protesters commandeered a Russian armored vehicle in one town and drove it through the streets.

Credit…Evgeniy Maloletka/Associated Press

While the protests in Melitopol were quickly put down, the Ukrainian government renewed efforts to bring aid to Mariupol, dispatching dozens of buses with food and medicine, Ukrainian officials said.

Similar relief efforts had failed in recent days as fighting raged around the city and land mines pocked roads in the area. In an overnight address, Mr. Zelensky said that the inability to bring aid to the city showed that Russian troops “continue to torture our people, our Mariupol residents.”

Still, he said, “We will try again.”

Marc Santora reported from Lviv, Ukraine, Michael Schwirtz from Mykolaiv, Ukraine, and Michael Levenson from New York. Reporting was contributed by Andrew E. Kramer in Kyiv, Ukraine; Eric Schmitt in Washington; Ivan Nechepurenko in Istanbul; Norimitsu Onishi in Paris; and Julie Turkewitz in Bogotá, Colombia.

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Live Updates: ‘No Water, No Heating, No Gas’ in Besieged Ukraine City as Maternity Hospital Is Hit.

Ukrainian government officials said Wednesday that damage by Russian forces had left the former Chernobyl nuclear power plant “disconnected” from outside electricity, leaving the site of the worst nuclear accident in history dependent on power from diesel generators.

The International Atomic Energy Agency, the United Nations agency on nuclear power, said Wednesday that it saw “no critical impact on safety” at the complex.

The American Nuclear Society, a professional group, agreed. “The loss of power is a serious matter but it does not pose a threat to the public,” it said in a statement.

But officials warned that the situation around the plant, where there was an explosion and fire at one of the reactors in 1986, was still of grave concern.

The plant has not produced electricity since the last of its four reactors was shut down in 2000, but if its generators stopped working, that could affect the operations to store the large quantities of radioactive nuclear waste there.

Since the plant was captured by Russian forces not long after the invasion began last month, the I.A.E.A. has said that there have been interruptions in the feed of data it receives automatically from radiation monitors and other sensors at the plant.

A full loss of power would cut that feed completely, leaving the agency’s experts with little knowledge of what is going on there, except what could be gathered using portable devices. On Tuesday, the I.A.E.A. said it had lost communications with its sensors at the plant.

The most hazardous waste at Chernobyl is found in two locations.

As is common practice in the nuclear power industry, used fuel from all four reactors is stored in pools of water that dissipate the heat produced as the fuel decays radioactively. When fuel is newly removed from a reactor, there is a lot of decay and thus a lot of heat, so plants need power to run pumps that circulate the storage water to remove excess heat.

The I.A.E.A. has said that the used fuel assemblies at Chernobyl — there are more than 20,000 of them — are old enough and decayed enough that circulating pumps are not needed to keep them safe.

“The heat load of the spent fuel storage pool and the volume of cooling water contained in the pool is sufficient to maintain effective heat removal without the need for electrical supply,” the agency said.

The other main source of nuclear waste are the ruins of the destroyed reactor itself. An estimated 200 tons of fuel remain there, in a lava-like mix with molten concrete, sand and chemicals that were dumped on the reactor during the disaster. This mixture is found throughout the remains of the reactor. Some parts of it are completely inaccessible and have only been studied by boring into them.

A functioning reactor requires pumps that circulate water around the core, keeping it cool and moderating the nuclear reaction to avoid a meltdown. There is no cooling water in the chaotic, jumbled remains of the reactor, so the loss of power would not affect them.

But in recent years there have been incidents in which nuclear reactions have started spontaneously in pockets of these fuel-containing materials, leading to spikes in radiation levels. Without monitoring — of humidity in addition to radiation levels — workers would not know if any new incident was occurring.

Since 2017, the destroyed reactor has been covered by a large arched structure, intended to confine the waste and safeguard against any release of radiation. The structure is also meant to allow the work of removing waste to long-term storage.

The facility was only granted an operating license by Ukraine’s authorities last year, so that work had only just begun, and will take decades to complete. There are several large cranes and other specialized equipment to allow crews to work safely. Without power, most if not all of that work could not proceed.

On Wednesday, Russia’s Energy Ministry said that Belarus, whose border is not far from the Chernobyl zone, was working on restoring the power supply of the complex from its own grid.

William J. Broad and Ivan Nechepurenko contributed reporting.

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Live Updates: Biden Bans Russian Oil Imports as Civilian Toll in Ukraine Grows

One million children have fled Ukraine in less than two weeks of war, James Elder, a spokesman for UNICEF, said on Tuesday, calling it “a dark historical first.”

Since the start of the Russian invasion on Feb. 24, two million people have fled Ukraine, according to the U.N. — more than those who left Syria in the first three years of the civil war there.

“We have not seen a refugee crisis of this speed and scale since World War II,” Mr. Elder said. “and this is a children crisis.”

About one in seven Ukrainian children have already left the country. At least 29 have been killed, by bombings or by mortar shells, in the street as they tried to escape, a figure that humanitarian groups say is almost certainly an underestimate. Since the start of the conflict, UNICEF estimates that 4,000 babies have been born in Ukraine “including dozens in makeshift maternity wards and underground shelters,” the agency said in a statement to The New York Times.

“Despite the best efforts of doctors and midwives, they are setting up I.C.U.s or surgeries in basements and bunkers — no way it can be as safe as where a child should be born,” Mr. Elder said.

In some areas, families are living without electricity and water, with children exposed to the cold, disease, hunger and thirst. Families from Mariupol recounted that some children drank water from water heaters, Mr. Elder said.

Catherine M. Russell, the executive director of UNICEF, called the situation of children in Ukraine “a moral outrage,” and said that countless of them were traumatized.

In a bunker near her home in Kharkiv, 5-year-old Eva Zozulia learned how to distinguish the sound of Ukrainian and Russian artillery before she and part of her family fled the city. The first produced only loud “booms” but when the Russians struck, the whole building trembled.

“It was scary,” Eva said in a phone call from the train station in the western city of Lviv, where she had spent the previous night, sleeping in a restaurant with her mother and older brother.

Many of the children fleeing are unaccompanied, according to a U.N. statement. Their parents or family members stayed in Ukraine, or were killed, Mr. Elder said, adding that he had met a mother who was traveling with her three children and three children of her sister, with whom she had lost contact.

About 100,000 children, half of them with disabilities, are living in institutions and boarding schools that are at risk, as schools, orphanages, homes and hospitals had all come under attack, the U.N. said.

Rev. Vyacheslav Grynevych, the executive director of Caritas-Spes, a Ukrainian Latin Catholic charity, said the group took in 200 children with their mothers in a center in the ski resort of Yablunytsia, in Western Ukraine.

Rev. Grynevych said in a phone call from Yablunytsia that while many orphans had left Ukraine, his organization was still trying to coordinate the evacuation of many of them who are still in bomb shelters around the country, sometimes alone.

Children have also shown great resilience, from singing in bomb shelters to undertaking trips alone to join relatives abroad. Vardkes Arzumanyan, a restaurant owner who has been distributing meals at the Lviv train station, said he saw a child tearing the piece of the cardboard he was sitting on, to offer part of it to a stranger.

Most of the Ukrainian refugees in other countries are women and children, because men between the ages of 18 and 60 are not allowed to leave. But to some mothers, their 18-year-old sons are still children.

Eva Zozulia’s brother Kyryll, a high school student, turned 18 on March 1, a day before the family fled Kharkiv.

“He is not prepared,” said Irene Zozulia, Eva and Kyryll’s mother. “The only way in which he could help is go in front of a Russian soldier and say, ‘kill me.’”

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