The Republican presidential candidate has made inaccurate or misleading claims about abortion, trans youth, foreign policy and domestic issues.Nikki Haley, the former governor of South Carolina, was the first prominent candidate to announce a challenge to former President Donald J. Trump’s bid for the Republican presidential nomination.Since entering the race in February, Ms. Haley has weighed in on social issues and tapped into her experience as a former United Nations ambassador under Mr. Trump to criticize current U.S. foreign policy.Here’s a fact check of her recent remarks on the campaign trial.Sex and gender issuesWhat Ms. Haley SAID“Roe v. Wade came in and threw out 46 state laws and suddenly said abortion any time, anywhere, for any reason.”— in a CNN town hall in JuneThis is exaggerated. Ms. Haley is overstating the scope of the landmark ruling Roe v. Wade, which established a constitutional right to abortion. The 1973 decision also ensured that states could not bar abortions before fetal viability, or when a fetus cannot survive outside the womb. That is not the same as “any time,” as Ms. Haley said. That moment was around 28 weeks after conception at the time of the decision and now, because of advances in medicine, stands at around 23 or 24 weeks.Before the Supreme Court overturned Roe in June 2022, most states had laws banning the procedure at some point, with 22 banning abortions between 13 and 24 weeks and 20 states barring abortion at viability. A spokesman for Ms. Haley noted that six states and Washington, D.C., had no restrictions when Roe was overturned.What Ms. Haley SAID“How are we supposed to get our girls used to the fact that biological boys are in their locker rooms? And then we wonder why a third of our teenage girls seriously contemplated suicide last year.”— in the CNN town hallThis lacks evidence. In February, the Centers for Disease Control and Prevention reported record levels of sadness and suicidal ideation among teen girls. And depression among teenagers, particularly girls, has been increasing for over a decade. The causes are debated, but experts said no research points to the presence of trans youth athletes in locker rooms, or increased awareness of L.G.B.T.Q. issues in general, as a causal or even contributing factor.“I can say unequivocally that there is absolutely no research evidence to support that statement,” said Dr. Kimberly Hoagwood, a child psychologist and professor at New York University. “The reasons for the increased prevalence of depression and suicide among teenage girls are complex, but have been researched extensively.”Dr. David Brent, a professor of psychiatry at the University of Pittsburgh, noted that teen depression rates have been increasing since the 2000s while widespread discussion and awareness of gender issues are a more recent development.“It could be stressful for some people, for the trans kids as well,” he said. “But to try to say that this is the cause, well, it just can’t be because this is a public health crisis has been going on for 15 years.”Possible factors in rising rates of teen depression include economic stress, the rise of social media, lower age of puberty, increased rates of opioid use and depression among adult caretakers, Dr. Brent said. There is also the general decrease in play and peer-related time, decreases in social skills, and other social problems, Dr. Elizabeth Englander, a child psychologist and professor at Bridgewater State University, wrote in an email. L.G.B.T.Q. youth also have a higher risk for mental health issues, according to the C.D.C.“Even if someone has found an association between being around trans or L.G.B.T.Q. youth and increased depression in heterosexual youth (which, to my knowledge, no one has), it seems incredibly unlikely that such contact is an important cause of the current crisis in mental health that we see in youth,” Dr. Englander added, calling Ms. Haley’s theory “outrageous.”Ms. Haley has weighed in issues of identity and abortion and tapped into her experience as former United Nations ambassador.John Tully for The New York TimesForeign policyWhat Ms. Haley SAID“If we want to really fix the environment, then let’s start having serious conversations with India and China. They are our polluters. They’re the ones that are causing the problem.”— in the CNN town hallThis needs context. Ms. Haley has a point that China is the top emitter of greenhouse gasses and India is the third-largest emitter, according to the latest data from the European Commission. But the United States is the second-largest emitting country.Moreover, India and China are the most populous countries in the world and release less emissions per capita than many wealthier nations. In 2021, China emitted 8.7 metric tons of carbon dioxide per capita and India 1.9 metric tons, compared to the 14.24 metric tons of the United States.Ms. Haley’s spokesman noted that emissions from China and India have increased in recent years, compared with the United States’ downward trend, and are the top two producers of coal.Still, the two developing countries bear less historical responsibility than wealthier nations. The United States is responsible for about 24.6 percent of historical emissions, China 13.9 percent and India 3.2 percent.What Ms. Haley SAID“Last year, we gave over $50 billion in foreign aid. Do you know who we gave it to? We gave it to Pakistan that harbored terrorists that try to kill our soldiers. We gave it to Iraq that has Iranian influence, that says ‘death to America.’ We gave it to Zimbabwe that’s the most anti-American African country out there. We gave it to Belarus who’s holding hands with Russia as they invade Ukraine. We gave money to communist Cuba, who we named a state sponsor of terrorism. And yes, the most unthinkable, we give money to China.”— in a June fund-raiser in IowaThis is misleading. In the 2022 fiscal year, which ended in September, the United States gave out $50 billion in foreign aid. But the six countries Ms. Haley singled out received about $835 million total in aid or 1.7 percent of the total. Moreover, most foreign aid — about 77 percent, according to the nonpartisan Congressional Research Service — is channeled through an American company or nonprofit, international charity or federal agency to carry out projects, and not handed directly to foreign governments.Zimbabwe received $399 million, Iraq $248 million, Pakistan $147 million, Belarus $32.8 million, Cuba $6.8 million and China $1.7 million.The biggest single contracts to aid Zimbabwe and Pakistan were $30 million and $16.5 million to the World Food Program to provide meals and alleviate hunger. In Iraq, the largest contract of $29 million was awarded to a United Nations agency. And in Cuba, the third-largest contract was carried out by the International Republican Institute — a pro-democracy nonprofit whose board includes Senator Joni Ernst of Iowa, the host of the fund-raiser Ms. Haley was speaking at.In comparison, the country that received the most foreign aid, at about $10.5 billion or a fifth of the total amount, was Ukraine, followed by Ethiopia ($2.1 billion), Yemen ($1.4 billion), Afghanistan ($1.3 billion) and Nigeria ($1.1 billion).Another $12 billion was spent on global aid efforts in general, including about $4 billion in grants to the Global Fund, an international group that finances campaigns against H.I.V., tuberculosis and malaria.Domestic policyWhat Ms. Haley SAID“We will stop giving the hundreds of billions of dollars of handouts to illegal immigrants.”— in the CNN town hallThis is disputed. Unauthorized immigrants are barred from benefiting from most federal social safety net programs like Medicaid and food stamps. But the spokesman for Ms. Haley gave examples of recent payments made by local governments that allowed unauthorized immigrants to participate in benefit programs: $2.1 billion worth of one-time payments of up to $15,600 to immigrants in New York who lost work during Covid-19 pandemic, totaling $2.1 billion; $1 million for payments to families in Boston during the pandemic; permitting unauthorized immigrants to participate in California’s health care program for low-income residents, which could cost $2.2 billion annually.These, however, do not add up to “hundreds of billions.” That figure is in line with an estimate from an anti-immigration group that other researchers have heavily criticized for its methodological flaws.The group, the Federation for American Immigration Reform, estimated in March that illegal immigration costs the United States and local governments $135.2 billion each year in spending on education, health care and welfare, as well as another $46.9 billion in law enforcement.But the Cato Institute, a libertarian think tank, has found that an earlier but similar version of the estimate overcounted welfare benefits that undocumented immigrants receive, and undercounted the taxes that they pay. The net cost, according to Cato, is actually $3.3 billion to $15.6 billion.The American Immigration Council similarly concluded that education and health care account for more than half of the costs, and that the benefits were afforded to many American-citizen children of undocumented immigrants.The estimated 11 million unauthorized immigrants living in the United States are barred from the vast majority of the federal government’s safety net programs. In 2017, the National Academies of Sciences, Engineering and Medicine found that immigration, illegal and legal, benefited the economy.What Ms. Haley SAID“Let’s start by clawing back the $500 billion of unspent Covid dollars that are out there.”— in the CNN town hallThis is exaggerated. Ms. Haley overstated the amount of unspent coronavirus emergency funding. In reality, the amount is estimated to be much smaller, roughly $60 billion. What is more, a budget deal between President Biden and Speaker Kevin McCarthy that was signed into law a day before Ms. Haley spoke rescinded about $30 billion of that leftover money.Lawmakers passed trillions of dollars in economic stimulus and public health funding, most of which has already been spent. The federal government’s official spending website estimates that Congress has passed about $4.65 trillion in response to Covid-19 (referred to as “budgetary resources”) and, as of April 30, paid out $4.23 trillion (or “outlays”), suggesting that about $423 billion has not gone out the door. But that calculation fails to consider the promises of payment (or “obligations”) that have been made, about $4.52 trillion. That is a difference of about $130 billion, but some of initially approved funding that was unspent and not yet promised has already expired.In April, the Congressional Budget Office estimated that rescinding unobligated funding from six laws between 2020 and 2023 — the four coronavirus packages, President Donald J. Trump’s last spending measure, and President Biden’s $1.9 trillion stimulus package — would amount to about $56 billion. The Committee for a Responsible Federal Budget, a nonpartisan group that supports reduced government spending, estimated about $55.5 billion in unspent funds. More