Mr. Easterly and others have criticized Mr. Sachs as not paying enough attention to bigger-picture issues like governance and corruption, which have stymied some of the best-intentioned and best-financed aid projects.

Image Sauri was the first of more than 80 projects across Africa. Credit... The New York Times

For example, one can easily picture what would happen in Kenya, where corruption is essentially a national pastime, if there were a free, donor-supported fertilizer program for the entire nation. The fertilizer would very likely never reach its intended target and would disappear like the national grain reserves that were plundered during a famine in 2008, or the billions of dollars of foreign aid that have ended up in the pockets of Kenyan politicians, according to numerous reports by human rights groups and financial auditors.

Mr. Sachs says he is the first to admit that he cannot do it all.

In Kenya, he says, to eradicate poverty nationwide, the country’s leaders would need to improve infrastructure and urban industries substantially.

“What we’re focusing on,” he said, “is about one-third of the problem.”

Another criticism is that Mr. Sachs is not evaluating his programs in a rigorous, scientific way. Many aid experts have suggested that the only way to really know if the Millennium Villages are worth the expense (around $110 per capita, per year) is to collect data from similar “control” villages that are receiving no help.

“No one would dream of ‘scaling up’ the use of a new pharmaceutical in the U.S. without rigorous evidence comparing people who got the medicine to people who did not,” said Michael Clemens, a research fellow at the Center for Global Development.

But Mr. Sachs says that “Millennium Villages don’t advance the way that one tests a new pill.”

Beyond that, he does not like the idea of going into a village, subjecting poor people to a battery of questions and then leaving them empty-handed, though other aid specialists have said that studying poor people without giving them anything in return is done all the time.

“It pains me to be in a village that doesn’t have bed nets” to protect against malaria-carrying mosquitoes, he said, adding that some comparison studies were under way.