It’s the beginning of a new month, and that’s a good thing in America’s schools, because life seems to get worse there as a month goes by. Students get in more trouble toward the end of the month than at the beginning.

New research suggests that’s especially true for students from families on food stamps, perhaps because life at home gets more stressful as benefits run out. Modifying the food-stamp program so that benefits are paid out twice, rather than once, a month could help eliminate these cycles.

As Sir Thomas More noted in the 16th century, money has a tendency to burn a hole in one’s pocket. Social Security beneficiaries illustrate this truth; they splurge a little when they receive their monthly checks. And among households in general, spending tends to decline between paydays.

The behavior may extend to benefits under the food-stamp program, now formally known as the Supplemental Nutrition Assistance Program, or SNAP. In 2011, almost one in seven Americans received support from SNAP. About half of the roughly 45 million beneficiaries are children.

The average monthly benefit for a family of four is about $500, and the funds can be used only for buying food. Gone are the old paper food stamps, which often stigmatized shoppers at the checkout register. SNAP benefits now come in the form of an electronic card that looks and operates like a debit card.

Families that use food stamps naturally tend to buy more food at the beginning of the month, after receiving their benefit. In fact, more than a quarter of beneficiary households redeem their entire monthly allotment within the first week of receiving it, the Agriculture Department’s Food and Nutrition Service, which oversees the SNAP program, has found. More than half the families take just two weeks to use up their full benefit. And 86 percent of families redeem more than half within the first half of the month.

Presumably, bulk purchasing toward the beginning of the month need not mean that families run out of food before the month is out - especially since most families are supposed to supplement food-stamp benefits by buying some food with their own income. In reality, however, it often does. Research by economist Jesse Shapiro of the University of Chicago has found that caloric intake among food-stamp beneficiaries is 10 percent to 15 percent lower, on average, at the end of the month than at the beginning.

About 40 percent of food-stamp households make only one major grocery-shopping trip per month, research by Parke Wilde of the Agriculture Department and Christine Ranney of Cornell University has shown. And among those households, caloric intake drops substantially over the month.

For the other households, who shop more frequently, caloric intake remains steady through the month.

(Note that these studies were conducted before the 2009 stimulus legislation, which temporarily increased SNAP benefits. It is possible that the results would be different or less pronounced today, but I suspect the same broad pattern still exists.)

A recent analysis by Lisa Gennetian of ideas42, a new nonprofit research organization dedicated to real-world applications of behavioral economics, suggests that the decline in food at home and the associated increase in family stress may be causing problems at school. (Full disclosure: I serve on the board of directors of ideas42.)

Gennetian and her co-authors linked SNAP beneficiary data with disciplinary records for all fifth-to-eighth graders in Chicago’s public schools. Among students from SNAP families, disciplinary problems such as fighting, vandalism or weapons possession increased by almost 50 percent in the final week of the month compared with the first week, the researchers found. (For non-SNAP families, disciplinary events also rose, but significantly less.)

Strikingly, the researchers did not find an increase in disciplinary events among SNAP families in schools with after- school snack programs. They conclude: “The most plausible explanations for students’ inability to adhere to proper school behavior include hunger caused by reduced consumption of calories and/or increase in household stress due to exhausting all forms of liquid assets.”

So one approach that could address the school disciplinary problem is to expand after-school snack programs. But a more comprehensive strategy worth exploring would be to split the SNAP benefit into two semi-monthly installments. Then food purchases and caloric intake might be smoother over time. With the electronic cards, this would be pretty easy to do.

It could be inconvenient for families that have a difficult commute to a supermarket and therefore want to make only one trip a month. This is a complex problem, and would benefit from research. On the one hand, more shopping trips are time-consuming and the travel involved can use up resources better spent on food itself. On the other hand, the single-trip families seem to be the ones running low on food, and it’s plausible that their children are among those getting in more trouble at school.

Right now, federal law prohibits splitting SNAP benefits into two installments, but the rule is waivable for demonstration purposes. So perhaps a city (Chicago comes to mind) would like to test the possibility that two monthly components would help reduce disciplinary events at school. To do the study right, we would need to compare the current system to two alternatives: a higher level of benefit, still paid out once a month, and the same level of benefit, but split into two monthly payments. If the problems associated with once-a-month benefits persist even with higher payments, but diminish with more frequent ones, there’d be good reason to try adjusting the system.

Peter Orszag is vice chairman of global banking at Citigroup and a former director of the Office of Management and Budget in the Obama administration.