Earlier this year, a Republican state lawmaker in New Mexico proposed a constitutional amendment that would give his colleagues (and himself) something most workers take for granted: a paycheck. Since 1912, when New Mexico entered the union as a sparsely populated frontier settlement, its state legislators have worked without a salary, although lawmakers receive a per diem that amounts to approximately $7,000 for up to two months of work per year. Today, it’s the only state with an unsalaried legislature. In an op-ed published in January, the amendment’s sponsor, Terry McMillan, argued that a volunteer legislature has its limits. We tend to prefer a professional fire department to a squad of volunteers, he said — why don’t we feel the same about the people in our government?

The amendment, which would have raised New Mexico legislators’ salaries to match the state’s median household income, around $45,000, died quietly when the session ended in February. But arguments like McMillan’s raise a tricky question for American taxpayers: How much are our lawmakers really worth?

“The question of salaries has haunted American legislatures since the 1640s,” said Peverill Squire, a professor of political science at the University of Missouri and an expert on state legislatures. “It has been a chronic issue where lawmakers generally ask for more pay and the public is almost always resistant.”

When they ask for more money, lawmakers like McMillan try to make the case to voters that they deserve a pay raise because of the time and knowledge required to do their jobs well. It’s a hard sell, because higher–compensated legislatures such as those in Illinois, Pennsylvania and New York, where lawmakers are paid well above the state’s median income, routinely face accusations of incompetence or corruption. According to Squire and other political scientists, higher pay isn’t a magic bullet for better governance — but there’s evidence that when it comes to state legislatures, we get what we pay for.

Lawmaker salaries vary wildly across the country, from California, where legislators make nearly $100,000 a year, to New Hampshire, where they are compensated with $100 annually and no per diem. Overall, though, they tend to skew low. In 2014, according to research by Squire and Gary Moncrief, a political science professor at Boise State University, the median base pay was $20,833.

Legislators in some states receive more money through per diems and expense allowances. Take Oklahoma, where legislators’ base salary is $38,400. With the per diem of $153 per day, Oklahoma legislators took home an additional $10,404 in 2014, according to estimates by Squire and Moncrief. That put the lawmakers’ total earnings close to the state’s median household income.

Untangling just how much legislators take home is difficult, because at least in theory, any per diem should go toward on-the-job expenses like meals and lodging. In about half of states, per diems are given without strings attached. This means that short of examining a legislator’s tax return, it’s impossible to know how much went toward actual expenses. But even with this extra cash, only 12 states (including Oklahoma) pay their state legislators a salary that matches or exceeds the state’s median household income — and most compensate well below this marker.

SOURCES: AMERICAN COMMUNITY SURVEY, NATIONAL COUNCIL OF STATE LEGISLATURES, SQUIRE & MONCRIEF

In this varying landscape, figuring out whether pay raises are justified can be a struggle: Are higher-paid legislators better at running their states? Squire and Moncrief, along with other political scientists, have worked over the years to measure the relationship between salary and legislative effectiveness, a slippery benchmark that can include a variety of measures, including efficiency (the number of bills passed), contact with constituents, and the innovativeness of a state’s policies.

The researchers concluded that the best way to test the efficacy of a state legislature is through a concept called professionalism, which includes three components: salary, the number of days in a legislative session, and the size of the legislature’s staff.

Most of the time, these factors align. Some big states like California and New York have “full-time” legislatures, as classified by the the National Conference of State Legislatures; they meet for most of the year, and their legislators serve larger districts and receive relatively high salaries. Some states with smaller populations, like Montana and New Hampshire, are “part-time” legislatures, with short sessions and fewer constituents. Lawmaker pay in those states tends to be nominal.

About half the states, though, are classified as “hybrids” — they generally have low pay but might have a long session or larger staffs.

Using the U.S. Congress as a benchmark, Squire created a scale to assess professionalism. With this scale, he and other political scientists found that the state legislatures that meet for longer and give their legislators more resources (both in terms of staff and salary) are more efficient, passing a greater percentage of bills overall and enacting more bills per legislative day. They have more contact with constituents and are more attentive to their concerns. They are also more independent, both from party leadership and the governor, and more likely to take on government reforms and enact complex and innovative policies. “When you compensate a legislator well and give them a staff, they’re able to put more time into their work and actually develop some knowledge around different policies,” Squire said.

Low pay also puts limits on who can realistically serve in a legislature. In states like New Mexico that have short legislative sessions, lawmakers must leave their day jobs for one or two months every year and travel to the state capital — in addition to dealing with year-round demands from constituents. Many lawmakers must be independently wealthy or have flexible jobs that allow them to juggle politics and everyday work. Part-time legislators are also more likely than full-time legislators to be retirees, Moncrief said. It’s no surprise, then, that state lawmakers tend to be older than their constituents.

Lawmakers with less time to spare and no staff to guide them may rely more heavily on lobbyists to advise them about legislation, Squire said. A lawmaker in Missouri, a hybrid state, recently got into hot water when he declared that he sees lobbyists as “unpaid staff.”

Thad Kousser, a professor of political science at the University of California, San Diego, worked in the New Mexico legislature when he was a graduate student. Although he was only a page, a grant he’d received for school meant that he was making more money than the House speaker. It was a stark contrast with the California legislature, where he’d worked for several years previously. There, legislators were not only paid more — but they also had access to highly trained staff. “In California, people with J.D.s and Ph.D.s are writing the bills and investigating the legislation,” he said. “In New Mexico, you have the governor’s analysis and a Xerox machine.”

So when state legislators ask for more money, should voters listen? Neil Malhotra, a professor of political economy at Stanford University, said his research shows that when legislators ask for raises, they are responding to the demands of an increasingly complicated job. In his view, when lawmakers ask for more pay, they’re not promising to work better or more efficiently — they’re asking to be compensated adequately for what they’re already doing.

“It’s all relative, of course,” Moncrief said. “Legislators in low-population states where the legislature only meets a couple of months do not need to be paid six figures. But virtually all political scientists who’ve looked at this issue would agree, I think, that most legislators are underpaid for the work they do.” His co-author, Squire, suggested that at a minimum, legislative pay be pegged to the state’s median household income.

Malhotra said Americans’ suspicion of political institutions puts lawmakers in a bind. “It’s really irrational,” he said. “We don’t want to equip politicians with the resources to do their jobs, and then we blame them when things don’t work the way we want.”

CORRECTION (April 7, 12:15 p.m.): Because of a technical error, three paragraphs (beginning with the words “Lawmaker salaries vary wildly”) were omitted from the original version of this article. As a result, the full name and affiliation of Gary Moncrief, a political science professor at Boise State University, were left out. The paragraphs have been restored.

CORRECTION (April 8, 2:15 p.m.): Because of problems with the data source, an earlier version of the table in this article misstated compensation figures for Pennsylvania, Arkansas, Georgia, Maryland, Louisiana, Oregon, Idaho and Nebraska. We have updated the table with the correct figures.