Ask just about any politi­cian whether finan­cial con­tri­bu­tions influ­ence their deci­sion mak­ing and you will hear that they’re entire­ly incorruptible.

Politicians may boast about their personal integrity as a bulwark against corruption, but the influence of political spending is far-reaching, murky and often shapes real legislative outcomes.

Take Hillary Clin­ton. At a Feb­ru­ary 2016 town hall with CNN, the then-pres­i­den­tial-hope­ful said she accept­ed $675,000 in speak­ing fees from Gold­man Sachs because, ​“that’s what they offered.” She went on to explain why this cor­po­rate cash wouldn’t have any impact on her deci­sion-mak­ing any­way. ​“Any­body who knows me, who thinks that they can influ­ence me, name any­thing they’ve influ­enced me on. Just name one thing,” she said.

Many crit­ics point to Clinton’s record on Wall Street reg­u­la­tion as a prime exam­ple. Dur­ing her two terms as a U.S. sen­a­tor, Gold­man Sachs, Cit­i­group and J.P. Mor­gan Chase were all among Clinton’s top five cam­paign donors. In 2001, soon after enter­ing the Sen­ate, Clin­ton vot­ed for a bank­rupt­cy bill that was being pushed by big banks, earn­ing her the ire of con­sumer advo­cates at the time, includ­ing Eliz­a­beth Warren.

Over the course of Clinton’s career in the Sen­ate, she leg­is­lat­ed with a light touch on the indus­try, co-spon­sor­ing only 25 out of 189 bills that finan­cial-indus­try lob­by­ists iden­ti­fied as sig­nif­i­cant bank­ing or finance leg­is­la­tion. As the Boston Globe has report­ed, this hands-off approach helped con­tribute to the finan­cial sector’s abil­i­ty to large­ly avoid regulation.

Oth­er politi­cians sug­gest there’s hard­ly a need to reg­u­late polit­i­cal spend­ing at all. After the Supreme Court’s 2010 Cit­i­zens Unit­ed rul­ing, which opened the flood­gates for unlim­it­ed out­side polit­i­cal spend­ing from cor­po­ra­tions, then-GOP Sen­ate can­di­date Mar­co Rubio laud­ed the court’s decision.

Claim­ing that the reg­u­la­tions over­turned by Cit­i­zens Unit­ed ​“infringe on fun­da­men­tal rights,” Rubio explained that, rather than advo­cate for cam­paign-finance restric­tions, vot­ers should sim­ply ​“elect lead­ers who val­ue pol­i­cy and prin­ci­ples over pol­i­tics and spe­cial interests.”

There may be no con­vinc­ing Clin­ton or Rubio, but a new report explains that mon­ey impacts politi­cians’ deci­sions far more than they are will­ing to admit.

The authors of a recent Roo­sevelt Insti­tute paper iden­ti­fied a series of high-pro­file cas­es in which polit­i­cal con­tri­bu­tions influ­enced mem­bers of Con­gress on key floor votes involv­ing finan­cial reform.

To exam­ine the influ­ence of big mon­ey, the authors of the study focused on five votes in the U.S. House of Rep­re­sen­ta­tives relat­ing to the Dodd-Frank finan­cial-reform bill. They iso­lat­ed spe­cif­ic rep­re­sen­ta­tives who ini­tial­ly vot­ed in favor of the bill and sub­se­quent­ly vot­ed to dis­man­tle some of its key pro­vi­sions. What they found was a direct link between vot­ing behav­ior and cam­paign con­tri­bu­tions from the finan­cial sector.

Accord­ing to the paper, ​“for every $100,000 that Demo­c­ra­t­ic rep­re­sen­ta­tives received from finance, the odds they would break with their party’s major­i­ty sup­port for the Dodd-Frank leg­is­la­tion increased by 13.9 per­cent. Demo­c­ra­t­ic rep­re­sen­ta­tives who vot­ed in favor of finance often received $200,000 – $300,000 from that sec­tor, which raised the odds of switch­ing by 25 – 40 percent.”

The authors found sim­i­lar results with telecom­mu­ni­ca­tions leg­is­la­tion. In a 2006 vote on net­work neu­tral­i­ty, every $1,000 in con­tri­bu­tions from an anti-net-neu­tral­i­ty firm equat­ed to a 2.6 per­cent greater chance of vot­ing in those inter­ests’ favor.

Thomas Fer­gu­son, Pro­fes­sor Emer­i­tus at the Uni­ver­si­ty of Mass­a­chu­setts Boston, a Roo­sevelt Insti­tute Senior Fel­low and a co-author of the paper, says clear­ly mon­ey doesn’t just influ­ence pol­i­tics — it dri­ves it. But many aca­d­e­mics, like politi­cians, reject this view, argu­ing that con­tri­bu­tions are unre­lat­ed to vot­ing behavior.

This trend, Fer­gu­son says, aris­es from an aca­d­e­m­ic envi­ron­ment where ide­ol­o­gy and fund­ing are as insep­a­ra­ble as ​“siamese twins.” Aus­ter­i­ty mea­sures have slashed uni­ver­si­ty fund­ing and put pres­sure on aca­d­e­mics to seek pri­vate grant mon­ey for research. As a result, says Fer­gu­son, ​“There aren’t very many out­side grants to do seri­ous stud­ies of polit­i­cal money.”

The out­side inter­ests dri­ving aca­d­e­m­ic fund­ing oper­ate in sub­tle ways, as does most polit­i­cal spending.

Fer­gu­son and his co-authors, Jie Chen and Paul Jor­gensen, point out that direct cam­paign con­tri­bu­tions only scratch the sur­face of mon­ey in pol­i­tics. ​“Polit­i­cal mon­ey resem­bles the elec­tro­mag­net­ic spec­trum,” they write. ​“The por­tions that you see rep­re­sent but a frac­tion of the whole phenomenon.”

Their ​“spec­trum of polit­i­cal mon­ey” high­lights eight ways out­side cash shapes polit­i­cal deci­sion-mak­ing. These include pay­ments to lawyers, politi­cians and foun­da­tions; mon­ey spent on lob­by­ing and think tanks; for­mal cam­paign spend­ing; the val­ue of stock tips to polit­i­cal fig­ures and pub­lic rela­tions spend­ing. Mon­ey flow­ing through these avenues is per­fect­ly legal but often dif­fi­cult to trace, cre­at­ing count­less oppor­tu­ni­ties for corruption.

For­tu­nate­ly, vot­ers seem far more attuned to this dire sit­u­a­tion than many politi­cians and aca­d­e­mics. Ferguson’s paper cites a June 2015 CBS News poll that found 84 per­cent of Amer­i­cans believe mon­ey has too much influ­ence in polit­i­cal campaigns.

So what reforms can the pub­lic push to tame the undue influ­ence of mon­ey over U.S. pol­i­tics? Fer­gu­son stress­es that pub­licly fund­ed elec­tions would go a long way toward less­en­ing cor­rup­tion. Under such sys­tems, which exist in some form in 13 states and some cities, can­di­dates raise mon­ey through democ­ra­cy vouch­ers or matched con­tri­bu­tions from pub­lic funds, allow­ing their plat­forms to reach vot­ers with­out the mega­phone of cor­po­rate cash.

The oth­er major reform cham­pi­oned by Fer­gu­son is a con­sti­tu­tion­al amend­ment bar­ring all cor­po­rate and spe­cial-inter­est mon­ey from elec­tions. ​“Cor­po­ra­tions are crea­tures of the state; they’re legal enti­ties. They’re not nat­ur­al per­sons,” he says. ​“So I would ban them from direct polit­i­cal con­tri­bu­tions, and I would also put ceil­ings on cash [from indi­vid­ual contributors].”

Even these reforms wouldn’t solve the revolv­ing door issue in which for­mer gov­ern­ment offi­cials use their Capi­tol Hill clout to score access for their new pri­vate-sec­tor employ­ers. Fer­gu­son offers two solu­tions to this prob­lem. ​“I would ban any con­tact with super­vised enti­ties by reg­u­la­to­ry per­son­nel for many years, not just one or two,” he says. ​“And I would pay gov­ern­ment employ­ees, espe­cial­ly at high lev­els, enough so that they do not need to go to the pri­vate sec­tor to get their chil­dren educated.”

Politi­cians may boast about their per­son­al integri­ty as a bul­wark against cor­rup­tion, but the influ­ence of polit­i­cal spend­ing is far-reach­ing, murky and often shapes real leg­isla­tive outcomes.

Only by acknowl­edg­ing how mon­ey dri­ves pol­i­tics can we hope to pass demo­c­ra­t­ic reforms that force politi­cians to be account­able to their con­stituents, not their wealthy donors.