Is political corruption actually on the rise? Who knows?
Making the scientific connection between corporate political influence and the inequities (if not down-right corruption) that results is Mara Faccio, who studied thousands of corporations in dozens of countries and found that "[p]olitically connected firms have higher leverage (in the form of preferential loans), pay lower taxes, have regulatory protection, are eligible for government aid, and have stronger market power. They differ more dramatically from their peers when their political links are stronger, and in more corrupt countries, although these characteristics can be observed worldwide." (PDF)
Faccio defines a politically connected firm as "[a] company where at least one of its large shareholders (anyone controlling at least ten percent of voting shares) or one of its top officers (CEO, president, vice-president, chairman, or secretary) is a member of parliament, a minister, or is closely related to a top politician or party." Her definition would appear to exclude non-relatives, but I would argue that a non-relative with extremely deep pockets will exert similar influence over the politicians to whom they donate.
However, in an article in the New York Times following the Citizens United decision, David D. Kirkpatrick points out the inability of researchers to show that the lack of campaign-contribution regulations leads to corruption, nor that the presence of such regulations prevents corruption. Also, scientists haven't been able to draw a correlation to date between contributions made by corporations and the performance of their stock price: increased contributions don't necessarily translate to higher corporate value, and decreased contributions don't necessarily translate to lower corporate value. Is campaign finance reform a solution looking for a problem? That would appear to be a possibility, at least based on research conducted in the U.S. and in countries with more and less regulation of campaign funding (the United Kingdom and Australia are cited as examples of more and less regulation, respectively).
However, the lack of evidence of the negative effect of the unfettered campaign contributions, and of the positive effect of regulation, begs the question: What's the difference between actual influence and the mere perception of influence? As with many important issues in the Information Age, the key to an informed electorate is transparency. A report authored by Brendan Fischer of the Center for Media and Democracy and Blair Bowie of the U.S. PIRG Education Fund found that nearly 17 percent of all business donations to Super PACs in the 2012 national election were from "phony for-profit corporations." (PDF) The report claims that "dark-money" non-profits (organizations that don't disclose the source of their funds) contributed in excess of $299 million to campaigns in 2012. The organizations are able to skirt disclosure requirements by running "issue ads" that are ostensibly unaffiliated with any particular candidate. As the authors point out, "it is almost impossible to identify violations of election or tax law, such as the infiltration of foreign funds" when dealing with such shell corporations and dark-money non-profits.
Experience shows that throwing legislation at a problem is no guarantee of a solution. To quote Thomas Jefferson, "Whenever the people are well informed, they can be trusted with their own government; that whenever things get so far wrong as to attract their notice, they may be relied on to set them to rights." Determining whether there is indeed an undue -- perhaps illegal -- influence by corporations on politics in general and elections in particular starts with disclosure. Campaign financing must come out from the shadows, whether voluntarily or by force of law. An informed electorate depends on it.
 http://www.sciencedaily.com/releases/2010/09/100921101348.htm; http://news.heartland.org/sites/all/modules/custom/heartland_migration/files/pdfs/28756.pdf
 http://www.prwatch.org/news/2013/01/11944/“elections-confidential”-report-reveals-role-dark-money-nonprofits-and-shell-corp; http://www.prwatch.org/files/Elections_Confidential.pdf