When it comes to the international pattern of corruption, the beginning of wisdom is to know how little we know. I have been studying the topic for almost 20 years, and progress has involved many steps back as well as forward. Despite tens of thousands of papers written by scholars during that period, virtually the only thing one can say with confidence today is that richer countries, such as the United States, tend to have cleaner government than poorer ones.

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Since the mid-1990s, the nongovernmental organization Transparency International has published an annual “Corruption Perceptions Index,” which rates countries on the extent of graft in their public sectors. The World Bank has a similar measure. The ratings are based mostly on polls of international businesspeople and evaluations by risk analysts and other experts. Such indexes tend to match the conventional wisdom about which countries are more — and less — corrupt. In 2015, North Korea and Somalia did “worst,” and Denmark “best.”

When scholars such as myself analyzed what factors predicted higher scores, we found that “less corrupt” countries tended to be richer, more democratic, ethnically homogeneous, politically centralized and open to international trade. They were more likely to have a Protestant tradition, media freedom, a parliamentary (as opposed to presidential) constitution, plurality rather than proportional elections, and — if former colonies — a history of British rule. More natural resources and intrusive state regulations were bad; more women in government were good.

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But the results were too good. It seemed suspicious that almost any reasonable-sounding hypothesis could be confirmed. Think back to those experts in New York or London, filling out forms about large numbers of countries, some of which they might never have visited. Like you or me, such experts have preconceived notions about what kinds of countries have clean bureaucracies. So do the journalists whose articles the experts read, and the editors who commission the articles. Who wouldn’t expect a mildly regulated Protestant country where women dominate the government to have less graft than one ruled by an oil-rich dictator who gags the press? My guess is that such preconceptions are already in the experts’ minds as they check the boxes. If the ratings are themselves formed from such hunches, it is not surprising — and tells us nothing — that they later “validate” the same ideas.

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How can we study corruption better? Researchers have found inventive ways to measure what is — almost by definition — an extremely secret phenomenon. Miriam Golden of UCLA and Lucio Picci of the University of Bologna added up the total value of the infrastructure stock in Italy’s regions and compared this with the amount that had been spent to build it. The bigger the gap, they reasoned, the greater the kickbacks and theft along the way. Benjamin Olken of MIT dug up sections of road in Indonesian villages to see how much of the materials had been pilfered or replaced with low-cost substitutes by the construction teams.

But Picci has also experimented with cross-national measures of anti-corruption prosecutions. Another method that I favor is to use surveys of different countries’ populations that ask respondents about their actual experience. Besides measuring perceptions, Transparency International also polls populations on whether they have paid a bribe to a public official in the previous year. Of course, these data have their own problems — people might not answer frankly — but in practice, these problems seem less serious than those associated with the perceptions measures.

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The percentage reporting having paid a bribe correlates with the experts’ perceptions — but not so strongly as one might think. The latest CPI rates Paraguay slightly more corrupt than Sierra Leone. But while 84 percent of respondents in Sierra Leone reported having paid a bribe in TI’s latest survey, only 25 percent in Paraguay did so. In both the Czech Republic and Sudan, 15 percent to 17 percent of respondents said they had paid a bribe. Yet while the Czech Republic fell in the “least corrupt” quarter of the countries in the latest CPI, Sudan was rated the fourth most corrupt.

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If one analyzes respondents’ reports of their own experience rather than expert perceptions, most of the neat results about corruption’s causes disappear. The one factor that is strongly associated with lower corruption — regardless of the measure used — is economic development. Richer countries tend to be less corrupt.

Since corruption probably hinders economic development, however, it’s not clear what causes what. Some argue that countries’ fates were set hundreds of years ago and that only those with institutions that discourage corruption have grown rich. However, since all the countries that are now rich were once much more corrupt — recall Britain’s gin-soaked elections and New York’s Boss Tweed — many countries must have cleaned up their governments as they developed economically.

Economic development might help in several ways. Better-educated citizens can monitor officials and use legal protections to defend their rights. Modern media can discipline politicians. Development also induces shifts in values, perhaps reducing tolerance for nepotism and venality.

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One idea with which I’ve played for some years is that countries grow out of corruption in part by developing legal substitutes. Instead of taking bribes, members of Congress can take the revolving door that leads to lucrative lobbying jobs after Capitol Hill. Similarly, American presidents can accumulate wealth after stepping down, in the form of six-figure speaking fees and publishing advances.

By providing alternative ways for politicians to grow rich — without the risk of jail time — the system makes it easier for them to remain more-or-less honest while in office. Michael Kinsley, the great columnist and editor, coined what used to be known as “Kinsley’s Law” in U.S. politics: “The scandal’s not what’s illegal, the scandal’s what’s legal.” Yet, cynical as it might sound, providing such functional equivalents of corruption is preferable to living with the real thing. Most people would probably choose the distorting influence of lobbyists on K Street over the all-consuming graft of Tammany Hall.