But why is Mr. Putin, despite his willingness to start military wars, reluctant to declare a real war on corruption — even though, as Mr. Xi has found, anti-corruption campaigns are usually popular with the public?

Only a fool would argue that there’s a dearth of corruption in Russia. Recent opinion polls from Moscow’s independent Levada Center indicate that a majority of people view state bureaucracy as irremediably corrupt. Russian movies and novels are full of officials who take bribes. Why then is the Kremlin so unwilling to undertake a cleanup, particularly in a moment when cutting the cost of corruption could compensate for depressed oil prices?

The commonplace explanation in the Western media is that Mr. Putin himself is deeply corrupt — indeed, that he sits at the epicenter of Russia’s corrupt edifice. This may be so. But as someone who has spent his life in the Balkans (and therefore knows a thing about corruption), I have learned that being corrupt is hardly a reason not to declare a war on corruption; on the contrary, it could be an incentive, because there is nothing that corrupt politicians hate more than other people’s corruption.

The reason for Mr. Putin’s reluctance, then, is more complicated.

On one hand, for him, mutual accusations of corruption are the dirty bombs of the intra-elite wars, which cause a lot of collateral damage. Research has long demonstrated that corruption, although hitting the poorest groups in society hardest, is primarily a middle-class concern — and in today’s Russia, the middle class to a great extent is composed of these same bribe-taking officials that anti-corruption campaigns should target.

On the other hand, what matters in politics is not the levels of corruption, but the public’s perception of how corrupt their country is, and very often the link between the two is not direct. Small and successful wars abroad can be a better instrument to change people’s perception of how corrupt their country is than the actual efforts to reduce corruption. Correlation is not causation, but in the wake of Crimea’s annexation, the number of Russians who believed that corruption was increasing plummeted to 30 percent, from 50 percent.