"We find that the successful assassination of autocrats produces institutional change - substantially raising the probability that a country transitions to democracy," say the American economists Benjamin Jones and Benjamin Olkin in a paper published yesterday by the National Bureau of Economic Research. George Bush, Tony Blair and John Howard might have had the right idea in trying to obliterate Saddam by bombarding his palace on the eve of the Iraq war. Their problem, or Iraq's problem, is they missed. Like so many idealists, they stumbled in the execution.

The Benjamins show in Hit and Miss? The Effect of Assassinations on Institutions and War that failed assassination attempts reduce the prospects of democracy, as gauged against a governance index called Polity IV. "The successful assassination of an autocrat creates a highly significant 13-percentage point increase in the probability of democratic transition, compared to the case where the assassination attempt failed," they say. The assassination gap is even greater, at 19 per cent, if democracy is defined simply by the nature of subsequent leadership transitions.

And political assassinations have always worked better with bullets than bombs, as our well-intended leaders should have known. Idi Amin survived when a hand grenade bounced off his chest (killing several bystanders) but John F. Kennedy was felled by a bullet from 80 metres. Democracy is more likely to be imposed through the barrel of a pistol than dropped from a stealth bomber - no matter how smart the bombs. Explosive devices have succeeded in just 7 per cent of assassination attempts, while guns have a strike rate of 30 per cent. Viewed through the democracy prism, the lives and deaths of 2440 world leaders over 130 years show that trying to kill dictators, on average, has not been worth the trouble.

"Since failures are much more likely than successes, the modest effects of failure and the (less likely but larger) effects of success tend to offset each other," the authors say. Assassinations, successful or otherwise, do not affect the likelihood of war. But knocking off a dictator will tend to exacerbate a small, existing conflict - and yet hasten the end of a full-scale war. The econometric innovation in Hit and Miss is that by tabulating assassination attempts, as well as successes, the researchers create a "natural experiment" that can identify causation as well as correlation. The paper shows the frequency of assassinations is now at a historical high - but that is because new micro-countries are mushrooming everywhere, spawning more leaders. For the average leader, the risk has fallen from about 1 per cent to 0.3 per cent since 1910.

Risks are much greater for autocrats than democrats (three strikes for the Dominican Republic). Among democratic countries, the larger the population the higher the death rate (Kennedy, Lincoln, McKinley and Garfield in the US). Dr Olken, the report's co-author, is a student of the "Great Man" theory of history. He already knew that the death of a dictator tends to have a large effect on economic growth, for better and for worse, while the death of a democratic leader does nothing. Hit and Miss shows that assassinating democratic leaders makes no difference to the evolution of a political regime, either.

It all goes to show, he says, that "if you want to make a difference, be an autocrat".