BOGOTÁ, Colombia—When Lima, Peru, hosted the joint annual meetings of the World Bank and the International Monetary Fund last October, it was supposed to be the ideal occasion for showcasing the new Latin America. At least that was the intention of Peru, probably the region’s most successful economy, whose government spared no expense receiving the more than 12,000 delegates, which included finance ministers and central bankers from 188 countries.

The venue was flawless. A convention center was inaugurated just days before the meetings; the impressive, newly constructed Grand National Theater hosted events; and the Peruvian Central Bank building housed delegations. Even the city’s challenging traffic was manageable thanks to the combination of a national holiday and an additional civic day that meant thousands of motorists left the capital for a long weekend just as the motorcades invaded.

The only variable that...

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