The Chilean model is, presumably, a model because a) other countries have decided to model themselves after it (some countries, like Russia, have attempted to copy Chile's private pension system, for example) and b) because international business and policy elites have decided that there was something in the Chilean case to be emulated.
The Economist -- a fairly good barometer of these elites -- has for some time been wary of where the Chilean model was going, and this week devotes a long essay to the current state of things. And it ain't pretty.
There are lots of interesting data in the piece, but I suspect that what it comes down to is Carlos Peña's final quote -- it's a crisis of expectations.
I have long felt that the Chilean model was built on a kind of Chilean Dream, analogous to the American Dream, where the citizen-consumer accepted a kind of Faustian pact of neoliberalism in exchange for improving living standards. When Peña speaks of a crisis of expectations, he is referring to how Chileans perceive those standards of living. It is no longer enough to have a fridge or a flat screen TV, if you feel the cable company is ripping you off. It is not enough to get a university degree if your family goes into debt for years to fund a degree which will not offer much in terms of employment.
That's the current model, and The Economist doesn't seem so eager to have others emulate it.