Why do people still say Chicago/Austrian theory is unproven, again? Why haven't I known about this until now?
So that's the whole of Austrian/Chicago economic theory? Run a surplus?
Not really. Here's a very basic view:
Under Keynesianism the government taxes to build the economy's infrastructure and regulate the economy. When times are tough, the government spends more to provide a stimulus to get the economy back into shape. When times are good, the government is supposed to cut back some and store up for hard times. Unfortunately the part of cutting back and storing during good times is politically unrealistic, so Keynesianism fails by not allowing the necessary corrections.
Chicago school economics is similar to Keynesianism except its more concerned with stability and limiting both inflation and government interference in the economy. The people managing things are actually expected to know what they are talking about, unlike under Keynes.
Austrian school economics understands that when government interferes in the economy in any way, it is actually harming the natural regulatory forces of the market.
What happened in Chile sounds like the people running things understood that the best way to stay in control was to manage things better for the economy than for their political careers - which turns out to be the best way to ensure a lasting political career. Running a small surplus and paying down debts has proven to be the best way to manage things because it lets the economy improve itself. If the surplus is too large then the taxpayers will demand refunds, making it harder to pay down long term debts. If there is a deficit then it looks bad for the economy and so it seems less profitable to invest in it, so that harms the economy. Its all pretty simple, but you do have to combat the short term political gains of stimulus and redistribution to get the long term gains of a stronger and healthier economy.