Austerity measures shrink a country’s economy, not its debt. When most governments talk about having an over-spending problem, more often than not, they actually have a tax revenue problem. They are not collecting enough money from taxation, and more often than not, that is because corporations and the wealthiest individuals pay little or no tax. So, Austerity reduces the incomes of the major tax base of the state, thus reducing the money they remit in taxes, and thus crippling the state’s ability to pay off debt.
Austerity is not a policy to enable a country to escape debt, it is a policy to ensure that they never do.