In practice, austerity has not reduced debt.  On the contrary, austerity has increased debt substantially. 

According the International Monetary Fund (IMF)’s Fiscal Monitor, the debt to GDP ratio of governments has seen an increase more or less proportionate to the degree with which austerity measures were implemented.

For example, from 2011-2013, the years that austerity was the core policy, debt significantly grew in Spain, France, Ireland, Portugal, Italy and Greece, the UK and the US.  Ireland’s debt-to-GDP ratio increased from 24.8% in 2007 to 125.1% in 2013, Portugal’s increased from 60.0% in 2006 to 127.2% in 2013 and Greece’s grew from 106% to in 2007 to 160.5% in 2013.

There have been very recent claims that the US economy is adding jobs, health care costs are declining and the deficit is shrinking.  However, this observation can be seen as a small temporary aberration in deficits, which will most likely be followed by higher deficits in the near future (according to all fiscal authorities).

The argument that austerity reduces debt is theoretically implausible, and is not borne out by the statistics.