A fall in aggregate effective demand and expenditure in an economy is the major feature of a recession. Private consumption is usually the largest component of aggregate demand, and it falls in the downturn, while consumers try to collectively increase their saving; that is, the income they do not spend.
Graphs of the saving rate in major economies over the economic cycle tend to show it falling during booms and rising in recessions. So an increase in the desired saving rate does lead to a rise in the actual rate.
In the current recession, consumers in many countries have seen a collapse in their personal wealth, due to a fall in asset prices, particularly in housing and stock markets. This is a further reason for them to cut borrowing and consumption and increase saving, as a way to rebuild their personal balance sheets.
At the same time, banks, other financial intermediaries and non-financial firms are also rebuilding their balance sheets by restructuring their financial positions ie reducing their exposure to debt.
The debt of households and firms is growing much more slowly than before the recession and household debt even recorded a recent fall in the US. As the economy returns to growth, however slow, it will be necessary for private debt to grow more slowly than income for some time, until balance sheets become more healthy. This is likely to slow private sector investment and consumption and hence overall growth, particularly in heavily indebted countries.
The rebuilding of private sector balance sheets can be seen as a debt-deflation process, which is one way of looking at the process of such a deep recession in many countries. While private sector debt as a percentage of national income has been falling, public sector debt has been rising as governments have run increased fiscal deficits, partly as automatic stabilizers have taken effect, but also as a result of stimulus packages aimed at mitigating the fall in aggregate demand.
Public sector balance sheets have in many cases worsened, notwithstanding the funds used to bail out the banks by injecting capital, which include the purchase of assets which, one hopes, will ultimately recover in value and eventually show governments, and hence taxpayers, some profit.
Conservative opinion seems to dislike debt and especially public debt. It may seem perverse to some for the government to be increasing its own debt while the private sector becomes increasingly thrifty. But an essential insight of macroeconomics is that governments can help to stabilize an economy using fiscal policy. Especially in such a deep recession as this one, such damage limitation is necessary to prevent unemployment from rising even further, with all the social ills that go with that phenomenon.
In fact, rising government debt may allow the private sector to pay down debt more rapidly and speed recovery from recession over the medium term. The process is unlikely to be smooth or mechanical, but during the period in which the private sector is increasing its saving and paying off debt in aggregate, and certainly reducing debt relative to income, the multiplier from a rising public deficit may be somewhat reduced, but a rising deficit can still in this instance mitigate the recession and speed recovery. For a time public debt may rise at an unsustainable rate. One hopes that the private sector can recover before public debt reaches unsustainable levels, whatever those might be.