This question is actually the title of ECB working paper #841 from December 2007 by Livio Stracca. Inside money is understood as “money produced by the private sector and not by the government or the central bank” (p. 5). The author incorporates inside money in the standard DSGE model and comes to the following conclusions:
Fourth, simulating a banking crisis as a simultaneous increase in the cost of bank lending to firms and of producing deposits leads to an unambiguous contraction of economic activity and inflation and to a fall in interest rates. Finally, the inside money shocks enter in an optimal simple linear monetary policy rule, but their contribution to the overall central bank loss is found to be minimal. In other words, it appears that reacting to inflation is sufficient for stabilization purposes.
It might seem unfair to use hindsight in order to highlight the mistakes of some author, but let me assure you: if we don’t learn from the mistakes of the past, then designing a better financial system will not be possible. For too long, central bankers have ignored endogenous (=inside) money and its implications. This ignorance led central bankers to focus on inflation while at the same time the biggest external instabilities of the post-WWII era built up.
The ECB could have done much better, if only they had more knowledge about the economy. If the ECB of today would understand that endogenous money creation – which is loans from banks to households with no connection to the money supply – is driving the economy they would understand that aggregate demand in countries like Spain and Ireland will not go up until either a) the creation of endogenous money moves up again (highly unlikely), b) external demand is rising or c) the government spends more (wherever the funds would come from). Option b) is problematic, because it implies that either the rest of the world increases its price level or Spain decreases hers. Which would lead to an increase in real debt and probably make matters worse until debt has come down to sustainable levels.
Let me stress one more time that this crisis is one of intellectual failure to grasp reality. Central-banking is not the only field where this happened, so no particular blame should be shifted to the institution. However, blame must be put on it if it refuses to learn. Perhaps the central bankers of today don’t like the (Post-)Keynesian academics that have been developing ‘endogenous money’, and they are reluctant to leave their DSGE models in which they have invested so many years of work, but this is not the time for academic bickering.