That influence tempted 1  See Tobin (1972), “Inflation and unemployment”, American Economic Review, 62. Inflation can have large redistributive effects. Volatile inflation arbitrarily re-distributes wealth across borrowers and savers. And most recently, there has been a debate about how the stance of monetary policy has affected the distribution of wealth and income. In a series of recent analysis and speeches, members of the MPC have shown that, while distribution is not an objective of monetary policy, the evidence strongly suggests that policy since the crisis has been associated with better outcomes. 2  2  All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches  2  authorities to promise low inflation in the future, but then to renege in order to boost activity. Electoral cycles 3  reinforced this predisposition. Firms and households began to anticipate these incentives, however, and eventually pre-empt them. The economy ended up in a worse equilibrium with higher inflation and 4  unemployment. Such time-inconsistent policies contributed to excessive inflation and higher structural unemployment in the UK during the 1970s and 1980s (when inflation averaged 9.5% and unemployment over 7.5%). In light of similar experiences, many societies came to recognise that macro outcomes can be improved by having society first choose the preferred rate of inflation and then delegate operational responsibility to the 5  monetary authority to take the necessary monetary actions to achieve that objective. By “tying the hands” of authorities, time inconsistency is resolved and better outcomes for both inflation and unemployment become possible.
32  An expression equivalent to the IS curve above can then be used to define  the natural interest rate, 𝑟𝑡∗ , which is the interest rate that would prevail in the absence of any nominal rigidities: ∗ 𝑦𝑡∗ = 𝐸𝑡 𝑦𝑡+1 −  1 ∗ 𝑟 𝜎 𝑡  Using this, the IS curve can be re-written in output gap form, using the output gap definition 𝑥𝑡 ≡ 𝑦𝑡 − 𝑦𝑡∗ and the definition of the natural interest rate to give:  (2)  1 𝜎  𝑥𝑡 = 𝐸𝑡 𝑥𝑡+1 − [(𝑖𝑡 − 𝐸𝑡 𝜋𝑡+1 ) − 𝑟𝑡∗ ]  31  In other words, the simple model here abstracts from all channels of monetary transmission other than the inter-temporal substitution channel. Of course, building in addition frictions and model features, like borrowing constraints and open economy features, can restore the roles of the other channels. 32 In particular, in the simple model, one can show that 𝑦𝑡∗ = 𝜓𝑎𝑡 , where 𝑎𝑡 is the log-level of TFP, assumed to follow an exogenous process. 18  All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches  18  This says that the output gap is negatively related to the sequence of “real rate gaps” (𝑖𝑡 − 𝐸𝑡 𝜋𝑡+1 ) − 𝑟𝑡∗ delivered by monetary policy. For example, when monetary policy delivers real interest rates equal to the natural rate, so 𝑖𝑡 − 𝐸𝑡 𝜋𝑡+1 = 𝑟𝑡∗ , the output gap is zero at all times.