Using this transformation, the policy problem can be re-stated as: min(𝜋𝑡 − 𝜋 ∗ )2 + 𝜆𝑥𝑡2 𝑥𝑡  𝑠. 𝑡. 𝜋𝑡 − 𝜋 = 𝛽𝐸𝑡 (𝜋𝑡+1 − 𝜋 ∗ ) + 𝜅𝑥𝑡 + 𝜀𝑡𝜋 ∗  Because the policymaker cannot commit to future policy actions, she takes expectations as given (i.e. does not internalise the possibility that, by committing to future policy actions, expectations can be manipulated having an effect on outcomes today). The first-order condition in this case is: 2(𝜋𝑡 − 𝜋 ∗ ) Using  𝜕𝜋𝑡 𝜕𝑥𝑡  𝜕𝜋𝑡 + 2𝜆𝑥𝑡 = 0 𝜕𝑥𝑡  = 𝜅, this simplifies to: 𝜆 𝜋𝑡 − 𝜋 ∗ = − 𝑥𝑡 𝜅  giving equation (1) after using 𝑥𝑡 ≡ 𝑦𝑡 − 𝑦𝑡∗ . This optimality condition has three intuitive features. First, positive inflation gaps should be matched by negative output gaps, and vice versa. Given a quadratic loss function, it makes sense to “spread the cost” associated with shocks across both target variables, rather than loading all the cost on to one alone. Optimal policy therefore returns inflation and output back to their target  (1−𝛽𝜃)(1−𝜃)  In particular, if firms re-set their prices with probability 1 − 𝜃 each quarter, then one can show that 𝜅 ≡ , such that as 𝜃 rises 𝜃 (i.e. as prices become more sticky), the slope of the Phillips curve falls. The average duration of a price is (1 − 𝜃)−1 .
Because its remit requires it to support strong yet sustainable and balanced growth, in exceptional circumstances, and in consultation with the FPC, the MPC could have to optimise – subject as always to society’s risk preferences – over a longer time horizon in order to avoid inter-temporal disequilibrium, with the 26  E.g. Mian, A and Sufi, A (2014), House of debt, Chicago. See for example, Aikman, D, Haldane, A and Nelson, B, (2015) “Curbing the credit cycle”, Economic Journal, 125(585), June. Though not the only one. Others included the absence of a credible resolution regime for failing institutions, inadequate capital and liquidity standards, excessive complexity and opacity in the financial system, and cultural failings alongside other perverse incentives for excessive risk taking. 29 The full FPC remit can be found here: http://www.bankofengland.co.uk/financialstability/Documents/fpc/letters/chancellorletter160316.pdf 27 28  14  All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches  14  result that inflation could deviate below target temporarily in order to achieve a more sustainable return to the target and more stable growth beyond the conventional policy horizon. 6. The Current Trade-off How do these factors relate to the recent conduct of monetary policy? In May, the MPC said that the effects of a vote to leave the EU on inflation would depend on the balance of its effects on demand, supply and the exchange rate.