Model of international policy reciprocity  Extending Aikman et al (forthcoming), the results in Chart 3 are from a new model that builds on their paper by adding a second country to their model and by examining international policy leakages and coordination. For simplicity, the model assumes that there is no market-based finance sector (𝑏 = 1). In its place, the model allows for an additional determinants of the crisis probability. Domestic credit growth (𝐵1 ) still predicts domestic crises (𝛾1 ), but the credit measure is split between credit borrowed from home banks (𝐵1𝐻 ) and credit borrowed from foreign ones (𝐵1𝐹 ). And to capture the empirical finding that global credit growth can help predict crises over and above domestic credit, the crisis probability also depends on credit growth in the foreign country (𝐵1∗ ). In addition, the CCyB setting (𝑘1 ) also still reduces the crisis probability by enhancing resilience. But the effective CCyB setting depends on whether there is a reciprocity arrangement, since it is a 20  Other than credit growth, all variables are measured as annual averages, such that σ = 0.6 implies that an increase in annual interest rates of 1pp for 1 period of 3 years, reduces output by an average of 0.6% in each of the 3 years. 12  All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx  12  weighted average of the CCyB settings applied to domestic banks’ domestic lending (𝑘1𝐻 ) and applied to foreign banks’ lending in the home country (𝑘1𝐹 ).
Higher interest rates can also reduce the probability of a banking sector crisis through the same leaning channel (𝜙𝑖 < 0), but do not increase resilience directly. The banking sector only provides a proportion (𝑏) of credit to the economy, the remaining (1 − 𝑏) share is provided by the market based finance sector (𝐵1𝑀 ). While higher interest rates have the same effect in reducing credit and the crisis probability in both sectors, increasing the CCyB leads to a leakage of credit from the banking sector to the market based sector, so the marginal effect of a higher CCyB on marketbased finance is to increase its growth rate (𝜙𝑠𝑀 > 0). This increases the probability of a crisis originating in the market based finance sector (𝛾1𝑀 ). In addition, there is no resilience benefit from a higher CCyB working to reduce the probability of crises originating in the market-based finance sector. The overall probability of a financial crisis is equal to the sum of the probabilities in each sector, weighted by their market-share. Both sectors are subject to shocks (𝜉1𝐵 , 𝜉1𝑀 ). A single policymaker sets both instruments, the CCyB and the interest rate, to minimise the joint loss function given below under discretion.