Setting interest rates is among the most consequential decisions a central bank makes -and one of the most contested.To make the trade-off between price stability and full employment transparent, central banks from Frankfurt to Mumbai have at various times turned to simple rules that link the policy rate to current inflation, an inflation target, and the gap between actual and potential output.The mechanical clarity is appealing, but the coefficients on each term embed value judgements about the central bank’s response.
The rule below, and the questions that follow, examine how those judgements shape outcomes.
A central bank uses the following rule to set its interest rate:
i = r* + π + 0.5(π − π*) + 0.5(y − y*)
where
i = nominal interest rate,
r* = long-run real interest rate,
π = current inflation,
π* = inflation target,
y = current real output,
y* = potential output,
(y − y*) = the output gap.
For all parts of this question, assume the following values for the central bank’s economy:
r* = 2%
π* = 2%
π = 5%
(y − y*) = − 1% (output is 1 percentage point below potential)
a) A second economy is identical except that its output is 2 percentage points above potential rather than 1 percentage point below.
By how many percentage points does the rule prescribe a higher policy rate in this second economy compared with the first? (2 marks)
b) The Taylor Principle states that a central bank must raise nominal rates by more than one-for-one with inflation to achieve real tightening. Does raising the coefficient from 0.5 to 1.5 satisfy the Taylor Principle? Why/why not? (2 marks)

设定利率是中央银行所做的最具深远影响的决策之一，也是最富争议的决策之一。为了使物价稳定与充分就业之间的权衡关系更加透明，从法兰克福到孟买的中央银行都曾诉诸于简单规则，将政策利率与当前通胀、通胀目标以及实际产出与潜在产出之间的缺口挂钩。这种基于公式的清晰性颇具吸引力，但其中每一项的系数都内含着对央行应对方式的价值判断。下文给出的规则以及随之而来的问题，旨在考察这些价值判断如何塑造政策结果。一家中央银行使用以下规则设定其利率：
i = r* + π + 0.5(π − π*) + 0.5(y − y*)
其中：
i = 名义利率
r* = 长期实际利率
π = 当前通胀率
π* = 通胀目标
y = 当前实际产出
y* = 潜在产出
(y − y*) = 产出缺口
对于本题的所有部分，假设该央行所在经济体的取值如下：
r* = 2%
π* = 2%
π = 5%
(y − y*) = − 1%（产出低于潜在产出 1 个百分点）
a) 第二个经济体与上述经济体完全相同，唯一区别是其产出高于潜在产出2 个百分点，而非低于潜在产出 1 个百分点。根据该规则，第二个经济体的政策利率应比第一个经济体高出多少个百分点？（2 分）
b) 泰勒原则（Taylor Principle）指出，央行要实现实际紧缩，必须将名义利率的升幅设定为高于通胀的升幅（即名义利率上调幅度要超过通胀上升幅度）。将系数从 0 .5提高到 1.5 是否满足泰勒原则？为什么？（2 分）