Advanced Macroeconomics LUBS 3505 2024-2025 Lecture Notes PDF

LEEDS UNIVERSITY BUSINESS SCHOOL Advanced Macroeconomics LUBS 3505 2024-2025 Lecture 8. Monetary Policy I. MP Consensus: Three Equations Model (IS-PC-MR) Bibliog Outline - Basis o...

LEEDS UNIVERSITY BUSINESS SCHOOL Advanced Macroeconomics LUBS 3505 2024-2025 Lecture 8. Monetary Policy I. MP Consensus: Three Equations Model (IS-PC-MR) Bibliog Outline - Basis of the Consensus - Building blocks of IS-PC-MR model: - IS-Curve (IS) - Phillips Curve (PC) - Monetary Rule (MR) - Full IS-PC-MR model - Interest Rate Rule: Taylor Rule - Summary Basis of the Consensus The consensus about how to conduct monetary policy centres around the following ideas: Business cycle is demand driven, but demand effects are limited to the short-run. Monetary policy (MP) affects output in the short-run: MP intervention has real short- run effects. This is due to nominal and/or real rigidities. Non-monetary neutrality in the short-run. In the long-run MP cannot affect output, it only affects inflation: there is a supply equilibrium, due to imperfect competition in goods and labour markets, i.e. ICE or NAIRU is exogenous. Monetary neutrality in the long-run. Phillips Curve must account for expectations, either forward or backward looking: Rational Expectations The central bank (CB) sets interest rates (money is treated as endogenous) with the aim of controlling inflation. There is a lag so CB needs to be forward looking. Fiscal policy is subject to crowding-out effects and/or interferes with the CB’s aims of controlling inflation. Predominantly New Keynesian, although with some strong influences from Monetarism and New Classical economics. Building blocks. IS curve Assumptions: 1.There is a negative relationship between real output (𝑦) and real interest rates (𝑟), an IS- curve, although in this case with a time lag: 𝑟0 → 𝑦1 (1) 𝑦1 = 𝐴 − 𝑎𝑟0 Where, 𝑦1 =real income (output) in period 1. A=public and private sectors exogenous demand, 𝑟0 =real interest rate in period 0, 𝑎 > 0 is the sensitivity of 𝑦1 with respect to 𝑟0. Graphically: 𝑟−1 Mathematically, plugging 𝑦𝑒 𝑟0 into equation (1) we can find 𝑟𝑠 the level of interest rate that Stabilizing would deliver it: interest rate (2) 𝑦𝑒 = 𝐴 − 𝑎𝑟𝑠 𝑟′0 IS 𝑦1 𝑦𝑒 𝑦′1 y 2.A accounts for fiscal policy (FP), but FP plays not role in the model due to assumption of crowding-out or to avoid interfering with monetary policy targets (inflation). 3.The economy has a potential output level or equilibrium output (𝑦𝑒 ). This is the level of output where both wage-setters and price-setters make no attempt to change the prevailing real wage, i.e. the output counterpart of the ICE employment or the NAIRU. Building blocks. IS curve A useful formulation of the IS equation, is the IS output gap form. By subtracting equation (2) from (1): 𝑦1 − 𝑦𝑒 output gap or deviations of output from (3) 𝑦1 − 𝑦𝑒 = −𝑎(𝑟0 − 𝑟𝑠 ) its potential output 𝒚𝒆 , in period 1. 𝑟0 − 𝑟𝑠 difference between current interest rates (𝑟0 ) and the stabilizing interest rates (𝑟𝑠 ), i.e. necessary change in real interest rates to stabilize the economy. Key characteristics of this IS curve in output gap form: Equation (3) shows that output will be away from 𝑦𝑒 as long as interest rates differ from the stabilizing rate 𝑟𝑠 (for a given A and 𝑦𝑒 ). This equation is also illustrative of how the Central bank (CB) will operate: ― The CB will choose (in t=0) the interest rates that allows them to close the output gap (in t=1). ― There is a policy lag, because changes in interest rates in this period (𝑟0 ) do not affect output until the next period (𝑦1 ). Building blocks. Phillips Curve (PC) Assumptions: 1.Phillips curve denotes a contemporaneous, positive relationship between output and inflation including inflation expectations: 𝜋1 = 𝜋 𝐸 + 𝛼(𝑦1 − 𝑦𝑒 ) where 𝜋1 =inflation rate in period 1, 𝜋 𝐸 = inflation expectations for the following period, 𝑦1 − 𝑦𝑒 output gap in period 1, 𝛼>0: sensitivity of inflation in period 1 (𝜋1 ) to the output gap in same period (𝑦1 − 𝑦𝑒 ). Be aware alpha "𝛼” in (4) is different from “a” in (3) 2.Inflation expectations are equal to inflation in previous period: 𝜋 𝐸 =𝜋0 = 𝜋𝑡−1. Hence, substituting 𝜋 𝑒 =𝜋0 in our initial PC, we obtain an inertial Phillips Curve: (4) 𝜋1 = 𝜋0 + 𝛼(𝑦1 − 𝑦𝑒 ) Two justifications to use inertial PC: i) Adaptive expectations with coefficient for error correction term=1. ii) Inertia in setting prices and/or wages, i.e. they are sticky. Graphically: PC (𝜋 𝐼 = 4) Family of PC depending on past inflation or 𝜋 𝑉𝑃𝐶 PC (𝜋 𝐼 = 2) inertial inflation 𝜋 𝐼. ∆𝜋 > 0 Upward sloping PC, 𝛼>0 and in terms of 𝜋=4 PC (𝜋 𝐼 = 0) output (Aggregate Supply). Hence: ∆𝜋 < 0 ―Positive output gap (𝒚𝟏 > 𝒚𝒆 ) inflation 𝜋=2 rises, ∆𝜋 > 0. (unemploymentNAIRU) 𝑦1 𝑦𝑒 𝑦1 y Building blocks. Monetary Policy Rule (MR) Assumptions: 1. There is a policy lag as follows: Period 0, t=0 𝜋0 𝑦0 𝑟0 From the PC curve: From IS curve: (4) 𝜋1 = 𝜋0 + 𝛼(𝑦1 − 𝑦𝑒 ) (1) 𝑦1 = 𝐴 − 𝑎𝑟0 𝜋1 𝑦1 Period 1, t=1 Consequently, the Central Bank setting 𝑟0 cannot affect inflation directly, but it can affect inflation via the influence of real interest rates on future aggregate demand. 2.Central Bank is assumed to set nominal rates in t=0 (𝑖0 ), but since the inflation rate in t=0 is predetermined, by setting nominal interest rate the central bank is choosing the real interest rates at which it wants the economy operates: 𝒓𝟎 = 𝒊𝟎 − 𝝅𝟎 Why is inflation in t=0 predetermined? As per the PC, inflation in t=0 (𝜋0 ) depends on output in t=0 (𝑦0 ) and past inflation (𝜋−1 ), both of which are predetermined or given (the central bank cannot modify them), hence inflation in t=0 is also predetermined. Building blocks. Monetary Policy Rule (MR) 3.It is assumed that the CB has two concerns: inflation (𝜋) and output (𝑦) and that it wishes to minimize fluctuations away from its inflation target (𝜋 𝑇 ) and potential output (𝑦𝑒 ). 4.This behaviour is characterized by assuming that the central bank tries to minimize the loss function (L) that would arise from deviations from the inflationary target and potential output: (5) L=(𝑦1 − 𝑦𝑒 )2 +𝛽(𝜋1 − 𝜋 𝑇 )2 ‒Deviations of output from ‒Deviations of inflation from CB’s potential level (𝑦𝑒 ) (output gap). target (𝝅𝑻 ). ‒Square denotes CB is equally ‒Square also denotes symmetric concerned by deviations above and preferences. below potential output. ‒An empirical issue! 𝜷 tells us of the relative weight of the two variables that concern the CB (next lecture): ―𝜷=1: CB attributes equal weight to output and inflation. ―𝜷>1: CB attributes more weight to inflation than output  CB is inflation averse. ―𝜷 𝝅𝑻 , it is optimal for the CB to cut output below potential output 𝒚𝟏 < 𝒚𝒆 (and vice versa). The slope of MR depends on 𝜷 and 𝜶: both alter the slope of the MR curve (next lecture). Full 3 equations model (IS-PC-MR): We can now put together the IS-PC-MR model: The CB is targeting inflation (𝜋 𝑇 ), 𝑟−1 and keeping the economy at IS-output gap form potential output (𝑦𝑒 ). (3) 𝑦1 − 𝑦𝑒 = −𝑎(𝑟0 − 𝑟𝑠 ) 𝑟𝑠 It is aware of the policy lag: 𝑟0 t=0 t=1 IS-curve 𝑦𝑒 y 𝜋1 PC 𝑦1 Inertial PC Hence, CB is constantly thinking 𝜋 (4) 𝜋1 = 𝜋0 + 𝛼(𝑦1 − 𝑦𝑒 ) forward (MPC) to check if its 𝑉𝑃𝐶 PC (𝜋 𝐼 = 𝜋 ′ > 𝜋 𝑇 ) current 𝑟0 can deliver 𝜋 𝑇 and 𝑦𝑒. MR PC (𝜋 𝐼 = 𝜋 𝑇 ) ‒ If so  no intervention. 𝜋1 = 𝜋 𝑇 + 𝛼(𝑦1 − 𝑦𝑒 ) ‒ If current 𝒓𝟎 cannot deliver 𝝅𝑻 and 𝒚𝒆  CB intervenes 𝜋𝑇 MR (change 𝑟y min its loss given (6) (𝑦1 − 𝑦𝑒 ) =-𝛼𝛽(𝜋1 -𝜋 𝑇 ) conditions). Then, CB will try to stabilise inflation and output to 𝑦𝑒 y return to 𝜋 𝑇 and 𝑦𝑒. Interest Rate Rule. “Taylor Rule” Sometimes the IS-PC-MR is summarised as an interest rate rule, popularised by Taylor (1993) as the Taylor Rule: IS: (3) 𝑦1 − 𝑦𝑒 = −𝑎(𝑟0 − 𝑟𝑠 ) 1 (7) (𝑟0 − 𝑟𝑠 ) = 1 (𝜋0 −𝜋 𝑇 ) 𝑎 𝛼+ PC: (4) 𝜋1 = 𝜋0 + 𝛼(𝑦1 − 𝑦𝑒 ) 𝛼𝛽 𝑇 MR: (6) (𝑦1 − 𝑦𝑒 ) =-𝛼𝛽(𝜋1 -𝜋 ) Interest rate Rule (Taylor Rule) See Basic Reading for calculation details Key characteristics: Eq. (7) tells us by how much the CB needs to change real interest rates, given 𝝅𝟎 ≠ 𝝅𝑻. Eq. (7) also tells us that the optimal interest rate to be set depends on the values of 𝛽, 𝛼 and 𝑎: − A more inflation averse CB (𝛽>1) will raise interest rates by more. − When the Phillips curve is steeper (𝛼 grows), the CB will raise interest rates by less (inflation is more sensitive to output). − When the IS-curve is flatter (𝑎 >1), the central bank will raise interest rates by less. Interest Rate Rule. “Taylor Rule” Whether Central Banks follow a Taylor rule/interest rate rule is unclear, but these rules can be used to evaluate actual policy: Taylor (2009) uses a Taylor Rule to evaluate US Fed’s response to the Financial crisis of 2007. Bernanke (2015) shows that a modified Taylor Rule more closely matches the actions of the US Fed’s from 1995 to 2015. Summary Basis of New Consensus in Macroeconomics (NCM): Non-money neutrality in the short-run due to nominal and/or real rigidities. Central banks set interest rates (money is endogenous) to control inflation. Phillips Curve with expectations. Only a temporary trade-off between inflation and unemployment; in the long-run we have a long-run supply equilibrium. Long-run neutrality of money  NAIRU is exogenous to demand (or ICE of employment). Fiscal policy crowds-out and/or interferes with the Central Bank’s aims. The 3 equations (IS-PC-MR) model illustrates this consensus: 𝑟−1 How to find MR? IS-output gap form (3) 𝑦1 − 𝑦𝑒 = −𝑎(𝑟0 − 𝑟𝑠 ) CB targeting inflation (𝜋 𝑇 ) and potential output (𝑦𝑒 ). 𝑟𝑠 Policy lag: t=0 𝜋 𝑦 0 0 𝑟0 y Inertial PC t=1 𝜋 (4) 𝜋1 = 𝜋0 + 𝛼(𝑦1 − 𝑦𝑒 ) 𝜋1 𝑦1 𝑉𝑃𝐶 MR PC (𝜋 𝐼 = 𝜋 ′ > 𝜋 𝑇 ) PC (𝜋 𝐼 = 𝜋 𝑇 ) Optimal problem of the CB: Min L=(𝑦1 − 𝑦𝑒 )2 +𝛽(𝜋1 − 𝜋 𝑇 )2 (5) 𝜋𝑇 MR s.t. 𝜋1 = 𝜋0 + 𝛼 𝑦1 − 𝑦𝑒 (4) (6) (𝑦1 − 𝑦𝑒 ) =-𝛼𝛽(𝜋1 -𝜋 𝑇 ) 1 Taylor Rule: (7) (𝑟0 − 𝑟𝑠 ) = 1 (𝜋0 −𝜋 𝑇 ) 𝑦𝑒 y 𝑎 𝛼+ 𝛼𝛽 Bibliography: Basic readings Carlin and Soskice (2015) Macroeconomics. Institutions, Instability and the Financial System. Ch.3 section 3.1.3 (p.92), section 3.2.1 (pp.92-97), Appendix 3.5.1 (pp.111-113 MR details); Ch.13 section 13.3.3 (pp.476-478), section 4 (pp.476-482 TR in practice) Or Carlin and Soskice (2006) Macroeconomics. Imperfections, Institutions and Policies. Preface (p.x) Ch.3.2 (pp.81-84), Ch. 5 sections 5.3 (pp.140-148) and 5.4.1 (pp.151-152) Advanced readings Carlin and Soskice (2006) Macroeconomics. Imperfections, Institutions and Policies. Ch.5 section 4.2 (pp.153-157 TR and lag structure) Other readings Taylor (1993). “Discretion versus policy rules in practice” https://www.sciencedirect.com/science/article/pii/016722319390009L Taylor (2009). “The Financial Crisis and the Policy Responses: An Empirical Analysis of What Went Wrong” NBER. WP14631 http://www.nber.org/papers/w14631 Taylor (2021). “Simple monetary rules: many strengths and few weaknesses” EJLE. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7802817/ Bernanke (2015). “The Taylor Rule: A benchmark for monetary policy?” https://www.brookings.edu/articles/the-taylor-rule-a-benchmark-for-monetary- policy/?b=1 Back