ECON 130: Controlling Interest Rates and IS-RR-PK Model

• ECON 130 Macroeconomics Lecture Note 9
• IS-RR-PK

Controlling Interest Rates

• Norges Bank uses different interest rates for short-term deposits from and loans to banks.
• Key rates include the deposit rate, reserve rate, and D-loan rate.
• These rates form a floor and ceiling for money market rates, particularly for short-term interbank loans.
• Short-term interest rates are directly controlled, while longer-term rates are influenced by expectations of future short-term rates.

Impact of Policy Rates on the Economy

• Several channels through which policy rates affect the economy:
• Consumption channel
• Investment channel
• Aggregate demand channel (sum of consumption and investment)
• Net export channel (via exchange rates)
• Expectations channel.

IS-RR-PK Model

• IS-LM, IS-MP, and IS-RR models are compared.
• IS summarizes the Keynesian multiplier model.
• LM represents traditional interest rate policy with a focus on managing the money supply.
• MP involves the central bank directly controlling the interest rate.
• RR sees the central bank managing interest rates based on a specific interest rate rule.

Closed Economy Assumption

• The chapter focuses on a closed economy.
• The exclusion of exchange rates limits the analysis of interest rate impact.

IS Equation Breakdown

Equation 9.1

• Y = C + I + G (Aggregate Demand)

Equation 9.2

• C = z^c + c1(Y - T) - c2(i - π^e)
• Consumption function where 0 < c1 < 1 and c2 > 0.
• Consumption depends autonomous consumption, disposable income, and real interest rate.

Equation 9.3

• I = z^I + b1Y - b2(i - π^e)
• Investment function where 0 < b1 < 1 and b2 > 0.
• Investment depends on autonomous investment, income, and real interest rate.

Equation 9.4

• T = z^T + tY
• Tax function where 0 < t < 1.
• Taxes depend on autonomous taxes and income.

Equilibrium Output

• Equation (9.5) expresses equilibrium output (Y) in terms of autonomous spending, the real interest rate, and government spending.

Change in Output

• Equation (9.6) shows how a change in the interest rate impacts output, with the change in output being negative.

Understanding the IS Curve

• Equations 9.5. and 9.6. are the solution to the Keynesian demand-side model
• It is possible to derive a curve by indentifying Y for every i
• An IS Curve Formula requires rearranging equation 9.5 so that interest rates (i) are on the left side.

Shifts in the IS Curve

• Shifts in the IS curve result from changes in variables not on the axes.
• Equation (9.7) defines the IS shift

Interpretation of IS Curve

• The IS curve is referred to as an aggregate demand curve in macroeconomics.
• Represents a macroeconomic demand curve, but differs from a standard microeconomic demand curve.
• Higher interest rates make future spending relatively cheaper, which reduces current aggregate demand.

Phillips Curve

Equation 9.8

• π = π^e + β(Y - Y^n)/Y^n + z^π
• Phillips curve equation where β > 0
• Inflation depends on expected inflation, the output gap, and a supply shock.

Aspects of Inflation

• Without inflation shocks, inflation equals expected inflation when output equals potential output.
• Expected inflation is assumed to be exogenous, guided by the inflation target
• If deviations from the inflation target are large, its credibility may erode, leading to more adaptive expectations.

IS-PK Model

• The text mentions the positive demand shock shifts the IS curve to the right

Effectiveness of Interest Rate Policy

• 1 percentage point interest rate cut reduces inflation by 0.3% and increases the GDP by 0.6%, but this effect is temporary.
• Implies a limited impact of interest rate adjustments when interest rates approach zero.

RR (Interest Rate Rules)

• Questions the effectiveness of simply fixing economic problems and choosing a point D
• Central banks typically use a gradual approach due to uncertainty.
• Empirically, central banks use interest rate rules to guide their behavior.
• Poses the question of wether holding back on intrest rate cuts makes sense

Taylor Rules

Equation 9.11

• i = r + π + d1(π - π*) + d2(Y - Y^n)/Y^n
• One version of taylor rule

Equation 9.13

• i = 0.01 + 1.5π + 0.5(Y - Y^n)/Y^n
• Another version of taylor rule

Equation 9.10

• i = z^i + d1(π - π*) + d2(Y - Y^n)/Y^n
• Another version of taylor rule, which is a general form of the Taylor rule expressing the policy interest rate.

RR Curve

• RR curves take Equation 9.10 as the base, while using a constant term instead of neutral interest rate, which makes it more transparent
• RR re-writes the interest-rate rules by leveraging the Phillips Curve to see how inflations happen and allow calculations backwards

RR Curve Slope

• Equation (9.14) Describes the RR curve slope

Interpreting the RR Curve

• An increase in GDP creates a positive GDP gap
• High intrest rate via two cannels
• The central bank will increase interest rates to mitigate any GDP gap
• GDP pressure boosts inflations, which results in the central bank boosting the intrest rates

Equilibrium

• Mentions Figur 9.6 Likevekt i IS-RR-PK-modellen
• Mentions Figur 9.7 Inflasjonen i likevekt

Increased Optimism

• Mentions Figur 9.8 Økt optimisme gir høyere BNP og høyere rentenivå.
• Mentions Figur 9.9 Økt BNP gir høyere inflasjon

Tighter Fiscal Policy

• Figur 9.10 Strammere finanspolitikk gir lavere BNP og lavere rente.

Cost Shocks Examples

• Oil price shock in the 1970s.
• China shock of the 2000s.
• Oil price shock leading up to 2014.
• COVID-19 supply chain disruptions in 2021-2022.
• The Ukraine war (2022-2025 implications).

Flexible Inflation Management

• Addresses whether to prioritize inflation or production gap control
• Figur 9. 11 Cost- Push shock, where the central banks must choose an OK inflation or reduced BNP

Economic Intervention

• Central Bank response to such shocks via economic intervention
• Figur 9.12 Cost shock gives lower BNP and higher interest rates