The IS, MP, and Phillips Curves + Derived Demand and Supply Framework Flashcards
National Income Accounting Identity
Yt = Ct + It + Gt + EXt – IMt
Yt = Ct + It + Gt + EXt – IMt
National Income Accounting Identity
What are the 3 approaches to measuring GDP?
- Expenditure Approach - counting all purchases
- Production Approach (value added) - Net value of goods produced in the economy
- Income Approach - Income earned in the economy
Expenditure = Production = Income
What does the IS curve capture/show?
Captures negative short-run relationship between r and y
– Interest rate increase depresses investment and lower consumption
– In turn, lower investment and consumption decreases output
How do you derive the IS curve?
- Rewrite National Income Accounting Identity to make It the subject:
It = Yt - Ct - Gt + IMt - EXt - Add and subtract tax revenues:
It = (Yt - Tt - Ct) + (Tt - Gt) + (IMt - EXt)
Investment = Private Savings + Public Savings + Foreign Savings - Each component is assumed to be a proportion of potential output:
EXt = āexȲt, IMt = āimȲt, Gt = āgȲt,
Ct = āc - bc[Rt-β]Ȳt - If these components are smooth, then GDP volatility must depend on Investment:
It/Ȳt = āi - bi(Rt - r)
(Where Rt = Real interest rate and r = MPK) - Divide national income accounting identity by Ȳt and substitute component assumptions:
Yt/Ȳt = āc - bc[Rt-β] + āi - bi(Rt - r) + āg + āex - āim - Condense all a components into a single a bar and (Yt/Ȳt) -1 becomes Ỹt:
Ỹt = ā - bc[Rt-β] - bi(Rt - r)
What does the - bc[Rt-β] component of the IS curve represent/show?
Short-run output fluctuations depend negatively on the gap
between real interest rate and discount factor
What does the - bi(Rt - r) component of the IS curve represent/show?
Short-run output fluctuations depend negatively on gap between real interest rate and MPK
What does the a bar component of the IS curve represent/show?
Captures aggregate demand shocks
Changes in sensitivity of expenditure to potential output
Describe the IS curve
A downwards-sloping straight line with gradient -1/b = -1/(bc+bi)
If b increases, what happens to the IS curve?
- Higher sensitivity of It or Ct to interest rate
- Gradient decreases in slope by pivoting about the point (0, r)
Suppose information technology improvements create an
investment boom. What will happen to the IS curve?
The ai parameter increases so a overall increases. This shifts the level of output higher for any given level of R so the IS curves shifts rightwards
This is true for any shock which affects an a component
How do different central banks control interest rates?
The Bank of England sets the ‘Bank Rate’ which is the interest rate on reserve balances
The Federal Reserve sets the ‘Federal Funds Rate’, the interest rate paid on an overnight loan
The European Central Bank sets the main refinancing operations rate which is the rate on weekly ECB loans
Fisher Equation
it = Rt + πt
Nominal interest rate = Real interest rate + Inflation rate
it = Rt + πt
Fisher Equation
Why does the Fisher Equation show how the Central Bank controls R?
Rearranged to Rt = it + πt, and assuming that inflation is sticky (as in acts very slowly), changing nominal interest rates has a direct short-run effect on real interest rates
Describe the MP curve
A perfectly horizontal line which intersects the R axis at r (nominal interest rates)
What would happen to the IS curve if there was a sharp fall in house prices and how might the central bank respond?
A sharp fall in prices is a negative aggregate demand shock.
The IS curve will shift leftwards, reducing Ỹ.
The central bank will respond by lowering nominal interest rates (the MP curve will shift downwards) so that the IS and MP curves again intersect at Y0
What equation do firms (essentially) use to set their prices?
πt = Etπ(t+1) + vỸt
Current Inflation = Expected inflation + Demand conditions
πt = Etπ(t+1) + vỸt
The equation which firms essentially use to set their prices
Backward-looking Inflationary Expectations Equation
Etπ(t+1) = π(t-1)
Etπ(t+1) = π(t-1)
Backward-looking Inflationary Expectations Equation
Phillips Curve
πt = π(t-1) + vỸt
( Δπt = vỸt )
πt = π(t-1) + vỸt
( Δπt = vỸt )
Phillips Curve
What is the NAIRU?
The Non-Accelerating Inflation Rate of Unemployment
Okun’s Law
ut - ũt = - (v/α)Ỹt
Short-run output is greater when cyclical unemployment is low
How do Okun’s Law and the concept of a NAIRU relate to the Phillips Curve?
Okun’s Law can be combined with Phillips Curve to integrate an ‘unemployment gap’ into the curve
πt = π(t-1) - α(ut - ũt)
How can temporary shocks be shown on the Phillips Curve?
Shocks are shown as extra components which contribute negatively or positively to the rate of inflation e.g.
Oil price shock raises oil prices –>
Δπt = vỸt + ot
Here the Phillips Curve shifts vertically upwards
Generalised Consumption Equation
Ct = (āc - bc[Rt-β])Ȳt + ꭓ(Yt - Ȳt)
Where ꭓ ∈ (0,1)
Normal consumption plus some multiple (ꭓ) of the output gap
Ct = (āc - bc[Rt-β])Ȳt + ꭓ(Yt - Ȳt)
Generalised Consumption Equation
IS Curve with Multiplier
Ỹt = (1/(1-ꭓ)){Ỹt = ā - bi(Rt - r) - bc[Rt-β] }
Condensed into…
Ỹt = â - b̂i(Rt - r) - b̂c[Rt-β]
Where â ≡ ā/(1-ꭓ) and similarly for bi and bc
IS Curve
Ỹt = ā - bi(Rt - r) - bc[Rt-β]
Ỹt = ā - bi(Rt - r) - bc[Rt-β]
IS Curve
Ỹt = â - b̂i(Rt - r) - b̂c[Rt-β]
IS Curve with Multiplier
How do the two rounds of a shock work with the multiplier?
Positive demand shock
1st round effect - Increase short-run output for a given value of Ct
2nd round effect - Consumption increases because Ct depends on Ỹt (which has increased)
Result: Ỹt increases by more than the initial shock
What were the trade offs of Volcker’s disinflation push in the late 1970s?
- Economy fell into recession
- Unemployment increased
- Reduced output
BUT
+ Much less costly than expected
+ Brought inflation under control
LM (liquidity money) Curve
Mt/Pt = L(Ỹt,Rt)
Real balances depend positively on
short-run output and negatively on real interest rate
Mt/Pt = L(Ỹt,Rt)
LM (liquidity money) Curve
Describe the LM Curve
A straight line which slopes upwards from left to right in Ỹt,Rt space
Why have central banks chosen to control it instead of Mt?
Money demand is subject to volatility many shocks and nominal interest rates are easier to control
When CB targets it, Mt absorbs money demand shocks which leads to less macroeconomic instability
What is the Taylor Principle?
Monetary policy is stabilizing when the nominal interest rate is higher than the increase in inflation
it = Φπt where Φ > 1 (nominal interest rule)
Combined Fisher and Nominal Interest Rule Equation
Rt = (Φ-1)πt
If Φ < 1, monetary policy response is destabilised
Rt = (Φ-1)πt
Combined Fisher and Nominal Interest Rule Equation
Inflation-Targeting MPR
Rt - r̄ = ψ(πt - π bar) where ψ>0
Coefficient ψ controls CB’s response to inflation deviations
If πt > π bar, then set Rt > r̄ (and vice versa)
Rt - r̄ = ψ(πt - π bar)
Inflation-Targeting MPR
How is the AD curve derived form the IS and Inflation-Targeting MPR curves?
Using the Inflation-Targeting MPR curve, substitute Rt - r̄ into the IS curve Ỹt = ā - b(Rt - r̄) [assuming that r̄ = β]
AD: Ỹt = ā - bψ(πt - π bar)
Ỹt = ā - bψ(πt - π bar)
AD Curve (derived from IS and MP curves)
Taylor Rule Equation
it = ī + (1+ψ)(πt - π bar) + ΦỸt
BoE and Fed set bank rate and FFR using this equation
it = ī + (1+ψ)(πt - π bar) + ΦỸt
Taylor Rule Equation
Dual-Mandate MPR
Rt - r̄ = ψ(πt - π bar) + ΦỸt
Rt - r̄ = ψ(πt - π bar) + ΦỸt
Dual-Mandate MPR
How is the AD curve derived form the IS and Dual-Mandate MPR curves?
Using the Dual_Mandate MPR curve, substitute Rt - r̄ into the IS curve Ỹt = ā - b(Rt - r̄) [assuming that r̄ = β]
AD: Ỹt = ā/(1+bΦ) - (bψ/1+bΦ)(πt - π bar)
Ỹt = ǎ - b̂ψ(πt - π bar)
Describe the behaviour of the dual-mandate AD curve
If b̂ < b, the dual mandate AD curve has a steeper gradient than the inflation-targeting curve (and vice versa)
How is the AS curve constructed in the AS-AD framework?
The Phillips Curve (with a cost-push shock +ot) is representative of the AS curve
πt = πt-1 + vỸt + ot
Short-run equilibrium is found where the AS and AD curves are equal. What are
Ỹt = â - b̂ψ(πt-1 - π bar + ot)
And
πt - π bar = vâ + (1 - vb̂ψ)(πt-1 - π bar + ot)
Where
â ≡ ā/(1+bψv) and b̂ ≡ b/(1+bψv)
Adaptive Expectations Equation
Et[πt+1] = πt-1
Motivated by inflation sluggishness
Et[πt+1] = πt-1
Adaptive Expectations Equation
Rational Expectations Equation
πt = Et[πt+1] + vỸt
πt = Et[πt+1] + vỸt
Rational Expectations Equation
If the central bank announces a lower inflation target, what will expected inflation be with rational expectations?
Et[πt+1] = π^1 < π^0
What are rational expectations and what is beneficial about them?
With rational expectations, the private sector uses all available information to best forecast all variables of interest
It’s beneficial because you get costless disinflation (without output downturn and higher unemployment)
