Term 2 Week 7: 3-equation model Flashcards
How can we explain what the Central Bank is trying to do with the 3 equation model (3)
-The central bank is trying to achieve its preference, mainly minimising the loss function
-The constraint stopping CB’s from achieving this preference is demand shock
-The CB translates its objectives into monetary policy through the Phillips Curve and Monetary Rule
What are the transmission channels of monetary policy with adaptive expectations (6,1)
-Start with inflation at target
-Then a negative (positive) demand shock occurs
-The CB then lowers (raises) the policy rate
-Output and inflation adjust
-The CB then gradually raises (lowers) the policy rate
-Over time, output returns to equilibrium and inflation to target
-This step by step adjustment process only occurs with adaptive expectations
Why do we dislike deflation (5)
-Consumers delay spending (expecting prices to fall in the future, lowering AD and EG)
-Real interest rate problems (deflation leads to higher real interest rate, lowering AD and EG)
-Zero lower bound problem (CB has a ZLB for nominal IR, so deflation hurts fighting recessions)
-Increase in real debt burden
-Labour market rigidity (nominal wages sticky downwards, falling prices lead to higher real wages, more costly hires and increasing unemployment)
What is the minimum real interest rate (4)
-When responding to economic shocks, the CB changes nominal interest rates (i), which then affect real interest rates (r), affecting AD through the IS relation
-To do this, we must take into account expected inflation, as shown in the fisher equation I = r + πE
-The CB responds to falling inflation by lowering the interest rate, but the ZLB means the lowest the nominal interest rate can go is 0
-With a ZLB, the lowest real interest rates can go = r ≥ -πE
How can we diagramatically analyse a deflation shock (1,5,6,1,1)
-Start at A, the central banks bliss point with ye, πT and rs
-Suppose there is a large negative AD shock, shifting IS to IS’ and creating negative inflation as we move to point B, with output y0, interest rate rs and inflation π0
-The CB then forecasts the PC for the next period, shifting outwards to PC(π1E = π0) to represent the fall in inflation
-Ideally, the CB would like to locate at C’ (y’1 > y0</sub, r’0 < 0), where PC(π1E = π0) = MR
-However, this requires an interest rate below the minimum real interest rate, the lowest they can achieve is r0 = -π0 (which is positive)
-The economy ends period 0 with y0, π0, r0
-The new IR boosts investment in period 1, increasing output and moving the economy to point C (expansion on IS curve), where output = y1
-However, this new output level is still below the CB’s best reponse level of y1 (where the MR curve hits the new PC curve)
-This causes inflation to fall further to π1, shifting the PC further downwards to PC(π2 E = π1)
-With this PC, the CB would want to locate at D’, but can;t as this needs interest rate r1’
-Therefore, the lowest real IR they can set is now higher, at -π1
-Period 1 ends with output y1, inflation π1, interest rate r1
-In period 2, the economy moves to D, as the higher IR dampends demand, reducing output to y2 and inflation to π2
-The economy has thus entered a deflation trap, as both output and inflation are constantly falling and conventional monetary policy is powerless, catching the economy in a viscous cycle
Does every negative AD shock lead to a deflation trap (2)
-No, not every -ive AD shock leads to a deflation trap.
-The assumption for one is being restricted at the ZLB due to a big enough shock to create negative inflation
What are the equations for the 3 equation model (3)
-Dynamic IS curve: yt = At - art-1
-(AE) PC curve: πt = πt-1 + a(yt - ye)
-Monetary Rule: (yt - ye) = -aβ(πt - πT)
How do we change the Phillips curve if we use rational instead of adaptive expectations (2)
-If wage and price setters use rational expectations, then for expectations of inflation to be fufilled, output must be at equilibrium
-The PC equation then becomes: πt = πT + a(yt - ye)
How does assuming rational expectations instead of adaptive change the IS curve (2)
-By assuming rational expectations behaviour, it is clear that the CB must set the real interest rate at the start of period t to deliver yt = ye
-This implies the IS curve must take the form: yt = At - art
How do adaptive vs rational expectations change when the central bank eliminates the inflation bias (2,2)
-With adaptive expectations, if they reduce their inflation target from π0 to πT, there will be a contraction on the PC(πt E = π0), as the MR curve shifts inwards to MR’, as the CB raises the interest rate to minimise their loss function
-It will take a number of periods of active adjustment (PC shift out to ye, expansion on MR’) to reach equilibrium
-With adaptive expectations, if they reduce their inflation target, the MR curve will shift inwards to MR’
-In the next period, the economy will instantly jump from A to Z, causing the desired disinflation with no adjustment period as the PC jumps from old to new equilibrium straight away
How does the 3 equation model change with rational expectations (3,1,1)
-The economy is at equilibrium output with inflation at target, apart from shocks
-The dynamic behaviour of the economy in response to shocks disappears
-Inflation is not built into the system, and thus there is no costly disinflation
-The CB has a simpler job, as they don’t need to take account of lags in the response of AD to its IR decisions (in the IS model)
-Since wage/price setters are forward looking, the CB can influence expectations directly, as opposed to actual inflation having to fall with AE before influencing expected inflation
What is the difference between rational and adaptive expectations for costless disinflation (2)
-Rational expectations have costless disinflation, with no unemployment rise
-Adaptive expectations haven’t got costless disinflation, as unemployment is above equilibrium for some periods
How can we anchor expected inflation (2)
-The expected inflation in the standard PC can be modified to make the equation for partially anchored expectations as πEt = χπT + (1-χ)πt-1
-χ is the credibility or weight on the inflation target (0-1, 0 = adaptive, 1 = rational)
How could we add anchored inflation to the standard PC (1,3)
-The PC could be written as: πt = [χπT + (1-χ)πt-1] + a(yt + ye0
-If the CB is fully credible, χ = 1, and the PC would reduce to the pure rational expectations formula (firmly anchored)
-If χ = 0, the equation would reduce to the pure adaptive expectations formula
-χ can be anywhere between 0-1, representing partial anchoring
What are the drivers of CB credibility (2)
-Transparency and communication
-Independence
