Term 2 Week 5-6: Monetary Rules Flashcards
What are tools for monetary rule (2)
-The central banks loss function (a quadratic equation)
-The Phillips curve as a constraint
Why don’t we like inflation (6)
-Erodes savings
-Discourages investment
-Stimulates capital flight
-Inhibits growth
-Difficult to make economic plans
-Provokes social and political unrest
Why is monetary policy > fiscal policy to stabilise the economy (3)
-The central bank isn’t impacted by politics/election manipulation like the government is
-MP is easy to implement
-MP won’t lead to budget deficits
Why is price stability explicitly recognised as a quantitative target (2)
-There is public announcement of a quantitative target (Rational Expectation Hypothesis), and accountability/transparency if it is not met
-MP is based on a wide set of information, including forecasting
What does the 3 equation model consist of (3)
-The IS curve (goods market equilibrium)
-The PC curve (unemployment-inflation relationship)
-The MR curve (how the CB responds to inflation)
What is an active rule-based MP (1)
-The best response real interest rate (r) to achieve the inflation target
How do we derive the monetary rule (4)
-Define the Central Bank’s preferences in terms of deviations from the inflation target and equilibrium output
-Define the CB’s constraints from the supply side (PC)
-Derive the best response monetary rule in the output-inflation space, giving the MR curve
-Once the optimal output-inflation combination is determined using the MR, the CB uses the IS curve to implement its choice (by setting the IR)
What is the CB’s loss function (3)
-L = (yt - ye)^2 + β(πt - πT)^2
-The function represents the tradeoff in preferences between inflation being away from target and output away from equilibrium
-The higher the loss, the worse off the CB
What does β mean in the CB’s loss function, and what are the implications of the components (3, 2)
-β represents the relative degree of inflation aversion by the CB
-if β = 1, output and inflation deviations are treated the same
-If β < 1, the CB is more aversed to output deviation than inflation deviation
-The CB is concerned as being above their target/output gap as below
-The function is convex (increasing as deviation increases)
How to draw the loss function and what does the value of β mean (3,2)
-y on the x axis, π on the y axis
-The Loss functions are circles going out from the bliss point (Ye and πT)
-Any point on the same curve represents the same value for the loss function (similar mental concept to indifference curve)
-if β < 1 (unemployment curve), the curves will be more steep,
-If β >1 (inflation averse) the curves will be more flat (lower inflation aversion means its less valuable for the CB than an OG)
How can we add the PC to the loss curve diagram, and what assumptions are made (2,2)
-The PC is a constraint for the CB because it shows all the output and inflation combinations which can be chosen for a given level of expected inflation
-Each phillips curve is labelled by a given level of expected inflation (for adaptive exp, expected PC = lagged inflation)
-Assume α = 1, so the gradient = 45 degrees
-Assume expected = target = lagged inflation, so the CB can start off at bliss point A
How does the Phillips curves react to an inflation shock (4)
-An inflation shock will lead to the PC’s continually shifting up (current inflation = lagged + output gap)
-These shifts mean the bliss point is no longer attainable
-The CB must face a trade-off, on whether to accept an inflation rate above target, or to accept an output gap
-The new point chosen will be where the PC is tangent to a loss function curve
What is the MR curve, and what can we tell from the equation (1,4)
-yt - ye = -αβ(πt - πT)
-α is the slope of the phillips curve, the sensitivity of inflation to the output gap
-β is the loss preference of the central bank, the relative degree of inflation aversion
-The higher the value of α, the steeper the Phillips curve (less deviation in output = higher effect in inflation), and this makes the MR flatter (any given cut in output has a greater effect in reducing inflation)
-The higher the value of β, the flatter the loss curves, and this makes MR flatter as the gaps between the PC are bigger
How do we derive the equation for the MR curve (1, 5)
-The equation for the MR curve is yt - ye = -αβ(πt - πT)
-The central bank chooses y to minimise the loss functon (y1 - ye)^2 + β(πt - πT)^2
-This is subject to the phillips curve π1 = π0 + α(yt - ye)
-If we substitute the phillips curve into the loss function we get L = (y1 - ye)^2 + β((π0 + α(y1-ye) - πT)^2
-If we now differentiate this with respect to y1 (the variable the CB can control via its IR choice) we get (y1 - ye) + αβ = (π0 + α(y1-ye) - πT)
-Rearranging the Phillips curve to find π0 and subbing it back into the equation gives us y1 - ye = -αβ(πt - πT)
What would the CB prefer in terms of PC and MR curves (2)
-Steeper Phillips curves and flatter MR curves are better for the CB
-This is because a smaller rise in unemployment is required to achieve any fall in inflation
What is the Taylor principle (3)
-The Taylor Principle is the fact that the CB sets the nominal IR to achieve a particular real IR on the IS curve
-The CB only controls the nominal IR, but IS curve cares about real, and Fishers equation states it = rt + πt (nominal = real + inflation)
-The nominal IR has to be raised sufficiently to change the real
What are the real and nominal equations for the Taylor’s principle (4,3,1)
-rt - rs = γ1 (πt - πT) + γ2(yt - ye)
-The real IR in period t - real IR at equilibrium = inflation weight (inflation in period t - target) + output weight (output gap)
-The gamma coefficients will vary depending on the relative weight the CB assigns to stabilising inflation/output deviations
-it = ī + δ1(πt - πT) + δ2(yt - ye)
-the nominal interest rate in period t = nominal IR at equilibrium + inflation weight (inflation in period t - target) + output weight (output gap)
delta one and two will be higher than gamma one and two (nominal ir > real)
What is the central banks dynamic adjustment to an inflation shock (6)
-Start at medium run equilibrium with taregt inflation
-positive inflation shock occurs
-CB raises the IR
-Output and inflation fall
-CB gradually decreases IR
-Output and inflation gradually rise to target
How to diagramatically analyse the dynamic adjustment to an inflation shock (3,3,1)
-Start off with the 3 equation model in equilibrium, with the IS curve at output ye and real IR rs on one graph, and the MR curve and PC(π0E = πT) at output ye and inflation πT
-An inflation shock causes the PC to shift up to PC(π1E = π0), causing a movement on the MR curve which then causes a contraction on the IS curve
-Period 0 will end at output ye, inflation π0, IR at r0
-In period 1, there will be a movement on PC(π1E = π0), to the point where it equals the MR curve.
-From this point, you then shift the PC curve outwards to equilibrium output at this π1 level of inflation, to represent the change in inflation expectations caused by the decline in interest rates to r1
-Period 1 will end at output y1, inflation π1 and interest rate r1
-The PC will continually shift downwards, causing expansions on the IS curve and MR curve until output, interest rates and inflation return to target
How to diagramatically analyse the impulse response functions to an inflation shock (1,3)
-Have 3 diagrams ontop of eachother, all with time on the x axis, one with π, one with y and one with r on the y axis
-For the π diagram, at the time of the shock π rises from πT to π0, then slowly declines back to πT convexly
-For the y diagram, at the time of the shock y falls from ye to y1, and slowly rises back to ye concavely
-For the r diagram, at the time of the shock, r rises from rs to r0, then slowly declines back to rs convexly
How to diagramatically analyse the impact of a positive AD shock (1, 4, 3, 1)
-Start off with the IS curve at ye and rs, and the MR and PC (πE0 = πT)
-The positive AD shock will shift the IS curve outwards, placing the economy at point B, which is at output y0 and rs
-Point B causes a movement on the PC curve, thus leading to higher inflation π0
-The CB thus sees this higher inflation and forecasts the new higher PC at PC(πE1 = π0), and thus raises the interest rate to r0
-Period 0 is ended with inflation π0, output y0 and interest r0
-Once period 1 starts, the economy moves to point C, the intersection between PC(πE1 = π0) and the MR curve
-With output below equilibrium at y1, and inflation above at π1 (but lower than π0), the CB forecasts an outwards shift of the PC, thus causing a lowering of interest rates to r1
-Period 1 then ends at inflation π1, output y1 and interest r1, as the PC shifts to PC(πE2 = π1)
-This process repeats until the economy is back at equilibrium
What are the diagramatic impulse response functions to a temporary AD shock (1,3, 1)
-Have 3 diagrams ontop of eachother, all with time on the x axis, one with π, one with y and one with r on the y axis
-For the π diagram, have it raise from πT to π0 at the time of the shock, then slowly decrease in a convex manner
-For the y diagram, raise from ye to y1 at the time of the shock, then fall to y1 at period 1, then slowly rise to equilibrium
-For the r diagram, have it raise from πT to π0 at the time of the shock, then slowly decrease in a convex manner
-Period 0 is immediately after the shock, period 1 is how the economy responds to the changes in r in period 0
What are the differences between a temporary and permanent AD shock (3)
-The central bank has to forecast both the PC and IS curve, and the forecasting of the IS curve means predicting the persistence of the shock
-If the shock is permanent, the initial rise in the interest rate is much higher, as the permanent shock leads to a higher stabilising rate of inflation (r’s) in the new equilibrium
-Higher autonomous AD (improved confidence) is needed to be offset by lower interest sensitive AD (investment) to return output to equilibrium
How to represent inflation bias diagramatically (3,2,2)
-The government, ahead of an election, may raise the output target from ye to yT
-This leads to an outwards shift of the MR curve to MR’, increasing output to yT whilst keeping inflation constant at πT = 2
-The CB forecasts the PC will remain constant the next period, due to the change in output target and constant inflation, and the CB thus lowers IR to minimise their loss function and move to point B (lower output y1 < yT, inflation π = 3 > πT = 2), the intersection of MR’ and PC(π0E = πT)
-However, at point B there is pressure on inflation to change, and inflation has risen to π = 3
-Due to the change in π, PC shift up to PC(π1E = 3) and the CB optimises through a contraction on MR’ to C, where y2 < y1 and π = 3.5 > 3
-This process repeats itself until the economy reaches its new medium run equilibrium at z (ye, π = 4)
-This shows the inflation bias result and futility of governments to target an output level above equilibrium, as the only result is inflation above target
How can we mathematically derive the inflation bias with adaptive expectations (2,3,3,2)
-The Loss function the central bank now wants to minimize is L = (yt - yT)^2 + β(πt - πT)^2
-This is subject to the Phillips curve: πt = πt-1 + a(yt - ye)
-Minimising the CB loss function s.t the PC implies the FOC (sub PC into LF via πt):
-yt - yT = -βπ(πt - πT) = 0
-The new MR is thus yt - yT = -aβ(πt - πT)
-Since equilibrium requires there is no pressure on inflation to change, it must be yt = ye and πt = πt-1
-Subbing this into the MR gives us ye = yT - aβ(πt-1 - πY)
-πt = πt-1 = πT + (Yt - ye)/aβ
-In equilibrium, inflation will exceed target by (yT - ye)/aβ
-This is called the inflation bias
How is inflation bias under rational expectations (3,1)
-The new MR is yet again yt - yT = -aβ(πt - πT)
-Under RE πt = πEt when yt = ye
-Subbing this into the MR yet again gives us πt = πE = πT + (Yt - ye)/aβ
-The determinants of inflation bias are the same as before
What are the determinants of inflation bias (2)
-The steeper the CB’s MR (less inflation averse, lower β), the greater the inflation bias
-The less responsive inflation is to changes in output (a), the greater the inflation bias
How can we mitigate inflation bias (3)
-Commitment (optimal contracts between CB and government)
-Delegation (independent CB with more inflation aversity than government)
-Reputation building
