Dynamic Model of Economic Fluctuations Flashcards
How is monetary policy expressed in this dynamic model?
Monetary policy is expressed as a nominal interest rate. (rather than money supply as usual)
e.g in inflationary periods, respond with higher interest rates, as opposed to reducing money supply.
Notation within the dynamic model
We are discussing time periods so many have t or t-1 or t+1 added.
e.g Yt-1or
πt represents change in price level (inflation) between period t-1 and t
When are expectations operators needed?
For forward looking variables
e.g EtYt+1 (expected output in period t+1)
The t in the Et defines the information available when the expectation is formed.
Equation 1 refers to the demand side (G&S)
state which variables are endo/exogenous
(there are 5 equations in the dynamic model)
Exo - determined outside of model so taken as given
Endo - explained by the model
Yt = Ybart - a(rt - p) + εt
Yt= output (endo)
Ybar=Natural level of output (exo)
r=real interest rate (endo)
ε=demand shock (exo)
a and p are parameters > 0
a is demand sensitivity to a change in rt
p is the natural rate of interest
(2/5 parameters in this model)
Key Relationship in equation 1
Interest rate and demand for g&s is negatively related. (As r increases, Y falls)
What does parameter a determine within this equation?
a determines how sensitive demand is to a change in rt
(if demand for g&s goes down a lot following a rise in interest rates, then a is high/sensitive)
Relationship of demand for G&S and the natural level of output
The demand for G&S rises with the natural level of output.
Demand grows in proportion to the economy’s long run productive capacity. (I.e as living standards rise, demand rises)
Demand shock intuition
Think of it as a random variable, on average it tales a value of 0, but there is variation around this.
e.g εt>0 increase in consumer confidence
εt<0 a cut in gov spending or increase in taxes.
Interpretation of p
p is the natural rate of interest.
Why?
If εt = 0 (no demand shock) and rt=p, (interest rate=natural interest rate)
Yt=Ybart (output=natural output so we must also have the natural interest rate)
Equation 2: Fisher equation
rt = it- Etπt+1
it is nominal interest rate (endo)
rt is ex ante real interest rate
Equation 3: Phillips Curve
Also identify the endo/exo variables.
and which form of Phillips curve is used, and what explanation is used.
𝜋t=𝐸t-₁𝜋t+𝜑(𝑌t−𝑌bart)+𝑣t
𝜑 measures slope and we just use the output form of the Phillips curve. (We swapped 1/a for 𝜑
Usually adopt sticky price explanation for the short run tradeoff.
Inflation (𝜋t) and expected inflation (𝐸t-1𝜋t) are endogenous.
Vt is supply shock (exogenous)
(Vt) Supply shock for equation 3.
A random variable again, average = 0 but can fluctuate.
Vt >0 e.g oil price shock
Vt <0 tech progress or fall in world oil prices.
Equation 4: Expectations
Assume adaptive expectations.
𝐸𝑡𝜋𝑡+1 = 𝜋𝑡
Today’s expected inflation for tomorrow is just todays rate of inflation.
Equation 5: Monetary Policy Rule
𝑖t=𝜋t+𝜌+𝜃𝜋 (πt−𝜋*t) +𝜃Y(𝑌t−𝑌bart)
𝜋∗ is the central bank’s inflation target (final exogenous variable)
𝜃𝜋 - parameter representing responsiveness of nominal interest rate to inflation
𝜃𝑌 - parameter representing responsiveness of nominal interest rate to output
The central bank can control the real interest rate essentially, how?
What 2 equations are needed to derive this, and what can the final equation be used to influence (equation)
Rearrange 𝑖t=𝜋t+𝜌+𝜃𝜋 (πt−𝜋t*) +𝜃Y(𝑌t−𝑌bart)
to get
𝑖t-𝜋t=𝜌+𝜃𝜋 (πt−𝜋t*) +𝜃Y(𝑌t−𝑌bart)
Then using eq 2 and eq 4.
𝑖t-𝜋t = rt (real rate)
Then rt influences eq 1 (demand for G&S)
Importance of p in this equation
Taylors findings
If inflation is running at its target rate (πt=π*t) and output is equal to its natural level (Yt=Ybart),
𝑟t=p
(Real rate of interest=natural rate)
but in general rt≉p
Taylor rule shows us this theory it follows real data closely, except for when interest rates go below 0, the hypothetic rate will say interest rates will go below but in real life it wont happen, since banks would be paying people to borrow.
Long run equilibrium in the dynamic model assumptions (2)
No shocks (εt=vt=0)
Inflation stable (πt=πt-1) (THIS DOES NOT NECESSARILY MEAN AT 0)
Now we want to see the dynamic equilibrium (DAS=DAD)
What are the axis values for the diagram
πt y-axis (inflation)
Yt x-axis (output)
(Both endogenous)
How can we do this
Substitute out for any other endogenous variables e.g rt, it, Etπt+1
How can we derive the DAS curve?
Recall Phillips curve (eq.3)
𝜋t=𝐸t-₁𝜋t + 𝜑(𝑌t−𝑌bart) + vt
Use eq 4 (adaptive expectations),
To swap expected inflation in time t (which uses information available in time t-1) =inflation in t-1.
𝜋t=𝜋t-1 + 𝜑(𝑌t−𝑌bart) + vt
How to plot DASt, and what causes a shift in DAS? (3)
Upward sloping.
Changes in
πt-₁
Ybart
vt
Dynamic AD (DADt)
Yt = Ybart - [𝛼𝜃𝜋/1+𝛼𝜃𝑌] (πt-πt*) + [1/1+𝛼𝜃𝑌]εt
Complicated, we need 4 of the 5 equations to derive this DAD curve
Why is DAD downward sloping?
What causes a shift in DAD (3)
High inflation induces increased interest rate. Reducing demand for G&S
Shift are caused by changes in
Ybart (natural level of output)
π*t (inflation target)
εt (demand shock)
Draw diagram pg15.
When does Yt=Ybart , Yt>Ybart, Yt<Ybart
use DAD formula to confirm… also use common sense
Yt=Ybart if inflation=inflation target, or demand shock=0
Yt>Ybart if inflation<inflation>0 (inflation less than target so we buy more)</inflation>
Yt<Ybart>inflation target or if demand shock<0</Ybart>
basically demand more if inflation is lower than what is targeted, since cheaper than what it should be. vice versa
How can this model be used?
See the effect of changes in the 4 exogenous variables to assist in policy analysis
(Natural level of output, inflation target, demand/supply shocks)
WE ALWAYS ASSUME THE ECONOMY BEGINS AND ENDS IN A LONG-RUN EQUILIBRIUM
Reasons the long run level of output may change (3)
Supply side factors
Population growth
K accumulation (e.g through higher savings)
Technical progress
What happens if Ybart increases, and draw diagram (pg 17)
DAS and DAD shift right by the full amount of the change in Ybart, since it is part of BOTH DAD & DAS EQUATIONS.
Key Result: Increase in growth with stable inflation (DAD increasing prices is countered perfectly by DAS reducing inflation, so stable inflation remains)
Effect of a supply shock, explanation and diagram (pg 18)
Since we begin at a LR eq, v=0. (no shocks in LR)
Vt only part of DAS equation, DAS shifts up by the full amount of the shock and we are at SR eq(point B)
E.g if the shock was an oil price shock makes v=1% for period t, DAS shifts up by 1%.
Since this is a temporary shock at t, at the later period (t+1) inflation falls and output will recover (to point C) but inflation is still higher and output is still lower than the original level Yt-1. (Due to hangover effect of the shock - adaptive expectations)
Eventually as our inflation expectations and inflation keeps falling, DAS shifts further down till we end up back at the LR equilibrium Yt-1.
Draw diagram for this Vt shock. (Pg 18).
Keep in mind the time periods.
Demand shock (εt) : what do we assume?
Again, we start at LR eq. So ε=0
But demand shock is persistent (lasts more than a single period) (also assume ε=1)
Diagram for a positive demand shock εt (pg 19)
(Tip: draw demand curves really steep.
- Why does supply shift at a one period lag?
Start at LR eq - Yt-1, πt-1. (Time before shock)
Demand shock occurs at time t- DAD shifts right.
Output and inflation increases (point A>B). It persists for 5 periods.
Higher inflation shifts DAS upwards since expected inflation is also higher now (eq4 - expected inflation is based on prev inflation)
At t+5 (the 6th period) the demand shock disappears, and output falls to Point G, back on original DAD curve.
Then gradually economy returns back to inital state A.
So essentially demand shock causes supply to shift too but at 1 period lag, due to adaptive expectations. (Slow to realise demand shock is gone and inflation is falling)
Change in monetary policy through π*t (inflation target)
Suppose a fall from 2% to 1% target
Starting in LR eq. so Y=Ybart πt=π*t
πt is part DAD equation
A fall will shift DAD by full amount of the change in πt (2-1=1%).
DAS does not shift initially…
Change in monetary policy through π*t (inflation target) graphically (pg 20)
How could this be done quicker?
Fall in target inflation shifts DAD left.
Output and inflation falls (A>B)
(from Yt-1 to Yt and πt-1 to μt)
In next periods, lower inflation = lower expected inflation (eq 4) so DAS shifts down too (B>C)
From C onwards to Z, expected inflation continues to fall until gradually end up at long run equilibrium Z. (Which is same output as LR equilibrium A, but reached the lower inflation target 1%)
So new target inflation is reached but delayed due to adaptive expectations
- Could be done quicker under alternate assumption of expectations e.g rational expectations.
The Taylor principle
Considers 𝜃𝜋 and 𝜃𝑌.
𝜃𝜋 describes how strong central bank should respond to inflation. (how responsive interest rates will be to inflation)
𝜃𝜋>0
Intuition of central banks of 𝜃𝜋 when 𝜃𝜋>0
Why do they do this?
If inflation rises above target by 1%, the central bank increases the nominal interest rate by (1+𝜃𝜋) %.
I.E RAISE INTEREST RATES MORE THAN THE INFLATION RATE TO BE ABLE TO INFLUENCE THE REAL INFLUENCE RATE. (OVERREACT)
Recall monetary policy equation 5:
it -πt = rt = p+ 𝜃𝜋 (πt−𝜋t*) + 𝜃Y (𝑌t−𝑌bart)
If πt increases, CB can overreact and increase it by more to thus influence rt.
Stabilising effect of 𝜃𝜋>0
𝜃𝜋>0 it means an increase in inflation induces a monetary policy response (nominal overreacts) which can influence the real interest rate. The real interest then determines behaviour,
Thus reducing demand for G&S and stabilising inflation.
𝜃𝜋>0 Ensures DAD is downward sloping
So far we assume 𝜃𝜋>0 and so DAD is downward sloping.
But what if -1<𝜃𝜋<0? How would central bank respond?
Assume inflation rises above the target by 1%
If inflation rises above target by 1%.
CB increases the nominal rate by less than 1%.
(Underreact to influence r!!!)
So creates lower r, driving demand for G&S and further inflation. So monetary policy here IS A DESTABILISING FORCE.
What would 𝜃𝜋<0 look like graphically
An upward sloping DAD curve, since high inflation=higher expected inflation. (Since 𝜃𝜋<0 means CB will underreact by setting the nominal rate lower than the rise in inflation, thus r falls, creating higher demand for G&S and inflation)
Summary: So what is the Taylor principle
For inflation to be stable, CB must respond to an increase in inflation with an overreaction; set a greater increase in the nominal interest rate in order to create a STABILISING FORCE!
To be able to influence the REAL interest rate!
This is mathemetically expressed as 𝜃𝜋 > 0
Economic interpretation of the long run equilibrium solution - 2 conclusions
Classical dichotomy - real variables determined by nominal
Money neutrality - monetary policy (defined by i) cannot influence real variables in long run. (Can only control in SHORT RUN by influencing real interest rate - recall Taylor’s law)
If øπ small and øY is large, what does this mean for the DAD curve, and the impact on inflation and unemployment following a supply shock?
DAD curve is steep.
From this, a supply shock will lead to a larger effect to inflation than output.
If øπ large and øY is small , what does this mean for the DAD curve, and the impact on inflation and unemployment following a supply shock?
DAD curve will be flat.
Means a supply shock will impact output more than inflation.
So
øπ small, DAD steep (2 S’ small=steep)
Øπ large, DAD flat
