IS-MP & IS-LM

Question 1

What is the difference in order of causality between Classical and Keynesian analysis?

Answer 1

Classical: FoPs –> Output –> Demand
The economy has a given supply of capital and labour (in real terms), production function determines inelastic AS and AD adjusts to match
Keynesian: Demand –> Output –> FoPs
In the SR, firms sell what is demanded (in nominal terms), production adjusts elastically to absorb demand changes, this determines factor employment

Question 2

What is the difference between planned and actual expenditure?

Answer 2

Planned expenditure (in closed economy) E = C + I + G = aggregate consumption + aggregate planned investment + government final expenditure = C̄ + c(Y - T) + I(r) + G
Actual expenditure A = Y
The difference is in inventories as unsold products are “bought” by the producer for national accounting
Inventories are accumulated when A > E and depleted when A < E

Question 3

What is the Keynesian Cross?

Answer 3

The diagram of A, E against Y that plots E (+ve y-intercept and slope 0 < c < 1) and A (slope 1 starting at origin) which shows that there is a single goods market equilibrium where A = E (inventories unchanging)

Question 4

What happens on either side of the equilibrium in the Keynesian cross?

Answer 4

To the left inventories fall so firms raise production towards the eqm
To the right inventories accumulate so firms cut production towards the eqm

Question 5

How do you find the Keynesian multiplier algebraically?

Answer 5

Expand and rearrange Y = A = E to get Y on one side which will leave a multiplier of 1/(1 - c) > 1

Question 6

How do you represent the Keynesian multiplier graphically on the Keynesian cross?

Answer 6

An increase in G shifts the E curve up by ∆G which shifts Y* to the right by ∆Y = 1/(1 - c) ∆G

Question 7

What causes the multiplier effect?

Answer 7

An increase in government spending raises output which increases disposable income which increases consumption which further increases total planned expenditure which increases income and so on
Y increased by ∆G => C increased by c∆G => Y increased by c∆G + c²∆G and so on => income increased by ∆G(1 + c + c² + …) = ∆G/(1 - c)

Question 8

What variations of the multiplier exist in other models?

Answer 8

0 < multiplier < 1: C and/or I falls when G increases
multiplier = 0: Y solely supply-side determined
multiplier < 0: Y falls when G increases

Question 9

What does empirical evidence say about the multiplier?

Answer 9

IMF 2012: advanced countries had multiplier around 0.5 in three decades before 2009 and 0.9-1.7 after
This aligns with existence of underemployed factors in the Keynesian model

Question 10

What could decrease the multiplier?

Answer 10

If taxes were proportional to income C = c(1 - t)Y so the multiplier would be 1/(1 - c(1 - t)) < 1/(1 - c)
Leakages from the circular flow decrease the multiplier

Question 11

How is the IS curve derived?

Answer 11

From the relationship between Y and r in the expenditure (goods market) equilibrium Y = 1/(1-c) (C̄ - cT + I(r) + G)
A fall in r would increase I which shifts E upwards by ∆I which increases eqm income by ∆Y = ∆I/(1 - c) so the graph of r against Y has a similar shape to r against I (downward sloping)
When r falls, planned investment rises which causes SR disequilibrium E > A so firms raise production and output rises

Question 12

What is the IS curve?

Answer 12

The locus of points in (Y, r) space where a goods market eqm obtains
This is also the set of points where savings equal planned investment which comes from closed-economy GDP accounting assuming E = A => I(r) = (Y - T - C) + (T - G) = priv saving + pub saving = S

Question 13

What is the difference in approach to saving between the classical and Keynesian model?

Answer 13

In the Keynesian model investment generates its own saving (fall in r increases I which increases Y and some of this is saved, with Y increasing until S = I(r))
In the classical model there is a unique equilibrium between savings and investment determined by the fixed level of output, i.e. a unique real interest rate which equilibrates the loanable funds market (fixed supply)

Question 14

How would the IS curve be affected by changes to G or C̄?

Answer 14

Increase in G shifts E up by ∆G which increases Y by ∆Y = ∆G/(1-c) for all values of r so the IS curve shifts to the right by ∆Y
Same for C̄ or exogeneous changes to investment

Question 15

What can change the slope of the IS curve?

Answer 15

The sensitivity of I(r) to r: flatter (more responsive) I(r) schedule implies flatter IS
Size of multiplier (MPC): lower c implies less ∆Y for given ∆I so steeper IS

Question 16

What is the difference between the views on borrowing for government stimulus between the Keynesian and classical models?

Answer 16

In the Keynesian model this is very effective as the fiscal multiplier is greater than 1
In the Classical model increased government spending crowds out investment so savings becomes S’ = Ȳ - C - (G + ∆G) which corresponds to a lower level of investment
If G increases but T is fixed the effect can be analysed through the derivative of S = Y - C̄ - c(Y - T) - G
dS/dG = dY/dG - cdY/dG - 1, since dY/dG in the Keynesian model is the multiplier we get dS/dG = (1-c)/(1-c) - 1 = 0 so no crowding out but in the classical model dY/dG = 0 so dS/dG = -1

Question 17

What is the role of the CB in the IS-MP model?

Answer 17

To determine the nominal interest rate in the economy which via Fisher eqn and assumption of exogenous inflation expectations determines the real interest rate (set to a target R) which in turn determines income Y* from the IS curve giving a money market eqm

Question 18

What is the MP curve?

Answer 18

A plot of R in (Y, r) space usually alongside IS
In the simplest case, R = i - π^e = r̄

Question 19

What is the neutral real interest rate?

Answer 19

The rate r̄ which equates S with I when Y = Ȳ and there are no temporary shocks to planned expenditure (can think of it as coming from the classical model)

Question 20

What are the implications of the target real rate being equal to the neutral real rate?

Answer 20

R = r̄ means SR policy consistent with LR classical eqm but income may not be at its LR eqm level due to transitory shocks to C or I or G which affect demand side
There is a corresponding neutral nominal rate when inflation expectations are at some target π^e = π*

Question 21

What is the zero lower bound?

Answer 21

As long as there is cash, a nominal interest rate below 0 would mean everyone would hold cash and monetary policy would become ineffective so there is a ZLB on i (for consumers)
Negative rates were tried in e.g. Sweden and Switzerland and not passed on to consumers/firms significantly, in broader economy there is a constraint at/around zero

Question 22

How does the ZLB affect the monetary policymaker?

Answer 22

A ZLB on i means R is constrained to r ≥ -π^e which is problematic for low or deflationary inflation expectations as a neutral rate (to reach full employment) may be unattainable even without shocks
(Also applies to IS-LM)

Question 23

Why and how would a CB use unconventional monetary policy?

Answer 23

When conventional policy is ineffective (ZLB)
Unconventional policy aims to change determinants θ of the long-term real interest rate r_L (opportunity cost of investment) other than the overnight rate r which is constrained in order to shift I(r) and so IS
QE involves the CB buying long-term debt with the aim of raising its price which lowers the rate for borrowers
FG involves the CB making promises about rates in the future which allows effect on long term rates
Abolition of cash could also be used as it leads to the ZLB

Question 24

What is the difference between a horizontal and sloped MP curve?

Answer 24

A horizontal MP means the CB doesn’t change R so the multiplier from the Keynesian cross will pass directly to the money market eqm, a sloped MP is more likely as the CB will respond to shocks (endogenises CB policy)

Question 25

What is the Taylor rule?

Answer 25

A monetary policy rule to determine R so that it is above the neutral rate when the economy “needs stimulus” and below when the economy is “overheating”, giving rise to an upwards sloping MP curve
R = r̄ + m_π(π - π^T) + m_Y(Y - Ȳ) with feedback parameters m > 0 and π treated as exogenous

Question 26

Does the Taylor rule (as a description) hold up empirically?

Answer 26

Without feedback on the output gap (Jones rule) and with π^e = π, r̄ = 2, π^T = 2, m = 0.5, overpredicts in 60s, 70s, and post GFC, underpredicts in 80s
With feedback on output gap, results are slightly improved before GFC and significantly improved after GFC (error halved) but still overpredicts, suggesting -ve output gap is important to understand post-crisis low rates

Question 27

How are the feedback parameters of the Taylor rule represented graphically?

Answer 27

The slope is m_Y and changes to π shift the curve

Question 28

What is the Friedman rule?

Answer 28

CB should aim for constant growth rate of M rather than adjusting r because of long and variable lags between shock hitting, policy being enacted (inside lag), and policy having its effect (outside lag) so active stabilisation is destabilising
From the qty theory, Solow model, and assuming constant V, g_{M = π* + gY so gM can be used to fix the LR rate of inflation
Since nominal rate is a tax on holding cash it is efficient to have i = 0 so growth rate of M should be set at the level that ensures π* = -r̄
Aiming for ZLB because Friedman wants CB impotence}

Question 29

What are critiques of Friedman’s approach to monetary policy?

Answer 29

There is dispute about policy lags as they are hard to estimate, there has been success of policy activism, and constant growth rate of M hard to define

Question 30

What is the modern consensus on policy rules?

Answer 30

Policy activism is popular, especially post-crisis
Friedman rule is influential as a benchmark in academic literature but not used in practice

Question 31

What is the role of the CB in the IS-LM model?

Answer 31

To determine the money supply which determines a money market eqm and so determines eqm Y on the IS curve

Question 32

What is the relation between the money market and the quantity equation?

Answer 32

The demand for real money balances (M/P)^d is given by L(i, Y) with i being the opportunity cost of holding cash over bonds and Y leading to the transaction motive
Treating L as homogeneous of degree 1 in Y means L(i, Y) = Y x I(i) so money market eqm can be written M x 1/I(i) = PY which is the qty eqn with V = 1/I(i)

Question 33

Where does the classical “supply curve” come from?

Answer 33

M is exogenous growing at some fixed rate and P endogenously adjusts to equilibrate the money market so i = r̄ + g_M - g_Y = r̄ + π^e with the interest rate determined in the loanable funds market and inflation determined by money growth
Plotted with liquidity function (downward sloping)

Question 34

Where does the Keynesian “supply curve” in the IS-MP model come from?

Answer 34

From the Taylor rule and Fisher eqn i = π^e + r̄ + m_π(π - π^T) + m_Y(Y - Ȳ) with M being supplied perfectly elastically to implement this

Question 35

What is the difference between the classical and the IS-MP “supply curve”?

Answer 35

In both cases they are graphically a horizontal line in (M/P, i) space but the classical relation has P adjusting to ensure money market eqm whereas the IS-MP relation has M adjusting to ensure eqm while P is exogenous (to the market)
In the IS-MP model, fluctuations in money demand can lead to big changes in money supply even with constant nominal rates

Question 36

What is the empirical relationship between changes to nominal interest rates and changes to money supply?

Answer 36

They do not match up, suggesting the “supply curve” in the IS-MP model is not very helpful

Question 37

What is the Keynesian “supply curve” in the IS-LM model?

Answer 37

Instead of setting the interest rate using some rule, the CB can fix M so the real supply of money balances M/P is perfectly inelastic and therefore is a vertical line on an i against M/P plot with i adjusting to clear the market

Question 38

How does the fixed M approach to the money market hold up empirically?

Answer 38

It seems relevant to the UK in the 80s

Question 39

How do the effects of changes to money demand differ between the approaches to M?

Answer 39

Fixed M implies that a change in income will change the interest rate

Question 40

What is the LM curve?

Answer 40

The positive relation between Y and i or the set of (Y, i) points consistent with money market eqm given fixed M
Higher Y increases demand for real money via the transactions motive which decreases demand for bonds which drives down their price which increases the nominal interest rate until the opportunity cost of holding real money is high enough for eqm

Question 41

What can shift the LM curve?

Answer 41

Changes in M, P, and exogenous changes in liquidity demand
Higher M implies lower i for any Y so LM shifts down

Question 42

What can change the slope of the LM curve?

Answer 42

Income elasticity of money demand and interest elasticity of money demand
Former is the horizontal shift in (M/P)^d for some given i when Y changes, latter is how much i must increase to contract money demand back to the money supply after Y changes

Question 43

How can the LM curve be mapped to (Y, r) space?

Answer 43

Using the Fisher eqn and exogenous inflation expectations
Allows a unique SR eqm when combined with IS curve with goods market eqm given by Keynesian cross and money market given by supply and demand for real money balances

Question 44

What is the effect of government stimulus when the CB uses the Taylor rule?

Answer 44

Income increases by ΔY < ΔG/(1-c) because the CB wants to keep Y near its long run equilibrium value
Higher m_Y (less accommodative monetary regime) leads to a steeper MP curve, in the extreme the CB can fix Y = Ȳ
There can be some conflict between monetary and fiscal policy

Question 45

What is the difference between the fall in investment from government stimulus in the classical model and in the Taylor rule IS-MP model?

Answer 45

In the classical model private savings are fixed so higher G decreases public saving and so overall saving falls, in the IS-MP model investment falls because of the CB increasing r when Y rises, but the CB could respond differently

Question 46

What is the effect of fiscal contraction when there is a ZLB?

Answer 46

If the IS curve is on the constrained part of the MP curve, a fiscal contraction will have a more severe effect

Question 47

What could change the neutral rate?

Answer 47

Changes to investment opportunities or changes to LR gov spending as these shift the saving and investment schedules and so the equilibrium r in the classical model
In the SR model, a fall in the neutral rate corresponds to a downward shift in IS and an equal fall in the MP curve without ZLB so Ȳ doesn’t change, however if there is a ZLB then the eqm Y can change, suggesting CB should be concerned about the neutral rate falling too low as it undermines their ability to maintain LR output even without IS shocks (secular stagnation)

Question 48

How could policymakers respond to secular stagnation?

Answer 48

Increase components of expenditure to shift the IS curve rightward, e.g. fiscal expansion and unconventional monetary policy
These may not produce the required permanent IS shift, for that a lower LR S or higher LR I would be needed to raise the neutral rate but these are dependent on slow-moving demographic trends
Could also accept a low neutral rate and lower the lower bound by increasing inflation expectations