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## Macroeconomic Theory

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Roles of Fiscal policy

- To provide automatic stabilizers to insulate the economy from shocks to AD (tax and social security).
- To stabilize output around eq. rate using discretionary fiscal policy (another policy).
- To plan the financing of g and to maintain a sustainable burden of public debt.
- The Automatic Stabilizers
- Tax and benefit system depend on the level of activity. They reduce the size of the multiplier and dampen the impact of any exogenous changes in private spending on output. As a consequence budget deficit rises when activity falls and declines when activity rise.

Calculating the cyclically adjusted budget deficit, the deficit that would prevail given existing taxes and spending commitments if the economy was operating at ye, this indicates whether fiscal policy is expansionary or contractionary.

- Fiscal stance:

Primary B. deficit=cycl. Adj. B. deficit + impact of aut. stabilizers

=discret. fiscal impulse+ impact of aut. stabilizers

g(yt) – t(yt) ≡ [g(ye) – t(ye)] + a(ye – yt)

discretionary fiscal. Impulse automatic Stabilizers

- During recession a(ye – yt)>0, pushing up B. deficit and vice versa.
- At ye; a(ye – yt) = 0.
- A cycl. Adj. B deficit expansionary fiscal stance
- A cycl. Adj. B surplus contractionary fiscal stance

If the cycl. adj. surplus or deficit = 0 the actual deficit reflects the automatic stabilizers and will disappear once the economy returns to eq.

- When we have cycl. adj. deficit, the govt. has to recognize that eventually it may have to take measures to reduce the increase in debt when the economy returns to ye.
- Discretionary fiscal policy
- In the IS/LM g is normally assumed to be exogenous, t is either exogenous or a function of income. So far we did not consider how the increase in g is financed.
- First, assume that households and firms take the view that govt bonds comprise part of their wealth.

Second, we investigate the claim that bonds are not wealth for the personal sector “the Ricardian equivalence”. Far sighted household realizes that any bonds issued to finance g have to be repaid in higher t later.

- The government budget identity
- In nominal terms the govt budget identity in each period is:

G + iB ≡ T + ΔB + ΔH

Govt exp. Interest tax rev. new bonds new money

- The fiscal policy transmission mechanism

↑g → ↑ y → ↑ (M/p)D→ ↑ r → ↓ I.

See figure (6.1a)

- The IS shifts to RHS, the economy moves along LM (financial crowding out). y expands but because the increase in g is financed entirely by new bond issues, r rises. The full multiplier effect of the rise in g does not occur: y is higher but its composition is different (higher g and lower I). This crowding out does not occur if interest rate is held constant (i.e., MS expands to meet additional MD).

Figure 6.1a

Higherr and y

Tax finance and the balanced budget multiplier

- We know that if g increased, t will rise, but induced tax is insufficient to close the gap between g and t. assuming a proportional tax t = tyy. There will be a budget balance if:

Δg = Δt

= ty Δy

Δy/Δg = 1/ty

- The multiplier effect of the change in g is 1/ty, but the expenditure multiplier is:

Δy/Δg = 1/(sy + cyty)

Which is smaller than 1/ty.This implies that tax revenues at the new eq y < g.

- The boost to y from higher g leads to a budget deficit, since the rise in y generates saving plus taxation. Since there is a deficit, the government is borrowing to implement spending plans.

What is the effect on the economy of a fully tax-financed g? The impact on output of a change in g:

- Δy = Δg + cyΔg + cy(cyΔg) + …
- The impact on output of a change in t:
- Δy = -cyΔt - cy(cyΔt) - …
- since Δg = Δt, it is clear that the net effect of the balanced budget expenditure program is:
- Δy = Δg = Δt
- i.e., Δy/Δg = 1 (balanced budget multiplier)
- The balanced budget multiplier is important for policy purposes. The govt that is unable or unwilling to use debt or money financing can stillraise the level of activity by engaging in a balanced budget expenditure program. The size of the multiplier will be pulled down below one once the impact of higher y on MD and r are introduced (fig. 5.1b)

Bond finance

- As shown above a rise in g will not induce sufficient extra t to wipe out the deficit. There will be a continuing requirement to sell bonds to cover the gap between g and t. the stock of bonds will mount each year.
- The implications of this depend on whether government bonds are considered a net wealth by private sector agents or not.
- If bonds are net wealth, their stock will influence both consumption and MD. The govt should take into account these changes when setting both monetary and fiscal policy.
- In addition, the new bonds will produce a portfolio effect in the demand for money. At a given r higher wealth raises MD and bonds in proportion so as to keep the portfolio balanced. The LM will shift to the left (figure 6.1c).

Are bonds net wealth? The Ricardian equivalence debate

- If bonds are not net wealth by households, there will be two implications:
- The consequences of wealth changes due to govt bonds disappear.
- The expansionary impact of the spending program shrinks back to that of a balanced budget.
- Households take into account that taxes in the future will have to be raised to service the debt. This is known as the Ricardian equivalence. This result depend on the following assumptions:
- The absence of liquidity constraints on households, they are able to borrow against expected income at the current interest rate
- Interest r and time horizon faced by the govt and households are the same
- Households have heirs and incorporate their utility into their consumption behavior, i.e., households behave as if they last forever.

Money finance fiscal expansion

- The govt sells bonds to the CB to be used for spending. This is ruled out by the constitution of the CB in some countries. In money finance fiscal expansion, r will decline and y will increase in the short run.
- The short run effect of this type of finance is illustrated in in fig. 6.1d.

Deficits and debt

- What determines the path of debt overtime? And if it is rising will continue rising indefinitely?
- We take the analysis in two steps; first we exclude the possibility that the govt can borrow from the CB. The budget identity is:

G + iB ≡ T + ΔB

Govt exp. Interest tax rev. new bonds

- The actual deficit ≡ G + iB - T
- The primary deficit ≡ G - T
- By rearranging the budget identity the actual deficit is equal to the change in the stock of govt debt:
- ΔB ≡ (G – T) + iB
- Change in debt ≡ primary deficit + interest on outstanding debt
- Change in debt ≡ actual deficit

The debt ratio is

- Debt ratio ≡ b = B/py
- The actual deficit to GDP
- Actual deficit/GDP = ΔB/py ≡ (G-T)/py + iB/py

≡ d + ib

- The ratio of the primary deficit to national income is:
- Primary deficit/GDP = d ≡ (G-T)/py

B ≡ bpy

- Use approximation that

ΔB ≈ pyΔb + byΔp + bpΔy

ΔB/py = (bΔpy)/py + (bΔyp)/py + (Δbpy)/py

= bπ + bγy + Δb

- Where π is inflation and γy is the growth rate of output. Using r=i-π, we get the following change in the debt to GDP ratio:

Δb = d + (i-π-γy)b

= d + (r-γy)b

To interpret the equation let us consider tow cases:

- Case 1:r > γy. Total debt will be rising unless d is negative, i.e., unless there is a primary B surplus. Interest payments are rising faster than is GDP. Servicing the debt is pushing up the debtburden. the only way to offset that b does not rise is for the govt to run a primary budget surplus
- Case 2: r < γy. The growth of the economy is sufficient to reduce the impact of interest payments on the debt burden. If the govt were to run a B surplus, it would eventually end up with negative public debt.

Fig. 6.2b shows an economy with the same r and γy as in fig 6.2a but with a primary surplus (the intercept is below the horizontal axis).

Fig. 6.2Case 1. r > γy.

Phase line

The case of high and rising govt debt.

- In advanced countries it is typically the case that the real interest rate on govt bonds is risk free, this means it is well below real rate of return on fixed investment.
- When r > γy a substantial primary surplus is required to stop b from rising and reduce the debt burden. This is likely to create problems for a number of reasons:
- Increasing B. surplus either requires painful cuts in g or increase t, because of its supply side effects, t will raise eq. unemployment.
- A high level of debt may raise the concern that the govt may default, the govt will face a higher r which will worsen the debt burden and dampening investments.
- To continue to finance its expenditure the govt may resort to monetizing the debt.

Now let us highlight the potential feedback from b to r. assume that r < γy, the govt intertemporal budget identity can also be interpreted as its solvency constraint. Assume that there is a b > 0, for the debt to stop increasing Δb ≤ 0

- Since Δb = d + (r- γy).b
- This implies that for Δb ≤ 0
- b ≤ -d/r-γy
- i.e. debt/GDP≤ (primary surplus/GDP)/(r-γy)

Costs of fiscal consolidation: Cold turkey versus gradualism

- The fiscal consolidation refers to the implementation of fiscal policy so as to achieve as sustainable debt ratio. The trade off between a cold turkey and a gradualist strategy of fiscal policy is illustrated in fig. 6.5.

The govt wishes to reduce b to D: lower surplus

Fiscal policy can’t be relaxed immediately, and debt

Will grow forever,

D Long run sustainable position

The govt may tighten fiscal policy by raising s to S1

The economy would move from A to B and to C

Fiscal stance can be relaxed to S2, the cost is sharp

Tightening of policy

An alternative is a more gradual policy to get the economy at s’, then

Adjust the surplus to S’’ and so on till D is reached

Can fiscal consolidation be expansionary

- Why fiscal consolidation may stimulate AD? If the economy is already at fiscal stress (unsustainable fiscal position), because of the risk premium, r will be higher. Households may have lowered their estimation of their wealth. A fiscal consolidation may be viewed as credible, and boast investment and consumption by reducing risk premium and restoring optimism about wealth.
- Less dramatic argument if the govt announces a fiscal consolidation plan based on cutting govt consumption rather than investment or raising taxation, the public may believe that this signals a commitment to fiscal reform. This may lift wealthexpectations, the public is able to borrow against expected income, consumption would rise, and to the extent that consolidation is believed an enduring one, expected r will be lower and investment will rise.

Consolidation via cutting govt consumption is costly in political terms rather than govt investment or raising taxes, consolidation here may be more effectively signal its seriousness about fiscal reform and have a stronger effect on private sector expectations.

- The insights from the imperfect competition macro model highlights the need to take account when analyzing the impact of fiscal consolidation program of:
- The supply side impact of the consolidation policy
- The stance of monetary policy
- Other supply side policies.

Monetizing the debt: seignorage and hyperinflation

- If the govt cannot borrow (high risk of default) or raise tax, it may use monetary financing. We know the govt B constraint:

G + iB ≡ T + ΔB + ΔH

Govt exp. Interest tax rev. new bonds new money

- Where M= ĸ . H (ĸ=kappa is the multiplier). Now
- ΔB ≡ (G-T) + iB – ΔH
- Dividing by nominal GDP
- ΔB/py ≡ (G-T)/py + iB/py – ΔH/py
- = d + ib - ΔH/H . H/py
- = d + ib – γHh
- Where γHthe growth rate of H andh is H/py.
- Δb = d + (i-π-γy)b - γHh
- = d + (r-γy)b - γHh

i.e., the growth of the debt to GDP ratio will be reduced to the extent that the deficit is being financed by new money creation.

- In the medium run MS growth is equal to inflation rate. Assuming ĸ is constant, γM = γH = π.
- Higher π will reduce the growth of the debt ratio-assuming h remains constant. This has led to the use of the term inflation tax to refer to this method of finance.
- Seignorage revenue is therefore:
- S = ΔH/p
- = ΔH/H . H/p
- = γH . H/p
- In the medium run eq. S = π . H/p
- As a proportion of y
- S/y = γH . h

The definition of seignorage suggests that the govt can fiance more of its expenditure through seignorage by raising inflation.

- There is a limit to the extent that seignorage can be used as a source of revenue. As inflation goes up the public becomes less willing to hold money. Recall money market eq.
- (M/p)S = (M/p)D
- = L(i,y)
- = L(r + π, y)
- When π is high, the demand for money balances is low. If we substitute the demand for money into the seignorage expression
- S = π . H/p
- = π . (M/p) . 1/ĸ
- Whilst higher money growth pushes up seignorage, via the first term (π), it pushes it down via the second term (M/p) . 1/ĸ

To use the tax analogy, pushing up the rat of taxation (π), has the effect of reducing the tax base.

- Empirical research suggests that the second effect begins to outweigh the first when inflation rate go higher than about 200% p.a. this suggests that the maximum amount of revenue the govt could raise this way would be about 10% of GDP.
- Governments curtail their use of seignorage because the costs of higher inflation outweigh the benefits.

Fiscal policy rules

- A prudent fiscal policy is one in which the government is solvent based on long run or permanent values of the relevant variables. On this prudent fiscal policy rule (PFPR), it is possible to compare it already with existing fiscal policy rules.
- From budget constraint to PFPR

Δb = d + (r-γy)b 6.16

= (g/y – t/y) + (r-γy)b 6.17

Δb = d + (i-π-γy)b 6.18

= (d + ib) – (π + γy)b 6.19

- The debt ratio is raised by the actual deficit (d + ib) and reduced by the growth of GDP ((π + γy)b). It is also useful to write (6.19) in terms of the actual deficit:

Deficit/GDP=(d+ib)=Δb+(π + γy)b 6.20

- Deriving a rule for prudent fiscal policy begins from the conditionΔb≤0 for the debt ratio not to increase. This implies:

b ≤((t/y)p – (g/y)p)/(rp – γyp) 6.21

- Where p (permanent value). Assume that there is a given public expenditure program that entails a long run ratio of g, (g/y)p, how should this best financed? For the debt ratio not to increase, rewriting 6.21 implies

(t/y)p ≥ (g/y)p + (rp – γyp).b

- A prudent fiscal rule is to set the share of tax in GDP at a constant level required to satisfy the constraint:

(t/y)par = (t/y)p ≥ (g/y)p + (rp – γyp).b prudent fiscal policy rule

- Substituting the PFPR into 6.17 implies the debt ratio moves as follows

Δb≤ (g/y – (g/y)p) + (r – rp) – (γy - γyp).b 6.22

The rule implies that if govt expenditure is temporarily above its permanent level, borrowing should finance this-this entails a rise in the debt ratio and is consistent with the rule. This would be the case if there is a recession, or if major infrastructure investment is planned.

- Equally the rule says that an expected rise in permanent govt spending, for example, as a consequence of long run govt pension obligations must be funded by a rise in taxation.

How the PFPR deals with stabilization and structural problems

- Stabilization
- What does the PFPR imply about the balance between automatic stabilizers and discretionary fiscal policy?
- The rule implies that whilst g share can be expected to rise above long run level in cyclical downturns, this must be reversed in upswings. Averaged over the cycle, there is no case for a divergence between g/y and (g/y)p.
- The implication is that the prudent cyclically adjusted primary budget deficit will depend on pre-existing debt ratio and on the difference between r and γy. e.g., if the debt ratio is 0.6, and rp–γy is 2.4% then the PFPR says that the cyclically adjusted primary budget surplus should be at least 1.4% (0.6 x 0.024).

In introducing the concepts of actual and cyclically adjusted budget balance. Decompose the observed budget deficit into the part that is due to the operation of automatic stabilizers (a(ye-yt)) and the deficit that would characterize the economy at ye.

- If the automatic stabilizers are fixed, the center attention is on the use of discretionary policy to stabilize y in the face of the shocks. But another way of thinking about eq. 6.1:

g(yt)-t(yt) ≡ [g(ye)-t(ye)] + a(ye-yt)

- Is as a rule for fiscal policy. If the govt aim is to stabilize y at ye with the budget in balance, it should choose “a” to achieve this objective.

Structural fiscal policy

- Unlike monetary policy, fiscal policy relates not only to the cycle but to govt expenditure programs with effects lasting for decades.
- The govt may wish to introduce structural policies whose effects may not be permanent, despite extending over many B cycles.
- Other policies may be of indefinite duration (permanent).
- Of the first type renewing infrastructure ((g/y)>(g/y)p). Of the second type is commitment to pay pensions to aging population, ((g/y)p>(g/y)) and the tax share should be raised to its higher long term level.
- Why a constant share of taxation
- Why establish the PFPR rule in terms of a constant tax share? With diminishing marginal utility the optimal way for the govt is to smooth its tax revenue collection over time and borrows and saves in response to unforeseen fluctuations in expenditure

Comparing existing fiscal rules with the PFPR

- It is helpful to express the govt B constraint in the form:

Deficit/GDP = (d+ib) = Δb + (π + γy)b

- We can then rewrite PFPR by substituting this into 6.22 and rearranging:

Deficit/GDP ≤ ((g/y)-g(g/y)p) + [(r-rp)-(γy - γyp)] b + (π + γy).b

- This form of PFPR brings out the fact that higher deficit ratio is compatible with solvency if the growth rate of nominal GDP (π+γy) is higher.
- The stability and growth pact
- The Stability and Growth Pact of the European Union contains two rules:
- 1. d must be less than 3%

2. the cyclically adjusted deficit ratio should be in balance or in surplus

- i.e.;

Deficit/GDP ≤ 0.03 (rule 1)

Cyclically adjusted deficit/GDP ≤ 0 (rule 2)

- The first rule places a rigid limit on d and hence the scope for fiscal stabilization.
- The PFPR indicates that there is no economic reason for the deficit limit to be a fixed number.
- The second rule places a rigid limit on the extent to which fiscal policy can be used for structural purposes.

Golden Rule (e.g. UK)

- Cyclically adjusted deficit ratio must be no larger than is required to finance govt investment spending (as a share of GDP)
- ~
- Cyclically adjusted deficit/GPD ≤ gI/y
- Where (gI) ~ is the cyclically adjusted govt investment spending.
- This rule is less restrictive than the Stability and Growth Pact for two reasons: first it does not interfere with the operation of the automatic stabilizers and second it allows more scope for structural fiscal policy.

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