Appunti di Fiscal Macroeconomics

FISCAL MACROECONOMICS

GOALS OF BUDGET POLICY

• PROPER ALLOCATION OF RESOURCES
• PROPER DISTRIBUTION OF INCOME
• ECONOMIC STABILIZATION
• PUBLIC FINANCES SUSTAINABILITY

DEFINITIONS

GOVERNMENT'S BUDGET IDENTITY

NS + IS = R = DF = ΔD

INTERTEMPORAL BUDGET CONSTRAINT

THE GOVERNMENT IS SOLVENT IF ITS ASSET

PB = R - NS

₀ = ₁ + ₂ = ∑^∞_k=1 (1+i)^-k PB_k

LET'S DEFINE THIS IN RELATION TO GDP:

₀ = ₁^-1 + ₂^-2 + ...

₀ = ₁ (1+i)^-1 +

₀ = ∑^∞_k=1 (1+i)^-k

Fiscal Macroeconomics

Goals of Budget Policy

• Proper allocation of resources → Market failures require government's intervention
• Proper distribution of income
• Economic stabilization → Output gap should be close to 0
• Public finances sustainability

Definitions

Government's Budget Identity

NS + IS = R = DF = ΔD

Noninterest spending

Interest spending

Intertemporal Budget Constraint

The government is solvent if its asset (only the income stream of resources; we suppose there are no other public real or financial assets and there's no seignorage) is at least equal to its debt.

PB = R - NS

D₀ = PB₁ / (1+i) + PB₂ / (1+i)² = ∑_k=1^∞ (1+i)^-k PB_k

Let's define this in relation to GDP:

D₀ / Y₀ = Y₁ / Y₀ PB₁ / Y₁ (1+i)^-1 + Y₂ / Y₀ PB₁ / Y₂ (1+i)^-2 +...

d₀ = 1+g/1+i ρ₁ + (1+g/1+i)² ρ_n,2 + ... → Exactly the same with real rates

i_r = i - g / 1+g

d₀ = ρ₁ / 1+i + ρ₂ / (1+i)² + ... → d₀ = ∑_k=1^∞ (1+i)^-k ρ_n,k

NO-PONZI-GAME CONDITION

→ PUBLIC DEBT CAN INCREASE FOREVER, BUT AT A LOWER RATE THAN INTEREST RATE; SOONER OR LATER THE GOVERNMENT WILL NEED TO RUN PRIMARY SURPLUSES!

→ d_k MUST INCREASE AT A LOWER RATE THAN λ

IBC AND NPG ARE EQUIVALENT!

→ IF DEBT RATIO IS STABLE , IBC/NPG ARE ALWAYS MET (GROWTH RATE OF DEBT = g < i)

IBC/NPG MAY HOLD EVEN WITH A RISING DEBT RATIO HOWEVER THE PRIMARY BALANCE RATIO SHOULD RISE FOREVER (PBC), BUT d_k IS BOUNDED (IT OBVIOUSLY CANNOT GO ABOVE 100% OF GDP)

→ THE STABILITY OF THE DEBT RATIO DOES NOT IMPLY THAT IBC/NPG ARE MET (THERE CAN BE PERMANENT PRIMARY DEFICITS); GDP ACT AS COLLATERAL (FOR MANY ECONOMISTS THIS IS ENOUGH, EVEN WITHOUT IBC/NPG)

PUBLIC DEBT DYNAMICS EQUATION

D_k = D_k-1 + i D_k-1 - PB_t

d_k = ^D_k-1/_Yk + ^{i D_k-1}/_Yk - PB_t

d_k = ^D_k-1/_Yk(1+g) + ^{i D_k-1}/_Yk(1+g) - PB_t

d_k = ^d_k-1/_1+g + ^{i d_k-1}/_1+g - PB_t

Δdt + g dt_-1 = dt_-1 + i dt_-1 - (1+g) pb_t

→

Δdt = -g dt_t-1 + i dt_-1 - (1+g) pb_t

→

Δdtx = -g dt_t-1/1+g + g i dt_-1/1+g + g pb_t + i d_t-1 - (1+g) pb_t

→ Δdt_x - pb_xt = i-g / 1+g d_t-1 = -PRIMARY BALANCE + SNOWBALLING EFFECT

. IF Δdt NEEDS TO BE KEPT 0,

p = i-g / 1+g d_t-1

FISCAL SOLVENCY: DEBT RATIO STABILITY OR IBC/NPG

→ IF i > g

• IF p_bs < p_bs*, DEBT RATIO WILL FALL FOREVER, FASTER AND FASTER
• IF pbs > pbs*, DEBT RATIO WILL RISE FOREVER, FASTER & FASTER
  • slow process if i-g constant

→ IF i < g

• DEBT RATIO CONVERGES TO A SPECIFIC LEVEL; p_bs* IS LOWER THE HIGHER THE DEBT RATIO

→ WHY NOT STABILIZE THE DEBT RATIO AT A HIGH LEVEL? →

• LACK OF POLITICAL AND ECONOMIC WILLINGNESS TO KEEP HIGH PRIMARY SURPLUSES FOR A LONG TIME (IF i > g)

• EXPOSURE TO INTEREST RATE DIFFERENTIAL SHOCKS (i-g)
• EXPOSURE TO DEBT STOCK SHOCKS (IF p_bs IS CLOSE TO MAXI