F Policy Part 2 Flashcards
(22 cards)
Private sector budget constraint yields national income Y as
B) While normal output expression
C) combine 2 identities for Y
D) what does NX =
Y = C + S + T
B) Y = C+I+G+NX
C) S+(T-G) = I + NX
D) Where NX = NFI
net exports = net foreign investment
(investment from domestic residents abroad - domestic investment by foreign residents)
S + (T-G) = I + NX
Explain all the terms
S is private savings
T-G is public saving
I is investment at home
NX is investment abroad (as shown NX=NFI)
What happens if G-T>0 (deficit), what must happen
This means negative public savings, thus for equation to hold either;
S (private savings) needs to increase
Or I or NX/NFI fall (from RHS)
What is the traditional view on long run effect of a fall in public savings (T-G) through a tax cut.
B) what about short run
Private savings rise, but less than fall in public savings. (Since part of the tax cut is consumed today)
So national savings fall, so I or NFI has to fall. So lower capital stock and growth in long run.
B) AD increases since tax cut creates wealth effect - consumers feel wealth so increase c
So that is traditional view (private savings doesn’t compensate fall in public savings)
What about Ricardian
Says private savings should increase and match fall in public savings to leave I and NFI unaffected
So no long run adverse affects (on capital stock and growth) and no short run effects (no increase in consumption)
Next topic: Long Run Debt sustainability
What is the flow gov BC ΔΒ
B) how can we find debt-to-GDP ratio
C) can be simiplified further
ΔΒ = (G-T) + rB
I.e increase in debt (deficit) = Primary deficit (G-T) + debt servicing (interest r on outstanding debt b)
B) divide by GDP (Y)
ΔΒ/Y = (G-T)/Y + rB/Y
C) ΔΒ/Y= (ΔΒ)/Y - B/Y x ΔY/Y
Given ΔΒ = Bt - Bt-1
How else can Bt (debt in t) be written (hint: in time periods)
Bt = (Gt-Tt) + (1+r)Bt-1
= primary deficit + debt servicing
Change in debt-to-GDP ration in per capita terms
(Small case letters) Δb
Key: just rmb this equation (pg36)
Δb = g - t + (r-y)b
b = B/Y
g = G/Y
t = T/Y
y = GDP growth rate
Using this, what is the expression to stabilise debt-to-GDP ratio (no change in debt to GDP)
Δb = 0 (No change in debt-GDP ratio i.e stable)
Rearrange to get
t - g = (r-y)b
So to stabilise debt-GDP ratio we need Δb=0 which gives us
t-g=(r-y)b
What if y=0. How to stabilise now?
B) what if y>0
Only way to stabilise debt is run a primary surplus. (Since otherwise r makes debt grow)
B) gov can outgrow its debt since positive growth, whether it be in a deficit or surplus
What if r>y
B) if r<y
C) what if the only way to reduce debt if r>y
Debt process is explosive - debt accumulates
B) debt process stabilises - economy grows faster than cost of debt (interest r)
C) if r>y, only way to reduce debt by primary surplus
t-g > (r-y)b
Next topic: Fiscal gaps (harder)
So we ran large deficits to combat recession and COVID (spending>revenue) so increased debt
Flow gov BC Bt+1 (Same as last flow gov BC, except now Bt+1 so add extra period to everything)
B) rearrange to get (1+r)Bt on LHS
C) iterate it forward to get Bt = (hint… Σ and St+j)
Bt+1 = (Gt+1 - Tt+1) + (1+r)Bt
B)
(1+r)Bt = Bt+1 - (Gt+1 - Tt+1)
C) divide by 1+r
Bt = Σ(1+r) to the -j St+j + (1+r) to the -J Bt+J
St+j = (Ti+j - Gi+j)
First term: present value of future primary surpluses (from t+1 to t+j)
Second term: debt remaining at t+j (final period debt)!
So express today’s debt in terms of future primary surpluses + final period debt
How does he add the fiscal gap
B) what is the thing added, and what does it mean
Bt = Σ(1+r) to the -j [St+j + ΔGDPt+j]
(So lose the 2nd term from previous FC, instead add ΔGDPt+j)
Σ is j=1 to ∞
B) ΔGDPt+j : a fraction of GDP at date t+j
Is the permanent increase in taxes, or reduction in spending (as a fraction Δ of GDP) required to ensure future primary surpluses (St+j) = debt Bt.
E.g increases taxes Tt+j by ΔGDPt+j each year to ensure St+j = Bt
So what does a higher Δ imply
Larger fiscal gap! Hence topic name! (between future revenues and spending), thus requires
Larger fiscal policy adjustments (larger increases in tax/reductions in spending as a % of GDP) are required for sustainability (PV of future primary surpluses = debt Bt)
Another way to look at fiscal gap. How?
Increase in primary surplus required, from now till future year J, to make debt-GDP ratio = initial debt-GDP ratio (stabilise)
I.e make
Bt+j/GDPt+j = Bt/GDPt
What do they find for Δ empirically
9%!!! Large!
So permanently increase primary surplus by 9% of GDP every year!!
2 reasons for this big number
Fall in working age population (so less people paying taxes, and also more expenditure on old hence why need to either increase tax/reduce spending
Increases in health spending e.g MRI
Final topic: Taxes distort behaviour. Hence what do we need
Tax smoothing to minimise distortionary effects
Assume cost of distortions C(t,Y) = t²Y
Loss function (Total discounted cost of distortions (2 periods) L
Pg 48
L = t²₁Y₁ + t²₂Y2/1+p
Assume taxes are
T1 = t1Y1
T2= t2Y2
What is our government intertemporal BC
(originally T1 + T2/1+r = G1 + G2/1+r)
B) how does government tax smooth
Just sub in our T1 and T2
t₁Y₁ + t₂Y2/1+r = G1 + G2/1+r and let this = Ω
B) tax smooth by government minimising loss function (previous page) subject to their BC here, picking t1 and t2 optimally
Set up by lagrange: What is the starting expression
B) then take FOC to find t1
C) what is this result?
F = t²₁Y₁ + t²₂Y2/1+p + λ(Ω - t₁Y₁ - t₂Y2/1+r]
B)
t1 = (1+r/1+p)t2
C) short sighted gov i.e p>r (discount rate higher!)! They choose a low t1 relative to t2, i.e pain of taxation postponed to future
So p>r means short sighted gov, T1 will be lower than T2, pain of taxation postponed to future
What if p=r
B) how can this be expressed (t1=t2=…) (pg51)
T1 = T2! Tax smoothing!
B) T1=T2= G1 + G2/1+r / Y1 + Y2/1+r
I.e ratio of present value of gov spending to present value of income
