Fiscal Policy (RE And 4 Violations Of RE - Not Bad) Flashcards
(18 cards)
Most countries have large debt-gdp ratios
What is UK’s debt-to-GDP ratio March 2022
What is the UK deficit in 2022 March
Nearly 100%. 11.8% above EU average
(due to events like Covid, huge spikes in g. borrowing)
B) 2.5% of GDP
Ricardian equivalence
Government funding via tax, or bond finance have equivalent effects (to consumption, investments output and growth) - deficits dont matter and cannot provide macro-stabilisation
Ricardian equivalence intuition: why are tax and bond financing equivalent, and why does it not provide macro stabilisation?
If government issues bonds instead of taxes, rational individuals anticipate higher taxes in future and save today
Hence why can’t provide macro stabilisation, since running deficits via these ways doesn’t have effect on demand (Y=C+I unaffected! remember its fiscal policy!) because private sector is rational and thus neutralises the intended effects.
Start with the:
Household budget constraint. Assume no initial assets.
What is their savings in period 1 A₁
b) upon this, what is consumption in period 2
c) Using both, find the intertemporal BC
A1 = Y1 - T1 - C1
makes sense, savings = disposable income - consumption
b)
C2 = Y2 - T2 + (1+r)A1
So consumption in period 2 = disposable income + savings which earnt interest from period 1
c)
C2 = Y2 - T2 + (1+r)A1
divide by 1+r to get A1 alone, then sub in our values of A1.
Final answer C1 + C2/1+r = Y1 - T1 + Y2-T2/1+r
Now government budget constraint: like households with no initial assets, assume no initial debt.
Government spend G1,G2 and raises T1,T2.
What is gov period 1 deficit (B1)
B1 = G1 - T1
deficit is expenditure - revenue
So what must taxes cover in period 2 (2)
b) tax in period 2 expression (T2) , which can be simplified
c) then find gov intertemporal BC
Since a deficit in period 1, taxes in period 2 need to cover G2, and also the debt from period 1.
b)
T2 = G2 + (1+r)B1
simplify by sub in B1
T2 = G2 + (1+r)(G1-T1)
c) start with
T2 = G2 + (1+r)(G1-T1)
divide by 1+r and rearrange to get
G1 + G2/1+r = T1 + T2/1+r
Then, sub gov intertemporal BC into consumer intertemporal BC
we get 2 equations to show the Ricardian equivalence
C1 + C2/1+r = Y1 + Y2/1+r - (T1 + T2/1+r)
which is
= Y1 + Y2/1+r - (G1 + G2/1+r)
Shows only path of government spending matter matters for consumption. timing of taxes does not affect consumption (since removed from equation)
Diagram of Ricardian equivalence pg17 (my own drawing)
(hint: let one side = Ω)
Draw it with initial point, then show effect of a fall in T1.
Fall in T1 means T2 increases. Households antiicpate this thus increase savings increase! (shown by the move A>B)
Meanwhile consumption unchanged!
When does Ricardian equivalence not hold (4)
If govt lives longer than households, e.g 3 periods, consumer only 2
Distortionary (consumption) taxes, not lump sum
Credit constraints
Differential borrowing rates between gov vs HH
Assume govt lives for 3 periods and the consumers for two periods only.
Govt budget constraint (4) then becomes
G1 + G2/1+r + G3/(1+r)² = T1 + T2/1+r + T3/(1+r)²
So all we did is add the extra period 3, and then square the interest
How does this affect our combined intertemporal BC for consumers and gov tho
C1 + C2/1+r = Y1 + Y2/1+r - (T1 + T2/1+r)
= Y1 + Y2/1+r - (G1 + G2/1+r + G3/(1+r)² - T3/(1+r)²
Key difference from 2 period model: now we include -T3/(1+r)² ! Taxes in period 3 is taken into consumption decisions! (They consider even though beyond lifetime since have kids, so save more and reduce consumption) however if do not care about bequests, ignore T3!
Now see effect of distortionary (consumption taxes)
Taxes are now
T1 = t1C1
T2 = t2=C2
What does period 1 saving now A1 now become
(Previously A1 = Y1 - T1 - C1)
B) what does C2 become now? (Prev C2 = Y2-T2+(1+r)A1, then
C) sub in our A1 to find consumer Intertemporal BC.
Key result” (working pg23)
A1 = Y1 - t1C1 - C1
= Y1 - (1+t1)C1
B)
C2 = Y2 - t2C2 + (1+r)A1
C)
Sub in A1
= Y2 - t2C2 + (1+r)[Y1-(1+t1)C1]
Then rearrange to get final eq
(1+t1)C1 + (1+t2)C2/ 1+r = Y1 + Y2/1+r
Key result: tax rates affect consumption
Next topic: credit constraints
People can not borrow as much as they want. What would this imply for their consumption in period 1 expression C1?
so C1 ≤ Y1 − T1 (Consume less/equal than their disposable income!
Then let optimal consumption levels in ABSENCE of this constraint be C1* C2*.
What if C1* > Y1-T1
B) summary of result: why is RE violated
Consumers are forced to choose C1 = Y1-T1 and C2=Y2-T2.
(cannot achieve optimal which is > than their disposable income as constrained by their C1 ≤ Y1 − T1, so just equal it!)
B) timing of taxes now affect consumption (consumption relies on disposable income, which includes tax!) (Under RE, timing didn’t matter; e.g no taxes no implies taxes in future, so save today in anticipation!)
Next topic: differential rates of borrowing for gov vs households
Assume gov borrows at rg, households borrow at rate r
Which will be higher?
r > rg since gov is less risky thus gets borrow at lower rate
Now adjust government Intertemporal BC for rg
G1 + G2/1+rg = T1 + T2/1+rg
Then find total resources available to private sector!
By combining gov BC and HH BC
HH BC = C1 + C2/1+r = Y1-T1 + Y2-T2/1+r
(Don’t bother, not gonna be asked)
Final eq for combined BC
C1 + C2/1+r = Y1 - G1 + Y2-G2/1+r + (r-rg)/1+r x (G1-T1)
Key result: T1 affects consumption!
This essentially means private sector gets the lower interest rate too, raising consumer wealth.
How?
Since gov can borrow at lower rate rg, running the deficit (G1-T1) is essentially a lower interest rate.
