Long Run Fiscal Policy

2 key elements of government spending (denoted as Gov_t)

• G in national income: expenditure on consumption and public capital

• transfer payments eg pensions (affects C through change in disposable income)

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how has Gov spending in OECD countries changed over last 100 years

grown a lot: increases in health, edu, social security along traditional spending like infrastructure

how does Gov spending redistribute resources

1. over lifetime (taxes when young, benefits when old)

2. across hh (progressive tax)

3. across generations (state pension system)

difference between G_t in national accounts and total Gov spending Gov_t

G_t only includes spending on GNS & public capital

Gov_t also includes transfer payments (that affect C through change in disposable income)

what are LRFP concerns related to population ageing

rising health/pension expenditures →.

how do debt crises manifest (3 reasons)

• higher cost of borrowing

• harder to borrow in financial markets

• sell assets in home currency = depreciation of currency

Government per period budget constraint

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what happens if D_t+1 > D_t (what does this mean in terms of debt, tax and gov_t

real debt increases due to the budget deficit the gov ran in period t+1

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what is a primary budget deficit

Gov_t+1 > Tax_t+1

how to obtain the Gov Intertemportal Budget Constraint (GIBC)

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what does the present value of all primary surpluses mean in fiscal policy

measures whether future revenues can cover future spending

tax revenues - non interest gov spending from time t+1 onward using the borrowing rate r_D as the discount factor

what happens if the present value of primary surpluses is too low relative to D_t

the gov is fiscally unsustainable→ cannot repay debt without:

• raising future taxes (Tax_t+i)

• cutting spending (Gov_t)

• defaulting

what is the no-ponzi condition definition

a rule that prevents the gov from perpetually rolling over debt without repaying it

value of the debt must eventually shrink to zero, meaning debt cant grow faster than the interest rate indefinitely

what happens if no ponzi condition is violated

gov engages in ponzi scheme and issues new debt to pay interest on old debt indefinitely

D_T​ > D_t​(1+r_D​)^T−t

^{results in loss of creditor confidence, higher borrowing costs}

why is the no ponzi condition economically necessary (3 reasons)

• prevents explosive debt: debt can’t grow faster than GDP indefinitely

• credibility: ensures lenders are repaid, maintaining market trust

• sustainable: ties current debt to future fiscal capacity, not infinite borrowing

simple explanation of the GIBC

• if debt today, need budget surplus in future

• flexible in SR, disciplined in LR

• interdependence of FP over time (borrow now = higher future taxes or lower future spending in future)

alternative way to write GIBC & what does it say

total tax revenues (present value of future planned taxes) must equal current debt + all future government spending (PV of future planned gov spending)

what’s happened to debt/gdp ratio (D/Y = d) for many countries since the FC

seen d increased above 100%

derive budget constraints from gov per period budget constraint using debt to gdp ratios

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what happens to primary surplus to gdp ratio when government runs a balanced primary budget (spending = tax)

ps_t+1=0

what needs to happen to primary surplus to gdp ratio, real interest, growth for debt to gdp ratio to rise over time

primary surplus to gdp ratio = 0

real interest > economy growth rate

then d_t+1 > d_t

approximating r and g tilda (real interest rate and economy growth rate)

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using approximations for i and r in debt to gdp ratio equation

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show debt to gdp ratio if debt is stable & what does it show

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all rates and ratios constant

when rD>econ growth rate, stabilising debt requires primary surplus

if econ growth rate>rD, can run a small deficit without debt growing

when is it easier to reduce d (look at change in debt to gdp ratio equation)

• nominal interest is low

• inflation is high

• economy growing strongly

• large primary surplus

HH problem in basic 2 period Overlapping Generation model (OLG model)

max lifetime utility over 2 periods

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get lifetime budget constraint from subbing constraints into each other

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solve hh problem (max utility s.t. LBC) using lagrangian

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maximising OLG on diagram

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no adjustment costs meaning

firms maximise profits by choosing K_t and L_t, taking prices (r_t + δ, w_t) as given → rental cost of capital and wage rate respectively

work out MPL_t and MPK_t from cobb douglas production function

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using no adjustment costs to find marginal products = to input prices equations

MPK = r_t​+δ

MPL = w_t

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what is the aggregate supply of capital

total assets held by young + total assets held by old

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equilibrium supply of capital expression

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obtain transition equation of OLG model

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what does the transition equation of the OLG model show

equation links today’s capital (kt) to tomorrow’s (kt+1) through:

household savings into next period

firm investment

capital share, patience, growth rate of effective workers

OLG model on diagram (kt, kt+1 space)

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how do gov fund spending

income tax

NICs = national insurance → funds state pensions

VAT

OLG model but giving workers a choice between labour/leisure & introducing taxes (and what are the constraints)

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combining the constraints to get the LBC in the OLG model with tax and worker choice

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interpretation of LBC for OLG model with taxes and worker preferences for leisure (look at total effects for capital income tax & tax on wages)

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LRFP with no debt and balanced budgets optimisation method

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LRFP with no debt and balanced budgets obtaining transition equation

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LRFP with no debt and balanced budgets - what does the transition equation tell us and what shifts it (and k*)

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how do OLG model steady states differ with government and without government

with government = lower steady state due to tax rate

government spending and crowding out takeaways

crowding out: higher taxes reduce private savings and capital

but can improve welfare and even help private sector grow (eg roads make them more efficient)

what are the two types of government expenditure

G_t: make people happy but dont boost production (enter through hh utility)

Public capital K_G,t: help businesses produce more (enter production function)

how does government finance spending (tax revenue)

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results of the LR impact of Gov expenditure on consumption and public capital spending

consumption: crowding out but people get extra utility

public capital: can make capital more productive, but lower disposable income

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what changes with LRFP with debt

government can now finance spending by accumulating debt

now, the capital equilibrium is K_t+1 + D_t = L_t a_t+1

means capital stock available in period t+1 equals total national net wealth (private sector wealth - government’s outstanding debt)

3 key points about debt

• debt crowds out capital accumulation

• debt has redistributional impact across generations

• under certain circumstances, debt and taxes may be equivalent

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5 reasons for PAYG pension system

market failures

behavioural issues

free riding

redistribution across generations

redistribution within generations

pension systems by funding structure

• fully funded system - pensions come from invested savings from fund - less burden on future taxpayers but market risks

  • PAYG - workers pay taxes to fund today’s retirees - no market risk but may struggle if population ages (less workers per retiree)

pension structures by payout rules

• defined contribution - save fixed % of salary

• defined benefit - pension based on salary/years worked

balanced & sustainable PAYG system

total amount of contributions by young = total amount of benefits received by old

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households maximisation problem + constraints (PAYG Pension System)

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steady state PAYG system (economy growth rate needs to keep up with pensions)

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what do aging populations force upon pension systems

increased tax for young, lower pensions for old

solve hh maximisation problem with pensions (combine constraints and use bt+1 = (1+gtilda)tax x wage

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what do pension taxes do to consumption in period 1,2, savings and capital accumulation

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why is PAYG inefficient if r> gtilda (explain what r>g tilda means as well)

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why do govs still use PAYG when r>g tilda

redistribution: transfers wealth to low earners who wouldn’t save enough privately

private pensions might not protect against longevity risk

how funded systems are different to PAYG

pension is b_t+1 = (1+r)θ_b​w_t

(no dependency on g tilda and no crowding out because savings earn r but expose retirees to market risk)

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tax wedge from payg

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challenges in reforming PAYG

transaction costs

risk: demographic shocks eg aging population

risks of funded pension systems

market volatility

complicated

but better in LT → shift PAYG to funded where possible