Transcript Slide 1

Ec426 Public Economics
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Intertemporal public finance: A global
deal?
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Intertemporal public economics
1. Intertemporal welfare economics and the golden
rule
2. The burden of national debt
3. Discounting and the climate change controversy
4. Redistributing across people, across time, and
across generations
5. Conclusions: a global deal?
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1. Intertemporal welfare economics and
the golden rule
To introduce time, define “dated commodities”: xit is the consumption of
good i at date t, where t goes from period 1 to T. Then apply the static First
and Second Theorems of Welfare Economics to an intertemporal economy.
Competitive equilibrium is Pareto-efficient, and the introduction of any tax or
government expenditure is a distortion. There is an inevitable
equity/efficiency trade-off.
BUT
This assumes that there is a full set of markets: we can trade today in all
future goods and services. In reality, futures markets are highly incomplete. A
more realistic starting point is a succession of spot markets (one can only buy
xit in period t), linked by holdings of assets (savings).
AND
Time introduces a new dimension of justice: equity between generations.
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Away from the first-best
Where the pre-intervention equilibrium is not efficient, or where government
objectives are not welfarist*, then the policy problem is different. This
applies to government aims in a static economy:
where Pareto efficient
Minimise distortion of consumer choice
where not Pareto efficient/not welfarist
Discourage consumption of goods that generate
negative externalities (e.g. pollution)/encourage
those with positive externalities.
Level playing field in labour market.
Encourage people to enter labour market/
retire later.
AND TO AN INTERTEMPORAL ECONOMY
Minimise distortion of savings decisions.
Encourage people to save more (or less).
(Compensated elasticities crucial.)
(Total elasticities crucial.)
* The social welfare function is welfarist where it can be written as solely a non-decreasing
function of individual utilities, W[U1, U2, ..., Uh].
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A simple intertemporal (growth) model
Savings determine the level of consumption in period t: ct. Suppose that
output per unit of effective labour is given by f(kt), where kt is the level of
capital per head of effective labour at the start of period t. Assume f(0)=0,
f′>0, f″<0.
The labour force grows each period by a constant factor (1+n), and there is
labour-augmenting technical progress at rate λ, so that the effective labour
force grows at the rate of (1+n+λ).
The capital stock per unit of effective labour then evolves according to
kt+1 = [kt + f(kt) – ct]/(1+n+λ)
This is a steady state where kt+1 = kt, or (n+λ)k+ = f(k+)-c+.
In this steady state, consumption per head grows in each period by a factor
[1+ λ/(1+n)]; there is positive growth on account of technical progress. On
the other hand, if an increasing proportion of the labour force were required
to clear up environmental damage, then λ could be negative, and
consumption per head would fall.
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Golden rule
Per efficiency
unit of labour
Savings = f(kt)-ct = sf(kt)
At the Golden Rule, the savings rate is
equal to
(n+λ)k
●
The steady state with savings rate s is
given by k+.
Varying the savings rate, the highest
level steady state consumption path is
given by k* such that f′(k*) = n+λ, i.e.
the competitive rate of return is equal
to the growth rate. This is the Golden
Rule.
Slope
(n+λ) f(k)
Consumption
●
k+
sf(k)
k*
k
(n+λ)k*/f(k*) = f′(k*)k*/f(k*),
and hence is equal to the competitive
share of profits in national income.
For references to macroeconomic “golden rules”, see
F Balassone and D Franco,
Fiscal Studies, 2000.
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Slope
(n+λ)
Possible dynamic inefficiency
Should public policy aim to increase
the savings rate in order to move
the economy towards the golden
rule?
Not necessarily, since all we have
done is to compare steady states. If
k is below k*, then moving to k* will
involve lower consumption initially.
(n+λ)k
●
sf(k)
k*
k+
The one welfare conclusion that can
be drawn is that, if we start above
the golden rule, then it is possible
to consume more and move to a
higher steady state growth path.
A steady state with k+ greater than
the golden rule level k* is
dynamically inefficient (Myles, page
444).
BUT how are savings
determined?
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Overlapping Generations Model: Samuelson/Diamond
Myles, Chapter 13,
pages 434-445
Generation 1
Works in period 1
Retires in period 2
Earns w, saves w-c1
Consumes c2 =
(w-c1)(1+r)
No bequests
Lifetime utility max(1-σ)log(c1) + σlog(c2) subject to c1+c2/(1+r) = w
implies savings = σw
(NB savings do not depend on r, so no need to form expectations about future
interest rate.)
The savings of
generation 1 provide
the capital with which
generation 2 works
Generation 2
Works in period 2
Retires in period 3
Earns w, saves w-c1
Consumes c2 = (w-c1)(1+r)
With Cobb-Douglas utility function, gross savings are σw. The wage share is likely to
be larger than the profit share, but σ is less than 1, and allowance has to be made
for dissaving by older generation. So savings may be greater or less than Golden8
Rule (see Myles, page 444).
2. The burden of national debt
Can use of (internal) debt finance transfer to the future the burden of funding
current government?
For internal debt, different views:
•
Old “no burden” view: resources for current spending come out of today’s
production (Keynes);
•
Burden can be transferred via reduced capital accumulation (Modigliani);
•
Classical and new “no shifting of burden” view (Ricardo/Barro).
Begin with fact that taxation has intertemporal consequences.
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Government expenditure financed by taxation
Government expenditure E in period 1, financed by taxation T = E or by borrowing E.
Is there a different effect? Depends on who pays taxes.
Generation 0
TAXATION levied on retired generation
Works in period 0
Retires in period 1
Earns w, saves σw, consumes σw(1+r)-E in period 1 No impact on subsequent generations.
Generation 1
TAXATION levied on working generation
Works in period 1
Retires in period 2
Earns w - E, saves σ(w-E), consumes (1-σ)(w-E) in period 1
Capital with which generation 2 works is reduced by σE, causing r to rise and w to fall; rise in
r partly offsets loss to Generation 1.
Generation 2
Works in period 2
Retires in period 3
Earns a lower wage w, saves σw, consumes (1- σ)w
Where process stable (see Myles), capital with which generation 3 works is reduced by less
than σE, so that r in period 3 lower than in period 2, and wage in period 3 higher than in
period 2. In this way, the economy returns to previous equilibrium. Throughout transition, all
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generations are worse off.
Suppose now that government expenditure E in period 1 is financed by
borrowing from generation 1
Generation 1
Works in period 1
Retires in period 2
Earns w, saves σw, consumes σw(1+r) in period 2.
Capital available for production is σw-E, which is less than with tax finance, so r in
period 2 rises more and w falls more.
In period 2, government has obligation (1+r)E/(1+n+λ) per efficiency unit of labour.
Note that this is growing over time if r is greater than the rate of growth. There is
therefore the second-round effect of the taxes necessary to finance the debt. This
second-round effect depends on who pays the taxes, and on whether these taxes are
fully anticipated.
Where taxes are levied on the retired generation, this provides an incentive for them
to save (it is the reverse of a retirement pension).
In an extreme case, suppose that the government fully redeems the national debt in
period 2, levying a tax (1+r)E per retired person (NB there are 1/(1+n+λ) of them per
efficiency unit). Where this is fully anticipated, then it is the same as reducing w by E,
so that there is no difference between debt and tax finance. This is the case of
Ricardian equivalence.
BUT
“it must not be inferred that I consider the system of borrowing as the best calculated
to defray the extraordinary expenses of the state. It is a system that tends to make
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less thrifty” (David Ricardo, 1821, page 162).
Ricardian equivalence and generations
Ricardian equivalence has been extended beyond a single lifetime by the
assumption that the utility function of generation i is concerned not only
with its own consumption but also with the consumption of subsequent
generations.
This is represented by dynasty i maximising a dynastic welfare function
∑t=i ∞(1+δ)-t U(ct)
(1)
where δ is the discount rate applied to utility.
It is not obvious how this is combined with overlapping generations, where
each person in generation i gets lifetime welfare from consumption,
u(c1i)+ σ/(1-σ)u(c2i), denoted by Vi.
Suppose that 2 generations are alive at date i: generations (i-1) and i. The
consumption at date i is made up of c2(i-1) and c1i. Do we replace U(ci) in (1)
by u(c1i)+ σ/(1-σ)u(c2(1-1))? Or do we replace U(ci) by Vi? If the latter, what
happens to the second period consumption of generation (i-1)?
Where the population is growing, are the u() and V weighted by population
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size?
3. Discounting and the climate change
controversy
A project gives rise to a flow of costs and benefits in terms of consumption at
different dates, ct. If the social welfare function is an additive function of the
consumption at different dates, then the social marginal valuation of a unit of
consumption at date t is given by
1/φ(t) = 1/π(t) U′(ct)
Consumption at t may be “discounted” relative to consumption at an earlier
date either via the factor d(t) or via the value of ct being different.
Discounting raises strong passions, and there are strongly differing views: e.g.
• Should not discount (“ethically indefensible” (F P Ramsey));
• Should discount at the rate of return on private investments;
• Should (in UK) follow the Treasury Green Book methodology “used to make
an economic assessment of the social costs and benefits of all new policies,
projects and programmes”, and discount at 3.5% per cent.
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HM Treasury Green Book
“The discount rate [the social time preference rate, STPR] is used to convert
all costs and benefits to ‘present values’, so that they can be compared. The
recommended discount rate is 3.5 per cent (real). … For projects with very
long-term impacts, over thirty years, a declining schedule of discount rates
should be used.”
The STPR is made up of four elements*:
STPR = δ1+ δ2 + η g
where
δ1
is the risk of catastrophe;
δ2
is the pure rate of time preference applied to utility;
η
is the elasticity of marginal utility with respect to consumption;
g
is the expected future growth of consumption.
The Treasury takes the sum of δ = 1.5, η = 1 and g = 2 per cent.
Utility
discounting
Due to
growth
* These come from differentiating φ logarithmically:
(1/φ)dφ/dt = (1/π)dπ/dt + [-U″/U′] dc/dt and η = [-U″.c/U′]
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N H Stern, “The economics of climate change”, American Economic Review, May 2008.
All of these elements can be debated
This has been demonstrated in the discussion of the Stern Review on the Economics of
Climate Change: e.g. “the discount rate we choose is all important and Stern’s results
come from choosing a very low discount rate, [but] we are a lot less sure about core
elements of discounting for climate change than we commonly acknowledge” (M
Weitzman, Journal of Economic Literature (JEL), 2007).
STPR = δ1+ δ2 + η g
δ1
is the risk of catastrophe; Treasury take as 1 per cent; Stern as 0.1 per cent.
Latter implies 10 per cent chance that world ends in next 100 years.
δ2
is the pure rate of time preference applied to utility; Stern takes zero, which
Treasury describes as “implausible”.
η
is the elasticity of marginal utility with respect to consumption;
Treasury takes 1, as does Stern; but Nordhaus, JEL, 2007, takes 2.
g
is the expected future growth of consumption; the Treasury takes 2 per cent
on basis of past experience, but others question whether growth will continue.
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Problems with the underlying framework
• Constant discount rate is a straitjacket
HM Treasury applies lower rate after 30 years;
• Why not use the private return to capital?
Not starting from first-best;
Externalities;
Rising relative cost of environmental cleanup;
• Uncertainty versus risk
Knightian uncertainty;
Precautionary principle;
• Not a marginal change
SDR endogenous;
Growth rate depends on policies chosen;
• Non-welfarist ethical positions
Fairness;
Responsibility.
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4. Redistributing across people, across
time, and across generations
At the heart of the debate about climate change are
distributional issues that are not simply a matter of calendar
time:
• between rich and poor countries,
• between rich and poor within countries,
• between generations.
All of these
• involve judgments about the social marginal value of income
(consumption),
• and involve non-welfarist concepts of justice.
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Social marginal value of income across people at a point in time
The social discount rate was concerned with the treatment of consumption at
different dates, but should the principles differ from those applied to the
consumption of different people at the same date? If we discount the
consumption of person A in 2050 because he is 2.2 times richer (40 years of 2
per cent growth), should we not do the same for a person today who has
£110k rather than £50k?
The elasticity of the social marginal utility of income, η, appears in measures
of income inequality as the degree of relative inequality aversion. The values
typically taken are 1.0 or less: e.g. according to the US Census Bureau, the
parameter is bounded by the limits of 0 and 1. The Luxembourg Income Study
Key Figures uses values of 0.5 and 1.0.
The parameter has been interpreted in an inequality context in terms of the
“leaky bucket experiment”.
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Leaky bucket experiment (Okun)
leakage
Transfer
$1 from person with income Y to give $(1 - ℓ) to person with income Y/z
Denoting social marginal valuation of income by φ(Y), transfer desirable
where
φ(Y/z) > φ(Y)/( 1 - ℓ)
Depends on elasticity of φ(Y). If constant at , then require
ℓ < 1 – z -
elasticity = ½ implies accept transfer from US P50 (median) to US P10
(bottom decile) where loss less than 50% (since median approximately 4 x
bottom decile);
elasticity = 1 implies accept transfer from P50 to P10 where loss is less than
75%;
elasticity = 2 implies accept transfer from P50 to P10 where loss less than
93.75%.
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STPR
Citizens of UK today
rich
Leaky
poor bucket
Citizens of UK in 2050
rich
poor
Citizens of Africa in 2050
rich
ODA
poor
Citizens of Africa
today
rich
poor
Transfers across time and across countries
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5. Conclusions: the need for a global deal
• Climate change (Copenhagen);
• Development (MDGs);
• Macro-economic stability (G20);
• World trade and mobility of capital and
labour (DOHA+).
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