Download Financing of Public Good by Taxation in a General

Financing of Public Good by Taxation in a
General Equilibrium Economy:
Theory and Experimental Evidence
Shyam Sunder, Yale University
(with Juergen Huber and Martin Shubik)
Max Planck Institute for Collective Goods
Bonn, Germany, July 14, 2011
Importance and Financing of Public Goods
• Public goods are important; how do and should
societies finance them?
• Experimental work, mostly voluntary anonymous
contributions
• Ledyard survey of pre-1995 literature; more recently
Fehr and Gächter (2000); Gunnthorsdottir, Houser and
McCabe (2007); Brandts and Schram (2001); Palfrey
and Prisbrey (1997)
• High initial contributions ), e.g., 50 percent of optimal),
tend to decline towards 10 percent over time and
experience
Financing Public Goods in General Equilibrium
• We modify a general equilibrium model of the economy to include
government and a full process description of agents playing both
economic (market) and political (voting) roles.
• We use a process oriented strategic market game in which the provision of
public goods is financed through taxation on private income.
• The unique equilibrium solution for any tax rate yields an optimal
consumption/investment policy for each individual.
• A general dynamic programming analysis of our basic model enables us to
solve for an optimal rate of taxation for society as a whole using symmetry
of the agents in the model.
• Simplification some fundamental features of government control of
taxation, and public debt creation to provide valued public services.
• Hatzipanayotou and Michael (2001) who deal with public goods, tax
policies and unemployment in LDCs is closer to the spirit of our own
approach where institutional structure plays an important role in the
economy.
Experimental Design
• 2x2 treatment
• We examine the model in a laboratory setting when
– The economy starts from an optimum level of public good, and
– When it starts at 50 percent of the optimum level
• The efficiency of the outcomes of the economy will be compared
– When the rate of taxation is exogenously fixed at the theoretical optimal level,
which is practical only in a hypothetical world of an omniscient government;
and
– When the rate of taxation can be adjusted by the political process that moves
on a longer time scale than the day-to-day economic process (tax rate set to
the median of the individual proposals)
• Compare the outcomes of the human-subject against two benchmarks:
– The general equilibrium solution to the model, and
– Outcomes of economies populated by minimally-intelligent artificial agents
Determination of Tax Rate
• It is an open question as to whether government
coordination and taxes for the production and
maintenance of an optimal supply of public goods
dominates the informal coordination, and
decentralized mechanism to set the tax rate
provided by social and political pressure. We
suspect that the outcome depends on not merely
divergence of preferences, but on the
technological understanding of the costs and
benefits of the public goods involved.
Gaming, Context and Purpose
• Many of the experiments carried out so far in the area of “public
goods” are best interpreted as contributions to economic
anthropology and social-psychology.
• They stand in contrast with the pioneering work of Plott on testing
of existing and proposed institutional designs in addressing specific
problems.
• Evolution of institutions occurs in calendar time where history,
context, learning, experience, tradition and innovation all matter.
The extent to which we may make useful analogies and draw valid
inferences from laboratory games lasting but an hour or two in a
radically different time scale and context remains open, and is
worth mentioning here for caution. Contributions of experimental
gaming to the development of an economic science should be
considered in this institutional context.
Time compression problems
An Initial Attempt to Try Different Time
Scales
• In the experiments to date economists hardly
take into account the differences in time
scales concerning the various decision-makers
involved in public goods decisions. In our
experiment we take a small step to address
this matter by introducing “annual” economic
decisions on production and consumption
alongside “quadrennial” the politico-economic
decisions for choosing the tax rate, to
implement at 4:1 ratio in the two time scales.
Context
• Public goods decisions are not made in an institutional vacuum. The
British history of “the tragedy of the commons” does not offer
much in the way of insights as to how to finance or build a modern
network of roads. Modern states evolved by enforcing weights and
measures, commercial codes, accounting rules, law and order, and
tax collection. In the present work, we take the structure of
government as a given.
• Our experiments are directed towards the minimal institutional
underpinnings of economic theory. Institutions carry the socioeconomic processes and link the static models of much economic
theory to economic dynamics. As can be seen in Appendix A and
the appropriate references (KSS 2008) we consider a dynamic
version of Samuelson's pure public good (Samuelson, 1954)
embedded in a parallel dynamic programming control process that
has been solved for its type-symmetric non-cooperative (more
popularly called rational expectations) equilibria.
Endogenous Development of Public
Policy
• Our model is symmetric on purpose, so each
individual has the same valuation of the worth of
both the public and private good. Letting them
choose the level of public spending through a
vote allows us to explore the possibility of
endogenous development of cooperative sociopolitical norms among these student subjects, as
well as their ability, or lack thereof, to learn,
discern, and attain the level of the public good
that best serves their collective interest.
Experimental Setup
• 10 subjects in identical situation
• There is money and two kinds of goods in the economy
• The private good produced, sold, bought and consumed by the
participating subjects; some the private good is also bought by the
government and used to produce the public good.
• The public good (e.g., a public facility) which depreciates at the rate
of 10 percent per round. The government uses tax collected from
subjects to replenish the depreciating stock of public good.
• Each subject initially endowed with quantity of private good and
money (a, m) = (217, 4700).
• Private good production function is:
• UNITS OF THE PRIVATE GOOD PRODUCED = 80*(UNITS
INVESTED)0.25
Experimental Setup
• The government is endowed with G=427 units of the
public good and M = 13,000 units of money at the
outset.
• It also has the right to tax a fraction θ of individuals'
production of private goods, and a public good
production function that transforms its tax revenues
into public goods:
• UNITS OF THE PUBLIC GOOD PRODUCED = 2*(UNITS
OF PRIVATE GOOD INVESTED)0.5
• Public good stock depreciates by 10 percent each
period
• Production of public good is added to the stock
Market Structure
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Sell-all minimal market structure:
All money in the hands of the 10 agents (47,000 in period 1) and government
(13,000 in period 1) is pooled and divided by all units in the hands of the 10 agents
(2170 in period 1) to determine the price (27.65 in period 1)
Allocations to 10 agents (170 units of good and 6,000 units of money in period 1)
and government (13,000/27.65 units of private good in period 1)
Government collects taxes at rate theta on money income of agents
Agents divide their allocation of good between consumption and production of
private good for the next period
UNITS OF THE PRIVATE GOOD PRODUCED = 80*(UNITS INVESTED)0.25
Government converts its share of private goods to produce public goods:
UNITS OF THE PUBLIC GOOD PRODUCED = 2*(UNITS OF PRIVATE GOOD
INVESTED)0.5
Perod payoff of agents = private good consumed +public good stock/4
Money is just medium of exchange, has no other role in the economy
Stock of Public Good (Figure 1)
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The top left box in Figure 1 shows the time series of the stocks of public good observed during the four
independent sessions of the experimental economy with fixed tax rate (21.5%), starting with the optimal level
(427) of the public good in Period 1 (in thin grey lines). The mean of these four paths is shown in a dark thick line,
and the general equilibrium prediction is shown in a dark dashed line. Similar conventions are used to depict data
in the other boxes of Figure 1 and in other figures.
In all four of these sessions, the stock of public good gradually but quite steadily declined over the 26 rounds from
the optimal starting level (427) to the range of 350-399 and to an average of 376. The top right box in Figure 1
shows that in four runs of a similar economy with tax rate fixed at the optimal level (21.5%) but starting with 50
percent of the optimal level of public good (213.5), the stock of public good rose steadily from 213.5 to the range
of 351-366 and to an average of 360 (with very little variation across the four sessions).
In the bottom left box, the six sessions with endogenously determined tax rate starting with optimal level of public
good (427), the stock of public good tended to decline over the rounds to the range of 348-398 and to an average
of 364. In the bottom right box, the six sessions with endogenously determined tax rates but starting from half the
optimal level of public good (213.5), the stock of public good tended to rise to the range of 269-402 and to an
average of 340.
A comparison of the data in the four boxes of Figure suggests some differences but also some similarities. The
stock of public good shows great dispersion across economies when tax rates are endogenous instead of being
fixed. Starting from the optimal level, the stock of public good tends to decline to the neighborhood of 370
irrespective to whether the tax rate is fixed or determined by the vote of participants. Similarly, starting from the
suboptimal level, the stock of public good tends to rise gradually to the neighborhood of 360 irrespective of
whether the tax rate is fixed or determined by the vote of participants.
Perhaps it is not unreasonable to infer, on the basis of these 20 independent sessions of the economies that the
stock of public good tends towards the range of 350-375, and this range seems to form a domain of attraction for
these economies. This domain is below the optimum (427), but even further away from zero, which would also be
a possibility.
Figure 1: Stock of Public Good in Economies
Grouped by Four Types of Sessions
Efficiency (Figure 2)
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Efficiency of these economies is defined as the percent of the total points earned by all subjects as
a percent of the number of points they would have earned if the economies had achieved general
equilibrium outcomes. Results for the 20 sessions are presented in the four boxes of Figure 2 which
parallel the layout of boxes in Figure 1 for stock of public good.
With fixed tax rate and optimal start (top left box) efficiencies started close to 100 percent tended
to decline gradually, albeit noisily, to the range 67-91 percent and average of 80 percent. With
suboptimal start (top right box) efficiencies lie near 80 percent at the beginning and the end of the
sessions with little perceptible drift over time. With endogenous tax rates and optimal start
(bottom left box) efficiencies remain scattered around the low 90s. Only with endogenous tax rates
and suboptimal start (bottom right box) do the efficiencies show a steady rise from low 70s to mid
80s over the 26 rounds.
Perhaps it is reasonable to infer that 80-90 percent is the domain of attraction for the efficiency of
these economies. Also, efficiency is slightly higher with endogenous choice of tax rate.
While the stock of public good and efficiency of these economies are overall measures of their
performance, we can also assess the decisions made by subjects that led to these outcomes. In the
following paragraphs we present the analysis of the subject decisions.
Figure 2: Efficiency of Public Good Economies
Grouped for Four Types of Sessions
Figure 3: Total Production of Private Good in
Economies Grouped by Four Types of Sessions
Figure 4: Total Consumption as Percentage of Total Individual Purchases of
Private Good in Economies Grouped by Four Types of Sessions
Figure 5: Total Consumption as Percentage of General Equilibrium Consumption of
Private Good in Economies Grouped by Four Types of Sessions
Figure 6: Tax Rates
Conclusions
• We are not there yet!
Screen 2
History Screen
Production Function:
UNITS OF THE PRIVATE GOOD PRODUCED = 80*(UNITS INVESTED)0.25
125
Units of goods produced
100
75
50
25
0
0
10
20
30
40
50
60
Units of goods invested into production
70
80
90
100
Public Good Production Function:
UNITS OF THE PUBLIC GOOD PRODUCED = 2*(UNITS OF PRIVATE GOOD INVESTED)0.5
35
Units of public good produced
30
25
20
15
10
5
0
0
50
100
150
200
Units of private goods invested into production of public good
250
300
Payoff Function
• POINTS = CONSUMPTION OF PRIVATE GOOD +
PUBLIC GOOD/4