Juergen Huber, Martin Shubik and Shyam Sunder Indian Institute of Management, Calcutta
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Financing of a Public Good by Taxation in a General Equilibrium Economy: Theory and Experimental Evidence
Juergen Huber, Martin Shubik and Shyam SunderIndian Institute of Management, Calcutta
March 2, 2012
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Overview• Predictions of a general equilibrium model in which
public goods are efficiently financed by a democratically-chosen rate of taxation are largely supported in laboratory economies
• In contrast, voluntary anonymous contributions fail to support efficient level of public goods
• The results point to the possibility that the social institution of government-enforced taxation may have evolved to address the problem of under-production of public goods
• Q: Chances of success of continuing the search for decentralized mechanisms for financing public goods?
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Public Goods and Taxation
• Project to explore the role of institutions in economic life through theory and experimentation
• Complexity of public financing in a modern society
• Importance of taxation in providing the coordination needed for the provision of public goods
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Context and the success of Microeconomics
• Success of microeconomic analysis to specific problems such as industrial organization and taxation
• Context specificity of human rationality• Without the guidance from context and
institutions the individual may be overwhelmed by information overload and limited skills in a complex world
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Economic Dynamics• Much of microeconomic theory built on the
static model of utility or profit maximizing agent that provides a gross simplification of economic behavior
• Dynamics frequently treated by comparative statics
• Our basic premise: institutions and the context of the socio-political structures are critical to the understanding of economic dynamics.
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Minimal Institutions• We build (here and in related work) fully
specified game theoretic models of the phenomenon of interest, and to observe their performance in laboratory.
• Minimal institutional structures emerge as part of the rules of the game
• These include representations of markets, money, government, taxation enforcement mechanisms, and depending on the question at hand, financial instruments and institutions
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Comparing Theory and Experimental Observations
• These models of strategic market games are solved for their sub-game perfect non-cooperative equilibria, using dynamic programming
• Observations from experimental games are compared with these equilibrium predictions
• The experimental subjects are not briefed to solve dynamic programs; yet the institutional structures reflected in the rules of the game often yield outcomes that approximate optimal outcomes, even with agents having limited cognitive abilities
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“As If” versus Institutional
• This approach may appear to be consonant with Milton Friedman’s views that we merely have to show that individuals behave “as if” they are rational optimizers.
• Our argument: this apparently sweeping statement is in actuality highly context and institution specific
• It is the institution that bears the burden of providing the means for the ordinary individual agent acting relatively simply and locally to coordinate, and yield outcomes in the neighborhood of the optima
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Taxation with and without Voting
• In game theory, RE equilibrium (often used in macroeconomic studies) is the same as a sub-game perfect non-cooperative equilibrium with a continuum of agents
• Game theoretic models of tax-financed public goods yield different non-cooperative equilibria with and without voting
• These differences appear in experimental observations from laboratory exercises
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Prior Experimental Work on Public Goods
• Experimental work, mostly voluntary anonymous contributions in partial equilibrium economies
• 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 in laboratory
• Few, little noted, papers with voting on a contribution rate (tax) that is then either implemented or “cheating” is possible.
• Main finding: close to 100% contribution rates when enforced or punishment possible, otherwise low contributions (Kroll et al. Economic Inquiry, 2007)
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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
• Provision of public goods financed through taxation on private income
• Each tax rate yields a unique equilibrium solution and consumption/investment policy for individuals
• Dynamic programming solution for an optimal rate of taxation for society as a whole using symmetry of the agents
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The Model One private good that is produced and traded.Can be used for consumption or as input for production of private or public good.
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The Model Private good that is produced and traded.Can be used for consumption or as input for production of private or public good.
Public good (PG) that benfits everybody. Financed through tax (or voluntary contribution) on income. Governmentbuys private good from tax collected and produces public good. The production of public good is added to itsstock which depreciates over time at a given rate.
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The Model Private good that is produced and traded.Can be used for consumption or as input for production of private or public good.
Public good (PG) that benfits everybody. Financed through tax (or voluntary contribution) on income. Governmentbuys private good from tax and Provides PG from this. Stock of PG depreciates over time.
Money is just a means of exchange (and taxation)
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Procedure• 10 subjects in an economy, all are producer/consumers of the
private good. • Equal starting endowments (217 private goods, 4700 cash)• Government is computer-run; its only function is to collect
taxes (fixed or set by subjects by a vote), use all tax to produce public good (no waste).
• Initial endowment with – money (4,700 each subject, 13,000 government, for a total of 60,000,
remains fixed throughout the session) and – private goods (217 each subject), as well as – An initial stock of public goods (427 which is the optimal level, or one
half of that at 213)
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Sequence of decisions• Determine tax rate (exogenously, or by vote--median)• Stock of public good depreciates by 10%• Sell-all minimal market structure for private goods:
All the money (47,000 in period 1 in the hands of the ten agents and 13,000 with the government in period 1) is pooled and divided by all units of the private good in the hands of the ten agents (2,170 in period 1) to determine the price (27.65 in period 1)
• Allocations to ten agents (170 units of good and 6,000 units of money in period 1) and government (470 units of private good in period 1)
• Government collects taxes on money income of agents• Agents divide their allocation of good between consumption and
production of private good for the next periodUNITS OF THE PRIVATE GOOD PRODUCED = 80*(UNITS INVESTED)0.25
• Government converts its share of private goods to produce public goods:PUBLIC GOODS PRODUCED = 2*(UNITS OF PRIVATE GOOD INVESTED)0.5
• Period payoff of agents = private goods consumed +public good stock/4JSS: Public Goods 16
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2x2 Experimental Design
Starting Level of PG
Optimal 0.5 X Optimal
Tax Rate Determination
Exogenous T1: 4 Sessions T2: 4 Sessions
By Vote T3: 6 Sessions T4: 6 Sessions
Anonymous voluntary contrib. T0: 2 Sessions
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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 Tax rate exogenously fixed at the theoretical optimal level,
practical only in a world of an omniscient government;– When tax rate 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 : – The general equilibrium solution to the model
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Payoff FunctionPOINTS = CONSUMPTION OF PRIVATE GOOD + PUBLIC GOOD/4
224.061913541636
5101520253035404550556065707580859095
0
30
60
90
120
150
180
210
240
Consumption
Series3
Series5
Series7
Series9
Series11
Series13
Total Utility as a Function of Consumtion and Tax Rate
Consumption Rate
Total Utility
Tax Rate
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Different Time Scales
• Much economic theory (and experimental work) neutral in time scale
• But different decisions may involve quite different time scales
• 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.
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Figure 1: Stock of Public Good in Economies Grouped by Types of Sessions
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Figure 1: Stock of Public Good in Economies Grouped by Types of Sessions
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Figure 1: Stock of Public Good in Economies Grouped by Types of Sessions
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Figure 2: Tax Rates
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Figure 3: Efficiency Grouped for Four Types of Sessions
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Figure 4: Total Production of Private Good Grouped by Four Types of Sessions
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Figure 5: Total Consumption as Percentage of Total Individual Purchases of Private Good
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Summary• Contribution rates fall to zero when
contributions are voluntary, but remain fairly high when set through a (binding) vote on rate of taxation
• Consumption rates are on average higher than in the theoretical optimum
• In a fairly demanding public goods setting, democratic vote as a mechanism to set contribution rates achieves high levels of efficiency
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Thank you!Huber, Juergen, Shubik, Martin and Sunder, Shyam, Financing of
Public Goods Through Taxation in a General Equilibrium Economy: Theory and Experimental Evidence (October 28, 2011).
Cowles Foundation Discussion Paper No. 1830. Available at SSRN: http://ssrn.com/abstract=1950643
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Screen 2
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History Screen
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Private Good Production FunctionUNITS OF THE PRIVATE GOOD PRODUCED = 80*(UNITS INVESTED)0.25
0 10 20 30 40 50 60 70 80 90 1000
25
50
75
100
125
150
175
200
225
250
275
Units of goods invested into production
Units
of g
oods
pro
duce
d
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Public Good Production Function:UNITS OF THE PUBLIC GOOD PRODUCED = 2*(UNITS OF PRIVATE GOOD INVESTED)0.5
0 50 100 150 200 250 3000
5
10
15
20
25
30
35
Units of private goods invested into production of public good
Units
of p
ublic
goo
d pr
oduc
ed
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Payoff Function
• POINTS = CONSUMPTION OF PRIVATE GOOD + PUBLIC GOOD/4
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