Financing of a Public Good by Taxation in a General Equilibrium Economy: Theory and Experimental Evidence

Juergen Huber, Martin Shubik and Shyam Sunder3rd LeeX International Conference on Theoretical and Experimental

MacroeconomicsUniversitat Pompeu Fabra, Barcelona, June 18-19, 2012

Basic Question

• How can societies efficiently finance provision of public goods/infrastructure?

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Answer

• The same way that human societies have employed over the recorded history

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Answer

• The same way that human societies have employed over the recorded history–By taxation–Little is new under the sun

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Overview• Predictions of a general equilibrium model in which public

goods/infrastructure 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

• Evidence favors evolution of government-enforced taxation as a social institution to address the problem of under-production of public goods

• Results even point to the possibility of over-production under taxation

• 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/infrastructure

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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 “perfect” decisions by intuition

• Without the guidance from context and institutions the individual may be overwhelmed by information overload and limited cognitive 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, in spite of agents’ 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 Financing 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), and others

• High initial contributions (e.g., 50% of optimal), decline towards 10 percent over time and experience in laboratory

• Few, little noted, papers with voting on a contribution rate (tax) implemented with or without possibility of “cheating”

• Main finding: close to 100% contribution rates with punitive enforcement, 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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In the Model

A 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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In the Model A private good andPublic good/infrastructure

(PG) that benfits all agents, financed through tax (or voluntary contributions) on income. Government buys private good from tax collected and builds/adds infrastructure to the stock which depreciates over time at a given rate.

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In the Model Private goodPublic good (PG)

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, 4,700 cash)• Government is computer-run; its only function is to collect

taxes (fixed, or set by subjects‘vote), use all tax collected 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 (either the optimal level of

427 in T1 and T3, or one half of optimal at 213 in T2 and T4)

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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 goodin 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 uses its share of private goods (taxes) 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 19

2x2 Experimental Design

Starting Level of PG

Optimal 0.5 X Optimal

Anonymous Voluntary Contributions

T0: 2 Sessions

Tax Rate Determination

Exogenous T1: 4 Sessions T2: 4 Sessions

By Vote (median) T3: 6 Sessions T4: 6 Sessions

Institutional Evolution by Vote

Starting with Anon. Vol. Cont.

T5A: 2 Sessions

Starting with Vote T5B: 2 Sessions

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Experimental Design• We examine the model in a laboratory setting when

– The economy provides for public goods through voluntary anonymous contributions (T0)

– The rate of taxation is fixed exogenously (starting from an optimum level of public good in T1 and 50% of optimal in T2)

– The rate of taxation is determined through median of agent proposals once every four periods (starting from an optimum level of public good in T3 and 50% of optimal in T4)

– Agents choose between AVC and tax regime through majority vote every four periods (and in the later case, choose tax rate as median of agent proposals)

• Compare the efficiency of the outcomes of the human subjects economy with the general equilibrium solution to the model– Note: fixing tax rate at optimum level 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

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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

Con

sum

ptio

nS

erie

s3S

erie

s5S

erie

s7S

erie

s9S

erie

s11

Ser

ies1

3

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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Figure 6A: Evolution of AVC and Tax Regimes through Majority Vote of Agents:Vote for Taxation (vs. AVC) in Four Sessions and Average

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1st vote 2nd vote 3rd vote 4th vote 5the vote 6th vote

0

1

2

3

4

5

6

7

8

9

10

run 1 run 2

run 3 run 4

Average

Tax R

ate %

Figure 6B: Evolution of AVC and Tax Regimes through Majority Vote of Agents: Chosen Tax Rate (Median of Individual Proposals)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 260

10

20

30

40

tax

rate

/vol

unta

ry co

ntrib

ution

rate

Figure 6C: Evolution of AVC and Tax Regimes through Majority Vote of Agents: Stock of Public Good (Four Sessions and Average

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250

100

200

300

400

500

Period

stoc

k of

pub

lic g

ood

Figure 6D: Evolution of AVC and Tax Regimes through Majority Vote of Agents: Efficiency in Four Sessions and Average

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250%

25%

50%

75%

100%

125%

Period

efficie

ncy

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

• Given the choice (through majority vote) between AVC and taxation, a good majority choose taxation

• Taxation may even over-build infrastructure• Directions for future work on financing of public goods?

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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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