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International Tax and Public Finance

Erschienen in:

08.12.2016

Social planning and coercion under bounded rationality with an application to environmental policy

verfasst von: Beat Hintermann, Thomas F. Rutherford

Erschienen in: International Tax and Public Finance | Ausgabe 5/2017

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Abstract

We develop a theory of social planning with a concern for economic coercion, which we define as the difference between consumers’ actual utility and the “counterfactual” utility they expect to obtain if they were able to set policy themselves. Reasons to limit economic coercion include protecting minorities and preventing disenfranchised groups from engaging in socially costly behavior, or political economy considerations. If consumers are fully rational, we show that limiting coercion is equivalent to placing more welfare weight on coerced consumers at the expense of others. If, however, consumers’ rationality is bounded, counterfactual utility becomes endogenous to current policy, and the welfare loss associated with limiting coercion increases. We set up a numerical version of our model and find that the bias-related welfare loss can be substantial.

Vorheriger Artikel Can fiscal equalisation mitigate tax competition? Ad valorem and residence-based taxation in a federation

Nächster Artikel National income taxation and the geographic distribution of population

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Coercion is the “act, process or power of coercing”, with the definition of the relevant verb given by Merriam-Webster as (1) to restrain or dominate by force, (2) to compel to an act or choice, or (3) to achieve by force or threat. There are many forms of coercion. In this article, we abstract from physical coercion by assuming that the government has a mechanism to levy taxes and focus on the coercion that arises from the necessity of using some sort of collective choice mechanism.

Winer et al. (2014) call this the “individual-as-dictator” approach. Note that we maintain the assumption that consumers take the given tax system as given in the sense that they can only adjust existing tax rates rather than overhaul the entire tax system.

Even though members of a society are coerced by group rules, joining the group may convey greater utility for an individual than remaining outside, mainly due to the coercion of others, e.g., in the context of enforcing contracts (Baumol 2003).

For a legal discussion, see, e.g., http://law2.umkc.edu/faculty/projects/ftrials/conlaw/takings.htm, last accessed in August 2016.

For a review of this literature, see Bernheim and Rangel (2007).

We need public provision in our model in order to justify the need for raising and spending government revenue. Furthermore, we need more than one public good to allow for disagreement (and thus scope for economic coercion) not only with respect to the size of the government, but also with respect to the composition of public expenditure. Since environmental quality, and especially climate change, is a particularly salient example of a public good over which disagreement exists, we include it in our numerical illustration below.

To improve readability, this paper uses the masculine third-person personal pronoun in a gender-neutral sense for the remainder of the paper.

We assume constant production costs of the public good and normalize its unit (or their units, if G is a vector) such that the cost is one. If public production technology is general rather than linear, the cost of public provision would change with a marginal change in tax rates along with private producer prices.

An alternative way to account for coercion would be to incorporate it into the welfare function, along with the potential consequences of civil unrest, rather than imposing an exogenously defined coercion constraint. However, this requires a (presumably exogenous) weighting of coercion relative to the utility from consumption, such that the fundamental problem of trading off welfare versus coercion remains.

We allow the coercion constraint to differ across consumer groups in order to avoid having to trade off one consumer’s coercion against another’s. Note that the coercion constraint will generally be binding for one group only, such that there is no qualitative difference between uniform and individual coercion constraints.

The normative foundation for the coercion limit is implicit in the work by Wicksell (1896). If society accepts unlimited coercion in the interest of maximizing overall welfare, as defined by an individualistic welfare function, then the limit should be zero. If, however, society places a value on not inordinately coercing its members, then the limits to coercion have to be determined jointly with the weights in the social welfare function. Whether a democratic society is able to agree on such limits is, just like the social welfare function itself, subject to the critique raised by Arrow’s (1951) impossibility theorem.

Technically speaking, all derivatives in the summation terms of (8)–(11) that involve goods or factors \(k\ne i\) are general equilibrium effects. Any or all of these may be ignored even by quite rational consumers. A different type of error could occur if consumers maximize social welfare rather than their private utility, as has been suggested by Boadway (2014).

The update leads to an improvement, but not necessarily to a correction of the counterfactual utility at A\('\). Naturally, if no updating takes place, consumers’ counterfactual (even if incorrect) does not depend on current policy. A biased computation of counterfactual utility is therefore a necessary, but not a sufficient condition for the counterfactual to be endogenous with current policy.

The same is true if the government itself is unable to correctly compute the full equilibrium at different taxes and consumers make the exact same mistakes as the government. Because we are working with a social planning model, the implicit assumption is that the government makes no mistake, but this assumption could be relaxed in a political economy framework where both candidates and voters may make mistakes, and which also could be similar in nature, e.g., because they rely on the same consulting firms to produce forecasts.

With the exception of income levels, these parameters have been suppressed in the exposition, but they are implicit in the definition of preferences and the production possibilities frontier.

Recall that we do not capture potential losses from civil unrest or conflict in the social welfare function. If limiting coercion avoids severe social disruptions, it will increase welfare in a more general sense. As discussed in the introduction, this is an important reason to institute a coercion constraint in the first place.

In order to span the entire policy space, we need at least three types. Limiting the example to three homogeneous types makes the analysis simpler, but it also reflects a normative concern that households should be treated equally by the government, as argued by Wallis (2014). Rather than gearing policy to individual consumers, the government only differentiates between broad classes of consumers in our setup. In our numerical model, these classes are workers and two types of capital owners.

A completely correct counterfactual is a sufficient but not a necessary condition. A wrong counterfactual that is fixed, or a counterfactual that is wrong globally but correct locally satisfy the condition \({\partial {\tilde{V}^h}/\partial {t}=0}\) as well.

The introduction of coercion via an external constraint means that coercion does not count at all for groups that are coerced by less than \(\bar{K}_h\). An alternative way to model a concern with coercion would be to include it into consumers’ utility function. However, this would require a relative weighting of utility from private consumption versus the disutility from being coerced for each group, and it is not clear on what basis this weighting would be chosen. Using an external coercion constraint also implies a relative weighting of welfare and coercion, but we would argue that it is easier to determine the maximum level of coercion that is acceptable in society than the rate at which each consumer trades off individual consumption against coercion.

The slope of the indifference curve is \(\frac{\hbox {d}t_L}{\hbox {d}t_E}=-\frac{\partial {V}/\partial {t_E}}{\partial {V}/\partial {t_L}}\), whereas the slope of the iso-coercion curve is given by \(\frac{\hbox {d}t_L}{\hbox {d}t_E}=-\frac{\partial {\tilde{V}}/\partial {t_E}-\partial {V}/\partial {t_E}}{\partial {\tilde{V}}/\partial {t_L}-\partial {V}/\partial {t_L}}\). The two only coincide if \(\frac{\partial {\tilde{V}}}{\partial {t_L}}=\frac{\partial {\tilde{V}}}{\partial {t_E}}=0\).

To see this, note that pivoting the iso-coercion curve at point A\('\) in either direction allows for a policy solution that is at a higher social indifference curve than the one going through A\('\).

Naturally, the concept of counterfactual paternalism implies that the government knows not only consumers’ true optimal points, but also the nature of the counterfactual bias. If, on the other hand, the government expects a positive bias when the consumer in fact uses a negative one, a policy that aims to limit coercion would in fact exacerbate it.

Even if all consumers are subject to the same numeric constraint, this could imply different levels of coercion if tastes and consumer errors are heterogeneous. Note that (16) looks similar to an equal (absolute) sacrifice problem. However, because the constraint is specified as an inequality, the absolute level of coercion will generally not be equalized across households. In contrast, application of the equal sacrifice concept in taxation leads to all consumers giving up the same (absolute, proportional or marginal) utility.

This allows us to use one wage rate that applies to all consumers, as consumer heterogeneity is captured by variation in \(\bar{L}_h\).

These types of counterfactuals were at the heart of our original model. However, their implementation is not straightforward, because either the counterfactuals are assumed to be fixed, in which case introducing a coercion constraint simply places more weight on the coercion-constrained group (see above), or they are assumed to change, but this requires a set of additional assumptions about how exactly they depend on the current equilibrium. In contrast, our partial equilibrium representation of a general equilibrium world generates a counterfactual that depends explicitly on the observed equilibrium via the elasticities of labor supply and the demand for the dirty good.

For an overview of energy taxes around the world, see Parry et al. (2014).

Given that the Green Young represent the workforce, one could argue for a higher welfare weight on this group. We chose the parametrization of the model mainly with a view to produce an intuitive figure in order to generate insights about limiting economic coercion, rather than to recreate a realistic distribution of the population. From a political economy point of view, one could argue that the workers may not have much lobbying power and that therefore their preferences do not influence policy very much.

Intuitively, consumers do not perceive a policy change toward their true optima as an improvement, because they overestimate the costs and/or underestimate the benefits of such a policy change by ignoring general equilibrium effects.

Based on a suggestion made by an anonymous referee, we did, however, recompute our model after reducing the elasticity of labor supply to near zero (which simulates a lump-sum tax). Eliminating the distortive nature of the labor tax brings the PE equilibrium closer to the GE equilibrium and thus reduces the welfare loss implicit in limiting coercion and in consumers’ bias. However, the qualitative nature of the equilibrium remains the same, and the resulting figure looks very similar to Fig. 4. This means that it is not the distortive nature of the labor tax, but the disagreement about the size and distribution of the public budget that is at the root of the welfare losses inherent in limiting coercion under bounded rationality.

Arrow, K. (1951). Social choice and individual values. New Haven, CT: Yale University Press.

Barton, A., & Gruene-Yanoff, T. (2015). From libertarian paternalism to Nudging and Beyond. Review of Philosophy and Psychology, 6(3), 341–359.CrossRef

Baumol, W.J. (2003). Welfare economics and the theory of the state. In C. K. Rowley & F. Schneider (Eds.), The encyclopedia of public choice Vol. 2, (pp. 610–613). Dordrecht, Boston, London: Kluwer Academic Publishers.

Bernheim, B. D., & Rangel, A. (2007). Behavioral public economics: Welfare and policy analysis with nonstandard decision-makers. In P. Diamond & H. Vartiainen (Eds.), Behavioral economics and its applications (pp. 7–77). Princeton: Princeton University Press.

Boadway, R. (2014). Discussion: The role of coercion in public economic theory. In J. Martinez-Vasquez & S. Winer (Eds.), Coercion and social welfare in public finance (pp. 195–200). Cambridge: Cambridge University Press.

Buchanan, J. M., & Tullock, G. (1962). The calculus of consent. Logical foundations of constitutional democracy. Ann Arbor: University of Michigan Press.CrossRef

Congleton, R. (2014). Coercion, taxation, and voluntary association. In J. Martinez-Vasquez & S. Winer (Eds.), Coercion and social welfare in public finance (pp. 91–116). Cambridge: Cambridge University Press.CrossRef

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Lindahl, E. (1919). Just taxation, a positive solution. In R. Musgrave & A. Peacock (Eds.), Classics in the theory of public finance (1958) (pp. 168–176). London: MacMillan.

Parry, I., Heine, D., Lis, E., & Li, S. (2014). Getting energy prices right: From principle to practice. Washington, DC: International Monetary Fund.

Sehili, S., & Martinez-Vasquez, J. (2014). Lindahl fiscal incidence and the measurement of coercion. In J. Martinez-Vasquez & S. Winer (Eds.), Coercion and social welfare in public finance (pp. 201–240). Cambridge: Cambridge University Press.CrossRef

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Wallis, J. (2014). The constitution of coercion: Wicksell, violence, and the ordering of society. In J. Martinez-Vasquez & S. Winer (Eds.), Coercion and social welfare in public finance (pp. 29–59). Cambridge: Cambridge University Press.

Wicksell, K. (1896). A new principle of just taxation. In R. Musgrave & A. Peacock (Eds.), Classics in the theory of public finance (1958) (pp. 72–118). London: MacMillan.

Winer, S., Tridimas, G., & Hettich, W. (2014). Social welfare and coercion in public finance. In J. Martinez-Vasquez & S. Winer (Eds.), Coercion and social welfare in public finance (pp. 160–194). Cambridge: Cambridge University Press.CrossRef

Titel: Social planning and coercion under bounded rationality with an application to environmental policy
verfasst von: Beat Hintermann
Thomas F. Rutherford
Publikationsdatum: 08.12.2016
Verlag: Springer US
Erschienen in: International Tax and Public Finance / Ausgabe 5/2017
Print ISSN: 0927-5940
Elektronische ISSN: 1573-6970
DOI: https://doi.org/10.1007/s10797-016-9433-0

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