Tentative thoughts on an extension of the Peltzman model

Based on the insights provided by the Peltzman model, consider the scenario where a policy maker is considering the provision of a subsidy to a special interest group. Clearly M(.) still describes the isovote curve. However, order to consider this application of the model, it is necessary to find an analogues for

  • the profit made by the firm, and
  • for the price paid by consumers

This is because of the changes to the issues underlying the model imposed by this adaptation:

  • In this adapted model, the special interest receives a direct subsidy, the analogue of the firm/industry profit in the original model would be government expenditure “G”
  • In the original model, the firm’s profit is determined by the price, which is what the state sets and the firm collects. Because in this case the state can only provide a subsidy paid for by collecting a certain amount of taxes “T” its main tool is to set the tax rate “τ”.
  • For simplicity we can assume a balanced budget (tax revenues = government spending),

These changes should allow the representation of an appropriate  variation of the original model where instead of thinking of the profit curve of the firms/special interest, we can think of the Laffer curve. As a result of this,

  • Tax revenues will be limited for goods/activities that are easily substitutable or that are luxurious and easily abandoned (flat Laffer curves).
  • Tax revenues will be potentially very high for inferior, non-substituable or inelastic goods.

Given these changes to the original Peltzman model, it would seem intuitive that an adaptation of figure 2 is possible, assuming the meaning of the curves is kept in mind.

  • Along any given isovote curve describes a constant level of net support for the fiscal authority. However, this support is the net result of the support costs (α) of raising tax rates (τ) in order to increase tax revenues and of the support gains from using those tax revenues to provide (targeted) subsidies (T=G). It’s functional form should represent the trade-off between the support gains of spending more money  while loosing some support due to the fact that the funds have to be levied through taxes. It probably looks something like this:

Isovote curve

  • The Laffer curve describes the relationship between Tax revenues (which are equal to subsidies) and tax rates. Following Badel 2013 and Diamond and Baez 2011, the Laffer Curve’s formula can be generalised (from the special case of top income earners) to something like this:

Laffer Curve Formila.png

Clearly the most fundamental determinants of the tax revenue according to the Laffer curve are

  • “Exch_average” is the average value of the transaction being taxed (eg: salaries, purchases)
  • “N”, the number of times that the exchange takes place (how fast is money changing hands in this economy)
  • “Exch_minimum” is the minimum taxable transaction (eg: income tax allowance in the UK)
  • “Ω” (“e” in Badel 2013 ) is “the elasticity of reported income with respect to the net-of-tax rate”, ie: how much the reported value of the relevant taxable exchange (“Exch_average”) is reduced  by when the relevant tax rate increases by 1% (this assumes a constant value, where in fact it is possible that this elasticity may itself be a function of the tax rate). In the USA, Ω for top income earners is somewhere between 17% and 57%.

In this case figure 2 from Peltzman’s original article would look something like the figure below:

Peltzman-Laffer Curve_detail.png

Interpreting the equilibrium

Considering points A, B, C and D in the figure it is possible to get a better sense of the meaning of the equilibrium point A.

  • At point C, the fiscal authority can still increase tax rates to levy more tax revenues that it can redistribute in a manner that increases its support (from M1 to M2). The number of supporters that the fiscal authority looses by increasing the tax rate is still less than the number of supporters it gains by spending those tax revenues
  • Increasing tax rates until point A has the corresponding effect of increasing support. However, tax rate increases above those corresponding to point A lead to a decrease in popularity of the fiscal authority.
  • At point B, the fiscal authority is charging such high tax rates that it is becoming less popular. Although it will lose the support of the interest group, it will enjoy a net (weak majority – strong minority) gain in popularity if it decreases tax rates.
  • Although it might like to be at point D  because support is higher, the fiscal authority cannot impose tax rates that return such a level of tax revenues.
  • At point E, the fiscal authority still has room to raise more tax revenues with which to subsidise the special interest without having to increase the tax rate. Point E describes an inefficient tax collection system.

 

Four typologies of Equilibria

As was the case of the original, it is useful to consider the 4 possible equilbrium solutions based on the slopes of the two curves.

Implications of adapted Peltzman model

From the above considerations, it is possible to superficially expect that

  • The highest equilibrium tax rate is achieved when potential tax revenues are quite high but voters are not very sensitive to tax rates (steep Laffer curve) [T*(Vl,Sl)] [upper-right corner].
  • The lowest equilibrium tax rate is achieved when the voters sensitivity to tax rates is high but tax revenues rise very flatly with increases in the tax rate[T*(Vh,Sh] [lower-left corner].

 

Conclusion

Unfortunately, the range of possible interactions between the determinants of the Laffer and the Isovote curves is so wide that in this type of superficial analysis it is difficult to say anything meaningful about more than those extreme cases.

  • Based on the drivers that define the Laffer Curve’s function, it is likely that the effect of an increase in taxation of basic goods will be different depending on population size, income level and institutional checks on corruption.
  • The slope of the isovote curve will also depend on “α”, which is likely to depend on a the attentiveness (education) of voters, exaggerated centralisation, collective action problems and any fly paper effects resulting from these issues.

The figure below summarises these insights and tentatively suggests some examples.

Implications of adapted Peltzman model_Flypapper

 

 

 

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