write a essay (2000words),About a article

In this paper I review Eaton and Rosen’s 1980 article “Optimal Redistributive Taxation

and Uncertainty”. First I provide a brief summary of the article. Next I describe the methods used

to address the topic of uncertainty in the optimal redistributive taxation model and assess its

relevance and effectiveness in answering question. This is followed by an examination of why

the research question addressed in the article is interesting from the viewpoint of economics. I

conclude with suggestions of improvements that could be made to the analysis.

The main research question addressed in this article is if workers facing wage uncertainty

interacts with inequality in a way that has a significant impact on optimal redistributive tax rates. Eaton

and Rosen (1980) state that, with a few exceptions, studies of the theory of optimal taxation have

been undertaken under the assumption of certainty. They argue that ignoring the impact of

uncertainty in studies leads to incorrect optimal tax rate estimates. In order to determine if the

inclusion of uncertainty is important to consider, the results derived under imperfect wage

information (uncertainty) are contrasted with results derived under perfect wage information

(certainty). In order to determine if the inclusion of uncertainty is important to consider, the results

derived under uncertainty are contrasted with results that assume certainty about wages. The article uses a

model in which there are two classes of individuals deciding between labour and leisure. It then solves

the optimal tax redistribution problem by choosing tax rates that maximize the social welfare

function under the constraint that tax revenue minus lump sum transfers and government revenue

requirements must be non-negative. Four cases are considered in this article: (1) the effects of

changing risk aversion, (2) the effects of changing revenue requirements, (3) the effects of

inequality versus uncertainty, and (4) the effects of alternative loci of uncertainty. After

considering these cases, the authors conclude that uncertainty for even a small portion of society

could have a “significant impact on optimal tax rates” (Eaton & Rosen, 1980).

The article answers the question of optimal tax redistribution under wage uncertainty by

considering four simulations and contrasting the results of the uncertainty case with those of the

certainty case. The uncertainty case has each class of worker facing unknown wages (that is each

wage in the distribution occurs with a probability between one and zero) and the certainty case

has the workers facing a known wage (i.e. a guaranteed wage with probability equal to one).

Within each simulation it considers two classes of workers with different wage distributions (to

incorporate an inequality factor) that face random wages and are choosing how to divide their

time between labour and leisure before the wage is decided. Each simulation reports the optimal

(marginal) tax rate as the rate which maximizes the sum of the expected utilities of the two

classes of worker.

The first simulation considers the effect of changing risk aversion with the purpose of

“determining how uncertainty and risk aversion change the optimal tax rates” (Eaton & Rosen,

1980). The more risk averse a person is, the more the uncertainty would affect their expected

utility. Assuming that the government has no revenue requirements and considering four levels

of risk aversion the results are that, under both certainty and uncertainty, as an individual

becomes more risk averse they desires higher tax rates. This result seems logical as the more

risk averse a person is, the more they would desire insurance (provided by higher taxes) against

unexpected changes in their wages. While both the uncertainty and certainty cases have a similar

relationship between risk aversion and level of taxation, the uncertainty case has noticeably

higher rates at every level of risk aversion. However “the differences are most pronounced when

the degree of risk aversion is low” (Eaton & Rosen, 1980) so the gap closes as a person becomes

more risk averse. This means that the difference between uncertainty and certainty is affected by

the degree of risk aversion.

The second simulation in the article tests the effect of changing government revenue

requirements to see how this interacts with optimal taxation under certainty and uncertainty. This

simulation is important: while the goal of finding optimal tax rates is to maximize social

welfare, the government selecting the tax rates also has its own revenue requirements which

imposes a constraint on how the rates must be chosen. Again the article contrasts uncertainty and

certainty results under four different ‘levels’ of revenue requirements varying from where the

government returns money to individuals (a negative revenue requirement or “unearned

income”) to where the government requires money (a positive revenue requirement). While both

the uncertainty and certainty cases have positive revenue requirements connected to an increase

in the tax, the uncertainty case’s optimal tax rates are once again higher at every level of revenue

requirement. Therefore, we see that regardless of the level of government revenue requirements,

wage uncertainty results in a greater optimum.

The third simulation is interesting as it compares the effects of inequality and uncertainty

to see which one has a larger impact on optimal tax rates. While the whole purpose of this paper

is to determine if uncertainty alters the results of optimal tax rate models, inequality is the chief

reason behind a redistributive tax. Eaton and Rosen (1980) point out that without inequality or

uncertainty, “optimal tax rates would be zero”. A good tax model should consider vertical equity

(the unequal treatment of individuals who are unequal) and horizontal equity (the equal treatment

of equals) regardless of the incorporation of uncertainty in the model. This simulation differs a

little from the previous two as it juxtaposes uncertainty with equality against certainty with

inequality. For the uncertainty with equality case, both classes of worker are identical and they

both face uncertainty of wages. In contrast, the certainty with inequality case involves the

workers facing different (but guaranteed) wages. The results of each case are compared to each

other under different levels of risk aversion and under the assumption that the government has no

revenue requirements. Except for the lowest level of risk aversion the uncertainty-inequality case

yields lower optimal tax rates than the certainty-inequality case. However the different rates

determined under each case are not remarkably different, especially as risk aversion decreases.

The authors conclude that “the outcome depends upon the degree of risk aversion, and […]

uncertainty leads to less progressivity”. This could simply mean that the effect of having perfect

equality overpowers any adverse effect of uncertainty in deriving the optimum. If everyone were

equal and faced the same uncertainty, there would be no point in a redistributive tax as it would

create inequality and create excess burden with no gains.

The fourth and final simulation considers the effects of alternative loci of uncertainty.

This simulation examines optimal tax rates to see if they depend on who bears the risk of

uncertainty. It divides the two classes into ‘poor’ and ‘rich’ where the poor class faces a lower

expected wage than the rich class. The results are fascinating but perhaps unsurprising: when it is

the ‘poor’ class that faces uncertainty, the optimal tax rate is higher than when the ‘rich’ class

faces uncertainty. The authors mention that if it is the ‘poor’ class facing uncertainty, the tax

structure is more progressive than when it is the ‘rich’ class facing uncertainty. What is even

more intriguing is that the optimal tax rate under uncertainty for the ‘poor’ class is identical to

the rate derived in the third simulation when there was uncertainty and equality. Another result to

note is that even when both classes face the same expected wage (that is, they are equal), if one

class faces uncertainty the optimal tax rate jumps from zero (when there is certainty and

equality) to 44%. Granted, the article does not claim that the rates derived are realistic this jump

shows that when even part of society faces uncertainty, the optimal tax rates are greatly affected.

Overall the methods used to answer the research question are appropriate. Eaton and

Rosen (1980) first take a generally accepted theory of optimal taxation limited by its restriction

to a world of certainty and extend it to the more realistic world of uncertainty. Their simulated

numerical analysis yields results that there is a difference between optimal tax rates when

workers face perfect information about their wages and when they face imperfect information

about their wages. Though the article does not discuss actual optimal tax rates, the fact that

uncertainty results in noticeably different tax rates than certainty means that optimal taxation

models which do not incorporate uncertainty would be excluding a relevant variable.

The idea of scarce resources and how they should be allocated in order to maximize

utility is central to the study of economics. Money is a scarce resource for most of the population

and through the implementation of taxes, economists strive to improve societal utility. Therefore

this article is interesting to the study of economics because it draws attention to the assumptions

that underlie the models used to determine optimal tax rates. These assumptions must be valid in

order for its results to be relevant. Additionally, an understanding of the conditions that

individuals face when they make their leisure-labour supply decisions and its consequences for

the role of taxation are critical to the development of economic policies. At the time the article

was written “uncertainty appear[ed] to have had little influence on optimal tax research” (Eaten

& Rosen, 1980) which means that a potentially important factor in the determination of optimal

tax rates was omitted.

The article answers its research question effectively: through the four simulations

considered, it is apparent that wage uncertainty does result in different optimal tax rates than

those conceived under the assumption of wage certainty. Each table in the article clearly lays out

the optimal tax rates under both uncertainty and certainty, and even from a quick glance it is

apparent that the rates are different. While Eaton and Rosen (1980) emphasize that the rates

determined are not actual optimums that should be implemented as they used a “simple and

unrealistic model”, they did choose values for the other variables in their calculations that are

“consistent with recent empirical evidence”. Thus the results highlight the fact that even in a

simple model, the results under wage uncertainty differ from the results under wage certainty.

There are definitely other factors to consider than those mentioned in the article but since the

question was simply if inequality and uncertainty interact in a way that affects optimal

redistributive taxation, the article presents clearly and effectively that the answer is yes. In the

following paragraph I will suggest possible improvements on the paper that could improve how

Eaton & Rosen answered the research question.

The question of what optimal tax redistribution looks like when workers face uncertainty

and how it interacts with inequality could be better answered by expanding its scope beyond two

classes. The entire article is general in simply showing that the results from the assumption of

uncertainty are different from those of certainty. However, it would be better if it used more

empirical evidence about levels of uncertainty actually faced in order to make it apparent that the

distinction between the assumption of uncertainty and certainty is crucial and relevant to optimal

taxation models. I would consider incorporating more classes with realistic wage distributions,

changing the weights placed on the utility of each class when maximizing the social welfare

function, and widening the range of risk aversion values to better assess if uncertainty and

certainty rates eventually converge to the same point. The article focuses on two classes in the

simulation, each of which, in the uncertainty case, only takes on two different wages. This is

effective in contrasting the ‘rich’ and the ‘poor’ but actual income distributions are more

complex than ‘rich’ and ‘poor’. So while the difference appears relevant in this model with only

two classes, they could be less stark once more classes are incorporated. I suggest different

weights on the utility of each class because the entire problem is centred on maximizing a

simplistic equation where each class’s utility is weighted equally. The idea that each class’s

utility is equally valuable to society seems idealistic. In the fourth simulation where it is shown

that if the ‘poor’ class faces uncertainty, the tax structure is more progressive, but this is

assuming that the utility of each class is equally valued in the social welfare function. If this

assumption were not true, the tax structure could actually be regressive. Finally, I would suggest

widening the range of risk aversion values because in the third simulation where inequality

versus uncertainty is considered, when risk aversion is low the rates differ by only 0.02. It is

possible that at extremely high or low values of risk aversion, the differences between

uncertainty and certainty are negligible.

Despite the aforementioned suggestions, Eaton & Rosen present an effective argument

for the inclusion of uncertainty in the optimal redistributive tax model. Through considering a

simple model for optimal tax rates, they have shown that when workers face uncertainty about

their wages the optimal tax rates differ from when they know their wages. Excluding the idea of

imperfect information from optimal tax models seems negligent. While the article only presents a

simplified approach, it would be interesting and valid to see uncertainty better incorporated into

models that determine optimal tax rates.

Reference

Eaton, J., & Rosen, H. (1980). Optimal Redistributive Taxation and Uncertainty. The Quarterly

Journal of Economics, 95(2), 357-364. Retrieved February 23, 2015, from JSTOR.