# Auch österreichische Pärchen und Studierende reagieren auf Anreize

Statistik Austria hat anlässlich des 100. Jubiläums der Republik Österreich eine Zusammenstellung von interessanten Statistiken veröffentlicht. Unter den Highlights:

Man beachte die Ausreißer rund um Änderungen in der steuerlichen Behandlung von Ehepaaren in der Zeitreihe. Fazit: Österreichische Pärchen reagieren auf monetäre Anreize. Keine Überraschung für Ökonomen, aber immer wieder schön zu sehen.

Dasselbe gilt auch für Studierende:

Man beachte den Knick nach unten bei Wiedereinführung der Studiengebühren 2001 und den Knick nach oben bei der (De-Facto-)Abschaffung derselben ein paar Jahre später.

Die ganze Präsentation ist äußerst lesenswert!

# “Self-financing” tax reforms: a simple formula

There is much talk these days about tax reforms, both in Austria and around world. Most political parties seem to agree that taxes on labor are too high and that cuts should be made. There is disagreement as to whether these tax cuts should be accompanied by cuts in government spending or increases in other taxes.

One recurrent issue in this debate is the extent to which tax cuts are “self-financing”. This usually comes from a vague notion that reducing tax rates has a “stimulating” effect on “growth” and “job creation”. Such “stimulus” makes the tax revenue increase thus offsetting some of the revenue loss due to the reduction in tax rates.

Although I usually take great pleasure in brutally debunking popular myths with my profound knowledge of Economic Science (insert resounding laughter here), let me say that I think that in this matter the vague notion of the layman is broadly correct.

Economics being a hard quantitative science, the careful economist always strives to replace broadly correct but vague notions with mathematically exact but only vaguely correct formulas. In this spirit, I offer a formula for calculating to which degree a cut in the marginal labor tax rate is “self-refinancing”.

We start from a definition: total tax revenue (T) is the tax rate (t) times income (Y):

$\displaystyle T = t\times Y.$

We treat t as both the average and marginal tax rate. In fancy language: income taxes are assumed to be linear. Not true, but (one hopes) true enough.

We want to know how T changes if t is reduced by a small amount dt. There are two effects, one direct, one indirect. The direct effect is to reduce T by an amount $\displaystyle Y dt$. The indirect effect comes from realizing that Y depends on labor input L which, in turn, depends on the tax rate. So therefore, if we reduce the tax rate by dt, labor supply rises by $\displaystyle n dt$, where n is the elasticity of labor supply. The increase in labor input raises output and thus income. Suppose the elasticity of output with respect to labor input is a. Then the total change in income is: $\displaystyle dY = (\alpha\times n)dt.$

The indirect effect is where “self-financing” comes from. Let us measure the self-refinancing effect of the tax cut by $\displaystyle X = t\times dY/Y,$ which is the indirect change in revenue measured in percent of income.

$\displaystyle X = (t\times\alpha\times n)dt.$ *

The self-financing share X is larger, the higher the initial tax rate, and the higher the two elasticities $\displaystyle \alpha$ and n.

How big is $\displaystyle \alpha$? Well, consider a Cobb-Douglas production function $\displaystyle Y=K^{1-\alpha}\times L^{\alpha}$, where K stands for other factors of production which we hold fixed for purposes of this exercise. The labor elasticity of output is $\displaystyle \alpha.$ It is well-known that under competitive conditions a is equal to the labor share of income. In Austria, as well as in most developed countries, this share is about 2/3. So let’s take that as our answer.

How big is n? That’s a tough one to measure. Theoretically, it depends on the labor-leisure preferences of households as well as on other „deep” parameters of the economy. The empirical evidence I have seen suggests that a 1 percent decrease in t increases L by less than 1, but more than 1/3 of a percent. Let’s take 1/2 as a guess.

Finally, what is t? In Austria the marginal income tax rate is close to 50%, the average rate is in the area of 30%.

Feeding these numbers to our formula we arrive at the following conclusion. The self-financing share of a tax cut is in the range between 10 and 17 percent. This means that a tax cut of 1 billion euros indirectly creates additional revenues between 100 and 170 million euros. That still leaves a hole in the public budget of at least 830 million euros, though.

*) The General Formula is:

$\displaystyle dT = Ydt + t\times\frac{dY}{dL}\frac{L}{Y}\times\frac{dL}{L}\frac{1}{dt}\times Y dt$

# How privatization saved the Pilgrim Fathers

This summer I visited the historic site of Plymouth Plantation, the famous first settlement of the Pilgrim Fathers in Massachusetts. I was interested to see how the early settlers lived, what their houses looked like, what clothes they wore, what food they ate, what their relationships with the Native Americans were and how they managed to survive the first years in the wilderness. Luckily one of the colonists, William Bradford, wrote a book about all this which I am now reading. Among the many fascinating details of Bradford’s account, I found this passage describing how the colonists managed to overcome the insufficient output of corn which had caused a dangerous shortage of food during the first year and left many of them in danger of starvation.

So they began to consider how to raise more corn, and obtain a better crop than they had done, so that they might not continue to endure the misery of want. At length after much debate, the Governor with the advice of the chief among them, allowed each man to plant corn for his own household, and to trust to themselves for that; in all other things to go on in the general way as before. So every family was assigned a parcel of land, according to the proportion of their number with that in view,—for present purposes only, and making no division for inheritance,—all boys and children being included under some family. This was very successful. It made all hands very industrious, so that much more corn was planted than otherwise would have been by any means the Governor or any other could devise, and saved him a great deal of trouble, and gave far better satisfaction. The women now went willingly into the field, and took their little ones with them to plant corn, while before they would allege weakness and inability; and to have compelled them would have been thought great tyranny and oppression.

The failure of this experiment of communal service, which was tried for several years, and by good and honest men proves the emptiness of the theory of Plato and other ancients, applauded by some of later times,—that the taking away of private property, and the possession of it in community, by a commonwealth, would make a state happy and flourishing; as if they were wiser than God. For in this instance, community of property (so far as it went) was found to breed much confusion and discontent, and retard much employment which would have been to the general benefit and comfort. For the young men who were most able and fit for service objected to being forced to spend their time and strength in working for other men’s wives and children, without any recompense. The strong man or the resourceful man had no more share of food, clothes, etc., than the weak man who was not able to do a quarter the other could. This was thought injustice. The aged and graver men, who were ranked and equalized in labour, food, clothes, etc., with the humbler and younger ones, thought it some indignity and disrespect to them. As for men’s wives who were obliged to do service for other men, such as cooking, washing their clothes, etc., they considered it a kind of slavery, and many husbands would not brook it. This feature of it would have been worse still, if they had been men of an inferior class. If (it was thought) all were to share alike, and all were to do alike, then all were on an equality throughout, and one was as good as another; and so, if it did not actually abolish those very relations which God himself has set among men, it did at least greatly diminish the mutual respect that is so important should be preserved amongst them. Let none argue that this is due to human failing, rather than to this communistic plan of life in itself. I answer, seeing that all men have this failing in them, that God in His wisdom saw that another plan of life was fitter for them.

# How to make students honest in exams

One of my favorite economists, David Friedman, suggests an economic solution to a problem that every teacher has probably faced.

In most exams, students have an incentive to respond to a question even if they do not know the answer. If they do not respond at all, they will get zero points with certainty. If they write something – anything – there is some probability that they will get at least a few points, maybe because they guessed the correct answer or because the teacher reads what he or she wants to read.

Pretending to know the answer when you don’t is an economically wasteful activity. It is a waste of time for the student as well as for the teacher who has to grade the exam. It is also, at least potentially, a distortion of the signal embodied in exam grades, because students who pretend to know might do as well on the exam as students who really know.

Friedman’s solution: Award 20 percent of the points for the response “I don’t know”. Students who know less than 20 percent or are less than 20 percent sure that they know the right answer will respond, rationally and honestly, “I don’t know”. Students who know more or are more certain of their knowledge will give their answer.

Now behavioral economists might object that students may be overconfident, i.e. they overestimate their true abilities and give an answer not because they pretend to know, but rather because they truly believe they know. However, even overconfident students – those who, for instance, put the probability that they know the right answer at 50 percent when in fact they don’t know it – might still prefer to answer “I don’t know”, because that guarantees them a certain outcome of 20 percent of the points whereas writing an response they are unsure about means risking losing all the points on the question.

Anyway, I love the solution. I think I will try it in my course. It is also a good example of how simple economics – thinking through the implications of rational behavior – helps solving a non-economic problem.