<p>Find the complete paper here: <a href="https://www.jstor.org/stable/724835?seq=1" rel="nofollow noreferrer">https://www.jstor.org/stable/724835?seq=1</a></p>

<p>I am reading Director's Law of Public Income Redistribution by George Stigler, published in the Journal of Law and Economics (Vol. 13, No. 1 (Apr., 1970), pp. 1-10) and I came across some things which seem to me to be obvious mistakes. Yet a google search for possible errata of the paper turned up nothing. Since the paper passed peer review and is cited by scholars, I can't believe I found a mistake that didn't catch their eye. Therefore I'd like someone else's opinion on the matter.</p>

<p>The part of the paper I am talking about are the Mathematical Notes, to be found at the end of the paper. <a href="https://i.sstatic.net/qL7vE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qL7vE.png" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/VeDvV.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VeDvV.png" alt="enter image description here"></a></p>

<p>There are three questions I have about the above analysis.</p>

<p>First, in the equation just above (4) <span class="math-container">$(\Delta x)_L=(\Delta x)_u\frac{v(x_1)}{y(x_0)}$</span> is the substitution that was made, while I think it should be: <span class="math-container">$(\Delta x)_L=(\Delta x)_u\frac{v(x_1)}{v(x_0)}$</span> based on equation (3). Where does the <span class="math-container">$y(x_0)$</span> come from?</p>

<p>Second, the proposed alteration of the voting coalition is to add <span class="math-container">$(\Delta x)_u$</span>, that is to add a small number of rich households to the coalition who were previously excluded; also <span class="math-container">$(\Delta x)_L$</span> is removed from the coalition, that is, a small number of poor households are removed from the coalition, such that the vote share of the coalition remains the same (see equation (3)). Then the statement that aggregate taxes will be reduced if <span class="math-container">$t[y(x_1)(\Delta x)_u-y(x_0)(\Delta x)_L]&lt;0$</span> must be false. Why? Rich people are added to the coalition, thus taxes will decrease by what they payed, so <span class="math-container">$ty(x_1)(\Delta x)_u$</span>. Poor people are removed from the coalition, thus taxes increase by what they will pay, so <span class="math-container">$ty(x_0)(\Delta x)_L$</span> Thus aggregate taxes will be reduced if <span class="math-container">$ty(x_0)(\Delta x)_L-ty(x_1)(\Delta x)_u)&lt;0$</span>. Which is exactly the reverse of Stiglers condition for a tax reduction. As a consequence, every following inequality up to and including (4) should be the other way around, I think. Could someone explain to me if I'm missing something?</p>

<p>My last issue is the following: Even if I were to be wrong and equation (4) is right, then the statement that <span class="math-container">$\frac{v(x)}{y(x)}$</span> is decreasing in <span class="math-container">$x$</span> for all <span class="math-container">$x$</span> doesn't seem to be necessarily true. If <span class="math-container">$v(x)$</span> were constant it would be trivially true, but the paper earlier makes the statement that votes per household rise with income! In which case the change would be ambiguous of <span class="math-container">$\frac{v(x)}{y(x)}$</span> when changing <span class="math-container">$x$</span>. So again: what am I missing?</p>

<p>I hope someone can explain where I went wrong, since it really bothers me when I try to follow the author's argument and get hung up on this kind of stuff.</p>

<p>Thanks a lot in advance!</p>

CC BY-SA 4.0
2020-06-13T15:53:02.180Z
Yeah makes sense that that's just a typo, appreciate you taking a look!
user18214
CC BY-SA 4.0
2020-06-13T18:45:11.623Z
Published papers in economic theory are full of mistakes. Some of them are famous, but most of them go unnoticed. People usually only care if the mistake changes drastically the conclusions of the paper. For example, last year Econometrica published a corrigendum to a classic paper with almost 5000 citations https://www.econometricsociety.org/sites/default/files/ECTA17617.pdf
brunosalcedo
<errata>
Possible mistakes in Stigler, 1970 -- what am I missing?
user18214
# Possible mistakes in Stigler, 1970 -- what am I missing?

(Asked by: username_0 on 2020-06-13)

Find the complete paper here: <https://www.jstor.org/stable/724835?seq=1>

I am reading Director's Law of Public Income Redistribution by George Stigler, published in the Journal of Law and Economics (Vol. 13, No. 1 (Apr., 1970), pp. 1-10) and I came across some things which seem to me to be obvious mistakes. Yet a google search for possible errata of the paper turned up nothing. Since the paper passed peer review and is cited by scholars, I can't believe I found a mistake that didn't catch their eye. Therefore I'd like someone else's opinion on the matter.

The part of the paper I am talking about are the Mathematical Notes, to be found at the end of the paper. [![enter image description here](https://i.sstatic.net/qL7vE.png)](https://i.sstatic.net/qL7vE.png)

[![enter image description here](https://i.sstatic.net/VeDvV.png)](https://i.sstatic.net/VeDvV.png)

There are three questions I have about the above analysis.

First, in the equation just above (4) $(\Delta x)\_L=(\Delta x)\_u\frac{v(x\_1)}{y(x\_0)}$ is the substitution that was made, while I think it should be: $(\Delta x)\_L=(\Delta x)\_u\frac{v(x\_1)}{v(x\_0)}$ based on equation (3). Where does the $y(x\_0)$ come from?

Second, the proposed alteration of the voting coalition is to add $(\Delta x)\_u$, that is to add a small number of rich households to the coalition who were previously excluded; also $(\Delta x)\_L$ is removed from the coalition, that is, a small number of poor households are removed from the coalition, such that the vote share of the coalition remains the same (see equation (3)). Then the statement that aggregate taxes will be reduced if $t[y(x\_1)(\Delta x)\_u-y(x\_0)(\Delta x)\_L]<0$ must be false. Why? Rich people are added to the coalition, thus taxes will decrease by what they payed, so $ty(x\_1)(\Delta x)\_u$. Poor people are removed from the coalition, thus taxes increase by what they will pay, so $ty(x\_0)(\Delta x)\_L$ Thus aggregate taxes will be reduced if $ty(x\_0)(\Delta x)\_L-ty(x\_1)(\Delta x)\_u)<0$. Which is exactly the reverse of Stiglers condition for a tax reduction. As a consequence, every following inequality up to and including (4) should be the other way around, I think. Could someone explain to me if I'm missing something?

My last issue is the following: Even if I were to be wrong and equation (4) is right, then the statement that $\frac{v(x)}{y(x)}$ is decreasing in $x$ for all $x$ doesn't seem to be necessarily true. If $v(x)$ were constant it would be trivially true, but the paper earlier makes the statement that votes per household rise with income! In which case the change would be ambiguous of $\frac{v(x)}{y(x)}$ when changing $x$. So again: what am I missing?

I hope someone can explain where I went wrong, since it really bothers me when I try to follow the author's argument and get hung up on this kind of stuff.

Thanks a lot in advance!

**Tags:** errata

> **Comments:**
> **username_0**: Yeah makes sense that that's just a typo, appreciate you taking a look!  
> **username_1**: Published papers in economic theory are full of mistakes. Some of them are famous, but most of them go unnoticed. People usually only care if the mistake changes drastically the conclusions of the paper. For example, last year Econometrica published a corrigendum to a classic paper with almost 5000 citations https://www.econometricsociety.org/sites/default/files/ECTA17617.pdf  

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## 0 answers

