<p>The only thing I can think is that they &quot;backwards-coded&quot; Gini coefficient when running the regression.</p>

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2023-01-10T11:49:58.367Z
As in, 1 would imply perfect equality, and 0 would imply maximal inequality?
chris jude
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2023-01-10T13:05:56.560Z
That's what it looks like to me.
Michael Gmeiner
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2023-01-10T13:49:23.550Z
Thanks for the reply. The lack of information in the article prevents me from verifying. Just to reconfirm: The author mentions in footnote 3, "Due to the log transformation, coefficient of Gini ratio, which is between 0 and 1, has a negative value". Isn't it a conceptually wrong statement?
chris jude
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2023-01-10T13:50:02.453Z
From what I understood, there is a possibility for cov(log(x),log(y)) to be -ve even when Cov (x,y) is +ve; see comments in this query https://stats.stackexchange.com/questions/601063/sign-of-covariance-of-log-transformed?noredirect=1#comment1113821_601063 but that in itself is not sufficient or necessary to claim Cov (x,y) is +ve.
chris jude
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2023-01-10T14:31:58.827Z
It is true that $ln(Gini)<0$ because $Gini<1$.
But some Stata simulations don't convincee me that this necessarily explains the result.


clear all

set obs 100

gen x = runiform()

gen y = 2*x + runiform()


gen lnx = ln(x)

gen lny = ln(y)

reg lny lnx
Michael Gmeiner
CC BY-SA 4.0
2023-01-10T08:21:50.110Z
2023-01-10T08:21:50.110Z
Michael Gmeiner
<p>This might be a basic question.
The article given below checks the relationship between crime and income inequality.
<a href="https://www.sciencedirect.com/science/article/pii/S0165176508001110" rel="nofollow noreferrer">https://www.sciencedirect.com/science/article/pii/S0165176508001110</a>. Both crime and gini is log transformed.</p>
<p>Table 1 shows  -0.6942 as the coefficient for regressing crime on income inequality. There are other values for different types of crime but let's focus on violent crime in Table 1. The interpretation of the results is states as follows &quot;So when Gini ratio increases by 1%, violent crime increase by 0.6942%&quot;!
I am not able to understand the interpretation since the coefficient is negative.</p>
<p>My thoughts:</p>
<p>Assume
<span class="math-container">$$y=f(x), \quad 0&lt;x&lt;1 \text{ and } y \text{ is a non-negative real number}$$</span></p>
<p>if <span class="math-container">$cov(x,y)=+ve$</span>, then</p>
<p><span class="math-container">$$cov(ln(x),y)=E(ln(x)y)-E(ln(x))*E(y)$$</span></p>
<p>since <span class="math-container">$ln(x)$</span> is negative first term is negative.
The second term is also negative as <span class="math-container">$E(ln(x))$</span> is negative. However, I am not sure whether the outcome is <span class="math-container">$+ve$</span> or <span class="math-container">$-ve$</span>? Is it inconclusive?</p>

<econometrics><regression><inequality><development-economics>
Interpreting the regression results
chris jude
# Interpreting the regression results

(Asked by: username_0 on 2023-01-05)

This might be a basic question.
The article given below checks the relationship between crime and income inequality.
<https://www.sciencedirect.com/science/article/pii/S0165176508001110>. Both crime and gini is log transformed.

Table 1 shows -0.6942 as the coefficient for regressing crime on income inequality. There are other values for different types of crime but let's focus on violent crime in Table 1. The interpretation of the results is states as follows "So when Gini ratio increases by 1%, violent crime increase by 0.6942%"!
I am not able to understand the interpretation since the coefficient is negative.

My thoughts:

Assume
$$y=f(x), \quad 0<x<1 \text{ and } y \text{ is a non-negative real number}$$

if $cov(x,y)=+ve$, then

$$cov(ln(x),y)=E(ln(x)y)-E(ln(x))\*E(y)$$

since $ln(x)$ is negative first term is negative.
The second term is also negative as $E(ln(x))$ is negative. However, I am not sure whether the outcome is $+ve$ or $-ve$? Is it inconclusive?

**Tags:** econometrics, regression, inequality, development-economics


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## 1 answers

### Answer by username_1 on 2023-01-10. Score: 1

The only thing I can think is that they "backwards-coded" Gini coefficient when running the regression.

> **Comments:**
> **username_0**: As in, 1 would imply perfect equality, and 0 would imply maximal inequality?  
> **username_1**: That's what it looks like to me.  
> **username_0**: Thanks for the reply. The lack of information in the article prevents me from verifying. Just to reconfirm: The author mentions in footnote 3, "Due to the log transformation, coefficient of Gini ratio, which is between 0 and 1, has a negative value". Isn't it a conceptually wrong statement?  
> **username_0**: From what I understood, there is a possibility for cov(log(x),log(y)) to be -ve even when Cov (x,y) is +ve; see comments in this query https://stats.stackexchange.com/questions/601063/sign-of-covariance-of-log-transformed?noredirect=1#comment1113821_601063 but that in itself is not sufficient or necessary to claim Cov (x,y) is +ve.  
> **username_1**: It is true that $ln(Gini)<0$ because $Gini<1$. But some Stata simulations don't convincee me that this necessarily explains the result.   clear all  set obs 100  gen x = runiform()  gen y = 2*x + runiform()   gen lnx = ln(x)  gen lny = ln(y)  reg lny lnx  

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