<p>Welcome. Many things can be done. Some simple ones are:</p>

<p>Option 1: Do not care and just do OLS.</p>

<p>Option 2: Do some transformation such as <span class="math-container">$\ln (1+y) - \ln (1-y)$</span>, logit of <span class="math-container">$\frac12 (y+1)$</span>, to change the range from <span class="math-container">$(-1,1)$</span> to <span class="math-container">$(-\infty, \infty)$</span> and do OLS. I assumed that there are no <span class="math-container">$\pm 1$</span>.</p>

<p>Option 3: Change your model. Let <span class="math-container">$y_{1,ij}$</span> and <span class="math-container">$y_{2,ij}$</span> be the firm-level (<span class="math-container">$j$</span>=firm) variables from which you obtain the correlation coefficient <span class="math-container">$y_i$</span>. As <span class="math-container">$y_i$</span> is also obtained by regressing <span class="math-container">$y_{1,ij}$</span> on <span class="math-container">$y_{2,ij}$</span> (up to a scaling factor), you might want to regress <span class="math-container">$y_{1,ij}$</span> on <span class="math-container">$y_{2,ij}$</span> including other industry-level variables <span class="math-container">$x_i$</span> as regressors. But in that case you need to think about which one of <span class="math-container">$y_{1,ij}$</span> and <span class="math-container">$y_{2,ij}$</span> to use as the dependent variable. If you are worried about endogeneity, you can also consider instrumental variable estimation, but that's a different story.</p>

<p>I would choose Option 1 unless many correlation coefficients in the sample are very close to <span class="math-container">$\pm 1$</span>. Note that interpretation changes in Option 2.</p>

CC BY-SA 4.0
2018-09-28T00:21:58.520Z
2018-09-30T14:55:54.207Z
2018-09-30T14:55:54.207Z
chan1142
<p>I am new to this form. I am going to run an OLS regression with dependent variable as a correlation coefficient (between -1 and 1). I am aware that this dependent variable may be problematic in the OLS regression. But what can I do in order to implement the regression? Thanks!</p>

CC BY-SA 4.0
2018-09-27T15:47:02.807Z
A correlation coefficient between which two variables? How do they enter into the regression equation?
Herr K.
CC BY-SA 4.0
2018-09-27T17:02:44.120Z
Thanks for your reply. I use the correlation coefficient between firm size and productivity as a measure of allocative efficiency of a industry s. Then I want to investigate the correlation of this dependent variable and other industry level variables. Is there any suggestion how should I deal with this dependent variables?
gxxjjj
CC BY-SA 4.0
2018-09-28T00:59:11.620Z
Could you clarify your goal here? "Implementing" a regression is usually not the goal, unless in coursework just for practice. You presumably want some result/information from the data and care about whether the result is valid if you use a given method (like OLS). The goal determines the method.
Sander Heinsalu
<econometrics>
Running ols when dependent variable is correlation coefficient
gxxjjj
# Running ols when dependent variable is correlation coefficient

(Asked by: username_0 on 2018-09-27)

I am new to this form. I am going to run an OLS regression with dependent variable as a correlation coefficient (between -1 and 1). I am aware that this dependent variable may be problematic in the OLS regression. But what can I do in order to implement the regression? Thanks!

**Tags:** econometrics
> **Comments:**
> **username_1**: A correlation coefficient between which two variables? How do they enter into the regression equation?  
> **username_0**: Thanks for your reply. I use the correlation coefficient between firm size and productivity as a measure of allocative efficiency of a industry s. Then I want to investigate the correlation of this dependent variable and other industry level variables. Is there any suggestion how should I deal with this dependent variables?  
> **username_2**: Could you clarify your goal here? "Implementing" a regression is usually not the goal, unless in coursework just for practice. You presumably want some result/information from the data and care about whether the result is valid if you use a given method (like OLS). The goal determines the method.  

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## 1 answers

### Answer by username_3 on 2018-09-28. Score: 1

Welcome. Many things can be done. Some simple ones are:

Option 1: Do not care and just do OLS.

Option 2: Do some transformation such as $\ln (1+y) - \ln (1-y)$, logit of $\frac12 (y+1)$, to change the range from $(-1,1)$ to $(-\infty, \infty)$ and do OLS. I assumed that there are no $\pm 1$.

Option 3: Change your model. Let $y\_{1,ij}$ and $y\_{2,ij}$ be the firm-level ($j$=firm) variables from which you obtain the correlation coefficient $y\_i$. As $y\_i$ is also obtained by regressing $y\_{1,ij}$ on $y\_{2,ij}$ (up to a scaling factor), you might want to regress $y\_{1,ij}$ on $y\_{2,ij}$ including other industry-level variables $x\_i$ as regressors. But in that case you need to think about which one of $y\_{1,ij}$ and $y\_{2,ij}$ to use as the dependent variable. If you are worried about endogeneity, you can also consider instrumental variable estimation, but that's a different story.

I would choose Option 1 unless many correlation coefficients in the sample are very close to $\pm 1$. Note that interpretation changes in Option 2.


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