Running ols when dependent variable is correlation coefficient

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!

• A correlation coefficient between which two variables? How do they enter into the regression equation? Sep 27 '18 at 15:47
• 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? Sep 27 '18 at 17:02
• 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. Sep 28 '18 at 0:59

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.