Help related to calculation of a regression coefficient

[lal mohan kumar]

Dear Stata Members

I have a query related to the calculation of regression coefficients from a table of an article. The relationship being tested is the nature of the association between the leverage ratio of firm i in industry j in year t (dependent variable) and active holdings which is the % of shares held by institutional investors (independent variable of interest).
Leverage has a mean of 31.1% and SD of 27.0%
Active Institutional Investors have a mean of 15.8% and SD of 14.2%.

The regression table shows that the coefficient of active institutional investors on Leverage is -.245, SE 0.048 and the coefficient is significant at 1%. In the results section, authors state the following

The point estimate suggests leverage decreases by 0.47 percentage points for every percentage point increase in institutional ownership, all else equal. The magnitude of this change is consequential economically. For example, it suggests a 10 percentage point increase in active institutional ownership leads to a 4.7 percentage point reduction in leverage from an average leverage of 31.1%.

My doubts
1) How could the authors get the figure 0.47?
2) What are these percentage points, how it is different from percentage?
3) Is there a better way to report both statistical significance and economic significance with same results

Any help in this regard is appreciated.

[Carlo Lazzaro]

Ial:
without a link to the article is difficult (for me, at least) to reply positively.

[lal mohan kumar]

Dear Carlo
I am sorry for not providing the link earlier, here is the link -https://www.law.nyu.edu/sites/default/files/upload_documents/Grennan%20The%20Deleveraging%20of%20U.S.%20Firms%2 0and%20Institutional%20Investors%27%20Role.pdf

I am not sure how this .47 is arrived. Also, how do we actually interpret the coefficients like above when both (dependent and independent variables are in percentages)? Is there a difference when both of these variables are continous (rational form-0.3, .0523, 4.8 etc).

[lal mohan kumar]

Hi Stata Members
I am eager to know any thoughts on above or I have some simple inquiries, and it would make me very pleased if I could get some answers.First similar to the above variables how to interpret
1) If both the dependent variable and independent variables are in %. Let us assume the that dependent variable is the return on assets in %(Return/Assets*100) and the independent variable be the percentage of shares held by the government (shares held by government/total shares*100). If we get say a coefficient of .05, can we interpret that a one percetage increase in the percentage of shares held by the government can increase the percentage of return on assets by .05 or 5%. Or, more specifically how can one make an interpretation in this regard?
2) In the above case ROA is in % and Govt share is not multiplied by a hundred then for a coefficient of 5, what should be the interpretation?

[Carlo Lazzaro]

Ial:
actually I was not able to spont any correspondence between Table 3, column (2) and Authors' statement.

[lal mohan kumar]

Dear Carlo Lazzaro, my sincere apologies for spoiling your valuable time with my doubt. I too tried to figure it out but couldn't. However, can you help me with #4? I really want to understand the nuances of interpreting coefficients rather than saying that the beta coefficient implies for a unit change in iv, the depend variable changes by beta units.
I would like to understand where it makes more sense to multiply the betas with 100 and what difference can it make if only one of the variables that goes into regression is in % form and alike.
I hope I haven't annoyed with my repeated doubts

[Carlo Lazzaro]

Ial:
I'm in hurry at the moment.
However, see https://thewritingbusiness.com/the-d...entage-points/

[William Salazar]

Hi Stata Members
I am eager to know any thoughts on above or I have some simple inquiries, and it would make me very pleased if I could get some answers.First similar to the above variables how to interpret
1) If both the dependent variable and independent variables are in %. Let us assume the that dependent variable is the return on assets in %(Return/Assets*100) and the independent variable be the percentage of shares held by the government (shares held by government/total shares*100). If we get say a coefficient of .05, can we interpret that a one percetage increase in the percentage of shares held by the government can increase the percentage of return on assets by .05 or 5%. Or, more specifically how can one make an interpretation in this regard?
2) In the above case ROA is in % and Govt share is not multiplied by a hundred then for a coefficient of 5, what should be the interpretation?

Ial,

On the decimal -v- percentage issue, if I've understood what you are asking correctly try the following using very simple mock data:

[1]
dependent (y) variable: percentage
independent (x) variable: percentage
[where a value of 5 represents 5% for example]
Estimate.
Imagine we get y = 37 + 0.26x

Now run the same regression in decimal form:

[2]
dependent (y) variable: decimal
independent (x) variable: decimal
[where a value of 0.05 represents 5% for example]
Estimate.
We would get y = 0.37 + 0.26x

You will notice:

• In [1] the constant is 100 times bigger than in [2]
• The slope coefficient and t-statistic is the same.

Interpretation of slope: example: :

• In [1] an increase of "1" of x represents a 1% increase in x which corresponds to a 0.26% increase in y
• In [2] an increase of "1" of x represents a 100% increase in x which corresponds to a 0.26 decimal increase in y. 0.26 in decimal is 26% as a percentage.
  • Of course to see a 1% increase in [2] just divide 26% by 100... giving you 0.26% as per [1]!

You can see they are analogous..

[lal mohan kumar]

Dear William Salazar, thanks for the excellent reply. Many thanks to Carlo Lazzaro for sharing me the source