Variables omitted because of collinearity

[Winston Wu]

Hello, everyone! Firstly, I suspect that my issue may stem from the characteristics of the dataset rather than technical issues with STATA.
However, my professor believes that there may be problems in my data processing procedures. Therefore, I need a reasonable explanation to convey to him that perhaps it's the viability of research design.


My dataset is firm-year panel data, as shown below (partial):

coid	year	audit firm	accrual	SRTH	TWI_QC
2535	2022	D	0.063792	101.7	4
4551	2022	D	0.003987	101.7	4
8932	2022	D	0.040716	101.7	4
6689	2022	K	0.018856	12.5	1
3138	2022	K	0.026391	12.5	1
6284	2022	K	0.01487	12.5	1
1736	2022	E	0.005425	10.5	2
1445	2022	E	0.010722	10.5	2
3416	2022	E	0.077717	10.5	2
1215	2022	P	0.025043	11.6	0
2597	2022	P	0.023182	11.6	0
4966	2022	P	0.05779	11.6	0

In this context, "coid" represents the company code, and "accrual" is calculated based on the financial figures of each company. The last two variables represent characteristics of the audit firm, sourced from publicly available data of each audit firm. "SRTH" stands for manager training hours, while "TWI_QCS" represents the number of quality control deficiencies. Each of these variables has only 4 discrete values within a year. The composition of audit firms in the sample is as follows: D: 37%, P: 27%, K: 24%, E: 11%. The total sample size is 1,528, including 18 characteristics of audit firms (and other control variables), with only two presented here.

When I perform regression estimation with all 18 characteristics of audit firms as explanatory variables (with accrual as the dependent variable), STATA automatically excludes variables after the third one, citing issues of multicollinearity. Upon investigating through Pearson correlation analysis, I discovered a significant positive correlation of 0.998 between SRTH and TWI_QCS. However, these two variables seem unrelated on the surface. Why is that?
There are also many cases of correlation coefficients exceeding 0.7 among other audit firm characteristics variables. I suspect this might be the reason for errors encountered during regression analysis in STATA.

I processed the dataset by first calculating the dependent variable from the financial data of companies and then incorporating the characteristics of audit firms as explanatory variables. Upon inspection, I did not find any errors in the merging process.

I have another dataset with a similar structure but spanning 3 years (2019-2021), resulting in 12 discrete values of each audit firm characteristic variable. In this sample, there are only a few instances of high correlation among the variables related to audit firm characteristics. In this sample, only a few variables among audit firm characteristics exhibit high correlation, and in executing the same regression analysis, variables are automatically excluded by STATA due to collinearity only after the eighth variable. However, I'm unsure whether the milder situation is simply due to an increase in variation of variables.


Thank you in advance for your time!

[Carlo Lazzaro]

Winston:
welcome to this forum.
Please read and act on the FAQ when posting: your query is way too long and, much more substantively, you do not share what you typed ad what Stata gave you back. Thanks.

[Winston Wu]

Thank you for the reminder, Carlo.
I apologize for not reading the FAQ before posting. I thought providing as much detail as possible about the dataset would help Statalist understand my question.
Could you please advise on what parts, besides explaining why I posted the question, are unnecessary? I'll remember to share the Stata code and results later.

[Carlo Lazzaro]

Winston:
the issue is the way your message is drafted.
I would advise what follows:
0) a brief description of what you're after;
1) Stata code;
2) Stata results;
3) a brief description of the problem you're facing;+
4) full reference(s) if any.

As a rule of thumb, numbers/Stata code(s)/Stata results shoud be more informative than words.

[Winston Wu]

Thank you very much for your suggestion, Carlo.
I will revise the post according to this structure!