[Clyde Schechter]

You are correct that A. Douglas Rao never manages firm B by himself. And there is no such listing in the output. He does have a period where he manages firm C by himself, and that does appear in the output. Here's the output I get with code from #11 applied to the data example in #12:

    firm_name         manager_name   datebegin     dateend  
            A       Jon E. Quigley   29jul2013   29jul2014  
            B   Scott W. Schoelzel   21may2003   01jan2008  
            B            Ron Sachs   01may2008   28sep2012  
            C   Scott W. Schoelzel   21may2003   01jan2008  
            C            Ron Sachs   01may2008   04jun2013  
            C       A. Douglas Rao   04jun2013   01sep2013

(Well, actually the code in #11 has to be modified to rename begin and end as datebegin and dateend in order to run. But what you see here is the output from otherwise unchanged code from #11.)

[Romalpa Akzo]

If the cumulative range of time for each firm is not too large (over 7-8000 years), below code should also be working. For the given example or small data, you could directly use the program's content without using -runby-.

capture program drop each_firm
program define each_firm
    gen long obs = _n
    expand 1 + end - begin

    bys obs: gen date = begin +_n-1
    bys firm_name date: keep if _N==1

    bys firm_name manager_name (date): gen tag = sum(date != date[_n-1]+1)

    collapse (min) begin_S = date (max) end_S = date, by(firm_name manager_name tag)
    drop tag
end

runby each_firm, by(firm_name)
format %td begin_S end_S

[Mia Pham]

Clyde Schechter : Thank you very much. How silly I am. I got it now. The code run smoothly and no issue so far. Thank you again.
Romalpa Akzo: Thank you, I will run your code on my original data to see how it works. It's very helpful to see different solutions for the question.

Kind regards;
Mia

[Romalpa Akzo]

It should be noted that the code in #17 follows the strict level of date, therefore, its output would be silghly different from Professor Clyde's code in #11.

For example, the begin_Single of Jon E. Quigley (firm A) is 30 July 2013 instead of 29 July 2013. Similarly, the end_Single of Scott W. Schoelze (firm B) is 31 Dec 2007 instead of 01 Jan 2008.