Omitted Standard Deviation Variable in Fixed Effects Estimation

[mohina saxena]

Hello all,

I had posted this query on another thread in Stata forum, but starting it here as a new thread. I apologise if this is not the appropriate way of cross-posting. I need help with calcuating and then using in regression the below variable.

I want to create a variable that is business risk, following a paper this variable is measured as:

"The deviation of each company’s Return on Total Assets is computed from the sample average for each of the six consecutive years of firm observations during the period 2004–2009." The standard deviation of this measure is then considered as the value of risk.

Riski = Sqrt[1/n-1 Sigma t= 2004-2009 {ROTAit-1/n(sigma t= 2004-2009 ROTAit)}2], n =6

I have an unbalanced panel dataset (Firm id= Unique_Identifier] for 2001-2017 from several industries. I use the following command for my dataset to generate the above measure.

egen ebit_ROTA = sd(ROTA), by(Unique_Identifier)

With the above code, each firm has same value of risk [that varies for each firm] but remains same for all the years. So while performing FE since there is no within variation this variable omits out. I doubt if I have correctly understood the variable's construction. Can someone please help me out here. Attaching below the issue:

* Example generated by -dataex-. To install: ssc install dataex
clear

input long Unique_Identifier int Year double(NetSales ROTA) float ebit_ROTA
1 2001    40.3  -5.11 14.865506
1 2002   135.5 -10.68 14.865506
1 2003    77.2  -23.8 14.865506
1 2010     3.8 -17.18 14.865506
1 2011     4.3 -30.09 14.865506
1 2012    15.5 -11.14 14.865506
1 2013    35.9   6.71 14.865506
1 2015    64.2   2.78 14.865506
1 2016   106.9    6.8 14.865506
1 2017   155.2  16.75 14.865506
2 2001    3552   6.05  4.260055
2 2002  4129.9   8.88  4.260055
2 2003  4761.9  14.67  4.260055
2 2004  6145.4  16.03  4.260055
2 2005  6835.8  12.32  4.260055
2 2006  7547.7   8.81  4.260055
2 2007  9267.2  13.73  4.260055
2 2008 10657.5  12.45  4.260055
2 2009 12900.3    6.3  4.260055
2 2010 15717.4  13.64  4.260055
2 2011 19106.1  14.64  4.260055
2 2012 23471.1  13.15  4.260055
2 2013 27784.6   13.2  4.260055
2 2014 32368.8  16.05  4.260055
2 2015 30767.3   7.19  4.260055
2 2016 28223.4   2.31  4.260055
2 2017 30977.7    4.7  4.260055
3 2002    20.4   8.38 3.6527724
3 2003    21.7  14.33 3.6527724
3 2004    21.1   3.56 3.6527724
3 2005    18.8   1.29 3.6527724
3 2006    27.4   3.68 3.6527724
3 2008    37.1   9.97 3.6527724
3 2009    45.8   9.14 3.6527724
3 2010    60.6    6.8 3.6527724
3 2011    80.2   6.49 3.6527724
3 2012    49.8   3.33 3.6527724
3 2013   107.1   6.26 3.6527724
3 2014    67.5   3.02 3.6527724
3 2015    69.7   3.24 3.6527724
3 2016    65.4   1.84 3.6527724
3 2017    58.4   2.34 3.6527724
4 2001  2261.9  16.65  6.788861
4 2002  2681.7  18.48  6.788861
4 2003    2820  17.69  6.788861
4 2004  3050.7  15.65  6.788861
4 2005  3596.4  15.47  6.788861
4 2006  4608.9  15.29  6.788861
4 2007  5214.8  11.58  6.788861
4 2008    5565   5.95  6.788861
end
format %ty Year
label values Unique_Identifier UI1
label def UI1 1 "21_102524", modify
label def UI1 2 "21_102576", modify
label def UI1 3 "21_102816", modify
label def UI1 4 "21_103261", modify

Can someone please tell me is the construction of this variable correct or something else is wrong. Please help!
many thanks

[Jared Greathouse]

The issue here is FE are meant to address your exact issue here, unobserved, unit stable confounding.

Without getting into the mathematics, the simple answer is you can't include time invariant variables in FE models, so you'll need to take this variable out. Each variable needs to change over time at some point.

[mohina saxena]

So, I want to confirm that my understanding of the construction of the variable is correct? Is the code that I have used capturing the same what has been followed in the paper?

[mohina saxena]

Hello all,

Just in case it might be needed to someone out there so clarifying it. The code is correct, I did the maual calculation and cross checking for each firm's standard deviation and it shows exactly the same results as provided by the code.

many thanks Jared for the clarification.