FE Model, variable being omitted

[Kate Pryce]

* Example generated by -dataex-. For more info, type help dataex
clear
input float ID int(FiscalYear CompanyInitialPublicOffering) float(yr YearsSinceIPO) double mean_TenYRSetGR
4 1985 10227 1988 -3     .14902254389598965
4 1986 10227 1988 -2     .14685623841360212
4 1987 10227 1988 -1      .1481846054084599
4 1988 10227 1988  0     .13722927318885922
4 1989 10227 1988  1      .1366371256299317
4 1990 10227 1988  2      .1400796439498663
4 1991 10227 1988  3     .09788233302533626
4 1992 10227 1988  4     .10033785738050938
4 1993 10227 1988  5     .09218150936067104
4 1994 10227 1988  6     .07971623055636883
4 1995 10227 1988  7     .07831400446593761
4 1996 10227 1988  8     .07478203736245632
4 1997 10227 1988  9       .090913812443614
4 1998 10227 1988 10     .09140022061765193
4 1999 10227 1988 11     .09350091181695461
4 2000 10227 1988 12     .07397926524281502
4 2001 10227 1988 13    .056444597989320756
4 2002 10227 1988 14     .06080930270254612
4 2003 10227 1988 15    .061808962002396585
4 2004 10227 1988 16     .06581418849527836
4 2005 10227 1988 17     .07392313070595265
4 2006 10227 1988 18     .07548676915466786
4 2007 10227 1988 19      .0732811976224184
4 2008 10227 1988 20    .058723917417228225
4 2009 10227 1988 21    .042101201601326466
4 2010 10227 1988 22     .08808264452964068
4 2011 10227 1988 23     .13184541333466768
4 2012 10227 1988 24     .14137937258929015
4 2013 10227 1988 25     .12775963488966227
4 2014 10227 1988 26     .09139561150223016
4 2015 10227 1988 27     .07569748815149069
4 2016 10227 1988 28     .06374833416193723
4 2017 10227 1988 29    .032147650886327026
4 2018 10227 1988 30     .04668720616027713
4 2019 10227 1988 31    .053558845352381465
4 2020 10227 1988 32   .0012695188634097576
4 2021 10227 1988 33  -.0055182305164635185
4 2022 10227 1988 34 -.00043387608602643015
8 1985     .    .  .     .06737074926495552
8 1986     .    .  .     .08602120764553547
8 1987     .    .  .     .05038209520280361
8 1988     .    .  .     .04081597216427326
8 1989     .    .  .     .03778961934149265
8 1990     .    .  .    .033670494332909584
8 1991     .    .  .     .04145971070975065
8 1992     .    .  .    .050815104693174365
8 1993     .    .  .     .06038322150707245
8 1994     .    .  .     .04732297360897064
8 1995     .    .  .    .060763214528560636
8 1996     .    .  .     .05809178799390793
8 1997     .    .  .     .05835718661546707
8 1998     .    .  .    .059704972058534624
8 1999     .    .  .     .04420982599258423
8 2000     .    .  .    .045337119698524476
8 2001     .    .  .     .03254460394382477
8 2002     .    .  .     .05082338377833366
8 2003     .    .  .     .06324156522750854
8 2004     .    .  .     .07647959440946579
8 2005     .    .  .     .07177311331033706
8 2006     .    .  .    .055433349683880806
8 2007     .    .  .     .06845480538904666
8 2008     .    .  .     .07515728808939456
8 2009     .    .  .     .07240686453878879
8 2010     .    .  .     .07062025032937527
8 2011     .    .  .     .09319268800318241
8 2012     .    .  .       .072216771915555
8 2013     .    .  .     .06637011356651783
8 2014     .    .  .     .05872194673866034
8 2015     .    .  .     .06066859420388937
8 2016     .    .  .     .06797020640224219
8 2017     .    .  .     .07675650399178266
8 2018     .    .  .     .07348728086799383
9 1985     .    .  .     .18135447446256875
9 1986     .    .  .     .20615729335695504
9 1987     .    .  .      .1702531086280942
9 1988     .    .  .     .10492789018899203
9 1989     .    .  .     .20562590844929218
9 1990     .    .  .     .19770551100373268
9 1991     .    .  .      .1808270938694477
9 1992     .    .  .     .16773973330855368
9 1993     .    .  .     .08545763781294227
9 1994     .    .  .     .04254611814394593
9 1995     .    .  .     .09729992160573601
9 1996     .    .  .     .11625668862834573
9 1997     .    .  .     .10899080941453576
9 1998     .    .  .     .07530199224129319
9 1999     .    .  .    -.04137682383880019
9 2000     .    .  .    -.03538312641903758
9 2001     .    .  .    -.02205750634893775
9 2002     .    .  .    -.03074157303199172
9 2003     .    .  .     -.0640760375186801
9 2004     .    .  .   -.004610361903905869
9 2005     .    .  .   -.032065339386463165
9 2006     .    .  .   -.016252615302801133
9 2007     .    .  .   -.013504499942064286
9 2008     .    .  .   -.037926220893859865
9 2009     .    .  .   -.042932073771953586
9 2010     .    .  .    -.07847203798592091
9 2011     .    .  .    -.10087165758013725
9 2012     .    .  .    -.11243906989693642
end
format %tdnn/dd/CCYY CompanyInitialPublicOffering
label values ID ID
label def ID 4 "AAR CORP", modify
label def ID 8 "ACETO CORP", modify
label def ID 9 "ACMAT CORP  -CL A", modify

Hi all,

I've got a panel dataset with 323 companies, and I'm trying to regress average (averaged over 10 years) company growth over time. My regressions all seem to be working, but I wanted to include a dummy variable that would capture the number of years that have passed since a firm went public (code below). When I run this, however, the YearsSinceIPO variable is omitted. I am running a fixed effects model, but the YearsSinceIPO isn't the same every year, so I don't understand why it's being omitted. Does anyone see what I'm missing?

xtset ID FiscalYear

xtreg mean_TenYRSetGR FiscalYear YearsSinceIPO, fe vce (cluster ID)

[Clyde Schechter]

but the YearsSinceIPO isn't the same every year, so I don't understand why it's being omitted

What you observe is true. But YearsSinceIPO is exactly colinear with FiscalYear. While both variables do vary within panels, they vary in exactly the same way. In fact, we can write out the equation within any panel: FiscalYear - YearsSinceIPO = panel-specific-constant. Moreover, any panel-specific constant is perfectly colinear (in a complicated way) with the ID fixed effect. So that is how you get a colinearity that forces omission of either FiscalYear of YearsSinceIPO. You can't estimate them simultaneously in a fixed-effects model. (Actually, with this kind of colinearity within-panel you can't estimate them simultaneously in a random-effects model either.)

[Kate Pryce]

Ah Clyde, that makes absolute sense. I was hoping to being able to see if there was a relationship between when a firm went public and its growth rate but I suppose that's not a possibility here. Thanks very much for your explanation Clyde!

[Jeff Wooldridge]

As Clyde pointed out, you have a lack of identification of any variable that increases by the same amount in each period if you use fixed effects. The firm FE is perfectly collinear with the start time, and then, from there, the variable is perfectly collinear with the FiscalYear variable. I do wonder if you meant to use i.FiscalYear, as putting in a linear trend across a decent stretch of time is pretty restrictive.

Because you only have FiscalYear along with YearsSinceIPO, the only reason to use FE is if you want to account for endogeneity of the year of the IPO buyout and firm heterogeneity. If you want to estimate a coefficient on YearsSinceIPO, use random effects. If you add more control variables, use the Mundlak device but do not put in the time average of YearsSinceIPO.

[Kate Pryce]

Jeff, what a coincidence, I'm reading Econometric Analysis of Cross Section and Panel Data as I'm trying to figure out what model is best for my problem. Essentially, I'm looking at how a firm's growth varies over time and the raw data, unfortunately, regresses to the mean. So, to mitigate this effect, I'm using a FE model to control for firm-specific characteristics to isolate the impact of time on firm growth. I was also thinking that adding a year fixed effect might be good to add to control for anything that is affects all firms uniformly in a particular year (though I have not yet gotten this to work in state). The issue I'm now running into is that there are, obviously, other controls that influence growth and some of them vary with time and are thus easy to include and other do not (like years since IPO which doesn't vary but I feel could be influencing a firm's growth rate, or industry sector which I've been adding as an interaction term with Fiscal Year). If you've any suggestions I'd be grateful, otherwise I'll keep reading your book and familiarize myself with the Mundlak device.