Unexpected collinearity within fixed effects model

[Joseph Laverty]

Hi guys,

I am currently trying to run a fixed effects model testing the impact of institutions (coded 1 - 7) on city populations in pre-industrial europe, with time and regional fixed effects. However, when I run this model regions is always dropped for collinearity (alongside some other controls, such as whether a city was on a river, nearby soil quality, ecozone the city is in ....) and I do not understand why. This occurs even when city populations is regressed solely on regions. Any advice on why this may be occuring would be of immense help. There is no collinearity in random effects or pooled OLS models.

Please see below my regression and dataextract.

xtreg citypop_le5 i.polity i.countryid i.year, fe

And an extract from the data using data ex:

* Example generated by -dataex-. For more info, type help dataex
clear
 city               citypop  country     year  polity  river
"Abbeville"             3 "France"      1400 2 1
"Abbeville"             5 "France"      1500 2 1
"Abbeville"             9 "France"      1600 1 1
"Abbeville"            15 "France"      1700 1 1
"Abbeville"            18 "France"      1800 4 1
"Aberdeen"              3 "UK"          1400 5 1
"Aberdeen"              3 "UK"          1500 4 1
"Aberdeen"              6 "UK"          1600 3 1
"Aberdeen"             12 "UK"          1700 5 1
"Aberdeen"             27 "UK"          1800 7 1
"Acireale"              2 "Italy"       1400 3 0
"Acireale"              6 "Italy"       1500 3 0
"Acireale"              8 "Italy"       1600 2 0
"Acireale"             12 "Italy"       1700 1 0
"Acireale"             15 "Italy"       1800 1 0
"Afragola"              1 "Italy"       1400 3 0
"Afragola"              2 "Italy"       1500 3 0
"Afragola"              3 "Italy"       1600 2 0
"Afragola"              6 "Italy"       1700 1 0
"Afragola"             12 "Italy"       1800 1 0
"Agen"                  4 "France"      1400 2 1
"Agen"                  6 "France"      1500 2 1
"Agen"                  8 "France"      1600 1 1
"Agen"                 10 "France"      1700 1 1
"Agen"                 10 "France"      1800 4 1
"Agrigento"             4 "Italy"       1400 3 0
"Agrigento"            10 "Italy"       1500 3 0
"Agrigento"            11 "Italy"       1600 2 0
"Agrigento"            11 "Italy"       1700 1 0
"Agrigento"            14 "Italy"       1800 1 0
"Aix"                   4 "France"      1400 2 1
"Aix"                  13 "France"      1500 2 1
"Aix"                  18 "France"      1600 1 1
"Aix"                  27 "France"      1700 1 1
"Aix"                  21 "France"      1800 4 1
"Albi"                  7 "France"      1400 2 1
"Albi"                  8 "France"      1500 2 1
"Albi"                  7 "France"      1600 1 1
"Albi"                 10 "France"      1700 1 1
"Albi"                 10 "France"      1800 4 1
"Alcamo"                3 "Italy"       1400 3 0
"Alcamo"                6 "Italy"       1500 3 0
"Alcamo"                8 "Italy"       1600 2 0
"Alcamo"                8 "Italy"       1700 1 0
"Alcamo"               13 "Italy"       1800 1 0
"Alcazar de San Juan"   3 "Spain"       1400 5 0
"Alcazar de San Juan"  20 "Spain"       1500 4 0
"Alcazar de San Juan"  10 "Spain"       1600 3 0
"Alcazar de San Juan"   7 "Spain"       1700 2 0
"Alcazar de San Juan"  10 "Spain"       1800 1 0
"Alcoy"                 1 "Spain"       1400 5 0
"Alcoy"                 2 "Spain"       1500 4 0
"Alcoy"                 5 "Spain"       1600 3 0
"Alcoy"                 4 "Spain"       1700 2 0
"Alcoy"                16 "Spain"       1800 1 0
"Alencon"               3 "France"      1400 2 1
"Alencon"               4 "France"      1500 2 1
"Alencon"               7 "France"      1600 1 1
"Alencon"              10 "France"      1700 1 1
"Alencon"              13 "France"      1800 4 1
"Alessandria"           7 "Italy"       1400 3 1
"Alessandria"           8 "Italy"       1500 3 1
"Alessandria"          14 "Italy"       1600 2 1
"Alessandria"          12 "Italy"       1700 1 1
"Alessandria"          30 "Italy"       1800 1 1
"Alkmaar"               2 "Netherlands" 1400 3 0
"Alkmaar"               5 "Netherlands" 1500 3 0
"Alkmaar"              12 "Netherlands" 1600 5 0
"Alkmaar"              12 "Netherlands" 1700 5 0
"Alkmaar"               8 "Netherlands" 1800 4 0
"Altamura"              1 "Italy"       1400 3 0
"Altamura"              6 "Italy"       1500 3 0
"Altamura"             12 "Italy"       1600 2 0
"Altamura"             15 "Italy"       1700 1 0
"Altamura"             18 "Italy"       1800 1 0
"Amalfi"                2 "Italy"       1400 3 0
"Amalfi"                2 "Italy"       1500 3 0
"Amalfi"                2 "Italy"       1600 2 0
"Amalfi"                2 "Italy"       1700 1 0
"Amalfi"                5 "Italy"       1800 1 0
"Amiens"                6 "France"      1400 2 1
"Amiens"               20 "France"      1500 2 1
"Amiens"               25 "France"      1600 1 1
"Amiens"               35 "France"      1700 1 1
"Amiens"               40 "France"      1800 4 1
"Amsterdam"             3 "Netherlands" 1400 3 1
"Amsterdam"            12 "Netherlands" 1500 3 1
"Amsterdam"            60 "Netherlands" 1600 5 1
"Amsterdam"           180 "Netherlands" 1700 5 1
"Amsterdam"           217 "Netherlands" 1800 4 1
"Ancona"                3 "Italy"       1400 3 0
"Ancona"                5 "Italy"       1500 3 0
"Ancona"               10 "Italy"       1600 2 0
"Ancona"                9 "Italy"       1700 1 0
"Ancona"               17 "Italy"       1800 1 0
"Andria"                2 "Italy"       1400 3 0
"Andria"                5 "Italy"       1500 3 0
"Andria"               14 "Italy"       1600 2 0
"Andria"                7 "Italy"       1700 1 0
"Andria"               14 "Italy"       1800 1 0
end

Any advice would be greatly appreciated.

Kind regards,
Joseph Laverty

[Clyde Schechter]

There is nothing unexpected about this. I take it when you -xtset- your data, your panel variable was the city itself. Any given city is always in the same region. As with any other variable that is constant across all observations for the same city, it is going to be colinear and omitted.

If you are including region in your analyses simply to avoid omitted variable bias (i.e. a "control" variable), then there is no problem. The region effect is automatically adjusted for by the city fixed-effect itself, just as any other fixed attribute of the city is. If, on the other hand, your research goals include assessing regional effects, then you simply cannot do that in a fixed-effects model that includes city as a variable. Use a different model in that case.

[Joseph Laverty]

Thank you for your quick and detailed reply!

What would be an appropriate model to assess the impact of regional effects? A hausman test does not rule out the use of random effects, but I am worried about introducing bias into my model.

[Carlo Lazzaro]

Joseph:
as an aside to Clyde's helful reply, if the -hausman- test does not reject the null, you should go -re-, because -fe- is still consistent but inefficient in this instance.

[Joseph Laverty]

Thank you! All comments are much appreciated!