including a constant in a first difference mdoel

[Frederick den Hartog]

I have the following question:

I want to estimate the effect of retirement on the 'cesd-score' (which indicates someones mental health, using a panel dataset and the first difference model:

reg d.cesd d.retired d.age d.female d.education d.mstat2 d.mstat3 d.mstat4 d.white

My question is: should I include the constant or not? What do I base my decision on?

My data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input long id byte(wave education mstat) int age byte cesd float(female white retired)
    3010  1 12 1  56  . 0 1 0
    3010  2 12 1  58  0 0 1 0
    3010  3 12 1  60  3 0 1 0
    3010  4 12 1  62  3 0 1 0
    3010  5 12 1  64  1 0 1 0
    3010  6 12 1  66  1 0 1 0
    3010  7 12 1  68  0 0 1 0
    3010  8 12 1  70  0 0 1 1
    3010  9 12 1  72  0 0 1 1
    3010 10 12 1  74  0 0 1 1
    3010 11 12 1  76  0 0 1 1
10001010  2 12 4  55  4 0 1 1
10001010  3 12 4  57  1 0 1 0
10001010  4 12 4  58  5 0 1 0
10001010  5 12 4  60  1 0 1 1
10001010  6 12 4  62  1 0 1 1
10001010  7 12 4  64  1 0 1 1
10001010  8 12 4  66  1 0 1 1
10001010  9 12 4  69  1 0 1 1
10001010 10 12 4  71  1 0 1 1
10001010 11 12 4  72  1 0 1 1
10001010 12 12 4  74  0 0 1 1
10003020  1 16 1  58  . 0 1 0
10003020  2 16 1  60 .m 0 1 0
10003020  3 16 1  62 .m 0 1 0
10003020  4 16 1  64 .m 0 1 1
10003030  1 16 1  36  . 1 1 0
10003030  2 16 1  38  1 1 1 0
10003030  3 16 1  40  3 1 1 0
10003030  4 16 1  42  3 1 1 0
10003030  6 16 3  46  1 1 1 0
10003030  8 16 3  50  4 1 1 1
10003030 10 16 3  54  0 1 1 1
10003030 11 16 3  56  0 1 1 1
10003030 12 16 2  58  1 1 1 1
10083010  4 10 1  59  2 0 0 0
10083010  5 10 1  61  1 0 0 0
10083010  6 10 1  63  0 0 0 1
10083010  7 10 1  65  0 0 0 1
10083010  8 10 1  67  0 0 0 1
10083010  9 10 1  69  1 0 0 1
10094010  1 12 3  58  . 1 0 0
10114010  1 12 4  55  . 1 0 0
10114010  2 12 4  56  2 1 0 1
10114010  3 12 4  58  4 1 0 1
10114010  4 12 4  60  0 1 0 1
10114010  5 12 4  62  1 1 0 1
10124011  5 12 1 100 .m 0 0 0
10155010  1  7 2  53  . 1 0 0
10155010  2  7 2  55  1 1 0 0
10155010  3  7 2  57  0 1 0 0
10155010  4  7 2  59  1 1 0 0
10225010  1  8 4  57  . 1 0 0
10225010  2  8 4  59  7 1 0 0
10225010  3  8 4  61  8 1 0 1
10225010  4  8 4  63  5 1 0 1
10225010  5  8 4  65  2 1 0 1
10225010  6  8 4  67  1 1 0 1
10225010  7  8 4  69  1 1 0 1
10225010  8  8 4  71  0 1 0 1
10225010  9  8 4  73  1 1 0 1
10225010 10  8 4  76  2 1 0 1
10225010 11  8 4  77  2 1 0 1
10225010 12  8 4  79  4 1 0 1
10240010  1  9 2  53  . 0 1 0
10240010  2  9 2  55  1 0 1 0
10240010  6  9 2  63  8 0 1 1
10325020  3 14 1  57  0 1 1 0
10325020  4 14 1  59  0 1 1 0
10325020  5 14 1  60  1 1 1 0
10325020  6 14 1  63  0 1 1 1
10325020  7 14 1  65 .m 1 1 1
10325020 11 14 3  73  0 1 1 1
10325020 12 14 3  74  0 1 1 1
10346010  1 11 4  52  . 0 1 0
10372010  1 10 4  56  . 1 0 0
10372010  2 10 4  58  4 1 0 0
10372010  3 10 4  60  6 1 0 0
10372010  4 10 4  62  3 1 0 0
10372010  5 10 4  64  6 1 0 1
10372010  6 10 4  66  5 1 0 1
10372010  7 10 4  68  5 1 0 1
10372010  8 10 4  70  6 1 0 1
10372010  9 10 4  72  2 1 0 1
10372010 10 10 4  75  1 1 0 1
10372010 11 10 4  76  4 1 0 1
10372010 12 10 4  78  3 1 0 1
10378010  1 16 4  53  . 1 0 0
10378010  2 16 4  54  0 1 0 0
10378010  4 16 1  58  5 1 0 0
10378010  5 16 4  60  1 1 0 0
10378010  6 16 4  62  1 1 0 1
10378010  7 16 1  64  1 1 0 1
10394010  5 16 1  59  3 0 1 0
10394010  8 16 1  65  0 0 1 0
10404010  1 12 3  52  . 1 1 0
10404010  2 12 2  54  1 1 1 0
10404010  3 12 2  56  3 1 1 0
10404010  4 12 3  58  0 1 1 0
10404010  5 12 3  60  0 1 1 0
end
label values education EDYRS
label values mstat marital
label def marital 1 "Married or in partnership", modify
label def marital 2 "Separated or divorced", modify
label def marital 3 "Widowed", modify
label def marital 4 "Single", modify

[Frederick den Hartog]

In other words: if my first difference model shows a significant constant, can I conclude that I have to include the constant in my model (that there is a time trend that it is accounting for?)

[Phil Bromiley]

If you have a significant constant, then omitting it is arbitrarily forcing the line through the intercept. In your case, it is quite possible that mental health changes systematically over time regardless of your explanatory variables. I'd say include the intercept.

With panel data, it is often easier to use the panel data estimators like xtreg instead of trying to imitate them manually. Whether a first different or fixed effects estimator is better is not clear.