Interpreting coefficients in Panel data using Pooled OLS and Fixed effects models

[Denis Beuca]

Hi,

I'm not sure how to interpret the coefficients in the Pooled OLS model and Fixed effects model

I would really appreciate any clarification or examples


Kind regards,

Denis

[Joro Kolev]

You interpret the coefficients the same way as in standard linear regression. The estimated b = dE(Y|X)/dX, the partial derivative is after controlling for the fixed effects. It is easiest if you think of the fixed effects as a full set of dummy variables, the least squared dummy variable regression (LSDV).

[Nihat Mugurtay]

Dear Denis,

This depends on your DV, IV, and control variables. Is the DV logged? Is there any binary variable in your estimation? Do you cluster your units? There are multiple parameters that we need to know to answer your question. If you provide us a regression output with dataex then you will get some sound answers.

Best,

[Denis Beuca]

Thanks for the reply,

So for example my gender coefficient in Fixed effects cluster model is 0.962 in this instance do i say that the model predicts on average that the females have a 96.2% wellbeing rating compared to men ?

[Denis Beuca]

xtreg wellbeing lnincome gender children1 i.economicactivity i.education t if balanced==1, vce(cluster pidp )

[Joro Kolev]

Thanks for the reply,

So for example my gender coefficient in Fixed effects cluster model is 0.962 in this instance do i say that the model predicts on average that the females have a 96.2% wellbeing rating compared to men ?

This depends on what your dependent variable is.

[Denis Beuca]

my dependent variable is wellbeing

[Denis Beuca]

* Example generated by -dataex-. For more info, type help dataex
clear
input long pidp float(wave wellbeing) byte(economicactivity education) float lnincome byte children1 float(gender T balanced t)
22445 4 7 1 2 7.379426 0 0 5 0 3
22445 5 11 1 2 7.606884 0 0 5 0 4
22445 6 17 1 2 7.517521 0 0 5 0 5
22445 7 21 5 2 7.644776 0 0 5 0 6
22445 8 25 1 2 7.162165 0 0 5 0 7
29925 5 25 1 1 7.685069 1 0 4 0 4
29925 6 20 1 1 7.638618 1 0 4 0 5
29925 7 24 1 1 7.941534 1 0 4 0 6
29925 8 27 1 1 7.974027 1 0 4 0 7
76165 6 26 1 2 7.497856 0 0 3 0 5
76165 7 22 1 2 7.699992 0 0 3 0 6
76165 8 28 1 2 8.125237 1 0 3 0 7
280165 4 12 1 2 7.751118 1 0 4 0 3
280165 6 19 1 2 7.736176 1 0 4 0 5
280165 7 27 1 2 7.763319 1 0 4 0 6
280165 8 29 1 2 7.748331 1 0 4 0 7
333205 5 31 1 2 7.380362 0 0 4 0 4
333205 6 30 1 1 7.330294 0 0 4 0 5
333205 7 29 1 1 7.35137 0 0 4 0 6
333205 8 29 1 1 7.413566 0 0 4 0 7
387605 3 18 2 2 -2.525729 0 0 3 0 2
387605 4 14 2 2 -1.7719568 0 0 3 0 3
387605 5 14 2 2 5.736024 0 0 3 0 4
469205 8 23 5 2 7.524729 1 0 1 0 7
541285 5 18 1 1 7.027137 0 1 1 0 4
599765 4 29 1 1 7.478362 0 0 2 0 3
599765 8 30 1 1 7.642045 0 0 2 0 7
665045 4 29 1 2 6.480305 0 1 3 0 3
665045 5 26 1 2 6.131227 0 1 3 0 4
665045 7 29 1 2 6.649529 0 1 3 0 6
732365 8 1 5 3 7.012494 0 1 1 0 7
1587125 5 10 5 1 5.729028 0 0 4 0 4
1587125 6 24 1 1 8.128827 0 0 4 0 5
1587125 7 24 1 1 8.367195 0 0 4 0 6
1587125 8 24 1 1 7.938185 0 0 4 0 7
1697285 7 22 1 1 7.065613 0 1 2 0 6
1697285 8 26 1 1 7.040536 0 1 2 0 7
1833965 1 21 1 2 7.366755 0 1 7 0 0
1833965 2 28 1 2 7.192791 0 1 7 0 1
1833965 4 10 1 2 7.372684 0 1 7 0 3
1833965 5 16 1 2 6.879705 0 1 7 0 4
1833965 6 29 1 2 7.440834 0 1 7 0 5
1833965 7 7 5 2 7.091467 0 1 7 0 6
1833965 8 24 1 2 6.907755 0 1 7 0 7
2270525 6 26 5 2 6.711777 1 0 3 0 5
2270525 7 21 5 2 6.777305 1 0 3 0 6
2270525 8 13 5 2 7.301843 1 0 3 0 7
2297045 5 33 1 2 5.164786 0 1 1 0 4
2853965 2 22 1 1 7.377759 0 0 5 0 1
2853965 3 23 1 1 7.428333 0 0 5 0 2
2853965 4 13 1 1 7.495542 0 0 5 0 3
2853965 5 13 1 1 7.668561 0 0 5 0 4
2853965 6 25 1 1 7.654443 0 0 5 0 5
4192205 1 31 1 2 7.17012 0 0 3 0 0
4192205 2 31 1 2 7.212295 0 0 3 0 1
4192205 3 28 1 2 7.256177 0 0 3 0 2
4454005 1 25 3 1 7.140707 0 1 8 1 0
4454005 2 26 3 1 7.202907 0 1 8 1 1
4454005 3 30 3 1 7.099474 0 1 8 1 2
4454005 4 27 3 1 7.440146 0 1 8 1 3
4454005 5 26 3 1 7.553989 0 1 8 1 4
4454005 6 24 3 1 7.030893 0 1 8 1 5
4454005 7 25 3 1 7.993461 0 1 8 1 6
4454005 8 26 3 1 7.482113 0 1 8 1 7
4562125 1 24 1 1 7.208171 0 1 1 0 0
4626045 1 27 3 2 6.41277 0 1 3 0 0
4626045 2 26 3 2 6.660575 0 1 3 0 1
4626045 4 23 3 2 7.012115 0 1 3 0 3
4626725 1 24 3 3 5.792007 0 0 3 0 0
4626725 2 23 3 3 6.117921 0 0 3 0 1
4626725 4 29 3 3 5.655992 0 0 3 0 3
4794685 2 13 1 1 7.937375 0 0 4 0 1
4794685 3 12 1 1 7.984606 0 0 4 0 2
4794685 4 13 1 1 0 0 0 4 0 3
4794685 5 9 5 1 6.333866 1 0 4 0 4
68002045 1 28 1 1 6.216586 0 0 2 0 0
68002045 2 30 1 1 7.621141 0 0 2 0 1
68002049 1 30 1 1 7.495542 0 0 3 0 0
68002049 6 25 5 1 7.641723 1 0 3 0 5
68002049 7 28 1 1 8.091526 1 0 3 0 6
68002725 1 30 1 2 6.948581 0 0 6 0 0
68002725 4 24 1 2 7.083916 0 0 6 0 3
68002725 5 31 1 2 7.148464 0 0 6 0 4
68002725 6 28 1 2 6.975414 0 0 6 0 5
68002725 7 30 1 2 6.941896 0 0 6 0 6
68002725 8 29 3 2 7.148165 0 0 6 0 7
68004087 1 30 1 1 7.15201 0 1 8 1 0
68004087 2 28 1 1 6.818192 0 1 8 1 1
68004087 3 28 1 1 6.818192 0 1 8 1 2
68004087 4 25 1 1 6.923304 0 1 8 1 3
68004087 5 30 1 1 6.915227 0 1 8 1 4
68004087 6 29 1 1 7.137541 0 1 8 1 5
68004087 7 29 1 1 7.065613 0 1 8 1 6
68004087 8 26 1 1 7.286192 0 1 8 1 7
68006127 1 24 2 2 7.017497 1 0 7 0 0
68006127 2 23 5 2 7.069593 0 0 7 0 1
68006127 4 14 5 2 6.27854 0 0 7 0 3
68006127 5 7 5 2 7.01107 0 0 7 0 4
68006127 6 10 5 2 5.953243 0 0 7 0 5
68006127 7 9 5 2 7.207675 0 0 7 0 6
end
label values economicactivity economicactivity
label def economicactivity 1 "employed", modify
label def economicactivity 2 "unemployed", modify
label def economicactivity 3 "retired", modify
label def economicactivity 5 " other", modify
label values education education
label def education 1 "degree or other high degree", modify
label def education 2 "Alevel or GCSE or Other qual", modify
label def education 3 "No qual", modify
label values children1 children1
label def children1 0 "nokids", modify
label def children1 1 "kids", modify
[/CODE]

[Carlo Lazzaro]

Denis:
could you please also provide what you typed and what Stata gave you back (as per FAQ)? Thanks.

[Denis Beuca]

xtreg wellbeing lnincome gender children1 i.economicactivity i.education t if balanced==1, vce(cluster pidp)

I'm not sure how to show what Stata gave me back

[Joro Kolev]

It seems that your dependent variable is some index

. summ wellbeing

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   wellbeing |        100       22.91    7.128113          1         33

If you are estimating 0.962 coefficient on your gender regressor (unfortunate name, it should have been called either male or female so that we know what it is), this mean that the switch of the gender from 0 to 1 (whatever this means, depending on whether 0 is male of female) causes a 0.962 increase in the happiness index.

By the result I would guess that your gender is coded 0 for females, and 1 for males... women tend to be unhappy about many things in life.

[Denis Beuca]

Thats correct its 0 for females and 1 for males so in this instance is the 0.962 coefficient associated with male or females wellbeing ?

[Clyde Schechter]

Thats correct its 0 for females and 1 for males so in this instance is the 0.962 coefficient associated with male or females wellbeing ?

Neither. It is the difference between males' and females' expected wellbeing.

By the way, the command you show in #10 implements a random effects model, not a fixed effects model.

[Denis Beuca]

What would be the correct interpretation for this coefficient in regards to the random effect model ?

[Joro Kolev]

What would be the correct interpretation for this coefficient in regards to the random effect model ?

The same as above, but you are not controlling now for the fixed effects.