i.year vs c.year

[Taz Raihan]

I want to add time fixed effects to my panel data analysis. As far as I understood reading existing posts here, there are two ways to do it: (a) i.year (b) c.year. I understand the results obtained using the i.year. But I am not sure what c.year does. Is c.year the same as using just "year" as an explanatory variable? At least, that's what I understood from help fvvarlist. I will appreciate if someone could confirm this.

Thanks,

Taz Raihan

P.S. I already sent a request to change my name from T Raihan to Taz Raihan.

[Nick Cox]

c.year just adds year as a predictor and (as I understand it) the c. makes no difference to what is fitted, only to what is possible thereafter.


As a simple example you might study the results of

webuse grunfeld
xtreg mvalue c.year
xtreg mvalue year
reg mvalue c.year
reg mvalue year

[Carlo Lazzaro]

Taz:
you can see the difference between -c-. and -i.- in the following toy-example, too (by the way, I see no point in using -c.- with time variable):

use "http://www.stata-press.com/data/r15/nlswork.dta"
. xtreg ln_wage c.year

Random-effects GLS regression                   Number of obs     =     28,534
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.1022                                         min =          1
     between = 0.0804                                         avg =        6.1
     overall = 0.0709                                         max =         15

                                                Wald chi2(1)      =    3093.66
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |   .0186375   .0003351    55.62   0.000     .0179807    .0192942
       _cons |   .2039722   .0267605     7.62   0.000     .1515226    .2564218
-------------+----------------------------------------------------------------
     sigma_u |   .3715966
     sigma_e |  .30347936
         rho |  .59988609   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. testparm c.year

 ( 1)  year = 0

           chi2(  1) = 3093.66
         Prob > chi2 =    0.0000

. xtreg ln_wage i.year

Random-effects GLS regression                   Number of obs     =     28,534
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.1058                                         min =          1
     between = 0.0796                                         avg =        6.1
     overall = 0.0724                                         max =         15

                                                Wald chi2(14)     =    3198.67
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
         69  |   .0854251   .0123808     6.90   0.000     .0611592    .1096911
         70  |    .069889   .0115653     6.04   0.000     .0472215    .0925566
         71  |   .1196013   .0114272    10.47   0.000     .0972043    .1419983
         72  |   .1327835   .0117484    11.30   0.000      .109757    .1558099
         73  |   .1476736   .0113915    12.96   0.000     .1253467    .1700006
         75  |   .1609048   .0112586    14.29   0.000     .1388385    .1829712
         77  |   .2207951   .0112687    19.59   0.000     .1987089    .2428814
         78  |   .2596833   .0115128    22.56   0.000     .2371186     .282248
         80  |    .267724   .0116586    22.96   0.000     .2448735    .2905745
         82  |   .2852433   .0113995    25.02   0.000     .2629007    .3075859
         83  |   .3126372   .0115421    27.09   0.000     .2900152    .3352592
         85  |   .3653587   .0114383    31.94   0.000       .34294    .3877773
         87  |   .3813851   .0113703    33.54   0.000     .3590997    .4036706
         88  |   .4370689   .0113081    38.65   0.000     .4149054    .4592325
             |
       _cons |   1.426677   .0103611   137.70   0.000     1.406369    1.446984
-------------+----------------------------------------------------------------
     sigma_u |  .36928787
     sigma_e |  .30294584
         rho |  .59773703   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. testparm i.year

 ( 1)  69.year = 0
 ( 2)  70.year = 0
 ( 3)  71.year = 0
 ( 4)  72.year = 0
 ( 5)  73.year = 0
 ( 6)  75.year = 0
 ( 7)  77.year = 0
 ( 8)  78.year = 0
 ( 9)  80.year = 0
 (10)  82.year = 0
 (11)  83.year = 0
 (12)  85.year = 0
 (13)  87.year = 0
 (14)  88.year = 0

           chi2( 14) = 3198.67
         Prob > chi2 =    0.0000

.

[Taz Raihan]

Carlo Lazzaro Thanks, but sorry for my question was not clear. I know how the stata outputs differ across i.year and c.year. What I basically wanted to know was, how to interpret the coefficient on c.year? And if I want to add time fixed effect, which one is more appropriate? i.year or c.year?

Nick Cox Thanks for your response. Would you please explain what you meant by "c. makes no difference to what is fitted, only to what is possible thereafter"?

[Carlo Lazzaro]

Taz:
1) if you impose -c.year- Stata tells you that each year (no matter which one) increases -ln_wage- by about 1.88%:

. di (exp(.0186375)-1)*100
1.8812262

;
2) I would go -i.year-.

[Taz Raihan]

Carlo Lazzaro thank you so much for the clarification.

[Nick Cox]

#2, #4: Commands like margins are sensitive to what notation you used earlier.

#3 Not quite sure what Carlo means, but with environmental data I am often checking in the first instance for a linear trend.

[Carlo Lazzaro]

Nick:
my previous reply was probably influenced by the habit of checking for each year's contribution first: that's why I find more palatable (for an economist's taste, at least) to go -i.year- vs -c.year-.

[S. M. Woahid Murad]

Hi, I am using regife package for my panel data analysis. For example. to accommodate the interactive fixed effect model, I write the following command:

regife y x1 x2, a(country year) ife(country year, 1)

Since regife command does not work for 2SLS, how can I control the interactive fixed effect model in ivregress command? Can I write in the following way?

ivregress 2sls y x2 (x1=z) i.country i.year i.country#c.year, first

Thanks in advance for your time and effort.