Panel data set - country-fixed effects and country-specific (linear) time trends

[Saiming Liew]

I have read the paragraph below in an economic journal and would like to do something similar within Stata.

"All model specifications include country-fixed effects to capture the effects of within-country changes in leave duration. Time dummies and country-specific (linear) time trends are also added to eliminate the effect of exogenous factors on (changes in) labour market outcomes."

I have a cross-country panel data set and plan to use a fixed-effects model. Does declaring my panel data set as 'xtset country year' mean I have included the country-specific (linear) time trends or would this be another variable? If so, how would I go about it?

Thank you.

[Clyde Schechter]

-xtset country year- will automatically include country fixed effects in any -xt- regression command. But it will not incorporate time effects in any way.

So in your model, if you want to model a linear time trend, you need to include year as one of the predictor variables in your model. Just add it to the list of predictor variables in the regression command, e.g. -xtreg outcome predictor1 predictor2 year, fe-.

[Saiming Liew]

Thank you for your help, Clyde.

[Saiming Liew]

I have another question. What would make the variable a country-specific time trend? Would I replace the 'year' independent variable with an interaction variable of 'year x country'?

[Clyde Schechter]

Yes, if you want each country to have its own time trend, you include a year X country interaction. Use factor variable notation and make sure you specify it as c.year##i.country. The i.country main effect will not appear if you are using -xtreg, fe- (or any other -xt...,fe-). But the interaction terms will. Then to get the actual marginal effects of time in each year, use -margins-.

[Saiming Liew]

Thank you for your help.

[Eugenia Erningdianhastuti]

Hello Clyde, I am a new member of statalist.

I have more or less same kind of problem. I would like to consul about my problem..
I am working on a paper about the Environmental Kuznets Curve. I have already include i.year in my fixed-effects model to capture the effect of technological change.

I want to check the slope homogeneity assumption in my panel data. Can I do it by adding country specific trend (c.year##i.country) into the equation?
is there another way to check the slope homogeneity assumption?

Your help is really appreciated.
Thank you.

[Clyde Schechter]

Yes, you can do that. I wouldn't go so far as to say there is no other way to do it, but this is the simplest. Since it sounds like you are using -xtreg, fe-, you will not be able to use the other commonly used approach: -suest-. The use of an interaction term is the most straightforward way to test effect heterogeneity. Its only real drawback, that is assumes that the other effects are homogeneous can, in most instances, be overcome by adding more interaction terms for those. (And if you're in a situation where that approach fails because you are exhausting your degrees of freedom, you probably don't really have enough degrees of freedom to test heterogeneity of effect to start with.)

[Eugenia Erningdianhastuti]

Thank you for you quick response.

If I may further ask, I am using -xtreg, fe- , xtivreg, fe- and -xtivreg2, fe- commands for endogeneity checking.

For xtreg, I compare three results, which are:
fixed-effects country ----> xtreg depvar predictor1 predictor2, fe cluster(id)
fixed effects country and years -----> xtreg depvar predictor1 predictor2 i.year, fe cluster(id)
country specific trend ------> xtreg depvar predictor1 predictor2 i.year c.year##i.country, fe cluster(id)

If most siginificance relationshipe go away at the third estimation, does it mean the slope is heterogeneous?
Are these the correct way to do it?

However, it wont work for the IV estimation.
I am sorry for asking too many things, I am new to Stata, and still confuse.

Thank you for your time in advance.

[Carlo Lazzaro]

Eugenia:
unfortunately, you do not show us what Stata gave you back (please read the FAQ on how to use CODE delmiters for that purpose).
As far as endogeneity is concerned, set aside some self-apparent examples (e.g. regressing gross wage on education leaving indidual ability within the residuals), literature in your research field should give you same guidance.

[Eugenia Erningdianhastuti]

Dear Carlo,
Thank you for your reply.

I am still trying to understand how to put Stata's result on a post.

But meanwhile, if you don't mind, I want to clarify some things.
For the equation: xtreg depvar predictor1 predictor2 i.year c.year##i.country, fe cluster(id) --- by running this estimation, do I already have account for heterogeneity across country-year to account for heterogeneous slope?


And, when I run for IV estimation:
xtivreg depvar predictor1 predictor2 i.year c.year##i.id (y = age fert), fe vce(robust) small

Stata will response in error saying:
--- independent variables are collinear with the panel variable id ---
Is it because the -fe- options? Because when I try the estimation without mentioning -fe-, it works.

Is it correct not to write the -fe- option for the last estimation I mentioned?

I am sorry if I have not make myself clear enough, I am trying to understand how econometrics and Stata work. Thank you so much for your help.

Best regards,
Eugenia

[Carlo Lazzaro]

Eugenia:
it seems to me that Clyde reply #5 covers your first question.
As far as your second query is concerned, Stata warns you about collinearity with the panel variable under -fe- specification (that gets rid of time-invariant preditors).
If you do not mention -fe- you're actually invoking -re- (random effect) specification, which is a quite different tool.
In fact, Stata -xt- command use -re- as the default specification; hence, if you don't explicit type -fe-, Stata goes -re- automatically.

[Eugenia Erningdianhastuti]

Yes, sorry. Clyde has already confirmed my first question.

Thank you for your answer, I realise now that by excluding -fe- options is a wrong way in estimating my model. Although, I still don't understand how the collinearity exist while the same factorial interaction variable works for -xtreg-.
Do you know, if in any case, why it can happen?

Thank you for your time.

Best regards,
Eugenia

[Carlo Lazzaro]

Eugenia:
I would say that the apparently weird behaviour that you reported is due to the differences in -fe- and -re- machinery, as you can see from the following toy-example:

. use http://www.stata-press.com/data/r14/nlswork.dta
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age race i.year, fe
note: race omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.0914                                         avg =        6.1
     overall = 0.0805                                         max =         15

                                                F(15,23785)       =     188.00
corr(u_i, Xb)  = 0.0467                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0125992   .0102163     1.23   0.217    -.0074253    .0326238
        race |          0  (omitted)
             |
        year |
         69  |   .0748621   .0159011     4.71   0.000      .043695    .1060292
         70  |   .0478697   .0235673     2.03   0.042     .0016763     .094063
         71  |   .0865577   .0327939     2.64   0.008     .0222795     .150836
         72  |   .0856757   .0424903     2.02   0.044     .0023919    .1689594
         73  |   .0880069    .052344     1.68   0.093    -.0145906    .1906044
         75  |   .0778607   .0720304     1.08   0.280    -.0633235    .2190449
         77  |    .108365   .0922272     1.17   0.240    -.0724063    .2891363
         78  |   .1309518   .1028143     1.27   0.203    -.0705707    .3324743
         80  |   .1142649    .122792     0.93   0.352    -.1264152     .354945
         82  |   .1090451   .1431112     0.76   0.446    -.1714619    .3895522
         83  |   .1211272   .1532018     0.79   0.429    -.1791581    .4214125
         85  |   .1465637   .1736146     0.84   0.399    -.1937321    .4868594
         87  |   .1382642   .1941163     0.71   0.476     -.242216    .5187445
         88  |   .1799741   .2079871     0.87   0.387    -.2276938     .587642
             |
       _cons |   1.203731   .1952306     6.17   0.000     .8210667    1.586396
-------------+----------------------------------------------------------------
     sigma_u |   .4058746
     sigma_e |  .30300411
         rho |  .64212421   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23785) = 8.80                 Prob > F = 0.0000

. xtreg ln_wage age race i.year, re

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.1013                                         avg =        6.1
     overall = 0.0936                                         max =         15

                                                Wald chi2(16)     =    3322.24
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0129627   .0018813     6.89   0.000     .0092755      .01665
        race |   -.094396   .0119103    -7.93   0.000    -.1177398   -.0710522
             |
        year |
         69  |    .075438   .0125016     6.03   0.000     .0509353    .0999407
         70  |   .0471032   .0120412     3.91   0.000     .0235028    .0707035
         71  |   .0844863   .0125233     6.75   0.000      .059941    .1090315
         72  |   .0858609   .0135859     6.32   0.000     .0592329    .1124888
         73  |   .0879972   .0143298     6.14   0.000     .0599113     .116083
         75  |   .0763768   .0167026     4.57   0.000     .0436404    .1091133
         77  |   .1105803   .0196514     5.63   0.000     .0720643    .1490963
         78  |   .1359224   .0214146     6.35   0.000     .0939505    .1778942
         80  |    .118443   .0247018     4.79   0.000     .0700284    .1668576
         82  |   .1097735   .0279717     3.92   0.000     .0549501     .164597
         83  |   .1245107   .0297346     4.19   0.000     .0662319    .1827894
         85  |   .1510308   .0332019     4.55   0.000     .0859564    .2161052
         87  |   .1408315   .0367642     3.83   0.000     .0687751     .212888
         88  |   .1794208   .0391863     4.58   0.000      .102617    .2562246
             |
       _cons |   1.299731   .0414305    31.37   0.000     1.218529    1.380933
-------------+----------------------------------------------------------------
     sigma_u |  .36412525
     sigma_e |  .30300411
         rho |  .59085549   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Eugenia Erningdianhastuti]

Carlo,
Yes, I think it's because of the panel id effects..but I am not sure yet how to make the country specific time trend works in -xtivreg- command.
I think I am gonna re-evaluate the model.

Thank you so much for your help..

Best regards,
Eugenia