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Re: st: inconsistent results for two-dimensions fixed effects regressions using xtreg reg areg ivreg2


From   Nahla Betelmal <[email protected]>
To   "[email protected]" <[email protected]>
Subject   Re: st: inconsistent results for two-dimensions fixed effects regressions using xtreg reg areg ivreg2
Date   Thu, 15 Aug 2013 10:36:24 +0100

Hi Mike,

Thanks for the reply and help again. Yes, I understand that at
industry level I got many firms observations, so I dent set the panel
at industry. I tried to get around that by having a group variable for
industry-year , so each firm-year observation will belong only to one
industry-year identifier. I got the idea from this thread

http://www.talkstats.com/showthread.php/26900-how-can-I-include-two-fixed-effect-in-one-model

I modified the variable to be industry-year instead (because as you
said a firm can not belong to different industries). So, to use
xtcommand, I set the panel at the group variable industry-year only
and then included the year dummy in the regression ( I hope this does
not contradict sound way of thinking)

egen industry_year= group(industry year)
 xtset industry_year
 xtreg IV DV, fe

and the result were the same as using
reg IV DV i.year i.industry,
areg IV DV i.year , absorb (industry)


Regarding your kind comment about fixed effect and clustering and the
same level ( say firm level as widely done). In the finance field,
papers seem to include both year and firm dummies as well as
clustering for firms.
The most used wordings are " reported t-statistics adjusted for
heteroskedasticity (White, 1980) and firm-level clustering" and  "The
t-values are computed using Roger’s robust standard errors correcting
for firm clusters" with dummies for years and dummies for firms
already included in the regression.

for example see table 4 in this paper :
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1030359


Also, I found this thread which hints that fixed effect and cluster at
the panel variable is widely reported.
http://www.stata.com/statalist/archive/2006-09/msg00782.html

However, I totally got your point that the fixed effects will control
for correlation of error-terms within clusters. I wonder why large
number of finance papers published in well-known journals use firm
cluster as well!

Thanks a million, and I am sure that other users appreciate your
previous detailed explanation and help.

many thanks

Nahla

On 14 August 2013 19:57, Michael Barker <[email protected]> wrote:
> Hi Nahla,
>
> You are having trouble with the xtcommands, because you're not really
> doing a panel-data analysis. Panel data implies one observation per
> unit per year. You are analyzing this data using industry and year, so
> you have many observations (firms) per unit (industry) per year. That
> is why you got the error about repeated time values within panel. Your
> data may actually be panel data, at the firm-year level, but you are
> analyzing it as clustered data, not panel data.
>
> You said that you were using two-dimension fixed-effects, so I would
> keep industry and year as separate groups of dummy variables, rather
> than creating a single interaction. The results may come out the same,
> I'm not sure about that, but I think it is easier conceptually.
>
> Lastly, if you are including fixed effects at the industry-level, you
> don't have to compute clustered standard errors at the same level. You
> can just use the typical robust standard error estimator. The cluster
> fixed effects will control for correlation of error-terms within
> clusters.
>
> So I think you should use one of these two commands:
> reg IV DV i.year i.industry, robust
> areg IV DV i.year , absorb (industry) robust
>
> About the ivreg2 command, it is used for instrumental variables. I
> think your "IV" stands for independent variable, not instrumental
> variable, so it is not relevant to your topic. ivreg2 will not help
> you with a fixed-effects analysis.
>
> Mike
>
>
>
> On Wed, Aug 14, 2013 at 10:51 AM, Nahla Betelmal <[email protected]> wrote:
>> Thank you so much Mike, your detailed comments are great help. I do
>> appreciate it.
>>
>> As I am looking for industry year fixed effects rather than firm year,
>> I tried to set the panel accordingly, but did not work due to repeated
>> time values within panel.
>>
>> So, this time I grouped based on industry-year (thanks to ur note
>> about no repeated firms in different industries). I hope this time I
>> did it in the right way. Kindly let me know please. I got identical
>> coefficients for IV.
>>
>> Also, could you please explain more your comment about ivreg2 or give
>> and an example how to execute it right to get fixed effects please.
>>
>> the command are :
>> 1) egen industry_year= group(industry year) then xtset industry_year
>> then xtreg IV DV, fe vce (cluster industry)
>> 2) xi: reg IV DV i.year i.industry
>> 3)areg IV DV , absorb ( industry_year ) cluster (industry)
>>
>> In the first command , I could not put i.year as it is omitted because
>> of collinearity.
>> In the second, I could not apply cluster (industry) option as  F-test
>> became missing.
>> The third command gave almost identical results to the previous two
>> with and without the cluster option. However, it gave slightly
>> different R-Square 0.645 than that of regress 0.621. Is this OK or
>> they should be identical.
>>
>>
>>
>> egen industry_year= group(industry year)
>>  xtset industry_year
>> xtreg DV IV, fe vce (cluster industry )
>>
>> Fixed-effects (within) regression               Number of obs      =     23830
>> Group variable: industry_year                    Number of groups   =      1179
>>
>> R-sq:  within  = 0.5516                         Obs per group: min =         1
>>        between = 0.5262                                        avg =      20.2
>>        overall = 0.4955                                        max =       155
>>
>>                                                 F(1,57)            =   2233.13
>> corr(u_i, Xb)  = -0.1260                        Prob > F           =    0.0000
>>
>>                               (Std. Err. adjusted for 58 clusters in industry)
>> ------------------------------------------------------------------------------
>>              |                     Robust
>> DV|                Coef.     Std. Err.      t    P>|t|     [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>>   IV|              .4393407    .009297    47.26   0.000     .4207237    .4579577
>>        _cons |   5.675498   .0673395    84.28   0.000     5.540653    5.810343
>> -------------+----------------------------------------------------------------
>>      sigma_u |  .40739078
>>      sigma_e |  .58512671
>>          rho |  .32648834   (fraction of variance due to u_i)
>> ------------------------------------------------------------------------------
>>
>>
>>
>> Also I tried
>> xi: reg DV IV i.year i.industry
>>
>> without a cluster(industry) as F-test became missing
>>
>> IV= .4397811 and SE= .0026298
>> If I run xtreg without the cluster option, I get the same SE= .0026322
>>
>> the output is too long
>>
>> In addition
>> areg DV IV, absorb ( industry_year ) cluster (industry)
>>
>> Linear regression, absorbing indicators           Number of obs   =      23830
>>                                                   F(   1,     57) =    2122.73
>>                                                   Prob > F        =     0.0000
>>                                                   R-squared       =     0.6458
>>                                                   Adj R-squared   =     0.6274
>>                                                   Root MSE        =     0.5851
>>
>>                               (Std. Err. adjusted for 58 clusters in industry)
>> ------------------------------------------------------------------------------
>>              |               Robust
>> DV             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>>  IV             |   .4393407   .0095357    46.07   0.000     .4202457
>>   .4584357
>>        _cons |   5.675498   .0690685    82.17   0.000     5.537191    5.813805
>> -------------+----------------------------------------------------------------
>> industry_year |   absorbed                                    (1179 categories)
>>
>>
>> Many thanks again
>>
>> Nahla
>>
>>
>> On 14 August 2013 14:29, Michael Barker <[email protected]> wrote:
>>> Hi Nahla,
>>>
>>> You are actually running several different models there. I'll describe
>>> each one below, so you can see how they differ:
>>>
>>>> 1) xi: reg DV IV i.year, vce (cluster industry)
>>> - Year fixed effects only.
>>> - Include one dummy variable for each year:
>>>
>>>> 2) xtset firm year then xtreg DV IV i.year, fe vce (cluster industry)
>>> - Year and firm fixed effects
>>> - Equivalent to including one dummy for each year and one dummy for each firm.
>>> - xtreg includes fixed effects for the panel variable, firm and you
>>> include year dummies manually
>>>
>>>> 3) egen industry_firm= group (industry firm) then xtset industry_firm year then  xtreg DV IV i.year, fe vce (cluster industry)
>>> - year and industry-firm level fixed effects
>>> - equivalent to including one dummy for each year and one dummy for
>>> each industry-firm combination
>>> - apparently no firm is in multiple industries, so this regression is
>>> equivalent to regression 2.
>>>
>>>> 4) tsset industry_firm year then ivreg2  DV IV,cluster ( industry_firm year)
>>> - No fixed effects
>>> - You didn't specify the endogenous / IV variables, so this is just a
>>> regular regression with clustered standard errors
>>> - This is equivalent to "reg  DV IV,cluster ( industry_firm year)"
>>>
>>>> 5) areg DV IV, absorb ( year ) cluster (industry)
>>> - Year fixed effects only
>>> - Equivalent to regression 1, without reporting year coefficients
>>> - Notice that the coefficient and standard error estimates are the
>>> same as the first regression.
>>>>
>>>
>>> If you want firm and year fixed effects, I would use regression 2. If
>>> you want to see equivalent results with alternative regressions, try
>>> these:
>>> xi: reg DV IV i.year i.firm, vce (cluster industry)
>>> areg DV IV i.year, absorb (firm) cluster (industry)
>>>
>>> The first suggestion might not run, since you will have to include
>>> many dummy variables for all of your firms. You may exceed the maximum
>>> number of variables allowed, depending on your version of Stata.
>>>
>>> Mike
>>>
>>>
>>>
>>>
>>> On Wed, Aug 14, 2013 at 8:22 AM, Nahla Betelmal <[email protected]> wrote:
>>>> Hi Statalist,
>>>>
>>>> I have a panel data of firms and years, however, I would like to
>>>> perform industry and year fixed effect regression. using different
>>>> approaches, I got different IV coefficient and standard error,
>>>> although it should be identical if I am doing it right. I would highly
>>>> appreciate it if someone kindly explain what I am doing wrong and what
>>>> is the right way to get industry and year fixed effects.
>>>>
>>>> the commands I used are:
>>>>
>>>> 1) xi: reg DV IV i.year, vce (cluster industry)
>>>>
>>>> 2) xtset firm year then xtreg DV IV i.year, fe vce (cluster industry)
>>>>
>>>> 3) egen industry_firm= group (industry firm) then xtset industry_firm
>>>> year then  xtreg DV IV i.year, fe vce (cluster industry)
>>>>
>>>> 4) tsset industry_firm year then ivreg2  DV IV,cluster ( industry_firm year)
>>>>
>>>> 5) areg DV IV, absorb ( year ) cluster (industry)
>>>>
>>>>
>>>> under reg command: IV = 0.386 with SE= 0.022
>>>> under xtreg command with firm year panel set: IV =  .418 with SE= .0241
>>>> under xtreg command with industry-firm year panel set: IV = .418 with SE= .024
>>>> under ivreg2 command: IV = .410 with SE= .007
>>>> under areg command: IV = 0.386 with SE= 0.022
>>>>
>>>>
>>>> . xi: reg DV IV i.year, vce (cluster industry)
>>>> i.year         _Iyear_1992-2012  (naturally coded; _Iyear_1992 omitted)
>>>>
>>>> Linear regression                                      Number of obs =   23830
>>>>                                                        F( 21,    57) =  768.66
>>>>                                                        Prob > F      =  0.0000
>>>>                                                        R-squared     =  0.5461
>>>>                                                        Root MSE      =   .6461
>>>>
>>>>                                (Std. Err. adjusted for 58 clusters in industry)
>>>> -------------------------------------------------------------------------------
>>>>               |               Robust
>>>> DV                |      Coef.   Std. Err.      t    P>|t|     [95%
>>>> Conf. Interval]
>>>> --------------+----------------------------------------------------------------
>>>>   IV              |   .3869693   .0225831    17.14   0.000
>>>> .3417475    .4321911
>>>> _Iyear_1993 |    .150389   .0239546     6.28   0.000     .1024208    .1983573
>>>> _Iyear_1994 |   .2857099   .0271864    10.51   0.000     .2312702    .3401496
>>>> _Iyear_1995 |   .2927993   .0307951     9.51   0.000     .2311331    .3544654
>>>> _Iyear_1996 |   .4353512   .0304859    14.28   0.000     .3743044    .4963981
>>>> _Iyear_1997 |   .5286896   .0292151    18.10   0.000     .4701874    .5871917
>>>> _Iyear_1998 |   .5852497   .0337522    17.34   0.000     .5176621    .6528374
>>>> _Iyear_1999 |   .6969439   .0523892    13.30   0.000     .5920364    .8018514
>>>> _Iyear_2000 |   .8019949   .0666928    12.03   0.000     .6684448    .9355449
>>>> _Iyear_2001 |   .7710818   .0486744    15.84   0.000      .673613    .8685507
>>>> _Iyear_2002 |   .6978223   .0325914    21.41   0.000     .6325592    .7630854
>>>> _Iyear_2003 |   .6427671   .0347611    18.49   0.000     .5731593     .712375
>>>> _Iyear_2004 |   .7757021   .0394535    19.66   0.000     .6966978    .8547064
>>>> _Iyear_2005 |   .7806429   .0418054    18.67   0.000     .6969291    .8643566
>>>> _Iyear_2006 |   .7746051   .0462916    16.73   0.000     .6819076    .8673025
>>>> _Iyear_2007 |   .7758041   .0484202    16.02   0.000     .6788444    .8727639
>>>> _Iyear_2008 |   .7734638   .0508533    15.21   0.000     .6716317    .8752958
>>>> _Iyear_2009 |   .7319797   .0564072    12.98   0.000     .6190263    .8449332
>>>> _Iyear_2010 |   .8741285   .0506573    17.26   0.000      .772689     .975568
>>>> _Iyear_2011 |   .8889354   .0532101    16.71   0.000      .782384    .9954869
>>>> _Iyear_2012 |   .8979328   .0565989    15.86   0.000     .7845956     1.01127
>>>>         _cons |   5.403047   .1238831    43.61   0.000     5.154975    5.651118
>>>> -------------------------------------------------------------------------------
>>>>
>>>>
>>>>
>>>>
>>>>  xtset firm year
>>>>        panel variable:  firm (unbalanced)
>>>>         time variable:  year, 1992 to 2012, but with gaps
>>>>                 delta:  1 unit
>>>>
>>>> . xtreg DV IV i.year, fe vce (cluster industry)
>>>>
>>>> Fixed-effects (within) regression               Number of obs      =     23830
>>>> Group variable: firm                         Number of groups   =      2312
>>>>
>>>> R-sq:  within  = 0.4113                         Obs per group: min =         1
>>>>        between = 0.5998                                        avg =      10.3
>>>>        overall = 0.5456                                        max =        21
>>>>
>>>>                                                 F(21,57)           =    463.93
>>>> corr(u_i, Xb)  = -0.0970                        Prob > F           =    0.0000
>>>>
>>>>                               (Std. Err. adjusted for 58 clusters in industry)
>>>> ------------------------------------------------------------------------------
>>>>              |               Robust
>>>> DV             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
>>>> -------------+----------------------------------------------------------------
>>>>  IV              |   .4183645   .0241281    17.34   0.000     .3700488
>>>>    .4666802
>>>>              |
>>>>       year   |
>>>>        1993  |   .1560772   .0200202     7.80   0.000     .1159874     .196167
>>>>        1994  |   .2929982   .0224807    13.03   0.000     .2479813    .3380151
>>>>        1995  |   .3019359   .0268163    11.26   0.000     .2482373    .3556345
>>>>        1996  |   .4272691   .0264501    16.15   0.000     .3743038    .4802344
>>>>        1997  |   .5209287   .0266063    19.58   0.000     .4676506    .5742069
>>>>        1998  |   .5877827   .0276877    21.23   0.000     .5323391    .6432264
>>>>        1999  |   .6989115   .0427304    16.36   0.000     .6133453    .7844777
>>>>        2000  |   .7988406   .0477286    16.74   0.000     .7032657    .8944154
>>>>        2001  |   .7589164   .0375573    20.21   0.000     .6837091    .8341236
>>>>        2002  |    .687617    .034973    19.66   0.000     .6175848    .7576492
>>>>        2003  |   .6310008   .0488884    12.91   0.000     .5331035    .7288982
>>>>        2004  |   .7611996   .0507837    14.99   0.000      .659507    .8628921
>>>>        2005  |   .7687923   .0552525    13.91   0.000     .6581511    .8794336
>>>>        2006  |   .7524079   .0609127    12.35   0.000     .6304324    .8743834
>>>>        2007  |   .7519399   .0642041    11.71   0.000     .6233734    .8805064
>>>>        2008  |    .750493   .0684401    10.97   0.000     .6134441     .887542
>>>>        2009  |   .7118027    .067056    10.62   0.000     .5775254    .8460799
>>>>        2010  |   .8504969   .0632919    13.44   0.000     .7237569    .9772368
>>>>        2011  |   .8674839   .0664437    13.06   0.000     .7344328    1.000535
>>>>        2012  |    .863437   .0733127    11.78   0.000     .7166308    1.010243
>>>>              |
>>>>        _cons |    5.18669    .152373    34.04   0.000     4.881568    5.491812
>>>> -------------+----------------------------------------------------------------
>>>>      sigma_u |   .4935113
>>>>      sigma_e |  .47151369
>>>>          rho |  .52278302   (fraction of variance due to u_i)
>>>> ------------------------------------------------------------------------------
>>>>
>>>>
>>>> . egen industry_firm= group (industry firm)
>>>>
>>>> . xtset industry_firm  year
>>>>        panel variable:  industry_firm (unbalanced)
>>>>         time variable:  year, 1992 to 2012, but with gaps
>>>>                 delta:  1 unit
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> . xtreg DV IV i.year, fe vce (cluster industry)
>>>>
>>>> Fixed-effects (within) regression               Number of obs      =     23830
>>>> Group variable: industry_firm                    Number of groups   =      2312
>>>>
>>>> R-sq:  within  = 0.4113                         Obs per group: min =         1
>>>>        between = 0.5998                                        avg =      10.3
>>>>        overall = 0.5456                                        max =        21
>>>>
>>>>                                                 F(21,57)           =    463.93
>>>> corr(u_i, Xb)  = -0.0970                        Prob > F           =    0.0000
>>>>
>>>>                               (Std. Err. adjusted for 58 clusters in industry)
>>>> ------------------------------------------------------------------------------
>>>>              |               Robust
>>>> DV |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
>>>> -------------+----------------------------------------------------------------
>>>>  IV |           .4183645   .0241281    17.34   0.000     .3700488    .4666802
>>>>              |
>>>>       year |
>>>>        1993  |   .1560772   .0200202     7.80   0.000     .1159874     .196167
>>>>        1994  |   .2929982   .0224807    13.03   0.000     .2479813    .3380151
>>>>        1995  |   .3019359   .0268163    11.26   0.000     .2482373    .3556345
>>>>        1996  |   .4272691   .0264501    16.15   0.000     .3743038    .4802344
>>>>        1997  |   .5209287   .0266063    19.58   0.000     .4676506    .5742069
>>>>        1998  |   .5877827   .0276877    21.23   0.000     .5323391    .6432264
>>>>        1999  |   .6989115   .0427304    16.36   0.000     .6133453    .7844777
>>>>        2000  |   .7988406   .0477286    16.74   0.000     .7032657    .8944154
>>>>        2001  |   .7589164   .0375573    20.21   0.000     .6837091    .8341236
>>>>        2002  |    .687617    .034973    19.66   0.000     .6175848    .7576492
>>>>        2003  |   .6310008   .0488884    12.91   0.000     .5331035    .7288982
>>>>        2004  |   .7611996   .0507837    14.99   0.000      .659507    .8628921
>>>>        2005  |   .7687923   .0552525    13.91   0.000     .6581511    .8794336
>>>>        2006  |   .7524079   .0609127    12.35   0.000     .6304324    .8743834
>>>>        2007  |   .7519399   .0642041    11.71   0.000     .6233734    .8805064
>>>>        2008  |    .750493   .0684401    10.97   0.000     .6134441     .887542
>>>>        2009  |   .7118027    .067056    10.62   0.000     .5775254    .8460799
>>>>        2010  |   .8504969   .0632919    13.44   0.000     .7237569    .9772368
>>>>        2011  |   .8674839   .0664437    13.06   0.000     .7344328    1.000535
>>>>        2012  |    .863437   .0733127    11.78   0.000     .7166308    1.010243
>>>>              |
>>>>        _cons |    5.18669    .152373    34.04   0.000     4.881568    5.491812
>>>> -------------+----------------------------------------------------------------
>>>>      sigma_u |   .4935113
>>>>      sigma_e |  .47151369
>>>>          rho |  .52278302   (fraction of variance due to u_i)
>>>> ------------------------------------------------------------------------------
>>>>
>>>>
>>>>
>>>>  ivreg2  DV IV,cluster ( industry_firm year)
>>>>
>>>> OLS estimation
>>>> --------------
>>>>
>>>> Estimates efficient for homoskedasticity only
>>>> Statistics robust to heteroskedasticity and clustering on
>>>> industry_firm and fyear2
>>>>
>>>> Number of clusters (industry_firm) =   2312           Number of obs =    23830
>>>> Number of clusters (fyear2) =       21                F(  1,    20) =  2849.29
>>>>                                                       Prob > F      =   0.0000
>>>> Total (centered) SS     =  21896.66904                Centered R2   =   0.4955
>>>> Total (uncentered) SS   =  1891568.745                Uncentered R2 =   0.9942
>>>> Residual SS             =   11046.6797                Root MSE      =    .6809
>>>>
>>>> ------------------------------------------------------------------------------
>>>>              |               Robust
>>>> DV        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
>>>> -------------+----------------------------------------------------------------
>>>>  IV        |    .410624   .0075071    54.70   0.000     .3959104    .4253377
>>>>        _cons |   5.883496   .0562149   104.66   0.000     5.773317    5.993675
>>>> ------------------------------------------------------------------------------
>>>> Included instruments: IV
>>>>
>>>>
>>>>
>>>>
>>>>  areg DV IV, absorb ( year ) cluster (industry)
>>>>
>>>> Linear regression, absorbing indicators           Number of obs   =      23830
>>>>                                                   F(   1,     57) =     293.62
>>>>                                                   Prob > F        =     0.0000
>>>>                                                   R-squared       =     0.5461
>>>>                                                   Adj R-squared   =     0.5457
>>>>                                                   Root MSE        =     0.6461
>>>>
>>>>                               (Std. Err. adjusted for 58 clusters in twodigit)
>>>> ------------------------------------------------------------------------------
>>>>              |                     Robust
>>>> DV           |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
>>>> -------------+----------------------------------------------------------------
>>>>   IV          |   .3869693   .0225831    17.14   0.000     .3417475    .4321911
>>>>        _cons |    6.05483   .1337655    45.26   0.000     5.786969    6.322691
>>>> -------------+----------------------------------------------------------------
>>>>     year |   absorbed                                      (21 categories)
>>>>
>>>>
>>>>
>>>> Many thanks in advance,
>>>>
>>>> Nahla Betelmal
>>>> *
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