Testing for time-fixed effects - testparm!

[till deg]

Hi,

I am doing a fixed effects regression and I am a bit worried, that I should include year dummies, which I am currently not.
I did use the forum search, but I did not find a satisfying answer...
So - first I do:

xtreg $ylist $xlist i.Year, fe
testparm i.Year

resulting in:

 ( 1)  2005.Year = 0
 ( 2)  2006.Year = 0
 ( 3)  2007.Year = 0
 ( 4)  2008.Year = 0
 ( 5)  2009.Year = 0
 ( 6)  2010.Year = 0
 ( 7)  2011.Year = 0
 ( 8)  2012.Year = 0
 ( 9)  2013.Year = 0

       F(  9,   143) =   47.31
            Prob > F =    0.0000

Does that mean: We reject the null that the coefficients for all years are jointly equal to zero, therefore time fixedeffects are needed in this case.
And if I need time effects - is that simply done by including i.Year dummies?

[Ariel Karlinsky]

you are correct.
see slide 31 here:
http://www.princeton.edu/~otorres/Panel101.pdf

[Sebastian Kripfganz]

In short: yes and yes.

As an aside, you might want to consider robust standard errors by using the option vce(robust). In principle this affects the test statistic, although this will not change the conclusion in your case because the test statistic is far enough away from any critical value.

[till deg]

thanks very much to both of you....
allow me one follow-up question:

If i include the year-dummies, I inevetably get a much higher r²-within.
but now it doesnt explain the variance of my indepedent variables anymore - well yes it does, but they include the dummies - it makes the interpetation of r² tricky.
anyway to deal with this?

[Ariel Karlinsky]

I would suggest reading about the various R squared (overall, between, within) in the stata manual entry regarding xtreg (also probably in the Princeton slides i linked to). in short: yes, the interpretation of R^2 is tricky with panel models, but this is regardless of whether or not you're using time dummies

[till deg]

Jepp - that wasnt really my question - if its tricky or not =)
My mistake...
With time dummies, my r²-withing goes up from 0.599 to 0.909 - which would normally be a great value.
But since the time dummies obvioulsly have a huge impact, referencing the new r² makes no sense.
The time dummies are of course part of my modell but not part of my explenatory set of variables ...

[Valentina Cortes]

Jepp - that wasnt really my question - if its tricky or not =)
My mistake...
With time dummies, my r²-withing goes up from 0.599 to 0.909 - which would normally be a great value.
But since the time dummies obvioulsly have a huge impact, referencing the new r² makes no sense.
The time dummies are of course part of my modell but not part of my explenatory set of variables ...

I have the same question.
I read that you should run the OLS regression with the dummies and take the R^2 for interpretation from there, though I'm not sure. Could anyone clarify please?

[Clyde Schechter]

In general, you would be interested in the proportion of variance explained by the explanatory variables, not by nuisance variables like time indicators (dummies). To get that, you run the model twice. First you run the model with both the explanatory variables and the nuisance variables (full model). Then you run the model again with just the nuisance variables and be sure to restrict it to the estimation sample of the full model. This is called the reduced model. The difference R²_{full model} - R²_{reduced model} is the proportion of variance associated with the explanatory variables (when entered last). That is the most widely accepted way to describe things.

[Carlo Lazzaro]

Till:
you would get more helpful replies if you posted the outcome table of -xtreg, fe-, too. Thanks.

[Valentina Cortes]

In general, you would be interested in the proportion of variance explained by the explanatory variables, not by nuisance variables like time indicators (dummies). To get that, you run the model twice. First you run the model with both the explanatory variables and the nuisance variables (full model). Then you run the model again with just the nuisance variables and be sure to restrict it to the estimation sample of the full model. This is called the reduced model. The difference R²_{full model} - R²_{reduced model} is the proportion of variance associated with the explanatory variables (when entered last). That is the most widely accepted way to describe things.

Thank you Clyde!

[Katharina Maier]

In general, you would be interested in the proportion of variance explained by the explanatory variables, not by nuisance variables like time indicators (dummies). To get that, you run the model twice. First you run the model with both the explanatory variables and the nuisance variables (full model). Then you run the model again with just the nuisance variables and be sure to restrict it to the estimation sample of the full model. This is called the reduced model. The difference R²_{full model} - R²_{reduced model} is the proportion of variance associated with the explanatory variables (when entered last). That is the most widely accepted way to describe things.

Hi,
could you pease be a bit more detailed on the R² reduced model? How do I run the R² reduced model?
And how do I calculate the difference R²_{full model} - R²_{reduced mode} in Stata?

Thank you very much!

testparm i.year

 ( 1)  1996.year = 0
 ( 2)  1997.year = 0
 ( 3)  1998.year = 0
 ( 4)  1999.year = 0
 ( 5)  2000.year = 0
 ( 6)  2001.year = 0
 ( 7)  2002.year = 0
 ( 8)  2003.year = 0
 ( 9)  2004.year = 0
 (10)  2005.year = 0
 (11)  2006.year = 0
 (12)  2007.year = 0
 (13)  2008.year = 0
 (14)  2009.year = 0
 (15)  2010.year = 0
 (16)  2011.year = 0
 (17)  2012.year = 0
 (18)  2013.year = 0
 (19)  2014.year = 0
 (20)  2015.year = 0
 (21)  2016.year = 0
 (22)  2017.year = 0
 (23)  2018.year = 0

       F( 23,156197) =   69.98
            Prob > F =    0.0000

xtreg Z_score LLR LLP NPA, fe

Fixed-effects (within) regression               Number of obs     =    172,431
Group variable: id                              Number of groups  =     16,208

R-sq:                                           Obs per group:
     within  = 0.1567                                         min =          1
     between = 0.0345                                         avg =       10.6
     overall = 0.0779                                         max =         24

                                                F(3,156220)       =    9674.73
corr(u_i, Xb)  = -0.0715                        Prob > F          =     0.0000

------------------------------------------------------------------------------
     Z_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         LLR |   5.868449   .1225112    47.90   0.000     5.628329    6.108568
         LLP |  -.0000898   .0000228    -3.94   0.000    -.0001345   -.0000452
         NPA |   3.946458   .0328891   119.99   0.000     3.881996     4.01092
       _cons |  -1.742749   .0011278 -1545.21   0.000     -1.74496   -1.740539
-------------+----------------------------------------------------------------
     sigma_u |  .28282775
     sigma_e |  .19363385
         rho |  .68086244   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(16207, 156220) = 15.54              Prob > F = 0.0000

xtreg Z_score LLR LLP NPA i.year, fe

Fixed-effects (within) regression               Number of obs     =    172,431
Group variable: id                              Number of groups  =     16,208

R-sq:                                           Obs per group:
     within  = 0.1653                                         min =          1
     between = 0.0368                                         avg =       10.6
     overall = 0.0833                                         max =         24

                                                F(26,156197)      =    1189.56
corr(u_i, Xb)  = -0.0624                        Prob > F          =     0.0000

------------------------------------------------------------------------------
     Z_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         LLR |   5.743304   .1221302    47.03   0.000     5.503931    5.982676
         LLP |  -.0000905   .0000227    -3.99   0.000     -.000135   -.0000461
         NPA |   3.861483   .0348896   110.68   0.000       3.7931    3.929865
             |
        year |
       1996  |   .0011252    .002838     0.40   0.692    -.0044372    .0066875
       1997  |  -.0109436   .0029121    -3.76   0.000    -.0166514   -.0052359
       1998  |   .0014741   .0029709     0.50   0.620    -.0043489    .0072971
       1999  |   .0298605   .0030124     9.91   0.000     .0239563    .0357647
       2000  |   .0094353   .0030503     3.09   0.002     .0034568    .0154138
       2001  |   .0234683   .0030814     7.62   0.000     .0174288    .0295079
       2002  |   .0019659   .0031072     0.63   0.527    -.0041242     .008056
       2003  |   .0063794   .0031259     2.04   0.041     .0002528     .012506
       2004  |   .0015183   .0031485     0.48   0.630    -.0046527    .0076894
       2005  |   -.000328   .0031704    -0.10   0.918    -.0065419    .0058858
       2006  |  -.0185198   .0031924    -5.80   0.000    -.0247769   -.0122628
       2007  |  -.0325805   .0032142   -10.14   0.000    -.0388804   -.0262807
       2008  |   .0235797    .003257     7.24   0.000     .0171959    .0299634

[Clyde Schechter]

The reduced model contains only the "nuisance" variables, which in your case are the i.year indicators. So run

xtreg Z_score i.year, fe

Then look at the R² outputs from this and from the full model (the second one shown in #11). Subtract. (You are probably most interested in the within or overall R², less so in the between R².)

[Kim Pijl]

Hi all, I have been reading along. If the F-test turns out to be insignificant is it recommended to leave out the time fixed effects?

Thank you in advance!

[Clyde Schechter]

That will depend on who you ask.

In my opinion, selection of variables in a model should not be based on statistical tests. It should be based on the fit of the model to the data, the theoretical basis for including the variables, and, when possible, the ability of the model to predict results not in the data from which it was derived. Statistical tests play little or no role in any of that.

More recently, the American Statistical Association has recommended that the concept of statistical significance as a whole be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913, which would apply to this particular application as well.

[Katharina Maier]

The reduced model contains only the "nuisance" variables, which in your case are the i.year indicators. So run
Code:
xtreg Z_score i.year, fe
Then look at the R² outputs from this and from the full model (the second one shown in #11). Subtract. (You are probably most interested in the within or overall R², less so in the between R².)

Thank you very much. It worked perfectly. First I did the Hausman Test to see if I have to use the fixed-effects model and so I'm only interested in the Within R².

xtreg Z_score LLR LLP NPA i.year, fe vce(cluster id)

Fixed-effects (within) regression               Number of obs     =    172,431
Group variable: id                              Number of groups  =     16,208

R-sq:                                           Obs per group:
     within  = 0.1653                                         min =          1
     between = 0.0368                                         avg =       10.6
     overall = 0.0833                                         max =         24

                                                F(26,16207)       =    1007.76
corr(u_i, Xb)  = -0.0624                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 16,208 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     Z_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         LLR |   5.743304   .7524168     7.63   0.000     4.268484    7.218124
         LLP |  -.0000905   2.26e-06   -40.01   0.000    -.0000949   -.0000861
         NPA |   3.861483   .1238883    31.17   0.000     3.618648    4.104317
             |
        year |
       1996  |   .0011252   .0018337     0.61   0.539     -.002469    .0047194
       1997  |  -.0109436   .0023918    -4.58   0.000    -.0156319   -.0062554
       1998  |   .0014741   .0027731     0.53   0.595    -.0039615    .0069097
       1999  |   .0298605   .0029465    10.13   0.000     .0240851    .0356359
       2000  |   .0094353   .0030306     3.11   0.002      .003495    .0153756
       2001  |   .0234683   .0030928     7.59   0.000      .017406    .0295306
       2002  |   .0019659   .0030866     0.64   0.524    -.0040841    .0080159
       2003  |   .0063794   .0032659     1.95   0.051    -.0000221     .012781
       2004  |   .0015183   .0034244     0.44   0.657    -.0051938    .0082304
       2005  |   -.000328   .0036023    -0.09   0.927     -.007389     .006733
       2006  |  -.0185198   .0037269    -4.97   0.000     -.025825   -.0112147
       2007  |  -.0325805   .0039415    -8.27   0.000    -.0403063   -.0248548
       2008  |   .0235797   .0042141     5.60   0.000     .0153196    .0318397
       2009  |   .0513198   .0045123    11.37   0.000     .0424752    .0601643
       2010  |   .0143684    .004396     3.27   0.001     .0057517    .0229852
       2011  |  -.0244906   .0042772    -5.73   0.000    -.0328744   -.0161068
       2012  |   -.027744   .0041473    -6.69   0.000    -.0358732   -.0196149
       2013  |   .0094304   .0042133     2.24   0.025     .0011719    .0176889
       2014  |  -.0126633   .0041436    -3.06   0.002    -.0207852   -.0045414
       2015  |  -.0128751   .0040976    -3.14   0.002    -.0209068   -.0048434
       2016  |  -.0038756   .0042183    -0.92   0.358    -.0121439    .0043928
       2017  |  -.0094145    .004242    -2.22   0.026    -.0177292   -.0010997
       2018  |    -.03078   .0043065    -7.15   0.000    -.0392212   -.0223388
             |
       _cons |  -1.741384   .0069583  -250.26   0.000    -1.755023   -1.727745
-------------+----------------------------------------------------------------
     sigma_u |  .28227186
     sigma_e |  .19265795
         rho |  .68220173   (fraction of variance due to u_i)
------------------------------------------------------------------------------

xtreg Z_score i.year, fe vce(cluster id)

Fixed-effects (within) regression               Number of obs     =    172,431
Group variable: id                              Number of groups  =     16,208

R-sq:                                           Obs per group:
     within  = 0.0384                                         min =          1
     between = 0.0003                                         avg =       10.6
     overall = 0.0123                                         max =         24

                                                F(23,16207)       =     122.17
corr(u_i, Xb)  = -0.0284                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 16,208 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     Z_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
       1996  |  -.0001402   .0018755    -0.07   0.940    -.0038165     .003536
       1997  |   -.014736   .0024287    -6.07   0.000    -.0194965   -.0099755
       1998  |   -.003407   .0028025    -1.22   0.224    -.0089002    .0020861
       1999  |   .0238641   .0030128     7.92   0.000     .0179587    .0297694
       2000  |   .0043351   .0030994     1.40   0.162      -.00174    .0104102
       2001  |   .0236945   .0031746     7.46   0.000     .0174719    .0299172
       2002  |   .0044319   .0031419     1.41   0.158    -.0017267    .0105904
       2003  |   .0066334    .003308     2.01   0.045     .0001493    .0131175
       2004  |   -.004639   .0034737    -1.34   0.182    -.0114479    .0021699
       2005  |  -.0113147   .0037079    -3.05   0.002    -.0185826   -.0040468
       2006  |  -.0294296   .0038122    -7.72   0.000    -.0369019   -.0219573
       2007  |  -.0309481   .0039919    -7.75   0.000    -.0387726   -.0231236
       2008  |   .0700794   .0044908    15.61   0.000     .0612769    .0788819
       2009  |   .1420634   .0052618    27.00   0.000     .1317496    .1523772
       2010  |   .1165972   .0050311    23.18   0.000     .1067357    .1264587
       2011  |   .0657116   .0047502    13.83   0.000     .0564007    .0750224
       2012  |   .0408614   .0043411     9.41   0.000     .0323523    .0493705
       2013  |   .0570939   .0043688    13.07   0.000     .0485305    .0656572
       2014  |   .0175019   .0042253     4.14   0.000     .0092199    .0257838
       2015  |   .0065382   .0041446     1.58   0.115    -.0015857    .0146622
       2016  |   .0109244   .0042533     2.57   0.010     .0025876    .0192613
       2017  |  -.0001428   .0042102    -0.03   0.973    -.0083952    .0081097
       2018  |  -.0230611   .0043009    -5.36   0.000    -.0314913   -.0146309
             |
       _cons |  -1.659507   .0024727  -671.13   0.000    -1.664354   -1.654661
-------------+----------------------------------------------------------------
     sigma_u |  .28762961
     sigma_e |  .20677701
         rho |  .65927505   (fraction of variance due to u_i)
------------------------------------------------------------------------------

I calculated the R² by R²_{full model} - R²_{reduced model} with my calculator but unfortunatly not with Stata. I know that the command

xtreg, fe

stores the results in

e()

and that the Within R² model is e(r2_w). I also installed the

ssc inst regsave

command.
How can I only save the Within R²_{full model} and R²_{reduced model} results in my current (active) Stata Data Set and calculate the difference in Stata and save the result R² as well in my Stata data set?
Actually I have four bank risk proxies (Z_score, NPA, LLR, LLP) and for each I would like to calculate the R².

xtreg NPA Z_score LLR LLP i.year, fe vce(cluster id)
xtreg Z_score i.year, fe vce(cluster id)

Finally I would like to show in one graph the four R² values (for each risk proxy) from regeressions in which we explain one risk proxy k = 1, ..., 4 with the remaining j proxies.

Risk Proxy_kit = x´_{j not=k, it} ß + e_it

Thank you very much!