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  • Low or extremely high F statistic when applying clustered standard errors in fixed effects model when using -areg-

    Hi all,

    I have two questions regarding the use of clustered standard errors in my model. First, I will explain what kind of research I'm doing:
    For my thesis I investigate the relationship between bank quality (proxy by credit ratings, variable name: Hqualitybank which is a dummy) and market liquidity (proxy by cash over assets). I use several financial control variables in my model. My data is in panel data format where I have observations on multiple banks( id= gvkey) over the years 2001 untill 2014. I have a static linear panel model with bank fixed effects.

    In the beginning of my research I used xtreg for my fixed effects model. As cluster(gvkey) (so cluster on the bank level) or robust did not change the st dev of my coefficients, I thought that all my bank specif fixed effects took account of the potential autocorrelation. However, I am using -areg -now with absorbing the gvkey (bank) and i mentioned today that using clustered errors on the bank level yields different results than using robust st errors. The reason why this is happening, is already answered in a previous topic that I made today.

    My problem now: when I use clustered std errors when clustering on the bank level, my F statistic gets very low. Do any of you knows what this implies in terms of my research? Is this normal?

    Code:
     areg mliq L.Hqualitybank Hbank_Crisis size nim racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread, absorb(gvkey) cluster(gvkey)
    
    Linear regression, absorbing indicators Number of obs = 3755
    F( 10, 128) = 7.31
    Prob > F = 0.0000
    R-squared = 0.8284
    Adj R-squared = 0.8218
    Root MSE = 0.0258
    
    (Std. Err. adjusted for 129 clusters in gvkey)
    -------------------------------------------------------------------------------
    | Robust
    mliq | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    --------------+----------------------------------------------------------------
    Hqualitybank |
    L1. | -.0048984 .0041785 -1.17 0.243 -.0131663 .0033695
    |
    Hbank_Crisis | .0015327 .0045802 0.33 0.738 -.0075301 .0105955
    size | .0037935 .0048815 0.78 0.439 -.0058653 .0134524
    nim | -.0034218 .0028936 -1.18 0.239 -.0091473 .0023036
    racr | .0016601 .0009384 1.77 0.079 -.0001967 .0035168
    loanstoassets | -.046014 .0374986 -1.23 0.222 -.1202114 .0281834
    depositsloans | .0278706 .0115182 2.42 0.017 .0050799 .0506613
    |
    Crisisdummy |
    L1. | .0057142 .0033581 1.70 0.091 -.0009303 .0123586
    |
    fedfund | -.0014767 .0007933 -1.86 0.065 -.0030463 .0000929
    tedspread | -.0030272 .0018389 -1.65 0.102 -.0066657 .0006114
    _cons | -.002524 .0798735 -0.03 0.975 -.1605675 .1555194
    --------------+----------------------------------------------------------------
    gvkey | absorbed (129 categories)
    However, as I have data of banks which legal incorporation is in different countries, I can also cluster on the country level by using cluster(ISOINC), but this gives my extremly high F values (which can not be good I guess).

    Code:
    Linear regression, absorbing indicators           Number of obs   =       3755
                                                      F(  10,     14) = 1326070.70
                                                      Prob > F        =     0.0000
                                                      R-squared       =     0.8284
                                                      Adj R-squared   =     0.8218
                                                      Root MSE        =     0.0258
    
                                     (Std. Err. adjusted for 15 clusters in ISOINC)
    -------------------------------------------------------------------------------
                  |               Robust
             mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    --------------+----------------------------------------------------------------
     Hqualitybank |
              L1. |  -.0048984   .0014496    -3.38   0.004    -.0080075   -.0017892
                  |
     Hbank_Crisis |   .0015327   .0050501     0.30   0.766    -.0092987    .0123641
             size |   .0037935   .0027065     1.40   0.183    -.0020112    .0095983
              nim |  -.0034218   .0004105    -8.34   0.000    -.0043023   -.0025414
             racr |   .0016601   .0004722     3.52   0.003     .0006473    .0026728
    loanstoassets |   -.046014   .0153696    -2.99   0.010    -.0789786   -.0130495
    depositsloans |   .0278706    .000891    31.28   0.000     .0259597    .0297815
                  |
      Crisisdummy |
              L1. |   .0057142   .0006086     9.39   0.000     .0044089    .0070194
                  |
          fedfund |  -.0014767   .0003877    -3.81   0.002    -.0023083   -.0006452
        tedspread |  -.0030272   .0010628    -2.85   0.013    -.0053066   -.0007478
            _cons |   -.002524   .0406889    -0.06   0.951     -.089793    .0847449
    --------------+----------------------------------------------------------------
            gvkey |   absorbed                                     (129 categories)
    For your information, here the regression results without using clustered standard errors:

    Code:
    . areg mliq L.Hqualitybank Hbank_Crisis  size nim  racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread , absorb(gvkey) r
    
    Linear regression, absorbing indicators           Number of obs   =       3755
                                                      F(  10,   3616) =      47.10
                                                      Prob > F        =     0.0000
                                                      R-squared       =     0.8284
                                                      Adj R-squared   =     0.8218
                                                      Root MSE        =     0.0258
    
    -------------------------------------------------------------------------------
                  |               Robust
             mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    --------------+----------------------------------------------------------------
     Hqualitybank |
              L1. |  -.0048984   .0016164    -3.03   0.002    -.0080675   -.0017292
                  |
     Hbank_Crisis |   .0015327   .0027668     0.55   0.580    -.0038919    .0069573
             size |   .0037935   .0016172     2.35   0.019     .0006229    .0069642
              nim |  -.0034218   .0013215    -2.59   0.010    -.0060129   -.0008308
             racr |   .0016601   .0003776     4.40   0.000     .0009197    .0024004
    loanstoassets |   -.046014   .0131866    -3.49   0.000     -.071868     -.02016
    depositsloans |   .0278706   .0039685     7.02   0.000       .02009    .0356513
                  |
      Crisisdummy |
              L1. |   .0057142   .0017543     3.26   0.001     .0022745    .0091538
                  |
          fedfund |  -.0014767   .0002993    -4.93   0.000    -.0020635     -.00089
        tedspread |  -.0030272   .0011775    -2.57   0.010    -.0053358   -.0007185
            _cons |   -.002524   .0230106    -0.11   0.913    -.0476391    .0425911
    --------------+----------------------------------------------------------------
            gvkey |   absorbed                                     (129 categories)
    Certainly I do not expect one of you to tell me what is going on here from an economic perspective, but I hope one could give me an explanation of what is going on here in a econometric point of view. Furthermore, is it right that clustering on the country level (with 13 clusters) allows the error terms of different banks to be correlated (if they are in the same cluster)? Do you agree that this does not really makes sense?

    I hope some of you could provide me with an aswer, as this is one of the last steps in finalizing my thesis.

    Thank you in advance and best regards,

    Yannick

  • #2
    I wouldn't use cluster robust standard errors on country when there are only 13 countries. The cluster robust correction to standard errors only works with large numbers of clusters. While different people will give you different opinions about how large is large, most would agree that 13 is too few.

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