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  • fixed effects huge coefficients problem

    Hello Stata community members,
    I hope all of you are fine. I am working with panel dataset and I ran fixed effect by using the command xtreg and specifying the fe (options). My dataset as you can see is strongly balanced and there are no missing values (the only ones are those due to the fact that I created some lag variables. I must say that I took notes of some cross-sectional units with values far from the mean and other summary statistics. These cross-sectional units, as I am in the first stage of the analysis, are still embedded within the dataset I used to run the panel regression with fixed effects. The problem is that the coefficients are simply huge as you can see and by looking at the p-values it seems that most of the variables are not statistically significant. I still did not check for unit roots or other elements as I was shocked by the results.
    Please have a look.
    Code:
    Fixed-effects (within) regression               Number of obs     =      1,285
    Group variable: id                              Number of groups  =        117
    
    R-squared:                                      Obs per group:
         Within  = 0.3832                                         min =          9
         Between = 0.6398                                         avg =       11.0
         Overall = 0.5044                                         max =         11
    
                                                    F(21,1147)        =      33.93
    corr(u_i, Xb) = 0.3601                          Prob > F          =     0.0000
    
    -------------------------------------------------------------------------------------
                    NPL | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
    --------------------+----------------------------------------------------------------
      NetInterestMargin |   9800.016   27158.09     0.36   0.718    -43485.09    63085.13
     AvgEquityAvgAssets |  -4547.432   5256.832    -0.87   0.387    -14861.52    5766.653
           CosttoIncome |  -2946.611   812.1693    -3.63   0.000    -4540.115   -1353.107
                   ROAA |   358889.5   35828.86    10.02   0.000     288592.1      429187
                    LLP |    4.41977   .1830357    24.15   0.000     4.060647    4.778892
                 Assets |    1581764    1008226     1.57   0.117    -396410.9     3559938
         deltabankloans |    3270.26    4493.76     0.73   0.467    -5546.651    12087.17
           deltaFTSEMIB |  -502.3053   675.9783    -0.74   0.458    -1828.598    823.9874
          RealGDPGrowth |   8891.507   3234.141     2.75   0.006     2546.012       15237
       deltaNCLDeposits |   287.1092   2509.721     0.11   0.909    -4637.049    5211.268
               dummy_25 |   44582.71   76821.41     0.58   0.562    -106143.5      195309
            dummy_50_75 |    64392.4   47377.17     1.36   0.174    -28563.24      157348
            dummy_25_50 |   41988.99   62296.63     0.67   0.500    -80239.14    164217.1
           SIZE_25_ROAA |  -385542.2   43719.28    -8.82   0.000    -471320.9   -299763.5
           SIZE_50_ROAA |  -367153.7   60707.99    -6.05   0.000    -486264.8   -248042.5
           SIZE_75_ROAA |  -356867.5   48265.27    -7.39   0.000    -451565.6   -262169.4
       L1_RealGDPGrowth |   11184.54   4724.096     2.37   0.018     1915.705    20453.38
       L2_RealGDPGrowth |   8308.824   4608.882     1.80   0.072    -733.9618    17351.61
        L1_deltaFTSEMIB |   595.1859   463.5651     1.28   0.199    -314.3447    1504.717
      L1_deltabankloans |  -9624.766   4660.513    -2.07   0.039    -18768.85   -480.6798
    L1_deltaNCLDeposits |  -7147.126   2505.654    -2.85   0.004    -12063.31   -2230.946
                  _cons |   237585.7   90869.38     2.61   0.009     59296.84    415874.5
    --------------------+----------------------------------------------------------------
                sigma_u |   302894.1
                sigma_e |  261385.27
                    rho |  .57316486   (fraction of variance due to u_i)
    -------------------------------------------------------------------------------------
    F test that all u_i=0: F(116, 1147) = 8.89                   Prob > F = 0.0000
    Coefficients are insanely huge as conf interval and std errors. I made some research and just to help you a bit I can tell you that the variables of the original dataset I have on excel are as follows:
    NPL (dependent variables) in $000 which means that if it is saved on excel as 10 it equals to 10,000;
    NetInterestMargin; AvgEquityAvgAssets; CosttoIncome; ROAA, LLP as %;
    Assets in $000;
    deltabankloans; deltaFTSEMIB; RealGDPGrowth; deltaNCLDeposits as % since they are calculated as variation in nearby years (x1-x0)/x0.

    Could you please tell me why I got results as big as those that I provided you with? Is this all due to my dataset of on the other hand I did do something wrong before or during the launch of the command? Or it is due to the units of my variables?
    Because I do not have any clue about it and even though I expected the results to be quite different from those I expected based on the literature, the difference is well beyond any common sense and reasonable expectation.
    Thanks a lot to everybody who will try to give me some tips or support.
    Maybe could sound funny to some of you, but still I will appreciate any help.
    Kind regards,
    Salvatore

  • #2
    Salvatore:
    it may depend on the variables metric.
    Obviously, what above is my guess-work, as you did not provide any example/excerpt of your dataset.
    Kind regards,
    Carlo
    (Stata 19.0)

    Comment


    • #3
      Thanks Carlo,
      for your feedback. Attached you will find part of my dataset (long format for some cross sectional units) in order to provide you with a better understanding on what are the numbers I am working within my dataset.
      Code:
      id    year    NPL    NetInterestMargin    AvgEquityAvgAssets    CosttoIncome    ROAA    LLP    Assets    deltabankloans    deltaFTSEMIB    RealGDPGrowth    deltaNCLDeposits    dummy_25    dummy_50_75    dummy_25_50    SIZE_25_ROAA    SIZE_50_ROAA    SIZE_75_ROAA    L1_RealGDPGrowth    L2_RealGDPGrowth    L1_deltaFTSEMIB    L1_deltabankloans    L1_deltaNCLDeposits
      1    2011    19314    3.0665003    8.894316    62.530881    .64168311    1512    .00011159    2.4215157    -3.4026191    .85    1.4086561    1    0    0    .6416831    0    0                    
      1    2012    52350    3.4012127    7.81904    60.919118    .0662024    6397    .00017049    -.76626672    -31.591894    -3.01    -8.6237981    0    0    1    0    .0662024    0    .85        -3.402619    2.421516    1.408656
      1    2013    64777    2.2446172    7.3237025    66.958581    .34299635    3957    .00018873    -2.8740579    10.930995    -1.86    -9.3552189    0    0    1    0    .3429964    0    -3.01    .85    -31.59189    -.7662667    -8.623798
      1    2014    61749    1.9582811    7.5171206    65.863558    .33335957    4509    .00019803    1.1005573    44.138574    .07    -4.5525075    0    0    1    0    .3333596    0    -1.86    -3.01    10.93099    -2.874058    -9.355219
      1    2015    54397    1.9604366    7.7805375    77.657658    .31596684    1876    .00018999    .84090043    3.2348891    .66    -8.4978766    0    0    1    0    .3159668    0    .07    -1.86    44.13857    1.100557    -4.552507
      1    2016    73094    2.1448878    8.0798279    92.572374    -.32779643    3481    .00024428    .3816689    -23.208574    1.4    -3.4338776    0    0    1    0    -.3277964    0    .66    .07    3.234889    .8409004    -8.497876
      1    2017    73897    2.3868627    8.231432    74.750368    .36938713    2770    .00025721    1.23481    20.886378    1.74    -1.5405045    0    0    1    0    .3693871    0    1.4    .66    -23.20857    .3816689    -3.433878
      1    2018    70294    2.5765006    6.133131    73.268095    .12783611    9033    .00028366    -4.1319113    2.8530874    .81    7.9092475    0    0    1    0    .1278361    0    1.74    1.4    20.88638    1.23481    -1.540504
      1    2019    72401    2.2111859    4.6421887    71.355508    .52595686    3696    .00025955    -1.6286674    -1.3125943    .5    1.0139957    0    0    1    0    .5259569    0    .81    1.74    2.853087    -4.131911    7.909247
      1    2020    51485    2.0623895    4.4296105    79.59674    -.63414315    11306    .00026035    4.431668    -8.2740222    -9.09    -4.5538045    0    0    1    0    -.6341432    0    .5    .81    -1.312594    -1.628667    1.013996
      1    2021    51485    2.0623895    4.4296105    79.59674    -.63414315    11306    .00025123    5.0594383    29.455174    6.62    -5.1602501    0    0    1    0    -.6341432    0    -9.09    .5    -8.274022    4.431668    -4.553804
      2    2011    620110    3.2349247    17.237876    53.954779    .84728333    30845    .00161717    2.4215157    -3.4026191    .85    1.4086561    0    0    0    0    0    0    6.62    -9.09    29.45517    5.059438    -5.16025
      2    2012    784941    2.7195258    17.228454    56.402536    .68975915    33924    .00161806    -.76626672    -31.591894    -3.01    -8.6237981    0    0    0    0    0    0    .85    6.62    -3.402619    2.421516    1.408656
      2    2013    982703    2.3040631    16.615386    57.204414    -.22881157    88227    .00178251    -2.8740579    10.930995    -1.86    -9.3552189    0    0    0    0    0    0    -3.01    .85    -31.59189    -.7662667    -8.623798
      2    2014    1110154    2.1936202    16.109134    59.292962    .17999861    59386    .00175794    1.1005573    44.138574    .07    -4.5525075    0    0    0    0    0    0    -1.86    -3.01    10.93099    -2.874058    -9.355219
      2    2015    1184900    2.1452373    16.020317    60.044954    .23465928    56866    .00174936    .84090043    3.2348891    .66    -8.4978766    0    0    0    0    0    0    .07    -1.86    44.13857    1.100557    -4.552507
      2    2016    1178308    2.0612768    15.911901    65.398388    -.00233048    48769    .00162654    .3816689    -23.208574    1.4    -3.4338776    0    0    0    0    0    0    .66    .07    3.234889    .8409004    -8.497876
      2    2017    1129950    2.5462314    15.894939    59.670936    .25559979    48726    .00161476    1.23481    20.886378    1.74    -1.5405045    0    0    0    0    0    0    1.4    .66    -23.20857    .3816689    -3.433878
      2    2018    823055    2.590812    15.12528    70.538284    .2117942    75007    .00146113    -4.1319113    2.8530874    .81    7.9092475    0    0    0    0    0    0    1.74    1.4    20.88638    1.23481    -1.540504
      2    2019    394612    2.4109246    13.6811    70.754662    .23051058    31291    .00145384    -1.6286674    -1.3125943    .5    1.0139957    0    0    0    0    0    0    .81    1.74    2.853087    -4.131911    7.909247
      2    2020    276581    2.1381271    12.213402    76.745459    .0629762    29135    .00143596    4.431668    -8.2740222    -9.09    -4.5538045    0    0    0    0    0    0    .5    .81    -1.312594    -1.628667    1.013996
      2    2021    220345    1.9617634    11.075969    63.64592    .24074262    45235    .0014706    5.0594383    29.455174    6.62    -5.1602501    0    0    0    0    0    0    -9.09    .5    -8.274022    4.431668    -4.553804
      just to help you further, in my first message you will find what numbers type was intended for each variable (if it is a % or it is simple number in $000).
      Hope this would help.
      Thanks a lot for your help.
      Regards,

      P.s. Is there a way to show data using the code function in such a way that numbers are properly listed in the column which corresponds to the variable name? I am asking this to facilitate you in the comprehension of the data. This typically happens to me when numbers or variable names are too long. Thanks.

      Comment


      • #4
        I notice that ROAA has about the same magnitude (and opposite sign) of the size_#_ROAA variables. So they will offset each other for each observation, allowing for a reasonably small predicted dependent value. So the large values are not necessarily indicative of a problem. I am guesing you have an ommitted size_#_ROAA variable available that you could substitute for ROAA. I think that might improve the display, but it wouldn't actually change anything about the predicted values or standard errors.

        Lastly, are the size_#_ROAA variables significantly different from each other? Do you even need them in the regression?

        Comment


        • #5
          Hi feenberg, thanks for your help.
          the size_#_ROAA variables are built using the assets variable under the following idea: "a dummy_25 which corresponds to all the observations for the assets variables which are less than the first quartile value; a second dummy 25-50 for those values which are between the first and second quartile values and so on". This means that the dummy variables are based on the observation of the assets variable.
          Then I just created some interaction terms for these dummies and the ROAA variable in order to see if the effect of ROAA on NPL (dependent variable) changes if a bank gets bigger, a phenomenon I tried to represent using the relative asset size as a proxy.
          Having said that, the dummies can be eliminated. Indeed, I re-estimated the model getting rid of those variables and the result is the following.
          Code:
          . xtreg NPL NetInterestMargin AvgEquityAvgAssets CosttoIncome ROAA LLP Assets deltabankloans deltaFTSEMIB RealGDPGrowth deltaNCLDeposits L1_RealGDPGrowth L2_RealGDPGrowth L
          > 1_deltaFTSEMIB L1_deltabankloans L1_deltaNCLDeposits, fe
          
          Fixed-effects (within) regression               Number of obs     =      1,285
          Group variable: id                              Number of groups  =        117
          
          R-squared:                                      Obs per group:
               Within  = 0.3328                                         min =          9
               Between = 0.7332                                         avg =       11.0
               Overall = 0.5038                                         max =         11
          
                                                          F(15,1153)        =      38.34
          corr(u_i, Xb) = 0.4506                          Prob > F          =     0.0000
          
          -------------------------------------------------------------------------------------
                          NPL | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
          --------------------+----------------------------------------------------------------
            NetInterestMargin |   17605.28   28064.62     0.63   0.531    -37458.16    72668.73
           AvgEquityAvgAssets |  -5829.609   5205.042    -1.12   0.263    -16042.03    4382.807
                 CosttoIncome |  -3794.722   830.8115    -4.57   0.000    -5424.794    -2164.65
                         ROAA |   73960.89   21027.98     3.52   0.000     32703.49    115218.3
                          LLP |   3.597567   .1679536    21.42   0.000     3.268038    3.927096
                       Assets |    1911079    1042691     1.83   0.067    -134705.8     3956863
               deltabankloans |   3372.236   4648.949     0.73   0.468    -5749.112    12493.58
                 deltaFTSEMIB |  -716.1821   700.4407    -1.02   0.307    -2090.463     658.099
                RealGDPGrowth |   8308.259    3341.81     2.49   0.013     1751.549    14864.97
             deltaNCLDeposits |   1201.443   2579.857     0.47   0.642    -3860.298    6263.183
             L1_RealGDPGrowth |   8639.162   4863.521     1.78   0.076    -903.1814    18181.51
             L2_RealGDPGrowth |   7646.103   4744.039     1.61   0.107    -1661.814    16954.02
              L1_deltaFTSEMIB |   464.3461   477.2106     0.97   0.331    -471.9524    1400.645
            L1_deltabankloans |   -9637.63   4795.388    -2.01   0.045     -19046.3   -228.9653
          L1_deltaNCLDeposits |   -7537.18   2566.449    -2.94   0.003    -12572.61   -2501.748
                        _cons |   340521.5   88643.05     3.84   0.000     166601.7    514441.2
          --------------------+----------------------------------------------------------------
                      sigma_u |  306792.33
                      sigma_e |  271139.43
                          rho |  .56145661   (fraction of variance due to u_i)
          -------------------------------------------------------------------------------------
          F test that all u_i=0: F(116, 1153) = 8.41                   Prob > F = 0.0000
          Still, coefficients are large and it seemed to me that the effects of those variables are so huge on NPL levels.
          Thanks, please let me know what you think about it.

          Comment


          • #6
            Salvatore:
            two asides:
            1) with 117 panels cluster-robust standard errors are usually called for;
            2) did you investgated the correct soecification of the functional form of the regressand?
            Kind regards,
            Carlo
            (Stata 19.0)

            Comment


            • #7
              Hi Salvatore
              Not sure if you already figure this out, but in your data, the dep variable NPL has a very large scale. Based on your data example, it ranges from 10000 to 1110000. Whereas the rest of your explanatory variables have smaller ranges. (netmargin 2-3). Then it makes absolute sense that the coefficients will also be large.

              Perhaps you are thinking that NPL has a different scale? or that instead of NPL in levels you wanted to use log(NPL)?

              F

              Comment


              • #8


                Hi Fernando and Carlo,

                I really appreciate your professionalism and precision in the attempt to give me support. As regards Carlo's points and concerns, I can tell that once I got those huge numbers I stopped. Still, I have to implement all the tests typically used in panel analysis (heteroskedasticity, unit roots, specifications and so on).

                The cluster-robust standard errors, I guess, are called fo deal with heteroskedasticity in clusters, but still, I have to study how to implement it on Stata. Would you recommend me a way to get to know all these points in particular, because sometimes I know what I should do in theory, but often I ignore how to implement it on Stata.


                As regard the model specification, I made the dependent variable (NPL) as a percentage of the Net Customer Loans, and now the estimates are way better.

                Code:
                xtreg NPL_perc NetInterestMargin AvgEquityAvgAssets CosttoIncome ROAA LLP Assets Delta_Public_DebtGDP deltabankloans deltaFTSEMIB RealGDPGrowth deltaNCLDeposits L1_RealGD
                Code:
                > PGrowth L2_RealGDPGrowth L1_deltaFTSEMIB L1_deltabankloans L1_deltaNCLDeposits L1_Delta_Public_DebtGDP,fe
                
                
                Fixed-effects (within) regression               Number of obs     =      1,198
                
                Group variable: id                              Number of groups  =        109
                
                
                R-squared:                                      Obs per group:
                
                     Within  = 0.4165                                         min =         10
                
                     Between = 0.0566                                         avg =       11.0
                
                     Overall = 0.2562                                         max =         11
                
                
                                                                F(17,1072)        =      45.02
                
                corr(u_i, Xb) = -0.0146                         Prob > F          =     0.0000
                
                
                -----------------------------------------------------------------------------------------
                
                               NPL_perc | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
                
                ------------------------+----------------------------------------------------------------
                
                      NetInterestMargin |  -.0163542   .0053514    -3.06   0.002    -.0268545   -.0058539
                
                     AvgEquityAvgAssets |   .0036028   .0011846     3.04   0.002     .0012785    .0059272
                
                           CosttoIncome |  -.0013157   .0001788    -7.36   0.000    -.0016665   -.0009649
                
                                   ROAA |  -.0381744   .0051358    -7.43   0.000    -.0482517   -.0280971
                
                                    LLP |   3.07e-08   4.10e-08     0.75   0.454    -4.97e-08    1.11e-07
                
                                 Assets |   2.524521   1.753787     1.44   0.150    -.9167232    5.965766
                
                   Delta_Public_DebtGDP |  -.0133497   .0163364    -0.82   0.414    -.0454047    .0187053
                
                         deltabankloans |   -.000624   .0072559    -0.09   0.931    -.0148613    .0136133
                
                           deltaFTSEMIB |   .0002488   .0008042     0.31   0.757    -.0013292    .0018267
                
                          RealGDPGrowth |  -.0162193   .0221109    -0.73   0.463    -.0596048    .0271663
                
                       deltaNCLDeposits |  -.0009817   .0037163    -0.26   0.792    -.0082738    .0063104
                
                       L1_RealGDPGrowth |  -.0115226   .0223794    -0.51   0.607    -.0554349    .0323897
                
                       L2_RealGDPGrowth |  -.0052075   .0032375    -1.61   0.108    -.0115601     .001145
                
                        L1_deltaFTSEMIB |   .0003153   .0008029     0.39   0.695    -.0012602    .0018907
                
                      L1_deltabankloans |   .0006498   .0072574     0.09   0.929    -.0135906    .0148901
                
                    L1_deltaNCLDeposits |  -.0042178   .0037152    -1.14   0.257    -.0115077    .0030721
                
                L1_Delta_Public_DebtGDP |  -.0136822    .016361    -0.84   0.403    -.0457854     .018421
                
                                  _cons |   .2666903    .018892    14.12   0.000     .2296209    .3037597
                
                ------------------------+----------------------------------------------------------------
                
                                sigma_u |  .06287887
                
                                sigma_e |   .0582214
                
                                    rho |   .5384028   (fraction of variance due to u_i)
                
                -----------------------------------------------------------------------------------------
                
                F test that all u_i=0: F(108, 1072) = 9.74                   Prob > F = 0.0000



                However, lots of coefficients are not statistically significant. Do you think is due to the fact that starting from Delta_Public_DebtGDP I have just 11 observations (one per year) for those macroeconomic variables, while for the first ones I have 1287 observations? Or it is due to other problems within the model that I may investigate with further tests?


                Thanks a lot for your help.

                Sincerely

                Comment


                • #9
                  Salvatore:
                  1) among the tests you mention, unit root can be skipped for N>T panel datasets;
                  2) under -xtreg-, clustered-robust standard errors deal with both heteroskedasticity and autocorrelation; unlike -regress-, -robust- and -vce(cluster panelid)- do the very same job under -xtreg-:
                  3) to investigate the functional form of the regressand, you have to run an auxiliary regression with both fitted and squared fitted values as predictors (see the approach under -linktest- entry in Stata .pdf manual),with the proviso the you have to create them manually, as -linktest- does not work after -regress-.
                  Kind regards,
                  Carlo
                  (Stata 19.0)

                  Comment


                  • #10
                    Dear carlo:
                    1) "among the tests you mention, unit root can be skipped for N>T panel datasets" is this due to the fact that the reliability of unit-root tests is based on the interdependence of observations through time. Therefore, these tests are based on the assumption that N and T tend to infinity. What's the reason behind your statement?
                    2) "under -xtreg-, clustered-robust standard errors deal with both heteroskedasticity and autocorrelation; unlike -regress-, -robust- and -vce(cluster panelid)- do the very same job under -xtreg-" I used the following command
                    Code:
                     xtreg NPL_perc NetInterestMargin AvgEquityAvgAssets CosttoIncome ROAA LLP Assets Delta_Public_DebtGDP deltabankloans deltaFTSEMIB Real
                    > GDPGrowth deltaNCLDeposits L1_RealGDPGrowth L2_RealGDPGrowth L1_deltaFTSEMIB L1_deltabankloans L1_deltaNCLDeposits L1_Delta_Public_Deb
                    > tGDP,fe vce(cluster id)
                    The specification vce (cluster id) is carried out by taking into account the cross-sectional units of my datasets named id (basically they are the banks, you can check above in #3). I think I did it well, but maybe you can confirm.

                    Anyway, as you can see below, I still have some doubts.

                    Code:
                    Fixed-effects (within) regression               Number of obs     =      1,198
                    Group variable: id                              Number of groups  =        109
                    
                    R-squared:                                      Obs per group:
                         Within  = 0.4165                                         min =         10
                         Between = 0.0566                                         avg =       11.0
                         Overall = 0.2562                                         max =         11
                    
                                                                    F(17,108)         =      48.78
                    corr(u_i, Xb) = -0.0146                         Prob > F          =     0.0000
                    
                                                                  (Std. err. adjusted for 109 clusters in id)
                    -----------------------------------------------------------------------------------------
                                            |               Robust
                                   NPL_perc | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
                    ------------------------+----------------------------------------------------------------
                          NetInterestMargin |  -.0163542   .0073248    -2.23   0.028    -.0308731   -.0018353
                         AvgEquityAvgAssets |   .0036028   .0027065     1.33   0.186    -.0017618    .0089675
                               CosttoIncome |  -.0013157   .0003577    -3.68   0.000    -.0020247   -.0006068
                                       ROAA |  -.0381744   .0075991    -5.02   0.000    -.0532372   -.0231116
                                        LLP |   3.07e-08   1.21e-07     0.25   0.801    -2.10e-07    2.71e-07
                                     Assets |   2.524521   4.255744     0.59   0.554    -5.911103    10.96015
                       Delta_Public_DebtGDP |  -.0133497   .0052079    -2.56   0.012    -.0236726   -.0030268
                             deltabankloans |   -.000624   .0030248    -0.21   0.837    -.0066196    .0053716
                               deltaFTSEMIB |   .0002488   .0004064     0.61   0.542    -.0005568    .0010544
                              RealGDPGrowth |  -.0162193   .0061796    -2.62   0.010    -.0284683   -.0039702
                           deltaNCLDeposits |  -.0009817   .0013206    -0.74   0.459    -.0035994    .0016361
                           L1_RealGDPGrowth |  -.0115226   .0069093    -1.67   0.098    -.0252181    .0021729
                           L2_RealGDPGrowth |  -.0052075    .003157    -1.65   0.102    -.0114652    .0010501
                            L1_deltaFTSEMIB |   .0003153   .0004045     0.78   0.437    -.0004864     .001117
                          L1_deltabankloans |   .0006498   .0030286     0.21   0.831    -.0053534    .0066529
                        L1_deltaNCLDeposits |  -.0042178   .0012919    -3.26   0.001    -.0067786    -.001657
                    L1_Delta_Public_DebtGDP |  -.0136822   .0052238    -2.62   0.010    -.0240366   -.0033278
                                      _cons |   .2666903   .0315932     8.44   0.000     .2040671    .3293135
                    ------------------------+----------------------------------------------------------------
                                    sigma_u |  .06287887
                                    sigma_e |   .0582214
                                        rho |   .5384028   (fraction of variance due to u_i)
                    -----------------------------------------------------------------------------------------
                    The 4th column for the P values shows that some of the variables are still not statistically significant and this really surprises me, as it is well established that GDP growth rate has an impact on credit growth and non performing loans of banks.
                    Maybe it is due to the functional form or due to other elements?


                    3) I will have a look at it.

                    Thanks a lot.

                    Comment


                    • #11
                      regarding point 3)
                      I read the linktest command on Stata manual which basically runs an auxiliary regression with fitted valued and squared fitted values as predictors without including the other predictors.
                      here you see the steps:
                      as you told me after regress linktest does not work.
                      Code:
                       linktest
                      not possible after xtreg
                      r(131);
                      So I create the predict values for my model using the following command:
                      Code:
                      . predict pred_NPL_perc
                      (option xb assumed; fitted values)
                      (1 missing value generated)
                      Here you can see more data about this variable.
                      Code:
                         | pred_NP~c |
                            |-----------|
                         1. |  .0936172 |
                         2. |   .129798 |
                         3. |  .1435782 |
                         4. |   .150126 |
                         5. |  .1752412 |
                            |-----------|
                         6. |  .1207947 |
                         7. |  .1201167 |
                         8. |  .0760249 |
                         9. |  .1175646 |
                        10. |  .0606917 |
                      Then I create the square fitted values with the following command:
                      Code:
                      gen predsquare_NPL_perc= pred_NPL_perc^2
                      Here some data:
                      Code:
                      predsquare_NPL_perc
                      .0087642
                      .0168475
                      .0206147
                      .0225378
                      .0307095
                      .0145914
                      .014428
                      .0057798
                      .0138214
                      .0036835
                      Then I ran the regression.
                      Code:
                      xtreg NPL_perc pred_NPL_perc predsquare_NPL_perc,fe
                      
                      Fixed-effects (within) regression               Number of obs     =      1,198
                      Group variable: id                              Number of groups  =        109
                      
                      R-squared:                                      Obs per group:
                           Within  = 0.4202                                         min =         10
                           Between = 0.0791                                         avg =       11.0
                           Overall = 0.2686                                         max =         11
                      
                                                                      F(2,1087)         =     393.92
                      corr(u_i, Xb) = -0.0085                         Prob > F          =     0.0000
                      
                      -------------------------------------------------------------------------------------
                                 NPL_perc | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
                      --------------------+----------------------------------------------------------------
                            pred_NPL_perc |   .6467425   .1389244     4.66   0.000      .374152    .9193329
                      predsquare_NPL_perc |   1.344862   .5110423     2.63   0.009     .3421205    2.347603
                                    _cons |   .0198527   .0090736     2.19   0.029     .0020488    .0376565
                      --------------------+----------------------------------------------------------------
                                  sigma_u |  .06208917
                                  sigma_e |  .05763499
                                      rho |  .53715227   (fraction of variance due to u_i)
                      -------------------------------------------------------------------------------------
                      F test that all u_i=0: F(108, 1087) = 12.46                  Prob > F = 0.0000
                      "If the model really is specified correctly, then if I was to regress NPL_perc on the prediction and the
                      prediction squared, the prediction squared would have no explanatory power."
                      This is what I expect from what I read on Stata manual about the linktest command.
                      However, in my case the square fitted values (which I calculated with predict command) does have explanatory power.

                      How would you suggest me to go ahead? Use log specifications? And firstly, did I carry out what you said about the functional form in a proper way?

                      Thanks a lot Carlo.

                      Comment


                      • #12
                        Salvatore:
                        you did everything right.
                        As far as the coefficients of your auxiliary regression are concerned, it may be that you need:
                        1) more predictors and/or
                        2) interactions between predictors and/or
                        3) logging the regressand.
                        Kind regards,
                        Carlo
                        (Stata 19.0)

                        Comment


                        • #13
                          Carlo:
                          all the points you stated in #12 refer to the original model I created and not to the one which consists of the regression of the dependent variable and the fitted values and the square fitted values.
                          You are suggesting I work out some adjustments on the original model I used (that one I presented in #10); aren't you?
                          Thanks

                          Comment


                          • #14
                            Salvatore:
                            you're correct.
                            Kind regards,
                            Carlo
                            (Stata 19.0)

                            Comment

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