Dear Statalisters,


I am trying to test for an inversed U-shaped between credit risk index and adjusted Lerner index(A measure of market power in the banking market).
To test for a U-shaped pattern between edit risk index and adjusted Lerner index I used a random-effects negative binomial model (supported by a Hausman test - xtnberg) including the direct (significant and positive) and the squared term of my Lerner Index. To corroborate this pattern of findings I would like to conduct a Sasabuchi (1980) test for an inverted U-shape, however I am not sure whether the right command was used to perform Sasabuchi test.


Code:
Fixed-effect (Hausman test - xtnberg)
xtnbreg llrgl car  adjlerner adjlerner2 insitution  ownership_concentration cir deposit_asset loan_asset otherearningassets incomediversity size  tier1 fundingragility luqidasset logz gdp_growth inflation crisis_d listed_d, fe
Followed by

Code:
Lind and Mehlum's procedure for testing U-shaped relationships or Sasabuchi test
utest  adjlerner adjlerner2, prefix(llrgl)
Code:
My results are the following:

Conditional FE negative binomial regression     Number of obs      =      3124
Group variable: y                               Number of groups   =        14

                                                Obs per group: min =       223
                                                               avg =     223.1
                                                               max =       225

                                                Wald chi2(19)      =     95.47
Log likelihood  = -481.71589                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
       llrgl |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         car |   .0480899   .3682911     0.13   0.896    -.6737474    .7699271
   adjlerner |  -5.870174   1.569279    -3.74   0.000    -8.945904   -2.794444
  adjlerner2 |   7.036934   1.943191     3.62   0.000      3.22835    10.84552
  insitution |  -.1541609   .1247337    -1.24   0.216    -.3986344    .0903125
ownership~on |   .0115567   .2493661     0.05   0.963    -.4771918    .5003052
         cir |   .0020299    .002605     0.78   0.436    -.0030758    .0071356
deposit_as~t |    .686342   .4698969     1.46   0.144    -.2346389    1.607323
  loan_asset |  -2.129252   .5312894    -4.01   0.000     -3.17056   -1.087944
otherearni~s |    .216634    .346283     0.63   0.532    -.4620682    .8953361
incomedive~y |    .142058   .1615877     0.88   0.379     -.174648     .458764
        size |   .0747654    .039163     1.91   0.056    -.0019926    .1515234
       tier1 |   .0816059   .2788698     0.29   0.770     -.464969    .6281807
fundingrag~y |   .0959053   .4705931     0.20   0.839    -.8264402    1.018251
  luqidasset |    .860141   .4811945     1.79   0.074     -.082983    1.803265
        logz |   .0032852   .0652955     0.05   0.960    -.1246917    .1312621
  gdp_growth |  -5.295671   1.911873    -2.77   0.006    -9.042874   -1.548468
   inflation |   -.130405   1.155299    -0.11   0.910     -2.39475     2.13394
    crisis_d |   .0278075   1.120135     0.02   0.980    -2.167616    2.223231
    listed_d |    .356337   .1745903     2.04   0.041     .0141463    .6985277
       _cons |   13.40707   203.6382     0.07   0.948    -385.7164    412.5306
------------------------------------------------------------------------------

. utest  adjlerner adjlerner2, prefix(llrgl)
(325 missing values generated)

Specification: f(x)=x^2
Extreme point:  .4170974

Test:
     H1: U shape
 vs. H0: Monotone or Inverse U shape 

-------------------------------------------------
                 |   Lower bound      Upper bound
-----------------+-------------------------------
Interval         |   -.1606019         .9939588
Slope            |   -8.130464          8.11867
t-value          |   -3.729346          3.42437
P>|t|            |    .0000977         .0003121
-------------------------------------------------

Overall test of presence of a U shape:
     t-value =      3.42
     P>|t|   =   .000312

.
Any idea on how to interpret these results? Does this mean that since we reject the null hypothesis based on p-value, that we should accept the H1 (direct U-shape) which is confirmed by the regressions (positive coefficient of Lerner^2):
Can you please confirm that this is the way to perform Sasabuchi test or I have to run another/different test in order to get the required result?


Many thanks in advance for your always precious help,

Petko Bachvarov