r-squared results are negative and more than 1 for bilateral gravity model

[Junaid Ahmed]

Dear Statalist,

I have estimated a gravity model with external instruments for possible endogeneity between cost and remittances. however the results of r-square are negative and more than 1 in some cases. Could anyone explain where might be the issue?

Thanks and Regards,
Junaid

[Joao Santos Silva]

Dear Junaid Ahmed,

Please show us the command you used and the result you obtained.

Best wishes,

Joao

[Junaid Ahmed]

Dear Joao Santos Silva

*first step reg:

reg lcost2 instr3 instr4, robust

*Second step*
xtivreg2 lremit lgdpp lgdpp_hos lmig_st contig comlang_off colony exc_stab (lcost2= instr3 instr4 ), fe robust bw(2) gmm2 small

 xtivreg2 lremit  lgdpp lgdpp_hos  lmig_st contig comlang_off colony   exc_stab  (lcost2= instr3 instr4 ), fe  robust 
> bw(2) gmm2 small
Warning - singleton groups detected.  20 observation(s) not used.
Warning: time variable year has 7 gap(s) in relevant range
Warning - collinearities detected
Vars dropped:       contig comlang_off colony

FIXED EFFECTS ESTIMATION
------------------------
Number of groups =        88                    Obs per group: min =         2
                                                               avg =       4.5
                                                               max =         6
Warning - collinearities detected
Vars dropped:  contig comlang_off colony

2-Step GMM estimation
---------------------

Estimates efficient for arbitrary heteroskedasticity and autocorrelation
Statistics robust to heteroskedasticity and autocorrelation
  kernel=Bartlett; bandwidth=2
  time variable (t):  year
  group variable (i): pairid

                                                      Number of obs =      396
                                                      F(  5,   303) =     1.21
                                                      Prob > F      =   0.3037
Total (centered) SS     =  34.94097811                Centered R2   =  -4.1024
Total (uncentered) SS   =  34.94097811                Uncentered R2 =  -4.1024
Residual SS             =  178.2836691                Root MSE      =    .7671

------------------------------------------------------------------------------
             |               Robust
      lremit |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      lcost2 |  -4.611904   2.419147    -1.91   0.058    -9.372359    .1485511
       lgdpp |  -1.869395    1.26508    -1.48   0.141    -4.358851    .6200601
   lgdpp_hos |  -.3701742   1.879415    -0.20   0.844    -4.068531    3.328183
     lmig_st |   .9403234   .5063834     1.86   0.064    -.0561501    1.936797
      contig |          0  (omitted)
 comlang_off |          0  (omitted)
      colony |          0  (omitted)
    exc_stab |   1.524989   .7226998     2.11   0.036     .1028433    2.947135
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):              4.372
                                                   Chi-sq(2) P-val =    0.1124
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):                0.889
                         (Kleibergen-Paap rk Wald F statistic):          1.826
Stock-Yogo weak ID test critical values: 10% maximal IV size             19.93
                                         15% maximal IV size             11.59
                                         20% maximal IV size              8.75
                                         25% maximal IV size              7.25
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.041
                                                   Chi-sq(1) P-val =    0.8391
------------------------------------------------------------------------------
Instrumented:         lcost2
Included instruments: lgdpp lgdpp_hos lmig_st exc_stab
Excluded instruments: instr3 instr4
Dropped collinear:    contig comlang_off colony
------------------------------------------------------------------------------ 

[Junaid Ahmed]

Joao Santos Silva Dear Dr. Santos Silva, the command and the results can be shown above, I would like to know your take on it.
Thanks

[FernandoRios]

Hi Junaid,
When estimate a model using Instrumental variables, the Sum of squares identity (SST=SSE+SSR) does not hold anymore, and that can cause R2 to be negative.
What I would be far more concerned about is that your Instrumental variable is weak, which makes it harder to say anything about the results that correct for endogeneity.
HTH

[Joao Santos Silva]

Dear Junaid Ahmed,

R2s are rarely useful, but with IV estimation they are probably meaningless because they are not necessarily between 0 and 1, as this example shows.

Also, your instruments do not appear to be particularly strong.

Best wishes,

Joao

PS: Messages crossed in cyberspace, but I am glad to see the we agree.

[Junaid Ahmed]

FernandoRios Joao Santos Silva could you please let me know the interpretation of under and weak identification test using the above estimation results, Under identification test (Kleibergen-Paap rk LM statistic) and Weak identification test (Cragg-Donald Wald F statistic)
Thanks and regardsd,
Junaid