# st: Problems with HAUSMAN after XTIVREG, RE

 From Joana Quina To statalist@hsphsun2.harvard.edu Subject st: Problems with HAUSMAN after XTIVREG, RE Date Sun, 18 Sep 2005 19:30:59 +0100

```Dear all,

I am using xtivreg to estimate a random effects panel data model.  I
have one endogenous variable and one excluded instrument.  In order to
test for endogeneity, I am using the Hausman test with the sigmamore
option. When I do this, the Hausman test says that V_b-V_B is not
positive definite.

I would like to know your thoughts on the following:
1- What can be done to correct this?
2- Is there an "xtivreg2"?

Thank you for your help,

Joana

I enclose the output:

-------------output-----------------------
. xtivreg loda_pc lgdp_pc_d lpop  trade_gdp  polityp  us_un_friend_p
japan_un_friend_p Pperiod*
>  y_colony (corrupt=ethnic), re

G2SLS random-effects IV regression              Number of obs      =       111
Group variable: id                              Number of groups   =        31

R-sq:  within  = 0.5063                         Obs per group: min =         1
between = 0.6333                                        avg =       3.6
overall = 0.6213                                        max =         4

Wald chi2(11)      =    113.34
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
loda_pc |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
corrupt |  -.0429657   .1066427    -0.40   0.687    -.2519815    .1660502
lgdp_pc_d |   .0428328   .1272094     0.34   0.736    -.2064931    .2921586
lpop |   -.510157    .104499    -4.88   0.000    -.7149711   -.3053428
trade_gdp |   .0053404   .0024281     2.20   0.028     .0005813    .0100994
polityp |   .0140851   .0081874     1.72   0.085    -.0019619    .0301322
us_un_frie~p |  -.5324777   .4733456    -1.12   0.261    -1.460218    .3952627
japan_un_f~p |   2.920518   .8081029     3.61   0.000     1.336666    4.504371
Pperiod_1 |   .4201038   .2109389     1.99   0.046     .0066712    .8335365
Pperiod_2 |   .0078534   .1087593     0.07   0.942    -.2053109    .2210178
Pperiod_4 |  -.2225596   .2035832    -1.09   0.274    -.6215754    .1764562
y_colony |   .0006514   .0069568     0.09   0.925    -.0129837    .0142864
_cons |  -.8395967   1.498147    -0.56   0.575    -3.775911    2.096718
-------------+----------------------------------------------------------------
sigma_u |  .58004628
sigma_e |  .28688419
rho |  .80345955   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   corrupt
Instruments:    lgdp_pc_d lpop trade_gdp polityp us_un_friend_p
japan_un_friend_p Pperiod_1
Pperiod_2 Pperiod_4 y_colony ethnic

. est store ivrandom

. xtreg loda_pc lgdp_pc_d lpop  trade_gdp  polityp  us_un_friend_p
japan_un_friend_p corrupt Pp
> eriod* y_colony , re

Random-effects GLS regression                   Number of obs      =       111
Group variable (i): id                          Number of groups   =        31

R-sq:  within  = 0.5303                         Obs per group: min =         1
between = 0.6426                                        avg =       3.6
overall = 0.6435                                        max =         4

Random effects u_i ~ Gaussian                   Wald chi2(11)      =    128.55
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
loda_pc |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lgdp_pc_d |   .0181293   .1191414     0.15   0.879    -.2153837    .2516422
lpop |  -.5275332    .102472    -5.15   0.000    -.7283747   -.3266917
trade_gdp |   .0048886   .0022066     2.22   0.027     .0005637    .0092135
polityp |   .0143393   .0079024     1.81   0.070    -.0011491    .0298277
us_un_frie~p |  -.4735392   .4488587    -1.05   0.291    -1.353286    .4062077
japan_un_f~p |   3.167958   .6942995     4.56   0.000     1.807156     4.52876
corrupt |  -.1162393    .033678    -3.45   0.001    -.1822469   -.0502316
Pperiod_1 |   .5098709   .1617323     3.15   0.002     .1928815    .8268603
Pperiod_2 |   .0336761   .0990239     0.34   0.734    -.1604072    .2277594
Pperiod_4 |  -.2379928   .1948569    -1.22   0.222    -.6199053    .1439197
y_colony |  -.0014819   .0065505    -0.23   0.821    -.0143206    .0113568
_cons |  -.5709694   1.406288    -0.41   0.685    -3.327243    2.185304
-------------+----------------------------------------------------------------
sigma_u |  .57088029
sigma_e |  .26203147
rho |  .82598424   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. est store random

. hausman ivrandom random, sigmamore

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|    ivrandom      random       Difference          S.E.
-------------+----------------------------------------------------------------
corrupt |   -.0429657    -.1162393        .0732736        .0281962
lgdp_pc_d |    .0428328     .0181293        .0247035               .
lpop |    -.510157    -.5275332        .0173762               .
trade_gdp |    .0053404     .0048886        .0004518               .
polityp |    .0140851     .0143393       -.0002542               .
us_un_frie~p |   -.5324777    -.4735392       -.0589386               .
japan_un_f~p |    2.920518     3.167958       -.2474397               .
Pperiod_1 |    .4201038     .5098709       -.0897671               .
Pperiod_2 |    .0078534     .0336761       -.0258227               .
Pperiod_4 |   -.2225596    -.2379928        .0154332               .
y_colony |    .0006514    -.0014819        .0021332               .
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtivreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test:  Ho:  difference in coefficients not systematic

chi2(11) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=        6.74
Prob>chi2 =      0.8201
(V_b-V_B is not positive definite)

-------

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```