Too Large Wald chi2 Statistics

ByungHo Lee

Join Date: Oct 2020

Posts: 7
#1

Too Large Wald chi2 Statistics

14 Oct 2020, 20:46

I am following the work of Acemolug, Restrepo(2020). Trying to figure out the effect of adopting robot to labor market variables..

Main dependent variable is increase in real wage, and explanatory variable is index of adopting Robot called APR

I ran Panel IV with fixed effect(industry, time). I also added year dummy, and control variables like ratio of female workers

My problem is that when I include control variables like female rato, STATA shows me some unplausbly large Wald Chi2 Statistics...like 58903.17

Can this result simply be interpreted as the high goodness- of- fitness of this model? or is that related to lack of observations or so??

I attach the code i used and result of baseline Model and model of including control variable

Code:
xtivreg delta_wage (KoreanAPR = APR_WestEurope) i.year if year >= 2005, fe vce(robust)
xtivreg delta_wage (KoreanAPR = APR_WestEurope) i.year delta_female if year >= 2005, fe vce(robust)

Attached Files

question.smcl (8.9 KB, 1 view)

Last edited by ByungHo Lee; 14 Oct 2020, 21:00.
Tags: None

ByungHo Lee

Join Date: Oct 2020
Posts: 7

14 Oct 2020, 20:57

Code:

xtivreg delta_wage  (KoreanAPR = APR_WestEurope) i.year  if year >= 2005, fe vce(robust)

xtivreg delta_wage  (KoreanAPR = APR_WestEurope) i.year  if year >= 2005, fe vce(robust)

Fixed-effects (within) IV regression            Number of obs     =        186
Group variable: industry                        Number of groups  =         15

R-sq:                                           Obs per group:
     within  =      .                                         min =         11
     between = 0.0133                                         avg =       12.4
     overall = 0.0000                                         max =         13


                                                Wald chi2(14)     =    5570.31
corr(u_i, Xb)  = -0.4589                        Prob > chi2       =     0.0000

                              (Std. Err. adjusted for 15 clusters in industry)
------------------------------------------------------------------------------
             |               Robust
  delta_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   KoreanAPR |   37.34756   71.53228     0.52   0.602    -102.8531    177.5482
             |
        year |
       2006  |   4.301381   28.03751     0.15   0.878    -50.65113    59.25389
       2007  |   6.559273    27.4228     0.24   0.811    -47.18843    60.30698
       2008  |  -4.274475   24.33571    -0.18   0.861    -51.97159    43.42264
       2009  |  -2.065216   30.34125    -0.07   0.946    -61.53297    57.40254
       2010  |   4.011619    17.6048     0.23   0.820    -30.49315    38.51638
       2011  |  -19.10006   29.90251    -0.64   0.523     -77.7079    39.50777
       2012  |  -2.664256   15.86407    -0.17   0.867    -33.75725    28.42874
       2013  |  -21.49211   42.62362    -0.50   0.614    -105.0329    62.04866
       2014  |  -14.17789   25.09415    -0.56   0.572    -63.36152    35.00575
       2015  |  -31.58008   57.95919    -0.54   0.586     -145.178    82.01784
       2016  |  -55.80191   127.1773    -0.44   0.661    -305.0649    193.4611
       2017  |  -2.721155   35.88661    -0.08   0.940    -73.05762    67.61531
             |
       _cons |   2.387502   25.36503     0.09   0.925    -47.32705    52.10206
-------------+----------------------------------------------------------------
     sigma_u |  26.642091
     sigma_e |  55.031049
         rho |  .18987687   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   KoreanAPR
Instruments:    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
                2012.year 2013.year 2014.year 2015.year 2016.year 2017.year
                APR_WestEurope
------------------------------------------------------------------------------


xtivreg delta_wage  (KoreanAPR = APR_WestEurope) i.year delta_female if year >= 2005, fe vce(robust)


Fixed-effects (within) IV regression            Number of obs     =        186
Group variable: industry                        Number of groups  =         15

R-sq:                                           Obs per group:
     within  =      .                                         min =         11
     between = 0.0171                                         avg =       12.4
     overall = 0.0000                                         max =         13


                                                Wald chi2(14)     =   58903.17
corr(u_i, Xb)  = -0.4558                        Prob > chi2       =     0.0000

                              (Std. Err. adjusted for 15 clusters in industry)
------------------------------------------------------------------------------
             |               Robust
  delta_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   KoreanAPR |   31.01163   54.28861     0.57   0.568     -75.3921    137.4154
             |
        year |
       2006  |   5.235038   23.94094     0.22   0.827    -41.68833    52.15841
       2007  |   5.842981   22.22761     0.26   0.793    -37.72233    49.40829
       2008  |  -2.378216    22.0432    -0.11   0.914    -45.58209    40.82566
       2009  |  -3.299281   24.38023    -0.14   0.892    -51.08366     44.4851
       2010  |   3.508987   14.23509     0.25   0.805    -24.39128    31.40926
       2011  |  -16.78282   23.56316    -0.71   0.476    -62.96576    29.40011
       2012  |  -3.253034   12.97941    -0.25   0.802    -28.69222    22.18615
       2013  |  -17.92023   33.39964    -0.54   0.592    -83.38233    47.54187
       2014  |  -12.23234   20.33676    -0.60   0.548    -52.09166    27.62697
       2015  |  -26.78167   44.46508    -0.60   0.547    -113.9316    60.36828
       2016  |  -47.19806    99.1504    -0.48   0.634    -241.5293    147.1332
       2017  |  -2.855652   29.74257    -0.10   0.924    -61.15001    55.43871
             |
delta_female |   2.565031   3.895258     0.66   0.510    -5.069534     10.1996
       _cons |   3.333247   20.46997     0.16   0.871    -36.78715    43.45364
-------------+----------------------------------------------------------------
     sigma_u |  21.939044
     sigma_e |  46.104122
         rho |  .18463289   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   KoreanAPR
Instruments:    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
                2012.year 2013.year 2014.year 2015.year 2016.year 2017.year
                delta_female APR_WestEurope
------------------------------------------------------------------------------

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17675
#3

15 Oct 2020, 00:55

ByungHo:
my guess is that your model is misspecified, regardless endogeneity.
Despite your sky-rocketing chi2 ststistic, the confidence intervals of your predictors are remarkably wide.
Moreover, the Rsq-within is left unreported.

Kind regards,
Carlo
(Stata 19.0)
1 like
Comment

ByungHo Lee

Join Date: Oct 2020
Posts: 7

15 Oct 2020, 02:17

Thanks for comment! Carlo

As you mentioned the model seems to have some misspecification problems

But that could be happened because of the shortage of data. The data of robot before 2009 seems to have some problem so many missing values...

So, as I excluded sample before 2010, then the model seems to be fitted well

But the problem of sky-rocketting wald chi(2) problem still remains.

Under is the model which included control variables for female and export
The coefficient for year dummy still seems to have wide confidence intervals but the APR seems to have reasonable results

Code:

xtivreg delta_wage  (KoreanAPR = APR_WestEurope) i.year delta_female delta_export
>  if year > 2009, fe vce(robust)

Fixed-effects (within) IV regression            Number of obs     =        104
Group variable: industry                        Number of groups  =         13

R-sq:                                           Obs per group:
     within  =      .                                         min =          8
     between = 0.0147                                         avg =        8.0
     overall = 0.0082                                         max =          8


                                                Wald chi2(10)     =    1068.04
corr(u_i, Xb)  = -0.5174                        Prob > chi2       =     0.0000

                              (Std. Err. adjusted for 13 clusters in industry)
------------------------------------------------------------------------------
             |               Robust
  delta_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   KoreanAPR |  -5.924363   2.701318    -2.19   0.028    -11.21885   -.6298778
             |
        year |
       2011  |  -7.621427   9.667232    -0.79   0.430    -26.56885      11.326
       2012  |  -3.082289   2.174277    -1.42   0.156    -7.343794    1.179217
       2013  |  -1.184164   4.823908    -0.25   0.806    -10.63885    8.270522
       2014  |  -3.744533   2.922889    -1.28   0.200    -9.473289    1.984224
       2015  |  -.0192173    3.90352    -0.00   0.996    -7.669976    7.631541
       2016  |   5.073968   8.659806     0.59   0.558    -11.89894    22.04688
       2017  |  -6.080655   2.033888    -2.99   0.003      -10.067   -2.094308
             |
delta_female |   1.427692   4.478519     0.32   0.750    -7.350044    10.20543
delta_export |   .0199187   .1261606     0.16   0.875    -.2273514    .2671889
       _cons |   10.92142   4.854686     2.25   0.024     1.406409    20.43643
-------------+----------------------------------------------------------------
     sigma_u |  7.6395037
     sigma_e |  14.881591
         rho |  .20856704   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   KoreanAPR
Instruments:    2011.year 2012.year 2013.year 2014.year 2015.year 2016.year
                2017.year delta_female delta_export APR_WestEurope
------------------------------------------------------------------------------

And for the missing within R square, STATA homepage has some explanation about this situation

https://www.stata.com/support/faqs/s...least-squares/

It says when estimating IV Regression, negative R square problem happens quite a lot.

I thought this situation is also applied to my regression.

Regard,

Last edited by ByungHo Lee; 15 Oct 2020, 02:22.

Comment

Eric de Souza

Join Date: Mar 2014

Posts: 587
#5

15 Oct 2020, 02:30

It would be useful to see the results of the first stage regression: add the option -first- to your command
xtivreg delta_wage (KoreanAPR = APR_WestEurope) i.year delta_female delta_export if year > 2009, fe vce(robust) first
1 like
Comment

ByungHo Lee

Join Date: Oct 2020
Posts: 7

15 Oct 2020, 02:42

Thanks for Comment Eric!

As you recommended I attach the result of first stage regression

Code:

xtivreg delta_wage  (KoreanAPR = APR_WestEurope) i.year delta_female delta_export if year > 2009, fe vce(robust) first

First-stage within regression

Fixed-effects (within) regression               Number of obs      =       104
Group variable: industry                        Number of groups   =        13

R-sq:  within  = 0.1164                         Obs per group: min =         8
       between = 0.2093                                        avg =       8.0
       overall = 0.0378                                        max =         8

                                                F(10,12)           =     44.61
corr(u_i, Xb)  = -0.1774                        Prob > F           =    0.0000

                                (Std. Err. adjusted for 13 clusters in industry)
--------------------------------------------------------------------------------
               |               Robust
     KoreanAPR |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          year |
         2011  |   .2614847   .5947672     0.44   0.668    -1.034402    1.557371
         2012  |   .0050521   .2810461     0.02   0.986    -.6072947    .6173989
         2013  |   .4649152   .7970448     0.58   0.570    -1.271696    2.201527
         2014  |   .2827927    .327144     0.86   0.404    -.4299929    .9955783
         2015  |   .8409223    .668725     1.26   0.232    -.6161044    2.297949
         2016  |   1.643925   1.646634     1.00   0.338    -1.943782    5.231632
         2017  |  -.1701436   .5007379    -0.34   0.740    -1.261158    .9208705
               |
  delta_female |  -.1625432    .222538    -0.73   0.479    -.6474119    .3223255
  delta_export |    .004714   .0148685     0.32   0.757    -.0276816    .0371097
APR_WestEurope |   .7621269    .127648     5.97   0.000     .4840058    1.040248
         _cons |   .2110526   .6020859     0.35   0.732     -1.10078    1.522885
---------------+----------------------------------------------------------------
       sigma_u |  1.2445785
       sigma_e |  1.7898049
           rho |  .32593703   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(12, 12) = .                         Prob > F =      .

Fixed-effects (within) IV regression            Number of obs     =        104
Group variable: industry                        Number of groups  =         13

R-sq:                                           Obs per group:
     within  =      .                                         min =          8
     between = 0.0147                                         avg =        8.0
     overall = 0.0082                                         max =          8


                                                Wald chi2(10)     =    1068.04
corr(u_i, Xb)  = -0.5174                        Prob > chi2       =     0.0000

                              (Std. Err. adjusted for 13 clusters in industry)
------------------------------------------------------------------------------
             |               Robust
  delta_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   KoreanAPR |  -5.924363   2.701318    -2.19   0.028    -11.21885   -.6298778
             |
        year |
       2011  |  -7.621427   9.667232    -0.79   0.430    -26.56885      11.326
       2012  |  -3.082289   2.174277    -1.42   0.156    -7.343794    1.179217
       2013  |  -1.184164   4.823908    -0.25   0.806    -10.63885    8.270522
       2014  |  -3.744533   2.922889    -1.28   0.200    -9.473289    1.984224
       2015  |  -.0192173    3.90352    -0.00   0.996    -7.669976    7.631541
       2016  |   5.073968   8.659806     0.59   0.558    -11.89894    22.04688
       2017  |  -6.080655   2.033888    -2.99   0.003      -10.067   -2.094308
             |
delta_female |   1.427692   4.478519     0.32   0.750    -7.350044    10.20543
delta_export |   .0199187   .1261606     0.16   0.875    -.2273514    .2671889
       _cons |   10.92142   4.854686     2.25   0.024     1.406409    20.43643
-------------+----------------------------------------------------------------
     sigma_u |  7.6395037
     sigma_e |  14.881591
         rho |  .20856704   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   KoreanAPR
Instruments:    2011.year 2012.year 2013.year 2014.year 2015.year 2016.year
                2017.year delta_female delta_export APR_WestEurope
------------------------------------------------------------------------------

.

Although there seems to be some correlation between iv and residual, the correlation is not that high (-0.17)

Best Regard,

Comment

Eric de Souza

Join Date: Mar 2014

Posts: 587
#7

15 Oct 2020, 03:39

For the moment I have no explanation for the high Wald statistic. But there is another problem with your estimation. You only have 13 groups (industries). This is much too small for the cluster option.
1 like
Comment
Wei Zhang Vivian

Join Date: Nov 2020

Posts: 1
#8

27 Nov 2020, 05:10

When I deal with endogeneity issue in terms of corporate governance and firm performance in 2SLS model using xtivreg command. (xtivreg y xn (x2 x3 x4 x5 =z1 z2 z3 z4). endog(x2 x3 x4 x5)
I have 4 corporate governance variables and all corporate governance variables use the same instrument variable instead of each corporate governance variable with one specific instrument variable. How should I write the command？
Thanks for help!
Comment

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