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st: estimated autocorrelation coefficient changes sign when dummy variables are included


From   Lopa Chakraborti <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: estimated autocorrelation coefficient changes sign when dummy variables are included
Date   Fri, 25 Feb 2011 16:26:03 -0500

Hi,
I am running xtpcse with and without plant level dummy variables models 2 and 1, respectively. The two models are otherwise identical. The estimated autocorrelation coefficient changes sign from positive in model 1 to negative in model 2 when dummy variables are included. I am wondering if controlling for plant fixed effects by including dummy variables is appropriate in xtpcse/xtgls models. The estimated autocorrelation coefficient is positive when I use xtregar with fe option [model 3]. From the Hausman test of fixed versus random effects [models 3 and 4 respectively] it shows that controlling for plant fixed effects is required.
thanks much for any help and advice
Lopa

model 1:

. xtpcse lseaavglqavfoia04avglbs2   lagseaavgwqfoia04avg3 lagseaavgflowfoia04avg3 elec food mill paper chem petro rubber leather metal transp secu just rnwhite mhhi carpl manuf popt popu MD PA , hetonly corr(ar1)

Number of gaps in sample:  119
(note: computations for rho restarted at each gap)
(note: estimates of rho outside [-1,1] bounded to be in the range [-1,1])

Prais-Winsten regression, heteroskedastic panels corrected standard errors

Group variable:   npid                          Number of obs      =       411
Time variable:    seasoncycle                   Number of groups   =        88
Panels:           heteroskedastic (unbalanced)  Obs per group: min =         2
Autocorrelation:  common AR(1)                                 avg =  4.670455
                                                               max =        10
Estimated covariances      =        88          R-squared          =    0.9053
Estimated autocorrelations =         1          Wald chi2(21)      =   7309.21
Estimated coefficients     =        22          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
             |            Het-corrected
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagseaavgw~3 |   .0175739   .0096651     1.82   0.069    -.0013695    .0365172
lagseaavgf~3 |   .0141308   .0035826     3.94   0.000     .0071089    .0211526
        elec |  -1.274798   .2237193    -5.70   0.000    -1.713279    -.836316
        food |  -.7037066   .4622545    -1.52   0.128    -1.609709    .2022955
        mill |   .1025684   .1902175     0.54   0.590    -.2702511     .475388
       paper |   1.753649   .1934481     9.07   0.000     1.374498    2.132801
        chem |  -1.145819   .2759653    -4.15   0.000    -1.686701   -.6049368
       petro |  -.6660155   .2932991    -2.27   0.023    -1.240871   -.0911599
      rubber |  -4.779963   .2134669   -22.39   0.000     -5.19835   -4.361575
     leather |  -.8598458   .3122449    -2.75   0.006    -1.471834    -.247857
       metal |  -3.334442   .3719062    -8.97   0.000    -4.063365    -2.60552
      transp |  (dropped)
        secu |  -1.785632   .1604453   -11.13   0.000    -2.100099   -1.471165
        just |  -.6692307   .1983626    -3.37   0.001    -1.058014   -.2804472
     rnwhite |   .0042574   .0044486     0.96   0.339    -.0044616    .0129765
        mhhi |   .0220234   .0088036     2.50   0.012     .0047688    .0392781
       carpl |   .0159484    .015213     1.05   0.294    -.0138686    .0457654
       manuf |    .000531   .0054583     0.10   0.922    -.0101671    .0112291
        popt |   .0174839   .0044007     3.97   0.000     .0088586    .0261091
        popu |   .0032925   .0024354     1.35   0.176    -.0014809    .0080658
          MD |   -.832088   .1614986    -5.15   0.000    -1.148619   -.5155565
          PA |  -.2565289   .3490807    -0.73   0.462    -.9407145    .4276567
       _cons |   5.353551    .368632    14.52   0.000     4.631045    6.076056
-------------+----------------------------------------------------------------
         rho |   .7916129
------------------------------------------------------------------------------

model 2:

. xtpcse lseaavglqavfoia04avglbs2   lagseaavgwqfoia04avg3 lagseaavgflowfoia04avg3 elec food mill paper chem petro rubber leather metal transp secu just rnwhite mhhi carpl manuf popt popu MD PA plantdum*, hetonly corr(ar1)

Number of gaps in sample:  119
(note: computations for rho restarted at each gap)
(note: estimates of rho outside [-1,1] bounded to be in the range [-1,1])

Prais-Winsten regression, heteroskedastic panels corrected standard errors

Group variable:   npid                          Number of obs      =       411
Time variable:    seasoncycle                   Number of groups   =        88
Panels:           heteroskedastic (unbalanced)  Obs per group: min =         2
Autocorrelation:  common AR(1)                                 avg =  4.670455
                                                               max =        10
Estimated covariances      =        88          R-squared          =    0.9822
Estimated autocorrelations =         1          Wald chi2(89)      =  1.44e+07
Estimated coefficients     =        89          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
             |            Het-corrected
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagseaavgw~3 |   .0180936   .0071236     2.54   0.011     .0041316    .0320556
lagseaavgf~3 |   .0181603   .0008675    20.93   0.000       .01646    .0198607
        elec |  (dropped)
        food |  -4.603288    .236761   -19.44   0.000    -5.067331   -4.139245
        mill |  -1.579772   .4555319    -3.47   0.001    -2.472598   -.6869456
       paper |   1.039548   .1012485    10.27   0.000     .8411045    1.237991
        chem |  -2.747028   .1853032   -14.82   0.000    -3.110215    -2.38384
       petro |   -.099715   .0818765    -1.22   0.223      -.26019      .06076
      rubber |  -5.590311   .1229184   -45.48   0.000    -5.831227   -5.349396
     leather |  -1.408918   .3117076    -4.52   0.000    -2.019854   -.7979828
       metal |  -5.642789   .1517692   -37.18   0.000    -5.940251   -5.345326
      transp |  (dropped)
        secu |  -2.705448   .1586987   -17.05   0.000    -3.016492   -2.394404
        just |  -.4976849   .0287418   -17.32   0.000    -.5540178    -.441352
     rnwhite |    .033415   .0011554    28.92   0.000     .0311503    .0356796
        mhhi |   .0687624   .0027268    25.22   0.000      .063418    .0741068
       carpl |   .1050512   .0049816    21.09   0.000     .0952874    .1148149
       manuf |    .059941   .0017845    33.59   0.000     .0564434    .0634385
        popt |   -.013566   .0049359    -2.75   0.006    -.0232401   -.0038919
        popu |   .0214322   .0003912    54.78   0.000     .0206654    .0221989
          MD |   .6438677   .1216639     5.29   0.000     .4054109    .8823245
          PA |  -.3290206   .1106896    -2.97   0.003    -.5459682   -.1120729
   plantdum2 |  (dropped)
   plantdum3 |  (dropped)
   plantdum4 |  (dropped)
   plantdum5 |  (dropped)
   plantdum6 |  -.8737521   .2218897    -3.94   0.000    -1.308648   -.4388563
   plantdum7 |  -1.106989   .1822593    -6.07   0.000    -1.464211   -.7497677
   plantdum8 |   .3478083   .1596061     2.18   0.029     .0349861    .6606306
   plantdum9 |  -1.946071   .2701609    -7.20   0.000    -2.475577   -1.416566
  plantdum10 |   .2056404   .2093001     0.98   0.326    -.2045802     .615861
  plantdum11 |  -.9707295     .08547   -11.36   0.000    -1.138248   -.8032113
  plantdum12 |  (dropped)
  plantdum13 |   .0850417   .1997274     0.43   0.670    -.3064168    .4765002
  plantdum14 |  (dropped)
  plantdum15 |   1.872152   .0898308    20.84   0.000     1.696087    2.048217
  plantdum16 |   -.727815   .1884699    -3.86   0.000    -1.097209   -.3584207
  plantdum17 |  -2.288263   .2261976   -10.12   0.000    -2.731602   -1.844923
  plantdum18 |   .2269513   .1408603     1.61   0.107    -.0491297    .5030324
  plantdum19 |  -1.168687   .1662243    -7.03   0.000    -1.494481   -.8428932
  plantdum20 |   .5467179   .1741751     3.14   0.002     .2053409    .8880948
  plantdum21 |  -1.407528   .1072642   -13.12   0.000    -1.617762   -1.197294
  plantdum22 |   .7337238   .2054737     3.57   0.000     .3310027    1.136445
  plantdum23 |  (dropped)
  plantdum24 |  (dropped)
  plantdum25 |  -2.116513   .2587528    -8.18   0.000    -2.623659   -1.609367
  plantdum26 |  (dropped)
  plantdum27 |  (dropped)
  plantdum28 |  (dropped)
  plantdum29 |  (dropped)
  plantdum30 |  (dropped)
  plantdum31 |   .0519363   .2364972     0.22   0.826    -.4115898    .5154623
  plantdum32 |    5.76572    .167844    34.35   0.000     5.436751    6.094688
  plantdum33 |  (dropped)
  plantdum34 |  (dropped)
  plantdum35 |  (dropped)
  plantdum36 |   7.096475   .1449033    48.97   0.000     6.812469     7.38048
  plantdum37 |  (dropped)
  plantdum38 |  (dropped)
  plantdum39 |  (dropped)
  plantdum40 |   7.260004   .2132947    34.04   0.000     6.841954    7.678054
  plantdum41 |    1.41097   .0983095    14.35   0.000     1.218287    1.603653
  plantdum42 |  -.9692919   .0296649   -32.67   0.000    -1.027434   -.9111497
  plantdum43 |   1.084792   .0795524    13.64   0.000     .9288723    1.240712
  plantdum44 |   1.225428   .1070797    11.44   0.000     1.015556      1.4353
  plantdum45 |  (dropped)
  plantdum46 |  (dropped)
  plantdum47 |   4.555706    .150157    30.34   0.000     4.261403    4.850008
  plantdum48 |   2.111834   .2632353     8.02   0.000     1.595902    2.627766
  plantdum49 |   4.718928   .1469579    32.11   0.000     4.430895     5.00696
  plantdum50 |   2.041079   .1658375    12.31   0.000     1.716044    2.366115
  plantdum51 |  (dropped)
  plantdum52 |   1.992393   .4519647     4.41   0.000     1.106558    2.878227
  plantdum53 |   .7984359   .4564329     1.75   0.080    -.0961562    1.693028
  plantdum54 |   2.395141   .2303797    10.40   0.000     1.943606    2.846677
  plantdum55 |   3.523936   .1679183    20.99   0.000     3.194822     3.85305
  plantdum56 |  (dropped)
  plantdum57 |  (dropped)
  plantdum58 |  (dropped)
  plantdum59 |   1.060518   .0548449    19.34   0.000     .9530237    1.168012
  plantdum60 |  (dropped)
  plantdum61 |  (dropped)
  plantdum62 |   1.633855   .4632306     3.53   0.000     .7259401    2.541771
  plantdum63 |  (dropped)
  plantdum64 |   .1792942    .028385     6.32   0.000     .1236606    .2349277
  plantdum65 |  -.8104991   .1174556    -6.90   0.000    -1.040708   -.5802903
  plantdum66 |  -2.504236    .119425   -20.97   0.000    -2.738305   -2.270168
  plantdum67 |  -.2978648   .0570631    -5.22   0.000    -.4097065   -.1860232
  plantdum68 |  -.5260572    .101494    -5.18   0.000    -.7249818   -.3271327
  plantdum69 |   2.412183   .0613695    39.31   0.000     2.291901    2.532465
  plantdum70 |   .1437169   .0591522     2.43   0.015     .0277806    .2596531
  plantdum71 |    2.87729   .0947743    30.36   0.000     2.691536    3.063044
  plantdum72 |   .3985812   .1838042     2.17   0.030     .0383316    .7588308
  plantdum73 |   -.948565   .0512311   -18.52   0.000    -1.048976   -.8481538
  plantdum74 |   1.484547   .0595253    24.94   0.000      1.36788    1.601215
  plantdum75 |  -.2724068   .0815195    -3.34   0.001    -.4321821   -.1126316
  plantdum76 |  -1.063033   .1385774    -7.67   0.000     -1.33464   -.7914264
  plantdum77 |   1.452853   .0594178    24.45   0.000     1.336396     1.56931
  plantdum78 |    2.14592   .1364149    15.73   0.000     1.878552    2.413288
  plantdum79 |  -2.251174   .1105202   -20.37   0.000    -2.467789   -2.034558
  plantdum80 |   .5619839    .047046    11.95   0.000     .4697754    .6541925
  plantdum81 |   .4208893   .0913233     4.61   0.000     .2418988    .5998797
  plantdum82 |   1.527783   .0453195    33.71   0.000     1.438959    1.616608
  plantdum83 |  (dropped)
  plantdum84 |   1.125875   .0432152    26.05   0.000     1.041175    1.210575
  plantdum85 |   1.591836   .0577172    27.58   0.000     1.478713     1.70496
  plantdum86 |   4.006383   .1716238    23.34   0.000     3.670006    4.342759
  plantdum87 |  (dropped)
  plantdum88 |   .6000273   .1352842     4.44   0.000      .334875    .8651795
  plantdum89 |    -2.0558   .0780075   -26.35   0.000    -2.208691   -1.902908
  plantdum90 |   1.633073   .0935017    17.47   0.000     1.449813    1.816333
  plantdum91 |    .415067   .0848474     4.89   0.000     .2487693    .5813648
  plantdum92 |   1.401441   .1117379    12.54   0.000     1.182439    1.620443
  plantdum93 |   1.086346   .0447443    24.28   0.000     .9986492    1.174044
  plantdum94 |   .3558804   .1996679     1.78   0.075    -.0354614    .7472222
  plantdum95 |   .5308524   .0447122    11.87   0.000     .4432181    .6184866
  plantdum96 |    1.02588   .2040099     5.03   0.000     .6260276    1.425732
  plantdum97 |   2.448062   .1789877    13.68   0.000     2.097252    2.798871
  plantdum98 |   .6660908   .1088542     6.12   0.000     .4527406     .879441
  plantdum99 |  -2.903657   .0883717   -32.86   0.000    -3.076862   -2.730451
 plantdum100 |  -1.274899   .0404559   -31.51   0.000    -1.354191   -1.195607
       _cons |  (dropped)
-------------+----------------------------------------------------------------
         rho |  -.2280014
------------------------------------------------------------------------------


model 3:

. xtregar lseaavglqavfoia04avglbs2  lagseaavgwqfoia04avg3 lagseaavgflowfoia04avg3 elec food mill paper chem petro rubber leather metal transp secu just rnwhite mhhi carpl manuf popt popu MD PA ,fe
note: lagseaavgflowfoia04avg3 dropped due to collinearity
note: elec dropped due to collinearity
note: food dropped due to collinearity
note: mill dropped due to collinearity
note: paper dropped due to collinearity
note: chem dropped due to collinearity
note: petro dropped due to collinearity
note: rubber dropped due to collinearity
note: leather dropped due to collinearity
note: metal dropped due to collinearity
note: transp dropped due to collinearity
note: secu dropped due to collinearity
note: just dropped due to collinearity
note: rnwhite dropped due to collinearity
note: mhhi dropped due to collinearity
note: carpl dropped due to collinearity
note: manuf dropped due to collinearity
note: popt dropped due to collinearity
note: popu dropped due to collinearity
note: MD dropped due to collinearity
note: PA dropped due to collinearity

FE (within) regression with AR(1) disturbances  Number of obs      =       323
Group variable (i): npid                        Number of groups   =        88

R-sq:  within  = 0.9181                         Obs per group: min =         1
       between = 0.0837                                        avg =       3.7
       overall = 0.0136                                        max =         9

                                                F(1,234)           =   2624.70
corr(u_i, Xb)  = -0.2625                        Prob > F           =    0.0000

------------------------------------------------------------------------------
lseaavglqa~2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagseaavgw~3 |   .3303635   .0064484    51.23   0.000     .3176591    .3430679
       _cons |   6.462695   .0293006   220.57   0.000     6.404968    6.520421
-------------+----------------------------------------------------------------
      rho_ar |  .72041395
     sigma_u |  1.5826877
     sigma_e |  .42485831
     rho_fov |  .93278311   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(87,234) =     5.44              Prob > F = 0.0000

. estimates store fe


model 4:

. xtregar lseaavglqavfoia04avglbs2  lagseaavgwqfoia04avg3 lagseaavgflowfoia04avg3 elec food mill paper chem petro rubber leather metal transp secu just rnwhite mhhi carpl manuf popt popu MD PA

RE GLS regression with AR(1) disturbances       Number of obs      =       411
Group variable (i): npid                        Number of groups   =        88

R-sq:  within  = 0.0233                         Obs per group: min =         2
       between = 0.5535                                        avg =       4.7
       overall = 0.5000                                        max =        10

                                                Wald chi2(22)      =    129.40
corr(u_i, Xb)      = 0 (assumed)                Prob > chi2        =    0.0000

------------------- theta --------------------
  min      5%       median        95%      max
0.7118   0.7118     0.8239     0.8463   0.8619

------------------------------------------------------------------------------
lseaavglqa~2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lagseaavgw~3 |   .0224174   .0046985     4.77   0.000     .0132084    .0316263
lagseaavgf~3 |   .0160294   .0043707     3.67   0.000     .0074629    .0245959
        elec |  -1.390232     1.0631    -1.31   0.191    -3.473869    .6934058
        food |   -1.06088   .6023092    -1.76   0.078    -2.241385    .1196241
        mill |  -.0823007   .5450267    -0.15   0.880    -1.150533    .9859319
       paper |   1.496774    .540306     2.77   0.006     .4377936    2.555754
        chem |  -.9555481   .3960903    -2.41   0.016    -1.731871   -.1792253
       petro |  -.7947746   .5813898    -1.37   0.172    -1.934278    .3447286
      rubber |  -4.717306   1.051812    -4.48   0.000     -6.77882   -2.655793
     leather |  -1.087977    .759365    -1.43   0.152    -2.576305    .4003515
       metal |  -3.414902   1.115013    -3.06   0.002    -5.600287   -1.229517
      transp |  (dropped)
        secu |   -1.77943   .7244329    -2.46   0.014    -3.199292   -.3595675
        just |  -.6679765   1.034483    -0.65   0.518    -2.695525    1.359572
     rnwhite |   .0026329   .0083482     0.32   0.752    -.0137292    .0189949
        mhhi |   .0178696   .0149918     1.19   0.233    -.0115138     .047253
       carpl |   .0265838    .027233     0.98   0.329    -.0267919    .0799595
       manuf |   .0036588   .0119338     0.31   0.759     -.019731    .0270487
        popt |   .0142818    .009748     1.47   0.143    -.0048239    .0333875
        popu |   .0039242    .003679     1.07   0.286    -.0032865    .0111349
          MD |   -.753159   .3175429    -2.37   0.018    -1.375532   -.1307863
          PA |  -.1461052   .4249701    -0.34   0.731    -.9790313    .6868209
       _cons |   5.231199   .7215216     7.25   0.000     3.817042    6.645355
-------------+----------------------------------------------------------------
      rho_ar |  .72041395   (estimated autocorrelation coefficient)
     sigma_u |  .91797171
     sigma_e |  .20657905
     rho_fov |  .95179867   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. hausman fe .

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           .          Difference          S.E.
-------------+----------------------------------------------------------------
lagseaavgw~3 |    .3303635     .0224174        .3079461        .0044165
------------------------------------------------------------------------------
                         b = consistent under Ho and Ha; obtained from xtregar
          B = inconsistent under Ha, efficient under Ho; obtained from xtregar

    Test:  Ho:  difference in coefficients not systematic

                  chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =     4861.66
                Prob>chi2 =      0.0000

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