Pooled OLS - Durbin-Watzon?

[Isabel Cour]

hello,
I am analysing an small dataset with T=16 and N=6, and I am trying to get what is the appropriate test to use for checking autocorrelation with pooled OLS. Durbin-Watzon seems one of the test for checking autocorrelation but i am not sure for pooled OLS. I saw some post relate to this topic but still is not enough clear for me. Please, any comment relate to will be welcome, thanks in advance

[Carlo Lazzaro]

Isabel:
welcome to this forum.
If you have a T>N panel dataset, why not considering -xtgls-?

[Isabel Cour]

Carlo,

Thank you very much for the answer. I use a gravity framework to examine the effect of technology on trade flows. First a pooled OLS was estimated; this model includes year and countries fixed effect.Then I checked robustness via GMM. if I use pooled OLS I must check autocorrelation, however how can address this issues? in this context.

[Carlo Lazzaro]

Isabel:
you may want to consider something along the following lines:

. set obs 5
number of observations (_N) was 0, now 5

. g id=_n

. expand 3
(10 observations created)

. bysort id: g time=_n

. g y=runiform()*100

. g x=runiform()*.5

. reg y x, vce(cluster id)

Linear regression                               Number of obs     =         15
                                                F(1, 4)           =       0.82
                                                Prob > F          =     0.4160
                                                R-squared         =     0.0461
                                                Root MSE          =     30.244

                                     (Std. Err. adjusted for 5 clusters in id)
------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |  -43.13193      47.59    -0.91   0.416     -175.263    88.99911
       _cons |   75.74245   15.03339     5.04   0.007     34.00306    117.4818
------------------------------------------------------------------------------

. predict uhat, residuals

. forvalues j = 1/2 {
  2. quietly corr uhat L`j'.uhat
  3. di "Autocorrelation at lag `j' = " %6.3f r(rho)
  4.  }
Autocorrelation at lag 1 = -0.058
Autocorrelation at lag 2 = -0.731

.

*All credits for the code reported above goes out to https://www.stata.com/bookstore/microeconometrics-stata/, page 252*

[Isabel Cour]

Dear Carlo,

Thank you for your answer. I will try that command. Regards,

[Isabel Cour]

Dear Carlo,

Running the pooled OLS again I found that is dropping the gdp_exporter, also distance. That happens because I add year fixed effect. I am using a gravity framework I have one exporter and 6 importer, gdp_m gdp_x distance variables. I am estimating effect of tech on trade flows. Result shows a high coefficient of R, only the explicative variable is significant but not any control variables. However if I removed year fixed effect, gdp_m become significant, R squared remain almost the same.
Any comment will be very welcome, thank you Carlo in advance.

Kind regards,


The equation is,

regress lnimpo lnintus lngdp_m lngdp_x lndist lnidist exporter_* importer_* year_*, cluster(id)

note: lngdp_exp omitted because of collinearity
note: lndist omitted because of collinearity
note: exporter_6 omitted because of collinearity
note: importer_1 omitted because of collinearity
note: year_1 omitted because of collinearity
note: year_16 omitted because of collinearity

Linear regression                               Number of obs     =         96
                                                F(4, 5)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9453
                                                Root MSE          =     .48059

                                     (Std. Err. adjusted for 6 clusters in id)
------------------------------------------------------------------------------
             |               Robust
      lnimpo |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnintus |   .6558501   .1554177     4.22   0.008     .2563361    1.055364
     lngdp_m |    .725604   .5322272     1.36   0.231    -.6425297    2.093738
     lngdp_e |          0  (omitted)
      lndist |          0  (omitted)
     lnidist |  -.6969423   1.001261    -0.70   0.517    -3.270767    1.876882
  exporter_1 |  -.0359593   1.108767    -0.03   0.975    -2.886135    2.814216
  exporter_2 |   .3925353   1.775355     0.22   0.834    -4.171161    4.956232
  exporter_3 |   1.985593   1.325898     1.50   0.195    -1.422737    5.393923
  exporter_4 |  -1.726357   .8812586    -1.96   0.107    -3.991705    .5389901
  exporter_5 |   .5690413   .6103641     0.93   0.394    -.9999496    2.138032
  exporter_6 |          0  (omitted)
  importer_1 |          0  (omitted)
      year_1 |          0  (omitted)
      year_2 |  -.1791182   .1716109    -1.04   0.344     -.620258    .2620216
      year_3 |  -.1937245   .2774412    -0.70   0.516    -.9069098    .5194608
      year_4 |  -.1649017   .2791474    -0.59   0.580    -.8824728    .5526694
      year_5 |   .1806592    .098292     1.84   0.125    -.0720084    .4333268
      year_6 |   .1437831   .1277797     1.13   0.312    -.1846852    .4722513
      year_7 |   .0889293   .1295385     0.69   0.523    -.2440601    .4219186
      year_8 |   .2812087   .1120507     2.51   0.054    -.0068267    .5692442
      year_9 |   .1691415   .1544995     1.09   0.324    -.2280121    .5662951
     year_10 |  -.0819679   .1508932    -0.54   0.610    -.4698511    .3059154
     year_11 |   .1149215   .1189615     0.97   0.378    -.1908788    .4207219
     year_12 |   .0961005   .1533784     0.63   0.558    -.2981711    .4903721
     year_13 |   .0659792   .1188738     0.56   0.603    -.2395956    .3715539
     year_14 |   .0015395   .1104748     0.01   0.989     -.282445     .285524
     year_15 |   .1724051   .1519819     1.13   0.308    -.2182769     .563087
     year_16 |          0  (omitted)
       _cons |   1.272487   13.05932     0.10   0.926    -32.29758    34.84255
------------------------------------------------------------------------------

[Carlo Lazzaro]

Isabel:
a high R-sq with a handful of statistical significant coefficients shoul lead to suspect quasi-extreeme multicollinearity with your data.
I would investigate that issue via -estat vif- after -regress-.
Two asides:
- statistical significant in itself is not the goal a guiven regression model should be targetted to; give a fair and true view of the data generating process, instead;
- as far as categorical variables and interactions are concerned, I would exploit the wondeful capabilities of -frvvarlist-.

[Isabel Cour]

Dear Carlo,

I checked it and yes it is as you said, and stata remove those variables, however the specification model is what you follow in this research question, perhaps because I am studying few countries . I am not using categorical variables but an interaction term of tecno. Thank you very much Carlo!

[Carlo Lazzaro]

Isabel:
if you're using interactions among your predictors, -fvvarlist- is the notation to follow (see -help fvvarlist-).

[Isabel Cour]

thank you very much Carlo!

[Isabel Cour]

Dear Carlo,

I am running a new equation via pooled OLS as a benchmark model, then a ppml and ivpoisson. The framework is gravity model. OLS result shows as follow,

. reg lnamchsac lnintus lngdp lngdpch lndist lnidist lntariff exporter_* importer_* year_*, cluster(dist)
note: lngdpch omitted because of collinearity
note: lndist omitted because of collinearity
note: exporter_2 omitted because of collinearity
note: exporter_7 omitted because of collinearity
note: importer_1 omitted because of collinearity
note: year_1 omitted because of collinearity
note: year_2 omitted because of collinearity
note: year_4 omitted because of collinearity
note: year_5 omitted because of collinearity
note: year_6 omitted because of collinearity
note: year_21 omitted because of collinearity

Linear regression                               Number of obs     =         86
                                                F(4, 5)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8661
                                                Root MSE          =     1.4843

                                   (Std. Err. adjusted for 6 clusters in dist)
------------------------------------------------------------------------------
             |               Robust
   lnamchsac |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   lnintus   |   1.472002   .4711239     3.12   0.026     .2609392    2.683064
       lngdp |  -.1357364   1.708809    -0.08   0.940    -4.528369    4.256896
     lngdpch |          0  (omitted)
      lndist |          0  (omitted)
     lnidist |  -.2363665    1.53543    -0.15   0.884    -4.183315    3.710582
    lntariff |    .452788   .4531946     1.00   0.364    -.7121858    1.617762
  exporter_1 |   -3.34698   2.296368    -1.46   0.205    -9.249982    2.556022
  exporter_2 |          0  (omitted)
  exporter_3 |  -5.926601   3.785382    -1.57   0.178    -15.65723    3.804032
  exporter_4 |   -6.61961    3.46639    -1.91   0.114    -15.53025    2.291028
  exporter_5 |  -9.048581   5.533931    -1.64   0.163      -23.274    5.176842
  exporter_6 |  -8.964859    7.62402    -1.18   0.293    -28.56303    10.63331
  exporter_7 |          0  (omitted)
  importer_1 |          0  (omitted)
      year_1 |          0  (omitted)
      year_2 |          0  (omitted)
      year_3 |   1.404595   1.105926     1.27   0.260    -1.438277    4.247467
      year_4 |          0  (omitted)
      year_5 |          0  (omitted)
      year_6 |          0  (omitted)
      year_7 |    1.25089    2.09155     0.60   0.576    -4.125611    6.627392
      year_8 |  -1.600892   2.077176    -0.77   0.476    -6.940442    3.738659
      year_9 |  -.2773236   2.954371    -0.09   0.929    -7.871777    7.317129
     year_10 |  -.9183395    1.78202    -0.52   0.628    -5.499167    3.662488
     year_11 |   .3214608    1.24989     0.26   0.807    -2.891484    3.534406
     year_12 |  -.5872897   1.037801    -0.57   0.596    -3.255043    2.080463
     year_13 |   .4736747   .9093405     0.52   0.625    -1.863859    2.811209
     year_14 |  -.0355714   1.587321    -0.02   0.983    -4.115909    4.044767
     year_15 |  -1.041163   .8873181    -1.17   0.293    -3.322087     1.23976
     year_16 |  -.3526849   .9942915    -0.35   0.737    -2.908593    2.203223
     year_17 |   .1482775   .7291278     0.20   0.847    -1.726005     2.02256
     year_18 |  -.4334973    .625288    -0.69   0.519    -2.040851    1.173857
     year_19 |   .6455891   1.510222     0.43   0.687    -3.236561    4.527739
     year_20 |    .423954   .6250359     0.68   0.528    -1.182752     2.03066
     year_21 |          0  (omitted)
       _cons |   17.66975   47.75706     0.37   0.727    -105.0937    140.4332
------------------------------------------------------------------------------

I checked the specification of the model and according to the test it does not have omit variables.However when I check collin I got there is a high correlation. For that the result via OLS cannot take it into account but to compare to other estimator in term of efficiency. if i want to correct the huge correlation then i need to remove that tech variable which is correlated to growth. However, i use ppml and then ivpoisson for correct endogeneity. My question is should I correct the harmful correlation of the benchmark model? Any comment is welcome! thank you in advance . Regards

collin lnintuser lngdp lngdpch lndist lnidist lntariff
(obs=97)

  Collinearity Diagnostics

                        SQRT                   R-
  Variable      VIF     VIF    Tolerance    Squared
----------------------------------------------------
 lnintus       16.11    4.01    0.0621      0.9379
     lngdp      1.14    1.07    0.8768      0.1232
   lngdpch     15.11    3.89    0.0662      0.9338
    lndist      1.18    1.09    0.8467      0.1533
   lnidist      1.10    1.05    0.9056      0.0944
  lntariff      1.86    1.36    0.5371      0.4629
----------------------------------------------------
  Mean VIF      6.08

                           Cond
        Eigenval          Index
---------------------------------
    1     6.1458          1.0000
    2     0.5767          3.2646
    3     0.2048          5.4781
    4     0.0704          9.3449
    5     0.0022         52.3621
    6     0.0001        307.2682
    7     0.0000        541.4443
---------------------------------
 Condition Number       541.4443 
 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
 Det(correlation matrix)    0.0306

[Carlo Lazzaro]

Isabel:
at its face value, the VIF problem referes to -lnintus- only, as Stata omits -lngdpch-.
I would be curious to see what happens if you remove -lnintus-.
Some other points concerning your regression model:
- you have a scant number of observations and your coefficient reflect that feature;
- I would recommend you to use -fvvralist- notation for both categorical variable and interactions creation.

[Isabel Cour]

Dear Carlo,

Thank you very much for your answer. I am trying to use -fvvralist-, but it gave this message,

regress lnamchsac lnintus lngdp lngdpch lndist lnidist i.exporter i.importer i.year

exporter:  string variables may not be used as factor variables r(109);

The scant number of observation is because the sample is small and for developing countries. I can not remove lnintus becuase it is the explicative variables, I control via the other variables. Regards,

[Isabel Cour]

Dear Carlo,

I encode exporter and importer, changing to numerical variables. Then when I run the equation again, it omitted one exporter, one importer and to year, which is right but then when i check -vif-, it gave a very huge collineality. Why F( ) ad Prob are ommitted here? I am working with one importer country and 6 exporter countries, estimating the effect of tech on impo.

regress lnamchsac lnintus lngdp lngdpch lndist i.exporter2 i.importer2 i.year, cluster(dist)
note: 6.exporter2 omitted because of collinearity
note: 1.importer2 omitted because of collinearity
note: 2014.year omitted because of collinearity
note: 2015.year omitted because of collinearity

Linear regression                               Number of obs     =        100
                                                F(4, 5)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.8721
                                                Root MSE          =     1.4311

                                   (Std. Err. adjusted for 6 clusters in dist)
------------------------------------------------------------------------------
             |               Robust
   lnamchsac |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   lnintus  |   10.33298   3.910021     2.64   0.046     .2819487    20.38401
       lngdp |   .0284274   1.245275     0.02   0.983    -3.172655     3.22951
     lngdpch |  -12.51951   5.407564    -2.32   0.068    -26.42009    1.381076
      lndist |   175.8917   136.6446     1.29   0.254    -175.3644    527.1478
             |
   exporter2 |
         BA  |   20.87398   15.70306     1.33   0.241    -19.49201    61.23998
         CL  |  -.9865379   .5896953    -1.67   0.155    -2.502398    .5293221
         CL  |   36.31381   30.45178     1.19   0.287    -41.96497    114.5926
         EU  |   26.85489   23.44419     1.15   0.304    -33.41031     87.1201
         PR  |          0  (omitted)
             |
   importer2 |
        C    |          0  (omitted)
             |
        year |
       1996  |   4.553916   1.332133     3.42   0.019     1.129558    7.978274
       1997  |    6.71773   2.371106     2.83   0.037     .6226067    12.81285
       1998  |   3.874927   2.034063     1.91   0.115    -1.353798    9.103653
       1999  |    .347602   1.372735     0.25   0.810    -3.181125    3.876329
       2000  |  -.3890414   1.409714    -0.28   0.794    -4.012827    3.234744
       2001  |  -.9317118   2.013305    -0.46   0.663    -6.107076    4.243653
       2002  |  -6.600452   3.533016    -1.87   0.121    -15.68236    2.481456
       2003  |  -5.756303   4.268288    -1.35   0.235    -16.72829     5.21568
       2004  |  -5.531035   3.078244    -1.80   0.132    -13.44391    2.381843
       2005  |  -3.803244   2.140584    -1.78   0.136     -9.30579    1.699302
       2006  |   -4.33426   1.976139    -2.19   0.080    -9.414086    .7455656
       2007  |  -3.684837   1.924448    -1.91   0.114    -8.631788    1.262114
       2008  |  -3.934879   2.043277    -1.93   0.112     -9.18729    1.317532
       2009  |  -5.696587   2.047856    -2.78   0.039    -10.96077   -.4324058
       2010  |   -4.40091    2.16478    -2.03   0.098    -9.965653    1.163834
       2011  |  -2.456916   1.169522    -2.10   0.090    -5.463268     .549435
       2012  |  -1.947741   .9714993    -2.00   0.101     -4.44506    .5495772
       2013  |  -.3844076   1.064903    -0.36   0.733    -3.121827    2.353012
       2014  |          0  (omitted)
       2015  |          0  (omitted)
             |
       _cons |  -1382.636   1225.708    -1.13   0.311    -4533.418    1768.145
------------------------------------------------------------------------------

[Carlo Lazzaro]

Isabel:
about missing F and P see -help j_robustsingular-.
Stata tells you exacltly the reason for omitting some predictors: collinearity with other predictors.
High VIF can be read as a sign of model misspecification.
Eventually, I would also check whether it makes sense keeping -i-year- in your regression model via -testparm(i.year)-.