# st: Prais-Winsten regression: problem with coefficient estimates

 From "Herrnstadt, Evan" To Subject st: Prais-Winsten regression: problem with coefficient estimates Date Wed, 10 Oct 2007 17:38:48 -0400

```I am regressing energy projection errors against GDP projection errors.
Both are measured as percentages and are pretty well bounded by +/- 0.2
(20%).  We choose one prediction length and analyze a time-series of
such projections (1983 projection of 1988, 1984 projection of 1989, 1985
projection of 1990, etc.)

We are running Prais-Winsten regressions to address autocorrelation.
However, every so often we get very large (and completely absurd)
coefficients on either the variable or the constant term.  These do not
arise when we use OLS, though we worry that those estimates would be
biased.  These huge coefficients arise despite the fact that both Does
anyone know of any reason this might occur in a Prais-Winston
regression?  Thanks.

Here is the output from one problematic regression:

tsset trend, yearly

prais pct_error gdp_nom_error, ssesearch

time variable:  trend, . to 0103, but with gaps

Number of gaps in sample:  4
(note: computations for rho restarted at each gap)

Iteration 1:  rho = 0.8944 , criterion =  -.0259697
Iteration 2:  rho = 0.8944 , criterion =  -.0259697
Iteration 3:  rho = 0.8944 , criterion =  -.0259697
Iteration 4:  rho = 0.9282 , criterion =  -.02532865
Iteration 5:  rho = 0.9806 , criterion =  -.024677
Iteration 6:  rho = 0.9806 , criterion =  -.024677
Iteration 7:  rho = 1.0005 , criterion =  -.02401302
Iteration 8:  rho = 1.0005 , criterion =  -.02401302
Iteration 9:  rho = 1.0005 , criterion =  -.02401302
Iteration 10:  rho = 1.0005 , criterion =  -.02401302
Iteration 11:  rho = 1.0005 , criterion =  -.02401302
Iteration 12:  rho = 1.0005 , criterion =  -.02401302
Iteration 13:  rho = 1.0005 , criterion =  -.02401302
Iteration 14:  rho = 1.0005 , criterion =  -.02401302
Iteration 15:  rho = 1.0001 , criterion =  -.02400141
Iteration 16:  rho = 1.0001 , criterion =  -.02400141
Iteration 17:  rho = 1.0001 , criterion =  -.02400141
Iteration 18:  rho = 1.0000 , criterion =  -.02399868
Iteration 19:  rho = 1.0000 , criterion =  -.02399868
Iteration 20:  rho = 1.0000 , criterion =  -.02399868
Iteration 21:  rho = 1.0000 , criterion =  -.02399868
Iteration 22:  rho = 1.0000 , criterion =  -.02399868
Iteration 23:  rho = 1.0000 , criterion =  -.02399843
Iteration 24:  rho = 1.0000 , criterion =  -.02399843
Iteration 25:  rho = 1.0000 , criterion =  -.02399843
Iteration 26:  rho = 1.0000 , criterion =  -.02399843
Iteration 27:  rho = 1.0000 , criterion =  -.02399843
Iteration 28:  rho = 1.0000 , criterion =  -.02399841
Iteration 29:  rho = 1.0000 , criterion =  -.02399839

Prais-Winsten AR(1) regression -- SSE search estimates

Source |       SS       df       MS              Number of obs =
9
-------------+------------------------------           F(  1,     7) =
0.29
Model |  .000997375     1  .000997375           Prob > F      =
0.6064
Residual |  .023998394     7  .003428342           R-squared     =
0.0399
-0.0973
Total |  .024995769     8  .003124471           Root MSE      =
.05855

------------------------------------------------------------------------
------
pct_error |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
gdp_nom_er~r |   .2482773   .4603095     0.54   0.606    -.8401817
1.336736
_cons |   28857.82   72455.19     0.40   0.702    -142471.5
200187.1
-------------+----------------------------------------------------------
------
rho |          1
------------------------------------------------------------------------
------
Durbin-Watson statistic (original)    0.542795
Durbin-Watson statistic (transformed) 1.356947

reg pct_error gdp_nom_error, robust

Linear regression                                      Number of obs =
14
F(  1,    12) =
13.95
Prob > F      =
0.0028
R-squared     =
0.3418
Root MSE      =
.08149

------------------------------------------------------------------------
------
|               Robust
pct_error |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
gdp_nom_er~r |   1.297929    .347506     3.73   0.003     .5407782
2.055079
_cons |   .0729358   .0182218     4.00   0.002     .0332339
.1126377
------------------------------------------------------------------------
------

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