Difference Test for Specification Error in Regression
-----------------------------------------------------

AUTHOR:   Richard Goldstein, Qualitas
SUPPORT:  Written communication only, EMAIL goldst@@harvarda.bitnet
	  or 37 Kirkwood Road, Brighton MA 02135.

               ^pswdiff^ varlist [^in^ range] [^if^ exp]

^pswdiff^ is a test for general (i.e., non-specific) specification error in a
standard linear regression; it is implemented as a test for omitted variables,
via added variables as a function of lags and leads of the included right-hand-
side variables.  ^DO NOT^ include a constant, or seasonal dummies, or polynomial
terms in your model; do not include a lagged version of the left-hand-side var-
iable on the right-hand-side.  A version of this test including a lagged 
dependent variable is provided in the citation below.

The reported regression itself is of little (NO) interest; what is of interest
is the joint test of significance reported after the regression:  if signifi-
cant, you have left out at least one important variable or you have the wrong 
functional form; if not significant, then you may not have one of these 
problems.

The PSW difference test for specification error (see R. Davidson, L. Godfrey,
and MacKinnon, JG (1985), "A Simplified Version of the Differencing Test",
^International Economic Review^, 26, pp. 639-47) is a general test for
model misspecification--applicable to time-series data.  It is equivalent to a
test for omitted variables, and is accomplished via adding the omitted
variables which are defined as the sum of the lagged and leaded values of the
variables.

Example:
--------

 . ^use auto^
 (1978 Automobile Data)

 . ^pswdiff mpg weight weightsq^
 (2 missing values generated)
 (1 change made)
 (1 change made)
 (2 missing values generated)
 (1 change made)
 (1 change made)
  (obs=74)

   Source |     SS         df       MS           Number of obs =      74
 ---------+------------------------------        F(  4,    70) =  458.15
    Model |  34683.1966     4  8670.79916        Prob > F      =  0.0000
 Residual |  1324.80338    70  18.9257625        R-square      =  0.9632
 ---------+------------------------------        Adj R-square  =  0.9611
    Total |    36008.00    74  486.594595        Root MSE      =  4.3504
 
 Variable |  Coefficient    Std. Error       t    Prob > |t|        Mean
 ---------+--------------------------------------------------------------
      mpg |                                                      21.2973
 ---------+--------------------------------------------------------------
   weight |     .0070224      .0030402     2.310     0.024      3019.459
 weightsq |    -1.99e-06      5.13e-07    -3.875     0.000       9713003
    diff1 |     .0068591      .0015765     4.351     0.000      5966.757
    diff2 |    -1.13e-06      2.79e-07    -4.036     0.000      1.92e+07
 ---------+--------------------------------------------------------------

  ( 1)  diff1 = 0.0
  ( 2)  diff2 = 0.0

        F(  2,    70) =    9.63
             Prob > F =    0.0002

Clearly the results are highly statistically significant and something is
wrong with our specification of the model.  If we were actually analyzing this
we would next try to find out what specifically is wrong and then do something
about it.