Hello Declan:

One way to think about this is as follows.  Suppose that you 
hypothesise an underlying VAR(p) dgp for the m-vector series as:

P(L)y_t = e_t
 
where P(L) is a pth order lag polynomial.  Now, let y_t be a 
demeaned/detrended/de any deterministic terms (e.g., outliers, 
structural breaks etc), and z_t be the original vector containing the 
levels of the series; i.e., 

y_t = z_t - mu_t

where mu_t = a+bt+  other deterministic terms

and a, b are parameters etc.  Suppose mu_t=a+bt, a commonly 
selected process for the deterministic terms.  Unscrambling, leads 
to the following levels VAR:

z_t = mu*+b*t+sum (i=1 to p)B_i x z_(t-i) +e_t

where mu*=-PIxa+Qxb, b*=-PIxb, Q=sum (i=1 to p) ixB_i, where PI 
is the usual potentially reduced rank matrix that informs us about 
the number of cointegrating vectors.

Now, assuming that z_t (and y_t) has a unit root; i.e., the original 
dgp can be decomposed as:

(1-L)P1(L)y_t=e_t

where P1 is a (p-1) lag polynomial.  Unscrambling this leads to the 
following VECM(p-1):

Dz_t=Qxb + PI(z_(t-1)-a-bt)+sum (i=1 to p-1) GAM_i x Dz_(t-1) +e_t

where D is the first difference operator.  This form tells you exactly 
where to put the constants when using the Engle-Granger approach 
or Johansen's approach.  The former is working with the term:

PI(z_(t-1)-a-bt)

Assuming a normalization, and writing at time t, rather than time (t-
1), this can be written as:

z1_t = a*+b*t+c_1xz2_t+...+c_(m-1)xzm_t+u_t

where u_t is the error correction term.  So, the questions as to 
where to put the "constant", or, indeed, any other deterministic 
terms, depends on what assumptions you want to make about the 
fundamental dgp.

Hope that helps.

Judith


 




On 11 Jul 2005 at 11:02, O'Connor, Declan wrote: 

Hi all,

I would like to use the Engle-Granger 2 step approach to test for
cointegration. My question is as follows. Where do I place the
constant term. Does it appear in step 1 or 2. I have read a numer of
papers and it appears in equation 1 some of the time and equation 2
other times. There are instances where it appears in both 1 and 2. 
Any
advice will be appreciated.

Thanks Declan