Re: st: fully modified OLS and dynamic OLS

[Michael Hanson <mshanson@mac.com>]

On Mar 18, 2009, at 6:37 PM, Grant Peter Kabango wrote:

> I would like to estimate using the fully modified OLS (FMOLS) and  
> dynamic OLS (DOLS), and I wish to find out the Stata command for  
> these processes.


On Mar 18, 2009, at 7:01 PM, Martin Weiss wrote:

> -findit- does not return any results. Are these procedures known  
> under any other name?


The short answers are no (to Grant: "Are FM-OLS or DOLS currently  
implemented in Stata?") and no (to Martin: "Are they known by other  
names?").  Note that this request and the corresponding response  
about alternative names reappear on Statalist roughly every year or  
two (and apparently has been more popular recently):

<http://www.stata.com/statalist/archive/2004-08/msg00355.html>
<http://www.stata.com/statalist/archive/2006-05/msg00010.html>
<http://www.stata.com/statalist/archive/2008-01/msg00078.html>
<http://www.stata.com/statalist/archive/2008-04/msg00725.html>
<http://www.stata.com/statalist/archive/2008-08/msg01166.html>


FM-OLS and DOLS are single equation estimators for cointegrated  
relationships.  Given that this is a fairly specialized topic in time  
series analysis, I don't believe they can be found in other  
Stata .ado files under different names.  (Although I would be happy  
to be proven wrong on that point.)

Dynamic OLS is quite easy to implement in Stata, since it just  
involves augmenting a (super-consistent) OLS estimate of the  
cointegrating relationship with leads and lags of the RHS variable.   
For appropriate inference, HAC standard errors must be used.  Below  
is a simple (and very stylized) example.  Note that this example uses  
both -ivreg2- and -freduse-, which are available from SSC.


// Begin example

clear
freduse GDPC96 PCECC96
gen t = qofd(daten)
format t %tq
drop date*
tsset t

gen y = ln(GDPC96)
gen c = ln(PCECC96)

ivreg2 c y L(-4/4)D.y, bw(auto) robust
ivregress 2sls c y L(-4/4)D.y, vce(hac nw opt)

// End example

The coefficient on y in each regression will be the estimate of the  
parameter B in the cointegrating vector [1 -B], such that [c y] [1 - 
B]' ~ I(0).  Note that -ivreg2- will work with Stata 9 or better  
(once installed); -ivregress- was introduced in Stata 10.  They  
should return identical results in the above example.


The FM-OLS estimator is a little more sophisticated, and -- as far as  
I can tell -- no one has contributed a user-written version.  Thus,  
your options are (1) write it yourself (see the references below --  
would be a good exercise to implement in Mata); (2) use a system  
estimator (such as -vec-); or (3) use a different statistical  
package.  (For example, FM-OLS has been implemented in RATS: see  
<http://www.estima.com/procs_perl/fm.src> and <http://www.estima.com/ 
procs_perl/panelfm.src>.  Procedures may also have been written for  
R, but a quick search did not turn up anything.)

Hope this helps.  Perhaps the next time someone looks for the DOLS or  
FM-OLS estimators, they will search the mailing list archive first.

-- Mike


References:

Banerjee, Anindya, et al, "Co-integration, Error-Correction, and the  
Econometric Analysis of Non-Stationary Data," Oxford University  
Press, 1993.

Maddala, G.S. and In-Moo Kim, "Unit Roots, Cointegration, and  
Structural Change," Cambridge University Press, 1998.

Phillips, Peter and Bruce Hansen, "Statistical Inference in  
Instrumental Variables Regression with I(1) Processes," Review of  
Economic Studies, v.57, 1990, pp. 99-125.

Phillips, Peter, "Fully Modified Least Squares and Vector  
Autoregression," Econometrica, v.63 n.5, 1995, pp. 1023-1078.

Stock, James and Mark Watson, "A Simple Estimator of Cointegrating  
Vectors in Higher Order Integrated Systems," Econometrica, v.61 n.4,  
1993, pp. 783-820.

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