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# st: RE: long differencing estimator

 From "Millimet, Daniel" To "statalist@hsphsun2.harvard.edu" Subject st: RE: long differencing estimator Date Mon, 3 Oct 2011 12:17:58 +0000

```You can do this "by hand" very simply.  Assuming the panel is balanced,

1. tsset the data
2. create the LD for each variable as "gen X=X-L.#X" where # is = T-1
3. estimate the model using ivregress or ivreg2
4. generate the residuals based on parameter estimates
5. re-apply ivregress or ivreg2 with the augmented IV set
6. iterate as much as you want.

****************************************************
Daniel L. Millimet, Professor
Department of Economics
Box 0496
SMU
Dallas, TX 75275-0496
phone: 214.768.3269
fax: 214.768.1821
web: http://faculty.smu.edu/millimet
****************************************************

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Islam Abdeljawad
Sent: Monday, October 03, 2011 5:01 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: long differencing estimator

Dear
statalist

I posted a
question before two days. Here I will repeat and elaborate:

Anyone know
how I can do the long differencing estimator suggested by Hahn, Hausman, and Kuersteiner (2007) (see full reference below) for highly persistent data series using Stata.
The technique uses long differencing instead of first differencing and iterated two-stage least square in estimating persistent dynamic models with short time dimension. The setup for the model

Lit − Lit−k = λ(Lit−1 − Lit−k−1) + δ(Xit−1 − Xit−k−1) + εit− εit−k

or

ΔLit,t−k = λΔLit−1,t−k−1 + δΔXit−1,t−k−1 + u it,t−k.

Hahn et al. (2007)
suggest that Lit−k−1 is a
valid instrument. Using this instrument, we first estimate the equation with two-stage least squares (2SLS) and obtain the initial values of the estimated coefficients λ and δ. Hahn et al. (2007) suggest that the residuals
Lit−1 − λLit−2 − δ Xit−2, . . . , and Lit−k − λLit−k−1 − δXit−k−1 are also valid instruments.
We then use Lit−k−1 and the
residuals as instruments to estimate the equation with 2SLS.
We call this the first
iteration. We then further iterate this estimation. Hahn et al. (2007) suggest that three iterations are often sufficient.

The full
reference is

Hahn, J.; J. Hausman; and G. Kuersteiner. “Long Difference Instrumental Variables Estimation for Dynamic Panel Models with Fixed Effects.”  Journal of Econometrics, 140 (2007), 574–617.

Appreciate

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```