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# st: long differencing estimator

 From Islam Abdeljawad To "statalist@hsphsun2.harvard.edu" Subject st: long differencing estimator Date Mon, 3 Oct 2011 03:01:27 -0700 (PDT)

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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