Since in the standard, un-collapsed form each instrumenting variable generates one column for each time
period and lag available to that time period, the number of instruments is quadratic in T. To limit the
instrument count (c.f. subsection 2.6), one can restrict the lag ranges used in generating these instrument
sets. Or one can collapse them; this is non-standard but available in xtabond2.9
In addition, a large instrument collection can overfit endogenous variables. For intuition, consider that in
2SLS, if the number of instruments equals the number of observations, the R2’s of the first-stage regressions
are 1 and the second-stage results match those of (biased) OLS.
Unfortunately, there appears to be little guidance from the literature on how many instruments is “too
many” (Ruud 2000, p. 515), in part because the bias is present to some extent even when instruments are
few. In one simulation of difference GMM on an 8 × 100 panel, Windmeijer (2005) reports that cutting
the instrument count from 28 to 13 reduced the average bias in the two-step estimate of the parameter of
interest by 40%. On the other hand, the average parameter estimate only rose from 0.9810 to 0.9866, against
a true value of 1.000.
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