Title

xtdynestimb ablasso -- Arellano-Bond LASSO estimator for dynamic
linear panel models (Chernozhukov, Fernandez-Val, Huang & Wang 2024)

(part of xtdynestimb. See also dd,
csdgmm,
postestimation.)

Syntax

xtdynestimb ablasso depvar [indepvars] [if] [in]
[, options]

Model
lags(#) autoregressive order p; default lags(1)

Instrument selection
lambda(#) LASSO penalty; default is a data-driven plug-in
(# < 0)

cons(#) constant in the plug-in penalty; default cons(1.1)

Cross-fitting (AB-LASSO-SS)
crossfit turn on sample-splitting / cross-fitting

kfold(#) number of folds; default kfold(2)

nsplits(#) number of random splits to average over; default
nsplits(1)

seed(#) random-number seed for reproducible splits

Reporting
graph coefficient plot

graphname(name) name for the graph

notable suppress the output table

level(#) confidence level; default level(95)

Description

xtdynestimb ablasso implements the Arellano-Bond LASSO (AB-LASSO) estimator
of Chernozhukov, Fernandez-Val, Huang & Wang (2024) for dynamic linear panels in
which the time dimension T is moderately long. When T is large the
number of Arellano-Bond moment conditions grows like T^2, and the
resulting overidentification biases the standard GMM estimator (the bias is of
order T/N). AB-LASSO removes this bias by selecting, period by period, only
the most informative moment conditions.

This estimator is the long-T complement to dd and
csdgmm, which target short panels.

Method

The model is first-differenced and demeaned over the cross-section (to remove the
time effects). Then, for each period t:

1. LASSO selection. The differenced endogenous regressors
(Dy_i,t-1, ..., Dy_i,t-p) are regressed by LASSO on the candidate
instruments (the lagged levels y_i,1, ..., y_i,t-2). The fitted values
are the estimated optimal instruments. Under weak time-series dependence the
effective number of selected instruments is very small relative to N.

2. Instrumental-variables estimation. The parameters are estimated by
IV pooling the optimal instruments across all periods. The variance is
cluster-robust on the panel unit.

With crossfit (the AB-LASSO-SS estimator), the cross-section is split into
folds; the LASSO is fit on the auxiliary folds and used to predict the held-out
fold, which removes the over-fitting bias from re-using the same observations for
selection and estimation. nsplits() averages over several random splits so
the estimate does not depend on an arbitrary partition; the reported variance
adds the between-split variance to the average within-split variance.

The LASSO penalty is, by default, the data-driven plug-in level (a
Belloni-Chen-Chernozhukov-Hansen-type rule); supply lambda() to fix it.

Options

lags(#) sets the autoregressive order. The empirical illustration in
the source paper uses four lags; long panels typically support lags(2) or
more.

lambda(#) fixes the LASSO penalty (on the standardized design). A
negative value (the default) requests the plug-in penalty; cons(#) scales
it.

crossfit, kfold(#), nsplits(#), seed(#) control
the sample-splitting / cross-fitting. For a stable answer use, e.g.,
crossfit kfold(5) nsplits(5) seed(...).

Note. AB-LASSO needs a reasonably long, (near-)balanced panel: each period's
candidate instrument set must be observed for enough units. Very short or heavily
unbalanced panels may yield too few usable periods.

Stored results

In addition to the common e() results:

Scalars

e(Tmax) maximum number of time periods

e(n_selavg) average number of selected instruments per period

e(lambda) LASSO penalty (negative = plug-in)

Macros

e(crossfit) cross-fitting configuration

e(vce) cluster-robust (panel)

Examples

. webuse abdata

. xtset id year

Plain AB-LASSO

. xtdynestimb ablasso n, lags(1)

AB-LASSO-SS with 5-fold cross-fitting averaged over 5 splits

. xtdynestimb ablasso n, lags(2) crossfit kfold(5) nsplits(5) seed(123) graph

Compare with the (long-T-biased) Arellano-Bond estimator

. xtdynestimb dd n, lags(2) variant(difference)

. xtdynestimb ablasso n, lags(2) crossfit kfold(5) seed(1)

References

Chernozhukov, V., I. Fernandez-Val, C. Huang, and W. Wang. 2024.
Arellano-Bond LASSO estimator for dynamic linear panel models. cemmap working
paper CWP09/24.

Belloni, A., D. Chen, V. Chernozhukov, and C. Hansen. 2012. Sparse models
and methods for optimal instruments with an application to eminent domain.
Econometrica 80: 2369-2429.

Chernozhukov, V., et al. 2018. Double/debiased machine learning for
treatment and structural parameters. Econometrics Journal 21: C1-C68.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane