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Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models

Victor ChernozhukovIv\'an Fern\'andez-ValChen HuangWeining Wang
Feb 2024
The Arellano-Bond estimator can be severely biased when the time series dimension of the data, $T$, is long. The source of the bias is the large degree of overidentification. We propose a simple two-step approach to deal with this problem. The first step applies LASSO to the cross-section data at each time period to select the most informative moment conditions. The second step applies a linear instrumental variable estimator using the instruments constructed from the moment conditions selected in the first step. The two stages are combined using sample-splitting and cross-fitting to avoid overfitting bias. Using asymptotic sequences where the two dimensions of the panel grow with the sample size, we show that the new estimator is consistent and asymptotically normal under much weaker conditions on $T$ than the Arellano-Bond estimator. Our theory covers models with high dimensional covariates including multiple lags of the dependent variable, which are common in modern applications. We illustrate our approach with an application to the short and long-term effects of the opening of K-12 schools and other policies on the spread of COVID-19 using weekly county-level panel data from the United States.
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