Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models

The Arellano-Bond estimator is a fundamental method for dynamic panel data models, which is widely used in practice. However, the estimator is severely biased when the data's time series dimension $T$ is long due to the large degree of overidentification. We propose a simple two-step approach to remove the bias. First, apply LASSO to the cross-section data at each time period to select the most informative moment conditions, using lagged values of suitable covariates. Second, apply a linear instrumental variable estimator using the instruments constructed from the selected moment conditions. Combine the two stages using cross-fitted generalized method of moments to avoid overfitting bias. Under weak dependence of time series we show the new estimator is consistent and asymptotically normal under much weaker conditions on the growth of $T$ than the Arellano-Bond estimator. Our theory covers models with high dimensional covariates, including multiple lags of the dependent variable, common in modern applications. We illustrate our approach by applying it to weekly county-level panel data from the United States to study the short and long-term effects of opening K-12 schools and other mitigation policies on COVID-19's spread.