Neural Networks in Economics

The chapters of this dissertation explore the theoretical and empirical potential of neural networks and deep learning as estimation techniques in economics. The first chapter provides a novel approximation result for two hidden layer neural networks that makes clear the trade-off between width and depth. I leverage this result to provide consistency and $o_p(n^{-1/4})$ convergence rates for this estimator and demonstrate its flexibility in finite samples. In addition, I introduce a new algorithm called cross-training that allows construction of asymptotic confidence intervals for linear functionals. In the second chapter I provide a new neural network designed for a panel data setting with a common index. I allow for unobserved heterogeneity to enter in the form of additive cross-sectional fixed effects and provide a correction for the incidental parameter bias by re-centering the score. I apply this estimator to the demand for cigarettes in the United States. In the third and final chapter I explore the role of autoencoders as a dimensionality reduction technique when outcomes are binary. The autoencoder outperforms other dimensionality reduction techniques, like principal components analysis, in uncovering latent choice probabilities. This estimator is applied in a consumer segmentation exercise