This paper addresses the issue of estimating structural graph/network models on data from a single graph/network. While there exist methods for estimating structural models on many independent and identically distributed (iid) graphs/networks (Banerjee et. al., 2013), there are limited general-purpose algorithms to fit structural models on a given single network. With most graphs/networks, the likelihood function is both intractable, and graphs/networks can't easily be split into many iid components, so traditional methods like maximum likelihood and method of moments will not work. This study proposes an algorithm adapted from Deep Learning, dubbed Sequential Neural Posterior Estimation (SNPE), for network analysis. SNPE is a simulation-based estimator that can estimate likelihoods without a likelihood function and does not require a cross-section of iid samples. These two facts allow for general-purpose estimation of structural network/graph models. SNPE can recover calibrated parameter values that generate a ground truth graph/network from a structural model. Additionally, the algorithm is applied to estimate the homophily model (Bramoulle et. al. 2012) on empirical data which was not attempted in the original paper. This study presents a promising algorithm for fitting structural models on a single network, opening avenues for future research in network estimation.
Economic forecasting is both an essential exercise and a way to discipline the construction of models. We show that pooling data from many countries in a cross-sectional dimension to macroeconomic data can statistically significantly improve the generalization ability of structural, reduced-from, and machine learning models in forecasting GDP. This procedure reduces root mean squared error (RMSE) by 12 percent across horizons for certain reduced form models and by 24 percent across horizons for structural DSGE models. A central result in this paper is that, in contrast with theory, DSGE or reduced from models forecast better, or at least as well, when estimated on more recent time series across a cross-section of countries rather than data that extends further back in time but only from the country of interest. Finally, given the comparative advantage of “nonparametric” Machine Learning forecasting models in a data-rich regime, we demonstrate that our Recurrent Neural Network (RNN) model and Automated Machine Learning (AutoML) approach outperform all baseline Economic models and even the Survey of Professional Forecasters at long term horizons when using pooled macroeconomic data. Robustness checks indicate that machine learning techniques are reproducible, numerically stable, and generalize across models.