Generating density nowcasts for U.S. GDP growth with deep learning: Bayes by Backprop and Monte Carlo dropout

TL;DR

The paper tackles GDP nowcasting with uncertainty by introducing density-nowcasting methods for neural networks. It adapts Bayes by Backprop and Monte Carlo dropout to a 1D CNN framework trained on real-time FRED-MD indicators, enabling predictive densities rather than mere point forecasts. Empirically, both methods outperform a naive benchmark and, in many settings, the standard dynamic factor model, providing density nowcasts that adjust in mean, variance, and skew—particularly during crises such as the COVID period. The work demonstrates that neural networks, when equipped with principled uncertainty mechanisms, can be a competitive and policy-relevant alternative to classical time-series approaches for macroeconomic nowcasting.

Abstract

Recent results in the literature indicate that artificial neural networks (ANNs) can outperform the dynamic factor model (DFM) in terms of the accuracy of GDP nowcasts. Compared to the DFM, the performance advantage of these highly flexible, nonlinear estimators is particularly evident in periods of recessions and structural breaks. From the perspective of policy-makers, however, nowcasts are the most useful when they are conveyed with uncertainty attached to them. While the DFM and other classical time series approaches analytically derive the predictive (conditional) distribution for GDP growth, ANNs can only produce point nowcasts based on their default training procedure (backpropagation). To fill this gap, first in the literature, we adapt two different deep learning algorithms that enable ANNs to generate density nowcasts for U.S. GDP growth: Bayes by Backprop and Monte Carlo dropout. The accuracy of point nowcasts, defined as the mean of the empirical predictive distribution, is evaluated relative to a naive constant growth model for GDP and a benchmark DFM specification. Using a 1D CNN as the underlying ANN architecture, both algorithms outperform those benchmarks during the evaluation period (2012:Q1 -- 2022:Q4). Furthermore, both algorithms are able to dynamically adjust the location (mean), scale (variance), and shape (skew) of the empirical predictive distribution. The results indicate that both Bayes by Backprop and Monte Carlo dropout can effectively augment the scope and functionality of ANNs, rendering them a fully compatible and competitive alternative for classical time series approaches.

Figures (16)

• Figure 1: The percent change (relative to the preceding period) of the US Gross Domestic Product. Source: Federal Reserve Economic Data (FRED).
• Figure 2: Real personal income (RPI). Source: FRED-MD.
• Figure 3: Time series used in the course of dynamic factors analysis. Source: Own calculations based on FRED-MD.
• Figure 4: Empirical distribution of the estimated parameters (weights and biases) for the bottleneck (encoder) layer in the 1D CNN. Source: Own editing based on FRED-MD.
• Figure 5: Estimation of the DFM specification given by (\ref{['eq:dfm_measurement']})--(\ref{['eq:dfm_factor']}): Full-sample filtered estimates of one unobserved common factor ($f_t$). Source: Own calculation based on FRED-MD.