Forecasting Public Expenditure Using LSTMs: A Multi-Task Learning Approach for Volatile Data

Accurate forecasting of public expenditures is critical for effective budget planning. This paper introduces a multi-task Long Short-Term Memory (MTL-LSTM) model for predicting public expenditures within the welfare sector with the time series of all 16 federal states in Germany. The model addresses challenges such as strong seasonality, structural reforms, and limited data availability. A monthly standardization technique is proposed to improve LSTM performance under intra-year volatility. For uncertainty quantification of the LSTM predictions Monte Carlo Dropout and the Winkler Score are used. The forecasting performance of single-task and multi-task LSTM models is evaluated against statistical baselines, including Holt-Winters Exponential Smoothing, SARIMA, and SARIMAX. Results show that (MTL-) LSTM models outperform traditional approaches in annual forecasts, independently of base or shock year, while Holt-Winters Exponential Smoothing remains more robust for monthly volatility. The findings demonstrate the value of deep learning in real-world government budget planning scenarios.