20220602-IMF-Systematizing_Macroframework_Forecasting_High-Dimensional_Conditional_Forecasting_with_Accounting_Identities_25页_1mb

Summary: Systematizing Macroframework Forecasting: High-Dimensional Conditional Forecasting with Accounting Identities

Authors: Sakai Ando, Taehoon Kim (IMF Working Paper WP/22/110)

Key Contribution: Introduces a method to systematically forecast large macroeconomic frameworks, especially those constrained by accounting identities, using machine learning.

Problem Addressed

• Forecasting entire macroeconomic frameworks is challenging. Forecasts often rely on partial information, and reconciling forecasts to satisfy accounting constraints is difficult, requiring manual iteration and risking errors.

Proposed Method

1. Step 1: High-Dimensional Conditional Forecasting: Use machine learning (Elastic Net regression) to forecast individual unknown variables based on known variables (provided by forecasters) and historical data. Time-Series Cross-Validation is used. (Adapted from literature on high-dimensional forecasting, suitable when time series length < number of variables).
2. Step 2: Forecast Reconciliation: Project the Step 1 forecasts onto the space defined by the accounting identities. This ensures the final forecasts are internally consistent. For affine identities, a closed-form solution exists, enabling handling of large numbers of variables. This extends methods like Reconciliation for Hierarchical Time Series to incorporate conditional forecasts from Step 1.

Key Features

• Integration: Combines probabilistic forecasting (Elastic Net) with reconciliation techniques.
• Handling Constraints: Explicitly accounts for linear (affine) accounting constraints.
• Scalability: Capable of managing many variables due to the closed-form reconciliation approach.
• Automation: Automates the process, reducing manual effort and potential inconsistency cascades.
• Flexibility: Can incorporate various transformations (log-differences, etc.) for different variables.

Empirical Application (France & Seychelles)

• Applied the method to forecast components of the French GDP expenditure approach using known variables (GDP, fiscal, current account).
• Compared it to WEO forecasts using historical data and multiple past vintages (2016-2020).
• Results: The new method generated significantly lower root mean squared forecast errors (around 20% improvement on average) for unknown variables.

Caveats

• Relys on historical correlation, potentially failing if the future differs significantly from the past (Lucas critique).
• Forecast accuracy depends on the quality of the provided known variable forecasts.
• Variables with weak independent information should ideally not be forced into known status if input inaccuracies could bias unknown forecasts.
• Requires affine accounting identities for the closed-form solution.

Significance

Provides a more disciplined, automated, and accurate approach to constructing internally consistent macroeconomic forecasts for policy analysis and planning.