Residual-Based Correction Framework for Compression Bias in Economic Indices (SCF-lite Model)

This registration specifies a methodological study proposing and validating a residual-based correction framework for structural compression bias in economic indices. Many economic indices (e.g., CPI, GDP growth, composite indicators) compress high-dimensional economic activity into low-dimensional scalar measures. Such compression introduces structural information loss, distributional distortion, publication lag effects, and procedural friction. Existing research addresses index construction and measurement error but does not provide a general post-construction correction framework for compression bias. This project defines a Structural Correction Framework (SCF-lite) in which an observed index I is corrected via a log-linear operator: log I* = log I + βᵀ z where z = [DL, SV, Lag, Friction] is a feature vector capturing compression-related distortion. The dimensional loss component (DL) is theoretically grounded in conditional entropy H(X|I) and implemented using a statistical proxy: DL = sqrt(CV² + skew² + (kurtosis − 3)²) Structural volatility (SV), lag, and friction are defined using multi-scale volatility ratios, revision and publication delay measures, and revision-process proxies, respectively. Coefficients β are pre-specified using equal weights in the baseline model, with optional later calibration. Validation is conducted in two stages: (1) Synthetic validation using simulated high-dimensional latent states with known compression structure, allowing direct measurement of reconstruction error and correction performance. (2) Empirical demonstration using publicly available CPI time series and revision data, evaluating volatility, revision sensitivity, and shock-period behavior before and after correction. Primary hypotheses: H1: The DL proxy increases monotonically with true compression distortion in synthetic simulations. H2: SCF-lite correction reduces reconstruction RMSE relative to raw compressed indices. H3: In CPI data, corrected indices show improved stability and reduced revision sensitivity during high-distortion periods. All feature definitions, window parameters, and model forms are fixed prior to analysis. This registration establishes the model structure, correction formula, proxy definitions, and validation design before final empirical execution.