Does Wagner's Law Hold for India? Five Versions Reduced to Two, a Proof That Levels Regressions Mostly Compare Trend Growth Rates, and Evidence from 96 Economies, 1960–2025

Wagner's law says that public spending grows faster than national income as an economy develops. It is tested in at least five forms, and studies of India disagree. Using World Bank constant-price data on general government final consumption, GDP and population for 1960 to 2025, I show three things. First, the five versions reduce to two: by the linearity of least squares the Mann slope is the Peacock–Wiseman slope minus one, and the Musgrave slope is the Gupta slope minus one, exactly (to 10⁻¹⁵ in the data); the Goffman slope exceeds the Gupta slope by the regression slope of log population on log income per head, 0.5499 for India. Second, I prove a Frisch–Waugh decomposition: the levels elasticity is a weighted average of the ratio of trend growth rates and the detrended slope, and for India the trend receives weight 0.9873. The levels elasticity of 1.0721 is therefore mostly a statement that real government consumption grew 1.09 times as fast as GDP on trend; the detrended relation is −0.0270. Third, the long-run answer depends on the period. Government consumption grew faster than GDP from 1961 to 1990 (6.58% against 4.09% a year) and slower from 1991 to 2025 (5.22% against 5.92%); the 20-year elasticity fell from 1.920 in 1980 to 0.890 in 2025. Across 96 economies the median 1990–2024 elasticity is 1.008, and 52.1% exceed one.