Is India's Growth Constrained by Its Balance of Payments? Thirlwall's Law on 1961–2025 Data, and Why the Usual Test Is Close to an Identity

Thirlwall's law says that a country's long-run growth rate cannot exceed its export growth divided by its income elasticity of imports. I test it for India with World Bank constant-price data for 1960–2025. Growth-rate regressions give an import elasticity of 0.890 (standard error 0.498) for 1961–2025 and 1.313 (0.575) for 1991–2025. The implied constrained growth rate for 1991–2025 is 7.19% a year against actual growth of 5.92%, but its 95% Fieller interval runs from 3.42% to 51.18%; for three of the five periods studied the interval is unbounded. Across 50 rolling 15-year windows, actual and constrained growth are uncorrelated (0.038) and differ by a median of 11.78 percentage points. I prove three results. First, a Fieller interval for the constrained rate is bounded only if the elasticity is significantly different from zero. Second, if the elasticity is measured as the ratio of mean import growth to mean output growth, the law reduces to the statement that export and import growth are equal on average, which is an accounting regularity rather than a test. Third, the levels regression of log imports on log GDP converges to the ratio of trend growth rates even when imports and output are unrelated apart from their trends; for India the levels slope is 1.615 and the trend ratio 1.609, and the Engle-Granger test does not find cointegration. The arithmetic of the constraint is still useful: with an elasticity of 1.5, sustained 7% growth needs exports to grow at 10.5% a year in real terms.