Does India Have Baumol's Cost Disease? Relative Prices and Productivity Gaps Between Industry and Services in India and 95 Economies, 1991-2023, with an Exact Decomposition and a Measurement-Error Bound

Baumol's cost disease predicts that the relative price of services rises one for one with the gap between productivity growth in the progressive sector and in services. I derive an exact identity for the growth of the services to industry relative price: it equals the industry minus services labour productivity gap plus the growth of nominal value added per worker in services relative to industry. The strict Baumol model sets the second term to zero, so the cross-country slope of relative price growth on the productivity gap equals one plus the slope of the residual term, exactly. Because measured real output enters both the price and the productivity gap, classical error in real output pushes the slope towards one; I prove that the observed slope is then a weighted average of the true slope and one, so an observed slope below one is an upper bound on the true slope. Using World Bank value added and employment data for 95 economies over 1991 to 2023, the slope is 0.405 (robust standard error 0.091; Theil-Sen 0.452), well below one. India is an outlier in direction: its services labour productivity grew 1.48 points a year faster than industry's, the reverse of Baumol's premise, while the services relative price was almost unchanged (minus 0.04 points a year). Services' share of nominal value added in industry plus services rose from 58.8% to 65.1% and their constant-price share from 57.8% to 64.4%, so in India the services share grew through volume, not price.