Revealed Preference, Homogeneous Production, and Returns to Scale (Under Review) with Isambert Leunga
We develop a finite-data revealed-preference framework for identifying returns to scale under exact cost minimization. Given observations on outputs, input bundles, and input prices, we characterize the sharp set of homogeneity degrees for which the data are rationalizable by a single time-invariant homogeneous production technology. For any fixed degree of homogeneity (k>0), a power transformation of outputs reduces the rationalizability problem to Varian's constant-returns test. When (k) is unknown, the resulting pairwise restrictions identify the complete set of admissible homogeneity degrees, which may be empty, unbounded, degenerate, or nondegenerate. We further construct the pointwise maximal monotone (k)-homogeneous technology consistent with the data and derive transparent conditions for both point and set identification. The interval characterization yields a sparse falsification result: every rejection of homogeneous cost rationalization is witnessed by at most two pairwise comparisons, providing an economically interpretable certificate of model failure. We further introduce measures of approximate and subset rationalizability that remain informative even when exact rationalization fails. We illustrate the framework using a panel of 361 U.S. manufacturing industries. Because the data do not report the price of capital, we construct it using the Jorgensonian user-cost approach and show that the results are robust to an alternative four-input specification that treats capital as quasi-fixed. Exact stable homogeneous rationalization is systematically rejected over long horizons, whereas shorter subsamples display substantial local consistency. Overall, the proposed framework provides a sharp, nonparametric, and computationally tractable approach to testing, identifying, and diagnosing returns to scale in production technologies without imposing functional-form, substitution, or curvature restrictions.
