Specification, Heterogeneity and Functional Form in the Determinants of Small-Firm Profitability

Studies of small-firm profitability estimate financial structure as the focal regressor and treat cost composition as an unexamined control. This paper reverses the emphasis and places both blocks in one equation, estimated on 91,756 firm-year observations covering 14,913 unlisted Italian firms across three regulatory regimes. Three methods interrogate different assumptions on the same sample: panel estimation across fourteen specifications, unsupervised partitioning selected on eleven validity criteria, and machine-learning regression applied to the same firm-demeaned data. The capitalisation coefficient is not identified. It moves from +0.177 under two-way fixed effects to between −0.12 and −0.28 under five instrument sets, all of which fail because profitability persists at 0.271, so any lagged financial ratio embeds past profit. The labour-share coefficient is stable across estimators, groups and functional forms, and the paper tests whether that stability is arithmetic, since return on assets and the labour share are consecutive lines of one statement. It is not: value added over total assets varies by a factor of 2.8 across the four operating archetypes recovered from the data, while the coefficient varies by 1.07. The accounting identity explains part of the magnitude and none of the stability.