Local Public Expenditure with Piecewise-Linear Nonconvex Budget Constraints

The author analyses local authority expenditure decisions under the Block Grant system, that is, the grant distribution scheme that was in place in Britain from 1981 to 1990. The Block Grant system creates a piecewise-linear, and potentially nonconvex, budget constraint. As the choice of segment is endogenous—cither as a result of unobserved preference heterogeneity or as a result of random optimisation error—a demand function for local public expenditure cannot be consistently estimated by ordinary least squares (OLS). Instead, a two-error maximum likelihood (ML) estimation procedure is used. The results show a positive income effect and a negative price effect, both of high significance. The OLS estimate of the price coefficient is underestimated relative to its ML counterpart—because of spurious positive correlation between expenditure and price—but the OLS estimate of the income coefficient does not show a substantial bias. The two-error ML estimation results show significant evidence of unobserved preference heterogeneity and some weaker evidence of random optimisation error.