A Mathematical Theory of Adaptive Fiscal Policy Under Resource Revenue Volatility for Nigerian Sub-National Governments

Sub-national governments in Nigeria's oil-dependent federation face extreme fiscal volatility driven by fluctuations in federal statutory allocation, which is heavily conditioned on global crude oil prices and production volumes. The absence of a rigorous mathematical theory of adaptive fiscal policy for resource-revenue-dependent sub-national governments constitutes a critical gap in Nigerian public finance and mathematical economics literature. This dissertation develops an original theoretical framework for adaptive fiscal policy design under resource revenue volatility for Nigerian state governments, integrating stochastic control theory, fiscal multiplier analysis, and a political economy model of expenditure rigidity. The first theoretical contribution is a stochastic dynamic programming model of the state government's intertemporal budget problem, with oil revenue modelled as a two-state Markov-switching process estimated from federal allocation data for 1999 to 2023. An original sufficient condition for the optimality of a countercyclical buffer fund rule is derived, showing that the optimal fund accumulation boundary is a function of the variance of the oil price process and the fiscal multiplier differential between capital and recurrent expenditure. The second contribution extends the framework to incorporate political economy constraints modelled as restrictions on the admissible control set, proving that political rigidity in wage bill adjustment reduces the welfare gain from the optimal buffer fund by up to 41 percent. Application to cross-state panel data confirms the theoretical predictions regarding optimal buffer fund accumulation behaviour. Keywords: adaptive fiscal policy, stochastic control, resource revenue volatility, Nigerian federalism, fiscal buffer fund.