A Fuzzy ARDL Model for Estimating the Dynamic Relationship between Government Revenues and Fiscal Balance

The relationship between government revenues and the fiscal balance represents a central pillar in the analysis of fiscal sustainability. However, its modeling faces a fundamental challenge in the form of structural uncertainty, which is not captured by point estimates in traditional models such as ARDL, as these models assume structural stability that is inconsistent with the nature of rentier economies. The current study aims to develop a fuzzy framework by constructing a Fuzzy Autoregressive Distributed Lag (FARDL) model. This is achieved through integrating the Autoregressive Distributed Lag (ARDL) approach with fuzzy logic theory, thereby enabling the incorporation of uncertainty into the inherent structure of the economic relationship rather than confining it to the stochastic error term. The fuzzy parameters are estimated using a Quadratic Programming (QP) algorithm, and the proposed model is empirically applied to quarterly data for the Iraqi economy over the period (2013-2025). The results provide evidence of a long-run equilibrium relationship between government revenues and the fiscal balance, alongside a persistent structural tendency toward fiscal deficits. Government revenues are shown to have a positive impact on the fiscal balance, however, this impact is uncertain due to revenue uncertainty and resource efficiency. The results of stability tests reveal the dynamic stability of the model, suggesting the existence of a self-equilibrating mechanism. Additionally, the difference between the ARDL and FARDL models shows a descriptive superiority of the fuzzy model in terms of forecasting performance (in-sample and out-sample) with statistically equivalent predictive efficiency. At the same time, the FARDL model offers a more flexible representation with the possibility of interval estimates and multiple scenarios, thus improving the analysis of fiscal sustainability under structural uncertainty.