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Theoretical and empirical literature suggest that public expenditure plays very important role in economic growth, especially in the developing countries. Available statistics show that Nigeria's 5-year average annual real public expenditure/GDP ratio grew during the greater part of the study period 1981-2015, while the 5-year average annual real GDP growth and real GDP per capita growth rates are positive during the same study period, except for 1981-1985 and 1986-1990, respectively. The incidence of poverty, however, maintained upward movement, except for 2006-2010. The foregoing interactions have been seldom, the focus of empirical studies in Nigeria. This study examines the effects of public expenditure on economic growth and poverty reduction in Nigeria from 1981-2015, using variants of two models and simulation exercise: augmented Solow growth model and growth-poverty model. Real public expenditure/GDP ratio is used as the policy variable and the simulation duration is for 5-years, 2016-2020. We use the autoregressive distributed lag (ARDL) bounds testing procedure by Pesaran et al. (2001) to estimate the two models, given that the annual data used for the models' estimations were integrated of order I(1) and I(0) and small sample size. The results from the two models confirmed that public expenditure increases economic growth, though not significant, while economic growth does not reduce poverty. The same findings are confirmed through the simulation exercise. We, however, offer measures that would ensure growth and poverty reduction in Nigeria; public expenditure switch that encourages more investments in capital public expenditure, social sector public expenditure and private capital investment.