This paper develops a non-monotonic theoretical relationship between public spending and economic growth in a neoclassical framework. The model identifies the size of government and the composition of government spending which maximize the rate of growth and the long run level of per capita income. Transitional dynamics to the steady state can be rather long. This reinforces the need for short-medium term analysis such as in this work. Given the size of the government, different allocations of public resources lead to different growth rates in the transition dynamics, depending on their elasticity. We argue that neglecting the hypothesis of non-monotonicity and the different impact different kinds of public spending have on economic performance results in models which suffer from mis-specification. Traditional linear regression analysis may thus be biased.