Public Expenditure Composition and Economic Growth: Optimal Adjustment by Using Gradient Method

Previous researches studied how the components of fiscal spending affect the economic growth but did not explicitly enquire into how to adjust the components in order to achieve the highest rate of economic growth starting from the present shares of components. We investigate how to determine the optimal adjustment by introducing a gradient method which explicitly takes account for the adjustment cost and incorporates the constraint that shares of components are summed up to one. The resulting optimal adjustment shares are proportional to the deviations from the average over elements of a gradient vector and independent from the choice of regression equations. The optimal adjustment share is completely estimated by using the linear regression with any choice of omitted variable if the adjustment cost is given. The result is free from multicollinearity problem but is considering all adjustment costs unlike most of previous researches. The paper also provides an illustrative example taken from the annual panel data for the Japanese prefectural governments.