Such ideas have been formalised in the endogenous growth literature as a non-monotonic relationship between growth and the increasingly distortionary effect of the rising tax rates which are required to fund ever larger government expenditure. In one such model, due to Robert Barro, when government is relatively small growth rises with increases in productive government services, as the positive effects of more public goods dominates, but beyond some critical point the disincentive effects of higher taxes on savings and investment reduce the growth rate. If the non-linear hypothesis is valid and the effect of government spending on long-run economic growth does vary with its size this would offer clearer guidelines on the appropriate fiscal policy prescription for a country of a particular government size. Furthermore, implicit in the non-linear hypothesis is the existence of some optimal size of government which would maximise economic growth.
There is a new paper - The Effect of Government Spending on Economic Growth: Testing the Non-Linear Hypothesis by Tamoya Christie - in the Bulletin of Economic Research which examines the relationship between government size and long-run economic growth. The paper explicitly accounts for the likelihood of a non-linear effect. It contributes to the literature in a number of ways.
First, in terms of methodology, the paper makes improvements to previous empirical studies by applying threshold analysis (Hansen, 2000) to a panel of countries. This technique has been widely used as the preferred method to identify threshold effects (Khan and Senhadji, 2001; Adam and Bevan, 2005; Chen and Lee, 2005; Falvey et al., 2006; Haque and Kneller, 2009), particularly when the variable of interest is observable, but the position of the threshold is not known. The methodology uses a sample-splitting framework and follows an objective strategy for identifying and testing changes in the slope. One important advantage of threshold analysis is that it avoids the ad hoc, subjective pre-selection of threshold values – a major critique of previous studies. In addition, the generalized method of moments (GMM) dynamic panel technique is applied to address potential endogeneity of government expenditure, which is measured as a share of GDP. Second, with respect to data, the study employs an updated dataset with a broad cross-section of countries over a long time span. Pulling data from the IMF's Government Finance Statistics (GFS), the sample contains 136 countries over the period 1971–2005. Most important, this data source offers a more comprehensive measure of government size by using total government expenditure (excluding interest payments) as opposed to government consumption expenditure as the proxy. The consumption measure, though widely used in empirical studies, does not include public capital formation and so cannot fully capture the productivity-enhancing effects of government services. Moreover, the GFS data contain sectoral decompositions of government spending, which facilitates isolating productive elements of government spending from the total.
Likely the most interesting result of the paper is that it finds evidence in support of Barro's non-linear hypothesis. For total government spending above 33 percent of GDP, there is a strong negative effect on growth. However for governments of a size less than this level the negative effects are much smaller and even becomes positive when productive government spending is singled out. The paper's findings also suggest that the level of economic development and the quality of government present additional sources of potential non-linearities.