Stability and determinants of the public debt-to-GDP ratio: an Input Output – Stock Flow Consistent approach

The paper develops a dynamic Input Output - Stock Flow consistent model based on the Supermultiplier approach. This framework integrates the dimension of output determination with the system of relative prices. Through this model, we define the determinants of the public debt-to-GDP ratio and the conditions for its stability. The main results of the research show that: i) Given the interest rate, the saving rate, the tax rate, the industrial profit rate and the coefficients of production there exist a steady-state value of the public debt-to-GDP ratio ingrained in the economic system. This result calls into question the idea of imposing budgetary rules with threshold levels independently from the very specific features of each economic system; ii) Expansions in the level of public expenditure have a permanent effect on the public debt-to-GDP ratio only in the presence of the accelerator effect, that is, through an induced increase in the share of private indebtedness on GDP and aggregate debt. Because of the accelerator channel, the public debt-to-GDP ratio depends on the capital intensity of the aggregate production process and, thus, on the system of relative prices. With this respect, the capital intensity determines the elasticity of private indebtedness with respect to one-point change in public spending; iii) Conversely to the neoclassical argument, the relationship between the interest rate and public debt-to-GDP ratio goes from the first to the second. In particular, changes in the interest rate modify the public debt-to-GDP ratio through both variations in the quantitative and value dimension. Such variations have a puzzling effect on the steady-state value of the public debt-to-GDP ratio. For instance, the reverse capital deepening implies that an increase in the interest rate produces a decrease in the public debt-to-GDP ratio. Finally, we point out that, in contrast to the standard argument proposed by mainstream macroeconomics, the condition of fiscal balance jointly a positive differential between the growth rate of output and the interest rate has no relevance for the stability conditions of the public debt-to-GDP ratio. In this regard, we develop a taxonomy of the growth regimes depicted by the model deriving such conditions in each scenario. The necessary condition of stability is the absence of budgetary constraints, it becomes sufficient when one of the following is respected: the growth rate of primary public expenditure is higher than zero, the interest rate is higher than zero or the propensity to consume out of wealth is non-zero.