Algorithmic recognition of quasipositive 4-braids of algebraic length three

Abstract

The paper provides an empirical analysis of the macroeconomic factors that enhance revenue gap in South Africa using the multivariate cointegration techniques for the period 1965 to 2012. The results from the cointegration analysis indicate that the revenue gap in South Africa is negatively associated with the level of imports while positively related to external debt and underground economy. The former finding is consistent with the notion that imports are subjected to more taxation than domestic activities because of certain features of international trade that tend to make tax evasion difficult. On the other hand, the positive relationship between external debt and tax gap shows that the South African government relies upon external debt to finance its budget deficit resulting from missing revenues. Furthermore, the observed negative effect of the post-apartheid dummy confirms that the tax policy reforms that South Africa introduced following the liberation in 1994 have led to a reduction in missing revenues. The results from the Granger causality test also show that there is a unidirectional causality running from imports and underground economy to revenue gap, while revenue gap on the other hand is found to Granger-cause national income and external debt in South Africa.