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Theoretical Background
At the moment, most tax systems around the world are not completely indexed to ensure that the price-level changes leave real tax rates and real tax revenue unchanged. Inflation-induced distortions generated by the interaction of inflation and the non-indexed tax system have the potential to be much larger than the revenue-related effects on which most of the seigniorage and optimal inflation literature has focused (Walsh, 2003).
One important distortion arises when nominal income and not real interest income is taxed. It must be realized that it is after tax real rates of return that is relevant for individual agents in making saving and portfolio decisions, and if nominal income is subject to a tax rate of , the real after –tax return will be ra (1 )i (1 )r , (5.1) where i r is the nominal return and r is the before-tax real return. Thus for a given pre-tax real return r , the after-tax real return is decreasing in the rate of inflation. Practically speaking, let us consider a two–period overlapping generations model, where individual work and earn income when young and also decides on how much to consume currently and save for their old age. Suppose that savings are invested at the rate of r . Therefore, consumption in old age is related to savings by the following equation:
T c s(1 r) (5.2) where T is the length of the period between saving while young and dissaving in the old age. Then price of retirement consumption can be defined as T r p . (5.3)
Clearly, the relative price of old-age consumption P is affected by both tax system and inflation, since they distort the choice between current consumption and future consumption. Graphically, the scenario is depicted in Figure 5-1. The figure 5-1 depicts the individual‟s compensated demand for retirement consumption, labeled as Quantity, as a function of the price of retirement consumption p , denoted as Price, at the time of the decision to save. The different points on the graph represent different scenarios. With combination 0 0 c , p representing consumption decision without tax and inflation, the consumer surplus is A+B+C….+F. Introducing income taxes in an environment of price stability (no inflation) moves the equilibrium point from 0 0 c , p to 1 1 c , p which leads to a lesser retirement consumption at a higher price. Consumer surplus is now reduced to the area: C+E+F and the tax revenues corresponding to that area is B+D. Triangle A, thus, represents the deadweight loss, which, in turn, is the reduction of consumer surplus not compensated by higher tax revenues. When we introduce both taxes and inflation the equilibrium point from c1, p1 to 2 2 c , p , and again there is a reduction in consumption at high price. The consumer surplus remaining is F and tax revenue is the rectangle D+E. The deadweight loss increases from triangle A to triangle A+B+C.
Distortions to Saving Behavior
The household has two main decisions to be make on their expenditure, namely, how much to consume and how much to invest in each period. Feldstein (1997) derives the welfare gain from reducing inflation in a two period consumption model. Individuals are given an initial endowment and then they decide on the portions of their income to consume and save in the first period in order to consume when they are retired in the second period. The agent‟s first period savings earns a real rate of return, and in period one, the price of retirement consumption ( p ) is thought to be inversely related to this rate of return, i.e., the higher the rate on saving, the cheaper the effective price of retirement consumption. The rate of return on saving depends on both inflation and the tax system. According to Feldstein et al., (1978), inflation is a source of irregular change on the effective tax rate of capital income, which leads to changes in real net of post- tax return.
Reducing the equilibrium inflation rate from two 2 percent to zero lowers the effective tax rate at both corporate and individuals levels. At the corporate level, this has two opposing effects: First, the changes in the equilibrium inflation rate alter the effective tax rate by changing the value of depreciation allowances, and; second, it changes the value of the deduction of interest payments.
Because the depreciation schedule that is allowed for calculating taxable profits is defined on the basis of historical nominal terms, a higher rate of inflation reduces the present value of depreciation and thereby increases the effective tax rate. This relation was approximated by Feldstein (1997) using a rule of thumb of 0.57 percent increases in taxable profit for each percentage point of inflation. Due to lack of this estimate in South Africa, we use the same value as Feldstein (1997). With marginal corporate income tax rate at 30 percent45, a 2 percent reduction in inflation raises the net of tax return and hence decreases effective tax rate by 0.30(0.57)(0.02) = 0.0034 or 0.34 percentage points. The interaction of the interest deduction and inflation moves the after tax yield in the opposite direction. If each percentage point of inflation raises the nominal corporate borrowing rate by one percentage point46, the real pre-tax cost of borrowing is unchanged but companies get an addition deduction in calculating their taxable income. With debt to capital ratio of 59 percent47 and a corporate tax rate of 30 percent, a 2 percent decline in inflation raises the effective tax rate by 0.30(0.59)(0.02)=0.0035 or 0.35 percentage points. The difference of the two effects at corporate level is almost insignificant. Beside the impact of inflation at corporate level, the lower inflation rate affects the taxes at the individual level as well. As individual income taxes are levied on nominal interest payments and nominal capital gains, a reduction in the rate of inflation further reduces the effective tax rate and raises the real after-tax of return. The part of this relation that is associated with the taxation of nominal interest at the level of the individual can be approximated in a way that mirrors the effect at the corporate level. If the nominal interest rate increases by one percentage point for every percentage point of inflation, the individual investors‟ real pretax return on debt is unchanged, but the after tax return falls, and is given by the product of the statutory marginal tax rate and the change in inflation. Assuming the same 59 percent debt share at the individual level, as assumed for the corporate capital stock, and 25 percent average individual marginal tax rate, a 2 percent decline in inflation lowers the effective tax rate by 0.25(0.59)(0.02)=0.003 or 0.3 percentage points.
1 Introduction
1.1 Introduction
2 Measuring the welfare cost of inflation in South Africa*
2.1 Introduction
2.2 The theoretical foundations
2.3 Data
2.4 Empirical results
2.5 Conclusion
3 Measuring the welfare cost of inflation in South Africa: A reconsideration*
3.1 Introduction
3.2 The theoretical foundations
3.3 Data
3.4 Empirical methodology and results
3.5 Conclusion
4 Time aggregation, long-run money Demand and the welfare cost of inflation*
4.1 Introduction
4.2 The theoretical foundations
4.3 Data and Results
4.4 Conclusions
5 Some Benefits of Reducing Inflation in South Africa*
5.1 Introduction
5.2 Theoretical Background
5.3 Inflation and the Inter-Temporal Allocation of Consumption
5.4 The Gain from Reducing Distortion in Housing Demand
5.5 Seigniorage and Distortion of Money Demand
5.6 Debt Service and the Government Budget Constraint
5.7 The Net Effect of Lower Inflation on Economic Welfare
5.8 Conclusion
6 Evaluating the Welfare Cost of Inflation in a Monetary Endogenous Growth General Equilibrium Model: The Case of South Africa*
6.1 Introduction
6.2 The General Equilibrium Model
6.3 Competitive equilibrium
6.4 General Equilibrium effects of inflation tax
6.5 Model calibration
6.6 The quantitative effects of inflation in the general equilibrium model
6.7 Conclusion
7 Dynamic time inconsistency and the SARB*
7.1 Introduction
7.2 The Modified Barro-Gordon (1983) Model
7.3 Data and Results
7.4 Conclusions
8 Comparing South African Inflation Volatility across Monetary Policy Regimes: An Application of Saphe Cracking*
8.1 Introduction
8.2 Application to Inflation Volatility
8.3 Conclusions
9 Conclusion
Bibliography
