# The Tax-Smoothing Hypothesis

As explained above, using a fiscal deficit for stimulating aggregate demand has limited effects. Contrary to Keynesian policy, the tax-smoothing hypothesis uses counter-cyclical measures so as to smooth the tax burden over time.

Imagine that a bad shock occurs and GDP declines. Then, tax revenue would also decline. Fiscal deficits normally increase because of a decline in taxable income at a given level of spending. With the balanced-budget rule, the government has to raise tax rates. Alternatively, the balanced-budget rule means a huge cut in government spending.

Such a response hurts private agents and destabilizes tax revenue and government spending in the long run. From the viewpoint of smoothing the tax burden over time, tax revenue or the tax rate should be stabilized. Similar smoothing behavior should also be applied to government spending. The tax-smoothing hypothesis means that the government uses a fiscal deficit and public debt so as to alleviate fiscal fluctuations in response to exogenous GDP shock.

Figure 6.1 explains this policy. The vertical axis denotes the size of spending G and taxes T, and the horizontal axis denotes time or periods. Suppose during period AB that a negative shock such as a natural disaster or war occurs and government spending G has to be raised temporally. Then, it is desirable to raise taxes T from period A by a small amount. Further, most temporal spending during AB should be financed by temporal debt issuance. This is the tax-smoothing response.

The tax-smoothing hypothesis may be explained in a simple two-period model. Suppose levying taxes T; produces excess burden Q in period i = 1.2. Thus,

This excess burden increases with T;. As explained in Chap. 8, the shape of this function is convex, as shown in Fig. 6.2a. The slope of this curve increases with taxes. The objective of government is to minimize the present value of the total excess burden at the given level of government spending. The present value of the total excess burden H is expressed as

Fig. 6.1 **Tax smoothing and temporal debt issue**

Fig. 6.2**a The excess burden curve**

The government budget constraint in each period is given as

where G_{i} is government spending in period i (i = 1,2) and Bj is public debt issued in period 1. r is the rate of interest. The present value government budget constraint is given by

We also assume that the optimal time path of government spending (G_{1}, G_{2}) is exogenously given.

Thus, the government minimizes the total excess burden (6.2) by choosing T_{1 }and T_{2}, subject to its budget constraint (6.5) at given levels of G_{1} and G_{2}.

The optimal condition is given as

which is the tax-smoothing condition. It is optimal to collect the permanent level of tax in each period. Figure 6.2b explains this outcome. The CC curve means the combination of T_{1} and T_{2} that gives a constant value of H, the slope of which is given by

which is equal to 1 + r if T_{1} = T_{2}. Line AB is the government budget constraint, the slope of which is given by 1 + r. Point G denotes the combination of given levels of G_{1} and G_{2}. At the optimal point E, line AB is tangent to curve CC. Since point E is on the 45° line, it is optimal to have the tax-smoothing condition (6.6).

Fig. 6.2**b Tax-smoothing hypothesis**

Economic intuition is as follows. Since the excess burden of taxes increases with taxes, it is desirable to maintain a stable time path for taxes over time. Then, as in period 1, G_{1} is greater than T_{1} in Fig. 6.2b and the government should issue public debt by the amount of G_{1} — T_{1}. Fluctuations of government spending should be absorbed by issuing debt so that tax revenue may be stabilized. This is the taxsmoothing hypothesis.

In reality, when a large shock such as a national disaster or war occurs, government spending increases considerably but temporally. In such a situation, the balanced-budget rule is undesirable; rather, the government should issue public debt to meet the temporal need of a revenue increase. See Barro (1995).