Topic 4. Tax Cuts Financed by Issuing Public Debt: Ricardian Equivalence


We now analyze the effects of a tax cut when the short-fall of revenue from expenditure is financed by selling bonds to the public. The government borrows funds from the private sector to finance the expenditure that was previously being paid for by the tax revenue that is now forgone.

Look again at the government's budget constraint developed in the previous topics.

        G  =  T  +  ΔB  +  ΔH

The government reduces  T  and increases  ΔB  by the same amount. The public receives a reduction in its taxes but ends up buying an equivalent amount of bonds issued by the government.

It would seem that the public gains from this policy since it now receives bonds for the money, and hence goods, it gives to the government and these bonds bear interest. In order to pay the interest on these bonds, however, the government has to levy appropriate additional future taxes.

Let us suppose that the government cuts taxes by $100 per person and sells everyone $100 worth of government bonds bearing interest at 8 percent. In every future year the government must raise $8 additional taxes per person to pay these same people their $8 interest. The public receives a $100 reduction of this year's taxes in return for an $8 increase in taxes in all future years. Letting  i  be the nominal interest rate, the present value of future taxes is

        PV  =  $8 / i  = $8 / 0.08  =  $100

which is identical to the tax cut. We assume here that the bonds are perpetuities or consols---if they were not, the result would be the same except that the above equation would take a more complicated form.

Consider, for example, a case where the government cuts taxes this year and finances its revenue short-fall with an issue of government debt maturing in one year. This means that taxes must be raised next year to pay interest on and retire the debt. A per-person tax cut of $100 this year will be financed by $100 worth of bonds which will cost $108 to redeem (at 8 percent interest) next year. This means that each person gets a $100 tax break this year buy pays $108 additional taxes next year. The present value of these tax changes is

        PV  =  − 100 + 108 / (1 + i )  =  − 100 + 108 / (1 + 0.08)  =  0

The tax cut is really nothing more than a tax postponement on which interest must be paid at market rates. If people are forward looking they will realize that they can't get something for nothing---the present value of the future taxes equals the amount of the current tax cut.

The public is no better off than it would have been by paying the $100 taxes in the first place. By buying bonds it gives the government $100 for the privilege of paying itself $8 interest each year. By paying taxes it gives the government $100 outright. The transfer to the government is the same in both cases. Wealth does not increase, so there appears to be no reason why consumption should increase.

This idea that the community's wealth and consumption will be the same whether the government finances its expenditure by levying taxes or borrowing from the public is called Ricardian Equivalence after the famous 19th Century British economist David Ricardo (1772 - 1823).

Another way of visualizing the Ricardian Equivalence idea is to recall that when the government makes an amount of expenditure  G  it must take G-dollars worth of resources away from the private sector to create the government goods it will give free to private individuals. This amount of resources will be the same whether the government borrows them from the private sector or obtains them through taxation. Private sector output will be reduced by the same amount in the two cases. And since the government acts as agent of the public, the public must transfer to it the necessary resources without any ultimate compensation other than the free goods the government is going to produce and distribute using those resources.

In the case of bond as opposed to tax finance the government is perpetrating what seems to be a slight-of-hand. Rather than simply taking the funds directly, the government is giving paper assets in return on which the public gets to pay itself interest every year. This interest is simply a switch of funds from one of the public's pockets to another with no net gain. Why might the government want to do this? We will see why in the next topic.

Before proceeding it should be noted that the Ricardian Equivalence Principle does not apply unequivocally to situations where the government finances a tax cut by printing money. To be sure, the same resources are taken from the private sector but, when the price level is fixed and there is less-than-full-employment, private wealth will increase because real money holdings rise. In the full-employment case the equivalence principle holds unequivocally because the government is simply substituting a tax on money holdings for a tax on something else.

Its time for a test. Be sure to think up your own answers to the questions before looking at the ones provided.

Question 1
Question 2
Question 3

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