Wednesday, May 27, 2015

Government bonds and borrowing

In my previous post "What is fiscal policy?", I laid out a brief explanation of what fiscal policy is and mentioned that deficit/debt financing allows a government to make current expenditures with the commitment to pay back expenditures in the future. Often, a government resorts to issuing a bond rather than a loan from a bank. A bond is basically just a loan which is to be paid to the holders of a security.

From the point of view of individuals, the bond is a security that one can buy which will yield payment(s) in the future. The demand for the bond once it is issued is determined by the rate of interest that investors require given their perception of the risk that the issuer will not repay the bond as agreed. This will be reflected in the market price of the bond which, in turn, determines its interest rate. Consider the following simple example. A government has a number of capital improvement projects that it wishes to fund with borrowing. Rather than borrowing a specific amount, policymakers decide that they are reasonably certain about their ability to pay back an amount the next year, so the government issues a 1-year zero-coupon (aka, discount) bond in the amount of $50 million.[1] Given the risk profile of the government, investors are willing to lend at an annual interest rate of 5%. Here is the equation for a 1-year maturity discount bond:


Thus, at 5%, the Current Price which would be offered in the market would be about $47.6 million for the payment of $50 million in 1 year. If the market interest rate were instead 10%, the Current Price would be about $45.5 million. It is not hard to see that this is identical to the case where a $45.5 million 1 year maturity bond is issued, investors are willing to lend at 10% interest and the ultimate amount to be paid in 1 year is $50 million.

There are several different types of bonds, but one thing to keep in mind is that the price of the bond is going to be inversely related with its rate of interest. If individuals become more willing to invest in a given bond, the interest rate will decline.

There are constraints to how much debt a country can issue. One is whatever restraints are put on the issuance of debt, for example, there are formal debt limits that are set by constitutional provisions or the laws of a jurisdiction. In Guam, it is 10% of the aggregate real property valuation, which is expected to rise considerably soon.

A second consideration is the total debt that the market will bear. As total debt rises, investors will tend to view the ability or willingness of a government to pay for the additional debt with increasing skepticism, which will eventually translate into rising interest rates, generally.  This will raise the burden of interest payments and make it harder for a government to service additional debt.

A third consideration is the technical sustainability of government debt.  In the long run, individuals generally need to make means and ends meet (i.e., the present discounted value of lifetime expenditures should equal the present discounted value of lifetime revenue). A  crucial difference between an individual's ability to pay and the government's is that a government is presumed to be a permanent institution. The definition of solvency for a government, then, is that the present value of revenues should equal or exceed the present value of expenditures. What this means is that taking together current revenues and future revenues, properly discounted at a given rate of interest, would need to equal or exceed the current expenditures and future expenditures, properly discounted at a given rate of interest.[2]

These, however, are constraints, not definitions of the optimal public policy with regard to the accumulation of debt. Some may argue the desirability of targeting a nominal amount of debt, a real amount of debt (discounted by the price level), or a debt-to-output ratio, as I discussed briefly in the previous post. I am personally inclined to favor targeting a long-run debt-to-output ratio.

[1] As a practical matter, the amount raised can be determined, but could not be known for certain well before the issuance.
[2] Just to clarify the issue a little for those mathematically inclined, but unfamiliar with the concept of present value, here's an expression of present value for a current value at time "t":

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