Government debt constraint I am reading Some Unpleasant Monetarist Arithmetic (Sargent and Wallace, 1981) and I had some questions about a claim made by the authors. They say:


  The public's demand for interest-bearing government
  debt constrains the government of a monetarist economy in at least two ways. One way the public's demand for bonds
  constrains the government is by setting an upper limit on
  the real stock of government bonds relative to the size of
  the economy. Another way is by affecting the interest rate
  the government must pay on bonds.


First of all, are we assuming that the government borrows from the private sector and spends it on something that improves productivity? For example, the government could borrow from the private sector and spend it on a road (something that increases productivity) or they could spend it on unemployment benefits (beneficial, but not productive). I think "real stock of government bonds" is what is confusing me. So the way I understand the first reason is that if government debt becomes too high and the interest payments exceed the growth rate of the economy, this will not be sustainable because the government will have to pay more to the private sector than is produced by the private sector.

For example, consider a extremely simplified economy where corn is the only thing produced and the agents are: (i) the government (ii) the private sector. So the government borrows 1 ton of corn from the private sector and promises to pay back 2 tons next year. They use that corn to improve corn producing ability of the private sector. However, the private sector was only able to produce 1.5 tons of corn the following year. Hence the real government debt is too high relative to the real size of the economy. Is this what Sargent and Wallace are referring to?

The second reason sounds very logical but I just want to ensure I understand it correctly. Is it simply saying that if the interest payments on government debt becomes too high, they will have to raise taxes to a level that is not optimal?

However, the second reason appears to be very similar to my corn example so it feels like I am not understanding the authors reasoning very well. If anyone could explain or refer me to a source, I would greatly appreciate it.
The government just consumes within this model, as is similar to other standard DSGE models. Therefore, its consumption (G) never has an effect on productivity. Imagine a wartime situation where the government is buying goods that are used to provision the army; the goods are consumed, but will not help develop the domestic economy. If you wanted to simulate government infrastructure spending raising productivity within these models, the government infrastructure build would have to be added to business investment (raising the capital stock).

The "real government debt" constraint says that although the nominal level of debt is fixed, if future taxation policy is expected to be "too low" relative to the nominal stock of debt, the price level will rise now. This the Fiscal Theory of the Price Level. The governmental budget constraint is used to determine the formal relationship between the expected primary surpluses and the real value of current government debt (effectively, the current price level, since the initial nominal debt level is fixed).

With regards to your examples, even if debt due was greater than GDP, the situation can be sustained. (We have seen debt-GDP ratios greater than 100% in a number of countries, including Japan at present.) Most of the debt will be rolled over into new debt. That is, in year 2 of your example, the government could just borrow the nominal amount equivalent to two tons of corn, and roll over the debt from year one. (This is possible since these are models of monetary economies, in which nominal claims - money and bonds - are used in exchange, and not just goods themselves, see below.) The issue with sustainability is whether the debt/GDP ratio will tend to infinity.

If transactions were barter transactions with real goods, you could then have "real debts" which are payable by goods (corn, say). What the limits are for paying back debt depends upon your assumptions about the payment system. Normally these models assume simultaneously clearing of all transactions in a period. However, if we assume that there are multiple transactions possible within a period (and we are only simulating the aggregate), the government in your example could borrow corn from some members of the private sector, and then use that to pay off other lenders, and then repeat the process until the entire debt stock is rolled over. If that is assumed not be posisble, the government would have to lengthen maturities, so that only part of its debt stock needs to be rolled over, and the previously described procedure is again possible. Having debt with multiple maturities is avoided in DSGE models due to complexity concerns, but it would be necessary if the payments system was restricted like this.