# Government debt and Fiscal Theory of Price Level

I am trying to understand the Fiscal Theory of Price Level (FTPL) and how it explains inflation. I've been reading several papers by Eric Leeper and I am slightly confused about some of his claims. For example in this paper he argues:

Suppose that higher deficits do not create higher expected surpluses and that central banks either peg short-term nominal interest rates or raise them only weakly with inflation. Because a tax cut today does not portend future tax hikes, individuals initially perceive the increase in nominal debt to be an increase in their real wealth. They try to convert higher wealth into consumption goods, raising aggregate demand. Rising demand brings with it rising prices, which continue to rise until real wealth falls back to its pre-tax-cut level and individuals are content with their original consumption plans.

I understand that he is explaining 'non-Ricardian' policies. However, if the government increases its deficit by issuing bonds, would that not decrease AD in the period the bonds are sold? Say that the government increases its deficit in period $t$ by selling bonds. Private agents buy these bonds and thus give up consumption goods. So in period $t$, should AD not decrease? And when the bond matures and the agents receive their payoff, they will spend it as long as the government is credible enough in not raising taxes. I might be overcomplicating things about this is just a thought I have had.

And lastly;

By preventing nominal interest rates from rising sharply with inflation, monetary policy prevents debt service from growing too rapidly, which stabilizes the value of government bonds.

I understand the reasoning that keeping interest rates stable will stabilize the debt servicing. However, suppose that interest rates rose. If the interest rate is higher than the growth rate of the economy, the government will have to monetise its debt in order to pay the interest component, this will obviously be inflationary. Or, they can issue more debt. If they choose the roll over on the debt (i.e paying the interest by issuing even more debt), will this be inflationary or deflationary? Using the same reasoning as above, I would think this is deflationary because by selling bonds to private agents, they have to give up consumption goods, thus reducing AD.

I'm trying to understand the intuition behind fiscal and monetary authority interaction. So if my questions can be answered by academic literature, I would gladly give it a read.

Question:

I understand that he is explaining 'non-Ricardian' policies. However, if the government increases its deficit by issuing bonds, would that not decrease AD in the period the bonds are sold? Say that the government increases its deficit in period t by selling bonds. Private agents buy these bonds and thus give up consumption goods. So in period t, should AD not decrease?

The act of issuing bonds does not directly affect AD, it only results in a rebalancing of portfolios: the household sector gives up money balances in exchange for government bonds. (If your model implies that spending depends upon money balances, there might be an indirect effect on the economy. In many models, money balances are zero, and so there is no effect. See below.) In any event, the end-of-period money holdings of the household sector depend upon the reaction function of the central bank within the model, and so that reaction function will effectively determine the final household portfolio allocation between money/bonds. (The reaction function is usually specified as a rule for the interest rate, which determines money holdings within the household's money demand function.)

The lack of relationship between money balances in macro models and transaction volume is not entirely obvious. The reason is that money balances are meant to represent end-of-period holdings, and transactions clear simultaneously. This means that a household with \$100 income can spemd \$100, and leave a \\$0 cash balance at the end of the period. Since it is better to hold bonds/bills if interest rates are positive, the end-of-period money holdings woukd normally end up at zero. It can do this in every period, and so it is continuously transacting, yet measured money balances never appear. This is obviously unrealistic, and so other classes of models introduce reasons for end-of-period money holding. Two typical cases are a cash-in-advance requirement, or money in the utility function. The cash-in-advance requirement is that money holdings have to be at least some percentage of consumption spending (which simulates the reality that most wages are paid at a lower frequency than spending). Money in the utility function creates a demand for money within the optimisation problems, which usually depends upon the rate of interest. The end result is that the model assumptions imply a relationship between money holdings and the economy; change the assumptions, and the relationship changes.

Leeper is discussing a tax cut, which can trivially give rise to unchanged consumption (multiplier of 0). The government consumes the same amount as before, and thus runs a higher deficit (which is matched by greater bond issuance). If the household sector consumes the same amount, its savings rises by the amount of the tax cut, which it invests in bonds.

If the "multiplier" on the tax cut is positive, it implies that the household consumes more as a result of the tax cut, and so we have greater output. The exact effect depends upon the model you are using.

However, suppose that interest rates rose. If the interest rate is higher than the growth rate of the economy, the government will have to monetise its debt in order to pay the interest component, this will obviously be inflationary.

The quote from Leeper is a discussion of "Regime F." Within the analysis of the paper, monetising of debt has nothing to do with determination of the price level. The paper, the price level in regime F is given in equation (14), which is described:

At time t, the numerator of this expression is predetermined, representing the nominal value of household wealth carried into period t. The denominator is the expected present value of primary fiscal surpluses from date t on, which is exogenous.

That is, the expectation is that future primary surpluses will be used to stabilise the debt level.

• Thank you so much for the answer, it really clarified a lot of my questions. I'm still a bit confused two things: (i) How can a model not include spending as a function of money balances? I'm just an undergrad so I've not seen all the different models yet (just basic RBC and OLG models) but not including money balances seems very counter intuitive. (ii) Could you explain a little bit more about how the CB's reaction function affects household portfolio allocation? Thanks once again! – BenBernke Apr 21 '17 at 11:07