Thursday, June 16, 2022

Fiscal Histories

Fiscal Histories  is a new paper, a second try at an essay on fiscal theory for the Journal of Economic Perspectives. 

The basic concept is to explain the fiscal theory of the price level with no equations by applying it, by seeing how it might be able to explain and interpret a wide variety of historical episodes. Abstract: 

The fiscal theory states that the price level adjusts so that the real value of government debt equals the present value of real primary surpluses. Monetary policy remains important. The central bank can set an interest rate target, which determines expected inflation, and news about the present value of surpluses drives unexpected inflation. I exposit fiscal theory by offering an interpretation of historical episodes, including the gold standard, currency pegs, the ends of hyperinflations, the success of inflation targets, the rise and fall of inflation in the 1970s and 1980s, the long quiet zero bound of the 2010s, and the 2021-2022 inflation. Going forward, fiscal theory warns that inflation will have to be tamed by coordinated monetary and fiscal policy. 

I thank Erik Hurst and Tim Taylor for the concept. Most of the stories are summarized from the Fiscal Theory of the Price Level, but pulling them out, putting them in one place and simplifying them is a great idea. The key idea

I think through how fiscal theory can account for important episodes. A first purpose is expositional: by this method we can understand how fiscal theory works, and what elaborations it might need. A second purpose is more serious: analyzing episodes is the crucial way we evaluate all macroeconomic models. 

I mostly tell plausible stories, rather than summarize well-worked out and published economic history or quantitative analysis. Fiscal theory is new, and that work is just beginning. But stories rightly come first. Formal analysis always builds on plausible stories. Moreover, that there are such plausible stories, that it provides a framework that can possibly account for history as MV=PY and IS-LM do, is news, since many people opine that fiscal theory can be quickly dismissed by well-known episodes. I also hope to inspire detailed analysis. 

The paper also shows the results of a nice model, and sneaks the model in a footnote, that gets at the basics of fiscal theory with sticky prices more simply than I did in FTPL. The graph: 

Figure 1: Responses of inflation and output in a simple fiscal-theory sticky-price model. Top: 1% deficit shock with constant interest rate. Bottom: Interest rate shock with constant surpluses

You can think through a lot of fiscal theory with these graphs. The first graph is a fiscal shock with no change in interest rate, which is roughly what I think we saw in 2021. It leads to protracted inflation, and devalues outstanding bonds with a period of negative real interest rates. The second graph is an interest rate rise with no change in surpluses. It gives a temporary inflation decline. Reality combines the two graphs. The Fed's rate rises will add the second graph on the first, which will help. A bit. For a while. 

Yes, repackaging the same ideas in a lot of different ways. I hope to find one that works, or at least to offer different packages for different tastes. 

I'm not sure of the title yet. Fiscal Fables? Fiscal Bedtime Stories? ; ) 

The model is $$\begin{aligned}x_{t}  &  =E_{t}x_{t+1}-0.5(i_{t}-E_{t}\pi_{t+1})\\\pi_{t}  &  = E_{t}\pi_{t+1}+0.5 x_{t}\\i_{t}  &  =  i_{t-1} + \varepsilon_{i,t} \\ \rho v_{t+1}  &  =v_{t}+r_{t+1}^{n}-\pi_{t+1}-\tilde{s}_{t+1}\\E_{t}r_{t+1}^{n}  &  =i_{t}\\r_{t+1}^{n}  &  =0.9q_{t+1}-q_{t}\end{aligned}$$where \(x\) = output gap, \(i\)=interest rate, \(\pi\)=inflation, \(v\)= real value of government debt, \(r^n\)=nominal return on government debt,   \(\tilde{s}\) = real primary surplus scaled by value of debt, \(q\)= log price of government debt. Debt has a geometric maturity structure with coefficient 0.9. I plot the response to an unexpected \(\sum_{j=0}^\infty \rho^j{\tilde{s}}_{1+j}=-1\) and \(\varepsilon_{i,1}=1\). 


  1. "the real value of government debt equals the present value of real primary surpluses."

    What happens if there is no surplus -- nothing but deficits as far as the eye can see?

  2. This comment has been removed by the author.

  3. This comment has been removed by the author.

  4. This comment has been removed by the author.

  5. Maybe: "Fiscal Stories for Inflations Past"?

  6. 1. You can't explain changes in price levels without understanding the levels.
    First, make a model that predicts the value of a currency.
    Second, take the first derivative of the parameters of the model.
    That will give you a model for inflation.

    2. In the long run, prices are a function of only two things:
    1. Supply of Money
    2. Technological change (assets that the money can buy)
    3. Number of people using the currency. (total demand for money)

    The interest rate is only interesting because it changes the expected future supply of money. Given the long history of Governments expanding the money supply, the market knows that the money supply will expand to cover interest expenses.

    2. The number of people that use the currency worldwide is incredibly important, but is totally missing from these models. the USD's global expansion over the 20th century enabled a huge expansion of the money supply without causing much inflation. Is that over?

    3. This model shows a very nice dynamic for "output". "Output" that is driven by debt will have to revert, so that's not interesting in the long term. Any realistic model for "output" that is driven from conversion from savings to consumption would have this revert back to zero to show the full effects of the interest rate. For example, reducing interest rates to zero will cause everyone to refinance their houses, until people are just maxed out in terms of debt. Then the refinancing will stop.

    Similarly, raising rates will prevent people from borrowing and consuming, but eventually, people will just consume what they can in cash. When that happens, people will stop paying off debt in net.

    4. Technological progress affects prices by expanding the number of assets that money can by, driving down prices in terms of assets.

  7. Here's my model for prices:

    P = A*D/M

    P := price
    A := total assets that can be bought
    D := Number of people using the currency (demand)
    M := nominal supply.

    Thus, inflation will be:

    dP = dA*dD/dM

    dP := infaltion (change in price)
    dA := pace of technological development (aka real GDP growth)
    dD := population growth
    dM := change Money supply

    In turn, change in money supply is given by:


    To the extent that interest rates caputure that, we can substitute interest rates. However, given interest rates complex affects on behavior in the population, it's better not to refer to the interest rate at all.

  8. I always enjoy listening to economist – like Milton Friedman and yourself John – who profess to be libertarian or free market champions and then advocate a monetary policy that constrains (i.e., put limits on) economic behavior.

    How would your explanation of the price level hold up in U.S. history during the period of Andrew Jackson to the Civil War?
    (1) when there was no government debt,
    (2) no ubiquitous tax collection,
    (3) no effective gold standard (in the U.S., remembering gold was discovered in California during this period),
    (4) alternating periods of inflation and deflation (which was common during the 19th Century),
    (5) the federal government did not print money and had no currency,
    (6) and even at the state level it was not uniform,
    (7) along with the issuance of credit instruments which was not uniform,
    (8) and this is also a period when not only was there no central bank but there was also no well organized corresponding relationships between and among the private banks big and small like there was in the latter part of the 19th Century.

  9. This is a "concurring opinion", not a dissent. I've kept up with and taught the fiscal theory since your EER draft years ago. While your explanation in the "Fiscal Histories" JEP draft and other places isn't wrong, I think that it often undercuts the buy-in to your point. Yes, the PV approach can be distinguished from an MV=PY approach based on definitions, but I find it useful and more convincing define things in a way that brings the two into harmony (which is how I took the original EER draft). If "M" is treated broadly as all transactional assets (a sort of divisia aggregate including B) along with the associated V, then MV=PY and the PV equation are two sides of the same coin. MV=PY is always operational as a tautology (that can be empirically validated). Whatever is going on in MV=PY is going on somewhere in the PV equation and vice versa. One way of thinking of the PV equation is giving a lot more detail (or, at least, an additional perspective) on V changes in terms of expectations and risk attitudes about government liabilities. I think that David Beckworth said similar things in his blog several years back.

  10. Thanks, but I disagree. There is a difference whether at rock bottom, we have an intrinsically worthless asset valued by a transactions demand, or we have a claim to fiscal surpluses, valued as such. Does inside money count in M? Does an exchange of M for B matter? Though the accounts of history may be similar, especially when much M is provided by government, and though a realistic model includes both (M+Mi)V=PY and (B+M)/P = EPV(s), the underlying idea is quite different.

  11. This comment has been removed by the author.

  12. M*Vt = P*T Milton Friedman’s income velocity, Vi, is a contrived figure (Vi = Nominal GDP/M). It is a “residual calculation - not a real physical observable and measurable statistic” whereas Vt, the transactions’ velocity of circulation, is an “independent” exogenous force acting on prices. The product of M*Vi is obviously N-gDp. Income velocity has moved in the opposite direction as the transaction’s velocity of money.

  13. This reminds of a book I read "Double Speak" by William D. Lutz. It is odd why some well trained professionals choose double speak over clear, well defined terms.

  14. The conditional expectation Eₜ{πₜ₊₁} can be eliminated from the expressions for xₜ and πₜ using the relations set out in fourth through sixth equations of the model, but the conditional expectation Eₜ{xₜ₊₁} cannot be eliminated and it remains in both the first and second equations of the model after Eₜ{πₜ₊₁} has been replaced using the fourth through sixth equations of the model.

    Without an estimate for Eₜ{xₜ₊₁}, the validity of the charts produced from the model is sensibly incomplete. Eₜ{xₜ₊₁} is a key input to the NK IS curve and it is undoubtedly affected by both the interest rate, iₜ , and Eₜ{πₜ₊₁} in some complicated manner, esp. when the central bank is on the warpath, as it is at this time, to “fight inflation”.

    In replacing Eₜ{πₜ₊₁}, conditional expectations are required for variables vₜ₊₁ , qₜ₊₁ , and s̃ₜ₊₁ . Whether generating conditional expectations for those variables is easier (more reliable?) than obtaining expectations Eₜ{xₜ₊₁} and Eₜ{πₜ₊₁}, is a matter of judgement, or speculation.

    Taking the anti-logarithm of the resulting equation for πₜ gives a sense of the difficult estimation task associated with solving the fuller NK models. Estimates for these variables will be required: Yₜ₊₁ , Ȳ, Vₜ₊₁ , Qₜ₊₁, and, Sₜ₊₁.

    And, should those variables be estimated, there is then still no guarantee that the result will prove accurate, because of the restrictive assumptions underpinning the model’s structure. Conversely, if the real world situation meets the model’s restrictive assumptions, will the model return an accurate estimate of the future path of inflation and the output gap of the economy?


Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.