LECTURE 7: SEIGNORAGE & HYPERINFLATION

1. LECTURE 7: SEIGNORAGE & HYPERINFLATION • Key Question:Government attempts to stimulate the economy may explain moderate levels of money growth & inflation…. • but why do high rates of inflation -- even hyperinflation -- sometimes occur? API120 - Prof. J.Frankel

2. The world’s most recent hyperinflation: Zimbabwe, 2007-08 Inflation reached 50% per month in March 2007, meeting definition of hyperinflation. It reached 2,600% per mo. in mid-2008. API120 - Prof. J.Frankel

3. The latest rival for world record for hyperinflation Nov. 2008: inflation rate p.a. supposedly estimated at 89.7 sextillion (1021) %. Dec. 2008: inflation p.a. estimated at 6.5 quindecillionnovemdecillion % (6.5 x 10108 %, or 65 followed by 107 zeros – 65 million googols %) In April 2009, printing of the Zimbabwean dollar stopped; the S.Afr. Rand & US $ became the standard currencies for exchange. API120 - Prof. J.Frankel

4. The driving force?Increase in money supply: The central bank monetized government debt.

5. The exchange rate increased along with the price level. Both increased far more than the money supply.Why? When the ongoing inflation rate is high, the demand for money is low, in response.For M/P to fall, P must go up more than M. API120 - Prof. J.Frankel

6. How do governments finance spending? • Taxes • Borrowing ● Domestic † ● Abroad • Seignorage ≡ creatingmoneytofinancedeficits Money creation in excess of increased money demand from real growth ≡ inflation tax. † Regarding government borrowing, you may encounter -- “Ricardian” debt neutrality (Barro): people know taxes eventually will rise. So Saving ↑ . -- “Fiscal dominance” (Sargent & Wallace; Woodford): people know that the debt eventually will be monetized. So P ↑ . API120 - Prof. J.Frankel

7. But a government that relies on seignorage to raise real resources risks“killing the goose that lays the golden egg.” • High money growth eventually gets built into expected inflation; and so the public reduces money demand • whether because πe is built into i (Fisher effect) • or because πe enters the money demand function directly. • Bond markets often break down in hyperinflations. • So M/P = L(πe, Y) • When demand for realmoneybalances falls, there is less of a “tax base” that thegovernment can exploit. API120 - Prof. J.Frankel

8. INFLATION TAX Real money supply = real money demand. If πe rises, real money demand falls, as households protect themselves against the loss in purchasing power. In LR: Y = , and πe = π = gM, where gM≡ , => In “steady state,” the actual & expected rates of inflation = the rate of money growth. The fall in real M takes the form of a rise in P > rise in nominal M. Seignorage = The government gets to spend at rate dM/dt in nominal terms. Divide by P to see what that buys in terms of real resources. = gML(π,) “Inflation ↑ ↑ tax = “tax “tax revenue” rate” base” A higher “tax rate” (inflation) lowersthe “tax base” (real money holdings). API120 - Prof. J.Frankel

9. 27.2 Where πwent the highest, P went up the most, even relative to the increase in M: M/P ↓ π API120 - Prof. J.Frankel

10. Inflation tax revenue is “tax rate” times “tax base.” API120 - Prof. J.Frankel

11. Seignorage revenue as a function πL(π) of money growth rate If inflation is very high, seignorage is very low. You have killed the goose that laid the golden eggs. If money growth = 0, seignorage = 0. The seignorage-maximizing rate of money growth 11.7 API120 - Prof. J.Frankel

12. For govt. to maximize seignorage, Seignorage = π L(π,Y) E.g., following Cagan, we choose exponential functional form: Let L( , ) ≡ ea-λπ Y . => dL(,)/dπ = - λea-λπ Y = -λL(,). = L(,) – πλL(,) = L(,) [1– πλ] Set derivative = 0. We thereby find that revenue- maximizing π is inversely related to λ, i.e., the sensitivity of money demand to π. =0 when π = 1/ λ E.g., if λ=1/2, revenue-maximizing π=200%. Or higher, if in SR λ is lower. API120 - Prof. J.Frankel

13. The seignorage-maximization approachdoesn’t get to true levels of hyperinflation,if the revenue curve peaks at lower levels of inflation. • One needs a dynamic process, where • money-holders respond more adversely to inflation over time than they do in the short run, and • the central bank chases a receding seignorage target. • Cagan (1956)modeled adjustment in continuous time. (Or Romer, 4th ed., pp. 572-576) API120 - Prof. J.Frankel

14. Consider a stylized example of the dynamic process, which could end up at hyperinflation • Assume • Elasticity rises over time from short run to long, and • GovernmenttellsCB tofinance a budgettarget byseignorage(say,92%GDP). • In VSR, elasticity is low.Seignorage target can be reached with moderate rates of money creation & inflation π1. • Then, in SR, elasticity rises. => demand for money falls => π1 no longer raises enough real revenue. • CB raises money growth & inflation to π2 to attain required revenue. • In MR, elasticity rises more=> π2 no longer raises enough revenue. • CB raises money growth & inflation to π3 . • In LR, elasticity rises more => π3 no longer raises enough revenue. • CB raises money growth & inflation to π4 , which is now past the revenue-maximizing hump. A foolish government might chase its target indefinitely. API120 - Prof. J.Frankel

15. Seignorage = π L(π) with functional form L(π) =ea-λπY. VSR SR · · · Assume govt. requires seignorage 92% of GDP MR · LR ? inflation rate π API120 - Prof. J.Frankel

16. Appendix: Exchange rates in hyperinflations Increases in the exchange rate S.Hanke

17. The exchange rate in Zimbabwe’s hyperinflation “Parallel rate” (black market) Official rate