Maintaining Central-Bank Solvency under New-Style Central Banking

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1 Maintaining Central-Bank Solvency under New-Style Central Banking Robert E. Hall Hoover Institution and Department of Economics Stanford University Ricardo Reis Department of Economics Columbia University The Past and Future of Monetary Policy Federal Reserve Bank of San Francisco 1 March

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3 New-style central banking CB borrows from banks by issuing reserves and invests in long-term bonds 3

4 New-style central banking CB borrows from banks by issuing reserves and invests in long-term bonds Uses the interest rate on reserves as the instrument of inflation-stabilization policy 3

5 New-style central banking CB borrows from banks by issuing reserves and invests in long-term bonds Uses the interest rate on reserves as the instrument of inflation-stabilization policy Highly profitable carry trade central banks are successful hedge funds 3

6 New-style central banking CB borrows from banks by issuing reserves and invests in long-term bonds Uses the interest rate on reserves as the instrument of inflation-stabilization policy Highly profitable carry trade central banks are successful hedge funds But when interest rates rise, capital losses on bonds plus higher rate paid on reserves could cause trouble 3

7 Our approach Study the issue in a model founded on modern financial economics 4

8 Our approach Study the issue in a model founded on modern financial economics Assume inflation stabilization and reserve rate equal to short nominal rate on other safe debt 4

9 Our approach Study the issue in a model founded on modern financial economics Assume inflation stabilization and reserve rate equal to short nominal rate on other safe debt Assume a central government able to satisfy its intertemporal BC without resort to inflationary finance 4

10 Our approach Study the issue in a model founded on modern financial economics Assume inflation stabilization and reserve rate equal to short nominal rate on other safe debt Assume a central government able to satisfy its intertemporal BC without resort to inflationary finance Previous work focused mainly on projections, not on CB in RE equilibrium 4

11 Evolution of reserves V = (1 + r s )V + q s [B s (1 δ)b s ] c s B s n s,s + d s 5

12 Evolution of reserves V = (1 + r s )V + q s [B s (1 δ)b s ] c s B s n s,s + d s V(y s ) = present value of random future payoff 5

13 Evolution of reserves V = (1 + r s )V + q s [B s (1 δ)b s ] c s B s n s,s + d s V(y s ) = present value of random future payoff q s = V(c s + (1 δ)q s ) 5

14 Evolution of reserves V = (1 + r s )V + q s [B s (1 δ)b s ] c s B s n s,s + d s V(y s ) = present value of random future payoff q s = V(c s + (1 δ)q s ) n s,s = p N s pn s p 5

15 Dividends based on net worth W = q s B s V N s 6

16 Dividends based on net worth W = q s B s V N s p W = pw 6

17 Dividends based on net worth W = q s B s V N s p W = pw ( d s = c s + q s q ) s δq s B s i sv 1 + π s 1 + π s 6

18 Dividends based on net worth W = q s B s V N s p W = pw ( d s = c s + q s q ) s δq s B s i sv 1 + π s 1 + π s V s = q s B s N s 6

19 No re-capitalization, dividends keep nominal net worth constant W = W 1 + π s z 7

20 Deferral and catchup d = max(y D, 0) 8

21 Deferral and catchup d = max(y D, 0) ( ) D 1 = min D, (D max(y d, 0) + max( y, 0)) 1 + π s 8

22 Deferral and catchup d = max(y D, 0) ( ) D 1 = min D, (D max(y d, 0) + max( y, 0)) 1 + π s Z = π s Z + d y 8

23 Inputs from Data Model inputs Other data State number Safe rate, r Bond holdings, B Currency, N Inflation, p'/p-1 Reported income, y

24 Real Interest Rate, Marginal Utility, and Delta-Bond Price State Safe rate, r Marginal utility, µ Coupon, c Bond price, q

25 Interest Rate and Bond Price 9 State 1: Normal State 5: Crisis State 3: Normal 8 7 Bond price, dollars Nominal interest rate, percent Year 11

26 The Values of the Fed s Bond Holdings and Reserves Outstanding, Billions of Dollars 3,000 State 1: Normal State 5: Crisis State 3: Normal 2,500 2,000 Value of bonds 1,500 Value of reserves 1, Year 12

27 Components of the Fed s Dividend to the Treasury 150 State 1: Normal State 5: Crisis State 3: Normal Coupon less deprecia:on Capital gain Interest on reserves Dividend Year

28 Flows Into and Out of Reserves 2,000 State 1: Normal State 5: Crisis State 3: Normal 1,500 Interest on reserves Bond cost 1,000 Coupon receipts Seignorage 500 Dividend payments ,000-1, Year

29 How the D Account Generates a Speedy Elimination of Extra Reserves from a Capital Loss State 1: Normal State 5: Crisis State 3: Normal Dividends Balance in D account and extra reserves Z Net income, y Year

30 Components of Dividends with Bond Default 150 State 1: Normal State 5: Crisis State 3: Normal Coupon less deprecia:on Capital gain Interest on reserves Dividend Year 16

31 Inputs for ECB version Model inputs Other data State number Safe rate, r Repos, Br Direct bond holdings, Bd Currency, N Coupon, c Bond price, q

32 Net income under alternative scenarios 400 State 1: Normal State 2: Crisis State 1: Normal With full holdings Only direct holdings With op?on on repos Year 18

33 Balance in D account and extra reserves Z 400 State 1: Normal State 2: Crisis State 1: Normal D with full holdings Z with full holdings D=Z with only direct holdings D with repo op@on Z with repo op@on Year 19

34 Conclusions 1. If the central bank has a draw on the treasury when its income is negative, reserves are stationary and the central bank is always solvent. 2. Under old-style central banking, with no interest on reserves and short-term assets, net income is always positive and solvency issues never arise. 3. Focus on d < 0. If the treasury does not pay in, the prospect of insolvency cannot be eliminated, even if a deferred account lowers its probability. 4. Absent complete meltdown with defaults on bonds, the problem is not entering or staying in crisis, it is the recovery period, when losses on bond portfolio occur. 5. Fed and ECB seem in good shape right now. ECB is not nearly as exposed to interest-rate increases. 20

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