Public budget accounting and seigniorage. 1. Public budget accounting, inflation and debt. 2. Equilibrium seigniorage

Transcription

1 Monetary Economics: Macro Aspects, 2/ Henrik Jensen Department of Economics University of Copenhagen Public budget accounting and seigniorage 1. Public budget accounting, inflation and debt 2. Equilibrium seigniorage Literature: Walsh (Chapter 4, pp ) 3. Plan for next lecture c 2015 Henrik Jensen. This document may be reproduced for educational and research purposes, as long as the copies contain this notice and are retained for personal use or distributed free.

2 Introductory remarks Inflation or the nominal interest rate have been viewed as a tax on household s resources in the previous lectures. In particular, through the erosion of real money balances This inflation tax has been shown to have implications for private sector behavior (money demand, consumption, labor supply etc.) The flip-side of the tax-coin has been ignored: All proceedings from the tax have been returned as lump-sum transfers. I.e., the government budget includes no spending or government debt servicing One ignores central, and highly relevant, questions like: Can inflation be used as a means of financing public expenditures, deficits and debt? Will monetary and fiscal policy interact in ways that qualify some of the conclusions reached so far from the flex-price models? Will fiscal policy (e.g., deficit creation) have implications for monetary policy and thus, e.g., inflation? If inflation is used as a tax, what will its optimal value be? (will the Friedman rule robust to public finance considerations?) Can inflation always save the day for a public budget, or can it ultimately ruin the day? 1

3 Seigniorage across (some) countries, Source: Aisen and Veiga (2005) 2

4 Continued 3

5 Public budget accounting, inflation and debt The core link between monetary and fiscal policy is the public budget constraint The fiscal branch of government (the Treasury) faces the following budget identity in nominal terms G t + i t 1 B T t 1 = T t + ( B T t B T t 1) + RCBt (4.1) Superscript T denotes total public debt; RCB t is receipts from the central bank The central bank s budget identity ( ) B M t Bt 1 M + RCBt = i t 1 Bt 1 M + (H t H t 1 ) (4.2) Superscript M denotes public debt held by the central bank; H t is high-powered money the monetary base (the central bank s own liabilities: Currency in circulation and reserves held by commercial banks) Let B t = Bt T Bt M be public debt held by the private sector. The two budget identities are combined to the consolidated budget identity G t + i t 1 B t 1 = T t + (B t B t 1 ) + (H t H t 1 ) (4.3) 4

6 Expressed relative to total nominal income P t y t, and ignoring population and output growth: g t + r t 1 b t 1 = t t + (b t b t 1 ) + H t H t 1 P t y t ; (4.4 ) lower-case letters are variables relative to total nominal income and is the ex post real interest rate r t i t π t 1 Define the ex ante real interest rate as r t i t π e t 1, = g t + r t 1 b t 1 = t t + (b t b t 1 ) + (1 + r t 1) (π t π e t) 1 + π t b t 1 + H t H t 1 P t y t (4.5 ) Higher-than-expected inflation, π t > π e t, erodes the real servicing costs of debt The last term of (4.5 ) is seigniorage, the real proceedings from issuing non-interest-bearing debt: Money Seigniorage relative to total nominal income is s t H t P t y t H t 1 P t y t = h t π t h t 1 = h t h t 1 + π t 1 + π t h t 1 (4.6 ) Even in steady state, s t > 0: As h is a real liability for the government, inflation erodes its real value 5

7 What if inflation is zero? Will there be no revenue from seigniorage? Yes, by issuing non-interest bearing debt (=money) instead of interest bearing debt (bonds), the government saves interest payments for given total debt To see this, rewrite budget identity, defining d t b t + h t as total liabilities: g t + r t 1 (d t 1 h t 1 ) = t t + (d t d t 1 ) + (1 + r t 1) (π t π e t) 1 + π t (d t 1 h t 1 ) + π t 1 + π t h t 1 g t + r t 1 d t 1 = t t + (d t d t 1 ) + (1 + r t 1) (π t π e [ t) πt (1 + r t 1 ) (π t π e ] d t 1 + t) + r t 1 h t π t 1 + π t g t + r t 1 d t 1 = t t + (d t d t 1 ) + (1 + r t 1) (π t π e t) 1 + π t d t 1 + i t π t h t 1 When constraint is formulated in terms of total liabilities, the steady-state seigniorage is s = It is positive for i > 0. Represents saved interest on b i 1 + π h (4.9) 6

8 In general, irrespective of definition of seigniorage, a change in monetary financing requires offsetting changes in either taxes, spending or debt In which manner monetary changes affect fiscal policy depends on the definition of fiscal policy If it is in terms of fixed spending and interest rate bearing debt, changes in s and the offsetting changes in taxes are monetary policy If it is in terms of fixed spending and total liabilities, changes in s and offsetting taxes and composition of liabilities are monetary policy So which seigniorage definition is appropriate, depends on how fiscal policy is conducted Note implication of simple version of budget identity (ignoring unanticipated inflation) g t + rb t 1 = t t + b t b t 1 + s t, the solvency requirement : (1 + r) b t 1 + i=0 g t+i (1 + r) i = holds when lim i (1 + r) i b t+i = 0 no Ponzi games i=0 t t+i + s t+i (1 + r) i So, if government has initial debt, runs deficits in the future, it must at some point run surpluses, t t+i + s t+i > g t+i, generated through taxes or seigniorage 7

9 This raises the issue of whether government debt or deficits will ultimately create seigniorage and potentially inflation This will depend on the fiscal-monetary regime If fiscal policy is dominant (or active ), monetary policy must be passive, and secure solvency If monetary policy is dominant, fiscal policy must secure solvency Hence, in regimes of fiscal dominance, it may be the case that debt and deficits will be inflationary Also, it may be the case that monetary contractions (e.g., aimed at reducing inflation) will reduce seigniorage revenues, increasing deficits and debt, which ultimately requires increased seigniorage, and thus, inflation in the future (Sargent and Wallace s Unpleasant Monetarist Arithmetic ) This emphasizes that treating money as independent of fiscal policy, could be misleading, as monetary policy changes could very well be the result of changes in fiscal policy 8

10 A simple model to prove the point Assume government spending is zero. The budget constraint then becomes (1 + r t 1 ) b t 1 = t t + b t + s t (4.15) Let the present value of taxes cover a fraction of current government liabilities (1 + r t 1 ) b t 1 : ( ) s t 1 T t t s = ψ (1 + r t 1) b t 1, 0 < ψ r s s=t For ψ = 1, any debt is fully backed by taxes over time (this is sometimes referred to as a Ricardian fiscal policy or, non-dominance in fiscal policy) For ψ < 1 only a fraction is backed. I.e., some fiscal dominance is present The present value of taxes is the bounded solution to the forward-looking difference equation T t = t t + 1 T t r t Hence, T t = t t + 1 ψ (1 + r t ) b t 1 + r t = t t + ψb t From the assumption about T t one gets ψ (1 + r t 1 ) b t 1 = t t + ψb t Note that with ψ = 1 one gets the government budget constraint with s t = 0. So, for ψ < 1, seigniorage is necessary 9

11 Now consider the households budget constraint (y t is endowment) y t + (1 + r t 1 ) b t 1 + m t π t t t = c t + m t + b t (4.16) Inserting the expression for t t from the government budget constraint one gets y t + (1 ψ) (1 + r t 1 ) b t 1 + m t π t = c t + m t + (1 ψ) b t For ψ = 1, debt disappears. In general equilibrium, it plays no role for determination of the price level; only the money stock matters For ψ < 1, debt will matter for price level determination To exemplify the role of debt for prices and inflation, consider a MIU preference specification for households, where the per-period utility function is given by u (c t, m t ) = ln c t + δ ln m t, δ > 0, The households then maximize life-time discounted utility subject to the budget constraint 10

12 Deriving the money demand function and consumption-euler equation. Material not for lecturing, but for reading Maximization characterized by V (b t 1, m t 1 ) = max {ln c t + δ ln m t + βv (b t, m t )} where maximization is over c, m, and b and subject to the budget constraint. As usual, use the budget constraint to eliminate b t to obtain an unconstrained maximization problem over c and m First-order condition w.r.t. c: First-order condition w.r.t. m: 1 c t = δ m t + βv m (b t, m t ) = β 1 ψ V b (b t, m t ). (i) β 1 ψ V b (b t, m t ). (ii) Relationships between partial derivatives of the value function by the envelope theorem: V b (b t 1, m t 1 ) = β (1 + r t 1 ) V b (b t, m t ), (iii) β V m (b t 1, m t 1 ) = (1 + π t ) (1 ψ) V b (b t, m t ). (iv) Forward (iii) and multiply by β/ (1 ψ) on both sides to get: β 1 ψ V b (b t, m t ) = β2 1 ψ (1 + r t) V b (b t+1, m t+1 ). 11

13 Then use (i) to obtain the consumption Euler equation (the Keynes-Ramsey rule): 1 1 = β (1 + r t ) c t c t+1 c t+1 = β (1 + r t ) c t (v) Then use (iv) on (ii) to get δ m t + β 2 (1 + π t+1 ) (1 ψ) V b (b t+1, m t+1 ) = δ β 1 + m t (1 + π t+1 ) δ m t (1 + π t+1 ) (1 + r t ) c t+1 = 1 c t β 1 ψ V b (b t, m t ) = 1 c t c t where the last two equations follows from applying (iv) and (i), and finally (v). From this the money demand relationship follows as: [ ] 1 1 m t = δ 1 c t (1 + π t+1 ) (1 + r t ) [ m t = δ 1 1 ] 1 c t (1 + i t ) and thus ( ) 1 + it m t = δ i t c t (vi) 12

14 Note that this follows immediately from the general characterization of optimal money demand from the MIU approach in Chapter 2 u m (c t, m t ) u c (c t, m t ) = i t 1 + i t This indeed gives and thus the money demand function (vi) δ/m t 1/c t = i t 1 + i t, End of material not for lecturing 13

15 Define w t m t + (1 ψ) b t as the total real wealth net of taxes: Real money balances plus non-tax-backed government debt Household budget constraint then becomes y t + (1 + r t 1 ) w t 1 i t π t m t 1 = c t + w t Remark i t 1 m t 1, 1 + π t which is the deduction from total net wealth arising from the fact that real money pays no interest Use the lagged money demand function and consumption-euler equation derived above, ( ) 1 + it 1 m t 1 = δ c t 1, c t = β (1 + r t 1 ) c t 1 i t 1 i t 1 y t + (1 + r t 1 ) w t 1 δ 1 + i t 1 c t π t i t 1 = c t + w t y t + (1 + r t 1 ) w t 1 δ (1 + r t 1 ) c t 1 = c t + w t y t + (1 + r t 1 ) w t 1 δ β c t = c t + w t Use that y t = c t in equilibrium and examine the steady state: w ss = δ = M ss + (1 ψ) B ss βr ssyss P ss 14

16 The price level is thus determined as P ss = βrss δy ss [M ss + (1 ψ) B ss ] Government debt matters for the price level when ψ < 1, i.e., when there is some fiscal dominance Empirics (Resende and Rebei, 2008): Canada, ψ US, ψ South Korea, ψ Mexico, ψ

17 Equilibrium seigniorage Before considering (next lecture) how inflation is optimally used as a tax, and before (re)considering the optimality of the Friedman rule, we assess: What can seigniorage achieve in terms of financing given deficits? Anything? Or are there limits? What are the inflationary implications of relying on seigniorage? Can hyperinflations result from seigniorage collection? Are there limits to collection of seigniorage? Yes! On the one hand, higher inflation and nominal interest rates, increase seigniorage for given real money balances On the other hand, real money balances will fall as inflation and nominal interest rates increase (a money demand response) Hence, as the inflation tax goes up, the tax base is going down This is shown formally in a MIU model 16

18 Here, it suffi ces to find the money demand function from the usual first-order condition: Specific form of per-period utility function: Resulting money demand relation leading to A standard specification of money demand u m (c t, m t ) u c (c t, m t ) = i t 1 + i t I t u (c t, m t ) = ln c t + m t (B D ln m t ), B > D > 0 B D ln m t D 1/c t = I t m t = Ae I t/dc t, A e (B D)/D. (4.24 ) [Often replaced by m t = Ke απe t, α > 0, in studies of hyperinflations (where assumption is that real interest rate and consumption/output fluctuates relatively little), or for steady-state/long-run analyses, where by the Fisher relationship inflation and nominal interest rate moves one-for-one] 17

19 Steady-state seigniorage is [from (4.9)] s = Using the money demand function one gets i 1 + π m = (1 + r) i m = (1 + r) I m 1 + i s = (1 + r) I A exp [ I ] Dc Assume r and c are invariant to monetary policy in steady-state For I close to zero, seigniorage is close to zero; this will be a characteristic of relatively low inflation For I very high, seigniorage is also close to zero; this will thus be a characteristic of relatively high inflation Hence, with inflation increasing from a low level, seigniorage is increasing, but eventually the falling money demand reduces seigniorage. A maximal amount of seigniorage thus exist. I other words an inflation rate π exists for which seigniorage is at a maximum. For π > π equilibrium seigniorage is decreasing in π For π < π equilibrium seigniorage is increasing in π A seigniorage Laffer curve is faced by the government 18

20 Inflationary implications of relying on seigniorage The Laffer-curve property implies that two steady-state inflation rates can finance the same deficit; a high and a low inflation rate Stability properties of the two steady states, both accomplishing the same financing target? Walsh (2010) demonstrates example where low-inflation equilibrium is stable but high-inflation equilibrium is unstable An increase in finance requirements will then raise inflation, but cause accelerating inflation if the economy was in the unstable equilibrium Also, the Laffer curve property shows that there are limits as to how much one can finance by seigniorage If financing requirement suddenly increases above what is feasible to finance by seigniorage, the government may engage in futile financing attempts by printing money at a faster rate In both cases, hyperinflations arise (often defined as monthly inflation rates of +50%), which can only be stopped by fiscal reform Examples: Weimar Republic in the 1920s, Zimbabwe in

21 Children using money as toys in Weimar Republic during

22 Money printed within a year in Zimbabwe

23 Inflation bubbles Hyperinflations can also be non-fundamental; i.e., occur in isolation of money growth. These are labelled speculative hyperinflations (or bubble paths ) As an example, let money demand be (now variables are logarithms): m t p t = α (E t p t+1 p t ), α > 0, This is rearranged as an expression for the (log of) price level: p t = α α 1m t α 1E tp t+1 This is a first-order expectational difference equation in p t (as it depends on its expected future value) Money is for simplicity assumed to be constant, m t = θ 0 The variable θ 0 is the model s fundamental, and a solution of p t depending only on the fundamental and parameters is a fundamental solution To find this solution, use the method of undetermined coeffi cients: Conjecture a form of the solution by undetermined coeffi cients Forward the conjecture, take expectations and insert into the expectational difference equation Identify the coeffi cients 22

24 Here: Conjecture the solution p t = Xθ 0, where X is the undetermined coeffi cient Forward the conjecture and take expectations: E t p t+1 = Xθ 0 and insert into difference equation: p t = α α 1θ α 1Xθ 0 = α 1 + X 1 + α θ 1 0 The undetermined coeffi cient is then identified as X = α 1 + X 1 + α 1 and thus X = 1 Hence, p t = θ 0 is the fundamental solution However, it is easy to see that infinitely many solutions of the form exists for p t = θ 0 + bub t, bub t 0 E t bub t+1 = ( 1 + α 1) bub t (bub t will grow with α 1 bub t 1 ) To see this, note that is it fully consistent with the difference equation: α 1 1 θ 0 + bub t = 1 + α 1θ α 1E t [θ 0 + bub t+1 ] α 1 θ 0 + bub t = 1 + α 1θ 0 + θ 0 = θ 0 1 [ θ0 + ( 1 + α 1) ] bub 1 + α 1 t Hence, if bub t > 0, we have explosive prices increasing inflation even though the money supply is constant 23

25 Summary Monetary and fiscal policy are linked through the public budget constraint Ignoring this may be valid if governments have access to lump-sum taxation and follow policies that fully back interest-bearing debt with taxes (no fiscal dominance) Otherwise, important channels from monetary policy to fiscal policy and vice versa may be overlooked, as the financing properties of inflation is ignored Also, it is important to stress that an observed change in monetary policy may or may not be due to fiscal considerations, and therefore have different implications for the real economy depending on the source of the change While a potential financing tool, one must be aware of the dangers of hyperinflation associated with reliance on seigniorage as a means of financing public expenditures 24

26 Plan for next lecture Monday, March 9 Seigniorage, inflation and optimal taxation 1. Optimal taxation and seigniorage 2. Robustness of the Friedman rule? Literature: Walsh (Chapter 4, pp ; pp ) 25