Macroeconomics: Policy, 31E23000, Spring 2018 Lecture 8: Safe Asset, Government Debt Pertti University School of Business March 19, 2018
Today Safe Asset, basics Government debt, sustainability, fiscal policy rules GDP-linked bonds
Safe Asset 1 Monetary unions, especially EMU, have problems in a ZLB-situation: Standard monetary policy ineffective in dealing with unionwide problem. Fiscal policy powerful, in principle, but in the absence of union wide policy depends on the coordination of national fiscal policies. National fiscal policies should take care also of national problems. Safe asset: can ensure that standard monetary policy can be used also in ZLB-situation. Shortage of safe assets as one reason why ZLB emerges to begin with.
Safe Asset 2 I transfer the closed economy model in Caballero, Farhi and Gourinchas (2016) Safe Asset Scarcity and Aggregate Demand, American Economic Review,https://economics.mit.edu/files/11333, into our framework. Recall the 3-equation short-term model: y = A ar, a > 0 (IS) (1) π π 1 = α (y y e ) (PC) (2) π π T = αβ (y y e ) (MR) (3) With the safe asset the IS-curve is y = A ar 1 br s 1, a, b > 0 (4) In (4) r s is the return to the safe asset. The coefficient b is small: private sector capacity to create (issue) safe asset is limited.
Safe Asset 3 PC- and MR- equations are the same, but there is a market for the safe asset. With gross (flow) supply of s the equilibrium condition for the safe asset market is ϕ y y + ϕ s r s ψ (r r s ) = s, ϕ y, ϕ s > 0, ψ 0 (5) r s is now the policy rate. r is the risky market interest rate, r r s is the market risk premium. Caballero et. al. argue that ψ = 0: it measures how easy it is for the private sector to create safe assets. Here we use this assumption. With this the key point is that risk premium is determined by the IS-curve, output and the safe interest rate by the remaining part of the model.
Safe Asset 3 To understand the role of the safe asset supply look at the value of the natural safe interest rate when output is at its Wicksellian level y e. From (5): r s = s ϕ yy e ϕ s (6) Clearly, if the supply of the safe asset is so low that s ϕ y y e < 0 the economy is driven to the ZLB-equilibrium with r s = 0 and output at the Keynesian level y = s ϕ y. Role for Q(uantitative) E(asing)? (4) implies that the shortage of assets increases the risk premium at y = y e.
Safe Asset 4 Assume now that the safe asset is supplied at high enough level for the safe interest rate to be positive. To see how the economy adjusts when a shock hits assume that the shock is a temporary negative demand shock reducing current output to y 0 whereby current inflation is reduced to (from the PC-curve) to π 0 = π T α (y e y 0 ) In period 1 the inflation is π 1 = π 0 + α (y 1 y e ). This together with the MR-equation π 1 π T = αβ (y 1 y e ) determine the output level and inflation rate y 1, π 1. We know that y 1 > y e and π T > π 1 > π 0.
Safe Asset 5 Given the one-period lag for the change in the interest rate change to have an effect on inflation and output, the CB sets the interest rate today,r 0 s, at a level that leads the economy to y 1, π 1 next period: r0 s = s ϕ yy 1 (7) ϕ s The IS-equation can be solved for the market interest rate r 0. How does the risk premium change in period 0?
From short run to long run 1 Be it as it is, most also academic economists support the claim that fiscal policies should be sustainable, the public debt relative to GDP cannot grow without limits without causing troubles. How do we evaluate the sustainability of the debt? As already noted, debt should be evaluated against the resources to pay it back. As tax revenues grow with the GDP and the government has in addition right to tax citizens, the proper measure for sustainability analysis is the debt/gdp-ratio. The basic budget equation for change in public debt can be obtained from the government budget constraint and is B t = G t T t + i t B t 1 (8)
From short run to long run 2 Here B = government debt, denotes change, B t B t B t 1. The nominal value of GDP is P t y t To get to the development of the debt/gdp-ratio divide both sides of (8) by P t y t : B t = d t + ib t, d t G t T t P t y t P t y t d t = primary deficit/gdp and b t = debt/gdp. We are interested in the development of b t., b t B t 1 P t y t (9)
From short run to long run 3 Now B t B t P t+1 y t+1 = B t 1 P t y t P t+1 y t+1 P t y t P t y t (10) = b t+1 (1 + π t ) (1 + g t ) b t (11) = b t+1 b t + (π t + g t + π t g t ) b t+1 (12) Here g t is the growth rate of the real GDP. Use (12) in (9) to get b t+1 b t = d + ib t (π t + g t + π t g t ) b t+1 d + (i t π t g t ) b t (13) Here we assume that π t g t is a small number as also are the inflation and growth rates and the period to make the difference (i π t g t ) b t+1 (i π t g t ) b t small.
From short run to long run 4 Now we have it, after remembering that the real rate of interest is r t = i t π t The first question we can analyze is how large the primary surplus must be if one wants to stabilize the debt at its current level, immediately. The answer is d = (r g) b t (14) Here the interest rate and the growth rate are projections of long run real interest rate and growth rate. This equation is known as the Domar-equation. It shows that if r g > 0 there must be a primary surplus while if r g < 0 debt can be stabilized even by running primary deficit.
From short run to long run 5 Conversely, one can ask what happens if the primary deficit or surplus is fixed to some level d. Obviously, if there is primary deficit and r g > 0, the debt will explode while with a surplus the debt will either explode (surplus too small) or the public sector will become net creditor (and the credit goes to infinity), unless the surplus is exactly at the level given by the Domar-equation. I leave the case with r g < 0 for you to look at the textbook, the answer is that there is no explosion, the economy will converge either to a finite indebtedness or finite creditor position.
From short run to long run 6 But should we take such sudden adjustments like adjusting from current primary deficit levels to primary surpluses given by the Domar-equation? With current knowledge the answer is no. Why? Theory supports tax smoothing, tax rates should be constant or change very slowly. We follow the study by Portes and Wren-Lewis (published 2015 in Manchester School), the working paper version can be found at https://www.niesr.ac.uk/sites/default/ files/publications/dp429.pdf.
From short run to long run 7 The idea is easy to understand. Let τ t be the (average income tax rate). By the Harberger-triangle arguments the efficiency cost associated with this tax can be approximated by τ 2 t. Since b t = (1 + r) b t 1 + d t and by assuming that the government does not allow its debt to explode the optimal path for the tax rate is given by minimizing the total discounted costs τ1 2 2µ 1 [b 2 (1 + r) b 1 g 1 + τ 1 ] + 1 [ τ2 2 2µ 2 [b 3 (1 + r) b 2 g 2 + τ 2 ]] +... 1 + ρ ( ) 1 t 1 [ + τt 2 2µ t [b t+1 (1 + r) b t g t + τ t ]] +... 1 + ρ Here, and just for now, g = government expenditure/gdp, µ t 1 is the cost of respecting the budget constraint (Lagrange-multiplier), ρ is the social time preference.
From short run to long run 8 The optimality conditions with respect to the choice of the tax rate and debt are which implies that τ t = µ t (15) µ t = 1 + r 1 + ρ µ t+1 (16) τ t = 1 + r 1 + ρ τ t+1 (17) In the Permanent-Income-Hypothesis case, r = ρ the tax rate is constant, τ t = τ t+1. This is the case of perfect tax smoothing. But even with other cases the realistic values for the interest rates imply very small changes in the tax rate.
From short run to long run 9 Tax smoothing is thus optimal in managing public finances. This has strong implications: All shocks should be absorbed by public debt, not by changing the tax rate. There is no optimal level of debt. But obviously (?) public sector should not be allowed to become insolvent. The optimal fiscal policy rule would then set both some target level for the debt/gdp-ratio and some adjustment parameter determining how fast the target should be reached.
From short run to long run 10 The adjustment parameter should be small to make the adjustment slow. To see more clearly the implications of tax smoothing we can see from (13) that the debt does not increase if ( T y ) P ( G y ) P b r P g P (18) where P refers to permanent or long-run and especially ( ) P G y refers to a long-run government plan. The question is now how to fund this plan.
From short run to long run 11 Tax smoothing implies that ( T y The previous equation then implies that ) P is constant ( T y ) P = τ. ( ) G P τ + ( r P g P) b (19) y Since d = G y T y, (13) implies that ( ( ) ) G G P b y + [( r r P) ( g g P)] (20) y
From short run to long run 12 Burden of debt: Ricardian neutrality Burden of debt: taxation crowding out Burden of debt: intergenerational transfers and other functions of debt.
Fiscal Policy Rules 1 Optimal fiscal policy: tax smoothing, no fixed level of debt optimal, but policies must ensure solvency of the public sector. Optimal policy rule: fix the target level for debt/gdp b and adjust either public expenditure or average tax rate (or both) to reach the target in the long run: g t g = a (b t 1 b ), a > 0 (21) τ t τ = c (b t 1 b ), c > 0 (22) τ t g t = rb t 1 + f (b t 1 b ), f > 0 (23) g and τ are the expenditure and tax rate consistent with b. Tax smoothing: the adjustment parameters a, c and f must be small. Also research results: a b.
Fiscal Policy Rules 2 The problem with the rules like (21) is that with a small adjustment coefficient the target debt will not be achieved in typical conditions under the lifetime of a government adopting the target. Also, or the other side of the coin, is that there is no incentive for a government to fulfill the requirements given by a rule like (21), deviations do not matter. There also no incentive to implement the policy: unforeseen events can be blamed for not implementing. This is an issue of transparency also. The rules reflect partly the household fallacy : debts have to paid back?
Fiscal Policy Rules 3 One way around the problems is to specify the required percentage adjustment in debt implied by the optimal rules for the electoral term, given the forecasts of growth and interest rates. The problem then is that with surprise adverse changes in growth reaching the goal could imply very large changes in taxes or expenditure. This can be mitigated by specifying debt reduction targets in terms of equivalent reductions in (primary) deficits, the impact of adverse shocks would have less deflationary implications. Swiss rule: deviations from plans allowed but too rapid a return to norm required. Deficit targets: rolling targets (fixing only the date by which the target is achieved) allows debt to work as shock absorber.
Fiscal Policy Rules 4 Conditional targets: adjusting for cyclicality. Threat of manipulation but allows shock absorbers to work efficiently. Role for fiscal councils in reducing manipulation: independent evaluation of the adjustments needed? Treatment of public investment? Golden rule : public investment not included in deficit calculations.
Fiscal Policy Rules 5 EMU rules? Target for both deficit and debt, but allowing some rolling. Rationale? De facto prevented automatic stabilization to work efficiently.
Does public debt matter? 1 Ricardian equivalence: as long as the government is committed to servicing and paying back its debt, the debt is not net wealth: Private agents understand that the present value of future taxes equals the value of debt, in net terms changing the structure of funding of the public sector does not have any real effects, the Modigliani-Miller theorem for the public sector. Assume that there is one household in the economy, the economy exists for two periods. The public sector has a fixed expenditure plan over the economy s lifetime, G 1 and G 2. The household consumes C i, i = 1, 2, in period i and its net saving in period 1 is S.
Does public debt matter? 2 Assume that the household face the same interest rate r as the government. Assume also that the taxes are lump-sum taxes. Then the budget constraints of the household are C 1 + S = Y 1 T 1 (24) C 2 = Y 2 + (1 + r) S T 2 (25) Similarly, the budget constraints of the government are G 1 = B + T 1 (26) T 2 = G 2 + (1 + r) B (27) Here B = borrowing by the government. Assume capital markets are perfect: the household and the government can freely choose S and B.
Does public debt matter? 3 Solve S from (24) and substitute in the second household budget constraint, and solve B from (24) and substitute in the second government budget constraint (this is OK by the assumption of perfect capital markets). The resulting equations, intertemporal budget constraints, are These imply that C 1 + C 2 1 + r = Y 1 + Y 2 1 + r T 1 T 2 1 + r G 1 + G 2 1 + r = T 1 + T 2 1 + r (28) (29) C 1 + C 2 1 + r = Y 1 + Y 2 1 + r G 1 G 2 (30) 1 + r Thus, only the present value of government purchases matters for the household behavior, not how government purchases are financed. This is the Ricardian Equivalence (RE).
Does public debt matter? 4 RE needs all the assumptions made above (in bold) to hold. Given this, it is not suprising that empirics does not support its relevance. RE is also known as Debt Neutrality. This tells what exactly the issue is: If debt neutrality holds it is hard to see what burden public debt can be and how borrowing could be harmful to future generations: the present generation undoes the negative impacts of debt. Note also the implication that government expenditure just crowds out private consumption. Implications for the effectiveness of fiscal policy?
Burden of Public Debt Change assumptions needed for RE and debt matters for the private sector. Overlapping (finite-lifetime) generations (OLG): Without perfect altruims RE is not valid. If taxes are not lump sum but are distortionary then debt can be a burden to future generations: the taxes needed to pay back the debt reduce aggregate output. But what if the rate of interest is below the growth rate? ZLB and debt funded increase in government expenditure? Public debt crowding out private investment? Public debt need not to paid back ever, burden to future generations? Debt has to be serviced. Many, heterogeneous households: Those not holding any debt will share in paying back the debt. But, in general, current debt is taken care of by the generations currently living.
Interest rates and growth rates 1 The difference between the interest rate on government debt and economic growth is crucial for the sustainability of debt and the burden of debt on future generations. Jorda et. al. (2017) have collected data on government short and long term debt (in addition to other returns) and economic growth in 17 rich countries for 1870-2015, see e.g. https://www.ineteconomics.org/uploads/papers/ Jorda-Knoll-Kuvshinov-Schularick-Taylor-The-Rate-of-Re pdf. Next figure shows the development of safe returns and economic growth, both in real terms.
SugarSync/Luennot/Macro2018/L8, F1.pdf L8, F1
Interest rates and growth rates 2 To get a longer view, let us have a look at short and long term interest rates since 3000 BC. The numbers come from Andrew Haldane s speech, https://www.bankofengland.co.uk/-/media/boe/ files/speech/2015/stuck.pdf?la=en&hash= 3247D34307D99E8E4E11E5B890837AD6C6CAEFFB:
SugarSync/Luennot/Macro2018/L8, F2.pdf L8, F2
GDP-linked government bonds Robert Shiller proposed in 1993 that governments should issue bonds with the interest rate indexed to the GDP growth rate: lower interest rate with lower growth, higher with higher growth. This would improve automatic stabilization: in booms increased pressure to contain/reduce government expenditure, in recessions maintain/increase expenditure. Benefits to governments: fiscal space (e.g. the sustainable level of government debt relative to GDP) would increase from 20-60 per. Benefits to investors: lower risk of government bankruptcy, access to returns from all factors of production (e.g. human capital). How to create? Linking to GNI instead of GDP.