price stability and debt stability: a wicksell-lerner-tinbergen framework for macroeconomic policy

Price Stability and Debt Stability

Price Stability and Debt Stability: AWicksell-Lerner-Tinbergen Framework for

Macroeconomic Policy

J. W. Mason and Arjun Jayadev

September 25, 2014


Introduction

I Debate: Is ability to reach full employment through fiscaldeficits constrained by public debt sustainability?

I Debate about definition of sustainability.

I One useful definition of sustainable debt: stable debt-GDPratio

I Question: Does expansionary fiscal policy imply risingdebt-GDP ratio?

I Answer: No. (Sometimes requires debt-GDP ratio to convergeto higher, but finite, level).

I Why? Interest rate and deficits affect debt trajectory


Our Framework

I Wicksellian “natural interest rate” (zero output gap) and“sustainable budget balance” (constant debt-GDP ratio) arejointly determined.

I Medium-run analysis: Given average level of private demand,inflation and growth over a business cycle or decade, whatcombinations of interest rate and budget balance areconsistent with each goal?

I Simplest solution: Coordination of monetary and fiscal policyto achieve both.

I But political and practical arguments for distinct portfolios, orfor central bank “independence”


Dynamics of Policy Adjustment

I Tinbergen issue: we have two instruments (interest rate andbudget balance) and two targets (constant debt ratio and fullemployment/price stability).

I “Sound finance” rule assigns interest rate to output gap andbudget balance to debt-GDP ratio. “Functional finance” rulehas opposite assignment.

I In principle, assignment makes no difference. Both implyidentical equilibrium values for interest rate and budgetbalance.

I Sound finance and functional finance appear radically differentbut do not generally imply different policy outcomes

I But in practice, wrong assignment can amplify shocks,creating endogenous “policy cycles” or divergence


Policy Goals: Price Stability or Full Employment

Standard assumptions of textbook “3-equation” macroeconomicmodels, shared by all practical forecasters:

I There is a well-defined level of potential output

I Goal of macro policy: minimize “output gap”I Keeping output at potential encompasses goals of both price

stability and full employment

I Current output is a negative function of the interest rate anda positive function of government deficits

I Private demand (including the trade balance) varies over time


IS equation

y = z − ηi − γb + τ id (1)

Implies linear combinations of interest rate and budget balancecompatible with price stability – for each fiscal surplus or deficit,there is a different “natural” interest rate

I y : output gap, as percent of potential output

I z : output gap when interest rate and primary deficit are zero

I i : interest rate (average rate on government debt)

I b: primary budget surplus

I d : debt-GDP ratio

I γ: average multiplier on government spending and taxes

I η: percent change in GDP from one point change in i

I τ : multiplier on interest payments on public debt


Price stability or Full Employment Locus


Policy Goals: Debt Stability

I Strong definition of sustainability: debt-GDP ratio cannot risefrom current level

I By definition, ensures that ratio will not rise above any criticalthreshold

I Analysis would be the same if we instead required debt ratioto fall (or rise) by fixed percent of GDP each period


DS equation

“Least Controversial Equation in Macroeconomics”: change indebt-GDP ratio is depends on i interest, b budget balance and g ,GDP growth rate. Debt can reduced by raising b or lowering i(historically both)

∆d =i − g

1 + gd − b (2)

g : growth rate of GDP∆d = 0 satisfied by linear combinations of i and b. For everyinterest rate, there is a different sustainable budget balance


Debt Stability Locus


IS curve and law of motion of government debt together defineunique combination of fiscal balance and interest rate with outputat potential and constant debt-GDP ratio:


Tinbergen and assignment of rules

I Sound Finance:

I Interest rate =⇒ output gapI Budget balance =⇒ debt stability

I ’Functional’ Finance:I Interest rate =⇒ debt stabilityI Budget balance =⇒ output gap

I Sound finance = moving vertically toward potential outputlocus and horizontally toward debt stability locus.

I Functional finance = moving horizontally toward potentialoutput locus and vertically toward debt stability locus.

I Adjusting each instrument independently based on its owntarget can produce cycles in interest rate-fiscal balance space.Dynamics matter!


Feedback effects in Policy Space

Intuition:

I Raising interest rate to eliminate a positive output gapincreases interest burden of government debt, requiring highertaxes or lower expenditure to keep debt ratio stable.

I Moving the fiscal balance toward surplus to stabilize the debtratio reduces demand, requiring lower interest rate to keepoutput at potential.

I A lower interest rate implies slower growth in the debt ratio,encouraging spending increases or tax cuts.

I As fiscal balance moves toward deficit, demand increases,requiring higher interest rate to keep output at potential.


Convergence or Divergence?

I Whether these cycles converge or diverge depends on theparameter values and the level of debt.

I Conclusions from formal stability analysis:

I Sound finance converges most quickly when η is large, γ and τare small, and the debt ratio d is low.

I Functional finance converges most quickly when γ is large, η issmall, and the debt ratio d is high.

I For plausible parameter values (e.g. from FRBUS model),critical value of d for sound finance to converge is between 0.5and 1.


Implication of stability analysis: when debt ratio is high, to avoidexplosive policy cycles budget balance must target output gap andinterest rate must target debt stability.Fiscal space metaphor is backwards!

I At high debt ratios, change in debt ratio depends relativelymore on interest rate, and relatively less on current spendingand taxes.

I Historically, interest rate policy has focused on public debtrather than output when debt ratios were high.

I World War II-era USI “Financial repression” (Reinhart et al.)


Locating the PS and DS Loci HistoricallyWe estimate PS and DS loci by decade, on following assumptions(proof of concept):

I Output gap measured as deviation from BEA “potentialoutput” trend (other useful measures behave similarly)

I Given output gap and trade balance plus chosen values of γ, ηand τ , can calculate state of private demand as a residual

I Nominal interest rate measured as average rate on federal debt

I Interest rate that matters for private demand is nominal rateminus 0.5× observed inflation.

I Even with strong assumptions of forward-looking, rationaltransactors this parameter should be less than 1

I Net exports add to final demand one for one.

I Parameter values: γ = 1.5, η = 1, τ = 0.5 (typical fromforecasting models)


Price Stability and Debt Stability Loci, 1950s


Price Stability and Debt Stability Loci, 2004-2013


Historical Estimates as Model Validation

I Any forecasting model uses certain parameter values. Incombination with historical data, these values imply certainpath for autonomous private demand.

I “Autonomous” here meaning independent of fiscal andmonetary policy.

I Tool for model validation – are implied variations in privatedemand consistent with everything else we know abouteconomy?

I Historical variations in private demand informative aboutrange of variation policy will have to respond to in future.


Implied Contributions to Demand

Contributions to Output Gap in Percent of GDP, 5-Year Moving Averages


The current situation

I Sharp fall in private demand after 2008 implied by appearanceof substantial negative output gap despite increase in demandfrom other sources

I Lower net imports: +2 pointsI Lower interest rates: +3 pointsI Shift toward primary deficit: +7 points

I Movement of private demand of 15-20 points in just a fewyears seem hard to offset with either monetary or fiscal policy

I Implies that macro stabilization needs to focus on underlyingshifts of private demand


Conclusions

I Need to better define ‘debt sustainability’. No increase fromcurrent debt-GDP ratio is one plausible definition

I Debt sustainability in this sense is not generally a constrainton active fiscal policy

I If fiscal policy targets output and monetary policy targets debtratio, will normally keep output at potential and debt ratioconstant

I If private demand is very weak and inflation and growth arelow (as now), neither “sound finance” nor “functional finance”rule can achieve both targets

I With each instrument committed to one target, will seeendogenous “policy cycles.” Magnitude of cycles depends onparameters and current debt ratio


A 40-Year Sound Finance Spiral?

10-Year Moving Averages, US i and b


I 1970s: Debt stable, positive output gap

I Interest increase moves economy toward price stability locusbut off debt sustainability locus

I Increased debt under Reagan due mostly (60 - 80%) to higheri , not primary deficits!

I Rising debt leads to primary surplus in 1990s. Reachesdebt-sustainability locus, moves off price-stability locus.

I Primary surplus under Clinton =⇒ negative output gap;initially masked by tech boom.

I Shift towards surpluses =⇒ lower i required for potentialoutput (near zero 2000, zero in 2008)

I Standard estimates of multiplier, interest elasticity of outputsuggest Clinton surpluses reduced “natural rate” by 5 points.

price stability and debt stability: a wicksell-lerner-tinbergen framework for macroeconomic policy

Economy & Finance

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