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Price Stability and Debt Stability 
Price Stability and Debt Stability: A 
Wicksell-Lerner-Tinbergen Framework for 
Macroeconomic Policy 
J. W. Mason and Arjun Jayadev 
September 22, 2014
Price Stability and Debt Stability 
Introduction 
I Debate: Is ability to reach full employment through
scal 
de
cits constrained by public debt sustainability? 
I Debate about de
nition of sustainability. 
I One useful de
nition of sustainable debt: stable debt-GDP 
ratio 
I Question: Does expansionary
scal policy imply spiraling 
debt-GDP ratio? 
I Answer: No. (Sometimes requires debt-GDP ratio to converge 
to higher, but
nite, level). 
I Why? Interest rate and de
cits aect debt-trajectory
Price Stability and Debt Stability 
Aim: Framework 
I Framework: Wicksellian natural interest rate (zero output 
gap) and sustainable budget balance (constant debt-GDP 
ratio) are jointly determined. Unique (r, b) combination that 
assures both. 
I First best: Coordination of Monetary and Fiscal Policy to 
achieve this. 
I But political preference for independence-so dierent 
'portfolios'
Price Stability and Debt Stability 
Aim: Dynamics of Adjustment to Sustainable Equilibrium 
I Tinbergen issue: we have two instruments (interest rate and 
budget balance) and two targets (constant debt ratio and full 
employment/price stability). 
I Sound
nance rule assigns interest rate to output gap and 
budget balance to debt-GDP ratio. Functional
nance rule 
has opposite assignment. 
I In principle, assignment makes no dierence. Both imply 
identical equilibrium values for interest rate and budget 
balance. 
I But in practice, `wrong' assignment can amplify shocks, 
creating endogenous policy cycles or divergence
Price Stability and Debt Stability 
Aim: Historical Calibration and Measurement 
I Estimate the interest rate - budget balance combination 
consistent with constant debt ratio and zero output gap for 
the US historically (Proof of Concept). 
I Propose explicit reporting of policy-relevant demand 
parameters and the implied historical changes in autonomous 
private demand
Price Stability and Debt Stability 
Policy Goals: Price Stability or Full Employment 
Standard assumptions of textbook macroeconomics, used in all 
practical forecasting models: 
I There is a well-de
ned 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 and 
a positive function of government de
cits 
I Private demand (including the trade balance) varies over time
Price Stability and Debt Stability 
IS equation 
y = z  i  
b +  id (1) 
Implies linear combinations of interest rate and budget balance 
compatible with price stability { for each
scal surplus or de
cit, 
there is a dierent natural interest rate 
I y: output gap, as percent of potential output 
I z: output gap when interest rate and primary de
cit are zero 
I i : interest rate (average rate on government debt) 
I b: primary budget surplus 
I d: debt-GDP ratio 
I 
: average multiplier on government spending and taxes 
I : percent change in GDP from one point change in i 
I  : multiplier on interest payments on public debt
Price Stability and Debt Stability 
Price stability or Full Employment Locus
Price Stability and Debt Stability 
Policy Goals: Debt Stability 
I Strong de
nition of sustainability: debt-GDP ratio cannot rise 
from current level 
I By de
nition, ensures that ratio will not rise above any critical 
threshold 
I Analysis would be the same if we instead required debt ratio 
to fall (or rise) by
xed percent of GDP each period
Price Stability and Debt Stability 
DS equation 
Least Controversial Equation in Macroeconomics: change in 
debt-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 + g 
d  b (2) 
g: growth rate of GDP 
d = 0 satis
ed by linear combinations of i and b. For every 
interest rate, there is a dierent sustainable budget balance
Price Stability and Debt Stability 
Debt Stability Locus
Price Stability and Debt Stability 
IS curve and law of motion of government debt together de
ne 
unique combination of
scal balance and interest rate with output 
at potential and constant debt-GDP ratio:
Price Stability and Debt Stability 
Tinbergen and assignment of rules 
I Sound Finance: 
I Interest rate =) output gap 
I Budget balance =) debt stability 
I 'Functional' Finance: 
I Interest rate =) debt stability 
I Budget balance =) output gap 
I Sound
nance = moving vertically toward potential output 
locus and horizontally toward debt stability locus. 
I Functional

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HLEG thematic workshop on "Intra-generational and Inter-generational Sustainability", Arjun Jayadev

  • 1. Price Stability and Debt Stability Price Stability and Debt Stability: A Wicksell-Lerner-Tinbergen Framework for Macroeconomic Policy J. W. Mason and Arjun Jayadev September 22, 2014
  • 2. Price Stability and Debt Stability Introduction I Debate: Is ability to reach full employment through
  • 4. cits constrained by public debt sustainability? I Debate about de
  • 5. nition of sustainability. I One useful de
  • 6. nition of sustainable debt: stable debt-GDP ratio I Question: Does expansionary
  • 7. scal policy imply spiraling debt-GDP ratio? I Answer: No. (Sometimes requires debt-GDP ratio to converge to higher, but
  • 8. nite, level). I Why? Interest rate and de
  • 10. Price Stability and Debt Stability Aim: Framework I Framework: Wicksellian natural interest rate (zero output gap) and sustainable budget balance (constant debt-GDP ratio) are jointly determined. Unique (r, b) combination that assures both. I First best: Coordination of Monetary and Fiscal Policy to achieve this. I But political preference for independence-so dierent 'portfolios'
  • 11. Price Stability and Debt Stability Aim: Dynamics of Adjustment to Sustainable Equilibrium I Tinbergen issue: we have two instruments (interest rate and budget balance) and two targets (constant debt ratio and full employment/price stability). I Sound
  • 12. nance rule assigns interest rate to output gap and budget balance to debt-GDP ratio. Functional
  • 13. nance rule has opposite assignment. I In principle, assignment makes no dierence. Both imply identical equilibrium values for interest rate and budget balance. I But in practice, `wrong' assignment can amplify shocks, creating endogenous policy cycles or divergence
  • 14. Price Stability and Debt Stability Aim: Historical Calibration and Measurement I Estimate the interest rate - budget balance combination consistent with constant debt ratio and zero output gap for the US historically (Proof of Concept). I Propose explicit reporting of policy-relevant demand parameters and the implied historical changes in autonomous private demand
  • 15. Price Stability and Debt Stability Policy Goals: Price Stability or Full Employment Standard assumptions of textbook macroeconomics, used in all practical forecasting models: I There is a well-de
  • 16. ned 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 and a positive function of government de
  • 17. cits I Private demand (including the trade balance) varies over time
  • 18. Price Stability and Debt Stability IS equation y = z i b + id (1) Implies linear combinations of interest rate and budget balance compatible with price stability { for each
  • 20. cit, there is a dierent natural interest rate I y: output gap, as percent of potential output I z: output gap when interest rate and primary de
  • 21. cit are zero I i : interest rate (average rate on government debt) I b: primary budget surplus I d: debt-GDP ratio I : average multiplier on government spending and taxes I : percent change in GDP from one point change in i I : multiplier on interest payments on public debt
  • 22. Price Stability and Debt Stability Price stability or Full Employment Locus
  • 23. Price Stability and Debt Stability Policy Goals: Debt Stability I Strong de
  • 24. nition of sustainability: debt-GDP ratio cannot rise from current level I By de
  • 25. nition, ensures that ratio will not rise above any critical threshold I Analysis would be the same if we instead required debt ratio to fall (or rise) by
  • 26. xed percent of GDP each period
  • 27. Price Stability and Debt Stability DS equation Least Controversial Equation in Macroeconomics: change in debt-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 + g d b (2) g: growth rate of GDP d = 0 satis
  • 28. ed by linear combinations of i and b. For every interest rate, there is a dierent sustainable budget balance
  • 29. Price Stability and Debt Stability Debt Stability Locus
  • 30. Price Stability and Debt Stability IS curve and law of motion of government debt together de
  • 32. scal balance and interest rate with output at potential and constant debt-GDP ratio:
  • 33. Price Stability and Debt Stability Tinbergen and assignment of rules I Sound Finance: I Interest rate =) output gap I Budget balance =) debt stability I 'Functional' Finance: I Interest rate =) debt stability I Budget balance =) output gap I Sound
  • 34. nance = moving vertically toward potential output locus and horizontally toward debt stability locus. I Functional
  • 35. nance = moving horizontally toward potential output locus and vertically toward debt stability locus. I Adjusting each instrument independently based on its own target can produce cycles in interest rate-
  • 36. scal balance space. Dynamics matter!
  • 37. Price Stability and Debt Stability
  • 38. Price Stability and Debt Stability
  • 39. Price Stability and Debt Stability Feedback eects in Policy Space Intuition: I Raising interest rate to eliminate a positive output gap increases interest burden of government debt, requiring higher taxes or lower expenditure to keep debt ratio stable. I Moving the
  • 40. scal balance toward surplus to stabilize the debt ratio reduces demand, requiring lower interest rate to keep output at potential. I A lower interest rate implies slower growth in the debt ratio, encouraging spending increases or tax cuts. I As
  • 41. scal balance moves toward de
  • 42. cit, demand increases, requiring higher interest rate to keep output at potential.
  • 43. Price Stability and Debt Stability Convergence or Divergence? I Whether these cycles converge or diverge depends on the parameter values and the level of debt. I Sound
  • 44. nance converges most quickly when is large, and are small, and the debt ratio d is low. I Functional
  • 45. nance converges most quickly when is large, is small, and the debt ratio d is high. I For plausible parameter values (e.g. from FRBUS model), critical value of d for sound
  • 46. nance to converge is between 0.5 and 1.
  • 47. Price Stability and Debt Stability Implication of stability analysis: when debt ratio is high, to avoid explosive policy cycles budget balance must target output gap and interest rate must target debt stability. Fiscal space metaphor is backwards! I At high debt ratios, change in debt ratio depends relatively more on interest rate, and relatively less on current spending and taxes. I Historically, interest rate policy has focused on public debt rather than output when debt ratios were high. I World War II-era US I Financial repression (Reinhart et al.)
  • 48. Price Stability and Debt Stability
  • 49. Price Stability and Debt Stability Locating the PS and DS Loci Historically We estimate PS and DS loci by decade, on following assumptions (proof of concept): I Output gap measured as deviation from BEA potential output trend (other useful measures behave similarly) I Given output gap and trade balance plus chosen values of , and , 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 rate minus 0:5 observed in ation. I Even with strong assumptions of forward-looking, rational transactors this parameter should be less than 1 I Net exports add to
  • 50. nal demand one for one. I Parameter values: = 1:5, = 1, = 0:5 (typical from forecasting models)
  • 51. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 1950s
  • 52. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 1960s
  • 53. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 1970s
  • 54. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 1980s
  • 55. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 1990s
  • 56. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 2000s
  • 57. Price Stability and Debt Stability Price Stability and Debt Stability Loci, 2004-2013
  • 58. Price Stability and Debt Stability Historical Estimates as Model Validation I Any forecasting model uses certain parameter values. In combination with historical data, these values imply certain path for autonomous private demand. I Autonomous here meaning independent of
  • 59. scal and monetary policy. I Should present this path explicitly { ask, what combinations of
  • 60. scal and monetary policy would have been required to eliminate output gap in dierent periods historically? I Important because: 1. Tool for model validation { are implied variations in private demand consistent with everything else we know about economy? 2. Historical variations in private demand informative about range of variation policy will have to respond to in future.
  • 61. Price Stability and Debt Stability Implied Contributions to Demand Contributions to Output Gap in Percent of GDP, 5-Year Moving Averages
  • 62. Price Stability and Debt Stability The current situation I Sharp fall in private demand after 2008 implied by appearance of substantial negative output gap despite increase in demand from other sources I Lower net imports: +2 points I Lower interest rates: +3 points I Shift toward primary de
  • 63. cit: +7 points I Movement of private demand of 15-20 points in just a few years seem hard to oset with either monetary or
  • 64. scal policy I Implies that macro stabilization needs to focus on underlying shifts of private demand
  • 65. Price Stability and Debt Stability Improving Macroeconomic Data I Participants in macro policy debates should give explicit parameter estimates I Many published estimates of
  • 66. scal multipliers, relatively few of output-interest rate sensitivity I Any set of parameter values imply certain historical uctuations in private demand. Forecasters should compute publish these I Validation of parameter estimates { timing or size of implied demand shifts may not be plausible I Better estimates of historical demand uctuations helps establish if existing policy tools will be adequate in the future I Private forecasters and/or national statistical agencies should provide estimates of interest rates and budget balances needed to reach targets.
  • 67. Price Stability and Debt Stability Conclusions I Need to better de
  • 68. ne `debt sustainability'. No increase from current debt-GDP ratio is one plausible de
  • 69. nition I Debt sustainability in this sense is not generally a constraint on active
  • 71. scal policy targets output and monetary policy targets debt ratio, will normally keep output at potential and debt ratio constant I If private demand is very weak and in ation and growth are low (as now), neither sound
  • 73. nance rule can achieve both targets I With each instrument committed to one target, will see endogenous policy cycles. Magnitude of cycles depends on parameters and current debt ratio I Important to have consistent historical accounting for demand shifts given chosen parameters
  • 74. Price Stability and Debt Stability A 40-Year Sound Finance Spiral? 10-Year Moving Averages, US i and b
  • 75. Price Stability and Debt Stability I 1970s: Debt stable, positive output gap I Interest increase moves economy toward price stability locus but o debt sustainability locus I Increased debt under Reagan due mostly (60 - 80%) to higher i , not primary de
  • 76. cits! I Rising debt leads to primary surplus in 1990s. Reaches debt-sustainability locus, moves o price-stability locus. I Primary surplus under Clinton =) negative output gap; initially masked by tech boom. I Shift towards surpluses =) lower i required for potential output (near zero 2000, zero in 2008) I Standard estimates of multiplier, interest elasticity of output suggest Clinton surpluses reduced natural rate by 5 points.