D ECEMBER 11, 2012 The Plan O UTLINE Basics of Ramsey optimal - - PowerPoint PPT Presentation

OPTIMAL FISCAL AND MONETARY POLICY DECEMBER 11, 2012

December 11, 2012 4

OUTLINE

The Plan  Basics of Ramsey optimal policy problem (the microeconomics)  Applying the Ramsey framework to macroeconomic policy  Modern benchmark Ramsey (monetary policy) results

 Optimality of the Friedman Rule  Inflation very volatile and serially uncorrelated  Dynamic results: Fiscal Theory of the Price Level (FTPL) foundations

 How palatable is the strict Ramsey approach for monetary policy prescriptions?  Nominal price rigidity in the Ramsey environment (SGU 2004 JET)  Nominal wage rigidity in the Ramsey environment

 Chugh (2006 RED): embedded in Walrasian labor markets  Arseneau and Chugh (2008 JME): embedded in labor markets with search and matching frictions

December 11, 2012 7

THE ORIGINAL RAMSEY PROBLEM

Ramsey Basics  Static problem – no lump-sum taxes  Optimally finance exogenous government spending by levying proportional taxes on a vector of N goods – use N – 1 taxes  Household optimality:  A straightforward formulation of policy problem: choose to maximize household utility subject to

 Resource constraint  All household optimality conditions  Government budget constraint (equivalently, hh budget constraint)

 Primal formulation: implementability constraint

 Choose allocations directly

1

(1 )

N i i i i

p c y 



 



Consumer budget constraint (endowment model)

(.) (1 ) (.) (1 )

i i i j j j

u p u p     

For any pair i, j EXCEPT FOR ONE GOOD

 

1 N i i



 1

(.)

N i i i

u c







Condenses

 

1 N i i

c



NO TAX ON ONE GOOD

December 11, 2012 9

THE ORIGINAL RAMSEY PROBLEM

Ramsey Basics  Basic Result

 Tax most heavily the good(s) with the least elastic demand  Basic (now, undergraduate…) intuition: taxing goods with low price elasticity of demand creates smallest deadweight losses  Ramsey problem one of optimally spreading distortions/deadweight losses across markets/commodities

 Uniform Commodity Taxation Theorem

 If preferences are homothetic in goods X and Y, tax them at equal rates – Atkinson and Stiglitz (1980)  Homothetic function  Monotone transformation of a homogenous function  Income expansion paths are rays through origin  for t > 0  Homogeneity a cardinal property of a function  Homotheticity an ordinal property of a function

( c) (c) ( c) (c)

i i j j

u t u u t u   

December 11, 2012 12

RAMSEY FRAMEWORK APPLIED TO MACRO POLICY

Ramsey Macro Models  Use Ramsey framework to study (joint) monetary and fiscal policy

 Consolidated (flow) government budget constraint  Original formulation by Lucas and Stokey (1983 JME)  Quantitatively studied by Chari, Christiano, and Kehoe (1991 JMCB)  Basic model and results summarized in Chari and Kehoe (1999 Macro Handbook)

 Basic model elements

 Cash good/credit good environment  No capital accumulation  Assets: fiat money and one-period nominal government bonds  Flexible prices and wages  Stochastic government spending and TFP

 Policy tools: labor income tax, nominal debt, money creation

1 1 1 n t t t t t t t t t t t

Pw n M M B R B Pg 

  

    

Nominally risk-free, one period bonds (key for dynamic results)

December 11, 2012 15

BASELINE DSGE RAMSEY MONETARY MODEL

Baseline Ramsey Monetary Model  Ramsey Problem: maximize lifetime utility of consumer subject to

 Resource constraint  Government (intertemporal) budget constraint (primal formulation: present-value implementability constraint (PVIC))  In principle, also a zero-lower-bound (ZLB) constraint (i.e., Rt = u1(.)/u2(.) >= 1), but can show this is always satisfied in the less- constrained Ramsey problem

 Main Result #1: Friedman Rule always optimal (i.e., Rt = 1)

 Interpretation: completely relax consumers’ CIA constraints  In all dates and states – i.e., not just a steady-state result  In steady-state, implies π = β (deflate at rate of time preference)  DOES NOT MEAN πt = β OUT OF STEADY STATE!

 

1 1 2 1 2 1 2 2

( , ) ( , ) '( )

t t t t t t t t t t

E u c c c u c c c v n n A 

 

  



Initial real liabilities of government

December 11, 2012 20

UNDERSTANDING THE FRIEDMAN RULE

Baseline Ramsey Monetary Model  Standard Ramsey theory: all final goods should be taxed

 Spread distortions/deadweight loss across all goods  Basic Ramsey monetary model: labor income tax taxes both cash goods and credit goods at the same rate

 Standard Ramsey theory: uniform commodity taxation

 Cash and credit goods enter preferences homothetically, so tax them at equal rates

 Alvarez, Kehoe, and Neumeyer (2004): any cash/credit model that exhibits balanced growth must have c1 and c2 homothetic in u(.)

 Because both c1 and c2 already taxed by labor income tax, do not tax cash good further by deviating from Friedman Rule

 Phelps (1973) conjecture

 Friedman Rule would not be optimal in a full public finance framework  Intuition behind conjecture: activities requiring money ought to be taxed  positive nominal interest rate a natural way to tax them  Basic intuition correct – but homotheticity makes R > 1 unnecessary

 Aruoba and Chugh (2010 JET): FR not optimal in a money search- public finance model – despite homotheticity

c1 and c2 already below their efficient levels

December 11, 2012 24

DYNAMICS OF OPTIMAL POLICY

Baseline Ramsey Monetary Model  Main Result #2: Inflation and money supply highly volatile

 In face of business-cycle magnitude (TFP and/or government spending) shocks (i.e., numerically solve and simulate)

OPTIMAL inflation rate varies between -11 percent and +4 percent two-thirds of the time! Opposite of NK prescription of having (virtually) zero variability in inflation over the business cycle. Zero persistence in optimal inflation – stems from lack of any endogenous state/accumulation variables. Chugh (2007 JME): introduce capital accumulation and/or habit persistence  high persistence in Ramsey-optimal inflation Friedman deflation on average

SGU (2004 JET) flex- price model Mean

• 3.390

SD 7.470 Persistence

• 0.028

December 11, 2012 26

FISCAL THEORY OF THE PRICE LEVEL (FTPL)

Ramsey and the FTPL  Present-value government budget constraint (aka PVIC)  FTPL supposes current and future fiscal surpluses are exogenous (aka non-Ricardian fiscal policy)  Shock revealed at time t (about t or beyond)

 Fluctuations in contemporaneous price level accommodate shocks…  …via variations in money supply process  (Nominal P adjusts because dollar value of bonds outstanding is pre- determined – assuming no defaults on face value here….)

 Christiano and Fitzgerald (Cleveland Fed Economic Review, 2000) provide good introduction to FTPL

present value of (future government primary surpluses + seignorage revenue)

t t

P B 

December 11, 2012 30

RAMSEY OPTIMALLY EXPLOITS THE FTPL

Ramsey and the FTPL  Present-value government budget constraint (aka PVIC)  Ramsey government

 Doesn’t take current and future surpluses as exogenous  Chooses them optimally!

 Shock revealed at time t (about t or beyond)

 Ramsey government faces tradeoff  Adjust current or future fiscal surpluses via changes in tax rates?  Or respond via (state-contingent) changes in Pt (achieved through state-contingent variations in the nominal money stock…a quantity-theoretic mechanism)?  Depends on relative deadweight losses stemming from the two…

 CCK result: with flexible P and W, changes in P much less welfare- diminishing, so engineer high volatility in P (and hence π)

present value of (future government primary surpluses + seignorage revenue)

t t

P B 

X

Main Result #3: Optimal labor income tax virtually constant over time

December 11, 2012 33

A THEORY OF MONETARY POLICY?

Big-Picture Issues  Should optimal monetary policy be driven by fiscal considerations?

 Maybe…  …but strikes many as crazy to recommend high inflation variability and high money supply variability

 Why is high inflation variability undesirable? Undergrad answers:

 Causes unintended redistributions between borrowers and savers?

 If so, requires heterogeneous-agent model to think about...

 Causes undesirable relative-price distortions?

 If so, from where do such relative-price effects stem?  New Keynesian view: some nominal prices simply do not adjust  Immediate implication: inflation distorts relative prices (relative quantities), hence optimal to stabilize inflation following shocks

 Ramsey framework a quantitative test of the power of some friction in the economy to make stabilizing inflation an important goal

 Isolates mechanisms (potentially) important for the objectives of cyclical monetary policy  Useful even if don’t literally want to formulate monetary policy on the basis of fiscal considerations

OPTIMAL FISCAL AND MONETARY POLICY WITH NOMINAL RIGIDITIES DECEMBER 11, 2012

December 11, 2012 2

OUTLINE

The Plan  Basics of Ramsey optimal policy problem (the microeconomics)  Applying the Ramsey framework to macroeconomic policy  Modern benchmark Ramsey (monetary policy) results

 Optimality of the Friedman Rule  Inflation very volatile and serially uncorrelated  Dynamic result: Fiscal Theory of the Price Level (FTPL) underpinnings

 How palatable is the strict Ramsey approach for monetary policy prescriptions?  Nominal price rigidity in the Ramsey environment (SGU 2004 JET)  Nominal wage rigidity in the Ramsey environment

 Chugh (2006 RED): embedded in Walrasian labor markets  Arseneau and Chugh (2008 JME): embedded in labor markets with search and matching frictions

December 11, 2012 4

STICKY-PRICE RAMSEY MODELS

Sticky Prices and Ramsey Inflation Stability  Flexible prices and wages

 Optimal inflation highly volatile – makes nominal government debt state-contingent in real terms  An insurance mechanism

 Schmitt-Grohe and Uribe (2004 JET) and Siu (2004 JME)

 Pit insurance value of generating state-contingent debt vs. deadweight costs associated with nominal price rigidity  A quantitative test

 Key elements of SGU model

 Standard NK separation into intermediate and final goods  Menu costs of nominal price adjustment

 A real resource cost (i.e., appears in economy-wide resource constraint)  Rotemberg (1982 JPE)  Alternative to Calvo and Taylor

2 1

1 2

it it

P P 



      

Every firm CAN adjust price every

• period. Quadratic cost limits

SIZE of price adjustments. Can map Calvo adjustment probability into parameter ψ

December 11, 2012 8

SGU MODEL

Sticky Prices and Ramsey Inflation Stability  Intermediate firm profit-maximization problem  FOC (in symmetric equilibrium) – no price dispersion in Rotemberg  Money demand motivated by transactions cost function  Formulation of Ramsey problem

 Primal form: eliminate all prices/policies, solve for optimal allocations, then construct supporting prices/policies  Dual form: optimize directly with respect to only policies  PVIC is no longer the only Ramsey constraint (apart from resource constraint)

 Because NK Phillips Curve imposes sequence of constraints on evolution of nominal P, which is the heart of the FTPL-esque Ramsey mechanism

 

1| 1 1

(1 ) ( 1) ( 1)

t t t t t t t t t

mc y E        

  

           

   

1| 1 1 1 1 2 2 1 1 1

1 1 2 2 max

it

it it t it i it t t it t t t t it t t i t t P

P Pmc y P E P P m y P P P c P P  

       

                                             

s.t.

it it t t

P y y P

 

      

New Keynesian Phillips Curve Puts additional restrictions on the time-path of the price level beyond that implied by the FTPL

December 11, 2012 9

STICKY-PRICE RAMSEY MODELS

Sticky Prices and Ramsey Inflation Stability

SGU flex- price model SGU (2004 JET) Siu (2004 JME) Mean

• 3.390
• 0.160
• 2.835

SD 7.470 0.171 0.323 Persistence

• 0.028

0.037 0.033

Flexible prices/flexible wages: (large) fluctuations in Pt not so costly… Sticky prices/flexible wages: (large) fluctuations in Pt quite costly…

Friedman deflation on average Near-zero inflation on average Friedman deflation on average

December 11, 2012 11

STICKY-PRICE RAMSEY MODELS

Sticky Prices and Ramsey Inflation Stability  Friedman Rule not optimal in SGU model

 Due to absence of profit tax  Positive nominal interest rate indirectly taxes monopoly rents, which are a “fixed factor” of production (hence non-distortionary)  Ramsey framework useful in identifying rents  Siu (JME 2004): allows profit tax and recovers optimality of Friedman Rule

 Inflation volatility dramatically lower than in flex-price model

 Insurance value of ex-post (non-zero) inflation dominated by resource cost of non-zero inflation  Supports “standard” New Keynesian prescription of stabilizing inflation

 Quantitative: sticky-price distortion dominates

 King and Wolman (1999) result: sticky-price distortion should be completely eliminated with zero inflation all the time absent any other distortions

December 11, 2012 13

A STICKY-WAGE RAMSEY MODEL

1 w t t t t

w w  





Renewed interest in sticky-wage models since EHL (2000) and CEE (2005) Hypothesis: Nominal rigidity in wages alone may make Ramsey inflation stable Conjectured Mechanism: If efficient path of real wage is not very volatile  any concern for stabilizing nominal wage inflation will translate into concern for stabilizing nominal price inflation Because Ramsey government tries to come close to the efficient path of real wages (since the Ramsey government does care about efficiency…)

Sticky WAGES and Ramsey Inflation Stability?

Via the equilibrium restriction

Growth of real wage = Nominal wage inflation Nominal price inflation

December 11, 2012 14

A STICKY-WAGE RAMSEY MODEL

Sticky WAGES and Ramsey Inflation Stability?  “Final labor” and “intermediate labor” (standard EHL)

 Monopolistic competition in intermediate labor markets  Each household faces Rotemberg menu cost of changing its nominal wage

 Money demand motivated by cash/credit structure  Key equilibrium condition (and hence Ramsey constraint):

 Non-trivial in sticky-wage models

 Formulation of Ramsey problem

 PVIC again does not capture all equilibrium conditions  So formulate a problem hybrid between the primal and dual approaches

1 w t t t t

w w  





December 11, 2012 15

A STICKY-WAGE RAMSEY MODEL

Sticky Prices and Ramsey Inflation Stability

SGU flex- price model SGU (2004 JET) Siu (2004 JME) Chugh (2006 RED) Mean

• 3.390
• 0.160
• 2.835
• 0.113

SD 7.470 0.171 0.323 0.911 Persistence

• 0.028

0.037 0.033

• 0.019

Flexible prices/flexible wages: (large) fluctuations in Pt not so costly… Sticky prices/flexible wages: (large) fluctuations in Pt quite costly…

Friedman deflation on average Near-zero inflation on average Friedman deflation on average

Flexible prices/sticky wages: (large) fluctuations in Pt costly…because they would induce large fluctuations in REAL wages GIVEN THAT Ramsey stabilizes Wt…

Near-zero inflation on average

December 11, 2012 17

LABOR MARKET RELATIONSHIPS?

Sticky Wages in Non-Walrasian Labor Markets? Goodfriend and King (2001): “…potential allocative inefficiencies from [costly] setting of nominal wages are likely to be offset in the context

• f long-term employment relationships..” and “…unlikely to influence

recommendations for policy.” How might policy prescriptions change when we model long-term labor market relationships?

In ongoing (i.e., not spot) relationships, “prices” (wages) may play a very different role than in neoclassical models – and may be determined by very different forces than neoclassical (i.e., supply and demand) market forces… Is Walrasian-based view fundamentally the most natural way to think about labor markets? (Or even some other markets?...)

December 11, 2012 20

A STICKY-WAGE RAMSEY MODEL II

Sticky Nominal Wages In Long-Term Employment Relationships

Arseneau and Chugh (2008 JME) Model  Labor market with search and matching frictions  Determines quantity of labor (a non-Walrasian allocation mechanism)  Search frictions  when workers and firms do find each other, they have an incentive to remain together – a long-term employment relationship  Wage payment determined by Nash bargaining between individuals and firms  Determines price of labor (a non-Walrasian pricing mechanism)  Bargaining over the nominal wage  Costly wage adjustment – modeled using simple Rotemberg cost  Embedded inside wage bargaining problem  Key equilibrium restriction (and hence Ramsey constraint):  Money demand motivated by cash/credit structure  Key Ramsey constraints: PVIC, wage Phillips Curve, vacancy-creation condition, Nash wage outcome (and standard Ramsey monetary constraints)

1 w t t t t

w w  





December 11, 2012 21

A STICKY-WAGE RAMSEY MODEL II

Sticky Wages and Ramsey Inflation Stability?

SGU flex- price model SGU (2004 JET) Siu (2004 JME) Chugh (2006 RED) Arseneau and Chugh (2008) Mean

• 3.390
• 0.160
• 2.835
• 0.113

0.574 SD 7.470 0.171 0.323 0.911 5.575 Persistence

• 0.028

0.037 0.033

• 0.019

0.017

Flexible prices/flexible wages: (large) fluctuations in Pt not so costly… Sticky prices/flexible wages: (large) fluctuations in Pt quite costly…

Friedman deflation on average Near-zero inflation on average Friedman deflation on average

Flexible prices/sticky wages: (large) fluctuations in Pt costly…because they would induce large fluctuations in REAL wages GIVEN THAT Ramsey stabilizes Wt…

Near-zero inflation on average

Unless the underlying model of the labor market is non-Walrasian

Near-zero inflation on average

December 11, 2012 23

DYNAMICS OF REAL WAGE THE KEY

1 w t t t t

w w  





Walrasian labor market  Efficient real wage is relatively stable  any desire to stabilize nominal wages translates into desire to stabilize nominal prices Labor market with search and bargaining  Bargained real wage  Divides match surplus  Path does not affect current allocations  Price inflation stability not so important even with sticky nominal wages

Sticky Wages and Ramsey Inflation Stability?...

Via the equilibrium restriction

Time

Firm reservation wage Worker reservation wage

ANY path for the real wage inside this bargaining set keeps match (hence production) intact

Growth of real wage Nominal wage inflation Nominal price inflation

=

Think of as the surplus between demand and supply

December 11, 2012 26

SUMMARY

 The Ramsey Monetary Model  A testing ground for frictions/features that make inflation stability an important goal of policy  Which frictions are important?  Sticky prices? Clearly…  Sticky nominal wages?  Depends on underlying view of the labor market  Relative price distortions must stem from more deep-rooted reasons than ad-hoc “sticky prices”…  …because (old and New) Keynesian intuition continues to ring true  Aruoba and Chugh (2010 JET): frictions underlying monetary exchange  Other (non-monetary) search frictions in goods markets? (in progress)  Other Interesting Future Directions  Heterogeneity/dynamic redistributive effects of inflation  Political considerations: separate the fiscal and monetary authority?

Conclusion