Advanced marcoeconomics test

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ECON 401

Advanced Macroeconomics

Topic 3

Macroeconomic Policy

Fabio Ghironi

University of Washington

OPTIMAL MONETARY POLICY: THE FLEXIBLE PRICE CASE

BASICS OF OPTIMAL POLICY ANALYSIS

Introduction

 Describe the demand-side environment (i.e., consumers)  Arguments of utility function?  Which assets trade in private-sector financial markets?  Derive consumer optimality conditions

 Describe the supply-side environment (i.e., firms)  Which inputs are used in production process?  Derive firm profit-maximizing conditions

 So far: simple factor price = marginal product conditions (i.e., wage = mpn, etc.)  Soon: New Keynesian firm analysis more involved (price-setting decisions)

 Describe actions/role of government  How is monetary policy conducted? How is fiscal policy conducted?  How do government policy choices affect private sector behavior?

 Describe resource constraint

 Describe private-sector equilibrium  For given policy choices by government, how does market equilibrium arise?  How does price adjustment/setting affect market clearing?

 Optimal policy analysis best thought of as picking a government policy that induces the “best” private-sector equilibrium

CASH-IN-ADVANCE FRAMEWORK

Demand-Side Environment

 Cash-in-advance (CIA) an alternative way of modeling role of money  Alternative to MIU framework  Highlights medium-of-exchange role of money

 Representative consumer  Period-t utility function u(c, 1-n)  Subjective discount factor β  Period-t budget constraint just as in MIU model

…and so on for period t+1, t+2, etc.

 In each period, a cash-in-advance constraint

Captures idea that (nominal) consumption expenditures limited by how much cash (money) an individual has

(Technically want to model as inequality constraint, , but equality suffices to illustrate main ideas)

Total time is “1 unit.”

t t tPc M

1 1 1t t tP c M  

in period t

in period t+1

2 2 2t t tP c M   and so on…

t t tPc M

1 1 1( ) b

t t t t t t t t t t t t t tt tPc P B M S a P w n B M S D a            Lump-sum tax (used to effect changes in money supply – more soon…)

CASH-IN-ADVANCE FRAMEWORK: ANALYSIS

Demand-Side Environment

 Lagrangian

 FOCs

ct:

nt:

Mt:

Bt:

at:

 Combine into “MRS = price ratio” type of optimality conditions

 

2 1 1 2 2

1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1

1 1

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

( )

t t t t t t

b t t t t t t t t t t t t t t t t

t t t t

b t t t t t t t t t t t t t t t t

t t

u c n u c n u c n

W n M B S D a Pc P B M S a

M Pc

W n M B S D a P c P B M S a

M P

 

 



 



   

  

            

 

     

             

              1 1 ....

t tc  

λ is multiplier on budget constraint

μ is multiplier on CIA constraint

( ,1 ) 1

( ,1 ) 1 t t t

t t t t

u c n i w

u c n i

  

    

2 1

2 1 1 1

( ,1 ) (1 )

( ,1 ) t t t t

t t t t t

u c n W P r

u c n W P  

  

  

 Consumption-leisure optimality condition

Consumption-savings optimality condition

CASH-IN-ADVANCE FRAMEWORK: ANALYSIS

Demand-Side Environment

 Consumption-leisure optimality condition



Relevant relative price ratio depends on real wage…. …but also here on nominal interest rate

 Nominal interest rate (i.e., fact that transactions are monetary) acts as a tax on consumption-leisure margin

 Optimal policy analysis in CIA framework  Reduces to determining the welfare-maximizing (aka utility-

maximizing) tax to impose on consumption-leisure margin   What is the optimal nominal interest rate?

 Efficiency concerns will shape the answer to the optimal policy question

( ,1 ) 1

( ,1 ) 1 t t t

t t t t

u c n i w

u c n i

  

    

CASH-IN-ADVANCE FRAMEWORK

Supply-Side Environment

 Firms  Very simple model of production  Production technology in every period

 Can think of Cobb-Douglas with capital share = 0

 Profit maximization  In every period, representative firm maximizes profit (in real terms)

  Labor demand function

 Perfectly elastic labor demand function reflects lack of diminishing marginal product

( )t t ty f n n 

( )t t tf n w n

1tw t 

CASH-IN-ADVANCE FRAMEWORK

Government Policy

 Government  Assume only monetary policy is operative  Ignore fiscal policy considerations

 Central bank’s budget constraint – in every period t,

 Lump-sum tax τ used to implement changes in nominal money supply

 Lump-sum assumption allows for  Ignoring fiscal considerations – i.e., monetary policy is independent of

fiscal policy  Private sector views central bank’s policy decisions as independent of

any individual market participant’s decisions  “Independent of” is the crux of the idea of “lump sum”…

 Suppose policy set according to a money-growth-rate rule

 gt the growth rate of money supply in period t; isomorphic to interest rate rule

1t t tM M  

1 1(1 )t t t t t tM g M g M    

CASH-IN-ADVANCE FRAMEWORK

Private-Sector Equilibrium

 Resource constraint – in every period t,

 All output used for (only) consumption

 Summarize private-sector equilibrium conditions

 Consumption-leisure optimality condition

 Consumption-savings optimality condition

 Cash-in-advance constraint

 Labor-demand condition

 Resource constraint

t tc n

1tw 

( ,1 ) 1

( ,1 ) 1 t t t

t t t t

u c n i w

u c n i

  

    

2 1

2 1 1 1

( ,1 ) (1 )

( ,1 ) t t t t

t t t t t

u c n W P r

u c n W P  

  

  



t t

M c

P 

Describes demand side

Describes supply side

t tc n Describes market clearing

CASH-IN-ADVANCE FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = 1 and nt = ct everywhere

 Consumption-leisure optimality condition

 Consumption-savings optimality condition

 Cash-in-advance constraint

 Limit attention to steady-state (i.e., long run) policy questions

 Can express entire steady-state private-sector equilibrium as

( ,1 ) 1

( ,1 ) 1 t t t

t t t

u c c i u c c i

  

    

2 1 1

( ,1 ) (1 )

( ,1 ) t t

t t t

u c c r

u c c 

 

  



1 1

t t t t

t t t

M c g c

P c 

   

 Rewriting in terms of growth rates

   

,1 1 1 1,1

u c c g g gu c c 

  

   

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Can express entire steady-state private-sector equilibrium as

 Defines implicitly a reaction function

 A (potentially complicated..) summary description of how private-sector equilibrium quantities depend on any given choice of government policy g

 Maintained assumption  Central bank knows/understand perfectly the private-sector reaction function  Realism? Impossible for a central bank to literally know this…  …but provides a starting point for analysis

  Central bank takes into account the reaction function when setting (optimal) policy

   

,1 1 1 1,1

u c c g g gu c c 

  

   

( )c g

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Goal of policy makers  Maximize welfare (utility) of representative consumer  In steady-state

 The formal policy problem  Choose g that maximizes private-sector welfare  The c(g) function summarizes the behavior of private markets

    0

,1 ,1

1 s

u c c u c c







  

 

Recall infinite summation formula

    0

,( )1 ( ) ( ),1 ( )

1 s

u c g c g u c g c g







  

 

Taking into account private-sector reaction function

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Optimal monetary policy problem

 FOC with respect to g  KEY: NOW need to take into account the dependence of private-market outcomes

on the policy in place

 Compare with private-sector equilibrium

 If policy is set optimally

 QUESTION: What money growth rate g achieves this outcome?  g = β – 1 aligns the private-sector outcome with the policymaker’s

desired outcome

    0

,( )1 ( ) max ( ),1 ( )

1 s

g s

u c g c g u c g c g







  

 

   

,1 1 1 1,1

u c c g g gu c c 

  

   

   

,1 1

u c c

 



ALIGNING THESE IS THE GOAL!

FRIEDMAN RULE

Optimal Policy Analysis

 Optimal long-run money growth rate is g = β – 1  With β < 1…  …money supply should decrease in the long run!

 Optimal long-run inflation  Monetarist link

 Long-run deflation!  Central bank should seek to target negative inflation on average

 Optimal long-run nominal interest rate  i = 0 from Fisher relation (aka consumption-savings optimality

condition)

 The Friedman Rule  Seminal 1969 analysis  Whether stated in terms of long-run target for nominal interest rate or

long-run target for inflation/money growth

1 0g     A normative statement

UNDERSTANDING THE FRIEDMAN RULE

Optimal Policy Analysis

 What does g = β – 1 achieve?

 Eliminates the wedge in the consumption-leisure dimension  Economic efficiency achieved if

 Private-sector outcome

 Friedman Rule allows policy makers to achieve economic efficiency in private markets – even though central bank is NOT a Social Planner  Notice very nuanced/precise statements/logic…

 Sets the (opportunity) costs of holding alternative nominal assets (money and nominal bonds) equal to each other

 Makes CIA constraint “disappear” (examine consumer FOCs)

   

,1 1

u c c

 



Derive based on SOCIAL PLANNER problem.

Distinct from OPTIMAL POLICY problem!

   

,1 1 1 1,1

u c c g g gu c c 

  

   

1 00g i     

PRACTICAL RELEVANCE OF FRIEDMAN RULE

Conclusion

 A benchmark in the theory of monetary policy  Akin to the theoretical benchmark Ricardian Equivalence provides for

fiscal policy…

 Do monetary authorities actually follow the Friedman Rule?  Japan for the past 10+ years: nominal interest rates virtually zero  U.S. right now: nominal interest rates virtually zero

 But does this seem attributable to “good policy” in “normal times”  …or the need to run the best policy in bad times?

 Friedman Rule a very controversial result in monetary theory  Strikes many as simply not sensible or practical  Question: What (important) features of the economy are missing from

the analysis on which the Friedman Rule is premised?

 Keynesian/New Keynesian answer: sticky prices need to be considered in any normative analysis of monetary policy  Next: New Keynesian policy analysis

OPTIMAL MONETARY POLICY: THE STICKY-PRICE CASE

RELEVANT MARKET STRUCTURE(S)?

Introduction

 Real business cycle (RBC)/neoclassical theory  All (goods) prices are determined in perfect competition  In both consumption-leisure and consumption-savings dimensions  Critical assumption: no firm is a price setter  no firm has any market

power

 New Keynesian theory  Starting point: firms do wield (at least some) market power  Critical assumption: firms do set their (nominal) prices  Purposeful setting/re-setting of (nominal) prices may entail costs of

some sort  “Menu costs,” but soon interpret more broadly  Central issue in macro: how do “costs of adjusting prices” (“sticky prices”)

affect monetary policy insights and recommendations?

 Upcoming analysis  Step 1: Develop theory in which firms are purposeful price setters, not

price takers  Step 2: Superimpose on the theory some “costs” of setting/re-setting

nominal prices  Step 3: Study optimal monetary policyNOW

BASICS OF OPTIMAL POLICY ANALYSIS

Introduction

 Describe the demand-side environment (i.e., consumers)  Arguments of utility function?  Which assets trade in private-sector financial markets?  Derive consumer optimality conditions

 Describe the supply-side environment (i.e., firms)  Which inputs are used in production process?  Derive firm profit-maximizing conditions

 So far: simple factor price = marginal product conditions (i.e., wage = mpn, etc.)  Soon: New Keynesian firm analysis more involved (price-setting decisions)

 Describe actions/role of government  How is monetary policy conducted? How is fiscal policy conducted?  How do government policy choices affect private sector behavior?

 Describe resource constraint

 Describe private-sector equilibrium  For given policy choices by government, how does market equilibrium arise?  How does price adjustment/setting affect market clearing?

 Optimal policy analysis best thought of as picking a government policy that induces the “best” private-sector equilibrium

“CASHLESS” NK FRAMEWORK: CONSUMERS

Demand-Side Environment

 Basic NK tenet  Money demand issues (i.e., medium-of-exchange role of money) not very

important in modern developed economies  “Cashless” analysis

 Implications for formal NK analysis – monetary policy…  …does not operate on/through demand-side of economy (consumers)  …operates on/through supply-side of economy (firms)

 Recent events: monetary policy operates on/through financial sector of economy?  Intermediation between demand-side and supply-side…more research coming…

 Representative consumer  Period-t utility function u(c, 1-n)  Subjective discount factor β  Period-t budget constraint identical to CIA or MIU model, except no money

balances

…and so on for period t+1, t+2, etc.  No MIU component or CIA constraint

1 1( ) b

t t t t t t t t t t t t tPc P B S a P w n B S D a      

“CASHLESS” NK FRAMEWORK: CONSUMERS

Demand-Side Environment

 Lagrangian

 FOCs

ct:

nt:

Bt:

at:

 Combine into “MRS = price ratio” type of optimality condition

2 1 1 2 2

1 1

1 1 1 1 1 1 1 1 1 1 1 1

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

( )

....

t t t t t t

b t t t t t t t t t t t t t t

u c n u c n u c n

P w n B S D a Pc P B S a

P w n B S D a P c P B S a

 





   

 

           

     

                 



λ is multiplier on budget constraint

( ,1 ) ( ,1 )

t t t

t t

u c n w

u c n 

 

Consumption-leisure optimality condition AND

1 1 1 1

( ,1 ) (1 )

( ,1 ) t t t

t t t t

u c n P i

u c n P   

  



Consumption-savings optimality condition (from bond first-order condition)

KEY CONCEPTUAL DIFFERENCE BETWEEN NK ANALYSIS AND CIA ANALYSIS:

Instead, nom i.r. shows up only in consumption-savings optimality condition

RETAIL FIRMS

Supply-Side Environment

 Representative retail firm’s profit-maximization problem

 FOC with respect to yjt (for any j)

 …after several rearrangements

 IDENTICAL TO BASIC (FLEXIBLE-PRICE) DIXIT-STIGLITZ FRAMEWORK!

  0..

1 11/

0 0 max

it i t it it it

y P y di P y di

 

 

      Chooses profit-maximizing quantity of input of each wholesale good. Focus analysis on any arbitrary wholesale good – call it yjt.

1 jt

jt t t

P y y

  

    

DEMAND FUNCTION FOR GOOD j

WHOLESALE FIRMS

Supply-Side Environment

 Representative wholesale firm’s profit-maximization problem

2 2

1 1 1 1 1 1 1

1 1

max 1 2 1 1 2jt

jt jt jt jt t jt jt t jt jt t t jt tP

jt t jt

P P P y Pmc y P P y P mc y P

P P   

 

       

                        

Substitute in demand function for wholesale good j in both period t and t+1 (and t+2, t+3, t+4, …)

In period t, firm chooses Pjt So FOC with respect to Pjt

  1 1 1

1 (1 ) (1 ) 0 1 t t t t t t

mc y       

      

Symmetric equilibrium

New Keynesian Phillips Curve

WHOLESALE FIRMS

Supply-Side Environment

 So far haven’t considered (explicitly) the inputs to a wholesale firm’s production process

 Very simple model of production

 Production technology in every period (for any wholesale firm j)

 Can think of Cobb-Douglas with capital share = 0

 Labor hired by wholesale firm j taking market wage wt as given

 Recall: CRS production technology  marginal cost of production is independent of quantity produced

( )jt jt jty f n n 

“CASHLESS” NK FRAMEWORK: GOVERNMENT

Government Policy

 Money is a physical object in the “background”  DOES exist…  …so there IS a budget constraint for it  But not of direct importance for (routine) monetary policy issues

 (Hence doesn’t appear in consumers’ budget constraints….where does it go?...)

 Central bank’s budget constraint – in every period t,

 gt the growth rate of money supply in period t

 Money-supply rule technically isomorphic to interest rate rule

 But interest rates explicitly the “policy tool” in New Keynesian analysis  i.e., to implement an inflation target, what is the nominal interest rate the

central bank should set?  Instead of focusing on what is the money growth rate the central bank should set?

1 1(1 )t t t t t tM g M g M    

NONETHELESS: g = π in long run (i.e., steady state)

Even NK theory views basic monetarist quantity-theoretic link between money growth and inflation as being correct in the long run

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Resource constraint – in every period t,

 Total output used for private-sector consumption…  …and menu costs

 Recall: menu costs are a REAL cost – hence absorb some of the economy’s resources

 Summarize private-sector equilibrium conditions

 Consumption-leisure optimality condition

 Consumption-savings optimality condition

 Labor-demand condition

 New Keynesian Phillips Curve

 Resource constraint

   2 2

( )t tt tc n f n 

  

( ,1 ) ( ,1 )

t t t

t t

u c n w

u c n 

 

 2 2t t t

c n 

 

1 1 1 1

( ,1 ) 1 ( ,1 ) 1

t t t

u c n i u c n   

  

 

Describes demand side

Describes supply side   1 1

1 1 (1 ) (1 ) 0

1 t t t t t t mc n    

        

 Describes market clearing

'( ) 1t tw f n  Note wage is LESS THAN MP of labor

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Resource constraint – in every period t,

 Total output used for private-sector consumption…  …and menu costs

 Recall: menu costs are a REAL cost – hence absorb some of the economy’s resources

 Summarize private-sector equilibrium conditions

 Consumption-leisure optimality condition

 Consumption-savings optimality condition

 Labor-demand condition

 New Keynesian Phillips Curve

 Resource constraint

   2 2

( )t tt tc n f n 

  

( ,1 ) ( ,1 )

t t t

t t

u c n w

u c n 

 

 2 2t t t

c n 

 

1 1 1 1

( ,1 ) 1 ( ,1 ) 1

t t t

u c n i u c n   

  

 

Describes demand side

Describes supply side   1 1

1 1 (1 ) (1 ) 0

1 t t t t t t mc n    

        

 Describes market clearing

'( ) 1t tmc f n  mct = wt in every period

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 New Keynesian Phillips Curve

 2 2t t t

n c 

 

2 2

2 1

,1 ( ) 2

t t

t t t

u c c

u c c mc

 

            

2 1

2 1 1 1 1 1

,1 ( ) 12 1,1 ( )

t t t t

u c c i

u c c

 

     

          

 

  2 1 1 1

1 1 (1 ) (1 ) 0 1 2t t t t t tt

cmc 

        

            

Consumption-leisure optimality condition Consumption-savings optimality condition

One final substitution to condense things….

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 Consumption-savings optimality condition

 New Keynesian Phillips Curve

 2 2t t t

n c 

 

2 1

2 1 1 1 1 1

,1 ( ) 12 1,1 ( )

t t t t

u c c i

u c c

 

     

          

 

2 2

2 1 1

2 1

,1 ( ) 1 21 1 (1 ) (1 ) 0

1 2,1 ( ) 2

t t t

t t t t t t

t t t

u c c c

u c c

  

     

   

                          

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 Consumption-savings optimality condition in the steady state

 New Keynesian Phillips Curve in the steady state

 Limit attention to steady-state (i.e., long run) policy questions

 2 2t t t

n c 

 

2 1

,1 12 1,1

u c c i

u c c

 

  

          

 

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c c

u c c

  

     

 

                          

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 Consumption-savings optimality condition in the steady state

 New Keynesian Phillips Curve in the steady state

 Limit attention to steady-state (i.e., long run) policy questions  And (finally!...) use long-run monetarist relationship g = π

 2 2t t t

n c 

 

2 1

,1 12 1,1

u c c g i gu c c g



 

          

 

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  



                          

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 Consumption-savings optimality condition in the steady state

 New Keynesian Phillips Curve in the steady state

 Limit attention to steady-state (i.e., long run) policy questions  And (finally!...) use long-run monetarist relationship g = π

 2 2t t t

n c 

 

2 1

,1 12 1,1

u c c g i gu c c g



 

          

 

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  



                          

NK view:

Monetary policy does not operate through demand side…

Monetary policy operates through supply side

“CASHLESS” NK FRAMEWORK

Private-Sector Equilibrium

 Condense private-sector equilibrium conditions….

 …by imposing wt = mct and everywhere

 Consumption-savings optimality condition in the steady state

 New Keynesian Phillips Curve in the steady state

 Limit attention to steady-state (i.e., long run) policy questions  And (finally!...) use long-run monetarist relationship g = π

 2 2t t t

n c 

 

2 1

,1 12 1,1

u c c g i gu c c g



 

          

 

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  



                          

NK view:

Monetary policy does not operate through demand side…

Monetary policy operates through supply side

SO IGNORE C-S CONDITION IN ANALYSIS OF OPTIMAL POLICY PROBLEM….

ONLY TAKE INTO ACCOUNT NKPC!

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Can express entire steady-state private-sector equilibrium as

 Defines implicitly a reaction function  A (potentially complicated..) summary description of how private-sector

equilibrium quantities depend on any given choice of government policy g

  Central bank takes into account the reaction function when setting (optimal) policy

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  



                          

( )c g

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Goal of policy makers  Maximize welfare (utility) of representative consumer  In steady-state

 The formal policy problem  Choose g that maximizes private-sector welfare  The c(g) function summarizes the behavior of private markets

( ),1 ( ) 2( ),1 ( )

2 1 s

u c g c g g u c g c g g

 

 





            

Taking into account private-sector reaction function

,1 2,1

2 1 s

u c c g u c c g

 

 





            

Recall infinite summation formula

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 Optimal monetary policy problem

 FOC with respect to g  KEY: NOW need to take into account the dependence of private-market outcomes

on the policy in place

 If policy is set optimally

( ),1 ( ) 2( ),1 ( )

2 1 s

u c g c g g u c g c g g

 

 





            

Rearrange to MRS = … form

2 2

2 1

( ),1 ( ) '( )2

'( )( ),1 ( ) 2

u c g c g g c g

c g gu c g c g g



 

      

     

NOTE: If ψ = 0, exactly the same optimal-policy condition as in flexible-price analysis (Chapter 17) – i.e., RHS = 1

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 If policy is set optimally

 Compare with private-sector equilibrium

 QUESTION: What money growth rate g achieves this outcome?...

 Impossible to solve for g!....(in general, no g can achieve this….)

2 2

2 1

( ),1 ( ) '( )2

'( )( ),1 ( ) 2

u c g c g g c g

c g gu c g c g g



 

      

     

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  



                          

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 If policy is set optimally

 Compare with private-sector equilibrium

 QUESTION: What money growth rate g achieves this outcome?...

 Impossible to solve for g!.... (in general, no g can achieve this….)  …unless we slightly “modify” the condition (NKPC) describing private-sector

equilibrium…  Interpretation: a corrective fiscal policy intervention

2 2

2 1

( ),1 ( ) '( )2

'( )( ),1 ( ) 2

u c g c g g c g

c g gu c g c g g



 

      

     

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  

 

                           Introduce ε factor here…

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 QUESTION: What money growth rate g aligns these two conditions?

 By inspection…

2 2

2 1

( ),1 ( ) '( )2

'( )( ),1 ( ) 2

u c g c g g c g

c g gu c g c g g



 

      

     

2 2

2 1

,1 1 21 1 (1 ) (1 ) 0

1 2,1 2

u c c g c g g g g g

u c c g

 

  

                          

Summarizes outcome under optimal policy

Summarizes private-sector

equilibrium for any arbitrary policy choice

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 QUESTION: What money growth rate g aligns these two conditions?

 By inspection… g = 0 aligns the private-sector outcome with the policymaker’s desired outcome

   

( ),1 ( ) 1

( ),1 ( ) u c g c g u c g c g

 



   

 2 1

,11 1 1 0

1 ,1 u c c

c u c c

     

   

Summarizes outcome under optimal policy

Summarizes private-sector

equilibrium for any arbitrary policy choice

OPTIMAL POLICY ANALYSIS

Optimal Policy Analysis

 QUESTION: What money growth rate g aligns these two conditions?

 By inspection… g = 0 aligns the private-sector outcome with the policymaker’s desired outcome

   

( ),1 ( ) 1

( ),1 ( ) u c g c g u c g c g

 



   

 2 1

,11 1 1 0

1 ,1 u c c

c u c c

     

   

   

,1 1

,1 u c c u c c

 

that the equilibrium features

ALIGNING THESE IS THE GOAL!

Solution requires

ZERO INFLATION POLICY

Optimal Policy Analysis

 Optimal long-run money growth rate is g = 0  Money supply should remain constant in the long run!

 Optimal long-run inflation  Monetarist link

 Zero long-run inflation!  Central bank should seek to target zero inflation on average

 Optimal long-run nominal interest rate  i > 0 from Fisher relation (aka consumption-savings optimality

condition)

 Quite different policy recommendation from Friedman Rule!  Zero inflation, not negative inflation   Positive nominal interest rate, not zero nominal interest rate

 Fundamental difference: sticky prices vs. flexible prices

0g   A normative statement

UNDERSTANDING ZERO INFLATION POLICY

Optimal Policy Analysis

 What does g = π = 0 achieve?

 Eliminates the price adjustment costs in the resource constraint

 Adjustment costs are a cost!...  There is no benefit of “sluggish” or “sticky” prices!...  Basic economics: an activity has positive costs but no benefits 

optimally want none of that activity!

 Private-sector achieves efficiency along consumption-leisure margin

 Zero inflation allows policy makers to achieve economic efficiency in private markets – even though central bank is NOT a Social Planner  Notice very nuanced/precise statements/logic…

 HOWEVER: zero inflation only “works” if fiscal policy is also being set optimally – raises coordination issues, etc?...

2 c n

   c n

Zero inflation

   

,1 1

,1 u c c u c c

 



RECALL: A social planner doesn’t need to consider “prices” – hence would not care to incur “price adjustment costs”

PRACTICAL RELEVANCE OF ZERO INFLATION

Conclusion

 A benchmark in the theory of monetary policy  Has been a practical guide for the conduct of monetary policy in last 30 years

 Zero inflation technically only a long-run optimal policy recommendation  But has become the intellectual guidepost for central banks worldwide even

for business-cycle-frequency inflation goals

 Encapsulated in the mantra “low and stable inflation”

 No central banks target (explicitly or implicitly) EXACTLY ZERO inflation  Rather, positive long-run inflation targets

 What can rationalize positive long-run inflation targets?  WAGE (as opposed to price) rigidity  Financial frictions?  Hitting zero-lower-bound on nom i.r. during recessions the central

issue  i.e., Blanchard suggestion

 Nature of and costs (and benefits?) associated with price adjustment still not well understood

Active areas of research

ECON 401

Advanced Macroeconomics

The New Keynesian Model and Monetary Policy

Fabio Ghironi

University of Washington

Introduction

• Sanjay Chugh’s textbook and slides highlight the central role of the supply-side of the economy—specifically, the New Keynesian Phillips curve—in the conduct of monetary policy

in the New Keynesian framework.

• These slides expand and clarify the point he is making.

• Chugh explains New Keynesian macroeconomics and some of its important results without log-linearizing the model, but it turns out that using the log-linearized version of the New

Keynesian framework allows us to highlight some points most transparently.

• The model I introduce in the following slides can be obtained from log-linearizing the model that Chugh explains augmented with the introduction of uncertainty.

– You should have learned from the RBC model that the log-linear model with uncertainty

is identical to the log-linear model with perfect foresight except for having the expectation

operator applied to variables at t + 1 and for the introduction of random shocks in the

equations.

– This is the reason why many refer to log-linearization as delivering certainty equivalence.

• I introduce shocks in all equations of the model below to allow for different sources of fluctuations.

The Basic New Keynesian Macroeconomic Model

• The basic, log-linearized New Keynesian macroeconomic model consists of three equations.

The Intertemporal IS

• There is an equation that describes how output today depends on the ex ante real interest rate and on expected future output:

yt = −σ [it −Et (πt+1)]+ Et (yt+1)+ ut, (1)

where, as usual, σ > 0 measures the responsiveness of today’s output to the real interest

rate, it is the nominal interest rate, πt+1 is inflation next period, Et (.) is the expectation of

the variable inside the parentheses based on information available at time t, and ut is an

exogenous demand shock.

• This equation is an intertemporal IS equation.

– Today’s GDP contracts if the real interest rate increases; today’s GDP rises if it is

expected to rise tomorrow.

– ut is an exogenous demand shock.

• This equation follows from the log-linearized Euler equation for bond holdings once equilibrium conditions are imposed

• It describes the demand-side of the economy. 2

The Basic New Keynesian Macroeconomic Model, Continued

The New Keynesian Phillips Curve

• There is an equation that describes how today’s inflation depends on today’s output and on expected future inflation:

πt = λyt + βEt (πt+1)+ zt, (2)

where λ > 0 and β > 0 are parameters (β is the households’ discount factor, λ is a

parameter that depends on the extent of nominal rigidity and on the extent of monopoly

power), and zt is an exogenous shock.

– Current inflation rises if GDP rises and if inflation is expected to rise tomorrow.

• This equation is known as New Keynesian Phillips Curve (NKPC) and it describes the supply-side of the model.

• It can be obtained by log-linearizing the non-linear NKPC that Sanjay Chugh presents and imposing additional equilibrium conditions.

The Basic New Keynesian Macroeconomic Model, Continued

Monetary Policy

• Finally, there is an equation that describes monetary policy in terms of what is known as a Taylor-type rule for interest rate setting, from the 1993 article by John Taylor in the

Carnegie-Rochester Conference Series on Public Policy that started the literature on Taylor

rules.

• For instance: it = α1πt + α2yt + xt, (3)

where α1 > 0 and α2 > 0 are policy response parameters, and xt is an exogenous policy

shock.

• Equations (1)-(3) are a system of three dynamic equations for the three endogenous variables yt, πt, and it as functions of the exogenous shocks ut, zt, and xt.

• Usually, it is assumed that these shocks follow so-called first–order autoregressive processes, in which the level of the shock today depends on its level last period and on an

innovation in the current period.

Solving the Basic New Keynesian Macroeconomic Model

• If the policy response parameters α1 and α2 satisfy the following restriction:

(α1 −1)λ + α2 (1−β) > 0,

the log-linear system (1)-(3) has a unique solution.

– This can be verified using a method described in an appendix to the slides on the RBC

model.

• If the central bank is not responding to GDP (i.e., α2 = 0), the condition for a unique solution reduces to α1 > 1:

– The central bank must respond to inflation more than proportionally.

• This is known as Taylor Principle and it captures the idea that, to stabilize the economy, the central bank should cause the real interest rate to rise (by having the nominal interest rate

rise more than inflation) when the economy is “overheating” and inflation is increasing.

• Requiring that monetary policy be such that it ensures a unique equilibrium is important:

– Doing no harm (i.e., not introducing sunspot fluctuations in the economy by creating

indeterminacy) should be the minimum that is expected of policy!

Solving the Basic New Keynesian Macroeconomic Model, Continued

• Provided the condition for determinacy (uniqueness) of the solution is satisfied, the solution of the model can be written as:

yt = ηyuut + ηyzzt + ηyxxt,

πt = ηπuut + ηπzzt + ηπxxt,

ir = ηiuut + ηizzt + ηixxt, (4)

where the η’s are coefficients that can be found with the method of undetermined

coefficients. (Suggested exercise: Do this.)

• Notice: We can solve fully for output, inflation, and the interest rate without any reference to money and money supply.

• This happens because of the implicit assumption that, if we had money in the model, we would have introduced it via money-in-the-utility function in a separable way.

• Under this assumption, once monetary policy is conducted through interest rate setting, we need not worry about money, and its only role is (in the background) to implement the open

market operations through which the central bank affects the interest rate.

Some Properties of the Solution and Some Model Variants

• The shocks ut, zt, and xt describe the minimum state vector of the model.

• There is no endogenous, predetermined state (such as capital in the RBC model).

• This means that the endogenous variables yt, πt, and it are only as persistent as the shock themselves, and they will return monotonically to the steady state after shocks, without

displaying any hump.

• This is a well known weakness of the basic New Keynesian framework, as empirical evidence points to hump-shaped responses to shocks that this model cannot replicate.

• A solution to generate hump-shaped responses of inflation to shocks is to build models in which current inflation also depends on past inflation, so that the NKPC becomes:

πt = ρπt−1 + λyt + βEt (πt+1)+ zt,

with 0 < ρ < 1.

• In this case, πt−1 becomes part of the state vector, and the model can generate humps in inflation responses to shocks.

Some Properties of the Solution and Some Model Variants, Continued

• We could also assume that habits in consumption imply that output today depends also on output yesterday, so the intertemporal IS becomes:

yt = κyt−1 −σ [it −Et (πt+1)]+ Et (yt+1)+ ut,

with 0 < κ < 1.

• In this case, yt−1 becomes part of the state vector.

• Another variant of the model assumes that central bank policy is characterized by interest rate smoothing, so that the interest rate today depends also on the interest rate yesterday:

it = α1πt + α2yt + α3it−1 + xt,

with α3 > 0.

• In this case, it−1 becomes part of the state vector.

• If no other change to the model is made (i.e., equations (1) and (2) continue to hold) the condition for a unique solution becomes:

(α1 + α3 −1)λ + α2 (1−β) > 0.

Monetary Policy and the New Keynesian Phillips Curve

• But let us return to the basic model (1)-(3).

• Suppose the central bank commits to a policy of zero inflation, so that πt = Et(πt+1) = 0.

• We can use the NKPC equation (2) to back out the implied path of output:

yt = − 1

λ zt.

• And we could then use the intertemporal IS equation (1) to back out the path of the interest rate that would be consistent with this outcome:

− 1

λ zt = −σit −

λ Et (zt+1)+ ut,

or,

it = 1

σ ut +

σλ [zt −Et (zt+1)] .

• If we assume that the shock zt is such that zt = φzzt−1 + εz,t, where εz,t is a zero-mean innovation, Et (zt+1) = φzzt, and:

it = 1

σ ut +

σλ (1−φz)zt. (5)

Monetary Policy and the New Keynesian Phillips Curve, Continued

• This is the sense in which Sanjay Chugh says that monetary policy in the New Keynesian model works through the NKPC:

– Once the central bank has chosen the path of inflation it wants to implement, the NKPC

delivers the implied path of output, and the intertemporal IS then delivers the interest rate

path that will correspond to the desired path of inflation and the implied path of output.

• Does this imply that if the central bank wants to pursue a policy of zero inflation there is no role for the policy rule (3)?

• No! In fact, we could verify that if the policy rule (3) were replaced by equation (5) the model would not have a unique solution.

– The equilibrium would be indeterminate!

• It turns out that having the interest rate respond to endogenous variables of the model (such as inflation and output) and not just to exogenous shocks is crucial to deliver uniqueness of

the solution.

– This is a point that Michael Woodford (Columbia University) showed in his 2003 book on

Interest and Prices.

Implementing Zero Inflation

• If the central bank wants to deliver zero inflation (and ultimately the interest rate path (5)), it must commit to the policy:

it = α1πt + α2yt,

i.e., no exogenous monetary policy shock (xt = 0), with a very high value of the response

coefficient α1.

– In fact, you could verify from the solution equations in (4), once you have found the η’s,

that πt = 0 when α1 →∞. (You should check this as an exercise.)

• Of course, this is a policy that works well to deliver πt = 0 without problems in this simple model.

• In reality, a huge coefficient α1 would cause problems from large volatility of the interest rate in response to even minuscule deviations of inflation from 0 that could happen for many

reasons.

• This explains why the recommendation of a huge response coefficient can be good for a model, but not for reality.

ECON 401

Advanced Macroeconomics

Monetary Policy Commitment Versus Discretion

Fabio Ghironi

University of Washington

Introduction

• In solving for the optimal steady-state growth rate of money supply (and therefore the optimal steady-state inflation rate) in the sticky-price New Keynesian model, Sanjay Chugh

finds the apparently odd result that the problem has no solution unless a “convenient” ε is

added to the key equation in a specific spot.

• He interprets this ε as “help from the government through a fiscal policy action.”

• These slides clarify this point and relate it to the issue of monetary policy under commitment versus discretion.

A Distorted Flexible-Price Equilibrium

• Consider the New Keynesian model with flexible prices and use the notation ε = θ/(θ −1), where θ > 1 is the elasticity of substitution between differentiated wholesale products.

• Assume that output of each differentiated product is produced using only labor according to the production function yt = ZtNt, where Zt is exogenous productivity.

– I am dropping the individual firm identifier because we know that all firms make identical

choices in equilibrium.

• Letting pt be the price of an individual wholesale product and Pt be the price of the retail bundle, we know that optimal price setting implies:

pt Pt = µ

wt Zt ,

where µ ≡ θ/(θ −1) = ε is the markup, wt is the real wage, and wt/Zt is marginal cost.

• Since Pt = pt in equilibrium, this implies that:

wt = 1

µ Zt.

• The real wage is lower than productivity (since µ < 1).

A Distorted Flexible-Price Equilibrium, Continued

• When we impose equalization of the real wage to the marginal rate of substitution between leisure and consumption in an environment of endogenous labor supply, we have the familiar

result that monopoly power distorts the amount of labor employed in equilibrium:

U1−N (Ct,1−Nt) UC (Ct,1−Nt)

= 1

µ Zt.

• Because µ > 1, too little labor is demanded (and supplied) and too little output is produced.

• Firms with monopoly power have an incentive to reduce output supply in order to extract a higher price than under perfect competition.

• And workers who are comparing the benefit of consumption (priced at a markup) over leisure (priced at no markup) have an incentive to over-demand leisure relative to consumption.

• The result is under-production of output and under-employment of labor relative to the perfectly competitive outcome.

• The problem would be removed if we had θ → ∞, i.e., if wholesale goods were perfectly substitutable:

– In this case, wholesale firms would have no monopoly power, and it would be µ = 1.

Sticky Prices and Monetary Policy

• Now, when changing prices is costly, optimal price setting implies: pt Pt = µt

wt Zt .

• The markup becomes time-varying!

• In particular, it becomes a function of output and of current and expected future inflation.

• Let us write this compactly as:

µt = µ(yt,πt,Et (πt+1)) .

• If log-linearized around a steady state with zero inflation and steady-state output normalized to 1, this boils down to:

µ̂t = − ψ

θ −1 [π̂t −Et(π̂t+1)] ,

where hats denote percentage deviations from steady state and ψ is the scale parameter

for the cost of adjusting prices.

Sticky Prices and Monetary Policy, Continued

• This is important: The markup falls if inflation rises.

• Since costs of adjusting prices give firms an incentive to smooth price changes over time, firms will absorb the impact of rising inflation by letting the markup component of their prices

fall when inflation becomes higher.

• But this has implications for monetary policy:

– The central bank knows that an increase in inflation will erode the markup, causing it to

become lower than its flexible-price level θ/(θ −1).

• This creates a temptation for the central bank to use monetary expansion to boost output above the inefficient level that prevails under flexible prices!

Temptation to Expand

• When we introduced the issue of optimal monetary policy, we were careful to frame it in the following terms:

– If you were the central bank and you could commit to a choice of inflation rate, what

inflation rate would you want to commit to?

• The answer was πt = 0 because the central bank recognizes that it cannot address the effect of monopoly power directly, and so it better just focus on removing the effect of the

sticky-price distortion by choosing a policy of zero inflation.

• The word “commitment ” was important.

• What if the central bank cannot commit? What about the temptation to erode the impact of the markup by having πt > 0?

• This is the problem underlying the inability to solve the optimal monetary problem in Sanjay Chugh’s slides without the help from fiscal policy.

• Appropriate help from fiscal policy removes the issue.

Help from Fiscal Policy

• Return to optimal wholesaler price setting under flexible prices, but now assume that wholesale firm revenues are taxed at a rate τ > 0.

• If you make this assumption, optimal price setting implies: pt Pt =

1− τ wt Zt =

(1− τ)(θ −1) wt Zt .

– The markup is now adjusted for the rate of revenue taxation.

• This implies that the government can choose the τ such that: θ

(1− τ)(θ −1) = 1.

Help from Fiscal Policy, Continued

• If the government does that, we have pt Pt = wt Zt ,

or, in equilibrium, wt = Zt.

• The government has chosen the τ that removes the impact of monopoly power on the economy (an application of the idea that optimal policy is about minimizing—in this case,

removing completely—the effect of distortions), and the flexible-price economy has become

efficient, because we again have that:

U1−N (Ct,1−Nt) UC (Ct,1−Nt)

= Zt,

as in the RBC model.

• If the government does that, once we introduce sticky prices, the central bank no longer faces the temptation to try to use inflation to erode the markup relative to its flexible-price

level, and the optimal thing for it to do is to pursue a policy of zero inflation (in and outside

the steady state) regardless of whether it behaves under commitment or in a discretionary

fashion.

Help from Fiscal Policy, Continued

• This is the “trick” that Sanjay Chugh is using when he is adding that ε to the policy problem of the central bank (in his case, focusing only on steady-state inflation):

• He is implicitly assuming that a smart government has set τ appropriately to make things such that the flexible-price equilibrium is not distorted, making it unambiguously optimal to

have zero inflation to remove the effect of the only remaining distortion (sticky prices).

• Now let us spend a bit longer understanding the issue of commitment versus discretion.

Monetary Expansion in the AS-AD Diagram

• Consider a standard aggregate supply-aggregate demand (AS-AD) diagram, and suppose the central bank increases nominal money supply from M to M′.

• The following figure describes the short-run effect of this policy action.

• Assume that, before the change in M, AS intersected AD at point A: Y = Yn (the “trend” level of output) and P = Pe (the price level P was where it was expected to be when all

price and wage contracts in the economy had been signed).

– We are using a diagram with P on the vertical axis, but we could make the same

arguments below with inflation instead of the price level on the vertical axis.

• Think of point A as the pre-shock flexible-price equilibrium of the economy.

• The monetary police expansion causes the AD curve to shift to the right to AD′.

– Output increases to Y ′ and the price level increases to P′.

Figure 1 • Over time, adjustment of expectations comes into play: Y > Yn ⇒ P > Pe ⇒ Wage setters revise the expectations incorporated in their wage contracts, and the AS curve shifts up over time. • The economy moves up along AD’. Adjustment stops when Y = Yn again and price level = P’’ = Pe (> initial Pe). In the medium run, AS is given by AS’’, and the economy is at A’’, with Y = Yn and P = P’’. • The next figure shows the entire transition from the short run equilibrium to the medium run:

Monetary Expansion in the AS-AD Diagram, Continued

• Over time, adjustment of expectations comes into play: Y > Yn ⇒ P > Pe ⇒ Wage and price setters that did not get to adjust to the shock immediately revise the expectations

incorporated in their contracts, and the AS curve shifts up.

• The economy moves up along AD′.

• Adjustment stops when Y = Yn again and price level = P ′′ = Pe′ (> Pe).

Figure 2 * Note:

- We can pin down the exact size of the eventual increase in P. If Y is back at Yn, M/P must also be back at its initial value. - Then, it must be the case that the proportional increase in P equals the initial proportional increase in M: if M ↑ by 10%, P eventually ↑ by 10%.

The Neutrality of Money in the Medium Run

• In the short run, M ↑ ⇒ Y ↑, i ↓, P ↑. • How much of the effect of the monetary expansion falls initially on Y depends on the slope of the AS curve.

Monetary Expansion in the AS-AD Diagram, Continued

• In the long run, AS is given by AS′′, and the economy is at A′′, with output back at trend and the effect of the monetary expansion fully reflected into prices.

– We are implicitly assuming that long-run neutrality of money holds in the diagram, i.e.,

that the economy behaves as if there is a vertical long-run AS curve at Y = Yn.

– This notion has become a subject of discussion since the Global Financial Crisis of

2007-08 and the Great Recession that followed, with scholars arguing that the trend

position of the economy is itself endogenous to the management of aggregate demand

in the short to medium run.

– The sticky price model in the slides is such that monetary policy is not neutral in the

long run: You could verify that a non-zero long-run inflation rate would have long-run real

effects.

– But these would be small under plausible assumptions and it would still be the case

that a welfare-maximizing policymaker acting under commitment would choose a zero

inflation rate because of the costs that inflation would impose on the economy.

Expectations

• Now let us think about expectation formation.

• If all agents in the economy of the figure form expectations in a forward looking manner, use the information at their disposal optimally, and can renegotiate their contracts at the same

time after the initial surprise without incurring additional costs to implementing price and

wage changes, the transition from the short-run equilibrium to the long-run position following

a monetary policy expansion will take just one round of expectation and contract revision.

• Why is that? Because if all agents are forward-looking and they know the structure of the model, as soon as they observe the policy shock and find themselves in the short-run

equilibrium, they know that the economy must eventually converge to the long-run position.

• As soon as they get a chance to renegotiate contracts based on their revised expectations, they will immediately set the expected price level at the long-run equilibrium level.

• This will cause the economy to move from the short-run equilibrium to the long-run equilibrium in just one round of expectation and contract revision, thus shortening the

amount of time during which monetary policy causes output to be above trend.

Expectations, Continued

• If all agents are backward or current-looking, expectation revisions reset expectations (at best) to the currently observed price level, resulting in a transition to the medium run

equilibrium that may take several rounds of expectation and contract revision.

• If forward- and backward-looking agents coexist, as it is plausible, the transition will be faster than in the fully backward-looking case, but slower than in the fully rational one.

• Now, monetary policy is effective in terms of generating a level of output that differs from trend to the extent that it generates a price level that differs from the expected price level

embedded in contracts—either because of a full surprise effect at the time of the policy

action or because, even if agents knew that a policy change was coming, something (like

costs of adjusting prices or wages) prevented them from resetting prices fully before the

policy change.

• Unexpected policy has a larger impact because no agent will have had a chance to renegotiate her/his contract.

• Fully credible, anticipated policy will have no real effect (no effect on output) and will only affect prices and wages if all agents have a chance adjust prices and wages fully between

the announcement of the policy and the time when the policy change actually happens.

Expectations, Continued

• Now suppose that, once Y has returned to Yn, the central bank increases M again.

• The process will be repeated (taking the long-run equilibrium following the previous monetary expansion as the new initial position):

• Y will rise above Yn for some time but eventually return to Yn, with P increasing to match the further increase in M over time.

• If the central bank plays this game repeatedly, even if agents are not fully forward-looking and optimizing to begin with, they will eventually recognize the central bank’s behavior and

incorporate it in their own.

• Expectation and contract revisions will become more and more frequent, so that the deviations of Y from Yn caused by monetary expansion will become shorter and shorter

lived.

• Eventually the AS curve will become de facto vertical at Yn, and all the policymaker will accomplish by increasing M will be to increase P immediately.

• Think of this as an environment in which the scale parameter of costs of price adjustment is becoming smaller and smaller, as frequent, sizable price changes have become the norm.

Commitment Versus Discretion

• Now let us use the AS-AD model and our discussion of the role of expectations to talk about a theory of inflationary consequences of policymaker incentives and agents’ expectations

that was proposed by Finn Kydland and Edward Prescott in 1977 (Journal of Political

Economy ) to explain how high inflation can arise as outcome of the interaction (the “game”)

between the central bank and private agents.

– The theory was then reformulated by Robert Barro and David Gordon (1983, Journal of

Political Economy ) and has become known as the Barro-Gordon model.

– However, Kydland and Prescott were the first to propose it. Kydland and Prescott

received the Nobel Prize in 2004 for their work in macroeconomics.

• Suppose that the policymaker has a target of output Y ∗ above the natural level Yn because the latter is inefficiently low (for instance, as a consequence of monopoly power combined

with endogenous supply of labor as in the basic New Keynesian model of the slides).

• Suppose that, when price and wage contracts are being negotiated, the policymaker—who knows that she/he can only drive Y above Yn for some time—announces that she/he will

follow a rigorous monetary policy aimed at preserving price stability.

• Assume however that the policymaker has no way of actually precommitting herself/himself in a credibly binding way to implementing the announcement.

Commitment Versus Discretion, Continued

• Suppose that private agents have forward-looking, rational expectations.

• Moreover, they know the structure of the economy (the AS-AD model), the fact that the policymaker has an objective Y ∗ > Yn, and that the policymaker cannot precommit

herself/himself in a binding way to actually implementing her/his announced policy.

• If private agents believe the central bank’s announcement that monetary policy will preserve a stable price, they will embed this in their expectations and set prices and wages

accordingly.

• Now, once private agents have signed their contracts believing the policymaker’s announce- ment, it is no longer optimal for her/him to actually implement it.

• She/he has an incentive to expand monetary policy, exploiting nominal rigidity, to drive Y to Y ∗ at least for some time.

Commitment Versus Discretion, Continued

• However, private agents know that the policymaker has this incentive.

• They know that, if they sign contracts based on expectations of a stable price, since the policymaker is not bound by any credible precommitment device to implementing her/his

announced rigorous policy, she/he will fool them with a monetary expansion that erodes

markups and real wages.

• Rational, optimizing private agents recognize this, do not believe the policymaker’s announcement, and incorporate her/his expected behavior in their contract negotiation,

setting price expectations at the level that corresponds to the long-run equilibrium to which

the economy would have eventually converged if the policymaker had actually managed to

fool private agents for some time.

• Optimal behavior by rational private agents will thus cause the AS curve to shift up even before the policymaker actually takes any action.

Commitment Versus Discretion, Continued

• At this point, if the policymaker sticks to her/his announcement of stable monetary policy, the short run equilibrium will be not only below Y ∗, the policymaker’s target, but also below

Yn!

• What is the optimal thing to do for the policymaker if she/he wants at least to avoid having Y < Yn for some time?

• It is to validate agents’ expectations and do what they expected her/him to do in the first place: expand monetary policy, shift the AD curve to the right, and drive the equilibrium

where agents expected it to be: at Yn, but with a higher price level.

– If the policymaker does not validate agents’ expectations and surprises them by sticking

to her/his prior announcement, Y will be below Yn for as long as it takes for expectations

and contracts to be revised and the AS curve to return to its original position.

– This is how the central banker would establish her/his credibility for being “tough”: at a

potentially significant cost for the economy.

• Given our assumptions, high-price expectation and monetary policy expansion are the best responses of the private sector and the central bank, respectively, to each other’s behavior.

Commitment Versus Discretion, Continued

• Thus, as a consequence of the inability of the policymaker to precommit to a stable-price policy, her/his incentive to generate Y above Yn, and private agents’ recognition of the

policymaker’s lack of commitment and incentives, all that we see is no deviation of Y from

Yn and a higher price level.

• This is the Nash equilibrium of the game between the central bank and the private sector.

• Monetary expansion is the only possible equilibrium policy in this game.

• Inability to commit credibly to the stable-price policy—i.e., the fact that policy is conducted under discretion—results in a high-price-level (or high-inflation) outcome for the economy.

The Time Inconsistency of Optimal Policy

• Central to the theory is the concept of time inconsistency of the optimal policy:

– Ex ante, when private sector expectations embedded in wage and price contracts are

being formed, the rigorous, stable-price policy is optimal.

– Announcing anything different would simply result in an immediate change in price

expectations.

– Ex post, once private agents have committed to contracts based on believing the

policymaker’s announcement of a stable-price policy, the policy is no longer optimal.

– It is optimal for the policymaker to fool agents with a monetary expansion.

• Note that the policymaker is benevolent:

– If effective on the real economy, the monetary expansion increases Y above the

inefficient level Yn for some time.

– But the agents’ recognition of the policymaker’s incentive and their desire to protect

themselves from inflation prevent the policymaker from accomplishing this goal.

The Time Inconsistency of Optimal Policy, Continued

• The ex ante optimal policy is thus time inconsistent.

• The time consistent policy (expected by rational agents and implemented in equilibrium) is to expand monetary policy, which ends up only resulting in high prices without any output

gain.

• The “help from fiscal policy” that Sanjay Chugh introduces in his analysis of optimal monetary policy removes this problem by making the trend level of output efficient, eliminating the

temptation to expand that the central bank succumbs to under discretion.

A Repeated Interaction

• The fact that the interaction between the central bank and the private sector is repeated over time rather than just played once in a one-shot game such as the one described above

provides a possible mechanism that would support a stable-price equilibrium.

• Suppose that the game between the policymaker and the private sector is played each period over an infinite horizon.

• Suppose that the private sector “tells” the policymaker today: “Ok, we believe your stable- price announcement. But if you cheat on us later on, we will never believe you again, and

we will always set expectations consistent with the one-shot-game, monetary expansion

behavior.”

• In this case, when deciding what to do, the policymaker is trading off the gains from surprising the private sector in the short run against the losses from high price expectations (and high

actual price since, as we discussed, it will be optimal to validate those expectations) for the

infinite future.

• If the policymaker cares enough about the future, she/he will stick to the announced policy of monetary rigor.

A Repeated Interaction, Continued

• The problem with this mechanism is that policymakers definitely do not have an infinite horizon.

– Note that the fact that central bankers are generally appointed for long periods is another

way to strengthen their independence, and thus their credibility.

• If the game is played a finite number of times, the mechanism that sustains the stable-price policy in the infinite horizon case unravels, and the only possible policy equilibrium is the

monetary expansion of the one-shot game.

• Why?

• Because, in the last period of the game (call it period T), the interaction reverts to the single-period interaction in which the policymaker has a clear incentive to cheat on the

announcement of rigorous policy (since there is no future game to be played next period

involving that policymaker).

• Thus, monetary expansion is the only equilibrium policy in period T.

A Repeated Interaction, Continued

• But in period T − 1, agents know that this will happen in period T, i.e., they know that the policymaker will expand monetary policy in period T.

• They will respond to this by setting high price expectations already at T − 1, which the policymaker will find it optimal to validate to avoid a recession then.

• The same mechanism will apply at T −2, T −3, and so on.

• By backward induction, the only equilibrium policy outcome in all periods from T back to the current time will be monetary expansion and a high price level.

Commitment Mechanisms

• Bottom line: The ability (or inability) of the policymaker to precommit credibly to a course of policy is crucial for observed outcomes.

– Think of Ulysses and the sirens: It was only through the precommitment devices of filling

his sailors’ ears with wax and having himself tied to the mast of the ship that Ulysses was

able to escape the sirens.

• Policies that act directly on Yn (for instance, enforcement of anti-trust legislation or appropriate tax setting by the government as in the “trick” used by Sanjay Chugh) are better

suited than monetary policy to resolve the problem of an inefficiently low Yn.

• Absent such policies, precommitment mechanisms that bind policymakers to implement announced policies are a remedy for the inflationary consequences of time inconsistency,

by giving the policymaker a way to “resist the sirens” of an output target above Yn.

• The theory proposed by Kydland and Prescott and Barro and Gordon has been used to explain several high inflation episodes across countries and over time due to lack of

precommitment, including high inflation in the U.S. in the 1970s.

• The argument fit stylized facts in several countries, and it has been (and still is) central to the focus of monetary policy and the design of monetary institutions to establish and preserve

anti-inflationary credibility.

Commitment Mechanisms, Continued

Inflation Targeting

• A commitment mechanism that several countries have implemented beginning in the early 1990s is the adoption of an inflation targeting regime that clearly specifies the central bank’s

target and responsibilities with respect to inflation and puts an institutional setup in place to

ensure central bank independence in the pursuit of this target and accountability in case of

failure.

• Inflation targeting regimes are generally characterized by much transparency in commu- nication between the central bank and the public to help the establishment of necessary

credibility.

• Several countries are operating variants of such regime, including industrial countries and emerging markets.

Commitment Mechanisms, Continued

• As Michael McLeay and Silvana Tenreyro have argued in an NBER Macroeconomics Annual 2019 article on “Optimal Inflation and the Identification of the Phillips Curve,” the pursuit

of inflation targeting by central banks over a number of years may be responsible for the

inability to easily identify the Phillips Curve (or its New Keynesian variant) in the data that

has led some to argue that it is no longer a relevant concept.

• The Phillips Curve relation may be alive and well as part of the mechanisms of the economy.

• But if the central bank has successfully kept inflation low and stable over a number of years, the data will not show it “transparently.”

Commitment Mechanisms, Continued

• Now, some view the failure of central banks like the Federal Reserve or the European Central Bank to accomplish their 2 percent inflation targets consistently since the Global

Financial Crisis of 2007-08 as an indictment of the failure of inflation targeting.

• Remembering the times when inflation in the U.S. was well into double digits and, in Italy, it was above 20 percent, I was (and still am) much more lenient than these colleagues toward

an inflation rate stubbornly at, say, 1.7 percent when the target is 2 percent.

• Central banks have had to contend with a variety of pressures toward low-flation or even de-flation since 2007-08 (and some, like the Bank of Japan, since the early 1990s).

• The impact of the current COVID-19 crisis on inflation remains to be seen, but I certainly expect lively debates on the topic among policymakers and academics.

Commitment Mechanisms, Continued

Fixed Exchange Rate

• Adoption of a fixed exchange rate regime is another possible precommitment device— provided the commitment to pegging the currency is credible—when the domestic

institutional setup does not support a country’s independent, stable policies.

• For many countries, the strategy of adopting a fixed exchange rate that tied their monetary policies to those of established, low-inflationary central banks was indeed the

precommitment device that would otherwise have been missing.

• By pegging the exchange rate, a country can “import” the low inflation policy of the country to which it pegs.

Commitment Mechanisms, Continued

• This argument is the core of Francesco Giavazzi and Marco Pagano’s (European Economic Review, 1988) analysis of the European Monetary System (EMS) in place between 1979

and the advent of the euro:

– European central banks that could not implement a credible commitment to low inflation

policies of their own found it better to commit to shadowing the Bundesbank through the

EMS constraint rather than finding themselves in the high-inflation, discretionary-policy

outcome often generated by the inflationary pressures from their governments.

• In sum, a commitment device in the form of an explicit inflation targeting regime (if credible institutions for it are in place) or an exchange rate peg can be key to delivering price stability.

– Nominal GDP targeting and price-level targeting have also been receiving attention in

debates.

Rules

• Inflation targeting and exchange rate pegs are examples of policy rules.

• Kydland and Prescott’s and Barro and Gordon’s work started a huge literature on the advantages of rules versus discretion.

• The policymaker we looked at in our discussion of the time inconsistency problem operates under discretion.

• She/he is free to reoptimize her/his behavior at each point in time.

• The fact that what is optimal ex ante is no longer optimal ex post and the private sector’s forward-looking behavior then result in the unfavorable equilibrium with monetary expansion

and no output gain.

• Thus, it would be better if the policymaker could commit to a rule that forces her/him to implement the ex ante optimal policy by removing discretion.

Rules, Continued

• As we mentioned, inflation targeting and fixed exchange rate regimes are examples of policy rules to which the policymaker can precommit in order to establish independent domestic

anti-inflationary credibility (under a properly designed inflation targeting regime) or to import

the monetary policy credibility of the center country (under an exchange rate peg).

• The so-called Taylor rule (a rule for interest rate setting in response to inflation and output movement first studied by John Taylor in a 1993 article in the Carnegie-Rochester

Conference Series on Public Policy ) is another example of a rule to which the policymaker

could be committed in some binding form.

– Note an important difference: Inflation targeting or an exchange rate peg are targeting

rules, the Taylor rule is an instrument rule.

• Even if some macroeconomists went as far as suggesting that, say, the Federal Reserve should be committed to automatically implementing the Taylor rule in each period, Taylor

himself in his 1993 article interprets it more as a benchmark guideline for policymaking in

normal conditions, from which departures should be allowed in special circumstances.

Rules, Continued

• He views the rule as constrained discretion, whereby the policymaker operates under discretion, but subject to the constraint of a benchmark guideline for policymaking in normal

times.

• Clearly, such constrained discretion is feasible for institutions that do not lack credibility in the pursuit of a stable monetary environment.

• It is much less feasible for central banks that lack credibility, for which a more binding commitment can be the best way to bring inflation under control.

• Having said this, large crises—such as the Global Financial Crisis of 2007-08 or the current crisis created by COVID-19—are moments in which any rule designed for policymaking

under normal economic conditions must be abandoned.