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I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS T HE O PTIMAL I NFLATION TARGET IN AN E CONOMY WITH L IMITED E NFORCEMENT Gaetano Antinolfi Washington University Costas Azariadis Washington University and FRB-St. Louis James Bullard* Federal Reserve Bank of St. Louis 2 October 2008 Indiana University * Views expressed are those of the author and do not necessarily reflect official positions of the FOMC or the Federal Reserve System. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS C OMFORT ZONES Typical FOMC member statements: 1 to 2 percent inflation would be ideal. “Small positive inflation is the best inflation target.” Associated with short-term nominal interest rates near 5 percent. Economic theory: nominal interest rates should be zero. Why the difference? I NTRODUCTION M AIN IDEAS E NVIRONMENT T HEORY P LANNING PROBLEMS O PTIMUM INFLATION AND REALITY: T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS W HY THE DIFFERENCE ? Japan. Summers (1991): Zero bound on nominal interest rates interferes with stabilization policy. Adam and Billi (2006). Smith (2002). Deflation causes disintermediation, harming the operation of credit markets. We study a version of the latter: A small amount of inflation “deepens financial markets” in a way we make precise. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS W HAT WE DO Endowment economy with constant aggregate income. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS W HAT WE DO Endowment economy with constant aggregate income. A continuum of infinitely-lived households. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS W HAT WE DO Endowment economy with constant aggregate income. A continuum of infinitely-lived households. Endowments fluctuate. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS W HAT WE DO Endowment economy with constant aggregate income. A continuum of infinitely-lived households. Endowments fluctuate. Two assets: currency and consumption loans. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION A GENT TYPES Households are divided into two types. T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A GENT TYPES Households are divided into two types. “Townsend-Bewley-type” or cash agents can only use currency in nonnegative amounts to smooth consumption. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A GENT TYPES Households are divided into two types. “Townsend-Bewley-type” or cash agents can only use currency in nonnegative amounts to smooth consumption. “Kehoe-Levine-type” or credit agents can participate in either asset market subject to endogenous debt constraints. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A GENT TYPES Households are divided into two types. “Townsend-Bewley-type” or cash agents can only use currency in nonnegative amounts to smooth consumption. “Kehoe-Levine-type” or credit agents can participate in either asset market subject to endogenous debt constraints. Default is punished by perpetual exclusion from the loan market but still permits defaulting households to hold nonnegative currency. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A GENT TYPES Households are divided into two types. “Townsend-Bewley-type” or cash agents can only use currency in nonnegative amounts to smooth consumption. “Kehoe-Levine-type” or credit agents can participate in either asset market subject to endogenous debt constraints. Default is punished by perpetual exclusion from the loan market but still permits defaulting households to hold nonnegative currency. Inflation will make default less attractive, loosening participation constraints and strengthening the credit market. I NTRODUCTION M AIN IDEAS E NVIRONMENT P REVIEW P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS OF MAIN FINDINGS We study a particular social planning problem, made precise below. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P REVIEW P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS OF MAIN FINDINGS We study a particular social planning problem, made precise below. Deflation is infeasible if the planner assigns positive weight to credit households. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P REVIEW P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS OF MAIN FINDINGS We study a particular social planning problem, made precise below. Deflation is infeasible if the planner assigns positive weight to credit households. Inflation higher than the level required to slacken debt constraints will not be chosen if the planner assigns sufficient weight to cash households. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P REVIEW P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS OF MAIN FINDINGS We study a particular social planning problem, made precise below. Deflation is infeasible if the planner assigns positive weight to credit households. Inflation higher than the level required to slacken debt constraints will not be chosen if the planner assigns sufficient weight to cash households. If the planner puts a relative weight greater than zero but less than the population weight on credit households, the optimum inflation rate is positive. I NTRODUCTION M AIN IDEAS E NVIRONMENT P REVIEW P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS OF MAIN FINDINGS We study a particular social planning problem, made precise below. Deflation is infeasible if the planner assigns positive weight to credit households. Inflation higher than the level required to slacken debt constraints will not be chosen if the planner assigns sufficient weight to cash households. If the planner puts a relative weight greater than zero but less than the population weight on credit households, the optimum inflation rate is positive. Conclude: Independent central banks will set low positive inflation targets in economies that possess highly developed financial markets. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS R ECENT RELATED O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS LITERATURE Aiyagari and Williamson (2000 JET). Related environment, random endowments, outside option is Bewley, emphasis on financial intermediation, positive inflation deters default, computational. Berentsen, Camera and Waller (2007 JET). Related environment, Lagos-Wright, emphasis on financial intermediation, positive inflation deters default. Ragot (2007). OLG framework. Andolfatto (2007). Antinolfi, Azariadis, and Bullard (2007). Money is the only asset, emphasis on dynamics and equilibrium selection. Sanchez, Williamson, and Wright (2007). Blackboard version. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS E NVIRONMENT Continuum of infinitely-lived households. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS E NVIRONMENT Continuum of infinitely-lived households. λ “Kehoe-Levine” or credit type agents. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS E NVIRONMENT Continuum of infinitely-lived households. λ “Kehoe-Levine” or credit type agents. 1 λ “Townsend-Bewley” or cash type agents. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NVIRONMENT Continuum of infinitely-lived households. λ “Kehoe-Levine” or credit type agents. 1 λ “Townsend-Bewley” or cash type agents. All types have identical preferences ∞ ∑ βt u cit (1) t=0 with discount factor 0 < β < 1, u (c) standard, and i = 0, 1, 2, 3. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NDOWMENTS Credit households are divided into two sub-types, 0 and 1, with mass λ/2 each. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NDOWMENTS Credit households are divided into two sub-types, 0 and 1, with mass λ/2 each. Cash households are divided into two sub-types, 2 and 3, with mass 1 λ/2 each. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NDOWMENTS Credit households are divided into two sub-types, 0 and 1, with mass λ/2 each. Cash households are divided into two sub-types, 2 and 3, with mass 1 λ/2 each. Endowments, interpreted as income shares, are periodic: ω 0t , ω 1t = ω 2t , ω 3t = (1 + α, 1 α) if t = 0, 2, ... (1 α, 1 + α) if t = 1, 3, ... (2) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NDOWMENTS Credit households are divided into two sub-types, 0 and 1, with mass λ/2 each. Cash households are divided into two sub-types, 2 and 3, with mass 1 λ/2 each. Endowments, interpreted as income shares, are periodic: ω 0t , ω 1t = ω 2t , ω 3t = (1 + α, 1 α) if t = 0, 2, ... (1 α, 1 + α) if t = 1, 3, ... α 2 (0, 1) indexes the degree of income volatility. (2) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS E NDOWMENTS Credit households are divided into two sub-types, 0 and 1, with mass λ/2 each. Cash households are divided into two sub-types, 2 and 3, with mass 1 λ/2 each. Endowments, interpreted as income shares, are periodic: ω 0t , ω 1t = ω 2t , ω 3t = (1 + α, 1 α) if t = 0, 2, ... (1 α, 1 + α) if t = 1, 3, ... α 2 (0, 1) indexes the degree of income volatility. Aggregate income is constant. (2) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). No claims can be enforced on them or by them. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). No claims can be enforced on them or by them. The “unbanked.” C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). No claims can be enforced on them or by them. The “unbanked.” Credit agents may enter into loan arrangements to smooth consumption subject to endogenous debt limits, as in Kehoe and Levine (1993). I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). No claims can be enforced on them or by them. The “unbanked.” Credit agents may enter into loan arrangements to smooth consumption subject to endogenous debt limits, as in Kehoe and Levine (1993). Credit agents who default are forever excluded from the loan market and must instead use currency. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS N ATURE OF THE ENVIRONMENT Cash agents are anonymous households who may only use currency to smooth income fluctuations, as in Bewley (1980). No claims can be enforced on them or by them. The “unbanked.” Credit agents may enter into loan arrangements to smooth consumption subject to endogenous debt limits, as in Kehoe and Levine (1993). Credit agents who default are forever excluded from the loan market and must instead use currency. Future inflation rates will impact the payoff to default. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS T HE MONETARY AUTHORITY, BRIEF VERSION Benevolent social planner chooses a constant inflation rate at which cash agents can trade ... C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS T HE MONETARY AUTHORITY, BRIEF VERSION Benevolent social planner chooses a constant inflation rate at which cash agents can trade ... ... and directly selects consumption vectors for credit agents who may either accept their allocations or behave like cash agents in perpetuity. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS T HE MONETARY AUTHORITY, BRIEF VERSION Benevolent social planner chooses a constant inflation rate at which cash agents can trade ... ... and directly selects consumption vectors for credit agents who may either accept their allocations or behave like cash agents in perpetuity. The inflation target in this economy is similar to an optimal tax subject to an incentive constraint as understood by Mirrlees (1971). I NTRODUCTION M AIN IDEAS E NVIRONMENT C OSTS P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS AND BENEFITS OF POSITIVE INFLATION Positive rates of inflation impose a tax on cash agents ... C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT C OSTS P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS AND BENEFITS OF POSITIVE INFLATION Positive rates of inflation impose a tax on cash agents ... ... and confer two benefits on credit agents: C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT C OSTS P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS AND BENEFITS OF POSITIVE INFLATION Positive rates of inflation impose a tax on cash agents ... ... and confer two benefits on credit agents: a transfer of resources from the cash sector, and C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT C OSTS P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND BENEFITS OF POSITIVE INFLATION Positive rates of inflation impose a tax on cash agents ... ... and confer two benefits on credit agents: a transfer of resources from the cash sector, and a reduction in the default payoff which brings about higher debt limits. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION I NFLATION TARGETING AS T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A PLANNING PROBLEM Pure equal-treatment planning problem would choose a periodic consumption sequence for each agent. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION I NFLATION TARGETING AS T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A PLANNING PROBLEM Pure equal-treatment planning problem would choose a periodic consumption sequence for each agent. It would assign (cH , cL ) to high income and low income credit agents, and consumption (xH , xL ) to the corresponding cash agents. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION I NFLATION TARGETING AS T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A PLANNING PROBLEM Pure equal-treatment planning problem would choose a periodic consumption sequence for each agent. It would assign (cH , cL ) to high income and low income credit agents, and consumption (xH , xL ) to the corresponding cash agents. Equivalent to lump-sum taxes on some agents and lump-sum subsidies to others. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION I NFLATION TARGETING AS T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS A PLANNING PROBLEM Pure equal-treatment planning problem would choose a periodic consumption sequence for each agent. It would assign (cH , cL ) to high income and low income credit agents, and consumption (xH , xL ) to the corresponding cash agents. Equivalent to lump-sum taxes on some agents and lump-sum subsidies to others. Because inflation is a distortionary tax, we define a modified planning problem. I NTRODUCTION M AIN IDEAS E NVIRONMENT M ODIFIED P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS PLANNING PROBLEM First, the monetary authority sets a constant inflation factor π. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT M ODIFIED P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM First, the monetary authority sets a constant inflation factor π. Next, given π, high income cash agents choose a periodic consumption vector (xH , xL ) 0 to maximize stationary discounted utility 1 1 β2 [u (xH ) + βu (xL )] (3) subject to xH 1 + α, xH + πxL = 1 + α + π (1 u (xH ) + βu (xL ) (4) α) , u (1 + α) + βu (1 (5) α) (6) I NTRODUCTION M AIN IDEAS E NVIRONMENT M ODIFIED P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM First, the monetary authority sets a constant inflation factor π. Next, given π, high income cash agents choose a periodic consumption vector (xH , xL ) 0 to maximize stationary discounted utility 1 1 β2 [u (xH ) + βu (xL )] (3) subject to xH 1 + α, xH + πxL = 1 + α + π (1 u (xH ) + βu (xL ) (4) α) , u (1 + α) + βu (1 (5) α) (1) nonnegative currency; (2) money balances are used up to smooth consumption in low income dates; (3) agents can renounce money and consume endowments. (6) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION M ORE ON THE MODIFIED T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM Let xH (π ) and xL (π ) solve the previous problem. Given π, the planner now chooses consumption values (cH , cL ) 0 for credit households to maximize the equal-treatment welfare function 1 1 β2 [u (cH ) + u (cL )] (7) subject to the resource constraint λ ( cH + cL ) + ( 1 λ) [xH (π ) + xL (π )] = 2, (8) and the participation constraint u (cH ) + βu (cL ) u [xH (π )] + βu [xL (π )] . (9) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION M ORE ON THE MODIFIED T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM Let xH (π ) and xL (π ) solve the previous problem. Given π, the planner now chooses consumption values (cH , cL ) 0 for credit households to maximize the equal-treatment welfare function 1 1 β2 [u (cH ) + u (cL )] (7) subject to the resource constraint λ ( cH + cL ) + ( 1 λ) [xH (π ) + xL (π )] = 2, (8) and the participation constraint u (cH ) + βu (cL ) u [xH (π )] + βu [xL (π )] . Equal treatment of high income and low income households means that the discounted utilities are weighted equally. This gives the welfare function above. (9) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION M ORE ON THE MODIFIED T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM If cH (π ) and cL (π ) solve the previous problem for a given π > 0, the planner selects the stationary inflation factor π to maximize the social welfare function W (π, δ) = δ fu [cH (π )] + u [cL (π )]g + (1 δ) fu [xH (π )] + u [xL (π )]g . (10) I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION M ORE ON THE MODIFIED T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM If cH (π ) and cL (π ) solve the previous problem for a given π > 0, the planner selects the stationary inflation factor π to maximize the social welfare function W (π, δ) = δ fu [cH (π )] + u [cL (π )]g + (1 δ) fu [xH (π )] + u [xL (π )]g . (10) This SWF assigns equal weights to members of the same group but potentially different weights to different groups. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION M ORE ON THE MODIFIED T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS PLANNING PROBLEM If cH (π ) and cL (π ) solve the previous problem for a given π > 0, the planner selects the stationary inflation factor π to maximize the social welfare function W (π, δ) = δ fu [cH (π )] + u [cL (π )]g + (1 δ) fu [xH (π )] + u [xL (π )]g . (10) This SWF assigns equal weights to members of the same group but potentially different weights to different groups. A strictly utilitarian SWF would have equal weights for all, that is, δ = λ. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS O PTIMUM INFLATION WITHOUT INCENTIVE CONSTRAINTS To build up intuition, we first solve the planner’s problem ignoring for the moment the incentive constraints. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS O PTIMUM INFLATION WITHOUT INCENTIVE CONSTRAINTS To build up intuition, we first solve the planner’s problem ignoring for the moment the incentive constraints. We allow lump-sum income transfers. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS O PTIMUM INFLATION WITHOUT C ONCLUSIONS INCENTIVE CONSTRAINTS To build up intuition, we first solve the planner’s problem ignoring for the moment the incentive constraints. We allow lump-sum income transfers. The planner then maximizes the SWF subject to the economy’s resource constraint. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS O PTIMUM INFLATION WITHOUT C ONCLUSIONS INCENTIVE CONSTRAINTS To build up intuition, we first solve the planner’s problem ignoring for the moment the incentive constraints. We allow lump-sum income transfers. The planner then maximizes the SWF subject to the economy’s resource constraint. This gives a first best solution with π = β, RN = 1, and smooth consumption for both groups of agents. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS S ECOND BEST Suppose that the planner cannot impose a lump-sum tax on any agent but must instead use inflation or deflation and redistribute the resulting seignorage from one group to another. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS S ECOND BEST Suppose that the planner cannot impose a lump-sum tax on any agent but must instead use inflation or deflation and redistribute the resulting seignorage from one group to another. The planner must now choose (π, cH , cL ) to solve the modified planning problem, but still ignoring the incentive constraints. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS S ECOND BEST Suppose that the planner cannot impose a lump-sum tax on any agent but must instead use inflation or deflation and redistribute the resulting seignorage from one group to another. The planner must now choose (π, cH , cL ) to solve the modified planning problem, but still ignoring the incentive constraints. Suppose δ = 1, no welfare weight on the cash community. Then the planner chooses maximal seigniorage π̃ and smooths the consumption of the credit community completely. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS S ECOND BEST Suppose that the planner cannot impose a lump-sum tax on any agent but must instead use inflation or deflation and redistribute the resulting seignorage from one group to another. The planner must now choose (π, cH , cL ) to solve the modified planning problem, but still ignoring the incentive constraints. Suppose δ = 1, no welfare weight on the cash community. Then the planner chooses maximal seigniorage π̃ and smooths the consumption of the credit community completely. Suppose δ = 0, no welfare weight on the credit community. Then the planner will push the inflation factor as close to zero as possible. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS M ORE ON SECOND O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS BEST The second best trades off these two extreme cases. T HEOREM The second best optimum allocation under a utilitarian social welfare function satisfies (cH , cL , xH , xL ) = (c , c , xH (π ) , xL (π )). It is supported by a “modified Friedman rule” for some inflation factor π 2 ( β, 1) , and a nominal yield such that RN = π /β > 1. P ROOF . See the appendix. C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS ASSUMPTIONS A1. Income shares cannot be “too variable.” C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS ASSUMPTIONS A1. Income shares cannot be “too variable.” A2. Income shares cannot be “too smooth.” C ONCLUSIONS I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS ASSUMPTIONS A1. Income shares cannot be “too variable.” A2. Income shares cannot be “too smooth.” A3. It is within the power of the central planner to lower the rate of return facing users of cash to the point where the incentive constraint on credit users becomes slack. I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS ASSUMPTIONS A1. Income shares cannot be “too variable.” A2. Income shares cannot be “too smooth.” A3. It is within the power of the central planner to lower the rate of return facing users of cash to the point where the incentive constraint on credit users becomes slack. Call the associated inflation factor π̄. I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS ASSUMPTIONS A1. Income shares cannot be “too variable.” A2. Income shares cannot be “too smooth.” A3. It is within the power of the central planner to lower the rate of return facing users of cash to the point where the incentive constraint on credit users becomes slack. Call the associated inflation factor π̄. Perhaps more controversial? I NTRODUCTION M AIN IDEAS E NVIRONMENT K EY P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS ASSUMPTIONS A1. Income shares cannot be “too variable.” A2. Income shares cannot be “too smooth.” A3. It is within the power of the central planner to lower the rate of return facing users of cash to the point where the incentive constraint on credit users becomes slack. Call the associated inflation factor π̄. Perhaps more controversial? “The market for unsecured credit can be made to work perfectly.” I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS L EMMA 2 L EMMA Define Wπ (π, δ) = ∂W /∂π. Then (a) Wπ (π, δ) < 0 8 (π, δ) 2 [π̄, π̃ ] [0, λ] , and (b) limπ !1 Wπ (π, δ) = +∞ when π converges from above. Part (a) intuition. To raise π above π̄ does not improve the ability of the planner to smooth the consumption of the credit community any further. Doing so merely transfers income from the cash community. This transfer will reduce social welfare except when δ > λ. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS L EMMA 2 L EMMA Define Wπ (π, δ) = ∂W /∂π. Then (a) Wπ (π, δ) < 0 8 (π, δ) 2 [π̄, π̃ ] [0, λ] , and (b) limπ !1 Wπ (π, δ) = +∞ when π converges from above. Part (a) intuition. To raise π above π̄ does not improve the ability of the planner to smooth the consumption of the credit community any further. Doing so merely transfers income from the cash community. This transfer will reduce social welfare except when δ > λ. Part (b) intuition. A small increase in the inflation tax creates a credit market where one would otherwise not exist. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS L EMMA 3 L EMMA W (π, δ) is not defined for π < 1. It is decreasing in π for π 2 (π̃, 1/R̄) and constant for π 1/R̄. Deflation violates the participation constraint for high income credit households. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS L EMMA 3 L EMMA W (π, δ) is not defined for π < 1. It is decreasing in π for π 2 (π̃, 1/R̄) and constant for π 1/R̄. Deflation violates the participation constraint for high income credit households. The outcome of any deflation is that money has a higher payoff than credit. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS T HEOREM 4 T HEOREM Suppose assumptions A1, A2, and A3 hold, and 0 < δ λ. Then the optimum inflation factor is π ? (δ) > 1 and the associated nominal interest yield, RN 2 (π ? (δ) , π ? (δ) /β) , is even higher. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS C ONCLUSIONS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND EXTENSIONS In this paper, the optimal inflation target should strike a balance between the deadweight loss from inflation and the potential improvement in credit market conditions. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS C ONCLUSIONS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND EXTENSIONS In this paper, the optimal inflation target should strike a balance between the deadweight loss from inflation and the potential improvement in credit market conditions. Main conclusion: independent central banks will set low positive inflation targets in economies that possess highly developed financial markets. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS C ONCLUSIONS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND EXTENSIONS In this paper, the optimal inflation target should strike a balance between the deadweight loss from inflation and the potential improvement in credit market conditions. Main conclusion: independent central banks will set low positive inflation targets in economies that possess highly developed financial markets. U.S.A.: One to two percent. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS C ONCLUSIONS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND EXTENSIONS In this paper, the optimal inflation target should strike a balance between the deadweight loss from inflation and the potential improvement in credit market conditions. Main conclusion: independent central banks will set low positive inflation targets in economies that possess highly developed financial markets. U.S.A.: One to two percent. Republic of South Africa: Three to six percent. I NTRODUCTION M AIN IDEAS E NVIRONMENT P LANNING PROBLEMS C ONCLUSIONS O PTIMUM INFLATION T HE ROLE OF INCENTIVE CONSTRAINTS C ONCLUSIONS AND EXTENSIONS In this paper, the optimal inflation target should strike a balance between the deadweight loss from inflation and the potential improvement in credit market conditions. Main conclusion: independent central banks will set low positive inflation targets in economies that possess highly developed financial markets. U.S.A.: One to two percent. Republic of South Africa: Three to six percent. Sounds like “comfort zones” articulated by central bankers.
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