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O PTIMAL M ONETARY P OLICY FOR THE M ASSES James Bullard (FRB of St. Louis) Riccardo DiCecio (FRB of St. Louis) Barcelona GSE, Summer Forum Workshop on Monetary Policy and Central Banking Barcelona, Spain June 14, 2018 Any opinions expressed here are our own and do not necessarily reflect those of the FOMC. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM Introduction I NEQUALITY P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS I NEQUALITY AND MONETARY POLICY Interest in income, financial wealth, and consumption inequality has increased in the last decade. Can monetary policy conducted in a way that benefits all households even in a world of substantial heterogeneity? The answer in this paper is “yes.” I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS S OME RECENT LITERATURE Conference on “Monetary Policy and the Distribution of Income and Wealth,” held at the St. Louis Fed on September 11 and 12, 2015. Program available online. Kaplan, Moll, and Violante (AER, 2018): new Keynesian macro with uninsurable idiosyncratic risk and multiple assets (“HANK”). Produces reasonable Gini coefficients. The monetary transmission mechanism is altered relative to the representative agent case. Also provides a good discussion of the literature. This paper also produces reasonable Gini coefficients, and features incomplete markets due to a friction, with strictly limited idiosyncratic risk. The policymaker is able to repair the distortion caused by the friction for all households. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM H OUSEHOLD CREDIT IN A DSGE I NEQUALITY P OLICY C ONCLUSIONS MODEL We study an economy with a large private credit market essential to good macroeconomic performance. This market has an important friction: Non-state contingent nominal contracting (NSCNC). The role of monetary policy will be to keep this large credit market functioning properly (i.e., complete). We ignore ZLB issues in this talk. See the companion paper by Azariadis, Bullard, Singh and Suda (2015). I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM W EALTH , INCOME AND I NEQUALITY P OLICY C ONCLUSIONS CONSUMPTION INEQUALITY There is a lot of wealth, income and consumption inequality in this stylized model. The role of credit markets, if they work correctly, will be to re-allocate uneven income profiles across the life cycle into perfectly equal consumption shares by cohort, appropriately scaled by life cycle productivity. The model equilibrium will naturally rank: wealth Gini > income Gini > consumption Gini. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS T HE MONETARY POLICY IMPLICATIONS Optimal monetary policy in this model looks like “nominal GDP targeting”—countercyclical price level movements. This result continues to hold even when there is “massive” heterogeneity—enough heterogeneity to approximate income, financial wealth, and consumption inequality in the U.S. Hence, the main result is that NGDP targeting constitutes “optimal monetary policy for the masses” in this environment. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM Environment I NEQUALITY P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS L IFE CYCLE MODELS General equilibrium life cycle economy = many-period overlapping generations. Key variables are privately-issued debt, real interest rates and inflation. Think of privately-issued debt = “mortgage-backed securities.” There is no government spending or taxes of any kind. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS S YMMETRY ASSUMPTIONS We make a set of important “symmetry assumptions.” These assumptions involve the symmetry of the life cycle productivity endowment pattern of the households (detailed below), along with log preferences, no discounting, and no population growth. These assumptions help deliver the result that in the equilibria we study: The real interest rate is exactly equal to the output growth rate at every date, even in the stochastic economy. Could think of this as the Wicksellian natural real rate of interest. This in turn creates a set of easy to understand baseline results for this economy. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS E NVIRONMENT DETAILS Standard (T + 1)-periods (quarterly) DSGE life-cycle endowment economy. Each period, a new cohort of households enters the economy, makes economic decisions over the next 241 periods, then exits the economy. There is one asset in the model, privately-issued debt (consumption loans). The monetary authority controls the nominal price level P (t) directly. For a money demand version, see Azariadis et al. (2015). All households have log preferences with no discounting. Other assumptions: No population growth, no capital, no default, flexible prices, no borrowing constraints. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS K EY FRICTION : NSCNC Loans are dispersed and repaid in the unit of account—that is, in nominal terms—and are not contingent on income realizations. There are two aspects to this assumption. The non-state contingent aspect means that real resources are misallocated via this friction. The nominal aspect means that the monetary authority may be able to fix the distortion. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS L INEAR PRODUCTION TECHNOLOGY We model a growing economy in which a linear technology is improving over time. Aggregate real output Y (t) is given by Y (t) = Q (t) L (t) , (1) where L (t) is the aggregate labor input and Q (t) is the level of technology (also TFP and labor productivity). The level of technology grows at a stochastic rate λ (t, t + 1) between dates t and t + 1, Q (t + 1) = λ (t, t + 1) Q (t) , where the stochastic process for λ is defined on the next slide. (2) I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS S TOCHASTIC STRUCTURE The real wage w (t) is then exogenously given by w (t + 1) = λ (t, t + 1) w (t) , (3) where w (0) > 0, and λ (t, t + 1) is the gross rate of aggregate productivity growth between date t and date t + 1, and where λ (t, t + 1) = (1 ρ) λ̄ + ρλ (t 1, t) + σe (t + 1) , (4) where λ̄ > 1 represents the average gross growth rate, ρ 2 (0, 1) , σ > 0, and e (t + 1) is a truncated normal with bounds b, b > 0, such that the ZLB avoided. I NTRODUCTION E NVIRONMENT T IMING P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS PROTOCOL At the beginning of date t, nature moves first and chooses λ (t 1, t) , which implies a value for w(t). The policymaker moves next and chooses a value for P (t) . Households then decide how much to work, consume and save. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS N OMINAL INTEREST RATE CONTRACTS Households contract by fixing the nominal interest rate one period in advance. The non-state contingent nominal interest rate, “the contract rate,” is given by Rn (t, t + 1) 1 = Et ct ( t ) P (t) . ct ( t + 1 ) P ( t + 1 ) (5) This rate can be understood as expected nominal GDP growth. In the equilibria we study, this expectation is the same for all households, even those born at different dates or with different levels of productivity. I NTRODUCTION E NVIRONMENT P RODUCTIVITY W HAT MONETARY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS POLICY DOES The countercyclical price level rule delivers complete markets allocations: Rn (t 1, t) P (t) = r P (t 1) , (6) λ (t 1, t) where λr indicates a realization of the shock and Rn is the expectation given in the previous slide—similar to Sheedy (BPEA, 2014) and Koenig (IJCB, 2013). Given this policy rule, households consume equal amounts of available production, given their productivity, “equity share contracting,” which is optimal under homothetic preferences. This price level rule renders the households’ date-t decision problem deterministic because it perfectly insures the household against future shocks to income. Consumption and asset holdings fluctuate from period to period, but in proportion to the value of w (t) . I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY Life-Cycle Productivity P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS L IFE - CYCLE PRODUCTIVITY PROFILES Households entering the economy draw a scaling factor h i 1 x U ξ , ξ and receive a life cycle productivity profile which is a scaled version of the baseline profile, es : es,i = x es , where ξ 1 determines the within-cohort dispersion. Life cycle productivity profiles are deterministic. Huggett, Ventura and Yaron (AER, 2011) argue that differences in initial conditions are more important than differences in shocks. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS AVERAGE LIFE - CYCLE PRODUCTIVITY The baseline profile, es , is given by: " es = f (s) = 2 + exp s 120 60 4 # . Profiles begin at a low value, rise to a peak in the middle period of life, and then decline to the low value. Life cycle productivity profiles are symmetric. Agents can sell productivity units available in a particular period in the labor market at the competitive wage per effective efficiency unit. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS B ASELINE LIFE - CYCLE PRODUCTIVITY 3.5 3 2.5 2 1.5 0 60 120 180 240 quarters F IGURE : Baseline endowment profile. The profile is symmetric and peaks in the middle period of the life cycle. I NTRODUCTION E NVIRONMENT T HE MASS P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM OF LIFE - CYCLE PRODUCTIVITY F IGURE : The mass of endowment profiles: es,i es = 2 + exp I NEQUALITY s 120 60 4 , ξ = 6.5. es U ξ 1 ,ξ , P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS S TATIONARY EQUILIBRIA We let t 2 ( ∞, +∞) . We only consider stationary equilibria under perfectly credible policy rules governing P (t) . We let R (t) be the gross real rate of return in the credit market. Stationary equilibrium is a sequence fR (t) , P (t)gt+=∞ ∞ such that markets clear, households solve their optimization problems, and the policymaker credibly adheres to the stated policy rule. Key condition is that aggregate asset holding A (t) = 0 8t. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS S TATIONARY EQUILIBRIA T HEOREM Assume symmetry as defined above. Assume the monetary authority credibly uses the price level rule 8t. Then the general equilibrium gross real interest rate, R (t 1, t) , is equal to the gross rate of aggregate productivity growth, and hence the real growth rate of the economy, λ (t 1, t) , 8t. C OROLLARY For any two households that share the same productivity profile, consumption is equalized at each date t. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY Characterizing the Equilibrium C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS L ABOR / LEISURE 1 0.8 0.6 0.4 0.2 0 0 60 120 180 240 quarters F IGURE : Leisure decisions by age (green), labor supply by age (blue) and fraction of work time in U.S. data, 19% (red). The labor/leisure choice depends on the current-to-lifetime average productivity ratio. Productivity profiles of the form es,i = x es imply labor/leisure choices dependent on age only. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS L ABOR INCOME MASS F IGURE : Labor income profiles es,i (1 `) w; ξ = 6.5, η = 0.21, and w = 1. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS C ONSUMPTION MASS F IGURE : Consumption mass (red) and labor income mass (blue) along the complete markets balanced growth path with w (t) = 1. Under optimal monetary policy, the private credit market reallocates uneven labor income into perfectly equal consumption for each productivity profile. The consumption Gini is 31.8%, similar to values calculated from U.S. data. I NTRODUCTION E NVIRONMENT N ET P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS ASSET HOLDING MASS F IGURE : Net asset holding mass by cohort along the complete markets balanced growth path. Borrowing, the negative values to the left, peaks at stage 60 of the life cycle (age ~35), while positive assets peak at stage of life 180 (age ~65). The financial wealth Gini is 72.7%, similar to values calculated in U.S. data. I NTRODUCTION E NVIRONMENT P RODUCTIVITY T HREE NOTIONS C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS OF INCOME Three notions of income: 1 Labor income, Y1 = es,i [1 2 `t (t + s)] w (t + s) , Labor income plus non-negative capital income, Y2 = es,i [1 `t (t + s)] w (t + s) + + max [λ (t + s, t + s 3 1) 1] at,i (t + s 1) ,0 , P (t + s 1) The non-negative component of total income, ) ( es,i [1 `t (t + s)] w (t + s) + Y3 = max . a (t+s 1) + [λ (t + s, t + s 1) 1] Pt,i(t+s 1) , 0 Gini coefficients of income distributions: GY1 = 56.2%, GY2 = 51.6%, GY3 = 59.6%. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY L ABOR INCOME + NON - NEGATIVE CAPITAL INCOME F IGURE : Profiles of labor income and non-negative capital income es,i (1 `) w + max (λ 1) Pa , 0 ; ξ = 6.5, η = 0.21, and w = 1. C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY N ON - NEGATIVE TOTAL INCOME F IGURE : Profiles of non-negative total income max es,i (1 `) w + (λ 1) Pa , 0 ; ξ = 6.5, η = 0.21, and w = 1. P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM Inequality I NEQUALITY P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS D ENSITIES En dowm e n t 0.1 1 0.05 0 Labor in com e 0.5 0 0 10 0 C on su m pti on W e alth 0.02 0.5 5 0.01 0 0 2 0 0 100 F IGURE : PDFs of endowment, labor income, consumption and wealth. Note: the wealth subplot omits a mass point (121/241) at 0. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY D ATA ON INEQUALITY IN THE U.S. Consumption (Heathcote, Perri and Violante, RED, 2010): GC,U.S. = 32%. Income (CBO, 2016): pre-taxes/transfers GY,U.S. = 51%; post-taxes/transfers GY,U.S. = 43%. Financial wealth (Davies, Sandström, Shorrocks and Wolff, EJ, 2011): GW,U.S. = 80%. C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS I NEQUALITY IN THE MODEL Large amount of heterogeneity which depends in part on life cycle productivity dispersion. Financial wealth is defined as the non-negative part of net assets. Denote GW , GY , and GC as the financial wealth, income, and consumption Gini coefficients, respectively, in the model. For ξ = 6.5 and η = 0.21 GW = 72.7% > GY2 = 51.6% > GC = 31.8%, versus U.S. data GW,U.S. = 80% > GY,U.S. = 51% > GC,U.S. = 32%. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY P RODUCTIVITY DISPERSION AND G INI COEFFICIENTS 1 0.8 0.6 0.4 Wealth Labor income Consumption 0.2 0 2 4 6 8 10 F IGURE : As the dispersion of productivity profiles, ξ, increases, the Gini coefficients increase. The ordering GW > GY > GC is preserved. C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM Policy I NEQUALITY P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NTERPRETING MONETARY I NEQUALITY P OLICY POLICY The price level rule characterizes policy by “counter cyclical price level” movements. But the policy can also be interpreted more conventionally in interest rate terms. Contracts are made understanding policy ... And policy is made understanding contracts ... Interest rate policy is a fixed point of this process. C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS P OLICY CHARACTERIZATION The contract nominal rate is the expected rate of nominal GDP growth. Wicksellian natural real rate = λ. The contract nominal rate is always ratified ex post. This makes the real rate = λ. “Just like the simple NK model.” I NTRODUCTION E NVIRONMENT P RODUCTIVITY N OMINAL GDP C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS TARGETING Suppose ρ = 0 : Then the expected rate of NGDP growth never changes, and the economy never deviates from the NGDP path. “Perfect NGDP targeting.” Suppose ρ > 0 : Then the expected rate of NGDP fluctuates persistently with the shock, and it takes longer to return to the NGDP path. Nominal and real rates fall in a recession. I NTRODUCTION E NVIRONMENT E FFECTS P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS OF A SHOCK 1.06 1.02 1.04 1 1.02 0 5 10 0 quarters 5 10 quarters 1.4 1.06 1.04 1.2 1.02 1 0 5 quarters 10 0 5 10 quarters F IGURE : Monetary policy responds to a decrease in aggregate productivity, λ, by increasing the price level in the period of the shock. Subsequently, inflation converges to its BGP value, π , from below. The nominal interest rate drops in the period after the shock. I NTRODUCTION E NVIRONMENT P RODUCTIVITY C HARACTERIZING THE E QUILIBRIUM Conclusions I NEQUALITY P OLICY C ONCLUSIONS I NTRODUCTION E NVIRONMENT P RODUCTIVITY A LL HOUSEHOLDS C HARACTERIZING THE E QUILIBRIUM I NEQUALITY P OLICY C ONCLUSIONS FACE A CONSUMPTION SMOOTHING PROBLEM This paper attributes observed levels of U.S. inequality to life-cycle effects in conjunction with heterogeneous life-cycle productivity profiles. All households in this model, regardless of their assigned life-cycle productivity profile, face a problem of smoothing life-cycle consumption in a world with a NSCNC friction. The monetary authority can remove this impediment to life-cycle consumption smoothing for all households.
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