A M ODEL OF S ECULAR S TAGNATION Gauti B. Eggertsson and Neil R. Mehrotra Brown University Princeton February, 2015 1 / 35
S ECULAR S TAGNATION H YPOTHESIS I wonder if a set of older ideas . . . under the phrase secular stagnation are not profoundly important in understanding Japan’s experience, and may not be without relevance to America’s experience — Lawrence Summers Original hypothesis: ◮ Alvin Hansen (1938): Suggests a permanent demand depression. ◮ Reduction in population growth and investment opportunities. ◮ Concerns about insufficient demand ended with WWII and subsequent baby boom. Secular stagnation resurrected: ◮ Lawrence Summers (2013) ◮ Highly persistent decline in the natural rate of interest ◮ Chronically binding zero lower bound Goal here: ◮ Formlize these ideas in a simple model ◮ Propose a OLG model in the spirit of Samuelson (1958) 2 / 35
W HY ARE WE SO CONFIDENT INTEREST RATES WILL RISE SOON ? Interest rates in the US during the Great Depression: ◮ Started falling in 1929 (reach zero in 1933) ...... ◮ ...... only to increase in 1947 Started dropping in Japan in 1994: ◮ Remains at zero today Why are we so confident interest rates are increasing in the next few years? Need a framework where the answer is not baked into the cake – need a model that can account for arbitrary persistence of the recession 3 / 35
P REVIEW OF R ESULTS Permanently negative natural rate of interest can be triggered by: ◮ Permanent deleveraging shock ◮ Slowdown in population growth ◮ Increase in income inequality ◮ Fall in relative price of investment Stagnation steady state ◮ Permanently binding zero lower bound ◮ Low inflation or deflation ◮ Permanent shortfall in output from potential – no obvious adjustment mechanism (price flexibility paradox). Monetary and fiscal policy responses ◮ Raising the inflation target ◮ Increases in public debt ◮ Increases in government purchases 4 / 35
O UTLINE FOR P RESENTATION 1. Model ◮ Endowment economy - deleveraging shocks, income inequality, population slowdown - price level determination ◮ Endogenous production 2. Monetary and fiscal policy 3. Capital ◮ Fall in the relative price of investment 5 / 35
E CONOMIC E NVIRONMENT E NDOWMENT ECONOMY ◮ Time: t = 0, 1, 2, ... ◮ Goods: consumption good ( c ) ◮ Agents: 3-generations: i ǫ { y , m , o } ◮ Assets: riskless bonds ( B i ) ◮ Technology: exogenous borrowing constraint D 6 / 35
H OUSEHOLDS Objective function: � + β 2 log � � C y � �� C m C o � � max U = E t log + β log t + 1 t + 2 t C y t , , C m t + 1 , C o t + 2 Budget constraints: C y t = B y t t + 1 − ( 1 + r t ) B y C m t + 1 = Y m t + B m t + 1 C o t + 2 = Y o t + 2 − ( 1 + r t + 1 ) B m t + 1 ( 1 + r t ) B i t ≤ D t 7 / 35
C ONSUMPTION AND S AVING Credit-constrained youngest generation: D t C y t = B y t = 1 + r t Saving by the middle generation: 1 1 + r t = β E t C m C o t t + 1 Spending by the old: C o t = Y o t − ( 1 + r t − 1 ) B m t − 1 8 / 35
D ETERMINATION OF THE R EAL I NTEREST R ATE Asset market equilibrium: N t B y t = − N t − 1 B m t ( 1 + g t ) B y t = − B m t Demand and supply of loans: t = 1 + g t L d D t 1 + r t Y o β 1 t + 1 L s 1 + β ( Y m t = t − D t − 1 ) − 1 + β 1 + r t 9 / 35
D ETERMINATION OF THE R EAL I NTEREST R ATE Expression for the real interest rate (perfect foresight): Y o 1 + r t = 1 + β ( 1 + g t ) D t + 1 t + 1 Y m Y m β t − D t − 1 β t − D t − 1 Determinants of the real interest rate: ◮ Tighter collateral constraint reduces the real interest rate ◮ Lower rate of population growth reduces the real interest rate ◮ Higher middle age income reduces real interest rate ◮ Higher old income increases real interest rate 10 / 35
E FFECT OF A D ELEVERAGING S HOCK Impact effect: ◮ Collateral constraint tightens from D h to D l ◮ Reduction in the loan demand and fall in real rate ◮ Akin to Eggertsson and Krugman (2012) Delayed effect: ◮ Next period, a shift out in loan supply ◮ Further reduction in real interest rate ◮ Novel effect from Eggertsson and Krugman (2012) ◮ Potentially powerful propagation mechanism 11 / 35
E FFECT OF A D ELEVERAGING S HOCK 1.20 ¡ Loan ¡ Supply ¡ 1.15 ¡ 1.10 ¡ Gross ¡Real ¡Interest ¡Rate ¡ A ¡ D ¡ 1.05 ¡ 1.00 ¡ B ¡ 0.95 ¡ C ¡ Loan ¡ Demand ¡ 0.90 ¡ 0.85 ¡ 0.80 ¡ 0.200 ¡ 0.220 ¡ 0.240 ¡ 0.260 ¡ 0.280 ¡ 0.300 ¡ Loans ¡ 12 / 35
I NCOME I NEQUALITY Does inequality affect the real interest rate? ◮ Our result due to generational inequality that triggers borrowing and lending ◮ What about inequality within a given cohort? - Irrelevant if output of each individual same over time - Easy to come up with examples where it matter Generalization of endowment process: ◮ High-type households with high income in middle period ◮ Low-type households with low income in middle period ◮ Both types receive same income in last period 13 / 35
I NCOME I NEQUALITY AND R EAL I NTEREST R ATE Credit constrained middle income: ◮ Fraction η s of middle income households are credit constrained ◮ True for low enough income in middle generation and high enough income in retirement ◮ Fraction 1 − η s lend to both young and constrained middle-generation households Expression for the real interest rate: Y o 1 + r t = 1 + β ( 1 + g t + η s ) D t 1 t + 1 � + � β ( 1 − η s ) � � β Y m , h Y m , h ( 1 − η s ) − D t − 1 − D t − 1 t t 14 / 35
P RICE L EVEL D ETERMINATION Euler equation for nominal bonds: 1 1 ( 1 + i t ) P t = β E t C m C o P t + 1 t t + 1 i t ≥ 0 Bound on steady state inflation: 1 ¯ Π ≥ 1 + r ◮ If steady state real rate is negative, steady state inflation must be positive ◮ No equilibrium with stable inflation ◮ But what happens when prices are NOT flexible and the central bank does not tolerate inflation? ◮ Then the central bank’s refusal to tolerate high enough inflation will show up as a permanent recession. 15 / 35
E NDOGENOUS P RODUCTION - A GGREGATE S UPPLY - F ULL E MPLOYMENT Output and labor demand: ◮ Labor only factor of production (capital coming up) ◮ Firms are perfectly competitive Y t = L α t W t = α L α − 1 t P t Labor supply: ◮ Middle-generation households supply a constant level of labor ¯ L ◮ Implies a constant market clearing real wage ¯ W = α ¯ L α − 1 ◮ Implies a constant full-employment level of output: Y fe = ¯ L α 16 / 35
D OWNWARD N OMINAL W AGE R IGIDITY Partial wage adjustment: � L α − 1 � W t , P t α ¯ ˜ W t = max W t = γ W t − 1 + ( 1 − γ ) P t α ¯ ˜ L α − 1 where Wage rigidity and unemployment: ˜ W t is a wage norm ◮ ◮ If real wages exceed market clearing level, employment is rationed ◮ Unemployment: U t = ¯ L − L t ◮ Similar assumption in Kocherlakota (2013) and Schmitt-Grohe and Uribe (2013) 17 / 35
S TEADY S TATE A GGREGATE S UPPLY R ELATION For positive steady state inflation: Y = Y fe = ¯ L α For steady state deflation: α 1 − γ � � 1 − α Y Π = Y fe 1 − γ ◮ Upward sloping relationship between inflation and output ◮ Vertical line at full-employment 18 / 35
A GGREGATE S UPPLY R ELATION 1.20 ¡ Aggregate ¡ Supply ¡ 1.15 ¡ 1.10 ¡ Gross ¡Infla5on ¡Rate ¡ 1.05 ¡ 1.00 ¡ 0.95 ¡ 0.90 ¡ 0.85 ¡ 0.80 ¡ 0.80 ¡ 0.85 ¡ 0.90 ¡ 0.95 ¡ 1.00 ¡ 1.05 ¡ 1.10 ¡ Output ¡ 19 / 35
D ERIVATION OF A GGREGATE D EMAND Monetary policy rule: � Π t � � φ π � 1, ( 1 + i ∗ ) 1 + i t = max Π ∗ Above binding ZLB: � Π t � φ π 1 + i ∗ = 1 + β ( 1 + g t ) D t Π ∗ Y t − D t − 1 Π t + 1 β Binding ZLB: 1 = 1 + β ( 1 + g t ) D t Y t − D t − 1 Π t + 1 β 20 / 35
F ULL E MPLOYMENT S TEADY S TATE 1.20 ¡ Aggregate ¡ Supply ¡ 1.15 ¡ 1.10 ¡ Gross ¡Infla5on ¡Rate ¡ 1.05 ¡ FE ¡ Steady ¡ 1.00 ¡ State ¡ Aggregate ¡ Demand ¡ 0.95 ¡ 0.90 ¡ 0.85 ¡ 0.80 ¡ 0.80 ¡ 0.85 ¡ 0.90 ¡ 0.95 ¡ 1.00 ¡ 1.05 ¡ 1.10 ¡ Output ¡ Parameter Values 21 / 35
E FFECT OF A C OLLATERAL S HOCK 1.20 ¡ Aggregate ¡ Supply ¡ 1.15 ¡ 1.10 ¡ Gross ¡Infla5on ¡Rate ¡ 1.05 ¡ Defla5on ¡ 1.00 ¡ AD 2 ¡ Steady ¡ State ¡ 0.95 ¡ 0.90 ¡ AD 1 ¡ 0.85 ¡ 0.80 ¡ 0.80 ¡ 0.85 ¡ 0.90 ¡ 0.95 ¡ 1.00 ¡ 1.05 ¡ 1.10 ¡ Output ¡ 22 / 35
P ROPERTIES OF THE S TAGNATION S TEADY S TATE Long slump: ◮ Binding zero lower bound so long as natural rate is negative ◮ Deflation raises real wages above market-clearing level ◮ Output persistently below full-employment level Existence and stability: ◮ Secular stagnation steady state exists so long as γ > 0 ◮ If Π ∗ = 1, secular stagnation steady state is unique and determinate ◮ Contrast to deflation steady state emphasized in Benhabib, Schmitt-Grohe and Uribe (2001) ◮ Can do comparative statistics! Linearized Conditions 23 / 35
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