A Model of Secular Stagnation

AMODELOF SECULAR STAGNATION

Gauti B. Eggertsson and Neil R. Mehrotra

Brown University

Princeton February, 2015

1 / 35 SECULAR STAGNATION HYPOTHESIS 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: I Alvin Hansen (1938): Suggests a permanent demand depression. I Reduction in population growth and investment opportunities. I Concerns about insufﬁcient demand ended with WWII and subsequent baby boom. Secular stagnation resurrected: I Lawrence Summers (2013) I Highly persistent decline in the natural rate of interest I Chronically binding zero lower bound Goal here: I Formlize these ideas in a simple model I Propose a OLG model in the spirit of Samuelson (1958)

2 / 35 WHY ARE WE SO CONFIDENT INTEREST RATES WILLRISESOON?

Interest rates in the US during the Great Depression:

I Started falling in 1929 (reach zero in 1933) ...... I ...... only to increase in 1947

Started dropping in Japan in 1994: I 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 PREVIEWOF RESULTS Permanently negative natural rate of interest can be triggered by:

I Permanent deleveraging shock I Slowdown in population growth I Increase in income inequality I Fall in relative price of investment

Stagnation steady state

I Permanently binding zero lower bound I Low inflation or deflation I Permanent shortfall in output from potential – no obvious adjustment mechanism (price flexibility paradox).

Monetary and ﬁscal policy responses

I Raising the inﬂation target I Increases in public debt I Increases in government purchases

4 / 35 OUTLINEFOR PRESENTATION

1. Model

I Endowment economy - deleveraging shocks, income inequality, population slowdown - price level determination

I Endogenous production

2. Monetary and ﬁscal policy

3. Capital

I Fall in the relative price of investment

5 / 35 ECONOMIC ENVIRONMENT

ENDOWMENTECONOMY

I Time: t = 0, 1, 2, ...

I Goods: consumption good (c)

I Agents: 3-generations: ie {y, m, o}

i I Assets: riskless bonds (B )

I Technology: exogenous borrowing constraint D

6 / 35 HOUSEHOLDS

Objective function:

n y m 2 o o max U = Et log C + β log Ct+ + β log Ct+ y m o t 1 2 Ct,,Ct+1,Ct+2

Budget constraints:

y y Ct = Bt m m y m Ct+1 = Yt+1 − (1 + rt)Bt + Bt+1 o o m Ct+2 = Yt+2 − (1 + rt+1)Bt+1 i (1 + rt)Bt ≤ Dt

7 / 35 CONSUMPTIONAND SAVING

Credit-constrained youngest generation:

y y Dt Ct = Bt = 1 + rt

Saving by the middle generation:

1 1 + rt m = βEt o Ct Ct+1

Spending by the old:

o o m Ct = Yt − (1 + rt−1)Bt−1

8 / 35 DETERMINATION OF THE REAL INTEREST RATE

Asset market equilibrium:

y m NtBt = −Nt−1Bt y m (1 + gt) Bt = −Bt

Demand and supply of loans:

d 1 + gt Lt = Dt 1 + rt o s β m 1 Yt+1 Lt = (Yt − Dt−1) − 1 + β 1 + β 1 + rt

9 / 35 DETERMINATION OF THE REAL INTEREST RATE

Expression for the real interest rate (perfect foresight):

o 1 + β (1 + gt)Dt 1 Yt+1 1 + rt = m + m β Yt − Dt−1 β Yt − Dt−1

Determinants of the real interest rate: I Tighter collateral constraint reduces the real interest rate I Lower rate of population growth reduces the real interest rate I Higher middle age income reduces real interest rate I Higher old income increases real interest rate

10 / 35 EFFECT OF A DELEVERAGING SHOCK

Impact effect:

I Collateral constraint tightens from Dh to Dl I Reduction in the loan demand and fall in real rate I Akin to Eggertsson and Krugman (2012)

Delayed effect: I Next period, a shift out in loan supply I Further reduction in real interest rate I Novel effect from Eggertsson and Krugman (2012) I Potentially powerful propagation mechanism

11 / 35 EFFECT OF A DELEVERAGING SHOCK

1.20 Loan Supply 1.15

1.10 A

1.05 D

1.00 B 0.95 C Loan Demand 0.90 Gross Real Interest Rate

0.85

0.80 0.200 0.220 0.240 0.260 0.280 0.300 Loans

12 / 35 INCOME INEQUALITY

Does inequality affect the real interest rate? I Our result due to generational inequality that triggers borrowing and lending I 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: I High-type households with high income in middle period I Low-type households with low income in middle period I Both types receive same income in last period

13 / 35 INCOME INEQUALITYAND REAL INTEREST RATE

Credit constrained middle income:

I Fraction ηs of middle income households are credit constrained I True for low enough income in middle generation and high enough income in retirement

I Fraction 1 − ηs lend to both young and constrained middle-generation households

Expression for the real interest rate:

o 1 + β (1 + gt + ηs) Dt 1 Yt+1 1 + rt = + β m,h β (1 − ηs) m,h (1 − ηs) Yt − Dt−1 Yt − Dt−1

14 / 35 PRICE LEVEL DETERMINATION Euler equation for nominal bonds:

1 1 Pt m = βEt o (1 + it) Ct Ct+1 Pt+1 it ≥ 0

Bound on steady state inﬂation: 1 Π¯ ≥ 1 + r

I If steady state real rate is negative, steady state inflation must be positive I No equilibrium with stable inflation I But what happens when prices are NOT flexible and the central bank does not tolerate inflation? I Then the central bank’s refusal to tolerate high enough inflation will show up as a permanent recession.

15 / 35 ENDOGENOUS PRODUCTION -AGGREGATE SUPPLY -FULL EMPLOYMENT

Output and labor demand: I Labor only factor of production (capital coming up) I Firms are perfectly competitive

α Yt = Lt Wt α−1 = αLt Pt

Labor supply: I Middle-generation households supply a constant level of labor L¯ α−1 I Implies a constant market clearing real wage W¯ = αL¯ α I Implies a constant full-employment level of output: Yfe = L¯

16 / 35 DOWNWARD NOMINAL WAGE RIGIDITY

Partial wage adjustment:

n α−1o Wt = max W˜ t, PtαL¯ α−1 where W˜ t = γWt−1 + (1 − γ)PtαL¯

Wage rigidity and unemployment:

I W˜ t is a wage norm I If real wages exceed market clearing level, employment is rationed

I Unemployment: Ut = L¯ − Lt I Similar assumption in Kocherlakota (2013) and Schmitt-Grohe and Uribe (2013)

17 / 35 STEADY STATE AGGREGATE SUPPLY RELATION

For positive steady state inﬂation:

α Y = Yfe = L¯

For steady state deﬂation:

! α Y 1 − γ 1−α = Π Yfe 1 − γ

I Upward sloping relationship between inﬂation and output I Vertical line at full-employment

18 / 35 AGGREGATE SUPPLY RELATION

1.20 Aggregate Supply 1.15

1.10

1.05

1.00

0.95

Gross Inﬂaon Rate 0.90

0.85

0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output

19 / 35 DERIVATION OF AGGREGATE DEMAND

Monetary policy rule:

φπ ! ∗ Πt 1 + it = max 1, (1 + i ) Π∗

Above binding ZLB:

∗ φπ 1 + i Πt 1 + β (1 + gt)Dt ∗ = Πt+1 Π β Yt − Dt−1 Binding ZLB:

1 1 + β (1 + g )D = t t Πt+1 β Yt − Dt−1

20 / 35 FULL EMPLOYMENT STEADY STATE

1.20 Aggregate Supply 1.15

1.10

1.05 FE Steady 1.00 State Aggregate Demand 0.95

Gross Inﬂaon Rate 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 EFFECT OF A COLLATERAL SHOCK

1.20 Aggregate Supply 1.15

1.10

1.05

1.00 Deﬂaon Steady AD2 State 0.95

Gross Inﬂaon Rate 0.90

AD1 0.85

0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output

22 / 35 PROPERTIESOFTHE STAGNATION STEADY STATE Long slump: I Binding zero lower bound so long as natural rate is negative I Deﬂation raises real wages above market-clearing level I Output persistently below full-employment level

Existence and stability: I Secular stagnation steady state exists so long as γ > 0 ∗ I If Π = 1, secular stagnation steady state is unique and determinate I Contrast to deﬂation steady state emphasized in Benhabib, Schmitt-Grohe and Uribe (2001) I Can do comparative statistics!

Linearized Conditions

23 / 35 PARADOXOF FLEXIBILITY

I No obvious adjustment mechanisms to full employment I As wages get more ﬂexible output drops more

1.20 AD2

1.15

1.10

1.05

1.00 Deﬂaon Steady 0.95 State

AS2 Gross Inﬂaon Rate 0.90 AS1 Higher Wage 0.85 Flexibility Steady State 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output

24 / 35 PARADOXOF TOIL I Say’s Law inverted: Destroying Aggregate supply creates Aggregate Demand I Hysteresis/Reduction in labor force participation stabilizing (reduces deﬂationary pressures)

1.20 AS AD2 AS1 2

1.15

1.10

1.05

1.00 Deﬂaon Steady 0.95 State

Gross Inﬂaon Rate 0.90 High 0.85 Producvity Steady State 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output 25 / 35 MONETARY POLICY RESPONSES

Forward guidance: I Extended commitment to keep nominal rates low? I Ineffective if households/ﬁrms expect rates to remain low indeﬁnitely

Raising the inflation target: I For sufficiently high inflation target, full employment steady state exists. I Timidity trap (Krugman (2014)) I Multiple determinate steady states (secular stagnation and reflation) I Monetary policy not as powerful as in earlier models because no way to exclude secular stagnation.

26 / 35 RAISINGTHE INFLATION TARGET

1.20 Aggregate AD1 AD AD 2 3 Supply 1.15 Full 1.10 Employment Steady State 1.05

1.00

0.95

Gross Inﬂaon Rate 0.90

0.85 Deﬂaon Steady State 0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output

27 / 35 FISCAL POLICY

Fiscal policy and the real interest rate:

d 1 + gt g Lt = Dt + Bt 1 + rt o o s β m m 1 Yt+1 − Tt+1 Lt = (Yt − Dt−1 − Tt ) − 1 + β 1 + β 1 + rt

Government budget constraint:

g y m 1 o 1 + rt g Bt + Tt (1 + gt) + Tt + Tt = Gt + Bt−1 1 + gt−1 1 + gt−1 Fiscal instruments:

g y m o Gt, Bt , Tt , Tt , Tt

28 / 35 TEMPORARY INCREASEIN PUBLIC DEBT

y g Under constant population and set Gt = Tt = Bt−1 = 0:

m g Tt = −Bt o g Tt+1 = (1 + rt) Bt

Implications for natural rate: I Loan demand and loan supply effects cancel out I Temporary increases in public debt ineffective in raising real rate I Temporary monetary expansion equivalent to temporary expansion in public debt at the zero lower bound I Effect of an increase in public debt depends on beliefs about future ﬁscal policy

29 / 35 PERMANENT INCREASEIN PUBLIC DEBT (OR INVERSELY, AUSTERITYMEASURES)

Consider steady state following ﬁscal rule:

To = β (1 + r) Tm 1 + g Ld = D + Bg 1 + r β 1 Yo Ls = (Ym − D) − 1 + β 1 + β 1 + r

Implications for natural rate: I Changes in taxation have no effects on loan supply I Permanent rise in public debt always raises the real rate I Equivalent to helicopter drop at the zero lower bound I Public debt circumvents the tightening credit friction (Woodford (1990))

30 / 35 EXPANSIONARY FISCAL POLICY

1.20 AD2 AD3 Aggregate Supply 1.15

1.10

1.05 Full Employment Steady State 1.00 Deﬂaon Steady 0.95 State

Gross Inﬂaon Rate 0.90

0.85

0.80 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Output

31 / 35 GOVERNMENT PURCHASES MULTIPLIER

Slope of the AD and AS curves:

1 + β ψ = (1 + g) D β 1 − α 1 − γ κ = α γ

Purchases multiplier at the zero lower bound:

Financing Multiplier Value 1+β 1 Increase in public debt β 1−κψ > 2 Tax on young generation 0 0 1 Tax on middle generation 1−κψ > 1 1+g 1 Tax on old generation − β 1−κψ < 0

32 / 35 CAPITAL AND SECULAR STAGNATION Rental rate and real interest rate:

k k k 1 − δ rt = pt − pt+1 ≥ 0 1 + rt rss ≥ −δ

I Negative real rate now constrained by fact that rental rate must be positive

Relative price of capital goods: I Decline in relative price of capital goods I Need less savings to build the same capital stock I –> downward pressure on the real interest rate. I Global decline in price of capital goods (Karabarbounis and Neiman, 2014)

Land

33 / 35 CONCLUSIONS

Policy implications: I Higher inflation target needed I Limits to forward guidance I Role for fiscal policy I Possible important implications for financial stability

Key takeaway: I NOT that we will stay in a slump forever I Slump of arbitrary duration I OLG framework to model interest rates

34 / 35 GOING FORWARD

In progress: I A quantitative variation of the model: stochastic transitions across age groups. I Quantitatively decompose the effect of different channels on the real interest rate during the crisis. I Did the bubble mask a secular stagnation?

35 / 35