Stagnation Traps Gianluca Benigno and Luca Fornaro May 2015
Research question and motivation Can insu cient aggregate demand lead to economic stagnation? This question goes back, at least, to the Great Depression Recently, renewed interest due to: I Two decades-long stagnation a ecting Japan since early 1990s I Slow recoveries from 2008 financial crisis in US and Euro Area All these episodes featured policy rates close to the zero lower bound
Japan: discount rate (1990-2014)
Japan: unemployment (1990-2014)
Japan: potential output growth (1990-2014)
US, UK, Eurozone: policy rates (1998-2014) 8" Central(Bank(policy(rate((%)( Source:"IFS" 7" 6" 5" 4" 3" 2" 1" 0" 1998" 2000" 2002" 2004" 2006" 2008" 2010" 2012" 2014" US" Euro" UK"
US, UK, Eurozone: unemployment (1998-2014) Unemployment*rate*(%)* Source:"WEO"April"2015" 18" US" UK" Core"Europe" Peripheral"Europe" 16" 14" 12" 10" 8" 6" 4" 2" 0" 1998" 1999" 2000" 2001" 2002" 2003" 2004" 2005" Core"Europe:""Simple"average"of"Austria,"Belgium,"France,"Germany,"Luxembourg,"and" Netherlands." Peripheral"Europe:"Simple"average"of"Ireland,"Italy,"Portugal,"and"Spain." 2006" 2007" 2008" 2009" 2010" 2011" 2012" 2013" 2014"
US, UK, Eurozone: potential output growth Real%Poten*al%GDP%Growth%(%)% Source:#WEO#April#2015,#Congressional#Budget#Office,#OECD#Economic#Outlook## 5# US#(CBO)# UK#(OECD)# Core#Europe# Peripheral#Europe# 4# 3# 2# 1# 0#!1# 1998# 1999# 2000# 2001# 2002# 2003# 2004# 2005# Core#Europe:##Simple#average#of#Austria,#Belgium,#France,#Germany,#Luxembourg,#and# Netherlands.# Peripheral#Europe:#Simple#average#of#Ireland,#Italy,#Portugal,#and#Spain.# 2006# 2007# 2008# 2009# 2010# 2011# 2012# 2013# 2014#
This paper Keynesian Growth framework I I Unemployment due to weak demand when monetary policy is constrained by the zero lower bound Growth is the result of investment by profit-maximizing firms Two-way interaction between aggregate demand, interest rates and growth I I Weak aggregate demand has a negative impact on firms profits and investment, resulting in low growth Low growth depresses interest rates, thus undermining the central bank s ability to sustain demand by cutting policy rates
Overview of results Key result: Permanent, or very persistent, slumps characterized by high unemployment and low growth are possible Two steady states I Full employment, high growth, positive nominal rate I High unemployment, low growth, zero lower bound binds! stagnation trap Fluctuations determined by expectations and sunspots Policies that foster growth can eliminate the stagnation trap equilibrium if they are su ciently aggressive
Model Grossman and Helpman (1991) model of vertical innovation, augmented with nominal wage rigidities and zero lower bound on nominal interest rate Infinite-horizon closed economy Continuum of measure one of di erentiated goods produced by monopolistic firms Continuum of measure one of households that supply labor and consume Central bank that sets monetary policy
Households Representative household with expected lifetime utility " X 1 t C 1 # E t 1 0 1 0 t=0 Z 1 C t exp ln q jt c jt dj Z 1 Q {z} t exp ln c jt dj exp( R 0 1 0 ln q jt dj) One unit labor endowment, no labor disutility, but unemployment possible due to nominal wage rigidities Own firms, have access to nominal bonds paying interest rate i Z 1 P jt c jt dj + b t+1 = W t L t + b t + d t 1+i t 0
Households - Optimality conditions Households optimization gives the Euler equation c t = gt+1 (1 + i t )E t ct+1 / t+1 1 where g t+1 Q t+1 Q t and t+1 P t+1 P t Focus on >1: increase in growth (" g t+1 ) generates rise in demand for consumption (" c t )
Firms Every sector j is populated by A leader producing quality q j Competitors producing quality q j with >1 One unit of labor is needed to manufacture one unit of good! marginal cost = W t Optimal price set by leader P jt = W t = P t In equilibrium every leader faces demand y t and earns profits y t (P jt W t )=y t W t ( 1)
Firms and production Output produced using labor y t = L t I I yt =1! full employment yt < 1! unemployment and negative output gap Output can be consumed or invested in research y t = c t + t
Research and innovation Outsiders can innovate on a product and capture monopoly profits by investing in research Value of a successful innovation 2 0 V t = E t 6 4 t+1 t B @y t+1 W t+1 ( 1) + (1 {z } t+1 ) V {z t+1 } profits in t +1 value of leadership in t +1 Growth rate of the economy (productivity growth) 13 C7 A5 g t Q t Q t 1 =exp( t 1 ln ) Growth rate is increasing in investment in innovation t
Nominal wage rigidities and monetary policy Nominal wages are rigid and follow W t = (y t )W t 1 with 0 0, (1) = 1 Focus on special case of constant nominal wage inflation W t = W t 1 Prices are proportional to wages, so CPI inflation is constant and equal to Central bank follows the interest rate rule 1+i t = max (1 + ī) y t, 1 Monetary policy constrained by zero lower bound i 0
Equilibrium in compact form Euler equation c t = Growth equation 1 apple g t+1 ct ( = E t 1)yt+1 +1 c t+1 Market clearing 1 g t+1 (EU) (1 + i t )E t ct+1 ln g t+2 ln (GG) Policy rule c t = y t ln g t+1 ln 1+i t = max (1 + ī) y t, 1 (MK) (PR) Rational expectation equilibrium is a set of processes {y t, c t, g t+1, i t } +1 t=0 satisfying equations (EU ), (GG), (MK ) and (PR)
Non-stochastic steady states Aggregate demand max (1 + ī) y, 1 = g 1 (AD) Growth equation Market clearing g 1 + ln g ln = 1 y +1 (GG) c = y ln g ln (MK)
Two steady states AD growth g (1,g f ) GG (y u,g u ) output gap y
Understanding stagnation traps Aside from the usual full employment steady state, the economy can find itself in a permanent liquidity trap with: I Negative output gap (y u < 1) I Weak growth (g u < g f ) I Monetary policy constrained by zero lower bound (i u = 0) The liquidity trap steady state can be seen as a stagnation trap, the combination of a liquidity and growth trap The zero lower bound constraint and the dependence of growth from the current output gap are both crucial in generating a stagnation trap
No zero lower bound AD growth g (1,g f ) GG (y u,g u ) output gap y
No zero lower bound AD growth g (1,g f ) GG output gap y
No dependence of growth from output gap AD growth g (1,g f ) GG (y u,g u ) output gap y
No dependence of growth from output gap AD growth g (1,g f ) GG output gap y
The role of confidence shocks Equilibrium is determined by expectations and sunspots I I I I I Suppose agents expect that growth will be low Low expectations of future income imply low aggregate demand Due to zero lower bound, central bank is not able to lower the interest rate enough to sustain full employment Firms profits are low, weak investment in innovation Expectations of weak growth are verified! expectations of low growth can give rise to permanent, or very long lasting, liquidity traps characterized by low growth
Some extensions 1. Model can generate temporary liquidity traps arising from pessimistic expectations about future growth link 2. With precautionary savings, it is possible to have a liquidity trap steady state with positive inflation and positive growth link 3. Results robust to the introduction of a Phillips curve link
Growth policies during a stagnation trap Recent emphasis on job creating growth Indeed, an appropriately designed growth policy can eliminate liquidity traps driven by confidence shocks Consider a countercyclical subsidy s t = s(1 y t ) If s is su ciently large, this policy rules out the liquidity trap steady state, while leaving unchanged the full employment steady state
Countercyclical subsidy (cont d) AD growth g (1,g f ) GG GG 0 (y u,g u ) output gap y
Conclusions We develop a Keynesian growth model in which endogenous growth interacts with the possibility of slumps driven by weak aggregate demand The model features two steady states. One is a stagnation trap, a permanent liquidity trap characterized by weak growth Large policy interventions to support growth can lead the economy out of a stagnation trap
Thank you!
Sunspots and temporary liquidity traps We can also have liquidity traps of finite expected duration Denote a sunspot by t. Agents form their expectations after observing Two-state discrete Markov process, t 2 ( o, p ) o is an absorbing optimistic equilibrium, in which agents expect to remain forever around the full employment steady state p is a pessimistic equilibrium with finite expected duration 1/(1 q p ). In this state the economy is in a liquidity trap with unemployment
Sunspots and temporary liquidity traps (cont d) In the pessimistic sunspot state the equilibrium is described by (g p ) 1 c p = q p +(1 q p ) c f (g p ) 1 = q p c p +(1 q p ) c f 1 y p +1 c p c f = yp ln gp ln 1 ln g f ln ln g p ln 1 +1 ln g f ln +
Sunspots and temporary liquidity traps (cont d) AD (1,g f ) GG growth g (y p,g p ) output gap y
Sunspots and temporary liquidity traps (cont d) Potential output (log) Output gap Nominal rate 2 4 6 8 10 12 14 time 2 4 6 8 10 12 14 time 2 4 6 8 10 12 14 time back
Precautionary savings, inflation and growth In the benchmark model, positive inflation and positive growth cannot coexist in a permanent liquidity trap g u = 1 1 Assume that every period a household becomes unemployed with probability p An unemployed household receives a benefit, such that its income is equal to a fraction b of the income of employed households Unemployed households cannot borrow
Precautionary savings, inflation and growth (cont d) Aggregate demand is given by the Euler equation of employed households c t = g t+1 (1 + i t ) E t ct+1 1 1 p + p/b > 1 The unemployment steady state is now characterized by g u = 1 1 Since >1, an unemployment steady state in which both inflation and growth are positive is now possible back
Introducing a Phillips curve Assume that nominal wages are downwardly rigid W t (y t )W t 1 with 0 > 0, (1) = Wages more downwardly flexible if unemployment is higher! non-linear Phillips curve Full employment steady state is not a ected (y = 1, g = g f, i = i f and = f ) Growth in the unemployment steady state is now g u = (y u ) 1 1 " output gap, " inflation, # real interest rate, # growth
Steady state determination with variable inflation AD growth g (y u,g u ) (1,g f ) GG output gap y back