Monetary Policy and a Stock Market Boom-Bust Cycle Lawrence - PowerPoint PPT Presentation

Monetary Policy and a Stock Market Boom-Bust Cycle Lawrence Christiano, Cosmin Ilut, Roberto Motto and Roberto Motto, and Massimo Rostagno

Asset markets have been volatile Should monetary policy react to the volatility? Is monetary policy somehow responsible for the volatility? Suppose (following Beaudry-Portier) asset price booms triggered by expectation of improved future productivity, which are not realized. A standard monetary DSGE model implies: inflation targeting as implemented in practice inflation targeting as implemented in practice + sticky wages = suboptimal volatility hard to understand boom-busts without monetary policy

Our finding contradicts conventional wisdom: inflation stabilization also stabilizes asset markets and real economy (Bernanke-Gertler) Conventional wisdom assumes inflation rising in stock market booms market booms

Inflation and Stock Price Inflation and Stock Price (real terms) in Interwar Period Inflation and Stock Price (real terms) in 1950s to 1970s 1 2 1 600 450 1 5 1 0 350 1 200 1 0 8 250 5 6 6 800 800 1 50 0 4 50 -5 400 2 -50 -1 0 0 0 -1 5 -1 50 3 5 7 9 1 3 5 7 9 1 3 5 7 3 4 5 5 6 7 8 8 9 0 1 1 2 3 5 5 5 5 6 6 6 6 6 7 7 7 7 2 2 2 2 2 2 2 2 2 3 3 3 3 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Note : Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow Note : Inflation is computed as the year-on-year change in GNP Deflator. Stock Price is Dow Jones divided by GDP Deflator. Jones divided by GNP Deflator. Inflation appears to be falling during Inflation appears to be falling during Inflation and Stock Price (real terms) in 1990s to 2005 ( ) 5 1 6000 the start-up of boom-bust episodes 4 1 2000 3 8000 2 4000 1 Stock Price ( right-hand scale ) 0 0 1990 1991 1993 1994 1995 1996 1998 1999 2000 2001 2003 2004 2005 Inflation ( percentage points, left-hand scale ) Note : Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow Jones divided by GDP Deflator. J di id d b GDP D fl

‘ Stock Market Boom-Bust Cycle’ Episode in which: p • Stock prices, consumption, investment, output employment rise sharply and then fall output, employment rise sharply and then fall • Inflation – low during boom – tends to rise near end (Adalid-Detken, Bordo-Wheelock) )

Argument g • We argue that it is difficult to account for boom-bust with a non-monetary model. boom bust with a non monetary model. – Even with ‘bells and whistles’ non-monetary Even with bells and whistles , non monetary model has a hard time accounting for duration and magnitude. – Non-monetary model has a hard time accounting for procyclical stock prices. i f li l k i • Easy to account for in a monetized model.

Signal about future technology Signal about future technology • Time series representation: Time series representation: signal a t   a t − 1   t     t − p  a t  log, technology   t  p  −  t • If , then signal turns out to be false  t  p  0 • If , then signal turns out to be correct correct.

RBC Model with Bells and Whistles • Household preferences:  E 0 ∑  t  log  C t − bC t − 1    log  1 − h t  . t  0 • Production function:   exp  a t  h t  1 −  Y t  K t • Capital accumulation: I t I t K t  1   1 −   K t   1 − S  1   K  1  I  I t . K S I t − 1 • Resource constraint C t  I t ≤ Y t

Simple RBC model • No adjustment costs in investment: S ≡ 0 • No habit persistence: b  0 • Other parameters:   0.36,   1.03 − .25 ,   .02,   2.3. • Signal of future improvement in technology leads to: – Fall in employment, investment – Rise in consumption – Price of capital is constant Price of capital is constant • Terrible model of boom-bust cycle!

Adding bells and whistles • Investment adjustment costs S  S ′  0 in Steady State S ′ 0 i St d St t S S ′′  5 in Steady State • Habit persistence b  0.75 • Now we have a better theory of the boom- bust cycle bust cycle

Diagnosing the results • Role of habit persistence: major – Ensures that consumption rises in the boom • Role of investment adjustment costs: major – Ensures that investment rises in the boom – Adjustment costs in level of investment does not work work K t , S ′  0, S ′′  0 I t K t  1   1 −   K t  S K t • Puzzle: why does the theory imply a fall in the stock market?

Some Capital Theory • In a production economy, price of capital (‘stock market’) satisfies two relations – Usual present discounted value relation (‘demand side’) id ’) – Tobin’s q relation (‘supply side’) – Tobin s q relation especially useful for intuition Tobin’s q relation especially useful for intuition • First we derive the present discounted value First, we derive the present discounted value relation • Then, Tobin’s q

• Lagrangian ∑  t   C t − bC t − 1  1 − h t    1 −    t  K t    z t h t  1 −  − C t − I t 1 −   I t   t  1 −   K t   1 − S  I t − K t  1  I t − 1 • Consumption first order condition  t   C t − bC t − 1  −   1 − h t    1 −   −  b  C t  1 − bC t  −   1 − h t  1    1 −   . • First order condition with respect to K t  1  t    t  1   K t  1   − 1  z t  1 h t  1  1 −    t  1  1 −   .   − 1   1 −     K  1   h

• Divide both sides of FONC by :  t K t  1  t   K t  1   − 1  z t  1 h t  1  1 −    t  1    t  1   t   K t  1   z t  1 h t  1    t  1  1  1 −   .   .  t    • ‘Time t Price of Capital, ’ (Tobin’s q ): ‘Ti t P i f C it l ’ (T bi ’ ) K t  1 K dU t  t  t dC t dC t  t  dK t  1 dK  dK t  1 ≡ P k ′ , t . 1 dU t dC t • Rewrite FONC for : K t  1 P k ′ , t    t  1    K t  1   − 1  z t  1 h t  1  1 −   P k ′ , t  1  1 −   .  t

• Repeating FONC for K t  1 epea g O C o t  1 P k ′ , t    t  1   K t  1   − 1  z t  1 h t  1  1 −   P k ′ , t  1  1 −   .  t  t • Suppose households earn on bonds r t  1 – Household FONC:   t  1  1 1  1  r t  1 .  t • So • So,   K t  1   − 1  z t  1 h t  1  1 −   P k ′ , t  1  1 −   , 1 P k ′ , t  1  r t  1 1  r t  1

• Repeating: epea g   K t  1   − 1  z t  1 h t  1  1 −   P k ′ t 1  1 −   1 P k ′ t    K t  1   z t  1 h t  1   P k ′ , t  1  1   , P k ′ , t 1  r t  1 • Rental rate on capital under competition:    K t  1   − 1  z t  1 h t  1  1 −  k r t  1 • So • So, 1 P k ′ , t   P k ′ , t  1  1 −   . 1  r t  1  R t  1 k

• Repeating, 1 1 P k ′ , t   P k ′ , t  1  1 −   .   1  r t  1  r t  1  k  1 k P P • Recursive substitution yields usual present value relation:   1 −    1   1 1 P k ′ , t  k 1  r t  1 r t  1 1  r t  1 P k ′ , t  1   1 −     1 −   P k ′ 1 1   1  r t  1 r t  1  1  r t  1 1  r t  2 r t  2  1  r t  2 P k ′ , t  2 k k r r 1 2 2  1 −     1 −    1 −   1   k k 1  r t  1 r t  1  1  r t 1  1  r t 2  r t  2 1  r t  2 P k ′ , t  2 1  r t  1 1  r t  1 1  r t  1 1  r t  2  1  r t  1  1  r t  2   ...  i  ∑ i  1  1 k .  1 −   i − 1 r t  i 1  r t  j j  1

Tobin’s q (price of capital from q (p p supply side) • Lagrangian FONC w.r.t I: I t I t I t  −  t S ′ −  t   t  1 − S  t   t  1   t S S I I t − 1 I I t − 1 I I t − 1 2 I t  1 I t  1   t  1 S ′  0. I t I t t t • Taking into account the definition of the price of capital price of capital , 2 I t  1 I t  1 1 1 P K ′ t  1 − P K ′ t  1 S ′ 1 . . P K , t P K , t  1 S 1  r t  1 1 I I t I t I − S ′ 1 − S I t I t I t I t − 1 I t − 1 I t − 1