Monetary Policy and a Stock Market Boom-Bust Cycle
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1 Monetary Policy and a Stock Market Boom-Bust Cycle Lawrence Christiano, Cosmin Ilut, Roberto Motto, and Massimo Rostagno
2 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 + sticky wages = suboptimal volatility hard to understand boom-busts without monetary policy
3 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
4 Inflation and Stock Price Inflation and Stock Price (real terms) in Interwar Period Note: Inflation is computed as the year-on-year change in GNP Deflator. Stock Price is Dow Jones divided by GNP Deflator. Inflation and Stock Price (real terms) in 1990s to Note: Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow Jones divided id d by GDP Deflator Inflation and Stock Price (real terms) in 1950s to 1970s Note: Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow Jones divided by GDP Deflator. Inflation appears to be falling during the start-up of boom-bust episodes Stock Price (right-hand scale) Inflation (percentage points, left-hand scale)
5 Stock Market Boom-Bust Cycle Episode in which: Stock prices, consumption, investment, output, employment rise sharply and then fall Inflation low during boom tends to rise near end (Adalid-Detken, Bordo-Wheelock)
6 Argument We argue that it is difficult to account for boom-bust bust with a non-monetary model. 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 l stock prices. Easy to account for in a monetized model.
7 Signal about future technology Time series representation: signal a t a t 1 t t p a t log, technology If t p t, then signal turns out to be false If t p 0, then signal turns out to be correct.
8 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: Y t K t exp a t h t 1 Capital accumulation: K t 1 1 K t 1 S Resource constraint I t I I t. t 1 C t I t Y t
9 Simple RBC model No adjustment costs in investment: S 0 No habit persistence: b 0 Other parameters: 0.36, ,.02, 2.3. Signal of future improvement in technology leads to: Fall in employment, investment Rise in consumption Price of capital is constant Terrible model of boom-bust cycle!
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11 Adding bells and whistles Investment adjustment costs S S 0 in Steady Statet S 5inSteadyState Habit persistence b 0.75 Now we have a better theory of the boom- bust cycle
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13 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 K t 1 1 K t S I t K K t, S 0, S 0 t Puzzle: why does the theory imply a fall in the stock market?
14 Some Capital Theory In a production economy, price of capital ( stock market ) satisfies two relations Usual present discounted value relation ( demand side ) Tobin s q relation ( supply side ) Tobin s q relation especially useful for intuition First, we derive the present discounted value relation Then, Tobin s q
15 Lagrangian t C t bc t 1 1 h t 1 1 t K t z t h t 1 C t I t t 1 K t 1 S I t I t 1 I t K 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.
16 Divide both sides of K t 1 FONC by t : t t t 1 K t 1 z t 1 h t 1 1. t t t 1 Time t Price of Capital, K t 1 (Tobin s q): ) t du t dk 1 du t dk t 1 dc t t dc t dk t 1 P k,t. Rewrite FONC for K t 1 : P k,t t 1 t K t 1 1 z t 1 h t 1 1 P k,t 1 1.
17 Repeating FONC for K t 1 P k,t t 1 K t 1 1 z t 1 h t 1 1 P k t,t 1 1. t Suppose households earn r t 1 on bonds Household FONC: So, t 1 1. t 1 r t 1 P k,t 1 1 r t 1 K t 1 1 z t 1 h t 1 1 P k,t 1 1, 1 r t 1
18 Repeating: P t k t,t K 1 r t 1 z t 1 h t 1 P k t 1,t 1 1, Rental rate on capital under competition: k r t 1 K t 1 1 z t 1 h t 1 1 So, P k,t 1 k R 1 r t 1 t 1 P k,t 1 1.
19 Repeating, P k,t 1 k r 1 r t 1 P k t 1,t 1 1. Recursive substitution yields usual present value relation: P k,t 1 k 1 r 1 r t 1 P t 1 1 r k,t 1 t 1 1 k k r t 1 r rt 1 1 rt 1 1 r t 2 P t 2 1 rt 2 k,t 2 1 k 1 r t r k 1 1 t 2 P 1 r k,t 2 t 1 1 r t 1 1 r t 2 1 r t 1 1 r t 2... i 1 i j i 1 r 1 r k t i. t j
20 Tobin s q (price of capital from supply side) Lagrangian FONC w.r.t I: I t t 1 S t S It 1 I t I t I t 1 I t I t 1 t 1 S I t 1 I t I t 1 I t 2 0. Taking into account the definition of the price of capital, P t 1 1 K,t 1 P I 1 S t I t 1 S I t I t 1 r K,t 1 S t 1 I t 1 I t 1 P K t 1S I t 1 I t 1. I t I t 2
21 Repeating, I t 1 /I t 0 this term is big P K,t 1 I 1 S t I t 1 S I t I t P I t 1 r K t 1,t 1S I t 1 I t I t 1 I t 1 I t 2. Static Marginal Cost Dynamic Part This clarifies why falls during boom P K,t Anticipated High Future Investment Implies there is an Extra Payoff to Current Investment. Under Competition, This Extra Payoff Would Lead Sellers of Capital to Sell at a Lower Price.
22 A monetized model When we monetize the RBC model, get a more promising model of the response to an anticipated i t technology shock Intuition is simple, and can be explained in the CGG model. An anticipated future technology shock in principle drives up the real rate. Under standard d monetary policy, the monetary authority prevents the rise and thereby exacerbates the boom-bust in real variables, and causes the stock market to boom too.
23 The standard New-Keynesian Model a t a t 1 t t p a t log, technology p rr t rr 1 a t t 1 p (natural (Ramsey) rate) t E t t 11 x t t (Calvo pricing equation) x t r t E t t 1 rr t E t x t 1 (intertemporal t equation) r t E t t 1 x x t (policy rule)
24 The standard New-Keynesian Model a t a t 1 t t p a t log, technology p rr t rr 1 a t t 1 p (natural (Ramsey) rate) t E t t 11 x t t (Calvo pricing equation) x t r t E t t 1 rr t E t x t 1 (intertemporal t equation) r t E t t 1 x x t (policy rule)
25 Can we get a boom-bust out of this? Rise in output and employment, and weak inflation in boom Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1, 2,... loga t t logh t logy t , 1.5, x 0.5, 0.82 Can we get it in an empirically-based model?
26 Can we get a boom-bust out of this? Rise in output and employment, and weak inflation in boom Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1, 2,... loga t t logh t logy t , 1.5, x 0.5, 0.82 Can we get it in an empirically-based model?
27 Can we get a boom-bust out of this? Rise in output and employment, and weak inflation in boom Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1, 2,... loga t t logh t logy t , 1.5, x 0.5, 0.82 What happens in an empirically- constructed model?
28 Features: Empirically-based model Habit persistence in preferences Investment adjustment costs in change of investment Calvo sticky wages and prices Non-optimizers: P it P i,t 1, W j,t z W j,t 1 Robustness to version of Gertler-Trigari Ti imodel of labor market. Estimation by standard Bayesian methods
29 Shocks and observables Six observables: output growth, inflation, hours worked, investment growth, consumption growth, T-bill rate.
30 Shocks: E tj l 0 preference l 2 l l t l,j c,t l log C t l bc t l 1 L 2 K t K t 1 S marginal (in-) efficiency of investment i,t I t I t 1 I t 1 1 Y t Y jt f,t dj 0 ss markup f,t iid a t a t 1 t iid iid 4 t 4 8 t 8
31 Some parameters wage-stickiness parameter w 0.83, price stickiness parameter f 0.77, curvature on adjustment costs S 8.8 logr t log z target E t t 1 annualized target: 2.5% target 0.12log Y t /Y s logr mp t 0.79logR t logr t u t
32 Variance decompositions Percent Variance in Row Variable due to Indicated Column Shock Technology shocks variable innovation 4 quarter advance 8 quarter advance c,t i,t f,t monetary policy ΔC t ΔI t ΔY t logh t t R t
33 Variance decompositions Percent Variance in Row Variable due to Indicated Column Shock Technology shocks variable innovation 4 quarter advance 8 quarter advance c,t i,t f,t monetary policy ΔC t ΔI t ΔY t logh t t R t big bigger!
34 First and second moments of posterior distribution, iid shockstandarddeviations( 100) shock mode std. dev., posterior distribution std dev innovation to technology quarter advance signal, t quarter advance signal, t innovation to utility, c,t innovation to marginal efficiency of investment, i,t innovation to markup, f,t mp innovation to monetary policy, u t mode
35 Estimated technology shock process: a t a t 1 t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t.
36 Centered 5-quarter moving average of shocks NBER trough Signals 5-8 quarters in past NBER peak Current shock plus most recent Four quarters signals
37 Benchmark: Ramsey Response to Signal Shock Drop Monetary Policy Rule. Now, economic system under-determined. Many equilibria. We select the best equilibrium, the Ramsey equilibrium: optimal monetary policy.
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39 1. In the equilibrium, inflation is below steady state 2. In Ramsey, inflation has a zero steady state
40 Problem: monetary policy does not raise the interest rate
41 Price of capital (marginal cost of Price of capital (marginal cost of equity) rises in equilibrium
42 Sticky wages exacerbate the problem
43 Why is the Boom-Bust So Big? Most of boom-bust reflects suboptimality of monetary policy. What s the problem? Monetary policy ought to respond to the natural (Ramsey) rate of interest. Relatively sticky wages and inflation Relatively sticky wages and inflation targeting exacerbate the problem
44 Policy solution Modify the Taylor rule to include: Natural rate of interest Credit growth Stock market Wage inflation instead of price inflation. Explored consequences of adding credit p q g growth and/or stock market by adding Bernanke-Gertler-Gilchrist financial frictions.
45 Welfare effects of perturbations to policy Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium R t E t t 1 y log Y t Y t X t X t c $Credit Growth t s $Net Worth Growth t Baseline e c 1 s 1 replaced by w Boom-bust t Boom-bust signal 4) Boom-bust signal Cost push f,t lol Looking at credit growth helps Discount rate shocks c,t Marginal efficiency of investment i,t
46 Welfare effects of perturbations to policy Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium R t E t t 1 y log Y t Y t X t X t c $Credit Growth t s $Net Worth Growth t Baseline e c 1 s 1 replaced by w Boom-bust t Boom-bust signal 4) Boom-bust signal Cost push f,t Replacing price inflation by wage inflation is best! Discount rate shocks c,t Marginal efficiency of investment i,t
47 Welfare effects of perturbations to policy Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium R t E t t 1 y log Y t Y t X t X t c $Credit Growth t s $Net Worth Growth t Baseline e c 1 s 1 replaced by w Boom-bust t Boom-bust signal 4) Boom-bust signal Cost push f,t Discount rate shocks c,t Marginal efficiency of investment i,t Replacing price inflation by wage Replacing price inflation by wage inflation is the best in all but two cases
48 What do real wages do in boom-bust episodes? We looked at three 20 th century US episodes. Great Depression (real wage low) (real wage not low) (real wage low)
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56 Conclusion Difficult to account for boom-busts busts in a real version of standard DSGE models. A boom-bustbust explanation emerges when nominal frictions are introduced and monetary authority does not (or, cannot) respond to the natural rate Problem is most severe when wages are sticky relative to prices. Robust to: Various treatments of indexation Alternative models of labor market (Gertler-Trigari) that do not fall prey to Barro critique. Explored some modifications to policy that might help ameliorate the problem
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