... Monetary Policy and a Stock Market Boom-Bust Cycle Lawrence Christiano, Roberto Motto, Massimo Rostagno
... Stock Market Boom-Bust Cycle: Episode in Which: Stock Prices, Consumption, Investment, Employment, Output Rise Sharply and then Fall Sometimes Such an Episode is Referred to as an Overinvestment Boom Examples: US in 92s and 93s Japanin98s US in 99s 2
... We Explore a Version of Beaudry-Portier Theory of Boom-Bust Cycle Boom-Bust Cycle Triggered by: Expectation that Technology Will Be Strong in The Future An Expectation that is Ultimately Not Realized Example: A Widespread Belief that Fiber-Optic Cable Would Generate Huge Returns Led to Huge Investment in Fiber Optic Cable, Investment That Ex-post was Excessive. 3
Findings Monetary Policy May be Key to Full Understanding of Boom-Bust Cycle. Argument in a Nut-Shell: Begin with an Attempt to Build a Non-Monetary Theory of Boom-Bust Cycle With Investment Adjustment Costs, Habit Persistence, Variable Capital Utilization, Can Almost Get Successful Theory However, Miss on Stock Market. Theory Implies a Stock Market Drop When We Incorporate Monetary Factors Into the Analysis, We Finally Obtain a Successful Theory. 8
Outline Boom-Bust Cycle in Non-Monetary Economy. Simplest of All RBC Models No Boom-Bust Cycle at All! RBC Model with Investment Adjustment Costs, Capital Utilization and Habit Persistence Partial Theory of Boom-Bust Cycle Boom-Bust Cycle In Monetary Economy 9
Non-Monetary Economy Household Preferences: Production Function: X E β t t= h(c t bc t )( h t ) ψi γ. γ Y t = K α t (exp (z t ) h t ) α Physical Capital Accumulation: Resource Constraint: K t+ =( δ)k t +( S µ I t )I t. C t + I t Y t Technology Evolution: z t = ρz t + ε t 8 + ξ t.
Simple RBC Model No adjust costs in investment: S No Habit Persistence: b = Other Parameters: α =.36, β=.3.25,δ=.2, γ=,ψ=2.3. Signal of Future Improvement in Technology Leads to: Fall in Employment Fall in Investment Rise in Consumption Price of Capital is Constant Terrible Model of Boom-Bust Cycle!
IRFs: Anticipated shock to technology is not realized (Logs) Standard RBC Model K t+ C t.2 -.5. -. -.5 -. -.2 5 5 2 25 I t -.2 5 5 2 25 L t.5.4.2 -.5 - -.2 -.5 -. -.2 -.3 5 5 2 25 Y t -.4 5 5 2 25 2 x U -5 t - -.4 5 5 2 25-2 5 5 2 25 P K,t.5 -.5-5 5 2 25
Investment Adjustment Costs: RBC Analog of ACEL Model S = S =in Steady State S =5in Steady State b =.75 Now Have a Better Theory of Boom-Bust Cycle. 2
IRFs: Anticipated shock to technology is not realized (Logs) RBC Model With Habit Persistence and Investment Adjustment Costs, But No Variable Capital Utilization K t+ C t.5.4..3.5.2. -.5 5 5 2 25 I t 5 5 2 25 L t.5.5 -.5.6.4.2 5 5 2 25 Y t -.5 5 5 2 25 4 x U -5 t 2 -.2 5 5 2 25-2 5 5 2 25 P K,t -.2 -.4 -.6 -.8 5 5 2 25
Role of Habit Persistence: Major Diagnosing Results Ensures that Consumption Rises In Boom Part of Cycle Role of Investment Adjustment Costs: Major Ensures that Investment Rises in Boom Part of Cycle Puzzle: Why Does the Theory Imply a Fall in Stock Market????? 3
IRFs: Anticipated shock to technology is not realized (Logs) RBC Model with Investment Adjustment Costs, Variable Capital Utilization, No Habit Persistence in Consumption K t+ C t.8.4.6.2.4.2 -.2 5 5 2 25 I t -.4 5 5 2 25 L t 4 3 2.5 5 5 2 25 Y t -.5 5 5 2 25 U t.5.5 -.5 -.5 5 5 2 25-5 5 2 25 P K,t -.2 -.4 -.6 -.8 5 5 2 25
IRFs: Anticipated shock to technology is not realized (Logs) RBC Model with Variable Capital Utilization, Habit Persistence, No Adjustment Costs in Investment K t+ C t.5 -.. -.2.5 -.3 -.4 5 5 2 25 I t -.5 5 5 2 25 L t.2 -.5 - -.2 -.5 -.4-2 5 5 2 25 Y t -.6 5 5 2 25 U t.2.5 -.2 -.4 -.6 5 5 2 25 -.5 5 5 2 25 P K,t.5 -.5-5 5 2 25
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 Is Very Useful. First, We Derive the Usual Present Discounted Value Relation Then, Tobin s q 4
Some Capital Theory... Lagrangian: h(c t bc t )( h t ) ψi γ X β t { γ +µ t ( δ)k t +( S µ I t h i + λ t (K t ) α (z t h t ) α C t I t )I t K t+ } Consumption first order condition: λ t =(C t bc t ) γ ( h t ) ψ( γ) βb(c t+ bc t ) γ ( h t+ ) ψ( γ). First order condition with respect to K t+ : µ t = β h i λ t+ α (K t+ ) α (z t+ h t+ ) α + µ t+ ( δ). 5
Some Capital Theory... Divide both sides of K t+ FONC by λ t : µ t λ t = β λ t+ λ t Time t Price of Capital, K t+ (Tobin s q) : α (K t+ ) α (z t+ h t+ ) α + µ t+ ( δ). λ t+ µ t λ t = du t dk t+ du t = dc t. dk dc t+ t Rewrite Fonc for K t+ : P k,t = β λ t+ λ t h i α (K t+ ) α (z t+ h t+ ) α + P k,t+ ( δ). 6
Some Capital Theory... Repeating Fonc for K t+ : Note: P k,t = β λ t+ λ t h i α (K t+ ) α (z t+ h t+ ) α + P k,t+ ( δ). β λ t+ λ t = +r t+. So, Price of Capital: P k,t = h i α (K t+ ) α (z t+ h t+ ) α + P k,t+ ( δ), +r t+ 7
Some Capital Theory... Repeating: P k,t = h i α (K t+ ) α (z t+ h t+ ) α + P k,t+ ( δ), +r t+ With Rental Market for Capital: P k,t = +r t+ R k t+ + P k,t+ ( δ). 8
Some Capital Theory... Repeating: P k,t = +r t+ R k t+ + P k,t+ ( δ). Recursive Substitution, Gives Usual Present Discounted Value Relation: P k,t = Rt+ k + +r t+ = Rt+ k + +r t+ = Rt+ k + +r t+ =... X iy = i= j= +r t+j ( δ) P k,t+ +r t+ ( δ) R k ( δ) t+2 + P k,t+2 +r t+ +r t+2 +r t+2 ( δ) ( δ) ( δ) ( + r t+ )(+r t+2 ) Rk t+2 + P k,t+2 +r t+ +r t+2 ( δ) i R k t+i. 9
Some Capital Theory... Now, Go for SECOND Relation that Price of Capital Must Satisfy in Economy Where Capital I Produced (Tobin s q) First Order Condition of Lagrangian with Respect to I t : λ t + µ t ( S µ I t ) µ t S µ +βµ t+ S µ + I t I t I t µ + I t 2 =. Rewriting this, taking into account the definition of the price of capital, P K,t = S ³ I t S ³ I t I t µ +r t+ ³ ³ 2 PK,t+S + + I t I t S ³ I t S ³ I t I t. 2
Some Capital Theory... Repeating... P K,t = S ³ I t S ³ I t I t µ +r t+ ³ ³ 2 PK,t+S + + I t I t S ³ I t S ³ I t I t. = Static Marginal Cost + Dynamic Part This Expression Clarifies Why P K,t Falls During Boom Phase of Boom-Bust Cycle 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
Analysis in Monetary Economy Incorporate Above Ideas into A Monetary Economy (Analog of ACEL Model Already Discussed) Taylor Rule: Findings: R t =.5E t π Boom in Consumption, Investment, Output Greatly Amplified ThereisAlsoaStockMarketBoom Reason: In Monetary Economy, Boom Accompanied By Low Inflation Low Inflation Leads to Monetary Expansion ( Taylor Principle ) Monetary Expansion Creates Stock Market Boom, and Amplifies Response of Consumption, Investment, Employment, Etc. 23
Response in RBC Model (diamonds) and Monetary Model With Taylor Rule With Coefficient of.5 on Expected Inflation To a Technology Shock Expected 4 Quarters Later That Does Not Occur percent Output.8.6.4.2 2 percent Investment 2.5 2.5.5 2 percent Consumption.8.6.4.2 2 Hours Worked Inflation (APR) Interest Rate (annual) 6 percent.8.6.4.2 -.2 -.4 -.6 -.8 basis points 4 2 2 2 2 Stock Price Net Worth Premium (Annual Rate) 2 percent.5 percent.5.5 basis points -2-4 -.5 5 5 2 5 5 2 5 5 2
Not Yet Worked Out, So Not Sure! Policy Implications Important Consideration: Boom-Bust Cycle Studied Here Rare Event Do Not Necessarily Want to Base Policy on Rare Events Possibly, With Real Interest (Natural) Rate in Model, Monetary Policy Would Not Trigger a Boom This Will Be Investigated Consider other Factors in Taylor Rule 24