Gold Rush Fever in Business Cycles

Gold Rush Fever in Business Cycles Paul Beaudry, Fabrice Collard & Franck Portier University of British Columbia & Université de Toulouse UAB Seminar Barcelona November, 29, 26

The Klondike Gold Rush of 1896-194

The Klondike Gold Rush of 1896-194 First, Rushing

The Klondike Gold Rush of 1896-194 First, Rushing Second, Working Hard and Investing

The Klondike Gold Rush of 1896-194 First, Rushing Second, Working Hard and Investing Then, Registering

Plan of the talk 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion

Road map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion

Back to Modern Macro Gold rushes: economic boom large increases in expenditures securing claims near new found veins of gold. Define Market rush: economic boom securing position (monopoly rents) on a market. Define gold rush: inefficient market rush: Historically, gold eventually expands the stock of money. May business cycles fluctuations resemble market rushes? Gold rushes?

Macroeconomic Facts (1) A well known set of facts shed some light on the existence of market rushes Run a VAR on consumption and output (US quarterly data 1947Q1 to 24Q4) [in the line of Cochrane, QJE 1991]

Macroeconomic Facts (2) LR matrix associated with the Wold representation has 1 full zero column = puts some structure on the permanent/temporary and Choleski identifications: Permanent shock = Consumption shock C is only explained by the permanent shock (at all horizons) ( 96%) The other shock matters for Y in the BC ( 7% at 1 step)

Long Run Identification

Long Run Identification versus Choleski Identification

LR-SR Comparison 4 4 2 2 ε P ε T 2 2 4 4 2 2 4 ε C 4 4 2 2 4 ε Y

Very Robust Feature: Specification LR Identification Consumption ε P Output ε P 1.5 1.5 1 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters Consumption ε T Output ε T 1.5 1 Benchmark Coint. Est. 8 lags Levels 1.5 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters

Very Robust Feature: Specification (2) Choleski Identification Consumption ε C Output ε C 1.5 1.5 1 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters Consumption ε Y Output ε Y 1.5 1 Benchmark Coint. Est. 8 lags Levels 1.5 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters

Very Robust Feature: Data LR Identification Consumption ε P Output ε P 1.5 1.5 1 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters Consumption ε T Output ε T 1.5 1 Benchmark C Y C(ND+S) (I+C) 1.5 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters

Very Robust Feature: Data (2) Choleski Identification Consumption ε C Output ε C 1.5 1.5 1 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters Consumption ε Y Output ε Y 1.5 1 Benchmark C Y C(ND+S) (I+C) 1.5 1.5.5.5 5 1 15 2 Quarters.5 5 1 15 2 Quarters

Forecast Error Variance Decomposition, (C, Y ) Benchmark VECM. Horizon Output Consumption ε T ε Y ε T ε Y 1 62.1% 79.86% 3.9%.% 4 28.1 % 46.5 % 1.16% 1.25% 8 17.2 % 32.73%.91% 1.26 % 2 9.79 % 22.21 %.42% 2.13% % 3.89 % % 3.89%

Hours Worked (ML) Regression: x t = c + K k= ( αk ε P t k + β kε T t k + γ kε H t k), Level Specification Difference Specification Horizon ε p ε t ε H ε p ε t ε H 1 19 % 75 % 6 % 21 % 74 % 5 % 4 37 % 56 % 7 % 46 % 52 % 2 % 8 61 % 32 % 7 % 66 % 32 % 2 % 2 6 % 21 % 19 % 69 % 28 % 3 % 4 54 % 2 % 26 % 57 % 38 % 5 % H: mainly explained by the transitory component ( 8% at 1 step)

Nominal and Real Interest Rates Same regressions for the interest rate (Tbill, and Tbill-Pgdp) Tbill PGDP k ε P ε T Tbill PGDP+1 e ε P ε T 1.1116.97.683.66 4.817.99.875.831 8.598.826.686.729 Interest rates do not respond negatively to the second shock = Not a monetary shock

Summary Data suggest that There is a shock that acts as an investment shock,

Summary Data suggest that There is a shock that acts as an investment shock, with no long run impact,

Summary Data suggest that There is a shock that acts as an investment shock, with no long run impact, that explains a good part of the BC fluctuations in Y and H

Summary Data suggest that There is a shock that acts as an investment shock, with no long run impact, that explains a good part of the BC fluctuations in Y and H and that does not look like a technology, monetary or preference shock in the short run

Our View Suggest an alternative view Suggest something akin to gold rushes: Market rushes Role of investors expectations in fluctuations (Pigou, Wicksell, Keynes) Not a sunspot story Inherent aspect of capitalist economies: Uncertainty about investment profitability + News about it.

Elements of the Model Expanding varieties model

Elements of the Model Expanding varieties model The growth in the potential set of varieties is technologically driven and exogenous.

Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion

An Analytical Model The objective here is to derive an analytical solution to a model that possesses Market Rush properties I will then discuss some of the implications of the model

Technologies Final Good: Q t = (Θ t h t ) α h N No impact of N t Intermediate Good: (1 α h)(1 χ) χ t ( ) 1 αh Nt X χ j,t dj χ, Each existing intermediate good is produced by a monopolist, Survive with probability (1 µ), It takes 1 unit of the final good to produce 1 unit of X j,t. Startups: Invest 1 in t and be a monopolist in t+1 with probability ρ t

Households Preferences: Max E [log C t+i + g(h h t+i )] i= Budget constraint: Period t: C t + P E t E t + S t = w t h t + E t π t + P E t (1 µ)e t 1 + P E t ρ t 1 S t 1 Period t+1: C t+1 +P E t+1e t+1 +S t+1 = w t+1 h t+1 +E t+1 π t+1 +P E t+1(1 µ)e t +P E t+1ρ t S t

New Markets Probability that a startup at time t will become a functioning firm at t + 1: { ρ t = min 1, ɛ } tn t S t

New Markets Probability that a startup at time t will become a functioning firm at t + 1: { ρ t = min 1, ɛ } tn t S t Evolution of markets

New Markets Probability that a startup at time t will become a functioning firm at t + 1: { ρ t = min 1, ɛ } tn t S t Evolution of markets Parameters are such that it is always optimal to fill available space on the market

Value Added Value added is given by: Nt Y t = Q t P j,t X j,t dj = AΘ t h t

Value Added Value added is given by: Nt Y t = Q t P j,t X j,t dj = AΘ t h t Value-added Y t is used for consumption C t and startup expenditures (S t ) purposes Y t = C t + S t

Equilibrium From the household program: 1 ρ t C t = βe t 1 = βρ t E t [ πt+1 C t+1 τ=1 ] [ ] (1 µ) + βe t ρ t+1 C t+1 (1 µ) τ β τ C t π t+τ C t+τ Startup cost = discounted sum of expected profits Expectation driven startup investment

Equilibrium (2) Using labor decisions, equilibrium conditions collapse to [( ) ] 1 (h t ζ ) = βδ t ζ 1 E t [h t+1 ] + βδ t E t 1 (h t+1 ζ ). δ t+1 with δ t = ε t /(1 µ + ε t ) is a increasing function of the fraction of newly opened markets ε t, ζ and ζ 1 are complicated functions of the deep parameters.

Equilibrium (3) Result Employment is a purely forward looking, and therefore indirectly depends on all the future δ t

VAR Representation Output and consumption are given by s.t. Y t = k y Θ t h t and C t = k c Θ t log Y t = k y + log Θ t + log h t log C t = k c + log Θ t Assume log Θ t = log Θ t 1 + ε Θ t, ε t i.i.d., E(ε t ) = µ and ε N t = log(ε t ) log(µ).

Implications We have ( log(ct ) log(y t ) ) = ( 1 1 b(1 L) ) ( ε Θ t ε N t ) = C(L) ( ε Θ t ε N t ) Shares a lot of dynamic properties with the data: 1. Consumption is a random walk, only affected by ε Θ

Implications We have ( log(ct ) log(y t ) ) = ( 1 1 b(1 L) ) ( ε Θ t ε N t ) = C(L) ( ε Θ t ε N t ) Shares a lot of dynamic properties with the data: 1. Consumption is a random walk, only affected by ε Θ 2. Output is also affected in the short run by ε N 3. Orthogonalization would give: ε P = ε C = ε Θ and ε T = ε Y = ε N

Implications (2) One can prove that the decentralized investment decisions are the same that previously, so that the dynamics of h is the same. The socially optimal allocations are in this case h t = C te All ε N -driven fluctuations are suboptimal

Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion

An extended Model Turn to the quantitative aspect of the problem Aim: Assess the quantitative relevance of the model Some extra features: 1. Capital accumulation, 2. Adjustment costs to investment, 3. Habit persistence in consumption, 4. Two types of intermediate goods.

Extra Features Final Good Q t =K 1 αx αz α h t (Θ t h t ) α h... N ξ x,t ( Nx,t X t (i) χ di ) αx χ N e ξ z,t ( Nz,t ) αz Z t (i) χ χ di with α x, α z, α h (, 1), α x + α z + α h < 1 and χ 1.

Extra Features Final Good Q t =K 1 αx αz α h t (Θ t h t ) α h... N ξ x,t ( Nx,t X t (i) χ di ) αx χ N e ξ z,t ( Nz,t ) αz Z t (i) χ χ di with α x, α z, α h (, 1), α x + α z + α h < 1 and χ 1. ξ = α x (1 χ)/χ : N x,t has no impact

Extra Features Final Good Q t =K 1 αx αz α h t (Θ t h t ) α h... N ξ x,t ( Nx,t X t (i) χ di ) αx χ N e ξ z,t ( Nz,t ) αz Z t (i) χ χ di with α x, α z, α h (, 1), α x + α z + α h < 1 and χ 1. ξ = α x (1 χ)/χ : N x,t has no impact ξ = (χ(1 αx ) α z )/χ: Q t is linear in N z,t

Extra Features (2) Variety: N x,t+1 = (1 µ + ε x t )N x,t N z,t+1 = (1 µ + ε z t )N z,t.

Extra Features (2) Variety: Shocks: N x,t+1 = (1 µ + ε x t )N x,t N z,t+1 = (1 µ + ε z t )N z,t. log(ε x t ) = ρ x log(ε x t 1) + (1 ρ x ) log(ε x ) + ν x t log(ε z t ) = ρ z log(ε z t 1) + (1 ρ z ) log(ε z ) + ν z t log Θ t = log Θ t 1 + ε Θ t.

Estimation Simulated Method of Moments

Estimation (2) Not all parameters are estimated Preferences Discount factor β.9926 Technology Elasticity of output to intermediate goods α x.3529 Elasticity of output to hours worked α h.4235 Depreciation rate δ.25 Elasticity of substitution bw intermediates χ.8333 Rate of technology growth γ 1.6 Monopoly death rate µ.86

Impulse Response Functions VAR versus Model (LR identification) Consumption ε P Output ε P 1.5 1.5 1 S.D. Shock 1.5 Data Model 1 S.D. Shock 1.5.5 5 1 15 2 Horizon.5 5 1 15 2 Horizon Consumption ε T Output ε T 1.5 1.5 1 S.D. Shock 1.5 1 S.D. Shock 1.5.5 5 1 15 2 Horizon.5 5 1 15 2 Horizon

Impulse Response Functions VAR versus Model (SR identification) Consumption ε C Output ε C 1.5 1.5 1 S.D. Shock 1.5 Data Model 1 S.D. Shock 1.5.5 5 1 15 2 Horizon.5 5 1 15 2 Horizon Consumption ε Y Output ε Y 1.5 1.5 1 S.D. Shock 1.5 1 S.D. Shock 1.5.5 5 1 15 2 Horizon.5 5 1 15 2 Horizon

Estimated Parameters Persistence of the X Variety shocks ρ x.9166 (.336) Standard dev. of X Variety shocks σ x.2865 (.317) Persistence of the Z Variety shocks ρ z.9164 (.6459) Standard dev. of Z Variety shocks σ z.245 (.1534) Standard dev. of the Technology shocks σ Θ.131 (.15) Habit Persistence parameter b.59 (.128) Adjustment Costs parameter ϕ.4376 (.3267)

Goodness of Fit J stat(y) Chi stat(c) Chi stat(c,y) Test 17.41 42.51 92.78 P value [.99] [.12] [.6]

Does the model match Hours variance decomposition? (ML) Regression: h t = c + K k= ( αk ε P t k + β kε T t k + γ kε H t k), Data Model Horizon ε p ε t ε h ε p ε t ε h 1 19 % 75 % 6 % 35 % 65 % %

Business cycle accounting Horizon Output Consumption Hours ε Θ ε x ε z ε Θ ε x ε z ε Θ ε x ε z 1 64 % 36 % % 94 % 6 % % 15 % 85 % % 4 86 % 14 % % 95 % 5 % % 19 % 81 % % 8 92 % 8 % % 96 % 4 % % 32 % 68 % % 2 96 % 3 % 1 % 98 % 1 % 1 % 4 % 59 % 1% 96 % % 4 % 96 % % 4 % 41 % 57 % 2%

Alternative Stories Common to all models habit persistence, adjustment costs to investment permanent technology shock Shut down the permanent market shock Q t = K 1 αx α h t (Θ t h t ) α h Nx,t ξ ( Nx,t X t (i) χ di Compete our market shock against alternative shocks. ) αx χ.

Alternative Stories (2) Investment Specific Shock Y t = C t + S t + e ζt I t, PIS 1 PIS 2 TIS 1 TIS 2 J stat 17.31 6.96 14.89 59.48 [.99] [.86] [1.]) [.87] D(C, Y ) 99.42 92.34 [.3] [.6])

Alternative Stories (3) Investment Specific Shock: Variance decomposition Horizon Output Consumption Hours ε Θ ν x ζ ε Θ ν x ζ ε Θ ν x ζ PIS 1: ζ=permanent Investment Specific Shock 1 64 % 36 % % 95 % 5 % % 15 % 85 % % 1 % % % 1 % % % 44 % 56 % % PIS 2: ζ=permanent Investment Specific Shock 1 55 % 45 % % 84 % 16 % % % 99 % 1 % 96 % % 4 % 96 % % 4 % 26 % 63 % 11 % TIS 1: ζ=temporary Investment Specific Shock 1 53 % 42 % 5 % 93 % 6 % 1 % 19 % 73 % 8 % 1 % % % 1 % % % 34 % 5 % 16 % TIS 2: ζ=temporary Investment Specific Shock 1 56 % 42 % 2 % 84 % 15 % 1 % % 94 % 6 % 1 % % % 1 % % % 26 % 62 % 12 %

Alternative Stories (4) Transitory technology and preference shocks Transitory technology shock Q t = e ζt K 1 αx α h t (Θ t h t ) α h Nx,t ξ Preference shocks E t τ= ( Nx,t ) αx X t (i) χ χ di [ ] log(c t+τ bc t+τ 1 ) + ψe ζt+τ (h h t+τ ), T.T. T.P. J stat 54.65 5.56 [.95] [.98],

Alternative Stories (5) Horizon Output Consumption Hours ε Θ ν x ζ ε Θ ν x ζ ε Θ ν x ζ T.T.: ζ=temporary Technology Shock 1 21 % 38 % 41 % 44 % 17 % 39 % % 98 % 2 % 99 % % % 1 % % % 1 % 66 % 24 % T.P.: ζ=temporary Preference Shock 1 27 % 39 % 34 % 55 % 15 % 3 % 1 % 53 % 46 % 2 7 % 8 % 22 % 82 % 5 % 13 % 7 % 33 % 6 % 1 % % % 1 % % % 8 % 33 % 59 %

Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion

Conclusion We have found a new source of shocks, that looks like animal spirits, although it comes from a model with determinate equilibrium. A quite pessimistic view that a non trivial share of the Business Cycle is inefficient large welfare cost of fluctuations. Part of a research program in which we explore the importance of the arrival of information as a source of impulse in the BC.

Investment Specific Shocks vs TFP.8.7.6.5.4.3.2.1 1955 196 1965 197 1975 198 1985 199 1995 2 Quarters

Investment Specific Shocks vs TFP σ( TFP):.7999, σ( ISTP):.52.8.7.6.5.4.3.2.1 ISTP TFP 1955 196 1965 197 1975 198 1985 199 1995 2 Quarters Go Back

Alternative Stories? Estimation Results RBC P RBC T RBC Q CEE b.8813.8813.7181. (.289) (.289) (.739) (.) ϕ.6682.6683 2.353.6353 (.435) (.4369) (.6242) (.1811) σ γ.143.143.153.129 (.19) (.19) (.16) (.15) ρ T.5973.4974.624 (.996) (.124) (.921) σ T.155.99.36 (.77) (.5) (.33) J stat(y) 3.96 3.96 18.5 23.6 [.66]) [.66] [.99] [.96]

Alternative Stories? PIS 1 PIS 2 TIS 1 TIS 2 b.618.3125.6457.362 (.1229) (.1921) (.118) (.2184) ϕ.4195.2534.699.2775 (.3227) (.321) (.6675) (.4235) σ Θ.131.88.126.89 (.17) (.1592) (.17) (.16) ρ x.9117.8919.9143.8967 (.323) (.395) (.374) (.42) σ x.1575.1859.1594.1775 (.217) (.349) (.197) (.266) ρ T.5328.8478 (.2742) (.4974) σ T.3.38.118.32 (.243) (.82) (.137) (.48)

Alternative Stories? T.T. T.P. b.342.3877 (.1869) (.1472) ϕ.3125.3699 (.2645) (.3228) σ Θ.62.75 (.44) (.37) ρ x.9195.975 (.234) (.259) σ x.1768.1825 (.278) (.297) ρ T.9143.8799 (.1148) (.1959) σ T.46.68 (.21) (.3)