Gold Rush Fever in Business Cycles
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1 Gold Rush Fever in Business Cycles Paul Beaudry, Fabrice Collard & Franck Portier University of British Columbia & Université de Toulouse Banque Nationale Nationale Bank Belgischen de Belgique van Belgïe Nationalbank March, 22, 26 1
2 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 2
3 Road map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion 3
4 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] 4
5 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) 5
6 Long Run Identification 6
7 Long Run Identification versus Choleski Identification 7
8 LR-SR Comparison ε P ε T ε C ε Y 8
9 Very Robust Feature: Specification LR Identification Consumption ε P Output ε P Quarters Quarters Consumption ε T Output ε T Benchmark Coint. Est. 8 lags Levels Quarters Quarters 9
10 Very Robust Feature: Specification (2) Choleski Identification Consumption ε C Output ε C Quarters Quarters Consumption ε Y Output ε Y Benchmark Coint. Est. 8 lags Levels Quarters Quarters 1
11 Very Robust Feature: Data LR Identification Consumption ε P Output ε P Quarters Quarters Consumption ε T Output ε T Benchmark C Y C(ND+S) (I+C) Quarters Quarters 11
12 Very Robust Feature: Data (2) Choleski Identification Consumption ε C Output ε C Quarters Quarters Consumption ε Y Output ε Y Benchmark C Y C(ND+S) (I+C) Quarters Quarters 12
13 Forecast Error Variance Decomposition, (C, Y ) Benchmark VECM. Horizon Output Consumption ε T ε Y ε T ε Y % 79.86% 3.9%.% % 46.5 % 1.16% 1.25% % 32.73%.91% 1.26 % % %.42% 2.13% % 3.89 % % 3.89% 13
14 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) But C is not unlikely to be a preference shocks. 14
15 Nominal and Real Interest Rates Same regressions for the interest rate (Tbill, and Tbill-Pgdp) T bill P GDP T bill P GDP+1 e k ε P ε T ε P ε T Interest rates do not respond negatively to the second shock unlikely to be a monetary shock 15
16 Summary Data suggest that There is a shock that acts as an investment shock, with no long run impact (not technology), that explains a good part of the BC fluctuations in Y and H and that does not look either like a monetary or preference shock in the short run 16
17 A possible story Suggest shocks that essentially affect investment leaving consumption unaffected: Investment specific shock? Questions: 1. What are these shocks in, say, the business press, at a business cycle frequency? 2. Not much variability in the data 3. A quantitative problem 17
18 Investment Specific Shocks vs TFP Quarters 18
19 Investment Specific Shocks vs TFP σ( TFP):.7999, σ( ISTP): ISTP TFP Quarters 19
20 Our View Role of investors expectations in fluctuations (Pigou, Wicksell, Keynes) New (perceived) opportunities of profit lead to waves of investment Research program on the role of fundamental shocks to expectations ( news ) (Beaudry and Portier JME 24, AER 26, JET 27) Not a sunspot story Inherent aspect of capitalist economies: Uncertainty about investment profitability + News about it. 2
21 Elements of the Model Expanding varieties model The growth in the potential set of varieties is technologically driven and exogenous. 21
22 Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion 22
23 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 23
24 Technologies Final Good: Q t = (Θ t h t ) α h N (1 α h )(1 χ) χ t ( Nt Xχ j,t dj)1 α h χ, No impact of N t Intermediate Good: 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. 24
25 Technologies (2) Startups: Invest 1 in t and be a monopolist in t+1 with probability ρ t 25
26 Households Preferences: Budget constraint: Max E i= [log C t+i + g(h h t+i )] Period t: C t + Pt E E t + S t = w t h t + E t π t + Pt E (1 µ)e t 1 + Pt E ρ t 1 S t 1 Period t+1: C t+1 +Pt+1 E E t+1+s t+1 = w t+1 h t+1 +E t+1 π t+1 +Pt+1 E (1 µ)e t+pt+1 E ρ ts t 26
27 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 27
28 Important remark Parameters are such that it is always optimal to fill available space on the market 28
29 Value Added Value added is given by: Y t = Q t Nt 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 29
30 Equilibrium From the household program: [ ] 1 πt+1 = βe t ρ t C t C t+1 1 = βρ t E t 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 3
31 Equilibrium (2) Using labor decisions, equilibrium conditions collapse to with (h t ζ ) = βδ t ζ 1 E t [ ht+1 ] + βδt E t [( 1 δ t+1 1 ) (h t+1 ζ ) ]. 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. 31
32 Equilibrium (3) Result 1 Employment is a purely forward looking, and therefore indirectly depends on all the future δ t 32
33 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). 33
34 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 4. Hours are only affected by ε N 5. The interest rate does not respond to ε N 34
35 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 35
36 The Klondike Gold Rush of First, Rushing 36
37 The Klondike Gold Rush of (2) Second, Working Hard and Investing 37
38 The Klondike Gold Rush of (3) Then, Registering 38
39 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. The business cycles fluctuations we have modelled here resemble market rushes, and more precisely gold rushes. Can we bring this idea to the date with a more compte quantitative model? 39
40 Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion 4
41 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. 41
42 Extra Features Final Good Q t = K 1 α x α z α h t (Θ t h t ) α h... N ξ x,t ( Nx,t X t (i) χ di )αx χ N ξz,t ( Nz,t with α x, α z, α h (, 1), α x + α z + α h < 1 and χ 1. Z t (i) χ di )αz χ ξ = α x (1 χ)/χ : N x,t has no impact ξ = (χ(1 α x ) α z )/χ: Q t is linear in N z,t 42
43 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. Shocks: 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. 43
44 Estimation Simulated Method of Moments 44
45 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 45
46 Impulse Response Functions VAR versus Model (LR identification) Consumption ε P Output ε P S.D. Shock 1.5 Data Model 1 S.D. Shock Horizon Horizon Consumption ε T Output ε T S.D. Shock S.D. Shock Horizon Horizon 46
47 Impulse Response Functions VAR versus Model (SR identification) Consumption ε C Output ε C S.D. Shock 1.5 Data Model 1 S.D. Shock Horizon Horizon Consumption ε Y Output ε Y S.D. Shock S.D. Shock Horizon Horizon 47
48 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) 48
49 Goodness of Fit J stat(y) Chi stat(c) Chi stat(c,y) Test P value [.99] [.12] [.6] 49
50 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 % % 5
51 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% 51
52 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 α x α h t (Θ t h t ) α hnx,t ξ ( Nx,t X t (i) χ di )αx χ. Compete our market shock against alternative shocks. 52
53 Alternative Stories (2) Investment Specific Shock Y t = C t + S t + e ζ t I t, PIS 1 PIS 2 TIS 1 TIS 2 J stat [.99] [.86] [1.]) [.87] D(C, Y ) [.3] [.6]) 53
54 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 % 54
55 Alternative Stories (4) Transitory technology and preference shocks Transitory technology shock Q t = e ζ t K 1 α x α h t (Θ t h t ) α hnx,t ξ ( Nx,t X t (i) χ di )αx χ, Preference shocks E t τ= [ log(ct+τ bc t+τ 1 ) + ψe ζ t+τ (h h t+τ ) ], T.T. T.P. J stat [.95] [.98] 55
56 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 % 56
57 Road Map 1. Motivation (with Some Interesting Features of the Data) 2. An Analytical Model 3. Taking The Model to the Data 4. Conclusion 57
58 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. 58
59 Extra material 59
60 Alternative Stories? Estimation Results RBC P RBC T RBC Q CEE b (.289) (.289) (.739) (.) ϕ (.435) (.4369) (.6242) (.1811) σ γ (.19) (.19) (.16) (.15) ρ T (.996) (.124) (.921) σ T (.77) (.5) (.33) J stat(y) [.66]) [.66] [.99] [.96] 6
61 Alternative Stories? PIS 1 PIS 2 TIS 1 TIS 2 b (.1229) (.1921) (.118) (.2184) ϕ (.3227) (.321) (.6675) (.4235) σ Θ (.17) (.1592) (.17) (.16) ρ x (.323) (.395) (.374) (.42) σ x (.217) (.349) (.197) (.266) ρ T (.2742) (.4974) σ T (.243) (.82) (.137) (.48) 61
62 Alternative Stories? T.T. T.P. b (.1869) (.1472) ϕ (.2645) (.3228) σ Θ (.44) (.37) ρ x (.234) (.259) σ x (.278) (.297) ρ T (.1148) (.1959) σ T (.21) (.3) 62
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