gold rush fever in business cycles...gold rush fever in business cycles paul beaudry, fabrice...

Gold Rush Fever in Business Cycles

Paul Beaudry, Fabrice Collard & Franck Portier

University of British Columbia & Universite de Toulouse

Banque Nationale Nationale Bank Belgischende Belgique van Belgıe Nationalbank

March, 22, 2006

1

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

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

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 2004Q4) [in the line of Cochrane, QJE 1991]

4

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 (∼ 70% at 1 step)

5

Long Run Identification

6

Long Run Identification versus Choleski Identification

7

LR-SR Comparison

−4 −2 0 2 4−4

−2

0

2

4

εC

εP

−4 −2 0 2 4−4

−2

0

2

4

εYεT

8

Very Robust Feature: Specification

LR Identification

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εP

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εP

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εT

BenchmarkCoint. Est.8 lagsLevels

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εT

9

Very Robust Feature: Specification (2)

Choleski Identification

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εC

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εC

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εY

BenchmarkCoint. Est.8 lagsLevels

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εY

10

Very Robust Feature: Data

LR Identification

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εP

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εP

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εT

BenchmarkC−YC(ND+S)−(I+C)

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εT

11

Very Robust Feature: Data (2)

Choleski Identification

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εC

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εC

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Consumption − εY

BenchmarkC−YC(ND+S)−(I+C)

5 10 15 20−0.5

0

0.5

1

1.5

Quarters

Output − εY

12

Forecast Error Variance Decomposition, (C, Y ) Benchmark VECM.

Horizon Output ConsumptionεT εY εT εY

1 62.01% 79.86% 3.90% 0.00%4 28.10 % 46.05 % 1.16% 1.25%8 17.20 % 32.73% 0.91% 1.26 %20 9.79 % 22.21 % 0.42% 2.13%∞ 0 % 3.89 % 0% 3.89%

13

Hours Worked

• (ML) Regression: xt = c+∑Kk=0

(αkε

Pt−k + βkε

Tt−k + γkε

Ht−k

),

Level Specification Difference Specification

Horizon εp εt εH εp εt εH

1 19 % 75 % 6 % 21 % 74 % 5 %4 37 % 56 % 7 % 46 % 52 % 2 %8 61 % 32 % 7 % 66 % 32 % 2 %20 60 % 21 % 19 % 69 % 28 % 3 %40 54 % 20 % 26 % 57 % 38 % 5 %

• H: mainly explained by the transitory component (∼ 80% at 1

step)

• But C is not unlikely to be a preference shocks .

14

Nominal and Real Interest Rates

• Same regressions for the interest rate (Tbill, and Tbill-Pgdp)

Tbill −∆PGDP Tbill −∆PGDP e+1k εP εT εP εT

1 0.1116 0.0970 0.0683 0.06064 0.0817 0.0909 0.0875 0.08318 0.0598 0.0826 0.0686 0.0729

• Interest rates do not respond negatively to the second shock unlikely to be a monetary shock

15

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

A possible story

• Suggest shocks that essentially affect investment leaving con-

sumption 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

Investment Specific Shocks vs TFP

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Quarters

18

Investment Specific Shocks vs TFP

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Quarters

σ(∆ TFP): 0.7999, σ(∆ ISTP): 0.5020

ISTPTFP

19

Our View

• Role of investors’ expectations in fluctuations (Pigou, Wicksell,Keynes)

• New (perceived) opportunities of profit lead to waves of invest-ment

• Research program on the role of fundamental shocks to expecta-tions (“news”) (Beaudry and Portier JME 2004, AER 2006, JET2007)

• Not a sunspot story

• Inherent aspect of capitalist economies: Uncertainty about invest-ment profitability + News about it.

20

Elements of the Model

• Expanding varieties model

• The growth in the potential set of varieties is technologicallydriven and exogenous.

21

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

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

Technologies

Final Good:

• Qt = (Θtht)αhN

−(1−αh)(1−χ)χ

t

(∫Nt0 X

χj,tdj

)1−αhχ ,

• No impact of Nt

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 Xj,t.

24

Technologies (2)

Startups:

• Invest 1 in t and be a monopolist in t+1 with probability ρt

25

Households

Preferences:

Max E∞∑i=0

[logCt+i + g(h− ht+i)]

Budget constraint:

Period t:

Ct + P Et Et + St = wtht + Etπt + P Et (1− µ)Et−1 + P Et ρt−1St−1

Period t+1:

Ct+1+P Et+1Et+1+St+1 = wt+1ht+1+Et+1πt+1+P Et+1(1−µ)Et+P Et+1ρtSt

26

New Markets

• Probability that a startup at time t will become a functioning firm

at t+ 1:

ρt = min

{1,εtNt

St

}

• Evolution of markets

27

Important remark

Parameters are such that it is always optimal to fill available space

on the market

28

Value Added

• Value added is given by:

Yt = Qt −∫ Nt0

Pj,tXj,tdj = AΘtht

• Value-added Yt is used for consumption Ct and startup expendi-

tures (St) purposes

Yt = Ct + St

29

Equilibrium

• From the household program:

1

ρtCt= βEt

[πt+1

Ct+1

]+ βEt

[(1− µ)ρt+1Ct+1

]

⇐⇒ 1 = βρtEt∞∑τ=1

(1− µ)τβτCt

Ct+τπt+τ

• Startup cost = discounted sum of expected profits

• Expectation driven startup investment

30

Equilibrium (2)

Using labor decisions, equilibrium conditions collapse to

(ht − ζ0) = βδtζ1Et[ht+1

]+ βδtEt

[(1

δt+1− 1

)(ht+1 − ζ0)

].

with

• δt = εt/(1− µ+ εt) is a increasing function of the fraction of newly

opened markets εt,

• ζ0 and ζ1 are complicated functions of the deep parameters.

31

Equilibrium (3)

Result 1 Employment is a purely forward looking, and therefore in-

directly depends on all the future δt

32

VAR Representation

• Output and consumption are given by

Yt = kyΘtht and Ct = kcΘt

s.t.

logYt = ky + logΘt + loght

logCt = kc + logΘt

• Assume

– logΘt = logΘt−1 + εΘt ,

– εt i.i.d., E(εt) = µ and εNt = log(εt)− log(µ).

33

Implications

• We have(∆log(Ct)∆ log(Yt)

)=

(1 01 b(1− L)

)(εΘtεNt

)= C(L)

(εΘtεNt

)

• Shares a lot of dynamic properties with the data:

1. Consumption is a random walk, only affected by εΘ

2. Output is also affected in the short run by εN

3. Orthogonalization would give:

εP = εC = εΘ and εT = εY = εN

4. Hours are only affected by εN

5. The interest rate does not respond to εN

34

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

ht = Cte

• All εN-driven fluctuations are suboptimal

35

The Klondike Gold Rush of 1896-1904

First, Rushing

36

The Klondike Gold Rush of 1896-1904 (2)

Second, Working Hard and Investing

37

The Klondike Gold Rush of 1896-1904 (3)

Then, Registering

38

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” (monopolyrents) on a market.

• Define gold rush: inefficient market rush: Historically, gold even-tually expands the stock of money.

• The business cycles fluctuations we have modelled here resemblemarket rushes, and more precisely gold rushes.

• Can we bring this idea to the date with a more compte quantitativemodel?

39

Road Map

1. Motivation (with Some Interesting Features of the Data)

2. An Analytical Model

3. Taking The Model to the Data

4. Conclusion

40

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

Extra Features

• Final Good

Qt = K1−αx−αz−αht (Θtht)

αh × . . .

× Nξx,t

(∫ Nx,t0

Xt(i)χdi

)αxχ

Nξz,t

(∫ Nz,t0

Zt(i)χdi

)αzχ

with αx, αz, αh ∈ (0,1), αx + αz + αh < 1 and χ > 1.

• ξ = −αx(1− χ)/χ : Nx,t has no impact

• ξ = (χ(1− αx)− αz)/χ: Qt is linear in Nz,t

42

Extra Features (2)

• Variety:

Nx,t+1 = (1− µ+ εxt )Nx,t

Nz,t+1 = (1− µ+ εzt )Nz,t.

• Shocks:

log(εxt ) = ρx log(εxt−1) + (1− ρx) log(εx) + νxt

log(εzt ) = ρz log(εzt−1) + (1− ρz) log(εz) + νzt

logΘt = logΘt−1 + εΘt .

43

Estimation

Simulated Method of Moments

44

Estimation (2)

Not all parameters are estimated

PreferencesDiscount factor β 0.9926

TechnologyElasticity of output to intermediate goods αx 0.3529Elasticity of output to hours worked αh 0.4235Depreciation rate δ 0.0250Elasticity of substitution bw intermediates χ 0.8333Rate of technology growth γ 1.0060Monopoly death rate µ 0.0086

45

Impulse Response Functions VAR versus Model (LR identification)

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Consumption − εP

1 S

.D. S

hock

DataModel

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Output − εP

1 S

.D. S

hock

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Consumption − εT

1 S

.D. S

hock

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Output − εT

1 S

.D. S

hock

46

Impulse Response Functions VAR versus Model (SR identification)

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Consumption − εC

1 S

.D. S

hock

DataModel

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Output − εC

1 S

.D. S

hock

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Consumption − εY

1 S

.D. S

hock

5 10 15 20−0.5

0

0.5

1

1.5

Horizon

Output − εY

1 S

.D. S

hock

47

Estimated Parameters

Persistence of the X Variety shocks ρx 0.9166(0.0336)

Standard dev. of X Variety shocks σx 0.2865(0.0317)

Persistence of the Z Variety shocks ρz 0.9164(0.6459)

Standard dev. of Z Variety shocks σz 0.0245(0.1534)

Standard dev. of the Technology shocks σΘ 0.0131(0.0015)

Habit Persistence parameter b 0.5900(0.1208)

Adjustment Costs parameter ϕ 0.4376(0.3267)

48

Goodness of Fit

J–stat(Y) Chi–stat(C) Chi–stat(C,Y)Test 17.41 42.51 92.78P–value [0.99] [0.12] [0.06]

49

Does the model match Hours variance decomposition?

• (ML) Regression: ht = c+∑Kk=0

(αkε

Pt−k + βkε

Tt−k + γkε

Ht−k

),

Data Model

Horizon εp εt εh εp εt εh

1 19 % 75 % 6 % 35 % 65 % 0%

50

Business cycle accounting

Horizon Output Consumption HoursεΘ εx εz εΘ εx εz εΘ εx εz

1 64 % 36 % 0 % 94 % 6 % 0 % 15 % 85 % 0%4 86 % 14 % 0 % 95 % 5 % 0 % 19 % 81 % 0%8 92 % 8 % 0 % 96 % 4 % 0 % 32 % 68 % 0%20 96 % 3 % 1 % 98 % 1 % 1 % 40 % 59 % 1%∞ 96 % 0 % 4 % 96 % 0 % 4 % 41 % 57 % 2%

51

Alternative Stories

• Common to all models

– habit persistence,

– adjustment costs to investment

– permanent technology shock

– Shut down the permanent market shock

Qt = K1−αx−αht (Θtht)

αhNξx,t

(∫ Nx,t0

Xt(i)χdi

)αxχ

.

• Compete our market shock against alternative shocks.

52

Alternative Stories (2)

Investment Specific Shock

Yt = Ct + St + e−ζtIt,

PIS–1 PIS–2 TIS–1 TIS–2J–stat 17.31 60.96 14.89 59.48

[0.99] [0.86] [1.00]) [0.87]

D(C, Y ) 99.42 92.34[0.03] [0.06])

53

Alternative Stories (3)

Investment Specific Shock: Variance decomposition

Horizon Output Consumption HoursεΘ νx ζ εΘ νx ζ εΘ νx ζ

PIS–1: ζ=Permanent Investment Specific Shock1 64 % 36 % 0 % 95 % 5 % 0 % 15 % 85 % 0 %∞ 100 % 0 % 0 % 100 % 0 % 0 % 44 % 56 % 0 %PIS–2: ζ=Permanent Investment Specific Shock1 55 % 45 % 0 % 84 % 16 % 0 % 0 % 99 % 1 %∞ 96 % 0 % 4 % 96 % 0 % 4 % 26 % 63 % 11 %TIS–1: ζ=Temporary Investment Specific Shock1 53 % 42 % 5 % 93 % 6 % 1 % 19 % 73 % 8 %∞ 100 % 0 % 0 % 100 % 0 % 0 % 34 % 50 % 16 %TIS–2: ζ=Temporary Investment Specific Shock1 56 % 42 % 2 % 84 % 15 % 1 % 0 % 94 % 6 %∞ 100 % 0 % 0 % 100 % 0 % 0 % 26 % 62 % 12 %

54

Alternative Stories (4)

Transitory technology and preference shocks

• Transitory technology shock

Qt = eζtK1−αx−αht (Θtht)

αhNξx,t

(∫ Nx,t0

Xt(i)χdi

)αxχ

,

• Preference shocks

Et∞∑τ=0

[log(Ct+τ − bCt+τ−1) + ψeζt+τ(h− ht+τ)

],

T.T. T.P.J–stat 54.65 50.56

[0.95] [0.98]

55

Alternative Stories (5)

Horizon Output Consumption HoursεΘ νx ζ εΘ νx ζ εΘ νx ζ

T.T.: ζ=Temporary Technology Shock1 21 % 38 % 41 % 44 % 17 % 39 % 0 % 98 % 2 %∞ 99 % 0 % 0 % 100 % 0 % 0 % 10 % 66 % 24 %T.P.: ζ=Temporary Preference Shock1 27 % 39 % 34 % 55 % 15 % 30 % 1 % 53 % 46 %20 70 % 8 % 22 % 82 % 5 % 13 % 7 % 33 % 60 %∞ 100 % 0 % 0 % 100 % 0 % 0 % 8 % 33 % 59 %

56

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

Conclusion

• We have found a new source of shocks, that looks like animal

spirits, although it comes from a model with determinate equilib-

rium.

• 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

Extra material

59

Alternative Stories?

Estimation Results

RBC–P RBC–T RBC–Q CEEb 0.8813 0.8813 0.7181 0.0000

(0.0289) (0.0289) (0.0739) (0.0000)ϕ 0.6682 0.6683 2.0353 0.6353

(0.4305) (0.4369) (0.6242) (0.1811)σγ 0.0143 0.0143 0.0153 0.0129

(0.0019) (0.0019) (0.0016) (0.0015)ρT 0.5973 0.4974 0.6024 –

(0.0996) (0.1024) (0.0921)σT 0.0155 0.0099 0.0306 –

(0.0077) (0.0050) (0.0033)J–stat(Y) 30.96 30.96 18.05 23.06

[0.66]) [0.66] [0.99] [0.96]

60

Alternative Stories?

PIS–1 PIS–2 TIS–1 TIS–2b 0.6108 0.3125 0.6457 0.3062

(0.1229) (0.1921) (0.1180) (0.2184)ϕ 0.4195 0.2534 0.6099 0.2775

(0.3227) (0.3201) (0.6675) (0.4235)σΘ 0.0131 0.0088 0.0126 0.0089

(0.0017) (0.1592) (0.0017) (0.0016)ρx 0.9117 0.8919 0.9143 0.8967

(0.0323) (0.0395) (0.0374) (0.0420)σx 0.1575 0.1859 0.1594 0.1775

(0.0217) (0.0349) (0.0197) (0.0266)ρT – – 0.5328 0.8478

(0.2742) (0.4974)σT 0.0003 0.0038 0.0118 0.0032

(0.0243) (0.0082) (0.0137) (0.0048)

61

Alternative Stories?

T.T. T.P.b 0.3420 0.3877

(0.1869) (0.1472)ϕ 0.3125 0.3699

(0.2645) (0.3228)σΘ 0.0062 0.0075

(0.0044) (0.0037)ρx 0.9195 0.9075

(0.0234) (0.0259)σx 0.1768 0.1825

(0.0278) (0.0297)ρT 0.9143 0.8799

(0.1148) (0.1959)σT 0.0046 0.0068

(0.0021) (0.0030)

62