Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis Charles T. Carlstrom and Timothy S. Fuerst
March 2008
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Agency Cost, Net Worth, and Business Fluctuations
Motivation I
An in…nite period, computable general equilibrium model with endogenous agency cost to study business cycle dynamics.
I
Standard RBC model ∞
max E
∑ β t U ( ct , 1
lt )
t =0
s.t. ct + it = yt kt +1 = (1
δ)kt + it
yt = At F (kt , lt ) I
one-to-one transformation rate between consumption good and investment good Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Motivation
I
Replace the one-to-one transformation with a contracting problem I
The households fund entrepreneurial projects to purchase capital ) Agency problems
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Motivation
I
Output growth displays positive autocorrelation at short horizons. Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Outline
I
The Economy
I
The Financial Contract
I
The General Equilibrium Model
I
Calibration, Simulation and Discussion
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Basic Structure of the Economy
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Two goods: consumption goods and capital goods
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A continuum of agents with unit mass I I
Households with fraction 1 η Entrepreneurs with fraction η
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Consumption Producing Firms (CPFs)
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Capital Mutual Funds (CMFs)
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Households
I
Preference: ∞
E0
∑ β t u ( ct , 1
Lt )
t =0
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Sell labor Ht at wt and rent capital at rt to CPFs and get consumption goods from CPFs
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Purchase new capital at qt from CMFs
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Entrepreneurs
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Risk neutral
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Sell labor Hte at xt and rent capital at rt to CPFs and get consumption goods from CPFs
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Can produce ωi capital goods by i consumption goods I I I
ω is i.i.d. across time and across entrepreneurs Distribution Φ, density φ, mean of unit, nonnegative support Private information
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Comsumption Producing Firms I
Standard constant return-to-scale production function Yt = θ t F (Kt , Ht , Hte ) θ t : productivity shock Kt : aggregate capital Ht : aggregate households’labor Hte : aggregate entrepreneurs’s labor
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Not subject to any agency problems
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Capital Mutual Funds
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Risk neutral
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Sell (Buy) capital goods (consumption goods) to (from) households
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Sell (Buy) consumption goods (capital goods) to (from) entrepreneurs
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Make …nancial contracts with entrepreneurs
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Assumption
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The …nancial contract depends only on entrepreneur’s level of net worth and not on his entire past history of debt repayment I I
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Negotiated at the beginning of a period Resolved at the end of a period
Hence, although it is an in…nite time model, we can focus on one period contract
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract
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The objective is to …nance i consumption goods to produce capital goods and distribute capital goods produced, based on the entrepreneur’s net worth n and capital price q
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Two parties I I I
Entrepreneur with observable net worth n and private information ω Lender (CMFs, not Households) All are risk neutral
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract
I
Monitoring technology I
Lender can privately observe ω only at a monitoring cost of µi capital units
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract
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Assume that stochastic monitoring is impossible
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Assume that a commitment device exists
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract I
According to Gales and Hellwig(1985), the contract is: I
I I
I
_
Choose ω, which maximizes the expected payo¤ of the entrepreneur and guarantees the lender certain amount of return Lender commits to the _ strategy that he monitor the result only if the reported ω < ω_ _ _ Entrepreneur reports ω if ω > ω and reports ω if ω < ω _
If the entrepreneur reports ω < ω (default), all the returns from the project go to the lender
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract I
The expected payo¤ of the entrepreneur _
qif ω = qi f I
_
ωΦ(d ω )
_
_
Φ ω ]ω g
[1
ω
The expected payo¤ of the lender _
qig ω = qi f I
Z ∞
_ Z ω
0
ωΦ(d ω )
_
Φ ω µ + [1
_
_
Φ ω ]ω g
Notice that _
_
f ω +g ω = 1 Carlstrom and Fuerst
_
Φ ω µ
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Agency Cost, Net Worth, and Business Fluctuations
One Period Contract I
_
To determine ω, solve the following problem: _
max qif ω _
s.t.qig ω > (i
n)
_
qif ω > n I
_
The condition qif ω > n is always satis…ed
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Agency Cost, Net Worth, and Business Fluctuations
One Period Contract
I
First order conditions are: _
q f1
_
_
Φ ω µ + φ ω µ[ i=f
1
Carlstrom and Fuerst
f ω f
/
_
]g = 1
ω
1 _ gn g ω
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
One Period Contract I
We can derive the expected capital output _
I S (q, n) = i (q, n)[1
µΦ ω (q ) ]
with I1S (q, n) > 0 and I2S (q, n) > 0 I
The return to internal funds is _
_
qf ω i qf ω _ = n 1 qg ω
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Timeline I
First, consumption goods production: I I
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Second, capital goods production: I I
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Households and entrepreneurs sell labor, rent capital and get consumption goods Households decides their consumpution and the remainings go to CMFs for capital goods
Entrepreneurs sell all their capital goods in hand CMFs and Entrepreneurs make …nancial contracts and distribute capital goods
Finally, entrepreneurs make their consumption decisions
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Households Problem
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Households’…rst order conditions are: UL ( t ) = wt (1) Uc ( t ) qt Uc (t ) = βEt Uc (t + 1) [qt +1 (1
Carlstrom and Fuerst
δ) + rt +1 ] (2)
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Consumption Producing Firms’Problem
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Consumption Producing Firms’…rst order conditions are: rt = F1 (t ) (3) wt = F2 (t ) (4) xt = F3 (t ) (5)
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Contract Problem
I
Contract Problem’s …rst order conditions are: _
qt f1
Φ
_ ωt
µ+φ
it = f
1
_ ωt
µ[
f ωt f
/
1 _ gn g ωt
Carlstrom and Fuerst
_
]g = 1 (6)
ωt (7)
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Entrepreneurs’Problem I
Entrepreneurs’preference: ∞
E0
∑ ( βγ)t cte
t =0
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Agency costs imply that the return to internal funds is greater than the return to external funds, so we let entrepreneurs discount the future more heavily than household in order to make them need external funds
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Entrepreneurs’Problem I
The net worth of entrepreneur is nt = xt + zt [qt (1
I
δ) + rt ] (8)
The Euler equarion for entrepreneur is _
qt = Et βγ[qt +1 (1 I
δ) + rt +1 ]
f
qt +1 f ω t +1 1
_
qt +1 g ω t +1
g (9)
Aggregating across the entrepreneurs’budget constraints, _
Zt +1 = fηxt + Zt [qt (1
δ) + rt ]g
Carlstrom and Fuerst
f
qt f ω t 1
qt g
_ ωt
g
ηcte (10) qt
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Market Clearing Conditions I
Two labor markets Ht = ( 1
η ) Lt (11)
Hte = η (12) I
Consumption goods market η )ct + ηcte + ηit = Yt (13)
(1 I
Capital goods market Kt + 1 = ( 1
δ)Kt + ηit [1
Carlstrom and Fuerst
_
Φ ω t µ] (14)
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Recursive Competitive Equilibrium
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A Recursive Competitive Equilibrium_is de…ned by decision rules for Kt +1 , Zt +1 , Ht +1 , qt , nt , it , ω t , cte ,and ct , where these decision rules are stationary function of (Kt , Zt , θ t ) and satisfy (1)— (14).
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Agency Cost, Net Worth, and Business Fluctuations
Calibration I
Household U (c, L) = log (c ) + v (1
I
Consumption producing …rms Yt = θ t
I
L)
Kt0.36
Ht0.6399
Hte0.0001
Bankruptcy rate and risk premium are used to calibrate σ and γ I I
σ : standard deviation of Φ log normal βγ : the discount rate of entrepreneurs Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation
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"Standard" RBC Model, µ = 0
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RBC Model with Agency Cost, µ = 0.25
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Wealth Shock I
Wealth shock: one-time transfer of capital from households to entrepreneurs
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Wealth Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Wealth Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Productivity Shock I
The technology process θ t = (1
Carlstrom and Fuerst
ρ) + ρθ t
1
+ νt
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Productivity Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Productivity Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Productivity Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Stimulation–Productivity Shock
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Contribution
I
The model replicates the emperical fact that output growth displays positive autocorrelation at short horizons. (the hump-shaped output behavior)
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The reason is that households delay their investment decisions until agency costs are at their lowest— a point in time several periods after the initial productivity shock.
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
Agency Cost, Net Worth, and Business Fluctuations
Introduction The Economy The Financial Contract The General Equilibrium Model Calibration, Simulation and Discussion
Contribution
Carlstrom and Fuerst
Agency Cost, Net Worth, and Business Fluctuations
