A Theory of Income Smoothing When
Insiders Know More Than Outsiders
Viral Acharya
Bart Lambrecht
NYU-Stern, CEPR and NBER
University of Lancaster
Nottingham University Business School
Nottingham, 29/02/2012
Acharya and Lambrecht (2012)
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Introduction
Stock market pressures cause myopic behavior (Stein (1989)):
value dissipating earnings manipulation
yet: market efficient and not fooled
time series properties of income unchanged
Are stock price considerations really (only) root cause?
What is effect of introducing asymmetric information on:
efficiency of investment (production) policy?
time-series properties of income?
Asymmetric information (measurement error) creates:
discrepancy between reality and what is observed
tension between inside and outside shareholders (expropriation)
Implications for production policy and dynamics of reported
income?
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Jin and Myers (2006) framework:
outsiders can take collective action
property rights can be enforced to some degree:
φ% of shares =⇒ gives αφ% of distributable net income
with α ∈ (0, 1] a measure of investor protection
insiders avoid intervention at all costs by meeting outsiders’
expectations (Graham, Harvey, Rajgopal (2005))
But: no learning, investment exogenous, no inter-temporal
smoothing
This paper:
managers set output each period
stochastic marginal cost observed by insiders only
outsiders observe noisy proxy of output (sales)
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Results
Insiders attempt to “manage expectations”
Measurement error reduces incentive to distort
Asymmetric information introduces inter-temporal smoothing:
Financial smoothing (value-neutral)
Real smoothing (under-investment; value-destroying)
reported income follows target adjustment model
higher outside ownership share leads to more underinvestment
and more (real) smoothing
Outside equity value is inverted U-shaped function of outsiders’
stake
independent audited disclosure improves production efficiency
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Model Assumptions
All agents are risk neutral
All equity financed firm (insiders versus outsiders)
All income is paid out each period and given by
πt (qt ) = qt −
where xt = A xt−1 + B + wt−1
qt2
2xt
with wt−1 ∼ N(0, Q) ,
Choice variable: output (qt ) given wt−1
Infinite horizon
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First-best solution
- Risk-neutral shareholders maximize:
Vt =
max
qt+j ,j=0...∞
∞
X
Et [
β j πt+j ]
(1)
j=0
Proposition
The first-best production policy is
qto = xt ,
(2)
The corresponding actual income and total payout are:
πto = qto −
Acharya and Lambrecht (2012)
qto 2
xt
=
.
2xt
2
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Inside and outside shareholders
outsiders’ ownership stake: φ (with φ ∈ [0, 1])
Capital market constraint: St ≥ αφVt (with α ∈ (0, 1])
Insiders set payout, dt , such that
⇐⇒
St = dt + βαφEt [Vt+1 ] = αφVt
dt = αφπt ≡ θπt
Insiders’ optimization problem is now:
"∞
#
X
Mt =
max Et
β j (π(qt+j ) − θπ (qt+j ))
qt+j ;j=0..∞
(3)
(4)
(5)
j=0
Policies remain first best.
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Asymmetric information
xt only observed by insiders
Outsiders observe output (qt ) with measurement error (noise):
st = qt + t with iid t ∼ N(0, R) and E (wk l ) = 0 for all k, l
insiders (M) set qt before t is realized
outsiders (S) estimate x̂t = ES,t [xt |It ] where It = {st , st−1 , ...}
Insiders’ optimization problem is now:
"∞
#
X
Mt =
max Et
β j (π(qt+j ) − θES,t+j [π (qt+j )])
qt+j ;j=0..∞
Acharya and Lambrecht (2012)
j=0
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Proposition
qt = H xt = Hqto
for all t
H2
= θ H−
2
dt = θπ̂t
x̂t
(6)
where x̂t = (Ax̂t−1 + B) λ + K st
∞
X
λB
=
+K
(λA)j st−j .
1 − λA
j=0
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(8)
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Proposition
qt = H xt = Hqto
dt = θπ̂t
and where x̂t
for all t
H2
= θ H−
x̂t
2
= (Ax̂t−1 + B) λ + K st
∞
X
λB
=
+K
(λA)j st−j .
1 − λA
j=0
(9)
(10)
(11)
θ
f (H) ≡ H 2 K ( − βA) + H [βA(1 + K ) − 1 − θK ] + 1 − βA = 0
2
with K ≡
HP
,
H 2 P+R
λ ≡ (1 − KH) and P = A2 P −
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A2 H 2 P 2
H 2 P+R
+Q
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Learning (filtering) process:
st = H xt + t
(measurement equation)
xt = A xt−1 + B + wt−1 (state equation)
Steady state estimator:
x̂t = λ (Ax̂t−1 + B) + K st
Corollary
insiders underproduce (i.e., qt = Hxt = Hqto ≤ qt0 ). The noisier the
link between xt and its proxy, st , the weaker insiders’ incentives to
underproduce. Full efficiency is achieved for R = ∞ or Q = 0.
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Figure 1: Production efficiency
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Time-series properties of income
Proposition
H
The “actual income” is : πt = H 1 −
2
xt .
The “reported income” is given by:
π̂t = π̂t−1 + (1 − λA) (πt∗ − π̂t−1 ) where SOA ≡ 1 − λA
H
= λAπ̂t−1 + KH 1 −
st + hλB ≡ γ̂2 π̂t−1 + γ̂1 st + γ̂0 .
2
The “income target” πt∗ is given by:
hλB
KH
H
∗
πt =
+
1−
st ≡ γ0∗ + γ1∗ st .
1 − λA
1 − λA
2
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Corollary
Measurement errors (t ) create asymmetric information, which in
turn leads to smoothing of reported income.
Corollary
Reported income also smooths persistent shocks in the presence of
asymmetric information because in the short run outsiders cannot
distinguish between measurement error and shocks to the latent cost
variable.
Corollary
Less information asymmetry leads to less smoothing. πt = π̂t = πt∗
if R = 0 or Q = ∞.
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- Payout Policy
dt = λAdt−1 + θhKst + θk .
−→ Similarities with Lintner (1956) dividend model
−→ See also Lambrecht & Myers (2011) but their model based on:
complete information
habit formation + risk aversion
- Real versus financial smoothing
SOA = 1 − Aλ
= 1 − Aλ [H = 1] − (Aλ − Aλ [H = 1])
= 1 − financial smoothing − real smoothing
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Figure 2: Speed of Adjustment
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Forced disclosure and the “big bath”
Capital Market Constraint: St ≥ φαEt [Vt |It ]
Insiders’ participation constraint:
⇐⇒
Mt = Vt − ϕαEt [Vt |It ] ≥ Vt − ϕαVt − cVt
ϕα
Vt ≥
Et [Vt |It ]
αϕ + c
overoptimism (x̂t >> xt ) could trigger costly forced disclosure
Solutions:
lower φ or α (private firms)
voluntary audited disclosure (public firms)
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Audited disclosure
outsiders’ prior distribution of income: N(π̂t , σ̂ 2 )
auditors’ independent estimate of income: yt ∼ N(πt , σ 2 )
outsiders’ posterior estimate of income:
σ̂ 2
σ̂ 2 + σ 2
Insiders’ optimization problem similar as before except that
θ(≡ αφ) is replaced by:
ϕα(1 − κ)
θ(1 − κ)
G (ϕ, α, κ) ≡
≡
= (inverse) governance index
1 − ϕακ
1 − θκ
κyt + (1 − κ)π̂t
where κ =
Corollary
Higher quality audited disclosure (κ) has a similar effect as increasing
insiders’ ownership stake and it reduces real smoothing (i.e. less
underinvestment).
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Accounting quality, stock market value and growth
firm is set up at t = 0
initial investment required: E (all equity financed)
no adverse selection: x̂t = xt =⇒ V (x0 ; θ, κ) = V (x̂0 ; θ, κ)
∂V (x0 ;θ,κ)
∂θ
< 0 due to under-investment
constrained optimal value for θ is:
θo = min {θ| θV0 (x0 ; θ, κ) = E }
=⇒ “outside equity Laffer curve”
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Figure 3: Total firm value and outside equity value
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Empirical implications and conclusions
Reported income, π̂t is smoothed:
π̂t is driven by outside investors’ expectation
intertemporal smoothing due to asymmetric information
π̂t follows a target adjustment model
financial + real smoothing
income smoothing implies payout smoothing (cfr. Lintner
(1956))
insiders attempt to “manage expectations”
=⇒ under-investment
higher θ leads to more underproduction and more smoothing
“outside equity Laffer curves”
Possible solutions to under-investment problem:
low outside ownership (private firms; developing countries)
audited disclosure (public firms)
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