Errata for Accounting and Causal E§ects
• ch. 1, p. 5 the limits of integration at the bottom of the page
R Y +1
f (X2 , Y ) dX2 3 < Y < 1
1
should read
R Y +1
2
and
f (X2 , Y ) dX2
R1
Y 1
should read
R2
Y 1
3 < Y < 1
f (X2 , Y ) dX2
1<Y <3
f (X2 , Y ) dX2
1<Y <3
• ch. 2, p. 12 Econometric analysis of equilibrium earnings management
is pursed in chapters 3 and 13. should read Econometric analysis of
equilibrium earnings management is pursued in chapters 3 and 13.
• ch. 3, p. 20
i
XT Y | X
h
i
1 T

= E XT X
X X + " | X

1 T
=  + XT X
X E [" | X] =  + 0 = 
E [b | X] = E
should read
E [b | X] = E
h
XT X
h
XT X
1
XT Y | X
i
i
1 T
XT X
X (X + ") | X

1 T
=  + XT X
X E [" | X] =  + 0 = 
= E
• ch. 3, p. 20
V ar [b | X] = V ar
h
h
1
XT X
1
XT Y | X
i
h
i
1 T
= V ar X T X
X (X + ") | X
n

o n
 T 1 T
1 T oT
T
= E + X X
X "
X X
X "
|X
1 T  T   T 1
XT X
X E "" X X X
2 T 1 T

1
=  X X
X IX X T X

1
= 2 X T X
=

1
should read
V ar [b | X] = V ar
h
XT X
1
XT Y | X
i
h
i
1 T
= V ar X T X
X (X + ") | X
n

o n

1 T
1 T oT
= E  + XT X
X "
XT X
X "
|X

1 T  T   T 1
XT X
X E "" X X X



1
1
= 2 X T X
X T IX X T X

1
= 2 X T X
=
• ch. 3, p. 20
h

1 T i h

1 T iT
V ar [b0 | X] =  2 D + X T X
X
D + XT X
X
 T 1 T T
 T 1 !
DDT + X X
X D + DX X X
 T 1 T  T 1
= 2
+ X X
X X X X
should read
h

1 T i h

1 T iT
V ar [b0 | X] =  2 D + X T X
X
D + XT X
X

1 T T

1 !
DDT + X T X
X D + DX X T X
2

1 T  T 1
= 
+ XT X
X X X X
• ch. 3, p. 28
b OLS

should read
b OLS



b W G + X T X 1 X T PD X 
b BG
X T MD X 

1 T

1 T
= XT X
X MD X T MD X
X MD Y
 T 1 T
 T
1 T
+ X X
X PD X X P D X
X PD Y
 T 1 T
 T
1 T
= X X
X MD X MD X
X MD (X + u)
 T 1 T
 T
1 T
+ X X
X PD X X PD X
X PD (X + u)
=

1


b W G + X T X 1 X T PD X 
b BG
X T MD X 

1 T

1 T
= XT X
X MD X X T MD X
X MD Y
 T 1 T
 T
1 T
+ X X
X PD X X P D X
X PD Y
 T 1 T
 T
1 T
= X X
X MD X X MD X
X MD (X + u)
 T 1 T
 T
1 T
+ X X
X PD X X P D X
X PD (X + u)
=

XT X
XT X
1
2
• ch. 4, p. 60 Simplification yields
h 
 
 i
̂ c1 1  F ̂ + c2 F ̂

  h
i
  h
i
= c1 1  F ̂ E  | y, ̂   + c22 F ̂ E  | y, ̂ > 
should read Simplification yields
h 
 
 i
̂ c1 1  F ̂ + c2 F ̂

  h
i
  h
i
= c1 1  F ̂ E  | y, ̂   + c2 F ̂ E  | y, ̂ > 
• ch. 5, p. 78 where V = "a  "b . should read V = "a  "b .
L(yn | 1 )( 1 |b,W )
• ch. 7, p. 119 footnote 11 part (e) Calculate the ratio F = L(yn |n0 )( 0n|b,W )
n
n




where L yn |  1n is a product of logits, and   1n | b, W is the normal
density. should read
(e) Calculate the ratio  =
L( 1n |b,yn )( 1n |b,W )
L( 0n |b,yn )( 0n |b,W )


  1n | b, W is the


where L  1n | b, yn is the
likelihood for the proposal and
prior for the proposal with
 0

 0

L  n | b, yn and   n | b, W the analogs for the initial or previous draw.
• ch. 8, p. 135-141 The discussion of strategic choice models has been
substantially revised and is separately reported at
http://fisher.osu.edu/~schroeder.9/AMIS900/StrategicChoiceModel.pdf
• ch. 10, p. 219 Then, we can replace Pr (D1i  D0i = 1) with E [Di | Zi = 1]
E [Di | Zi = 0] and
Pr (D1i  D0i = 1) E [Y1i  Y0i | D1i  D0i = 1]
= (E [Di | Zi = 1]  E [Di | Zi = 0]) E [Y1i  Y0i | D1i  D0i = 1]
= (E [Di | Zi = 1]  E [Di | Zi = 0]) (E [Yi | Zi = 1]  E [Yi | Zi = 0])
should read Then, we can replace Pr (D1i  D0i = 1) with E [Di | Zi = 1]
E [Di | Zi = 0] and
(E [Yi | Zi = 1]  E [Yi | Zi = 0])
= Pr (D1i  D0i = 1) E [Y1i  Y0i | D1i  D0i = 1]
= (E [Di | Zi = 1]  E [Di | Zi = 0]) E [Y1i  Y0i | D1i  D0i = 1]
• ch. 13, p. 341
2
3
m
X
Y = exp 4
j {fj (X1 )  fj (X0 )}5
j=1
3
should read
Y =
m
X
j=1
j {fj (X1 )  fj (X0 )}
• ch. 13, p. 357 or green widgets (decision D3 ) is
L (D3 ; n1 , n2 , n3 ) = R (n1  S1  200) + R (n2  S2 ) + R (n3  S3  200)
should read or green widgets (decision D3 ) is
L (D3 ; n1 , n2 , n3 ) = R (n1  S1 ) + R (n2  S2 ) + R (n3  S3  200)
• ch. 13, p. 361
E [L (D2 )] =
1
X
p (n1 ) R (n1  100) +
n1 =0
1
X
+
n3 =0
1
X
n2 =0
p (n2 ) R (n2  350)
p (n3 ) R (n3  50)
= 6.902 + 3.073 + 10.06 = 10.06
should read
E [L (D2 )] =
1
X
p (n1 ) R (n1  100) +
n1 =0
1
X
+
n3 =0
1
X
n2 =0
p (n2 ) R (n2  350)
p (n3 ) R (n3  50)
= 6.902 + 3.073 + 0.085 = 10.06
• ch. 13, p. 362 Today’s total demands for red, yellow and green widgets
are
1
1
1
X
X
X
n1 =
rur , n2 =
yuy , n3 =
gug
r=1
y=1
g=1
whose expectations from stage 2 are E [n1 ] = 50, E [n2 ] = 100, and
E [n3 ] = 10. The total number of individual orders for red, yellow, and
green widgets are
m1 =
1
X
u r , m2 =
r=1
1
X
u y , m3 =
y=1
1
X
ug
g=1
should read Today’s total demands for red, yellow and green widgets are
n1 =
1
X
rur , n2 =
r=1
1
X
y=1
4
yvy , n3 =
1
X
g=1
gwg
whose expectations from stage 2 are E [n1 ] = 50, E [n2 ] = 100, and
E [n3 ] = 10. The total number of individual orders for red, yellow, and
green widgets are
m1 =
1
X
u r , m2 =
r=1
1
X
y=1
vy , m3 =
1
X
wg
g=1
• ch. 13. p. 402 mt = g mt1 + et should read mt = g mt1 + "t


 


den0
1
den0
t
t
t
• ch. 13. p. 402 B
= S S
should read B
=
num0
0
num0
 
1
St S 1
0
• ch. 13. p. 406 mt = g mt1 + et should read mt = g mt1 + "t
• missing reference, p. 435. Hogan, C. 1997. "Costs and benefits of audit
quality in the IPO market: A self-selection analysis," The Accounting
Review 72. 68-86.
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