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In the system of equations (1), dca denotes changes in current assets. InvMA , new
investment in machinery and equipment, InvBU, new investment in buildings and
structures, InvGW , change in goodwill, InvP , change in patents and copyrights, and
TA , the total assets of firms. 4 Subscript j,t means firm j and fiscal year t. The subscript
g denotes the pooled data for each industry because we estimate industry-wide
coefficients to minimize estimation errors from using individual firm data for
estimation. We pool five years of individual firm data for each industry and estimate
the coefficients for each industry with OLS. We also assume the error terms in (1) are
serially uncorrelated. 5 Then, given industry-wide coefficients, we plug in accounting
variables to get estimates of the variables for each firm.
Based on the time evolvement of the accounting variables above, we assume each
firm is equipped with the following power production function.
γ
γ
σ
w
OIBD
=
γ
(
CA
+
dca
)
(
MA
+
InvMA
)
e
g
,
1
g
,
2
j
,
t
(2)
j
,
t
g
,
0
j
,
t
1
j
,
t
j
,
t
1
j
,
t
In equation (2), OIBD denotes operating income before depreciation, CA , current
assets, and MA , the balance of machinery and equipment. For the error term, σ denotes
annualized volatility for each firm and w is a standard normal random variable. We
estimate the model using the log transformation of this equation and we estimate
gammas and sigmas for each firm in each industry with pooled data for five years.
We assume the topic and economic depreciation (Samuelson, 1964) coincide with
each other and the following (3) holds for depreciation expenses every period. We use
a depreciation rate of 25 percent for tax purposes in Japan 6 and depreciation expenses
for tax purposes must coincide with depreciation expenses for financial purposes.
Let δ denote the accounting depreciation rate. The accounting depreciation, DEPR ,
is defined in the following equation (3) where BU denotes the topic value of buildings
and structures and GW denotes goodwill,
DEPR
=
(
MA
+
BU
+
GW
+
P
)
δ
,
where
δ
=
0
.
25
.
(3)
j
,
t
j
,
t
1
j
,
t
1
j
,
t
1
j
,
t
1
With these preparations the time evolvement of firm accounting variables is governed
by the following accounting identity equations.
CA
=
CA
+
dca
,
MA
=
δ
MA
+
InvMA
,
j
,
t
j
,
t
1
t
j
,
t
j
,
t
1
t
(4)
BU
=
δ
BU
+
InvBU
,
GW
=
δ
GW
+
InvGW
,
P
=
δ
P
+
InvP
.
j
,
t
j
,
t
1
t
j
,
t
j
,
t
1
t
j
,
t
j
,
t
1
t
Furthermore, we define the earnings before tax, EBT , as
EBT
=
(
OIBT
DEPR
)
+
(
FI
FE
)
(5)
j
,
t
j
,
t
j
,
t
j
,
t
j
,
t
4 Goodwill is recorded as assets and depreciated at a maximum of 20 years in Japan. Patents
and copyrights were depreciated before, but are now fully expensed.
5 Because we estimate at the industry level, serial correlations will be less serious than the case
of estimating at an individual firm level.
6 The idea is similar to the modified accelerated cost recovery system (MACRS) in the U.S. by
the Tax Reform Act of 1986. It was enacted in fiscal year 2009 and from 2011 the rate was
reduced to 20 percent.
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