Resource Reallocation and Zombie Lendingin Japan’s 1990s∗
Machiko Narita†

Hyeog Ug Kwon

Futoshi Narita

Nihon University, RIETI

University of Minnesota University of Minnesota

September 24, 2009
Abstract
We investigate the eﬃciency of resource reallocation in Japan during the 1990s, a decade of economic recession, by measuring aggregate
productivity growth (APG) using a plant-level data set of manufacturers from 1981-2000. We ﬁnd that resource reallocation contributed
negatively to APG, mainly due to ineﬃcient labor reallocation. A
possible reason for the ineﬃcient labor reallocation is misdirected (orzombie) bank lending to failing plants. To quantify its impact, wedevelop a model with plant-level heterogeneity, calibrate it based on
the results of plant-level productivity estimation, and conduct a counterfactual exercise. The results show that zombie lending would resultin the loss of 37% of the actual decline in APG due to ineﬃcient labor
reallocation in Japan’s 1990s.

Keywords: Japan, Plant-level data, Productivity,
Proxy estimation, Reallocation, Zombie lending.
JEL Classiﬁcation Number: E23, E32, G21, O47.

∗

This research was conducted as a part of the RIETI (Research Institute of Economy,
Trade and Industry) research project “Productivity of Industry and Firm and Economic
Growth of Japan”. Kwon is grateful to the New Energy and Industrial Technology Organization (no.07D49003a) for ﬁnancial support. We would like to thank Pat Bajari,
Masahisa Fujita, Kyoji Fukao, Tom Holmes, Kyoo Il Kim, Masayuki Morikawa, Amil
Petrin for helpful comments and advice. Remaining mistakes are ours.
†
Contact Information: Hyeog Ug Kwon: kwon.hyeogug@nihon-u.ac.jp, Futoshi Narita:
narit002@umn.edu, Machiko Narita: fuji0065@umn.edu

11Introduction

The collapse of the bubble economy of the early 1990s was followed by adecade of economic stagnation and ﬁnancial crisis. During the severe economic recession, it was prevalent that Japanese banks continued to lend tootherwise insolvent ﬁrms (Peek and Rosengren (2005) and Caballero et al.
(2008)). Such “zombie lending” must have impeded eﬃcient resource reallocation by causing resources to reallocate from proﬁtable ﬁrms to unproﬁtableﬁrms. In this paper, we investigate how eﬀectively resources were reallocated and how much zombie lending distorted resource reallocation during
the 1990s.
In order to measure the eﬃciency of resource reallocation, we estimate its
contribution to aggregate productivity growth (APG) using the method proposed by Petrin and Levinsohn (2008). APG is deﬁned as aggregate change
in output holding input use unchanged, and its reallocation component captures the change in output resulting from resource reallocation among existing plants.1 Resource reallocation contributes to APG if inputs are reallocated from plants with lower marginal product to plants with higher marginal
product, because output increases without additional input use. Therefore,
from the estimated reallocation term, we can learn whether resources werereallocated in the way to increase output and how much change in output
was generated by the reallocation.
We estimate the reallocation term using a plant-level panel data set of
manufacturers from 1981 to 2000 and ﬁnd that resources were reallocatedin the way to decrease output, especially during the 1990s. The averagereallocation term was -0.18% during the 1980s and it was -0.85% during the
1990s. This result is in stark contrast with ﬁndings for Chile, Columbia, andthe United States, where the reallocation term is typically positive (Petrin
and Levinsohn (2008) and Petrin et al. (2009)).
When we further decompose the reallocation term into input-speciﬁc reallocation terms, we ﬁnd that labor reallocation made a large negative contribution to APG during the 1990s. The average labor reallocation term during
the 1990s was -0.66% and it accounted for 78% of the undecomposed reallocation term. The capital and material reallocation terms were also negativeon average during the 1990s.
1

APG consists of three components: technical eﬃciency, reallocation eﬀect, and netentry eﬀect. We estimate each component at plant-level and obtain APG by aggregatingthem up over all plants.

2

Now, the question is why resource reallocation negatively contributed to
growth in Japan. The negative reallocation eﬀect means that inputs werereallocated from higher margin plants to lower margin plants. However, in a
fully functioning market, resources must be reallocated in the opposite way.
As a possible cause of the negative reallocation eﬀect, we will investigate
the eﬀect of misdirected bank lending. As Peek and Rosengren (2005) and
Caballero et al. (2008) document, Japanese banks provided subsidized credit
to failing ﬁrms during the 1990s. Such zombie lending must have caused
resources to be reallocated from higher margin plants to lower margin plants.
In order to measure the distortion of zombie lending in reallocation eﬀect,
we developed a model with plant-level heterogeneity based on Restuccia andRogerson (2008). Subsidized credit for zombies is captured by eﬀective tax
rates in the model. We deﬁne zombies as plants whose technical eﬃciency
has fallen below 20th percentile of its distribution for a consecutive ﬁve years.
Then, we calibrate eﬀective tax rates of labor and capital using the averagesof the corresponding estimated margins for zombies and nonzombies, respectively. Using the calibrated model, we conduct a counterfactual exercise of
the no-zombie-lending case and show that the decline in labor reallocation effect due to zombie lending is 37% of the estimated negative labor reallocationeﬀect.
This paper contributes to the literature on Japan’s 1990s by providing
new evidence that resource reallocation was not eﬃcient. Fukao et al. (2006)
showed that the contribution of resource reallocation was strong in the 1990s
by using a measure which was originally proposed by Bailey et al. (1992).
However, their measure of reallocation eﬀect is based on plant-level TFP,
rather than marginal product, and thus its implication is misleading in somecases as Petrin and Levinsohn (2008) argued. We use the newly proposed
measure by Petrin and Levinsohn (2008) and document that resources werereallocated in the way to decrease output.
In addition, the quantitative measure of the zombie distortion contributes
to the ongoing discussion about why APG in the manufacturing sector slowed
down during the 1990s. Fukao and Kwon (2006) questioned the quantitative
implication of the “zombie lending hypothesis” by Caballero et al. (2008).
They pointed out the fact that the slowdown of APG in the manufacturingsector was most severe although zombie lending was least prevalent in the
sector. We provided a quantitative implication of zombie lending on theestimated reallocation eﬀect and showed that zombie lending had a nonnegligible negative impact on APG in the manufacturing sector.
3

The rest of the paper consists of four sections. Section 2 explains the
APG measures and their decomposition which we will use in our analysis. We
also discuss how we estimate plant-level technical eﬃciency using plant-level
panel data. Section 3 describes the data we use, and section 4 demonstrates
the empirical results. Section 5 describes the model and the counterfactual
exercise. Section 6 concludes.

2

MethodThere are two conceptually diﬀerent types of measures of aggregate productivity growth suggested in the literature; one is proposed by Petrin andLevinsohn (2008) and the other is proposed by Bailey et al. (1992). First, we
explain the index proposed by Petrin and Levinsohn (2008), which we mainly
use in the data analysis. Second, we explain the other index by Bailey et al.
(1992), focusing on similarities and diﬀerences. We also explain that Petrin
and Levinsohn (2008) captures the reallocation eﬀect on the aggregate productivity growth more precisely than Bailey et al. (1992). Third, we explain
how we measure these continuous-time indexes using discrete-time data, andhow entry and exit eﬀects are captured in this setting. Finally, we explain
how we estimate production functions and unobserved productivity.

2.1

PL Aggregate Productivity Growth

Petrin and Levinsohn (2008) propose the following index, P Llevel , in a continuous time setting as aggregate productivity growth:∑∑∑dP Llevel :=dVi −Wik dXik ,
(1)
i

i

k

where dVi is the change in the real value added, Wik is the price of primary
input k, and dXik is the change in primary input k in plant i. Subscriptk ∈ {L, K} for primary inputs represents either labor hours, L, or capitalstocks, K.
In this way, aggregate productivity growth is deﬁned by the change inaggregate real value added minus the change in aggregate input cost. Since
the index is deﬁned in a continuous time setting, all variables are the functionsof time t. We suppress time index t in most cases, but sometimes explicitly
write it as a subscript, such as Vit .
4

Entrants (exiters) are considered as plants with zero variables before entry(after exit). Therefore, a variable may not be a continuous function of time,and may include jumps. For example, if plant i starts operating at time t∗ ,then value added in plant i, Vi , takes zero for all t < t∗ , and takes positive
values after t ≥ t∗ . In this setting, the sum of a variable over plants who
exist at a point of time is equal to the sum over∑ all plants, including those
who may not exist at the point of time. We use i as the sum over all plants
in the latter sense, and thus the domain of the summation does not changeover time.
We consider gross output production function of the Cobb-Douglas form
with plant-speciﬁc technical eﬃciency:
Yi = Ai Lβi L KiβK MiβM ,(2)where Ai is the level of technical eﬃciency, Li is the labor-hour input, Ki is
the real capital stock in plant i, and β’s are coeﬃcients for each input.
For each plant, the real value added, Vi , is calculated by subtracting realintermediate materials from real gross output, that is,
Vi := Pi Yi − PiM Mi ,where Pi is the gross output price, Yi is the real gross output, PiM is the priceof intermediate materials, and Mi is the real intermediate materials in planti.
To make it the growth rate, we divide∑ (1) by the sum of the real value
added over all plants, denoted by V = i Vi .
dP Llevel ∑ dVi ∑ ∑ Wik dXik
=
−
V
V
V
i
i
k
∑ Pi dYi ∑ P M dMi ∑ ∑ Wik dXik
i
=
−
−
,
V
V
V
i
i
i
k
∑ Pi dYi ∑ ∑ Wik′ dXik′
=
−
,
V
V
′
i
i

dP L :=(3)kwhere subscript k ′ ∈ {L, K, M } represents one of the primary and intermediate inputs with notations WiM := PiM and XiM := Mi . Thus, P L isan aggregate productivity growth measure in terms of a percentage to thecurrent aggregate real value added.
5

We transform diﬀerentials in (3) into log diﬀerentials after separating theentrants and exiters from the summation over i. For entrants and exiters, log
diﬀerentials such as d ln Yi are not well deﬁned because level variables suchas Yi are equal to zero before entry or after exit, while log of zero is not welldeﬁned or minus inﬁnity. Let S be the set of plants who operate and neither
enter nor exit at time t, and dN E be the eﬀect on aggregate productivity
growth of entry and exit of plants, which is speciﬁed later. Using the formulad ln Z = dZ/Z, (3) can be written as∑∑ ∑dP L =
Di d ln Yi −(4)sik′ d ln Xik′ + dN E,
Di
i∈S

i∈S

k′

where Di := Pi Yi /V is the Domar weight and sik′ := Wik′ Xik′ /Pi Yi is theratio of cost to gross output for input k ′ ∈ {L, K, M }. We explicitly discuss
the eﬀect of entering and exiting plants in subsection 2.3.
The log diﬀerential form, (4), has an advantage that we can decompose
P L and investigate the driving forces of aggregate productivity growth. As
is stated in Petrin and Levinsohn (2008), P L can be decomposed into thetechnical eﬃciency term and the reallocation terms. By substituting d ln Yi
in (4) with∑d ln Yi = d ln Ai +εik′ d ln Xik′ ,(5)k′which is the log diﬀerential of (2), we obtain∑∑ ∑dP L =
Di d ln Ai +Di
(εik′ − sik′ )d ln Xik′ + dN E,
i

i

(6)

k′

i
is the elasticity of output with respect to input k ′ ∈where εik′ := ∂X∂Yi′/Y
ik /Xik′{L, K, M }. In our Cobb-Douglas speciﬁcation, each εik′ is equal to βk′ in (2)for all plant i for k ′ ∈ {L, K, M }. Note that (6) holds for any estimates ofβ’s.
The ﬁrst term in the right hand side of (6) represents the eﬀect of technological improvement, which we call the technical eﬃciency term. The second
term is the reallocation term, which represents the eﬀect of resource reallocation across existing plants. It is the sum of the reallocation terms of each
input k ′ ∈ {L, K, M }. Each term is the weighted sum of time diﬀerentialof logged input. The weight, (εik′ − sik′ ), is the margin that captures the6

diﬀerence between marginal productivity and unit cost of the input. The
reallocation terms give us more information about the contribution of resource reallocation to aggregate productivity growth. For example, we can
ask how eﬀectively labor was reallocated compared with capital. We can also
ask which resource reallocation is induced the most due to a speciﬁc policychange.
We construct the technical eﬃciency term by estimating the residual productivity, Ai , for each plant. The estimation methods of the residual productivity will be discussed in the subsection 2.4. The decomposition (6) is
independent of the method used to estimate production function. Calculating P L itself does not require the estimation of unobserved productivity ofeach plant.

2.2

BHC Aggregate Productivity Growth

A widely used alternative deﬁnition of aggregate productivity growth is theone originally proposed in Bailey et al. (1992). In this subsection, we will
explain this type of index, focusing on similarities and diﬀerences comparedto P L. We will also explain that Petrin and Levinsohn (2008) captures
reallocation eﬀects more precisely than Bailey et al. (1992). Among many
versions of the measure, we use the version in Foster et al. (1998);∑∑
dBHC :=
Di d ln Ai +ln Ai dDi + dN E BHC .
(7)
i

i

The ﬁrst term captures changes in the technical eﬃciency , the second term
captures the reallocation eﬀect, and the third term, which is speciﬁed later,
captures the net-entry eﬀect. Calculating BHC requires the estimation ofunobserved productivity, Ai . Once we obtain an estimate of Ai , we cancalculate both the reallocation term and the technical eﬃciency term, andthen we get BHC.
As is shown in Petrin and Levinsohn (2008), the technical eﬃciency termof BHC is equal to the technical eﬃciency term of P L under the use of thesame weight, Di . That is, the two measures capture the technical eﬃciency
in the same way. Therefore, the diﬀerence lies in the reallocation term andthe net-entry term.
Each measure captures a diﬀerent aspect of resource reallocation. P L
increases if resource reallocation leads to more output and/or less input cost.
Namely, P L measures the current increase in output and/or decrease in7

input cost due to resource reallocation. On the other hand, BHC increases
if resources are reallocated to more productive plants from less productiveplants, in terms of plant-level productivity, Ai . That is, BHC measures the
distribution of resources to plants with diﬀerent levels of productivity.
P L is more precise than BHC in the sense that P L is based on themarginal revenue product of each input, whereas BHC is based on the totalfactor productivity of the plant where resources are allocated. P L always
increases in the case where market competition results in reallocation of
resources from plants with low marginal productivity to plants with highmarginal productivity, while BHC may or may not increase according to thetotal factor productivity of plants associated with the resource reallocation.
There are several examples where P L is more favorable than BHC.
Petrin and Levinsohn (2008) give an example of a neo-classical competitive setting where plants smoothly reallocate their resource according to themarginal revenue product. In such a case, the reallocation should not aﬀect
aggregate productivity in theory, and the reallocation term of P L always
takes zero, whereas that of BHC may take the value other than zero. For
another example, if the resource is reallocated from less productive plants
to more productive plants, then BHC will increase, even if such a reallocation may decrease output and/or increase input cost. This is the case whereplants with low productivity cannot increase their input up to the optimallevel, and end up with decreasing their input due to some kind of friction,such as credit constraint. P L will decrease in this case, while BHC will
increase.
Nonetheless, we also calculate BHC, as well as P L, because BHC gives
us information on the pattern of resource reallocation. If BHC increases,
then more resources are reallocated to plants with high levels of total factor productivity. Thus, we can infer the direction of resource reallocationin terms of productivity, Ai . This is why it is interesting to compare thereallocation terms of P L and BHC.

2.3

Approximation of Continuous-time Indexes

To measure these continuous-time indexes of aggregate productivity growth,
we approximate them by discrete-time indexes as is often the case for theDivisia index (See Hulten (2008)). First, we integrate the index with respect to time from t − 1 to t, and consider it as a ideal discrete-time index.
Next, we approximate the integral, i.e., the ideal discrete-time index, by
Tornqvist approximation(See Appendix A for a detail description, and also8

Hulten (2008)). Therefore, as to (4), we obtain
∫ t
dP L

=

∫ t ∑

Di d ln Yi −∫ t ∑t−1 i∈S

t−1≅∑

t−1 i∈S

Dit ∆ ln Yit −

i∈S

D

∑

Dit

s

′

+s

∫ t
dN E

sik′ d ln Xik′ +

k′

∫ t

sik′ t ∆ ln Xik′ t +

t−1

dN E,

(8)

t−1

k′

i∈S

+D

∑

Di

∑

′

where Dit := i,t−12 it , sik′ t := ik ,t−12 ik t , and ∆ ln Zit := ln Zit − ln Zi,t−1
for Zi = Ai or Xik′ for k ′ ∈ {L, K, M }.
So far, we put aside the issue with entrants and exiters in measuring
aggregate
productivity growth, which is captured by the last term of (8),∫ti.e., t−1 dN E. In theory, entry and exit of plants create a jump in theaggregate productivity growth measure since we employ a continuous time
setting. We explain as follows how these jumps in a continuous time setting
will be captured by an approximated integral in a discrete time setting.
First, we integrate (3) from time t − 1 to t to obtain the ideal discretetime index. Next, after exchanging the order of the integral and the sum overall plants, we split the sum into the sums over three sets of plants: stayers,
entrants, and exiters2 . Thus, we obtain
∫ t
dP L
t−1

[
]
∑ ∫ t Pi dYi ∑ ∫ t Wik′ dXik′
=
−
V
V
t−1
t−1
i
k′
[∫
]
∫
t
∑
Pi dYi ∑ t Wik′ dXik′
=
−
V
V
t−1
t−1
i∈St
k′
[∫
]
∫
t
∑
Pi dYi ∑ t Wik′ dXik′
+
−
V
V
t−1
t−1
i∈Et
k′
[∫
]
∫
t
∑
Pi dYi ∑ t Wik′ dXik′
+
,
−
V
V
t−1
t−1
′
i∈Xt−1(9)kwhere St is the set of plants who operate throughout the period from timet − 1 to time t, Et the set of entrants who do not operate at time t − 1 but
start operating between time t − 1 and time t, and Xt−1 the set of exiters
who operate at time t − 1 but quit operating between
time t − 1 and time t.
∫t
The sum of the last two terms are denoted by t−1 dN E in (8).
2

In fact, every plant belongs to one of the four sets of plants: plants who keep operatingfrom time t − 1 to time t, plants who are not operating at time t − 1 but starting at somepoint before time t, plants who are operating at time t − 1 but quitting at some point
before time t, and plants who are not operating throughout the period from time t − 1 totime t. The sum of any variable over the plants in the forth category is equal to zero.

9

Next, we approximate the integral under a reasonable assumption addressed in detail in Appendix A. For the ﬁrst term in (9), we apply the
Tornqvist approximation as we discussed above. For the rest of terms, weapproximate them by ignoring the reasonably small terms. Finally, we obtain∫ t∑

dP L ≅

L
AP GP
:=
t
t−1

Dit ∆ ln Yit −

i∈St

+

∑

∑

Dit

i∈St

[
Dit 1 −∑∑]

sik′ t −k′i∈Etsik′ t ∆ ln Xik′ t

k′

∑

[
Di,t−1 1 −∑]sik′ ,t−1 .

k′i∈Xt−1(10)

We refer to the last two terms in (10) as entry and exit eﬀects, respectively.
Note that we do not need to estimate production function when we use (10)to measure AP GPt L . Thus, the measurement of AP GPt L does not require toestimate unobserved productivity of plants.
By applying decomposition (6), equation (10) becomes
L
AP GP
t

≅

∑
i∈St

+

∑

Dit ∆ ln Ait +

∑

Dit

i∈St

[
Dit 1 −∑]

k′sik′ t −

k′

i∈Et

∑
(εik′ − sik′ t )∆ ln Xik′ t∑[Di,t−1 1 −∑]sik′ ,t−1 .

(11)

k′

i∈Xt−1

We use (11) to measure the decomposed parts of aggregate productivity
growth. At this point, we use the estimates of unobserved productivity andelasticity to measure each term of the decomposed AP GPt L .
Similarly, BHC is also measured as the integral from time t − 1 to t.
Therefore, AP GBHC
is deﬁned as follows.
t∫ t

AP GBHC
:=
t

dBHC
t−1

=

∑

Dit ∆ ln Ait +

i∈St

+

∑

ln Ait ∆Dit

i∈St

[Dit ln Ait ] −

i∈Et

ln A

∑

∑

[Di,t−1 ln Ai,t−1 ] ,(12)i∈Xt−1

+ln A

i,t−1
it
where ln Ait :=. Note that equation (12) is not an approxima2
tion, but an identity, since the form of BHC allows us to exactly calculate
the integral.

2.4

Production Function Estimation

Our estimation procedure consists of two steps: plant-level estimation ofunobserved technical eﬃciency, and aggregation of those estimates over all
10

plants. Speciﬁcally, decomposing P L and calculating BHC require the ﬁrst
step, that is, the estimation of the plant level technical eﬃciency Ai and theelasticities εik . By taking log of both sides of (2), we haveln Yit = βL ln Lit + βK ln Kit + βM ln Mit + ln Ait .

(13)

We estimate the logged production functions industry by industry, by assuming that there is no correlation in error terms between any two industries.
We use the 2nd digit sic code in categorizing industries.
There are many ways to obtain an unbiased estimates of βs, depending the assumption on the error term, ln Ait . The argument on endogeneity
problem in the production function estimation is well discussed in Griliches
and Mairesse (1995). In this paper, we estimate (13) with the WooldridgeLevinsohn-Petrin (WLP) estimator as our benchmark. To see how the measures are sensitive to estimation methods, we also estimate them using othermethods such as the pooled OLS.
The assumption on ln Ait behind the WLP estimator isln Ait = νit + eit(14)

where νit is the unobserved productivity, and eit is the shock which is assumed
to be conditional-mean independent of current and past inputs. According
to Levinsohn and Petrin (2003), we assume that there exists a time-invariant
function g(·) such that νit = g(ln Kit , ln Mit ).
In order to identify β = (βL , βK , βM )′ , we assume
E[eit |xit , · · · , xi1 ] = 0
E[νit | ln Kit , xi,t−1 , · · · , xi1 ] = E[νit |νi,t−1 ]

(15)
(16)

where xit := [ln Lit ln Kit ln Mit ]′ . Also, we assume there exists a timeinvariant function f (·) such that E[νit |νi,t−1 ] = f (νi,t−1 ).
Deﬁne the innovation in νit ;ait := νit − E[νit |νi,t−1 ].

(17)

The equation (16) means that ln Kit , xi,t−1 , and all functions of these areuncorrelated with ait . Note, however, that ln Lit is allowed to be correlatedwith ait . Then, putting the assumptions into the equation (13) gives thefollowing estimation equation;ln Yit = βL ln Lit + βK ln Kit + βM ln Mit + f [g(ln Ki,t−1 , ln Mi,t−1 )] + uit ,(18)11where uit := ait + eit .
We non-parametrically estimate the two functions g(·) and f (·). For g(·),
we use the 3rd order polynomial. For f (·), we use the 1st order polynomial,that is a linear function. One reason for these choices is a computational
advantage that we can estimate (18) by linear GMM. Another reason is thathigh order polynomial regression leads to collinearity problems.
Since ln Lit and ln Mit can be correlated with ait , we need instruments
for them. Recall that ln Kit , xit−1 , and all functions of these are uncorrelated with ait by (16). Therefore, we use ln Li,t−1 , ln Li,t−2 , and ln Mi,t−2 as
instruments.

3

Data

We use plant-level panel data on Japanese manufacturing sector for the period 1981-2000. The panel data is compiled from the annual Census of Manufactures, which covers all plants in the manufacturing sector that hire 4
or more employees.3 The Census of Manufactures contains information on
shipments, number of employees, the book value of tangible ﬁxed assets, thewage bill, and other values. The census consists of two parts; one covers
all manufacturing plants with more than 30 employees (Part A) and othercovers those with 4-29 employees (Part B).4 There are about 50,000 plants
in Part A and about 550,000 plants in Part B in each year.
In this paper, we use Part A and B of the period 1981-2000 because
Part B of the Census of Manufactures stopped asking the book value oftangible ﬁxed assets in 2001. There are 8,149,190 plant-year observationsin this period. We dropped plants that did not provide information on thebook value of tangible ﬁxed assets and plants that report zero wage bill andintermediate inputs. This treatment reduced 4,828,041 observations, mainly
due to the lack of information on the book value of tangible ﬁxed assets. As
a result, there remain 3,321,149 observations in our sample.
3

The construction of the panel data from the Census of Manufactures data was a partof the RIETI project named “Study on industry and ﬁrm level productivity in Japan”.
Since the census data are not stored in a panel format, the project converted them into
panel data by assigning a relevant identiﬁcation number to each plant.
4Part A is called “Kou Hyo” and Part B is called “Otsu Hyo” in Japanese. The
manufacturing plants with 1-3 employees are also surveyed in the years ending in 0,3,5,
and 8. However, the data on these small plants are not publicly available and were nottreated in the RIETI project, either.

12All nominal output and input variables are available at plant level. The
nominal output is deﬁned as the sum of shipments, the revenue from repairing and ﬁxing services, and revenues from performing subcontracted work.
The real output is deﬁned as gross output deﬂated using sectoral output
deﬂators derived from the JIP 2008 (2000 base index).5 The nominal intermediate inputs are deﬁned as the sum of the material, fuel, and electricity
expenditures and subcontracting expenses for consigned production used by
the plant. Intermediate inputs are deﬂated by the intermediate input deﬂators provided in the JIP 2008 (2000 base index). Labor input is obtained bymultiplying the number of employees by the sectoral working hours from theJIP 2008. The real value of capital stock is obtained by deﬂating the nominal book value of capital stock with an industry-level price index of capital.
The nominal book value is the beginning period book value of tangible ﬁxed
assets including buildings, machinery, tools and transport equipment. The
industry-level price index of capital is calculated by dividing the sum of thenominal book values in the industry by the industry’s real net capital stock,which is obtained from JIP 2008.

4

Results

Our estimation results reveal a sharp contrast between the pattern of APG
during the 1980s and 1990s in the Japanese manufacturing sector. We document three main ﬁndings in comparison of the 1980s and the 1990s. In
addition, we examine the sensitivity of the main ﬁndings to the estimation
method used in productivity estimation. All main ﬁndings are fairly robust
to diﬀerent estimation methods, with a few exceptions.

4.1

Main Findings

We summarize the estimation results in three main ﬁndings. First, the estimated APG considerably dropped on average from the 1980s to the 1990s.
5The JIP 2008 Database was compiled as part of a RIETI research project. The
database contains annual information on 108sectors, including 56 non-manufacturing sectors, from 1970 to 2005. These sectors cover the whole Japanese economy. The databaseincludes detailed information on factor inputs, annual nominal and real input-output tables, as well as some additional statistics, such as Japan’s international trade by trade
partner, inward and outward FDI, etc., at the detailed sectoral level. An Excel ﬁle versionof the JIP 2008 Database is available on RIETI’s web site.

13

Second, all three components, i.e., the technical eﬃciency, reallocation, andnet-entry terms, became lower on average in the 1990s than in the 1980s.
Third, there was a huge drop in the labor reallocation term on average inthe 1990s, which contributed the most to the negative reallocation eﬀect in
the 1990s. In this subsection, we document these ﬁndings as well as explain
the main events during the 1980s and the 1990s.
The ﬁrst column of Table 1 shows the estimated AP GPt L . In the 1980s,
AP GPt L always took positive values and had an increasing trend until thelate 1980s. However, it started decreasing in 1989 and turned to be negativein 1992-93 and 1998-99. The average of AP GPt L in the 1990s was much lower
than in the 1980s: 4.99% in the 1980s and 1.38% in the 1990s. Japan’s
economy was in an economic slump during the 1990s.
The movement of AP GPt L agrees with what happened in Japan. In 1985,
when the G5 countries agreed to intervene in currency markets to depreciate
the overvalued U.S. dollar (the Plaza agreement), Japan went in a recession
due to the acute devaluation of the U.S. dollar against the Japanese yen.
The expansionary monetary policy issued in the following years boosted theeconomy, but it led to the Japanese asset price bubble during 1987-89. The
estimated AP GPt L took a relatively lower value in 1985 and rapidly increasedin the late 1980s.
The bubble’s collapse started in 1990 with a plunge in stock, land, andbuilding values. The estimated AP GPt L started decreasing in 1989 and tuned
to be negative in 1992-93. In 1997, the government decided that the economy
started recovering and increased taxes in April. However, the Asian ﬁnancial
crisis occurred in the summer and a series of failures of ﬁnancial institutions
occurred in the winter. The estimated AP GPt L took negative values again
during 1998-99.
Columns 2-4 show the decomposed terms of AP GPt L ; the technical eﬃciency, reallocation, and net-entry terms. This decomposition is based onequation (11) and shows the main sources of aggregate productivity growth.
In most of the years, technical eﬃciency contributed the most to APG andreallocation of resources had the second largest impact on APG.
The growth rates of all terms became lower in the 1990s than in the 1980s.
For example, the average technical eﬃciency term became less than a halfin the 1990s: 4.72% in the 1980s and 2.31% in the 1990s. The reallocation
term was always negative except for the bubble period, 1987-1991, and took
large negative values in 1992-94 and in 1998-99. Also, we ﬁnd that net-entry
eﬀect was almost always positive in the 1980s, but tend to be negative after14

Table 1: PL Aggregate Productivity and Its Decomposition
year

PL
APG

1982
3.19
1983
3.57
1984
5.03
1985
3.10
1986
3.42
1987
5.60
1988
8.54
1989
7.44
1990
5.31
1991
3.35
1992
-1.27
1993
-2.85
1994
1.53
1995
4.67
1996
3.85
1997
2.83
1998
-2.01
1999
-1.60
2000
5.63
1980s Average 4.99
(Std. dev.)(2.08)
1990s Average 1.38
(Std. dev.)(3.05)

Technical
Eﬃciency

Reallocation

Net-Entry

3.02
4.14
5.64
3.03
2.85
5.39
7.43
6.25
4.84
3.03
0.44
-0.78
3.32
4.59
3.66
3.44
-0.70
1.24
5.87
4.72
(1.71)
2.31(2.09)

-0.57
-0.50
-1.05
-0.36
-0.82
0.10
0.94
0.82
0.02
-0.07
-1.68
-1.68
-1.06
-0.04
0.14
-0.38
-1.61
-2.15
0.19
-0.18
(0.74)-0.85(0.88)

0.74
-0.07
0.45
0.43
1.38
0.11
0.17
0.37
0.45
0.39
-0.02
-0.39
-0.73
0.13
0.04
-0.23
0.30
-0.69
-0.42
0.45
(0.45)-0.07(0.42)

the collapse of the asset bubble.
The ﬁnding that reallocation eﬀect deteriorated during the 1990s is different from what was reported in Fukao et al. (2006). They ﬁnd that reallocation eﬀect was stronger in the 1990s using the BHC deﬁnition. We also
conﬁrmed this BHC ﬁnding using our sample; the BHC reallocation termincreased on average from −7.48% in the 1980s to −1.87% in the 1990s.6
6

However, we also ﬁnd that the BHC reallocation term is much more volatile than the
PL reallocation term. The standard deviation of the BHC reallocation term (9.62) is morethan 10 times larger than that of the PL reallocation term (0.86). Therefore, we have to
be careful in comparing the averages of the BHC reallocation terms.

15This diﬀerence comes from the diﬀerent measures of reallocation eﬀect.
The BHC reallocation measures the contribution of input reallocation basedon the level of productivity, ln Ait . If inputs are reallocate from a lower
ln Ait plant to a higher ln Ajt plant, the BHC reallocation term count it aspositive contribution∑
to aggregate
productivity. On the other hand, the PL∑
reallocation term is i Di k′ (εik′ − sik′ )d ln Xik′ . If inputs are reallocatedfrom a plant with a lower margin, εik − sik , to a plant with a higher margin,
εjk − sjk , then the PL reallocation term count it as positive contribution
to aggregate productivity. Recall that the margin captures the diﬀerence
between marginal productivity and unit cost of the input.
To further investigate the negative PL reallocation term, we break it down
into three terms by input: labor, capital stock, and intermediate materials.
The estimates of the decomposed terms are reported in Table 2. On average,
the contribution of labor and intermediate material reallocation decreased in
the 1990s, whereas the contribution of capital reallocation slightly increased.
Among them, the fall in the labor reallocation term was sizable: 0.02% in
the 1980s and -0.66% in the 1990s.
Table 2 also shows that reallocating input did not always positively contribute to APG. The capital reallocation term was negative in most of theyears although its magnitude was small. Growth generated by labor reallocation was positive in the late 1980s, but it became negative in the 1990s.
Especially, the negative growth from labor reallocation largely contributed
to the low APG in the 1990s. The contribution of material reallocation was
positive in the late 1980s and the early 1990s. The standard deviation of theintermediate material reallocation term is fairly large in spite of the small
magnitude of its mean.
Now the question is why resource reallocation negatively contributed to
APG. If input markets were functioning well, inputs should have been reallocated from plants whose wedge was negative to those with positive wedge.
Therefore, we expect that reallocating inputs always generate positive aggregate productivity growth. The negative reallocation eﬀect implies that
resource reallocation was not well functioning in Japan’s manufacturing sector.
As a possible reason for the negative reallocation eﬀect, we will investigate the eﬀect of misdirected bank lending in Section 5. Caballero et al.
(2008) show the wide-spread practice of Japanese banks of providing subsidized credit to otherwise insolvent ﬁrms. They also argue that this “zombie
lending” deteriorated eﬃciency of resource reallocation. Peek and Rosengren
16

Table 2: Decomposition of Reallocation Eﬀect
year

Reallocation

1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
1980s Average(Std. dev.)
1990s Average(Std. dev.)

-0.57
-0.50
-1.05
-0.36
-0.82
0.10
0.94
0.82
0.02
-0.07
-1.68
-1.68
-1.06
-0.04
0.14
-0.38
-1.61
-2.15
0.19
-0.18
(0.74)-0.85(0.88)

Decomposition
Labor Capital Materials

-0.53
-0.36
0.19
0.78
-0.57
-0.62
0.39
0.85
0.11
0.30
-0.80
-1.36
-1.22
-0.65
-0.32
-0.10
-0.89
-1.62
-0.82
0.02
(0.61)-0.66(0.65)

-0.04
-0.20
-0.32
-0.22
-0.29
-0.29
-0.13
-0.10
-0.06
-0.22
-0.44
-0.43
-0.18
0.11
-0.01
-0.14
-0.05
-0.02
0.02
-0.20
(0.10)-0.14(0.18)

0.00
0.06
-0.92
-0.91
0.04
1.01
0.68
0.07
-0.03
-0.15
-0.45
0.12
0.35
0.50
0.47
-0.14
-0.67
-0.50
0.98
0.00
(0.67)-0.05(0.41)(2005) also document the misallocation of credit in Japan. In section 5, we
measure the distortion of zombie lending in reallocation eﬀect, using a modelwith plant-level heterogeneity of technical eﬃciency.
Figure 1 shows the stacked column of all terms so that we can compare
the contributions of each source. In Figure 1, it is clear that the largest sourceof APG was technical eﬃciency. The high growth of aggregate productivity
in the 1980s was mainly explained by the high growth of technical eﬃciency.
We also ﬁnd that technical eﬃciency growth was volatile during the 1990s.
There were two troughs in 1992-93 and 1998-99.
The growth from net-entry was positive in the 1980s, but it tended to be17

Figure 1: Aggregate Productivity Growth and Its Decomposition.
negative in the 1990s. If we look at entry and exit terms respectively, we canﬁnd that the negative net-entry eﬀect was mainly explained by the decreasein the entry eﬀect. In the 1990s, entries of new plants did not bring growth
in productivity enough to cover the loss from exit.

4.2

Sensitivity Analysis

The estimation of APG consists of two stages: estimation of unobserved productivity for each plant, and aggregation over all plants. In this subsection,
we demonstrate how the aggregation results change in the second stage if we
use a diﬀerent method in the ﬁrst stage.
First of all, our ﬁndings on AP GPt L and the net-entry eﬀect are independent of the method used in productivity estimation. They are estimatedwithout using productivity or elasticity estimates. The ﬁndings on technical eﬃciency and reallocation terms are aﬀected by the choice of estimation
methods in the ﬁrst stage. Therefore, the ﬁrst main ﬁnding will be unchanged and the second and third main ﬁndings can possibly be changed
if we use a diﬀerent estimator in productivity estimation. The results from18

diﬀerent estimators show that both main ﬁndings are still observed with afew exceptions.
Our choice of diﬀerent estimation methods is a variation of regressiontype methods along the line with the base line proxy estimation. On estimation methods of productivity using panel data, Biesebroeck (2003) surveys
ﬁve estimation methods and concludes that those ﬁve ways of measuring
plant-level productivities are consistent in a sense that their estimates arehighly correlated and give similar insights on the major topics on productivity. Biesebroeck (2004) also shows by Monte Carlo simulation that proxyestimation, introduced by Olley and Pakes (1996) and modiﬁed by Levinsohn and Petrin (2003) and Wooldridge (2005), is the most accurate androbust to measurement errors among proposed ﬁve estimators. This is why
we use a proxy estimation method, the Wooldridge-Levinsohn-Petrin (WLP)
estimator, in our base line results.
We show the results from four other estimation methods: the pooled
OLS estimator (OLS), the ﬁxed-eﬀect estimator (FE), the ﬁrst-diﬀerences
estimator (FD), and the second-diﬀerences estimator (SD). Consistency ofeach estimator depends on the assumption on unobserved productivity νitin (14). We also show the results from the TFP estimator used in Fukao etal. (2006), with abbreviation (FKK). We brieﬂy explain the advantage anddisadvantage for each estimator.
OLS is one of the simplest methods to estimate (13). If plants choose labor inputs Lit and intermediate materials Mit without knowing unobserved
productivity νit , there is no endogeneity problem and thus OLS leads toconsistent estimates. However, if plants choose Lit and Mit after knowing
νit , OLS leads to inconsistent estimates due to the endogeneity of labor inputs and intermediate materials with unobserved productivity. Since ﬁrms
observe their productivity even though they are unobserved for econometrician, ﬁrm’s decision on labor inputs and intermediate materials should bepositively correlated with their productivity.
FE and FD resolve the endogeneity problem if νit is constant over timefor each plant, i.e.,νit = νi0 ,∀t = 1, . . . , T.

(19)

For consistency, FE requires the strong exogeneity assumption that regressors at time t must be uncorrelated with eiτ for all τ = 1, . . . , T . FD requiresa relatively weak exogeneity assumption. That is, regressors at time t must19

be uncorrelated with eit and ei,t−1 . However, we discard many variations indata by taking the ﬁrst diﬀerence of all variables. FE also discards variations by taking the mean deviation of regressors. Such data transformations
may deteriorate possible attenuation bias due to measurement errors, as is
discussed in Griliches and Mairesse (1998). In addition, as for FD, the diﬀerencing transformation may deteriorate the attenuation bias due to positive
autocorrelation in regressors in panel data (See Cameron and Trivedi (2005)
for example).
SD resolves the endogeneity problem if νit grows over time at a plantspeciﬁc constant rate, i.e.,∀νit = νi0 + ηi · t,

t = 1, . . . , T,(20)

which includes (19) as a special case with ηi = 0. For consistency, SD
requires that regressors at time t must be uncorrelated with ei,t−2 , ei,t−1 , andei,t . By taking the second diﬀerence of variables, we discard more variations
in regressors than in the case of FD.
Finally, we show the results from FKK to compare our results with theones in Fukao et al. (2006). FKK assumes that the output elasticities of each
input varies across plants and are equal to the cost shares for each plant. See
Fukao et al. (2006) for a detailed explanation. Note that the TFP estimatesin Fukao et al. (2006) are not exactly the same as the ones used in this paper
due to slight diﬀerences in the samples and deﬂator.
Table 3 summarizes the results in production function estimates by estimators. Since we estimate production functions by industry, we report theindustry averages of the coeﬃcients and the standard errors. The estimatesof returns to scale are almost equal to one for WLP and OLS, a little lessthan one for FE, and near to a half for FD and SD. The low estimates for FD
and SD can be attributed to the attenuation bias deteriorated by the loss ofvariations in regressors due to diﬀerencing transformations.
Tables 4 and 5 summarize the results by estimation method. Since theﬁrst main ﬁnding, that is, the fact that AP GPt L declined on average fromthe 1980s to the 1990s, remains the same across diﬀerent estimators, we only
show the results associated with the second and third main ﬁndings. We
omit the estimates of the net-entry eﬀect since they are the same acrossestimators.
Table 4 shows the averages of the technical eﬃciency and reallocation
terms in the 1980s and the 1990s, by estimation method. According to20

Table 3: Production Function Estimates by Method
MethodCoeﬃcients
Labor Capital Materials

Returns
To Scale

WLP

0.305
(0.009)0.037(0.004)0.617(0.026)

0.959

OLS

0.420
(0.008)0.096(0.003)0.522(0.005)

1.038

FE

0.368
(0.011)

0.069(0.003)0.399(0.007)

0.836

FD

0.296
(0.010)0.022(0.003)0.279(0.007)

0.597

SD

0.204
(0.013)0.011(0.003)0.246(0.008)

0.461

FKK

-

-

-

-

Standard errors are reported in parentheses. Our benchmark is WLP.
All values are the averages over industries.

Table 4, the second main ﬁnding is robust to estimation methods, except forthe decline in the reallocation term. The ﬁrst two columns show that thetechnical eﬃciency term declined on average from the 1980s to the 1990s forall estimates. Columns 3-4 show that the PL reallocation term also declined
for the WLP, OLS, and FKK estimates, whereas it increased for the FE, FD,
and SD estimates. Since the FD and SD estimates are much more volatile
than the others, the increase in the reallocation term for FD and SD may
result from ampliﬁed attenuation bias due to diﬀerencing transformations.
The last two columns in Table 4 show the averages of the BHC reallocation
term by estimators. All the estimates increased on average from the 1980s
to the 1990s. The implication on the reallocation eﬀect diﬀers across the two
measurement ways; it was increased in the BHC way, but decreased in the
PL way. This fact is observed for the WLP, OLS, and FKK estimates.
Table 5 shows the averages of the decomposed reallocation terms in the
1980s and the 1990s, by estimation method. Columns 1-2 show that the21Table 4: Technical Eﬃciency and Reallocation Terms
by Estimation Method
MethodTechnical Eﬃciency
1980s
1990s

PL Reallocation
1980s
1990s

BHC Reallocation
1980s
1990s

WLP

4.72
(1.71)

2.31(2.09)-0.18(0.74)-0.85(0.88)-7.48(10.94)-1.87(7.17)

OLS

4.40(2.99)

2.43(2.78)

0.14(1.08)-0.97(1.10)-0.97(1.63)-0.24(1.52)

FE

5.37(4.81)

2.11(3.93)-0.83(2.89)-0.66(1.40)-20.99(20.78)-1.83(11.14)FD

7.23(6.50)

2.34(5.23)-2.69(4.59)-0.89(2.57)-42.17(39.75)-4.75(19.93)SD

7.68(7.19)

1.99(5.86)-3.14(5.29)-0.53(3.15)-52.51(52.05)-6.61(26.93)FKK

4.17(1.75)

2.95(1.20)

0.37(1.81)-1.50(2.15)

0.28(0.32)

0.33(1.47)

Standard deviations are reported in parentheses. Our benchmark is WLP.

labor reallocation term declined on average from the 1980s to the 1990s forall estimation methods. The decline was large, except for the SD estimate.
For WLP and OLS, the decline in the labor reallocation eﬀect contributed
the most to the decline in the whole reallocation eﬀect in the 1990s. For
FE, the decline in the labor reallocation eﬀect was large, but oﬀset by thematerial reallocation eﬀect. For FD and SD, the increase in the capital andintermediate material reallocation eﬀects exceeded the decline in the labor
reallocation eﬀect, and the whole reallocation eﬀect increased in the 1990s
as in Table 4. Therefore, as to the third main ﬁnding, the labor reallocationeﬀect robustly decreased, but was not necessarily the main driving force of
the average change in the reallocation term from the 1980s to the 1990s.

22

Table 5: Decomposed Reallocation Terms by Estimation Method
MethodLabor
1980s 1990s

Capital1980s 1990s

Materials
1980s 1990s

WLP

0.02
(0.61)-0.66(0.65)-0.20(0.10)-0.14(0.18)

0.00(0.67)-0.05(0.41)

OLS-0.00(1.14)-1.22(1.19)

0.80(0.35)

0.30(0.40)-0.66(1.54)-0.05(0.74)

FE-0.05(0.89)-0.92(0.89)

0.51(0.26)

0.18(0.29)-1.29(3.30)

0.08(1.76)

FD

0.09(0.78)-0.74(0.80)-0.43(0.10)-0.24(0.27)-2.35(5.10)

0.09(3.09)

SD

0.12(0.41)-0.30(0.41)-0.63(0.14)-0.33(0.35)-2.63(5.61)

0.10(3.46)

FKK

-

-

-

-

-

-

Standard deviations are reported in parentheses. Our benchmark is WLP.

5

Eﬀect of Zombie Lending

We measure the impact of misdirected lending, so-called “zombie lending”,
on the negative labor reallocation eﬀect observed in Japan in the 1990s.
We develop a version of the model with plant-level heterogeneity provided
by Restuccia and Rogerson (2008) and conduct a counterfactual exercise.
The exercise shows that the decline in labor reallocation eﬀect due to the
distortion of zombie lending is 37% of the negative labor reallocation eﬀect
observed in the data.

5.1

Model

There are a mass of plants and one inﬁnitely-lived representative householdin the economy. The plants produce the same goods using labor, capital,
and intermediate input. They diﬀer only in the level of technical eﬃciency

23

(TFP). TFP of a plant i is modeled as follows;
Ait = Ai × At ,where Ai ∼ h(A), and At = γ t A0 ,where h(·) is the density of the idiosyncratic component of TFP, Ai .
There is an unlimited mass of potential entrants and they can enter themarket by paying a ﬁxed cost ce . After a new plant pays the cost, theidiosyncratic component of TFP Ai is revealed and it remains constant overtime. Plants exit from the market at a probability λ ∈ (0, 1).
Each plant faces diﬀerent tax or subsidy rates on capital and labor. Thesetaxes capture the government policy behind the zombie lending. The plantlevel tax rates are revealed when Ai is. The probability that a plant with Ai
faces a set of tax rates τ := (τ k , τ l ) is denoted by P(Ai , τ ). The joint densityof (Ai , τ ) is g(Ai , τ ) := h(Ai )×P(Ai , τ )11−βSince Ait grows at the rate γ, we detrend variables by At k in orderto make the economy stationary. The detrended variables are denoted withtilde, x̃.
Household Problem:max{C̃t ,K̃t+1 }∞
t=0

s.t.

∞
∑

∞
∑

β t u(C̃t )t=0

pt (C̃t + γ K̃t+1 − (1 − δ)K̃t ) =∞∑pt (rt K̃t + w̃t Lt + Π̃t + T̃t )

t=0

t=0

K0 is given, and Lt = 1 for ∀t.
where β ∈ (0, 1) is the time discount factor, C̃t is consumption at time t, K̃t
is capital at the beginning of period t, Lt is labor supply, pt is the time zero
price of consumption at time t, w̃t and rt are the period t rental prices oflabor and capital measured relative to period t consumption, δ ∈ (0, 1) is thecapital depreciation rate, Π̃t is the total proﬁt from all operating plants, andT̃t is the lump-sum transfer. Note that the household does not get utility
from leisure and thus Lt always equals to 1.
Existing Plant’s Problem:
}
{
βk βl
k
l
π(Ai , τi ) := max Ai k̃i li − (1 + τi )w̃t li − (1 + τi )rt k̃i − c̃f ,l,k≥0βk , βl ∈ (0, 1),

0 < βk + βl < 124where c̃f is a ﬁxed cost of operation measured in units of output.7
The policy functions are as follows:k̄˜(Ai , τi ) =((¯l(Ait , τi ) =

βk
rt
βk
rt

1−βl
) 1−β
(
−β
l

k

)−1 (

βl
w̃t

)

βl
w̃t

) 1−ββl−βlk11−βl −βkAi,k̄˜(Ai , τ ).

Entering Plant’s Problem:
We :=∑(Ai ,τ )max {χ̄(Ai , τ )W (Ai , τ ) − c̃e } g(Ai , τ )χ̄∈{0,1}

where χ̄(A, τ ) is the optimal entry decision which takes 1 (enter) or 0 (notenter). c̃e is a ﬁxed entering cost measured in units of output, and W (A, τ )denotes the discounted present value of an existing plant;
W (Ai , τi ) :=π(Ai , τi )1−ρ1−λwhere ρ := 1+R, λ is the exogenous exit rate, and R := r − δ.

Distribution of Plants: Let µ(Ai , τ ) be the distribution of operating plants
over (Ai , τ ). Then, its law of motion isµ′ (Ai , τ ) = (1 − λ)µ(Ai , τ ) + χ̄(Ai , τ )g(Ai , τ )E
where E is the mass of entering plants.
We can now deﬁne a steady-state competitive equilibrium.
Equilibrium: A steady state competitive equilibrium in the detrended economy is prices (w̃, r̃), a lump-sum transfer T̃ , a invariant distribution of plantsµ(Ai , τ ), a mass of entry E, value functions (W (Ai , τ ), π(Ai , τ ), We ), policy
functions (χ̄(Ai , τ ), k̄˜(Ai , τ ), ¯l(Ai , τ )), and aggregate variables (C̃, K̃) suchthat:
7

Note that the value added production function exhibits decreasing returns to scale.
This is a key assumption for a single-good model to allow plants with diﬀerent levels oftechnical eﬃciency co-exist in equilibrium.

25

1(1) (HH optimization) r = β̃1 − (1 − δ), where β̃ := β/γ 1−βl .
(2) (Plant Optimization) Given prices, value functions solve existing and entering plant’s problems and policy functions are optimal,(3) (Free Entry) We = 0,(4) (Market Clearing)∑¯l(Ai , τi )µ(Ai , τi ),1=(Ai ,τi )∑K̃ =k̄˜(Ai , τi )µ(Ai , τi ),(Ai ,τi )C̃ − (1 − δ − γ)K̃ + c̃e E =∑(Ai k̄˜βk ¯lβl − c̃f )µ(Ai , τi ),(Ai ,τi )(5) (Government Budget Constraint)
}
∑ {
l
k ˜
¯
τi w̃t l(Ai , τi ) + τi rt k̄ (Ai , τi ) µ(Ai , τi )T̃ =(Ai ,τi )(6) (Invariant Distribution)µ(A, τ ) = E

5.2

χ̄(A, τ )g(A, τ ),λ∀(A, τ ).

Calibration

We let one model period correspond to one year and assign 6% to R, implying
β = 0.994. As in Restuccia and Rogerson (2008), we set ce = 1.0, cf = 0.0,
and λ = 0.1. We assign 0.11 to δ so that the capital-output ratio in themodel becomes equal to aggregate capital over aggregate value added in the
manufacturing sector.
As Restuccia and Rogerson (2008) discussed, the most important parameter for a quantitative analysis of reallocation eﬀect is the extent of decreasing
returns to scale at plant-level because it aﬀects the magnitude of reallocationeﬀect. In order to obtain the extent of decreasing returns, we estimate thevalue-added production function by WLP, assuming the common production
function across industries. Then, the estimates can be directly used as thevalues of βs and TFP. The resulting values of β’s are βk = 0.10 and βl = 0.52.
26

Figure 2: Cumulative Distribution of Plant-level TFP Estimates in 1989.
Manufacturing plants in Japan. Estimated by the WLP method, assuming a common
value-added production function for all plants. The data less than 1%-tile and more than
99%-tile are trimmed. Normal c.d.f. shows a normal distribution function with the samemean and variance as the data.

As for h(A), which is the density of the idiosyncratic component of TFP,
we approximate the distribution of the estimated plant-level TFP, shown in
Figure 2, with 20 grid points. As Restuccia and Rogerson (2008) discussed,
h is a key determinant of the magnitude of distortion. The direct use of theestimates is our advantage.

5.3

Quantitative Analysis

If banks provided subsidized credits to the zombie plants (which we call“zombie lending”), it would deteriorate eﬃciency of resource reallocation. In
this subsection, we measure the distortion of such lending in each reallocation
term.
We assume that Japan’s economy was in diﬀerent steady states in 1989
and 1999. The steady state in 1989 was associated with γ = γ89 (=4.72%)
and another steady state in 1999 was associated with γ = γ99 (=2.31%). We
27

assume that the detrended economy attained the capital stock in the newsteady state in 1990 and that the original economy grew at the rate of γ99 .8
We deﬁne a zombie plant as a plant whose TFP has fallen below the 20th
percentile of the TFP distribution for 5 consecutive years. We assume thatzombies and nonzombies faced diﬀerent tax rates during the 1990s while they
didn’t during the 1980s.9 The diﬀerent tax rates during the 1990s captured
subsidized credits to the zombie plants because a plant faced lower eﬀective
rental rates if it received subsidized credit. The percentage of zombie plants
was 9% of all plants during the 1990s.
We calibrate the tax rates to match the average wedges of labor andcapital. From the ﬁrst order conditions of the existing plant’s problem, we
obtain the following theoretical relationship between the wedges and the tax
rates:()
1
εij − sij = βj 1 −, for j = k, l.
(21)(1 + τij )For the steady state in 1989, we calculate the average labor and capitallkwedges during the 1980s and solve for (τ89, τ89) that satisﬁes (21) given thecalculated wedges. For the steady state in 1999, we take the 90s’ averages ofthe labor and capital wedges for zombies and non-zombies, respectively. Thenlklkwe obtain {(τ99,Z, τ99,Z), (τ99,NZ , τ99,N Z )} according to (21). The calibrated
tax rates are shown in Table 6.
Table 6 shows that zombie plants actually received subsidized credit during the 1990s. This result conﬁrms that our deﬁnition of a zombie plant isreasonable because it is consistent with the previous studies, such as Peek
and Rosengren (2005) and Caballero et al. (2008). Table 6 also documentsthat non-zombies faced much higher tax rates than zombies during the 1990s.
It implies that healthy plants had more diﬃculty to receive bank credit thanunproﬁtable plants. This tax conﬁguration will lead resource reallocationfrom proﬁtable plants to unproﬁtable plants.
8

Instead, we could compute the transitional path from the initial steady state to the
new steady state. If we do so, we will provide a better measure on capital stocks. Since
our approach assumes that the economy immediately attains the new steady state capitalstock, the generated capital stock in 1999 was over-accumulated. However, since our focus
is on labor reallocation eﬀect and since it is not aﬀected by capital accumulation, we took
our approach to save our time.
9
Peek and Rosengren (2005) documented that bank lending to unproﬁtable ﬁrms increased during the 1990s. Also, Caballero et al. (2008) showed that subsidized credits
became prevalent during the 1990s.

28

Table 6: Capital and Labor Wedges, and Calibrated Taxes.
1990s Ave.

Wedgesεil − sil
εik − sik

1980s Ave. Zombie
0.20
-0.21
-0.04
-0.07

Non-Zombie
0.21
-0.05
1999

Calibrated Taxes
τl
τk

1989
0.62
-0.28

Zombie-0.29-0.42

Non-Zombie
0.68
-0.32

l
k
Note: τ89and τ89are calibrated so that the average labor and capital wedges, (εil −sil , εik − sik ), are respectively matched with the counterparts in the data in the 1980’s.
lklk(τ99,Z, τ99,Z) and (τ99,NZ , τ99,N Z ) are calibrated using (21) so that the average labor andcapital wedges are respectively matched with the counterparts in the data in the 1990’s
for zombie and non-zombie plants, respectively.

In the model, zombies are the plants whose idiosyncratic component of
TFP (Ai ) is bellow the 20th percentile. In the ﬁnal steady state in 1999,lk
lk
zombie plants face (τ99,Z, τ99,Z) and others face (τ99,NZ , τ99,N Z ). In order tomeasure the distortion of zombie lending, we consider the case where there isno misdirected zombie lending. For this “no-zombie lending case,” we assumelklkthat taxes didn’t change at all, i.e. (τ99, τ99
) = (τ89, τ89) for all plants.
The distortion of zombie lending in reallocation eﬀect is measured asfollows.
ZDj := REjN Z − REjZ ,for j = k, l.

where REjN Z is the reallocation term of input j in the no-zombie lending caseand REjZ is in the zombie lending case.
We explain how to calculate REjN Z and REjZ . First, we need to generate
the 1989 and 1999 data from the model. We solve the detrended initialsteady state and back out the level variables for the 1989 data. For the 1999
data, we solve the detrended ﬁnal steady state in the zombie lending case.
Then, we let all values grow to account for growth during 10 years from 1990
to 1999 and obtain the 1999 data in the zombie lending case. Similarly, we
obtain the 1999 data in the no-zombie lending case.
The growth rate, denoted by γ̂, is calibrated so that aggregate technicaleﬃciency (TE) in the no-zombie case is equal to what we observed in thedata from 1989 to 1999. Plant-level TFP grows at the rate of γ̂ for all29

1

plants. Output, capital stock, and the wage rate are multiplied by γ̂ 1−βk to
be consistent with the model.
We calculate PL-APG and its components in the same way as we calculatethem from the data. First, at every grid point of the TFP distribution h, we
calculate value added shares, cost shares over value added, and log diﬀerencesof factor inputs and productivity. Second, we apply Tornqvist approximation
and aggregate these numbers. At this point, we assume that the number ofstayers is the minimum of the stationary distributions of plants between 1989
and 1999. That is, the distribution of the plants who stay from 1989 to 1999,
denoted by µS (s), is calculated by µS (s) = min(µ89 (s), µ99 (s)) for each s.
In both ﬁnal steady states, we adjust c̃e so that the wage rate in the ﬁnal
steady state is equal to the one in the initial steady state. If we don’t controlc̃e , the model generates too much growth in the wage rate as opposed to thedata. When the TFP growth rate is low, the rental rate of capital also becomes low. The cheap capital greatly attracts potential entrants because thenet return from entering increases. In order to satisfy “free entry condition”
in equilibrium, the wage rate becomes high enough to discourage the excess
entry. As a result, all plants down-size their labor given the high wage rate.
However, we don’t observe such a large increase in the wage rate in the data.
Table 7 shows the benchmark results. It reports model-generated PLAPG and its component in each scenario: the zombie and no-zombie lending
scenarios. It also reports the measures calculated by the data in the ﬁrst
row.
The second row of Table 7 shows the results for the no-zombie lending
scenario. Without zombie (misdirected) lending, all indexes were positive,
except for capital reallocation eﬀect. Capital reallocation eﬀect was negative
due to the negative capital wedges10 , although capital was accumulated from1989 to 1999.
The third row of Table 7 shows the results for the zombie lending scenario.
In this case, reallocation eﬀects of both labor and capital were negative. Dueto the negative reallocation eﬀects, the measured PL-APG was lower thanthat in the no-zombie case.
The size of the zombie distortion, ZDj , is reported in the fourth row of
10

The capital wedges were negative for all plants in the data. Since we calibrated τkN Z
to match the model capital wedge to that in the data, the wedges are also negative in themodel, as well. Please note, however, that they they are close to zero, although they are
negative.

30

Table 7: Distortion of the Zombie Lending
Reallocation Eﬀect

Data
No-Zombie Case
Zombie Case
Distortion of Zombies
As % of Data

PL APG TE Labor
10.01
14.47 -3.96
13.89
14.47
0.87
12.33
14.57 -0.62
1.56
-0.10
1.48
37%

Capital
-0.50
-1.44
-1.63
0.18
36%

Note: Table shows the results between 1989 and 1999. “Data” row shows the PL-APG
and its components from 1989 to 1999, under a common value added production function
for all plants estimated by the WLP method using intermediate input as proxy. All values
are aggregated over the stayers, i.e., the plants who operated both in 1989 and 1999. “NoZombie Case” and “Zombie Case” rows show the results in the model with and without
zombie lending, respectively. “Distortion of Zombies” row shows the diﬀerences of values
in the second row and the third row for each column, which is ZDj , j = l, k. The last row
shows ZDj as a percentage of the values in the ﬁrst row. TE in “No-Zombie Case” is equal
to TE in “Data” because we calibrate plant-level TFP growth rate to let them have thesame value. TE in “Zombie Case” diﬀers a little from TE in “No-Zombie Case” because
the number of stayers is diﬀerent due to the zombie lending, although the plant-level TFP
growth rate is the same in both cases.

Table 7. Each column shows the diﬀerence between the indexes in the zombie
and the no-zombie lending cases. The zombie distortion in labor reallocationeﬀect ZDl was 1.48%. As reported in the last row, the magnitude of ZDl was
37% of the negative labor reallocation eﬀect observed in the data, which was-3.96%. The zombie distortion in capital reallocation eﬀect ZDk was 0.18%,
and its size was 36% of the negative capital reallocation eﬀect observed in
the data, which was -0.50%.11

Conclusion
Subsidized bank credit to poorly performing plants was broadly discussed
as a source of misallocation of resources in Japan in the late 1990s. To
11

Please note that capital reallocation eﬀect is biased as we discussed in footnote 7.
Although labor reallocation eﬀect is not aﬀected by this assumption, PL-APG reﬂects thebias in capital reallocation eﬀect.

31

the best of our knowledge, this is the ﬁrst study that quantiﬁes the loss inaggregate productivity growth (APG) from misdirected bank lending that led
to ineﬃcient resource reallocation across existing plants. Whereas Caballero
et al. (2008) quantify the eﬀect of “zombie lending” on the change in input
and output for individual non-zombie ﬁrms, we quantify the aggregated eﬀectof zombie lending on APG in the Japanese manufacturing sector.
Our approach consists of two parts. First, we measure the eﬀect on
APG of resource reallocation among manufacturing plants in Japan during
the 1990s, by applying the APG measure of Petrin and Levinsohn (2008).
Next, we calibrate a version of the model provided by Restuccia and Rogerson (2008) based on the results of plant-level productivity estimation, andquantify the eﬀect of the misdirected lending on APG by conducting a counterfactual exercise.
In the ﬁrst part, we ﬁnd that resource reallocation was not functioning
well in Japan’s economy in the 1990s. Resource reallocation was less eﬃcientin the 1990 than in the 1980s, especially due to deterioration of labor reallocation. Such negative reallocation eﬀect observed in Japan is not common toother countries such as Chile, Columbia, and the United States, as reported
by Petrin and Levinsohn (2008) and Petrin et al. (2009).
In the second part, we ﬁnd that so-called zombie lending in the 1990s
could induce the loss of 37% of the actual decline in APG due to ineﬃcientlabor reallocation in manufacturing plants. Therefore, zombie lending had anon-negligible impact on resource reallocation in the manufacturing sector,
although zombie lending was less prevalent in the manufacturing sector thanin the non-manufacturing sectors, as estimated by Caballero et al. (2008).
The novelty of our counterfactual exercise lies on the use of the results ofplant-level productivity estimation in calibrating the model. We apply a version of the proxy estimation method, originally proposed by Olley and Pakes(1996), to our panel data of manufacturing plants. Such estimation results
allow us to directly assign the parameter values that are important to resource reallocation, such as plant-level productivity and implied tax/subsidy
schedule that represents distortions in the economy. A similar exercise canbe applied to assess the eﬃciency of resource reallocation in other ﬁnancial
crises, such as the world-wide ﬁnancial crisis starting in the United States in
2007, if a plant-level panel data set is available.

32References[1] Bailey, M., Hulten C., and D. Campbell (1992) “Productivity dynamics in manufacturing plants,” Brookings Papers on Economic Activity: Microeconomics, 187-249.
[2] Biesebroeck, J. V. (2003) “Revisiting some productivity debates,” NBER Working
Paper series, 10065.
[3] Biesebroeck, J. V. (2004) “Robustness of productivity estimates,” NBER Working
Paper series, 10303.
[4] Caballero, R., T. Hoshi, and A. Kashyap (2008) “Zombie Lending and Depressed
Restructuring in Japan,” American Economic Review, vol. 98(5): 1943-77.
[5] Cameron, A. C., and P. K. Trivedi (2005) Microeconometrics, Cambridge University
Press.
[6] Foster, L., J. Haltiwanger, and C. Krizan (2001) “Aggregate Productivity Growth:
Lessons from Microeconomic Evidence,” in Charles R. Hulten, Edwin R. Dean, andMichael J. Harper, eds., New developments in productivity analysis. Chicago: University of Chicago Press, 2001.
[7] Fukao, K., G. Kim, and H. U. Kwon (2006) ”Plant Turnover and TFP Dynamics inJapanese Manufacturing,” Hi-Stat DP Series, No.180.
[8] Fukao, K. and H. U. Kwon (2006) “Why Did Japan’s TFP Growth Slow Down in the
Lost Decade? An Empirical Analysis Based on Firm-Level Data of Manufacturing
Firms,” Japanese Economic Review, 57(2): 195-228.
[9] Fukao, K., Hamagata, S., Inui, T., Ito, K., Kwon, H., Makino, T., Miyagawa, T.,
Nakanishi, Y., and Tokui, J. (2007) “Estimation Procedures and TFP Analysis of the
JIP Database 2006”, RIETI Discussion Paper Series, No. 07-E-003.
[10] Griliches, Z. and Mairesse, J. (1998) “Production Functions: The Search for Identiﬁcation”, in Econometrics and Economic Theory in the Twentieth Century: The
Ragnar Frisch Centennial Symposium (Cambridge University Press) 169-203.
[11] Hulten, Charles R. (2008) ”Divisia index,” The New Palgrave Dictionary of Economics. Second Edition. Eds. Steven N. Durlauf and
Lawrence E. Blume. Palgrave Macmillan. The New Palgrave Dictionary of Economics Online. Palgrave Macmillan. 27 February 2009.
<http://www.dictionaryofeconomics.com/article?id=pde2008_D000174>
doi:10.1057/9780230226203.0400[12] Levinsohn, J. and A. Petrin (2003) “Estimating production functions using inputs tocontrol for unobservables,” The Review of Economic Studies, 70 (2): 317-341.
[13] Olley, S. and A. Pakes (1996), “The Dynamics of Productivity in the Telecommunications Equipment Industry”, Econometrica, 64 (6): 1263-1298.
[14] Peek, J. and E. S. Rosengren (2005) “Unnatural Selection: Perverse Incentives andthe Misallocation of Credit in Japan.” American Economic Review, 95(4): 1144-66

33

[15] Petrin, A. and J. Levinsohn (2008) “Measuring Aggregate Productivity Growth Using
Plant-Level Data,” Working paper, University of Minnesota.
[16] Petrin, A., K. White, and J. P. Reiter (2009) “The Impact of Plant-level Resource Reallocations and Technical Progress on U.S. Macroeconomic Growth,” Working Paper,
University of Minnesota.
[17] Restuccia, D. and R. Rogerson (2008) “Policy Distortions and Aggregate Productivity
with Heterogeneous Plants.” Review of Economic Dynamics, 11: 707-720.
[18] Wooldridge, J. (2005) “On Estimating Firm-Level Production Functions using Proxy
Variables to Control for Unobservables,” Working Paper, Michigan State University.

Appendix A: A Detail Description of Discretetime Approximation
A.1 Tornqvist Approximation
The Tornqvist approximation is a way to approximate a Riemann-Stieltjes
integral by the values of functions at both endpoints of the domain of theintegral. The general formula is as follows.
[∫ tg(x)dF (x) ≅t−1]g(t − 1) + g(t)[F (t) − F (t − 1)] .
2This approximation is exactly the same as the true value if integrand g(x) isa linear function of F (x) in interval [t − 1, t]. In other words, by applying the
Tornqvist approximation, we approximate function g(x) by a linear functionof F (x) on [t − 1, t]: g(x) ≅ aF (x) + b, with some constants (a, b). See Hulten(2008) for a discussion on the relevance of the Tornqvist approximation.
In this paper, we apply the Tornqvist approximation in the following
form.
[

∫ t
si d ln Zi
t−1

≅

]
sit−1 + sit[ln Zit − ln Zit−1 ] = sit ∆ ln Zit ,2

with notation sit := sit−12+sit .

A.2 Approximation of Entry and Exit Eﬀects
In this subsection, we explain in detail how we deal with entrants and exiters
when we derive (11). To begin with, we assume that there are only four
possibilities for a plant during the period from time t − 1 to time t; a plant34

keeps operating, enters once, exits once, or does not operates at all. Thatis, we exclude the case where a plant repeats entering and exiting more thanonce during the period time t − 1 to time t.
For ease of exposition, we explain the idea by applying it to aggregate
value added growth. The ideal discrete-time index for aggregate value addedi
growth is the integral of the sum of dVover all plants from time t − 1 to timeV
t. In this case, the integral has a closed-form solution as follows.
∫ t ∑
dVi
t−1

i

V

∫ t

dV
= ln Vt − ln Vt−1 .
t−1 V

=

(22)

Alternately, we split the sum over all plants into the sums over three sets ofplants: stayers, entrants, and exiters.
∫ t ∑
dVi
V
t−1 i

∑ ∫ t dVi
t−1 Vi∫
∑ t dVi∑ ∫ t dVi
∑ ∫ t dVi
=
+
+
t−1 V
t−1 V
t−1 V

=

i∈St

i∈Et

(23)

i∈Xt−1

We explain how to deal with (23) term by term. For the ﬁrst term that is
the sum over stayers, we transform the integrand into a log form and apply
the Tornqvist approximation.
∑ ∫ t dVi
t−1 V

i∈St

=

∑ ∫ t ( Vi ) dVi∑∫ t∑
svi t ∆ ln Vit ,=svi d ln Vi ≅
V
Vi
t−1
t−1

i∈St

i∈St

i∈St

(24)
s

+s

where svi := VVi , and svi t := vi t−12 vi t .
For the second term that is the sum over entrants, we ﬁrst split the domainof the integral into the three parts: before, at the time, and after the plant
enters. Let τiE denote the time when plant i starts operating. Since Vi = 0
for all t < τiE , the ﬁrst term is equal to zero. The second term is calculated
as a Riemann-Stieltjes integral. And then, we apply integral by parts to the35third term.
∑ ∫ t dVi
t−1 V

=

[
∑ ∫ τiE dVi
i∈Et

i∈Et

=

=

=
≅

t−1

V

∫ τiE
+
τiE

dVi
+
V

∫ t

dVi
τiE V

]

]
∫ t
Vi
dVi
0+
+
E
V τi
τiE V
i∈Et
[( τ E ) ( ) ( τ E ) ∫
( )]
t
∑
Vi i
Vit
Vi i
1
−
+
−
Vi d
τiE
τiE
E
Vt
V
V
V
τi
i∈Et
]
[( ) ∫
t
∑
Vit
Vi
+
dV
t
2
V
τiE V
i∈Et
∑ (V t ) ∑
i
=
svi t
Vt
∑

[

(

i∈Et

τiE

)

(25)

i∈Et

For the last approximation, we assume that Vi << V 2 and hence Vi /V 2 ≅ 0.
For the third term that is the sum over exiters, we take the same way forthe sum over entrants. Thus, we obtain∑ ∫ t dVit−1 V≅i∈Xt−1(∑−i∈Xt−1

Vit−1
V t−1

)
=

∑

−svi t−1 ,(26)i∈Xt−1in the same way as we use to obtain (25). Note that we have a negative signin this case.
Combining (24), (25) and (26), we ﬁnally obtain
∫ t ∑
dVi
V
t−1 i

≅

∑

svi t ∆ ln Vit +

∑
i∈Et

i∈St

svi t −∑

svi t−1(27)i∈Xt−1In this way, we derive (11) from (9). We apply to each term of (9) thesame way of calculation and approximation as we described so far, and hence
obtain (11).

36Appendix B: Supplemental Tables and Figures
In this appendix, we show several supplemental tables and ﬁgures as a reference.

B.1 Another Decomposition of AP GPt L
Table 6 shows AP GPt L and its components using (10), not using (11) as in
the main text. As is shown in (10), AP GPt L is calculated as aggregate gross
output minus aggregate cost, which is the sum of aggregate labor cost, capitalcost, and intermediate material cost, plus the entry and exit eﬀects.

B.2 Time Series by Estimation Method
Figure 4 shows the time series of the technical eﬃciency term for each estimation method. All technical eﬃciency estimates are positively correlated,but the magnitude of movement over time diﬀers across estimators. Figure 5
shows the time series of the PL reallocation term for each estimation method.
Figure 6 shows the time series of the BHC reallocation term for each estimation method. Comparing Figures 5 and 6, we ﬁnd that the BHC reallocation
term ﬂuctuates much more than the PL reallocation term. Figure 7 shows
the time series of the BHC aggregate productivity growth, AP GBHC
, forteach estimation method. In general, all AP GBHC
estimates
showasimilartpattern and are highly positively correlated. Most of the time variations of
AP GBHC
are attributed to the BHC reallocation term, because the BHCtreallocation term varies much much more than the technical eﬃciency term
as in Figures 4 and 6.

37

Table 6: PL Aggregate Productivity Growth and Its Components.
year

PL
APG

1982
3.19
1983
3.57
1984
5.03
1985
3.10
1986
3.42
1987
5.60
1988
8.54
1989
7.44
1990
5.31
1991
3.35
1992
-1.27
1993
-2.85
1994
1.53
1995
4.67
1996
3.85
1997
2.83
1998
-2.01
1999
-1.60
2000
5.63
1980s Average 4.99
(Std. dev.)(2.08)
1990s Average 1.38
(Std. dev.)(3.05)

Aggregate
Gross Output

1.79
2.51
20.20
9.43
-10.81
12.69
23.53
20.85
12.04
5.87
-7.79
-8.87
0.17
9.06
7.34
10.77
-14.55
-5.04
15.58
10.02
(11.76)0.90(9.43)

38

Aggregate Cost
Labor Capital Materials

Entry

Exit

-0.54
-0.30
0.22
0.53
-0.55
-0.62
0.23
0.51
-0.05
-0.09
-0.85
-1.49
-1.29
-0.50
-0.24
-0.13
-1.02
-1.52
-0.55
-0.06
(0.49)-0.72(0.59)

3.67
2.98
3.11
4.09
4.60
2.75
2.43
2.42
2.59
2.45
1.82
1.59
1.71
1.99
1.43
1.84
2.24
2.12
1.78
3.26
(0.79)
1.98(0.37)

-2.92
-3.05
-2.66
-3.65
-3.22
-2.65
-2.26
-2.05
-2.15
-2.05
-1.85
-1.98
-2.44
-1.86
-1.39
-2.06
-1.94
-2.81
-2.20
-2.81
(0.52)-2.05(0.38)

1.10
0.98
1.03
0.84
0.92
0.75
0.54
0.63
0.75
0.97
1.08
0.87
0.31
-0.14
0.00
0.12
0.14
0.09
-0.08
0.85
(0.20)
0.42(0.45)

-1.21
-1.81
14.36
5.38
-13.21
7.07
14.39
12.64
6.48
2.04
-6.77
-5.79
-1.11
5.15
3.78
7.72
-11.36
-2.70
10.16
4.70
(9.67)-0.26(6.35)

10.00 15.00
5.00
0.00
−10.00 −5.00

1980

1985

1990
year
TE_OLS
TE_FKK
TE_SD

1995

2000

TE_FD
TE_FE
TE_WLP−10.00

−5.00

0.00

5.00

10.00

Figure 4: Technical Eﬃciency by Estimation Method.

1980

1985

1990
year
PL_RE_OLS
PL_RE_FKK
PL_RE_SD

1995
PL_RE_FD
PL_RE_FE
PL_RE_WLP

Figure 5: PL Reallocation Eﬀect by Estimation Method.
39

2000

50.000.00−150.00 −100.00 −50.00

1980

1985

1990
year

BHC_RE_OLS
BHC_RE_FKK
BHC_RE_SD

1995

2000

BHC_RE_FD
BHC_RE_FE
BHC_RE_WLP−150.00 −100.00 −50.00

0.00

50.00

Figure 6: BHC Reallocation Eﬀect by Estimation Method.

1980

1985

1990
year
BHC_OLS
BHC_FKK
BHC_SD

1995

2000

BHC_FD
BHC_FE
BHC_WLP

Figure 7: BHC Aggregate Productivity Growth by Estimation Method.
40

B.3 Comparison with Macro Data
Table VA and TFP compare value added and productivity estimates between
macro and micro data. All the macro data are obtained from JIP 2008. The
micro data are the plant-level panel data we use in this paper.
The ﬁrst two columns of Table VA show growth rates of the economywide and manufacturing value added, which are highly positively correlated;the correlation coeﬃcient is 0.89. Thus, the manufacturing sector seems torepresent Japan’s economy as a whole in terms of growth rate of value added.
The last column shows growth rate of manufacturing value added obtained
from our data set, which is highly positively correlated with the one obtained
from JIP 2008; the correlation coeﬃcient is 0.85. Therefore, our sample ofplant-level data represents the manufacturing sector as a whole.
Table TFP shows growth rates of TFP (Total Factor Productivity) estimates in the whole economy and the manufacturing sector, and PL APG
measured in this paper. The manufacturing TFP positively correlates withaggregate TFP with coeﬃcient 0.50, which is smaller than in the case ofvalue added growth rates. PL APG positively correlates with the manufacturing TFP with coeﬃcient 0.69, although the two measures are conceptuallydiﬀerent.

41

Table VA: Comparison of Growth Rate of Value Added.

year

Aggregate
Value added(Macro Data)

Manufacturing
Value added(Macro Data)

Manufacturing
Value added(Micro Data)

1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
1980s Average(Std. dev.)
1990s Average(Std. dev.)

3.01
3.11
4.86
5.01
2.12
4.23
6.23
5.04
5.25
3.95
0.58
0.31
0.56
1.82
3.48
1.43
-1.92
-0.08
1.68
4.20
(1.36)
1.54(2.14)

5.38
4.86
8.90
9.80
0.08
5.32
8.66
7.35
3.04
5.34
-1.81
-3.40
-1.73
3.98
4.17
2.33
-5.41
-0.92
5.43
6.29
(3.12)
0.56(3.67)

2.80
2.97
5.55
3.93
2.72
5.66
8.79
8.57
6.70
4.39
-0.91
-4.08
-0.31
4.24
3.78
3.01
-3.04
-3.64
5.96
5.12
(2.48)
1.01(3.88)

Correlation

AGG VA
1.00
.
.

MF VA
0.89
1.00
.

MF VA Micro
0.87
0.85
1.00

AGG VA
MF VA
MF VA Micro

The macro data are from JIP 2008. The micro data are what we use in this paper.

42

Table TFP: Comparison of TFP and PL APG.
year

Aggregate TFP(Macro Data)

Manufacturing TFP(Macro Data)

PL APG(Micro Data)

1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
1980s Average(Std. dev.)
1990s Average(Std. dev.)

0.10
-0.09
0.78
1.26
-0.24
0.62
1.49
1.00
1.65
0.79
-0.44
0.24
-0.16
-0.17
1.15
0.39
-0.81
0.33
-0.16
0.62
(0.64)
0.30(0.75)

1.27
0.51
1.08
2.25
-0.25
1.76
1.45
1.53
-0.13
0.94
-0.62
-0.25
-0.17
1.69
1.37
0.66
-0.76
0.34
1.57
1.20
(0.77)
0.31(0.83)

3.19
3.57
5.03
3.10
3.42
5.60
8.54
7.44
5.31
3.35
-1.27
-2.85
1.53
4.67
3.85
2.83
-2.01
-1.60
5.63
4.99
(2.08)
1.38(3.05)

Correlation

AGG TFP
1.00.
.

MF TFP
0.50
1.00.

PL APG
0.57
0.69
1.00

AGG TFP
MF TFP
PL APGThe macro data are from JIP 2008. The micro data are what we use in this paper. JIP
2008 contains their estimates of TFP, using the following equation:∆ ln T F Pt = ∆ ln Yt − ν L,t ∆ ln Lt − ν K,t ∆ ln Kt − ν M,t ∆ ln Mt ,(28)

where ν X,t is the average of the cost shares of input X ∈ {L, K, M } in time t − 1 and t.
See Fukao et al. (2007), which is for JIP 2006, but the same applies to JIP 2008.

43

B.4 HoursWorked and Number of Employees

Note: L = Hours worked (H) × Number of workers (N). ∆ ln H was negative during 198993. Legislation on workweek: 44 hrs (1988) → 40 hrs (1993). ∆ ln N was negative after
1993.

44

B.5 Industry-level Results
Table PL80 : PL Aggregate Productivity and Its Decomposition- Average in the 1980s by Industry.
SIC

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
41

Industry Name
Foods
Beverages and tabacco
Textile products
Wearing apparel and othertextile products
Timber and wooden products
Furniture and ﬁxtures
Pulp and paper products
Printing
Chemical products
Petroleum and coal products
Plastic products
Rubber products
Leather and miscellaneousleather products
Ceramic, stone and clay products
Iron and steel
Non-ferrous metals
Metal products
General machinery
Other electrical machineryand apparatus n.e.c.
Electronic computing equipment
and communication equipment
Semiconductor devices
and electronic components
Transportation equipment
Precision instruments
Miscellaneous manufacturing products
Publishing

PL
APG

Technical
Eﬃciency

Reallo-cation

Net-Entry

0.24
3.30
0.92
4.45

-0.32
0.85
2.92
2.65

0.50
0.09
-0.53
0.52

0.06
2.37
-1.47
1.28

2.59
1.77
4.73
4.03
10.05
2.69
6.72
4.35
-0.67

4.29
1.36
6.28
3.70
9.48
3.06
5.96
3.96
-0.77

-0.69
0.75
-1.45
0.15
0.44
-0.18
0.45
0.09
0.21

-1.01
-0.34
-0.11
0.18
0.13
-0.19
0.31
0.30
-0.11

2.75
4.16
2.86
3.91
3.70
4.45

2.96
5.62
5.57
3.10
3.08
2.79

-0.06
-1.54
-2.40
0.25
0.07
0.41

-0.16
0.09
-0.31
0.56
0.55
1.25

13.68

10.79

1.13

1.77

16.15

8.97

4.35

2.82

4.40
4.69
4.16
1.26

7.97
5.09
2.37
-0.79

-3.39
0.11
0.48
2.41

-0.18
-0.51
1.32
-0.36

All values are the averages in the 1980s. Industry is deﬁned by 2-digit SIC code.

45

Table PL90 : PL Aggregate Productivity and Its Decomposition- Average in the 1990s by Industry.
SIC

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
41

Industry Name
Foods
Beverages and tabacco
Textile products
Wearing apparel and othertextile products
Timber and wooden products
Furniture and ﬁxtures
Pulp and Paper products
Printing
Chemical products
Petroleum and coal products
Plastic products
Rubber products
Leather and miscellaneousleather products
Ceramic, stone and clay products
Iron and steel
Non-ferrous metals
Metal products
General machinery
Other electrical machineryand apparatus n.e.c.
Electronic computing equipment
and communication equipment
Semiconductor devices
and electronic components
Transportation equipment
Precision instruments
Miscellaneous manufacturing products
Publishing

PL
APG

Technical
Eﬃciency

Reallo-cation

Net-Entry

1.45
0.74
-2.53
-1.49

1.52
3.54
-0.67
0.78

-0.42
-2.40
-1.13
-1.57

0.35
-0.40
-0.73
-0.71

-1.30
-3.32
-0.22
0.76
1.97
1.33
0.99
0.09
-3.61

0.04
-0.92
1.08
0.75
2.34
1.95
1.60
0.84
-0.85

-0.87
-1.70
-1.22
-0.17
-0.32
-0.33
-0.56
-0.77
-1.51

-0.47
-0.70
-0.08
0.18
-0.05
-0.29
-0.05
0.03
-1.24

-0.48
-1.03
0.37
0.33
-0.15
1.53

1.04
0.29
1.27
1.25
0.73
2.43

-1.19
-1.17
-0.87
-0.88
-0.72
-0.47

-0.33
-0.14
-0.04
-0.04
-0.17
-0.43

7.20

9.98

-2.76

-0.02

12.83

12.05

0.24

0.54

0.19
1.47
2.44
-1.90

1.04
3.02
3.79
-1.80

-0.99
-0.77
-0.87
-0.64

0.14
-0.79
-0.47
0.54

All values are the averages in the 1990s. Industry is deﬁned by 2-digit SIC code.

46

Table RE80 : Decomposition of Reallocation Eﬀect- Average in the 1980s by Industry.
SIC

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
41

Industry Name
Foods
Beverages and tabacco
Textile products
Wearing apparel and othertextile products
Timber and wooden products
Furniture and ﬁxtures
Pulp and Paper products
Printing
Chemical products
Petroleum and coal products
Plastic products
Rubber products
Leather and miscellaneousleather products
Ceramic, stone and clay products
Iron and steel
Non-ferrous metals
Metal products
General machinery
Other electrical machineryand apparatus n.e.c.
Electronic computing equipment
and communication equipment
Semiconductor devices
and electronic components
Transportation equipment
Precision instruments
Miscellaneous manufacturing products
PublishingReallo-cationDecomposition
Labor Capital Materials

0.50
0.09
-0.53
0.52

-0.20
-1.08
-0.41
0.08

0.15
0.08
-0.25
-0.13

0.55
1.08
0.13
0.57

-0.69
0.75
-1.45
0.15
0.44
-0.18
0.45
0.09
0.21

-0.27
0.21
0.05
0.83
-0.20
-2.27
0.96
0.23
-0.01

-0.25
-0.07
-0.56
-0.46
-0.17
0.20
-0.58
-0.44
0.12

-0.16
0.61
-0.94
-0.22
0.81
1.89
0.07
0.30
0.11

-0.06
-1.54
-2.40
0.25
0.07
0.41

-0.25
-0.64
-0.22
0.36
0.18
0.48

-0.22
-0.48
-0.45
-0.22
-0.06
-0.23

0.41
-0.42
-1.73
0.11
-0.05
0.16

1.13

0.45

0.22

0.46

4.35

0.47

-0.96

4.84

-3.39
0.11
0.48
2.41

0.53
-0.09
0.23
0.30

-0.27
-0.37
-0.01
-0.13

-3.65
0.57
0.25
2.24

All values are the averages in the 1980s. Industry is deﬁned by 2-digit SIC code.

47

Table RE90 : Decomposition of Reallocation Eﬀect- Average in the 1990s by Industry.
SIC

9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
41

Industry Name
Foods
Beverages and tabacco
Textile products
Wearing apparel and othertextile products
Timber and wooden products
Furniture and ﬁxtures
Pulp and Paper products
Printing
Chemical products
Petroleum and coal products
Plastic products
Rubber products
Leather and miscellaneousleather products
Ceramic, stone and clay products
Iron and steel
Non-ferrous metals
Metal products
General machinery
Other electrical machineryand apparatus n.e.c.
Electronic computing equipment
and communication equipment
Semiconductor devices
and electronic components
Transportation equipment
Precision instruments
Miscellaneous manufacturing products
PublishingReallo-cationDecomposition
Labor Capital Materials

-0.42
-2.40
-1.13
-1.57

-0.35
-1.27
-1.04
-1.00

-0.01
-0.06
-0.10
-0.09

-0.05
-1.07
0.01
-0.47

-0.87
-1.70
-1.22
-0.17
-0.32
-0.33
-0.56
-0.77
-1.51

-0.83
-0.71
-0.97
-0.02
-0.32
-0.69
-0.33
-0.27
-0.96

-0.15
-0.11
-0.36
-0.20
-0.13
-0.18
-0.15
-0.19
-0.13

0.11
-0.87
0.11
0.05
0.13
0.55
-0.07
-0.32
-0.42

-1.19
-1.17
-0.87
-0.88
-0.72
-0.47

-0.45
-1.39
-0.60
-0.55
-0.33
-0.70

-0.14
-0.32
-0.52
-0.10
0.03
-0.13

-0.60
0.54
0.25
-0.23
-0.42
0.35

-2.76

-1.16

0.00

-1.60

0.24

-0.21

-0.55

1.01

-0.99
-0.77
-0.87
-0.64

-1.19
-0.51
-0.48
-0.33

-0.16
-0.09
0.15
-0.20

0.36
-0.17
-0.54
-0.11

All values are the averages in the 1990s. Industry is deﬁned by 2-digit SIC code.

48

B.6 Further Decomposition of Reallocation Eﬀect
Table LH: Labor Reallocation Eﬀect Decomposition by Margin and Input Growth.
Positive Margin Negative Margin
εL − siL ≥ 0
εL − siL < 0
d ln Li ≥ 0 80s
1.55
-0.07
90s
1.03
-0.05
d ln Li < 0 80s
-1.55
0.08
-1.73
0.11
90s
Table K: Capital Reallocation Eﬀect Decomposition by Margin and Input Growth.
Positive Margin Negative Margin
εK − siK ≥ 0
εK − siK < 0
d ln Ki ≥ 0 80s
0.30
-0.75
0.21
-0.68
90s
d ln Ki < 0 80s
-0.15
0.41
-0.16
0.48
90s
Table M: Intermediate Material Reallocation Eﬀect Decomposition by Margin and Input Growth.
Positive Margin Negative Margin
εM − siM ≥ 0
εM − siM < 0
d ln Mi ≥ 0 80s
2.67
-1.93
90s
2.15
-1.13
d ln Mi < 0 80s
-1.80
1.06
-2.22
1.14
90s
Each cell shows reallocation eﬀect aggregated over subgroups deﬁned according to whether
the plant increased or decreased their input and whether the plant’s margin was positiveor negative. Rows of 80s and 90s respectively correspond to the averages during the 1980s
and the 1990s. The sum of the four values in all cells for each decade is respectively equal
to the average reallocation eﬀect in the 1980s and the 1990s: 0.02 and -0.66 for labor,-0.20 and -0.14 for capital, and 0.00 and -0.05 for intermediate material.

49