DBJ Discussion Paper Series, No.1304

Misallocation of Capital During Japan's Lost Two Decades

Daisuke Fujii(University of Chicago)
Yoshio Nozawa(Development Bank of Japan)

June

2013

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and do
not reflect the views of the Institute.

Misallocation of Capital during Japan’s Lost Two Decades

Daisuke Fujii1
Yoshio Nozawa2

Abstract:
We show that misallocation of resource across firms is the key in explaining the slow Total
Factor Productivity growth rate in Japan since the late 1990’s.

The degree of resource

misallocation is summarized by the variation of Total Factor Revenue Productivity acrossfirms.

Using the accounting data for Japanese manufacturing firms, we quantify the effectof allocation inefficiency in Japan and show that misallocation is highly cyclical and usefulin explaining the fluctuation of aggregate Total Factor Productivity.

The resource

misallocation in Japan is driven mainly by capital misallocation due to lagged response offirms’ investments to idiosyncratic unexpected productivity shock.

1University of Chicago, Email: fujii@uchicago.edu
2Development Bank of Japan and University of Chicago.

1

Email: ynozawa@chicagobooth.edu

1 Introduction

Lower Total Factor Productivity (TFP) growth is the leading cause of the sluggish
GDP growth in Japan after the era of bubble economy. Fukao, Miyagawa, Pyo andRhee (2011) show that the TFP growth in Japan is lower by 1% after the late 1990’s
compared with the preceding period. There can be multiple causes for the lower TFP
growth rate such as slower technological progress and rapidly aging population in
Japan. In this paper, we examine the impact of resource misallocation across firms as
an alternative explanation for lower aggregate TFP growth rate in this period.
We quantify the effect of allocation inefficiency on aggregate TFP using the modelof monopolistic competition of Dixit and Stiglitz (1987) with allocation friction. Eachfirm in an industry produces differentiated products.

Within an industry, theproduction function is identical except for the productivity parameter.

Each firm,

however, faces different level of frictions which effectively raise the cost of inputs for thefirm.

Given the productivity level and frictions, a firm sets its own price as amonopolist.

Without frictions, the profit maximization implies that the marginal

revenue productivity of capital and labor should be equalized across firms in an industry.
If firm-specific frictions exist, however, then the marginal revenue productivities candiffer among firms.

The two measures of marginal revenue productivities can besummarized by the firm’s total factor revenue productivity (TFPR). We show that theaggregate TFP is a function of the deviation of the firm’s individual TFPR from theindustry average.
The variation of firm-level TFPR is the useful summary of the allocation efficiencyof the economy. We use firm-level accounting data for manufacturing firms in Japan to2measure the variation of TFPR each year since 1989. We find that the (cross-sectional)
variation of TFPR is highly cyclical and quantitatively important in explaining the GDP
growth rate in Japan since the late 1990’s.

Our findings show that the shock toaverage productivity is only a part of the TFP growth rate and the deviation ofindividual productivity from the average is a significant source of the aggregate
fluctuation.
We then examine the source of the frictions which drive a wedge in TFPR
across firms in an industry.

We find that an increase in uncertainty about

idiosyncratic productivity shocks is the major source of the frictions in Japan. As it
takes time/resources to adjust the level of inputs, an unexpected idiosyncratic shockleads to variation of TFPR across firms.

If a firm is hit by a positive (physical)

productivity shock, then it does not increase inputs immediately but rather with sometime lags.

Due to sluggish adjustments of inputs, the variation of TFPR becomeslarger as the magnitude of uncertainty (or the size of the shock) becomes larger.
We further investigate the alternative explanation for rising TFPR variation in
Japan and find that the learning-by-doing hypothesis can also help explain the part ofthe variation in TFPR while other potential explanations are not consistent with thedata.
Our research relates to the multiple strands of literature on productivity. The
preceding research closest to ours is Hsieh and Klenow (2009). Hsieh and Klenow(2009) show that a significant difference in TFP between the U.S. and developing
countries can be explained by the difference in allocation efficiency. They conclude
that government regulation and public ownership of the firms in China and India are
the leading cause for the resource misallocation in these countries. We also use firm’s

3first order condition to identify frictions using the data on Japan manufacturing firms.
Our conclusion, however, differs as we find that resource misallocation in Japan is
cyclical and unlikely to be explained by government intervention. Instead, we findthat lending by policy finance institution in Japan actually helps reduce allocation
inefficiency.
Hosono and Takizawa (2012) use plant-level data in Japan to examine to what
extent the variation of TFPR is due to financial frictions. To this end, they construct a
structural model of a firm with a borrowing constraint. Hosono and Takizawa (2012)
fit the model to their data and find that the borrowing constraint can explain about ahalf of the capital distortion.
Our paper differs from Hosono and Takizawa (2012) in three ways. First, we
focus on the time-series variation in allocation efficiency in Japan. Given that thefriction is measured as an error of the model, the level of the gain from efficient
allocation is subject to model misspecification.

Comparing the US and Japan andcomputing the efficiency gain in the hypothetical case where Japan achieves the US
efficiency is one way to avoid taking the model literally as truth. We, on the other
hand, focus on the time-series variation of resource misallocation. Thus, unless one
believes that model misspecification varies significantly over time, our evaluation of thechange in efficiency gain over time is robust to potential model misspecifications.
Second, we use firm-level data to measure productivity and frictions. There
are advantages and disadvantages in using firm level data as opposed to plant-level
data such as Hosono and Takizawa (2012).

If the local licensing or regional-level

regulation is the key source of the friction that a producer faces, then one should use
plant-level data to measure such friction. On the other hand, if firm-wide frictions

4

such as borrowing constraints or countrywide regulation which affect an entire firm as alegal entity as opposed to each plant, the use of firm-level data is preferred.
Third, we differ from Hosono and Takizawa (2012) in that our approach is lessstructural than theirs.

We investigate the cause of the variation in revenue

productivity not by fitting a structural model but by associating the productivity withother observables using the data. In this sense, our work is complementary to Hosono
and Takizawa (2012).
Our research also relates to Restuccia and Rogerson (2008) as they also suggestthat resource misallocation can have an important effect on aggregate TFP.

Ourmeasure of misallocation depends on TFPR, whose importance is highlighted by Foster,Haltiwanger and Syverson (2008).
The rest of the paper is organized as follows.

We present the model ofmonopolistic competition with firm heterogeneity in an industry in Section 2. We showthat the aggregate TFP depends on the deviation of firm TFPR from the industry
average. We then describe data in Section 3 and present the estimates of misallocationof resources across Japanese firms in Section 4.

The source of TFPR variation isanalyzed in the following two sections and the role of the government is examined in
Section 7. Section 8 concludes.

2 ModelWe model firms which operate within a framework of monopolistic competition of
Dixit and Stiglitz (1977). For the specific setup and the details about frictions, we5follow the model of Hsieh and Klenow (2009). There are industries s = 1, … , S which
produce industry-level aggregate output Ys . Each industry is populated by Ms firms
and each firm produces one type of output Ysi.

Each firm’s output is combined to

produce Ys with the production function
𝑀𝑆

𝜎
𝜎−1

𝜎−1
𝜎

YS = (∑ 𝑌𝑆𝑖 )𝑖=1

where σ denotes the elasticity of substitution among inputs.

Ys is in turn used to

produce the economy-wide aggregate output Y.
Given industry output, a cost minimization problem yields the demand function
𝑃𝑆 𝜎
YSi = 𝑌𝑆 ( )𝑃𝑆𝑖with the price index
11−𝜎 ]1−𝜎PS = [∑𝑃𝑆𝑖

Given the demand function, each firm maximizes profits by choosing optimallevel of labor and capital. Each firm has a production function:𝛼1−𝛼𝑠Ysi = 𝐴𝑠𝑖 𝐾𝑠𝑖𝑠 𝐿𝑠𝑖

A firm has its own level of productivity but the input share parameter αs is thesame within the industry. When choosing between labor and capital, we assume there
is a firm-specific wedge 1 + τKsi which adds extra funding cost for firm i. We also
assume that there is friction in the output parameterized by τYsi which prevents a firmfrom producing at the optimal level possibly due to licensing and government
regulation.
Their profit maximization problem solves
max(1 − 𝜏𝑌𝑠𝑖 )𝑃𝑠𝑖 𝑌𝑠𝑖 − 𝑤𝐿𝑆𝑖 − (1 + 𝜏𝐾𝑆𝑖 )𝑅𝐾𝑆𝑖
The first order conditions yield the restriction on the marginal revenue product6

of labor and capital for the firm:
𝑀𝑅𝑃𝐿𝑆𝑖 ≡𝜎−1
𝑃𝑆𝑖 𝑌𝑆𝑖w(1 − αs )=𝜎𝐿𝑆𝑖1 − τYSi(1)

1 + 𝜏𝐾𝑆𝑖
𝜎 − 1 𝑃𝑆𝑖 𝑌𝑆𝑖
𝛼𝑆
=R
𝜎
𝐾𝑆𝑖
1 − 𝜏𝑌𝑆𝑖(2)

𝑀𝑅𝑃𝐾Si ≡Equations (1) and (2) show that MRPLsi should be equalized across firms if
there is no friction τYsi .

Similarly, MRPK si should be equalized across firms if thefrictions τYsi and τKsi are both zero.
The profit maximization for the monopolistic firm yields the usual pricemark-up rule of𝛼𝑆𝜎𝑤 1−𝛼𝑆 𝑅 𝛼𝑆 (1 + 𝜏𝐾𝑆𝑖 )
PSi =
[
]
[ ]
𝜎 − 1 1 − 𝛼𝑆
𝛼𝑆 (1 − 𝜏𝑌𝑆𝑖 )𝐴𝑆𝑖
The optimal output is
YSi = 𝑌𝑆 𝑃𝑆𝜎 𝑃𝑆𝑖−𝜎= 𝑌𝑆 𝑃𝑆𝜎 (𝜎 − 1 𝜎 1 − 𝛼𝑆 𝜎(1−𝛼𝑆 ) 𝛼𝑆 𝜎𝛼𝑆 (1 − 𝜏𝑌𝑆𝑖 )𝐴𝑆𝑖
) [
[ ]
(
]
𝛼𝑆 )
𝜎
𝑤
𝑅
(1 + 𝜏𝐾 )𝜎

𝑆𝑖

The final output is produced using the production function𝜃Y = ∏ 𝑌𝑆 𝑆
The cost minimization yields
PS =

𝜃𝑆 𝑌
𝑌𝑆

Again, the labor demand for firm i isLSi =1 − 𝛼𝑆
1 − αS (𝜎 − 1)
𝑌𝑆𝑖 𝜆𝑆𝑖 =(1 − 𝜏𝑌𝑆𝑖 )𝑌𝑆𝑖 PSi𝑤𝑤
𝜎

We assume that the aggregate supply of capital and labor is fixed at K and L .
Equating the aggregate supply and demand of labor, the sector labor demand can be
written as

7LS = 𝐿̅̅̅̅̅̅̅̅̅𝑆
(1 − 𝛼𝑆 )𝜃𝑆 /𝑀𝑅𝑃𝐿̅̅̅̅̅̅̅̅̅̅
∑(1 − 𝛼𝑆 ′ )𝜃𝑆′ /𝑀𝑅𝑃𝐿
𝑆′

where the average MRPL is̅̅̅̅̅̅̅̅̅S =
MRPL

w
𝑃 𝑌

∑(1 − 𝜏𝑌𝑠𝑖 ) 𝑆𝑖 𝑆𝑖
𝑃𝑆 𝑌𝑆

Similarly, by aggregating capital demand and equating it to the aggregate supply of
capital K, we have
KS = 𝐾̅̅̅̅̅̅̅̅̅̅𝑆
𝛼𝑆 𝜃𝑆 /𝑀𝑅𝑃𝐾̅̅̅̅̅̅̅̅̅̅̅
∑ 𝛼𝑆 ′ 𝜃𝑆 ′ /𝑀𝑅𝑃𝐾
𝑆′

where
̅̅̅̅̅̅̅̅̅̅MRPK S =𝑅∑

1−𝜏𝑌𝑆𝑖 PSi 𝑌𝑆𝑖
1+𝜏𝐾𝑆𝑖 𝑃𝑆 𝑌𝑆

We can then express the aggregate output Y as a function of K s , 𝐿𝑠 and industry TFP:
𝛼

1−𝛼𝑠

𝛼

1−𝛼𝑠 θs

Ys = 𝑇𝐹𝑃𝑠 ⋅ 𝐾𝑠 𝑠 𝐿𝑠S

Y = ∏(𝑇𝐹𝑃𝑠 ⋅ 𝐾𝑠 𝑠 𝐿𝑠)

s=1

Next, we show that industry TFPs can be expressed as a function of the totalfactor revenue productivity (TFPR) variation of each firm within industry.

The

revenue productivity for the individual firm at the optimum is
𝛼𝑆

𝜎
𝑅 𝛼𝑆
𝑤 1−𝛼𝑆 (1 + 𝜏𝐾𝑆𝑖 )TFPR Si ≡ 𝛼𝑆 1−𝛼𝑆 =( ) ()
𝜎 − 1 𝛼𝑆
1 − 𝛼𝑆1 − 𝜏𝑌𝑆𝑖
𝐾𝑆𝐼 𝐿𝑆𝑖𝑃𝑆𝑖 𝑌𝑆𝑖

The point of the equation is to show that the revenue productivity can varyacross firms in an industry only due to τYsi and τKsi , not due to physical productivity
Asi .

Regardless of the physical productivity, the revenue productivity should beequalized across firms in our setup of monopolistic competition. If a firm has higher
physical productivity, it should expand the output such that its revenue productivity
falls until it is equal to the revenue productivity of other firms in the same industry.

8

Also, we can rewrite the definition of TFPR si as

TFPR si =𝜎−1

𝑃𝑆𝑖 𝑌𝑆𝑖𝛼𝑆 𝜎−1

𝑃 𝑌

𝑆𝑖

=

1−𝛼𝑆

𝑃 𝑌

𝑆𝑖 𝑆𝑖
( 𝜎 (1 − αs ) 𝑀𝑅𝑃𝐿)

𝑆𝑖 𝑆𝑖
( 𝜎 𝛼𝑆 𝑀𝑅𝑃𝐾
)

𝑆𝑖

(3)

σ
𝑀𝑅𝑃𝐾𝑆𝑖 𝛼𝑆 𝑀𝑅𝑃𝐿𝑆𝑖 1−𝛼𝑆
(
) (
)
σ−1
𝛼𝑆
1 − 𝛼𝑆

As TFPR si is a function of MRPK si and MRPLsi , TFPR si should be equalized
across firms in an industry if a firm can freely adjust the level of both labor and capital.
In other words, the variation of TFPRsi is the indicator for frictions which prevent firms
from achieving their optimal use of either labor or capital.
We also define the industry average total factor revenue productivity as̅̅̅̅̅̅̅̅̅S =
TFPR

𝛼
1−𝛼𝑆
̅̅̅̅̅̅̅̅̅̅σ
𝑀𝑅𝑃𝐾𝑆 𝑆 ̅̅̅̅̅̅̅̅̅
𝑀𝑅𝑃𝐿𝑆
(
) (
)
σ−1
𝛼𝑆
1 − 𝛼𝑆(4)

Then, the industry TFP can be written as
1
𝜎−1

𝑀𝑠

𝜎−1
̅̅̅̅̅̅̅̅̅
𝑇𝐹𝑃𝑅𝑠
TFPs = (∑ {𝐴𝑠𝑖} )𝑇𝐹𝑃𝑅𝑠𝑖𝑖=1

If there are no frictions, then the total revenue productivity must be equalized
within industry such that TFPR si = ̅̅̅̅̅̅̅̅̅𝑇𝐹𝑃𝑅𝑠 for all 𝑖 in Ms . Thus, industry TFP with
1

𝑀𝑠
𝜎−1
efficient allocation can be written as ̅̅̅
As = (∑𝑖=1
𝐴𝜎−1. The efficiency gain is defined𝑠𝑖 )as the ratio between actual output and the output with efficient allocation.
𝑆

𝜃𝑠

𝑀𝑠

𝐴𝑠𝑖 ̅̅̅̅̅̅̅̅
𝑇𝐹𝑃𝑅𝑠= ∏ [∑ { ̅̅̅}Yefficient
𝐴𝑠 𝑇𝐹𝑃𝑅𝑠𝑖
Y

𝑠=1

𝜎−1 𝜎−1

]

(5)

𝑖=1

The equation shows that to detect the allocation inefficiency, the key indicator is9the variation of TFPR from the industry average, not the level of TFPR. Suppose that
τYsi = 𝜏𝑌𝑠 ≠ 0 and τKsi = τKs ≠ 0 hold for all 𝑖 .

That is, there is a constant but̅̅̅̅̅̅̅ s = TFPR si still holds for all 𝑖 and TFPs is
non-zero friction in industry s. Then TFPR
at its ‘efficient’ level. If an industry has high level of τY s on average but they do notvary across firms, then industry level labor Ls and capital K s are low while TFPs isunaffected. Due to fixed supply of labor and capital, the labor and capital market
clearance guarantee that average inefficiency does not affect outputs in this framework.
The efficiency gain Y/Yefficient is less than one if the firm with higher physicalproductivity tends to have higher revenue productivity. That is, if a firm which should
expand their output (high Asi) does not do so in reality due to some frictions (high
TFPR si), then the economy-wide output is less than the efficient level of output, leading
to the efficiency gain.
To gain more insights, we rewrite equation (5) assuming that log Asi ≡ asi ,log 1 − τYsi ≡ 𝑥𝑠𝑖 and log(1 − τYsi )/(1 + 𝜏𝐾𝑠𝑖 ) ≡ zsi are jointly normally distributed.

In

this case, log TFPR si ≡ t si are also jointly normally distributed. Then,log 𝑌 − log 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡S1= − ∑ θs {(σ − 1)Vars [t si ] + αs Vars [zsi ] + (1 − αs )Vars [xsi ]}
2
s=1

S

− 2(σ − 1) ∑ θs Covs (𝑎si , t si )s=1

holds. Appendix 1 shows the derivation of the decomposition of efficiency gain under
log-normality assumption.
The loss in productivity from the inefficient allocation comes from two sources:
The first term is the variance of TFPR which is always negative. The second term isthe covariance between physical and revenue productivity. To the extent that two
measures of productivities are positively correlated, the covariance term lowers the10industry-level TFP.

3 DataThe data we use is the DBJ Financial Database of Listed Firms provided by
Development Bank of Japan. The database covers all firms listed in Tokyo andother regional stock exchanges in Japan from 1960 to present. The data provides
the financial statements and supplements at annual frequency.

The databaseincludes delisted firms; therefore there is no survivorship bias.
As our data is limited to listed firms, we are focusing on the sample withrelatively smaller frictions. Listed firms typically have better access to the capital
market due to better disclosure and smaller information asymmetry. Thus, firms
in our sample should find it relatively easier to adjust their capital level when hit
by productivity shocks.

Therefore, our estimates of TFPR variation can beconsidered as a lower bound of the true allocation inefficiency in Japan.
We use non-consolidated financial statements for our analysis. Since we needto classify each manufacturing firm into industries, it is better to use
non-consolidated data to narrow the scope of the business of the firm. Also, moredata items are available for non-consolidated financial statements thanconsolidated ones. For example, the detailed breakdown of Cost of Goods Sold isavailable only for non-consolidated statements.
Value added is computed by the following formula:

Value added = Ordinary Profit + Wage – Interests and Dividends Paid +11

Interests and Dividends Received + Tax Paid + Depreciation

where ordinary profit is operating profit plus net interest received.
Wage is computed by adding Labor Cost in the Cost of Goods Sold to Wage in
Selling, and General and Administration Expenses. This measure of labor cost
may miss the cost of pensions and other employment benefits. To examine theseverity of the problem, we compute the labor share for all firms each year andcompare the average to the labor share in GDP. We find that they are roughly thesame (around 70% in the latter half of the sample) and therefore decide to use Wageas a measure of labor cost.
We remove holding companies from the analysis, as their value-added is notcomparable to the firms that run business operation. Specifically, a holding firm
records their interests and dividends received as Sales instead of Interest Received.
Thus, the interests and dividends received by a holding firm will be included invalue added. As holding firms typically have no or very little fixed capital and few
employees, their productivity measure tends to be extremely high. The differencein accounting makes it hard to compare holding companies to other operatingcompanies.
To identify holding companies, we set the threshold on the ratio of financial
investments to total assets. If the ratio exceeds 95%, we judge that the firm is aholding firm and should be removed from the sample. We also test by removing
firms whose name includes ‘Holdings’. The two methodology yields essentially thesame result and thus we report the result based on the 95% threshold.
To classify manufacturing firms into industries, we use the DBJ industry code12

which mostly corresponds to the four digit SIC code in the US. To maintain thenumber of firms in each industry large enough for the analysis, we use the mediancategory of DBJ industry code. The median category classifies the manufacturingfirms into 17 sectors. Each median category mostly corresponds to the first 2
digits of the SIC codes. For example, the first sector (Food) corresponds to the US
SIC codes between 2000 and 2100 and the second sector (Textile) corresponds to the
SIC codes between 2200 and 2400 and so on.
Many Japanese firms have their fiscal year ending in March rather thanDecember.

When I calculate the productivity using the data as of (or before)

March in year t+1, then I treat it as year t observation.
To estimate industry capital share parameter αs, we use the capital share of
the US manufacturing plants obtained from NBER-CES Manufacturing Industry
Database. The database contains all manufacturing industries from 1958 to 2005
at4-digit SIC code level and provides the labor compensation and value added foreach industry.

4 Allocation Efficiency in Japan from 1989 to 2009
In this section, we show the estimates of the change in allocation efficiency over theperiod between 1989 and 2009. We focus on this period since 1989 is the peak of the
bubble economy in Japan and the beginning of the Japan’s lost two decades.
In order to estimate the efficiency gain Y/Yefficient from the data, we need to set
parameters to back out frictions.
Following Hsieh and Klenow (2009), we set the rental rate of capital to R = 0.1.
As we focus on the variation of the productivity of capital from the industry average,13

changing R does not change the estimated efficiency gain.
We set the elasticity of substitution between firms’ output to σ = 3. In general,
the efficiency gain is increasing in σ. Although we focus on the change in efficiency
gain between 1989 and 2009, the change can be exaggerated if the level of inefficiency isoverestimated. Empirically, estimates of the elasticity of substitution range from 3 to
10 (Broda and Weinstein (2006) and Hendel and Nevo (2006)), thus we make aconservative choice to avoid overestimating the efficiency gain.
We set the capital share for each industry αs to the level of capital share of thecorresponding industry in the U.S. With the most developed financial market andrelatively few government regulations, the resource allocation in the U.S. market isconsidered to be relatively undistorted. Thus, we use the capital share in the U.S. as
our benchmark to measure resource misallocation in Japan.
The use of the U.S. capital share is necessary to identify the friction in the data.
At the optimum, the capital/labor ratio for each firm depends both on the friction and on
the capital share parameter αs. Thus, we cannot separately identify industry average
friction and the capital share without exogenously determine either one of the two.
Following Hsieh and Klenow (2009), we estimate the capital share parameter in the
U.S. each year by
αs,t = 1 −3
𝑊𝑎𝑔𝑒𝑠,𝑡
2 𝑉𝑎𝑙𝑢𝑒 𝐴𝑑𝑑𝑒𝑑𝑠,𝑡

We multiply the labor share by 3/2 in order to adjust for the non-wage benefits. Thisway, the average labor share from the NBER-CES database approximately matches thelabor share in National Income and Product Accounts.
The estimated αs,t is highly stable over time in our sample period. Thus, we
assume that the capital share after 2006 is the same as that of 2005. As a robustness14

check, we also compared the difference in the TFPR distribution between 1989 and 2005
(instead of 2009) but the results are qualitatively the same as the case of 2009.
Figure 1 plots the cross-sectional distribution of Total Factor Physical Productivity1̅̅̅𝑠 in 1989 and 2009. It is evident that the distribution in 2009
(TFPQ) log 𝐴𝑠𝑖 𝑀𝑠𝜎−1 /𝐴
has longer left tail, suggesting that the variation in TFPQ becomes larger in 2009.

Figure 1: Distribution of Total Physical Productivity
The figure plots the cross-sectional distribution of the deviation of firms’ physical productivity from the1̅̅̅𝑠 in 1989 and 2009.
industry average log 𝐴𝑠𝑖 𝑀𝑠𝜎−1 /𝐴

The variation of the TFPQ itself does not imply inefficiency. In our model, it is TFPR
which should be equalized across firms. Figure 2 plots the distribution of the log TFPR
(relative to the industry average) in 1989 and 2009.
In Figure 2, the TFPR clearly varies more in 2009 than in 1989. Both tails
15become fatter in 2009.

This implies that the allocation efficiency in Japanesemanufacturing sector deteriorated during this period.

Figure 2: Distribution of Total Revenue Productivity
The figure plots the cross-sectional distribution of the deviation of firms’ revenue productivity from the̅̅̅̅̅̅̅̅̅𝑠 in 1989 and 2009.
industry average log 𝑇𝐹𝑃𝑅𝑠𝑖 /𝑇𝐹𝑃𝑅

Figure 3 shows the estimated TFP gains from efficient allocation in (5) estimatedfor each year from 1958 to 2011. As we can see, there is a sharp rise in allocation
inefficiency in Japan since the late 1990’s. The misallocation of resource peaked in
2008, when the Great Recession began in the U.S.

16

TFP Gains From Efficient Allocation
0.6
0.5
0.4
0.3
0.2
0.1

1959
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011

0

Figure 3: Efficiency Gains in Outputs
Figure plotsyear.

YefficientY− 1, where Yefficient is estimated by equalizing TFPR si at industry average each

The higher value of the TFP gain indicates there is more inefficiency in resource allocation.

To measure the economic magnitude of the change in allocation inefficiency, we
compute the contribution of the change in inefficiency to the GDP growth rate. We doso by multiplying the GDP share of manufacturing industry in Japan to the (negative)
log change in the efficiency gain. (Since a rise in efficiency gain means a fall in theobserved GDP relative to the efficient level, we use the negative of the change in theefficiency gain.) Figure 4 compares the historical real GDP growth rate in Japan andlog change in efficiency gain.

17

2.00%
1.50%
1.00%
0.50%

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

-0.50%

1995

0.00%

Change in
Efficiency
Gain
Real GDP
Growth-1.00%-1.50%-2.00%

Figure 4: Log Change in Efficiency Gain and Real GDP Growth Rate
Figure plots real GDP growth rate in Japan since 1995 (based on fiscal year ending in March). Change
in allocation efficiency is log 𝐺𝑎𝑖𝑛𝑡 /𝐺𝑎𝑖𝑛𝑡+1 , where 𝐺𝑎𝑖𝑛t ≡ 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡,𝑡 /𝑌𝑡

The higher value of the TFPgain indicates there is more inefficiency in resource allocation.

As we can see, the change in the efficiency gain is highly correlated with thereal GDP growth in the data.

This looks surprising at the first glance since theefficiency gain is computed based on the deviation from the industry average TFPR, notthe level of TFPR. If the productivity of all firms falls but the deviation from theaverage does not change, we should see a fall in real GDP growth rate but not in theefficiency gain.
Figure 4 shows that the shock to the efficiency gain is economically significant,when compared with the actual GDP growth rate. In 1998, the real GDP fell by -0.65%
per year while the efficiency gain increased by 0.62%. So nearly all of the fall of the
GDP in 1998 can be attributed to the rise in allocation inefficiency. Also in 2008, thereal GDP fell by 1.66% in a wake of the financial crisis in the US while the efficiency
gain rose by 0.87%, explaining more than half of the decrease in the GDP. These18

figures show that the change in allocation efficiency is an economically significant
driver for the value-added in Japan after the 1990s.
Table 1 shows the cross-sectional distribution of the ratio of the TFPR to its
industry average as well as the efficiency gain from 1958 to 2011. As we can see, thestandard deviation of the TFPR ratio rises from 0.33 in 1989 to 0.61 in 2009. The risein the standard deivation roughly lines up with the rise in efficiency gain, which
increases from 0.15 in 1989 to 0.48 in 2009. If the allocation inefficiency had been
constant since 1989 until 2009, the GDP would have been higher by 2.74% in 2009, or
0.27% in terms of annual growth rate. Given the average real GDP growth rate inJapan since 1994 is 0.35%, the magnitude of the loss from the increasing allocation
inefficiency in manufacturing sector is considerable.

Table 1: Distribution of TFPR from 1989 to 2009
# of
Obs.
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009

Distribution of TFPR
Percentiles
Mean
Std
Skew
Kurt
1%
1267
0.09
0.33
0.20
6.13
-0.67
1298
0.08
0.37
-0.41
9.95
-0.90
1302
0.09
0.35
-0.02
7.63
-0.75
1318
0.07
0.40
-0.65
7.58
-1.04
1338
0.06
0.45
-1.74
18.23
-1.20
1379
0.05
0.44
-2.01
17.58
-1.36
1404
0.04
0.41
-1.39
13.24
-1.09
1420
0.04
0.35
-0.30
3.99
-0.90
1431
0.04
0.41
-1.03
10.74
-1.10
1441
0.03
0.46
-0.83
11.15
-1.38
1441
0.05
0.45
-0.18
7.67
-1.20
1424
0.02
0.45
-0.25
5.91
-1.22
1399
0.01
0.49
-0.17
7.30
-1.42
1364
-0.01
0.51
-1.24
20.37
-1.29
1334
0.01
0.47
0.37
7.18
-1.24
1310
0.02
0.47
0.26
7.71
-1.18
1298
0.00
0.48
0.18
8.17
-1.31
1278
-0.01
0.51
-0.31
9.88
-1.40
1249
-0.02
0.50
-0.03
9.25
-1.34
1218
0.03
0.63
-3.03
45.75
-1.77
1193
0.01
0.61
-1.39
11.24
-1.78

25%
-0.12
-0.12
-0.11
-0.15
-0.15
-0.15
-0.16
-0.17
-0.17
-0.18
-0.19
-0.20
-0.23
-0.24
-0.23
-0.23
-0.25
-0.26
-0.28
-0.26
-0.27

50%
0.07
0.07
0.08
0.08
0.08
0.09
0.06
0.06
0.06
0.05
0.07
0.04
0.04
0.01
0.02
0.02
0.01
-0.01
-0.02
0.06
0.05

75%
0.28
0.29
0.28
0.30
0.30
0.30
0.28
0.27
0.28
0.29
0.31
0.28
0.29
0.26
0.26
0.26
0.25
0.26
0.25
0.36
0.35

̅̅̅̅̅̅̅̅̅𝑠 each year.
The table tabulates the summary statistics of the distribution of log 𝑇𝐹𝑃𝑅𝑠𝑖 /𝑇𝐹𝑃𝑅
efficiency gain is computed byYefficientY

Efficiency
99% Gain
0.98
0.15
1.00
0.18
1.01
0.16
0.98
0.18
0.98
0.18
0.90
0.17
0.96
0.17
0.85
0.17
0.92
0.20
1.03
0.27
1.08
0.33
1.12
0.30
1.21
0.36
1.24
0.34
1.29
0.39
1.41
0.48
1.43
0.49
1.49
0.45
1.43
0.44
1.43
0.56
1.31
0.48

The

− 1 , where Yefficient is estimated by equalizing TFPR si at

industry average each year.

19

Next, we examine if the allocation inefficiency captured by the variation of the
TFPR from the industry average comes from the misallocation of capital or labor.
From equations (3) and (4), we obtain𝛼

1−𝛼𝑆

TFPR si
𝑀𝑅𝑃𝐾𝑠𝑖 𝑆 𝑀𝑅𝑃𝐿𝑠𝑖=() ()̅̅̅̅̅̅̅̅̅S̅̅̅̅̅̅̅̅̅̅
̅̅̅̅̅̅̅̅̅
TFPR
𝑀𝑅𝑃𝐾𝑆
𝑀𝑅𝑃𝐿𝑆
Taking log and variance of the both sides yield
TFPR siVar [log ()]̅̅̅̅̅̅̅̅̅S
TFPR

𝑀𝑅𝑃𝐾𝑠𝑖
𝑀𝑅𝑃𝐿𝑠𝑖= Var [𝛼𝑠 log ̅̅̅̅̅̅̅̅̅̅ ] + Var [(1 − αs ) log ̅̅̅̅̅̅̅̅̅ ]
𝑀𝑅𝑃𝐾𝑆
𝑀𝑅𝑃𝐿𝑆
𝑀𝑅𝑃𝐾𝑠𝑖
𝑀𝑅𝑃𝐿𝑠𝑖+ 2Cov (𝛼𝑠 log ̅̅̅̅̅̅̅̅̅̅ , (1 − αs ) log ̅̅̅̅̅̅̅̅̅ )
𝑀𝑅𝑃𝐾𝑆
𝑀𝑅𝑃𝐿𝑆
This equation shows that we can decompose the variance of the TFPR into the varianceof MRPK and the variance of MRPL and their covariance.
Table 2 shows the result of the variance decomposition computed for 1989 and2009. As we can see, most of the variation of the TFPR comes from the variation in
MRPK. Throughout the period from 1958 to 2011, about 70% to 100% of the varianceof the TFPR is due to the variance of the MRPK and the small fraction of the variationis accounted for by the variance of MRPL and the covariance between MRPK and
MRPL.

Table 2: Variance Decomposition of TFPR

σ (𝑇𝐹𝑃𝑅)Year

σ (𝑀𝑅𝑃𝐾)σ (𝑀𝑅𝑃𝐿)

Cov(𝑀𝑅𝑃𝐾, 𝑀𝑅𝑃𝐿)

1989

0.11

0.11

(99.0%)

0.01(9.0%)-0.01(-8.0%)

2009

0.37

0.30

(80.0%)

0.02(6.0%)

0.05(13.0%)The table shows the variance decomposition of TFPR each year.
percentage of variance relative to the variance of TFPR.

20

The figures in parenthesis areThus, the major source of the allocation inefficiency in Japan between 1989 and2009 is the misallocation of capital rather than labor.

5 Idiosyncratic Physical Productivity Shocks
The fact that allocative efficiency is highly cyclical in Japan implies thatgovernment policy and change in regulations may not be the main driver for the
misallocation in Japan.

This observation contrasts the conclusion of Hsieh andKlenow (2009) who find that the regulation of the government is the key in explaining
the difference in allocation efficiency between the US and developing countries (such as
China and India).
In this section, we examine if the variation of TFPR is driven by idiosyncraticphysical productivity shocks.

If physical productivity Asi is stochastic and a firmcannot adjust its input level immediately, then TFPR can vary across firms.

If aphysical productivity shock is systematic, then the firm should be able to trade statecontingent claim so that its input revenue productivity is equalized with other firms
state-by-state.

On the other hand, if the shock is idiosyncratic, then it cannot beshared by other market participants, leading to deviation of TFPR from the industry
average. As we focus on the difference in variation of TFPR between 1989 and 2009,
the question is whether there is a rise in uncertainty in an idiosyncratic physicalproductivity shock.
To measure the magnitude of uncertainty, we first extract idiosyncratic componentof physical productivity by supposing 𝑎sit ≡ log Asit has the following structure𝑎sit = 𝑎̃t + ϵsit21where 𝑎̃t is a common shock and ϵsit is a firm-specific shock. We also assume that a
firm-specific shock follows AR(1) process
ϵsit = ρϵ ϵsit−1 + ηsit
Using the estimates of Asi for each year, we fit the model by assuming
1 1

𝑎̃t = S M ∑𝑠 ∑𝑠𝑖 𝑎𝑠𝑖𝑡 . We run a panel regression of idiosyncratic productivity ϵsit on itsslagged value to extract the residual η̂sit with time fixed effects. The residual η̂sit isthe estimate of the idiosyncratic physical productivity shock and we compute thestandard deviation of η̂sit each year.

Table 3: Idiosyncratic Productivity and AR(1) Estimates of Shocks

Model Estimates:ρϵσ(η̂sit )

0.90

1989

0.23

(0.014)

2009

0.71

The table shows the a panel estimate of ϵsit = ρϵ ϵsit−1 + ηsit with time fixed effects.

The figure inparenthesis is a standard error clustered by time and σ(η̂sit ) is the standard deviation of residualcomputed using the sample in a particular year.

As we can see in Table 3, the uncertainty of idiosyncratic productivity shocks rises
significantly from 1989 and 2009. The correlation (over time) between the standard
deviation of TFPR and the standard deviation of idiosyncratic physical productivity
shock is as high as 0.78. Thus, an unexpected shock to productivity is an importantsource of the deviation of TFPR. Explaining the variation of TFPR with shocks tophysical productivity is not a tautology. We find that uncertainty, rather than a trend,in physical productivity is the main driver of the resource misallocation. Estimating
the idiosyncratic shock as a deviation from the industry-specific average rather than22

overall average produces a very similar result.
One might be concerned about the fact that we use the estimated productivity Asi
using the same model as we use to extract TFPR si. If our assumption about the capitalshare parameter αs is wrong then the model specification error might drive both Asi
and TFPR si in the same direction. To mitigate this concern, we estimate a productivity
shock based on the method of Cooper and Haltiwanger (2006).

In Cooper andHaltiwanger (2006), the capital share parameter is estimated using instruments suchas lagged capital and sales. The detail of the estimation process is in Appendix 2. We
find that the uncertainty rises from 1989 and 2009 and that our result is robust to thedifferent way of estimating a physical productivity shock.
The correlation between uncertainty and the variation of TFPR is consistent withtwo potential explanations.

The first explanation is lagged response of firms to

unexpected productivity shocks. Since a firm can adjust capital only with some timelags as it takes time to install/discard capital. Thus, when hit by an idiosyncratic
productivity shock, a firm responds with lags and adjusts the input level sluggishly,
which leads to temporal variation of TFPR. With this lagged response, greater size ofan idiosyncratic shock leads to greater variation of TFPR.
The other explanation is hysteresis in firm’s investment as in Dixit (1989).
Making investment is the same as exercising an option to enter the market. Thus,
greater uncertainty increases the value of waiting. If more firms are in an inaction
region in 2009 than in 1989 due to rising uncertainty, the variation of TFPR becomes
greater in 2009. Unlike the first explanation, Dixit (1989)’s model does not forecast
that a firm will respond with lags. If a firm is in an inaction region today and nothing
happens next period, then the firm is still unlikely to make any adjustments. Though23both sluggish adjustments and real option theory implies the variation of TFPR due touncertainty, they differ in forecasting firms’ future behavior.
To see which of the two explanations better capture the reality, we examine therelationship between TFPR and a firm’s future adjustment behavior. If the lagged
response of a firm is the driver of the variation of TFPR, then high TFPR should
forecast an increase in investment. The typical convex cost function of investment
depends not on investment but on its ratio to the capital. Thus, we check if there isany positive relationship between TFPR and future investment/capital ratio.

Table 4: Investment-Capital Ratio and TFPR

k

-3

-2

-1

0

1

2

3

b1

0.05

0.05

0.08**

0.15***

0.45***

0.41***

0.36***b1 (𝑌𝑒𝑎𝑟)

0.03

0.03

0.06*

0.13***

0.47***

0.43***

0.37***

b1 (𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦)

0.06

0.05

0.09*

0.15***

0.46***

0.43***

0.37***The table shows the estimated slope coefficient of the regression TFPR it = 𝑏0 + 𝑏1 (𝐼/𝐾𝑖𝑡+𝑘 ) +𝜖𝑖𝑡 , where k = −3, −2, −1,0,1,2,3.
dummy variables.

The first row shows the panel regression result with no

The second row shows the regression with year dummies while the third

row shows the regression with industry dummies.
percentile to remove outliers.

IK it is winsorized at 1 percentile and 99

The standard errors are clustered by time first and added 5

lags in time with Newey-West weighting.

Table 4 shows the result of the regression of TFPR at time t onto
investment-capital ratio at t+k. We run a panel regression using all the data, with orwithout year and industry dummies. Regardless of the regression specification, thecurrent deviation of TFPR is highly related to future investment-capital ratio. As
capital does not vary too much over time, the variation is driven mainly by investments.
Thus, the data is consistent with the interpretation that a firm faces cost of investment

24

and start investing with lags.

This sluggish adjustment leads to the variation of

marginal revenue product of capital, which explains most of the variation of TFPR.
To summarize our findings thus far, the misallocation of resource in Japanesemanufacturing sector increases significantly since 1989.

The rising allocation

inefficiency of capital explains a sizable portion of Japan’s sluggish TFP growth rate
after the bubble period. The increase in resource misallocation is driven by rising
uncertainty in firm-level physical productivity shock. As the firm responds to a shockwith lags, a larger shock leads to greater misallocation of capital. These idiosyncraticphysical productivity shocks can be firm-specific technology shocks or shocks to
consumers’ preference.

6 Other Explanation of the Variation of TFPR
In this section we explore several alternative (but not mutually exclusive)
theories other than rising uncertainty that may explain the increased variation in
TFPR in Japan over the last two decades.

Overall, we do not find convincing

alternatives to rising uncertainty in explaining the greater variation of TFPR over timein Japan.
6.1

Increasing Model Error and IPO/delisting probability
The first obvious interpretation of our finding is that the fit of the model
becomes worse from 1989 to 2009. The increase in model specification error
can cause the variation of the TFPR to grow over time, which may drive ourresult. If that is the case, what we see in the data may have nothing to dowith the increasing allocation inefficiency but the model errors.
Thoughwecannotcompletely

25

deny

the

possibility

of

model

misspecification, we can check the reliability of the estimated TFPR variation
by relating it to something which we can observe and interpret.
One test we conduct here is whether there is any relationship between
the deviation of TFPR and IPO/delisting probability.

If we see higher

probability of IPO/delisting conditional on high/low deviation of TFPR, thensuch deviation of TFPR is less likely an artifact of model misspecification.
Also, finding the determinant of IPO/delisting is interesting on its own.

For

example, finding a factor that is associated with a higher probability of IPO isuseful in studying the role of venture capital (e.g. Miyakawa and Takizawa(2012)).
To test the hypothesis whether high/low TFPR is associated with theprobability of IPO/delisting, we estimate the following logit model via
Maximum Likelihood.
Prob(DIPOit = 1) =𝑒 𝑏0+𝑏1 𝑇𝐹𝑃𝑅𝑖𝑡
1 + 𝑒 𝑏0 +𝑏1𝑇𝐹𝑃𝑅𝑖𝑡

Prob(DDelistit = 1) =𝑒 𝑐0 +𝑐1 𝑇𝐹𝑃𝑅𝑖𝑡
1 + 𝑒 𝑐0+𝑐1 𝑇𝐹𝑃𝑅𝑖𝑡

Table 5: Logit Model Based On TFPR DeviationD

b1 , 1t(b1 ), t( 1 )Prob(D = 1)

Delist

-0.84

-4.22

-0.16

Listed

0.93

9.68

2.18

The table shows the Maximum Likelihood estimates of logit model using the entire panel data.
The left-hand variable is dummy variables which take value of one for delisting (or IPO) and zerootherwise.

The right hand side variable is the deviation of TFPR from the industry average.

The standard errors are clustered by time and t-statistics are computed without assuming theInformation Matrix Equality for robustness.

Prob(D = 1) is the change in probability ofdelisting (or IPO) when TFPR changes from the 5 percentile to 95 percentile value.

26

Table 5 shows the result of the estimated coefficient on TFPR
deviation. Higher TFPR is associated with higher probability of IPO and lower
probability of delisting.

The coefficients are statistically significant at thetraditional 5% cutoff level. When we compare the probability of delisting and IPO
between a firm with the 95 percentile of TFPR and a firm with the 5 percentile of
TFPR, the difference in probability of delisting is -0.16% while the difference inprobability of IPO is 2.18%.
Peters (2011) examines how TFPR is associated with firms’ entry using firmlevel data in Indonesia. He runs regression of TFPR on an entry dummy and findsthat new entrants have low TFPR rather than high TFPR.

Based on thisobservation, Peters (2011) concludes that credit market frictions are not likely to be
the cause of TFPR variation.

Our result based on Japanese data shows thecontrary: Newly-listed firms are likely to be more financially constrained thanalready listed firms. Our findings that newly listed firms tend to have high TFPR
is consistent with the hypothesis that financial market friction makes it hard for afirm to increase its capital level fast enough.
The fact that the deviation of TFPR is highly associated with IPO and delisting
probabilities alleviates the concern that the estimated TFPR deviation is due toincreasing model misspecification over time. In the next subsections, we associate
the deviation of TFPR to observables to see if we can attribute the friction to otherobservables in the economy.

6.2

Varying markups with plant size

27

Our model with the CES aggregation implies that the markup over themarginal cost is the same across all firms. On the other hand, larger firms may
have greater power to control the market and to achieve the higher markups. If
the variation in firm size becomes greater in 2009 than in 1989, the model
misspecification with growing variation in size may be the key driver for our result.
To attribute the TFPR variation to size, we run non-parametric kernel
regression of TFPR on log size. We use the Gaussian kernel and the bandwidth ischosen to minimize generalized cross-validation. Appendix 3 shows the details of
the kernel regression.
Figure 5 shows that there is no clear relationship between log size (measured
by value-added) and TFPR in 1989.

On the other hand, TFPR seems to be

increasing in log size in 2009. A theory (e.g. Melitz and Ottaviano (2008)) statesthat there is a stable negative relationship between size and elasticity of demand,but the prediction is not supported by the data in Japan.

The fact that therelationship between size and TFPR is not stable suggests that there must be someother mechanism that drives the TFPR variation.

28

Figure 5: Explaining TFPR with Log Size
Figure plots fitted values of non-parametric kernel regression of the form TFPR si = 𝑓(log 𝑆𝑖𝑧𝑒𝑠𝑖 ) + 𝜖𝑠𝑖
where f(⋅) is estimated using Gaussian kernel. Std(log 𝑆𝑖𝑧𝑒) is the cross-sectional standard deviationof log 𝑆𝑖𝑧𝑒si .

6.3

Adjustment costs
Young firms may have higher TFPR due to higher adjustment costs. That is, ayoung firm who grows rapidly may face higher constraint to raise capital thanan old firm. If there is a stable relationship between age of the firm and TFPR
and the variation of age is greater in 2009 than in 1989, then the variation in
TFPR can be explained by the variation in age.
Figure 6 shows the result of kernel regression of TFPR onto age of the
firm. We measure age of a firm by dividing the accumulated depreciation of29

their capital by the depreciation per year. For the relationship between TFPR
and ‘age’, we need to measure the physical age of the firms’ facilities rather
than the age of the firm as a legal entity. Therefore, estimating age using the
cumulative depreciation is preferred to using the legal age. The drawback of
the approach based on depreciation measure is that the depreciation per year
may not be constant over the life of the capital, causing the potential
mismeasurement of the vintage of the capital.
As we can see in Figure 6, there seem to be no reliable relationshipbetween the firm’s age and TFPR. The relationship is slightly positive in 1989
while it becomes negative in 2009. Thus, it is unlikely that the change in the
distribution of the age is the true driver of the increased variation in TFPR.

Figure 6: Explaining TFPR with Firm Age

30

Figure plots fitted values of non-parametric kernel regression of the form TFPR si = 𝑓(𝐴𝑔𝑒𝑠𝑖 ) + 𝜖𝑠𝑖
where f(⋅) is estimated using Gaussian kernel.

Std(Age) is the cross-sectional standard deviation of𝐴𝑔𝑒si .

Age may be a noisy measure of the growth rate of a firm. To directly
measure the firm’s growth, we compute the input growth rate for each firm over thelast one and three years. We measure input by K αs 𝐿1−𝛼𝑠 and compute the log
growth rate for each firm in sample.

Figure 7: Explaining TFPR with Input Growth Rate
Figure plots fitted values of non-parametric kernel regression of the form TFPR si = 𝑓(𝐼𝑛𝑝𝑢𝑡𝐺𝑟𝑜𝑤𝑡ℎ𝑠𝑖 ) +𝜖𝑠𝑖 where f(⋅) is estimated using Gaussian kernel.

𝛼

1−𝛼𝑠

InputGrowthsi is the log change in K si𝑠 𝐿𝑠𝑖

fromthe previous year. Std(InputGrowth) is the cross-sectional standard deviation of 𝐼𝑛𝑝𝑢𝑡𝐺𝑟𝑜𝑤𝑡ℎsi .

Figure 7 shows the relationship between input growth rate from time31

t-1 to t and TFPR at time t. The input growth rate from time t-3 to t shows
qualitatively the same result, thus we only show the result with the input growthover the last one year.
As we can see, the relationship between input growth rate and TFPR
is not stable over time. In addition, the (cross-sectional) standard deviation of
input growth in 2009 is similar to that in 1989. Therefore, the variation in firm
growth rate with adjustment cost is not a satisfactory explanation about theincreasing variation of TFPR.
The related hypothesis is that young (or small) firms may display
greater dispersion of TFPR. If the firms in 2009 are younger or smaller than thosein 1989, then it will help explain the greater variation of TFPR in 2009.

Figure 8: Distribution of (Log) Number of Employees in 1989 and 200932

In this case, we measure the firm size by the number of employees.

Figure 8shows that the median firm is smaller in 2009 than 1989. Thus, if there is a stable
relationship between TFPR and the number of employees, then it helps explain the
TFPR variation.
Figure 9 shows the kernel regression of TFPR on the number of employees for eachfirm in sample.

The relationship between TFPR and the number of employees isnegative in 1989 while it is slightly positive in 2009. Thus, the difference in size
measured by the number of employees will not explain the increasing variation of
TFPR.

Figure 9: Explaining TFPR with Firm Age
Figure plots fitted values of non-parametric kernel regression of the form TFPR si = 𝑓(# 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠𝑠𝑖 ) +𝜖𝑠𝑖 where f(⋅) is estimated using Gaussian kernel.

33

Std(# Employees) is the cross-sectional standard

deviation of the number of employees.

Figure 10: Distribution of Log Age in 1989 and 2009

Figures 10 shows the distribution of log age of the firms. We find that the firms in2009 are older than those in 1989. Thus, if anything, the variation of TFPR in2009 might have been even greater if the age of the firms were the same as in 1989.

6.4

Unobserved Investments
Learning by doing hypothesis states that a firm may own 'too much' capital orlabor in order to improve future productivity rather than to produce output today.
If that is the case, a firm with low TFPR today should experience higher TFPQ
growth in the future.

34

Figure 11 shows the result of kernel regression of TFPR on TFPQ growth rate

next year. The data seems to support this hypothesis, as there is negative
relationship between TFPR today versus TFPQ growth rate in the future. The
question is whether it explains the wider variation of TFPR in 2009 as opposed to1989. The standard deviation of the future TFPQ growth rate increases from
0.27% in 1989 to 0.59% in 2009. While the standard deviation increases by 119%
over the period, the slope coefficient of the linear regression of TFPR onto TFPQ
growth is -0.25. Thus, the increased variation in the future growth opportunity
can explain as much as 0.25*119%=30% increase of the TFPR variation from 1989
to 2009.

35

Figure 11: Learning by Doing Effect on TFPR
Figure plots fitted values of non-parametric kernel regression of the form TFPR si,t = 𝑓( 𝐴𝑠𝑖,𝑡+1 ) + 𝜖𝑠𝑖
where f(⋅) is estimated using Gaussian kernel.
cross-sectional standard deviation ofAsi,t+1 ≡ 𝐴𝑠𝑖,𝑡+1 − 𝐴𝑠𝑖,𝑡 and Std(dTFPQ) is theAsi,t+1 .

7 Conclusions
In this paper, we show that an increase in allocation inefficiency of capital acrossfirms is one of the major factors in explaining the low TFP growth rate in Japan during
the post bubble era.

As a firm can adjust its input level only sluggishly, greater

uncertainty of the idiosyncratic physical productivity shock to a firm leads to greater
misallocation of capital among firms. The remaining question for the future research36

is what an idiosyncratic productivity shock is and why its volatility increased over theperiod between 1989 and 2009.

37

References
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Variety, Quarterly Journal of Economics 121, 2,541-585
Cooper, Russell W. and John C. Haltiwanger, 2006, On the Nature of Capital
Adjustment Costs, Review of Economic Studies 73, 3, 611-633
Dixit, Avinash K. and Joseph E. Stiglitz, 1977, Monopolistic Competition and Optimal
Product Diversity, American Economic Review 67, 3, 297-308
Dixit, Avinash K., 1989, Entry and Exit Decisions under Uncertainty, Journal of
Political Economy 97, 3, 620-638
Foster, Lucia, John C. Haltiwanger and Chad Syverson, 2008, Reallocation, Firm
Turnover and Efficiency: Selection on Productivity or Profitability?, American Economic
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Fukao, Kyoji, Tsutomu Miyagawa, Hak K Pyo and Keun Hee Rhee, 2011, Estimates of
Total Factor Productivity, the Contribution of ICT, and Resource Reallocation Effects inJapan and Korea, Global COE Hi-Stat Discussion Paper Series 177
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Hosono, Kaoru and Miho Takizawa, 2012, Do Financial Frictions Matter as a Source of
Misallocation? Evidence from Japan, PRI Discussion Paper Series, No. 12A-17
Hsieh, Chang-Tai and Peter J. Klenow, 2009, Misallocation and Manufacturing TFP in
China and India, Review of Economic Studies 124, 4, 1403-1448
Melitz, Marc J. and Gianmaroco I.P. Ottaviano, 2008, Market Size, Trade andProductivity, Review of Economic Studies 75, 1, 295-316
Miyakawa, Daisuke and Miho Takizawa, 2013, Time to IPO: Role of Heterogeneous
Venture Capital,RIETI Discussion Paper Series 13-E-022
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Working Paper
Restuccia, Diego and Richard Rogerson, 2008, Policy Distortions and Aggregate
Productivity with Heterogeneous Plans, Review of Economic Dynamics 11, 707-720

38

A1.

Derivation of Industry TFP under Log-normality

In this appendix, we simplify the gain from reallocation assuming physicalproductivity and frictions are log-normally distributed.
𝜃𝑆

S

𝑀𝑠

s=1

𝑖=1

̅̅̅̅̅̅̅̅̅𝑆
𝐴𝑠𝑖 𝑇𝐹𝑃𝑅= ∏ [∑ { ̅̅̅}Yefficient
𝐴𝑆 𝑇𝐹𝑃𝑅𝑠𝑖
Y̅̅̅̅̅̅̅̅̅̅ 𝜎−1

̃S = log ∑𝑀𝑠 {𝐴𝑠𝑖 𝑇𝐹𝑃𝑅𝑆 }Taking log and define TFP
𝑖=1 ̅̅̅̅
𝐴𝑆 𝑇𝐹𝑃𝑅𝑠𝑖

𝜎−1 𝜎−1]. Then𝑆log 𝑌 − log 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = ∑
𝑠=1

𝜃𝑆
̃𝑆
𝑇𝐹𝑃
𝜎−1

1

Let

𝐴 𝑀𝜎−1𝑇𝐹𝑃𝑅𝑠𝑖asi = log 𝑠𝑖𝐴̅̅̅̅𝑠 and t si = log ̅̅̅̅̅̅̅̅̅̅
.
𝑇𝐹𝑃𝑅𝑆
𝑆

If we assume that asi and t si are jointly

normally distributed, then𝑀𝑠̅̅̅̅̅̅̅̅̅𝑆
𝐴 𝑇𝐹𝑃𝑅̃S = log ∑ { 𝑠𝑖
TFP
}
̅̅̅
𝐴𝑆 𝑇𝐹𝑃𝑅𝑠𝑖

𝜎−1

𝑖=1

1
∑ exp((𝜎 − 1)(𝑎𝑠𝑖 − 𝑡𝑠𝑖 ))𝑀𝑆
1= (𝜎 − 1)𝐸𝑠 [𝑎𝑠𝑖 − 𝑡𝑠𝑖 ] + (𝜎 − 1) Vars [𝑎𝑠𝑖 − 𝑡𝑠𝑖 ]2where Es [⋅] and Vars [⋅] denote the expectation and variance within industry 𝑠.
Therefore
= log

𝑆

𝑆

1
log 𝑌 − log 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = ∑ 𝜃𝑆 𝐸𝑠 [𝑎𝑠𝑖 − 𝑡𝑠𝑖 ] + (𝜎 − 1) ∑ 𝜃𝑆 𝑉𝑎𝑟𝑠 [𝑎𝑠𝑖 − 𝑡𝑠𝑖 ]
2
𝑠=1

𝑠=1

1
𝜎−1

̅̅̅s = (∑ 𝐴𝜎−1
By definition, we have A
𝑠𝑖 )which can be rewritten as

1
0 = Es [𝑎𝑠𝑖 ] + (𝜎 − 1)Var_s [𝑎𝑠𝑖 ]2Thus, we have𝑆𝑆

1log 𝑌 − log 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = − ∑ 𝜃𝑆 𝐸𝑠 [𝑡𝑠𝑖 ] + (𝜎 − 1) ∑ 𝜃𝑆 {𝑉𝑎𝑟𝑠 [𝑡𝑠𝑖 ] − 2𝐶𝑜𝑣𝑠 (𝑎𝑠𝑖 , 𝑡𝑠𝑖 )}
2
𝑠=1

𝑠=1

θs
σ−1

̅̅̅̅̅̅̅̅̅𝑆 σ−1
𝑇𝐹𝑃𝑅= log ∏ Es [() ]𝑇𝐹𝑃𝑅𝑠𝑖− (σ − 1) ∑ θs Covs (𝑎si , t si )What matters is not just a variance of t si but the covariance between 𝑎si and 𝑡si.
We can further work on t si from the definition
39

TFPR si
𝑀𝑅𝑃𝐾𝑠𝑖
𝑀𝑅𝑃𝐿𝑠𝑖log ( ̅̅̅̅̅̅̅̅̅ ) = 𝛼𝑆 log ̅̅̅̅̅̅̅̅̅̅ + (1 − 𝛼𝑆 ) log ̅̅̅̅̅̅̅̅̅
TFPR S
𝑀𝑅𝑃𝐾𝑆
𝑀𝑅𝑃𝐿𝑆
1 − 𝜏𝑌𝑆𝑖
1 − 𝜏𝑌𝑆𝑖 PSi 𝑌𝑆𝑖= αs {− log+ log ∑}
1 + 𝜏𝐾𝑆𝑖
1 + 𝜏𝐾𝑆𝑖 𝑃𝑆 𝑌𝑆+ (1 − 𝛼𝑠 ) {− log(1 − 𝜏𝑌𝑠𝑖 ) + log ∑(1 − 𝜏𝑌𝑠𝑖 )𝑃𝑆𝑖 𝑌𝑆𝑖}𝑃𝑆 𝑌𝑆Definexsi = log(1 − 𝜏𝑌𝑠𝑖 )1 − 𝜏𝑌𝑆𝑖
ysi = log ()
1 + 𝜏𝐾𝑆𝑖
𝑃𝑆𝑖 𝑌𝑆𝑖ωsi = logM
𝑃𝑆 𝑌𝑆 sWe can rewrite the weighted average as
1 − 𝜏𝑌𝑆𝑖 PSi 𝑌𝑆𝑖∑= Es [exp(𝑦𝑠𝑖 + 𝜔𝑠𝑖 )]1 + 𝜏𝐾𝑆𝑖 𝑃𝑆 𝑌𝑆
𝑃𝑆𝑖 𝑌𝑆𝑖∑(1 − 𝜏𝑌𝑠𝑖 )= Es [exp(𝑥𝑠𝑖 + 𝜔𝑠𝑖 )]𝑃𝑆 𝑌𝑆I assume that xsi , 𝑦𝑠𝑖 , 𝑎̃𝑠𝑖 ≡ log 𝐴𝑠𝑖 are jointly normally distributed.
From the cost minimization problem, we have
Psi 𝑌𝑠𝑖𝑃𝑠𝑖1−𝜎=𝑃𝑠 𝑌𝑠∑ 𝑃𝑠𝑖1−𝜎Thus
𝑃𝑠𝑖1−𝜎ωsi = log
𝐸[𝑃𝑠𝑖1−𝜎 ]Then we can rewrite t si ast si = 𝛼𝑠 {−𝑦𝑠𝑖 + log 𝐸𝑠 [exp(𝑦𝑠𝑖 + 𝜔𝑠𝑖 )] } + (1 − 𝛼𝑠 ){−𝑥𝑠𝑖 + log 𝐸𝑠 [exp(𝑥𝑠𝑖 + 𝜔𝑠𝑖 )]}As we have E[exp(𝜔𝑠𝑖 )] = 1, we can expand the expectation to obtain,1
log 𝐸𝑠 [exp(𝑦𝑠𝑖 + 𝜔𝑠𝑖 )] = 𝐸𝑠 [𝑦𝑠𝑖 ] + 𝑉𝑎𝑟𝑠 [𝑦𝑠𝑖 ] + 𝐶𝑜𝑣𝑠 (𝑦𝑠𝑖 , 𝜔𝑠𝑖 )2
1
log 𝐸𝑠 [exp(𝑥𝑠𝑖 + 𝜔𝑠𝑖 )] = 𝐸𝑠 [𝑥𝑠𝑖 ] + 𝑉𝑎𝑟𝑠 [𝑥𝑠𝑖 ] + 𝐶𝑜𝑣𝑠 (𝑥𝑠𝑖 , 𝜔𝑠𝑖 )2
Now we work on covariance. That is
Covs (xsi , 𝜔𝑠𝑖 ) = 𝐶𝑜𝑣𝑠 (𝑥𝑠𝑖 , (1 − 𝜎)𝑝𝑠𝑖 )Covs (ysi , ωsi ) = Covs (ysi , (1 − σ)psi )where
psi = log 𝑃𝑠𝑖 = (𝐶𝑜𝑛𝑠𝑡) − 𝛼𝑠 𝑦𝑠𝑖 − (1 − 𝛼𝑠 )𝑥𝑠𝑖 − 𝑎̃𝑠𝑖Therefore
Covs (xsi , 𝜔𝑠𝑖 ) = (1 − 𝜎){−𝛼𝑠 𝐶𝑜𝑣𝑆 (𝑦𝑠𝑖 , 𝑥𝑠𝑖 ) − (1 − 𝛼𝑠 )𝑉𝑎𝑟𝑠 (𝑥𝑠𝑖 ) − 𝐶𝑜𝑣𝑆 (𝑎̃𝑠𝑖 , 𝑥𝑠𝑖 )}Covs (ysi , 𝜔𝑠𝑖 ) = (1 − 𝜎){−𝛼𝑠 𝑉𝑎𝑟𝑠 (𝑦𝑠𝑖 ) − (1 − 𝛼𝑠 )𝐶𝑜𝑣𝑆 (𝑦𝑠𝑖 , 𝑥𝑠𝑖 ) − 𝐶𝑜𝑣𝑆 (𝑎̃𝑠𝑖 , 𝑦𝑠𝑖 )}Using these equations, we have

40

1
1
E[t si ] = 𝛼𝑠 { 𝑉𝑎𝑟[𝑦𝑠𝑖 ] + 𝐶𝑜𝑣(𝑦𝑠𝑖 , 𝜔𝑠𝑖 )} + (1 − 𝛼𝑠 ) { 𝑉𝑎𝑟[𝑥𝑠𝑖 ] + 𝐶𝑜𝑣(𝑥𝑠𝑖 , 𝜔𝑠𝑖 )}2211= 𝛼𝑠 𝑉𝑎𝑟(𝑦) + (1 − 𝛼𝑠 )𝑉𝑎𝑟(𝑥)22+ (1 − 𝜎){−𝛼𝑠 𝑉𝑎𝑟(𝑦) − 𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦) − 𝛼𝑠 𝐶𝑜𝑣(𝑎̃, 𝑦)− 𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦) − (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) − (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑎̃, 𝑥)}
Var[t si ] = 𝛼𝑠 𝑉𝑎𝑟(𝑦) + (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) + 2𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦)
Now we compute1−E[tsi ] + (𝜎 − 1)𝑉𝑎𝑟[𝑡𝑠𝑖 ]21
1= − 𝛼𝑠 𝑉𝑎𝑟(𝑦) − (1 − 𝛼𝑠 )𝑉𝑎𝑟(𝑥)22(𝜎+ − 1){−𝛼𝑠 𝑉𝑎𝑟(𝑦) − 𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦) − 𝛼𝑠 𝐶𝑜𝑣(𝑎̃, 𝑦)− 𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦) − (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) − (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑎̃, 𝑥)}1+ (𝜎 − 1)(𝛼𝑠 𝑉𝑎𝑟(𝑦) + (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) + 2𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦))211= − 𝛼𝑠 𝑉𝑎𝑟(𝑦) − (1 − 𝛼𝑠 )𝑉𝑎𝑟(𝑥)221− (𝜎 − 1){𝛼𝑠 𝑉𝑎𝑟(𝑦) + (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) + 2𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦)}2− (𝜎 − 1){𝛼𝑠 𝐶𝑜𝑣(𝑎̃, 𝑦) + (1 − 𝛼𝑠 )𝐶𝑜𝑣 (𝑎̃, 𝑥)}
Now we rewrite the three groups of terms:
The second row is
𝛼𝑠 𝑉𝑎𝑟(𝑦) + (1 − 𝛼𝑠 ) 𝑉𝑎𝑟(𝑥) + 2𝛼𝑠 (1 − 𝛼𝑠 )𝐶𝑜𝑣(𝑥, 𝑦) = Var(αs ysi + (1 − αs )xsi ) = Vars (t si )The third row is
𝛼𝑠 𝐶𝑜𝑣𝑠 (𝑎̃, 𝑦) + (1 − 𝛼𝑠 )𝐶𝑜𝑣𝑠 (𝑎̃, 𝑥) = Covs (𝑎̃, αs ysi + (1 − αs )xsi ) = 𝐶𝑜𝑣𝑠 (𝑎𝑠𝑖 , 𝑡𝑠𝑖 )The extra covariance terms between asi and t si come from the fact that weweight more on bigger firms when computing average. A greater friction (smaller x,ythus bigger t) leads to putting less weight on that firm the average. This weighting
scheme makes the average friction higher, and E[−t si ] smaller. Therefore, we obtainthe following expression:
𝑆

𝑆

𝑠=1

𝑠=1

1
log 𝑌 − log 𝑌𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = − ∑ 𝜃𝑆 𝐸𝑠 [𝑡𝑠𝑖 ] + (𝜎 − 1) ∑ 𝜃𝑆 {𝑉𝑎𝑟𝑠 [𝑡𝑠𝑖 ] − 2𝐶𝑜𝑣𝑠 (𝑎𝑠𝑖 , 𝑡𝑠𝑖 )}2S1= − (σ − 1) ∑ θs {Vars [t si ] + 4Covs (𝑎si , t si )}2
s=11− ∑ θs (αs Vars (ysi ) + (1 − αs )Vars (xsi ))2
s=1

We may also impose the identifying assumption for Asi for the data analysis,𝜎𝜅𝑆 (𝑃𝑠𝑖 𝑌𝑠𝑖 )𝜎−1

𝜎which is Asi = 𝐾 𝛼𝑠 𝐿 1−𝛼𝑠 . Then Covs (𝑎𝑠𝑖 , 𝑡𝑠𝑖 ) = 𝜎−1 𝑉𝑎𝑟𝑠 (𝑡𝑠𝑖 ) holds. In such cases, the𝑠𝑖𝑠𝑖efficiency gain is purely a function of the variance of xsi and ysi .
41

A2.

Measuring Uncertainty of Idiosyncratic Productivity Shockfollowing Cooper and Haltiwanger (2006)
We decompose the earnings shocks using the methodology of Cooper andHaltiwanger (2006).
We estimate the economy-wide capital share parameter
instrumenting on the once and twice lagged capital and twice lagged profits. The
residuals split between aggregate profitability shocks and the idiosyncratic shocks. We
fit AR(1) model to the idiosyncratic shocks to extract innovation to the idiosyncratic
profitability shocks.

Table A1: Measuring the Magnitude of Idiosyncratic Profitability Shock

A: Estimated Result
θ
ρϵ
0.855
0.924
(0.002)(0.002)

B: Size of ResidualsYearσ(ϵit )
1989
0.53
2009
0.70

The table shows the result of two-step regressions.

σ(ηit )
0.18
0.29

First regression is the panel IV estimates oflog 𝑆𝑎𝑙𝑒𝑠𝑖𝑡 = 𝜃 log 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑡 + 𝑒𝑖𝑡 , where the instruments are log Cap talit−1 , log 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑡− , log 𝑆𝑎𝑙𝑒𝑠𝑖𝑡− .
The estimates include time fixed effects.
1/𝑛 ∑𝑛𝑖=1 𝑒𝑖𝑡 .

The second step is ϵit =𝜖𝑖𝑡−1 +

𝑖𝑡where ϵit ≡ 𝑒𝑖𝑡 −The figures in parenthesis are standard errors.

Table A1 shows the estimated result. The standard deviation of the shockσ(η)
becomes 61% larger in 2009 than in 1989. During the same period, the standard
deviation of the TFPR becomes 85% larger. Thus, a significant portion of the TFPR
variation change can be explained by the greater unexpected shocks to firms’
profitability. The remaining component of the TFPR variation may be either due togreater cost of investment or more learning-by-doing activities in 2009.

42

A3.

Implementing Kernel Regression

To analyze the source of TFPR variation, I run non-parametric kernel regression of
the form
TFPR si = 𝑓(𝑧𝑠𝑖 ) + 𝜖𝑠𝑖
where the function ff(zsi ) is estimated non-parametrically using Gaussian kernel.
Specifically, the kernel regression estimator at z0 is given by1

f(z0 ) =∑𝑖=1 ((𝑧𝑠𝑖 − 𝑧0 )/ℎ)𝑇𝐹𝑃𝑅𝑠𝑖
1∑𝑖=1 ((𝑧𝑠𝑖 − 𝑧0 )/ℎ)= ∑ 𝑤𝑠𝑖 𝑇𝐹𝑃𝑅𝑠𝑖
𝑖=1

where (⋅) is the normal probability density function and h is the bandwidth of thekernel.
The optimal bandwidth is chosen to minimize the cross-validation CV (h),CV(h) ≡ ∑ (𝑇𝐹𝑃𝑅𝑠𝑖 − 𝑓̂−𝑖 (𝑧𝑠𝑖 ))(𝑧𝑠𝑖 )i=1

where𝑓̂−i (𝑧𝑠𝑖 ) =∑𝑖 𝑤𝑠 𝑇𝐹𝑃𝑅𝑠

∑

𝑖 𝑤𝑠

and (⋅) is an indicator function which is one if zsi is between 5 percentile and 95
percentile of the distribution and zero otherwise.
The idea of cross-validation procedure is that one has to strike a balance
between minimizing errors and improving efficiency of an estimate. Putting a large
weight on TFPR si to estimate 𝑓(zsi ) will reduce an error but will not use as muchinformation from the adjacent observations TFPR s , resulting in inefficiency. We
penalize inefficiency by using 𝑓̂−𝑖 (𝑧𝑠𝑖 ), or a leave one-out estimates in computing CV (h).
Minimizing CV (h) amounts to choosing an optimal balance between error minimizationand pursuit of efficiency.

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