Financial Frictions, Capital Misallocation and Structural Change∗
Naohisa Hirakata†

Takeki Sunakawa‡May 2019
Abstract
We develop a two-sector growth model with financial frictions to examine the effects of adecline in the working population ratio and change in the structure of household demand on
sectoral TFP and structural change. Our findings are twofold. First, with financial frictions,a decline in labor input reduces the real interest rate and increases excess demand for borrowing, tightening collateral constraints at a given credit-to-value ratio and generating capital
misallocation and lower sectoral TFP. Second, compared to the case with no financial frictions,such changes in sectoral TFP impede structural change driven by the change in the structureof household demand. We also estimate the model’s parameters using the Japanese data andundertake a counter-factual simulation to demonstrate the role of financial frictions and capital
misallocation in structural change.
Keywords: Financial frictions; heterogeneous firms; capital misallocation; total factor productivity; structural change
JEL codes: E23, E44, O41, O47∗

We appreciate the comments and discussions from an anonymous referee, Kosuke Aoki, Ryoichi Imai, Aubhik
Khan, Kiminori Matsuyama, Kengo Nutahara, Satoshi Tanaka, Julia Thomas, Takayuki Tsuruga, Kozo Ueda, as
well as seminar participants at Asian Meeting of the Econometric Society 2013 and Summer Workshop on Economic
Theory. Any remaining errors are ours. The views expressed herein are ours and should not be interpreted as thoseof the Bank of Japan.
†
Bank of Japan. E-mail address: naohisa.hirakata@boj.or.jp.
‡
Kobe University. E-mail address: takeki.sunakawa@gmail.com.

1

1

Introduction

In recent years, many developed countries have experienced significant demographic change, especially in the form of rapidly aging populations. As the number of retirees increases, the value-added
share of industries producing those goods and services necessary for the elderly, such as hygiene andmedical services, has also increased. For example, as shown in Figure 1, since about the 1980s in
Japan, the population ratio of persons aged 65 years and over to the total population has continued
to increase. This ratio was around 10% at the beginning of the 1980s, but increased to 26.7% in2015 and is projected to continue to increase to around 38% in 2060. During the same period,
the nominal value–added share of service sectors related to aging has increased by more than 5%.
In addition, firms in these industries in Japan are typically new and small, as shown in Table 1.
They tend to have low capital adequacy ratios and face higher loan interest rates, which implies
that they are financially constrained.1 Also, regarding the household side, Table 2 shows that theconsumption share of health of the elderly (age of 65 over) is much higher than that of young
persons (ages 0-14 and 15-64).
Table 1: Financial conditions for firms by sector in Japan.
Interest rates on loans
Capital/Assets
Small firms ratio
Liquidity/Short-term debt

All
1.3
39.9
63.6
140.3

Manu.
1.3
46.4
51.9
149.5

Service
1.2
45.4
72.3
126.9

Medical
1.9
28.4
84.9
133

Source: FY2015 Financial Statements Statistics of Corporations by Industry, Ministry of Finance of Japan.

Table 2: Consumption share of health in Japan.
age 0–14
0.07

age 15–64
0.09

age 65+0.27

Source: Tung (2011). The data is for Japan in 2004 from National Transfer Accounts accessed at
http://www.ntaccounts.org/web/nta/show/Browse%20database on April 2, 2019. The consumption ofhealth includes the private and public expenditures of health.
1Note that the service sector is more mature as a whole, and firms in the sector generally have higher capital
adequacy ratios and lower interest rates than those in the medical sector on average.

2

Figure 1: Aging population, value-added share, and relative TFP and price in Japan.
Aging population ratio

0.4

Value added share (demeaned)

0.1

Service related to aging
ServiceAgri., Fishery, mining
Manufacturing

0.08

0.35

0.06

0.3

0.04
0.02

0.25

0

0.2

-0.02
-0.04

0.15

-0.06

0.1
-0.08

0.05

-0.1

1980

1990

2000

2010

2020

2030

2040

2050

1975

2060

1980

1985

1990

1995

2000

2005

2010

relative TFP and price1.5
z 1 /z 2
p 1 /p 2

1.4

1.3

1.2

1.1

1

0.9

0.8
1975

1980

1985

1990

1995

2000

2005

2010

Notes: The relative price is the ratio of the value-added deflator. See Appendix A for details of the data.

At the same time, the growth rate of total factor productivity (TFP) has declined over thisperiod. The average growth rate of TFP from 1973 to 1990 was 1.5%, whereas that from 1991
to 2012 was only 0.3%. The relative TFP of the elderly-related sector (i.e., hygiene and medical
services) to the other sectors has also been low, whereas its relative prices have increased during
this period, especially after the 1980s.
Motivated by these facts, this paper provides a theory of how a reduction in the share of theworking population can explain the slowdown of the economy through a decline in aggregate TFP
caused by financial frictions and capital misallocation among firms. Our theory suggests that the
reduced working population ratio may have led to a disproportionate decline in sectoral TFP, which
affects the pace of structual change induced by demand shifts by the elderly.
This paper links capital misallocation, TFP, and structural change in the presence of financial
frictions in a unified dynamic general equilibrium framework. We develop a two-sector neoclassicalgrowth model with financial frictions and two household types: workers and retirees. We introduce3two types of firms to analyze financial frictions: borrowers and savers. We assume that borrowers arenewer and smaller firms dominant in industries such as hygiene and medical services, while savers
are older and larger firms typically found in manufacturing and in services other than hygiene andmedical services. For the most part, borrowers have large financial needs, but their borrowing islimited by collateral constraints (c.f., Kiyotaki and Moore, 1997). In contrast, savers have lessneed for financing, and their borrowing is unconstrained. Our model has two sectors: one new andthe other old. The new sector is more credit constrained (i.e., the new sector has more borrowers
than the old sector). As the number of retirees increases—that is, as the working population ratio
declines—the demand for goods produced in the new sector increases. This is the driving force forthe structural change explored in the paper.
Our findings are twofold. First, in the presence of financial frictions, a decline in the working
population ratio distorts the allocation of capital, which lowers TFP in both the new and old sectors.
The decline in the working population ratio also lowers real interest rates, thereby increasing
borrowing demand. This increased demand for borrowing tightens the collateral constraint at aconstant credit-to-value ratio because the value of collateral does not rise proportionally. This isbecause borrowers have too little capital, whereas savers have too much, and borrowers produce
fewer goods than they would do in the absence of financial frictions. This capital misallocation
then lowers sectoral TFP in both sectors.
Second, TFP in the new sector is more and disproportionately affected by financial frictions
than that in the old sector, impeding the structural change driven by changes in the structure ofhousehold demand. The number of borrowers in the new sector exceeds that in the old sector,
which means the new sector has a greater need for financial resources and is more vulnerable tofinancial frictions than the old sector. Thus, capital misallocation in the new sector is more severe
than in the old sector. This difference in the effect of financial frictions between sectors ensures
TFP in the new sector is lower than in the old sector, thereby impeding structural change. Thatis, it leads to too short a supply of goods produced in the new sector compared to that without
financial frictions.
To examine whether these theoretical findings can be supported empirically, we estimate the4model parameters by fitting the model to actual data. Our estimates are consistent with ourassumptions. That is, there are more borrowers in the new sector than the old sector and retirees
demand the new sector’s goods more than workers. We simulate the model for the Japanese
economy from 1973 to 2012 and undertake a counter-factual simulation in the absence of financial
frictions. We find that financial frictions and capital misallocation indeed impede structural change
as the price for the new sector’s goods becomes higher.

Related litarature Some recent studies argue that capital misallocation among firms is oneof the main reasons behind a decline in aggregate or sectoral TFP.2 For example, Moll (2014)
emphasizes the role of financial frictions as a cause of capital misallocation. Financial frictions may
be affected by changes in the working population ratio. Poterba (2001) and Ikeda and Saito (2014)
discusses the effects of demographic change on financial markets and asset prices.
Furthermore, a difference in TFP among sectors may affect inter-sectoral capital misallocation(i.e., structural change), a shift in sectoral output or employment share taking place over a long
period of time.3 Changes in the working population ratio, on the one hand, would affect thehousehold demand structure. On the other hand, asymmetric effects of such demographic changes
on sectoral TFPs would also be important for structural change. These economic consequences
associated with a decline in the working population ratio is significant to consider since many
countries have experienced or will experience such a decline.
Buera et al. (2011) develop a quantitative framework to explain the relationship between TFP,
structural change measured by the ratio of employment or output in the service sector to that in
the manufacturing sector, and financial development across countries. They analyze the effects ofexogenous change in financial frictions on sectoral TFP (for manufacturing and services) to explaincross-country differences in TFP and structural change.4 In contrast, the present paper focuses ontightening collateral constraints caused by a decline in labor input. We also focus on changes in2

For example, see Hsieh and Klenow (2009); Restuccia and Rogerson (2008). There is also a special issue in Review
of Economic Dynamics on “Misallocation and Productivity” (Restuccia and Rogerson, 2013).
3
For an excellent and extensive survey, see Matsuyama (2008).
4
Arellano et al. (2012); Khan and Thomas (2013) studies the effect of exogenous changes of financial frictions on
the measured TFP in heterogeneous agent models.

5the structure of household demand as a driving force for structural change, rather than traditional
sector-biased technological progress or non-homothetic preferences (Kongsamut et al., 2001; Ngai
and Pissarides, 2007).
Unlike Buera et al. (2011), we build a prototype two-sector economy with wedges whose allocations and prices are equivalent to those in the original two sector economy introduced above
in order to analytically investigate the relationship among financial frictions, capital misallocationand structural change.5 This method was originally proposed by Chari et al. (2007). Although ourapproach employs a simplified modeling of heterogeneity across firms, we obtain analytical results
as well as numerical ones.6
For estimating the model’s parameters, we follow the strategy used in Herrendorf et al. (2013);
Moro et al. (2017). Taking the sequence of the relative price as given, the intratemporal problem
is separated from the intertemporal problem as shown in Herrendorf et al. (2014). The equilibrium
conditions in the intratemporal problem are used for nonlinear estimations. Then, having estimatesat hand, we simulate the model and obtain a dynamic perfect–foresight path as in Buera andKaboski (2009). We also do a counter-factual simulation to evaluate the role of financial frictions
and capital misallocation for sectoral TFP and structural change in a general equilibrium.
The reminder of the paper proceeds as follows. We present the original two-sector economy
with financial frictions and households’ demand structure in the following section. Section 3 analyzes certain correspondences from financial frictions and demand structure to the wedges in the
prototype economy. Section 4 estimates the key parameters of financial frictions and household
preferences using the data of working population ratio, value-added share, sectoral TFP and relative price from 1973–2012 in Japan. Then we presents numerical exercises using the prototype
economy. Section 5 presents a conclusion. The details of data, the prototype economy with wedges,
and the proofs of propositions are presented in online Appendix.
5

The prototype two-sector economy with wedges is used in other papers, such as Hayashi and Prescott (2008),
Esteban-Pretel and Sawada (2014), and Cheremukhin et al. (2017).
6
See also Buera et al. (2011); Midrigan and Xu (2014); Moll (2014).

6

2

Two-sector model with financial frictions and demand structure

We build a two-sector neoclassical growth model with financial frictions. On the firm side, there
are two sectors, the old and the new. In each sector, there are a final-good producing firm andmultiple intermediate-good producing firms. The final-good producing firm uses intermediate goods
as inputs to produce final goods, and has a constant elasticity of substitution (CES) production
function. We assume that financial needs are different among intermediate-good producing firms;
a fraction of them have a lower discount factor. They are borrowers, who are bound by collateral
constraints (Kiyotaki and Moore, 1997). The other firms with a higher discount factor are savers,
who are unconstrained. Even though borrowers and savers have the same Cobb-Douglas production
function, their levels of holding capital are different depending on their financial frictions. Therefore,
the final-good producing firm with the CES function in each sector has lower sectoral TFP andhence output. We also assume that the number of borrowers is larger in the new sector, whichleads to differences in sectoral TFP.
On the household side, there are workers and retirees. Workers supply labor inelastically andconsume final goods in each sector, whereas retirees only consume final goods in each sector.
Workers and retirees have different preferences over final goods produced. When the number ofworkers declines, there are two effects; one is a decline in labor input, and the other is a change inthe structure of household demand.

2.1

Firms

There are two sectors, the old and the new. Let 1 denote the new sector, and 2 denote the old.
The final-good producing firm in each sector i = {1, 2} minimizes its expenditure:

pit yti =Z 1ipijt yjt
dj,

(1)

0

subject toZ 1
1/(1−ε−1 )ii 1−ε−1yt =(yjt )
dj
,
0

7

(2)

i of the intermediate good j ∈ [0, 1] andThe final-good producing firm in sector i purchases pijt yjt
i are the price and output of intermediate
sells pit yti of the final good to households, where pijt and yjt

goods, and pit and yti are the price and output of final goods. The firm produces final goods by
a CES production function (2), where ε > 1 is the elasticity of substitution between intermediate
goods. The first-order condition (FOC) is given byiyjt= (pijt /pit )−ε yti .

(3)This is the demand function of each intermediate good. The intermediate-good producing firmj ∈ [0, 1] maximizes its discounted sum of future profits:
∞
X
t=0

βjt



λt
λ0

−1


i
i
i
(1 − τti )(pijt yjt− wt nijt ) − p2t (kjt+1− (1 − δ)kjt) − qt bijt+1 + bijt ,subject toi
i α i 1−αyjt
= ζti (kjt
) (njt )
,

(4)

i
yjt
= (pijt /pit )−ε yti ,i−bijt+1 ≤ θp2t kjt,(5)

i of intermediate goods to the finalEach intermediate-good producing firm j in sector i sells pijt yjt

good producing firm in the same sector, pays wage bill wt nijt to workers, and purchases capital
goods produced in sector 2. wt is the real wage, and we assume that labor is freely mobile betweenQfirms and sectors. βjt (λt /λ0 )−1 = ts=1 β(λs /λs−1 )−1 is the cumulative stochastic discount factor,
where βj ∈ (0, 1) and λ−1is the Lagrange multiplier on the household’s budget constraint. Eachtfirm produces using a Cobb-Douglas production function (4) with capital share α ∈ (0, 1) subject tothe demand function (3). ζti is a sector-specific exogenous productivity and 1−τti is a sector-specificexogenous tax.7 Each firm also borrows or lends bijt+1 bonds priced at the risk-free bond price qt ,and faces a collateral constraint (5) with a parameter for the credit-to-value ratio θ ≥ 0. Let φijt
7
These variables may have trends and are needed for only fitting the model to the data of the Japanese economy
in Section 4.3.

8

be the Lagrange multiplier on the collateral constraint. The FOCs areiii∂kjt+1: p2t λt+1 = βj λt (1 − τti )(1 − ε−1 )αpijt+1 yjt+1/kjt+1+ p2t+1 (1 − δ + θφijt+1 ) ,∂nijt :

iwt = (1 − ε−1 )(1 − α)pijt yjt/nijt ,

∂bijt+1 : (qt − φijt )λt+1 = βj λt .

(6)
(7)
(8)

The complementary slackness conditions areiφijt (bijt+1 + θp2t kjt) = 0,

φijt ≥ 0.

Note that firms have different discount factors βj , which determine their financial needs and bondpositions. We assume that there are only two types of intermediate-good firms, borrowers andsavers, denoted by j = {b, s}. We further assume that
Assumption 1. βb < βs = β so that only the borrowers’ collateral constraint binds.
iii < 0 < biFrom Assumption 1, we immediately obtain bibt+1 = −θp2t kbt
st+1 , φbt > 0 and φst = 0.

Note that different financial needs and discount factors are the only source of heterogeneity amongfirms, and as long as the borrowers’ discount factor βb is common among sectors, φt ≡ φibt > 0 does
not depend on i.
Sectoral output yti , capital kti and labor nit are given byhi1/(1−ε−1 )i 1−ε−1i 1−ε−1
yti = χi (ybt)
+ (1 − χi )(yst
)
,

(9)

i
i
kti = χi kbt+ (1 − χi )kst,

(10)

nit = χi nibt + (1 − χi )nist ,(11)

where χi ∈ (0, 1) is the ratio of borrowers in each sector. We assume that
Assumption 2. χ1 > χ2 so that sector 1 is the more constrained sector.

9This assumption corresponds to the observation that the new sector such as medical is more
likely financially constrained. In Section 4.1, we estimate these parameters and show that theassumption is indeed satisfied. The TFP in each sector is defined as

zti ≡

yti
.
(kti )α (nit )1−α(12)

From Assumption 2, the more intermediate-good producing firms that are constrained, the more
allocation between the two types of firms is distorted; therefore, the sectoral TFP in the moreconstrained sector is lower; zt1 < zt2 holds. See also Section 3.

2.2

Households

There are two types of households, workers and retirees, denoted by k = {w, r}. They have different
preferences over different final goods produced in each sector. Each household k minimizes its
expenditure:2 2k
pkt ckt = p1t c1k
t + pt ct ,subject tohi1/(1−−1 )−1
1−−1
k −−1 2k 1−−1
ckt = (µk )− (c1k
)
+
(1
−
µ
)
(c
)
,
t
t

(13)

where pkt is the price of composition goods ckt consumed by household k. Composition goods are
2k
produced by a CES function (13) of c1kt and ct , which are the consumption of each sector’s goods

by household k. The function has parameters for the elasticity of substitution  ≥ 0 and thesector-bias effect µk ∈ (0, 1) for each type of household k. The FOCs are
k 1 k − kc1kt = µ (pt /pt ) ct ,(14)k
2 k − kc2k
t = (1 − µ )(pt /pt ) ct .

(15)

The sector-bias parameters µw and µr determine each household’s demand for goods produced in
sector 1. We assume that10

Assumption 3. µw < µr so that retirees demand for goods produced in sector 1 more than workers
do.
From Assumption 3, the decline in labor input implies a shift in the structure of household
demand from the old sector to the new sector. An increase in the number of retirees leads to anincrease in demand for goods produced in the new and more constrained sector (sector 1). As
in the previous case with Assumption 2, we show that this assumption holds with the estimatedparameters.

Utilitarian economy We assume that there is a utilitarian who insures the consumption risksrthat each household faces. Te consumption profile (cwt , ct ) then depends only on the household

demand structure.8 We ignore the lifecycle effect of demographic changes on consumption andsaving and hence the real interest rate (e.g., Carvalho et al., 2016), as this may also affect any
misallocation between firms and endogenous TFP. This effect usually exerts downward pressure on
the real interest rate and endogenous TFP may decline even more.9
r
The utilitarian chooses the allocation of composition goods to consume cw
t and ct , and theramount of the risk-free bond Bt . Given the prices of the composition goods pw
t and pt , and therisk-free bond price qt , the utilitarian maximizes the joint life-time utility of workers and retirees
∞
X

w
w
r
β t {nw
t log ct + (1 − nt ) log ct } ,t=0

subject to
w w
w r r
w
nw
t pt ct + (1 − nt )pt ct + qt Bt+1 ≤ wt nt + Bt + Dt ,−1
12
where nw
t = nt + nt is the total number of workers and Dt is the sum of firm transfers. Let λt be
8For example, if their demand preferences are identical, i.e., µw = µr , workers and non-workers consume the sameamount of goods.
9
We ignore household lifecycle because we wish to obtain an analytical mapping from the model with financial
frictions and the structure of household demand to the prototype model via the wedges.

11

the Lagrange multiplier. The FOCs are

∂cw
t :

w
λt = pw
t ct ,(16)∂crt :

λt = prt crt ,

(17)

−1
∂Bt+1 : qt λ−1
t = βλt+1 .

(18)

Note that a decline in the number of workers nw
t involves two effects; (i) a decline in the labor
input and the corresponding wage bill, and (ii) an increase in the number of retirees and the total
demand for goods produced in sector 1.10
10

We can decentralize the utilitarian economy as follows. Each household type maximizes their life-time utility∞X

β t log ckt

t=0

subject tokpkt ckt + qt Bt+1
≤ hkt + Btk + Dtk ,where hkt is the labor income and the transfers among households. The FOCs are
λkt = pkt ckt ,qt /λkt = β/λkt+1 .
rkk
We need to show λw
t = λt . Note that λt+1 /λt = β/q. Therefore, under the assumption of perfect foresight, it sufficeswr
to show λ0 = λ0 . We assume that there is a transfer between households in period 0 so that the marginal utilitiesr
are equalized between workers and retirees and λw
0 = λ0 holds.

12

2.3

Market-clearing conditions

The good market in each sector, the capital market, labor market and bond market all clear:

1ww 1r
c1t = nwt ct + (1 − nt )ct ,

(19)

2w
w 2r
c2t = nwt ct + (1 − nt )ct ,(20)

c1t = yt1 ,(21)

c2t = (1 − ψt )yt2 + (1 − δ)kt − kt+1 ,(22)

kt = kt1 + kt2 ,

(23)

1
2
nw
t = nt + nt ,X χi bib,t+1 + (1 − χi )bis,t+1 + Bt+1 = 0.

(24)
(25)

i∈{1,2}

c1t and c2t are the total amounts of consumption of each sectoral good. Goods produced in sector
1 are only consumed, whereas goods produced in sector 2 are also used for each firm’s investment
and the government expenditure.11 ψt = gt /yt2 is the ratio of government expenditure to output insector 2. There is an integrated bond market to which all firms and households have access, witha unique market-clearing bond price qt .
We denote the price of goods produced in sector 1 p1t = pt and normalize p2t = 1 hereafter. pt is
the relative price, i.e., the ratio of the price of goods produced in sector 1 to those in sector 2. We
detrend the model as the exogenous component of the sectoral TFP ζti for each sector may have atrend in time. A competitive equilibrium is defined as the set of prices and allocations satisfying
the relevant equations. See Appendix ?? for details.
11

These assumptions may have influence on the measurement of the value-added output in the old sector. However,the value-added share of the old sector is more than 90% and hygiene and medical services are usually not included
in investment.

13

3

Analysis

In this section, we present an analysis using the detailed model presented in the previous section.12
In neoclassical growth models, a decline in labor input leads to temporally lower real interest
rates, as the capital-labor ratio rises. We analytically show that such a drop in real interest
rates, i.e., higher risk-free bond prices, in turn leads to tighter collateral constraints and capital
misallocation among firms, which is also linked to sectoral TFP. Regarding structural change, we
present a prototype two-sector model with wedges (Chari et al., 2007) whose allocations and prices
are equivalent to the detailed two-sector model with financial frictions and structure of households
demand. By using this equivalence, we derive the demand and supply curves in terms of the relative
price and output.

3.1

Capital misallocation and sectoral TFPs

There is a relationship between the tightness of collateral constraints and capital misallocation
among firms. In Proposition 1, we analytically show that, given the relative price, a tighter collateral
constraint leads to capital misallocation. Also, capital misallocation leads to lower sectoral TFP.
Note that the FOC of the risk-free bond held by the utilitarian (18) determines the risk-freebond price qt . Combining it with the FOC of borrowers (8), we haveφt = (1 − βb /β)qt .

(26)

From Assumption 1, βb < β and φt > 0 holds; only borrowers’ collateral constraint binds. There isa one-to-one relationship between the risk-free bond price and the tightness of collateral constraints;
that is, the higher risk-free bond price is, the tighter collateral constraint is. As the risk-free bondprice increases, investment returns are relatively higher than bond returns, and borrowers havemore incentive to borrow, but the collateral constraint prevents them from doing so; therefore, thecollateral constraint becomes tighter.13
12

In this section, we use the model without detrending, but the discussion extends to the model with detrending
in a straight-forward way. Specifically, only the discussion on the sectoral TFP and relative price will be affected byincorporating trends.
13
Note that borrowers want to borrow infinite amount as their discount factor is less than savers’ discount factor,

14

The risk-free bond price, or the tightness of collateral constraints is linked to misallocation
among borrowers and savers. We show that
Lemma 1. (i) The ratio of marginal revenue product of capital (MRPK) among borrowers andsavers is given by

xt+1 ≡=iipibt+1 ybt+1/kbt+1,iipist+1 yst+1/kst+1β 1 − (qt − φt )(1 − δ + θφt+1 ).
βb
1 − qt (1 − δ)(27)(ii) If βb < β and the credit-to-value ratio is smaller than the threshold,θ < θ̄t+1 =β 1,βb qt qt+1

then xt+1 > 1 holds.
Proof. See Appendix C.1.
If xt+1 = 1, MRPKs of borrowers and savers are equalized, and capital is efficiently allocatedamong borrowers and savers. If xt+1 > 1, MRPK of borrowers is greater than that of savers, which
implies capital misallocation among borrowers and savers. We assume θ is far enough below θ̄t+1
so that xt+1 > 1 holds. As we assume that the borrowers’ discount factor βb is common among
sectors, and it is the only source of heterogeneity among firms, the ratio of MRPK is also common
among sectors.
Also, capital misallocation among firms is linked to sectoral TFP. We show the following propositioni
i
Proposition 1. (i) The sectoral TFP zt+1
can be decomposed into its exogenous component ζt+1
i . ηiand its endogenous component ηt+1
t+1 is a function of the ratio of MRPK xt+1 and the ratio of

the risk-free bond price in steady state, i.e., βb < β = q.

15

borrowers χi ,

i
i
i
zt+1
= ζt+1ηt+1,
ε"1−ν # ε−1
1 − χi + χi xγt+1i= ζt+1,α̃
1 − χi + χi xγ−1
t+1

(28)

where α̃ = (1 − ε−1 )α, ν = (1 − ε−1 )(1 − α) and γ = α̃/(α̃ + ν − 1) < 1.
∂η i

xt+1
φt
> 0 and ∂xt+1< 0 for i = {1, 2} hold.
(ii) ∂x∂φt+1
t xt+1t+1 η it+1(iii) If χ1 > χ2 , then

1
∂ηt+1
xt+1
1
∂xt+1 zt+1

>

2
∂ηt+1
xt+1
2
∂xt+1 ηt+1

holds.

Proof. See Appendix C.2.
Figure 2 shows the relationship between misallocation (the ratio of MRPK between borrowers
and savers) xt and endogenous TFP ηti . Note that if xt = 1, then ηti = 1 holds; if resources
are efficiently allocated among firms, the sectoral TFP is only exogenously given. Otherwise,
the sectoral TFP endogenously drops due to capital misallocation. The larger xt , the more ηti
drops. An increase in the bond price leads to a tighter collateral constraint. As the collateral
constraint is tighter, borrowers cannot produce a sufficient amount of their intermediate goods andsell them to the final-good producing firm; borrowers have too little capital, whereas savers havetoo much capital. Such a capital misallocation hurts the efficiency of final goods production andlowers sectoral TFP. Also, the sectoral TFP in the more constrained sector (i.e., there are moreborrowers) is dampened more by capital misallocation among firms. The larger χi , the more ηti
drops, given the degree of misallocation between borrowers and savers xt .

16

Figure 2: Misallocation and Productivity.
1
0.99
0.98

endogenous TFP,

0.97
0.96
0.95
0.94
0.93
0.92
=0.05
=0.15
=0.30

0.91
0.9
1

2

3

4

5

6

7

8

9

10

the ratio of MPRKs, x

Notes: The vertical line corresponds to the value of xt in the steady state calibrated in Section 4.1.

3.2

Structural change

In the previous subsection and Proposition 1, we showed that the sectoral TFP (we also call it theefficiency wedge hereafter, and these two terms are used interchangeably) zti = ζti ηti is a functionof the MRPK ratio, xt , which measures the degree of capital misallocation. In this subsection, we
will show that the relative price pt , which is defined by the relative efficiency of each sector, is also
a function of xt . The relative price of goods produced in the new sector increases as the new sector
is more constrained than the old sector. Such a change impedes structural change.
Structural change is measured by the relative price and output. To derive the relative demandand supply curves of the relative price and output, we write down the prototype two-sector economy
with wedges, which is described in details in Appendix B. We show the following “equivalence result”(Chari et al., 2007):
Lemma 2. In the prototype model with wedges, allocations and prices are equivalent to those in17

i , (1 + τ i−1
the detailed model, if and only if the wedges {zt+1
kt+1 ) , ϕt } satisfy

"
i
zt+1

i
(1 + τkt+1
)−1

ϕt

i
ζt+1

1 − χi + χi xγt+1ε1−ν # ε−1,α̃
1 − χi + χi xγ−1
"t+1#
i + χi xγ−1
1
−
χ
t+1
i
= (1 − τt+1)(1 − ε−1 ),1 − χi + χi xγt+1w
−1 −1= nw
t 1 + (1/µ − 1)(pt )r−1 −1+(1 − nw.
t ) 1 + (1/µ − 1)(pt )=(29)

Proof. See Appendix C.3.
ii)−1
Two things are worth noting here. First, the efficiency and capital wedges zt+1
and (1+τkt+1

depend on the MRPK ratio xt+1 and the ratio of borrowers χi ; these wedges represent financial
frictions and capital misallocation. If allocation among the sectors is efficient, xt = 1, zti = ζti andi )−1 = (1 − τ i )(1 − ε−1 ) hold, which includes the inverse of a gross markup stemming from
(1 + τkttmonopolistic competition of intermediate-good producing firms in the original detailed economy.
Second, the preference wedge ϕt is a utility-based weight on consumption in sector 1 in the prototype
economy (see also Equation (32)), and depends on the demand structure of households, i.e., theknumber of workers nw
t , the sector-bias parameters µ , and the relative price pt . As the number ofworkers declines and µw < µr , ϕt increases and a change in demand structure from the old sector(sector 2) to the new sector (sector 1) occurs.
In the prototype economy with wedges, we can easily derive the relative supply curve (Bueraand Kaboski, 2009). From firms’ profit maximization,pt =1 )r ]α ω 1−α[(1 + τkttt,
zt1 αα (1 − α)1−α1=2 )r ]α ω 1−α[(1 + τkttt,
zt2 αα (1 − α)1−α18Then we have

pt =

zt2
zt1



1
1 + τkt2
1 + τkt

α
.

(30)

Note that the supply curve is horizontal, as the production function has constant returns to scale.
i )−1 , which in turn depend on the
The relative price is a function of the wedges zti and (1 + τkt

MRPK ratio xt and the ratio of borrowers χi . Next, we show the following proposition:
Proposition 2. (i) The relative price pt is a function of the ratio of MRPK xt and the ratio ofborrowers χi ,ζ2
pt = t1ζt

1 − τt2
1 − τt1α 

1 − χ1 + χ1 xγt
1 − χ2 + χ2 xγt

1
 1−ε

.

(31)

(ii) If χ1 > χ2 , ζt2 (1 − τt2 )α > ζt1 (1 − τt1 )α , and xt > 1, then pt > 1 holds.
∂pt xt(iii) If χ1 > χ2 , then ∂x> 0 holds.
t pt

Proof. See Appendix C.4.
The price of goods in the new sector (sector 1), which is more constrained, becomes higher thanthat in the old sector (sector 2), as its sectoral TFP is more dampened and there is too little supply
in the new sector.
We can also derive the relative demand curve. From the utilitarian’s utility maximization,

pt c1t /λt = ϕt ,c2t /λt = (1 − ϕt ).

Then we have
1 − ϕtpt =ϕt

 1 −1
ct
.
c2t

(32)

Note that the demand curve has a 45-degree downward slope, as the elasticity of substitution in
the utilitarian’s utility function is one.14
14

For the detrended economy, Equation (31) becomes p̃t =

19



1−τt2
1−τt1

α h

γ

1−χ1 +χ1 xtγ
1−χ2 +χ2 xt

1
i 1−ε

and Equation (32) becomesFigure 3 graphically shows the relative demand and supply curves, (30) and (32). Let us
suppose there is a decline in labor input. The demand curve shifts upward. As the number ofworkers declines and the number of retirees increases, there is a change in households’ demand
structure from the old sector (sector 2) to the new sector (sector 1). Also, with financial frictions,the decline in labor input leads to endogenously strengthened collateral constraints and capital
misallocation, which lowers sectoral TFP (efficiency wedges), as shown in Proposition 1. In the
more constrained sector, the efficiency and capital wedges decrease more, the relative price increases
and the supply curve shifts upward, as shown in Proposition 2. In sum, after a decline in labor
input, the equilibrium shifts from A to B, with financial frictions. On the other hand, in the casewith no financial frictions, the supply curve is unchanged and only the demand curve shifts upward.
Equilibrium shifts from A to C. Comparing the two equilibria, equilibrium B with financial frictions
and equilibrium C with no financial frictions, the relative price is higher and the relative output
is lower in B than C. That is, financial frictions and capital misallocation impede the structuralchange driven by the change in households’ demand structure.

4

Numerical results

In this section, we numerically demonstrate the analytical findings shown in the previous section
using calibrated parameters. We first estimate the parameters for household preferences and firm
technologies. Then, having the parameters calibrated and estimated at hand, we simulate themodel for the Japanese economy during the period 1973–2012.

4.1

Calibration and estimation

The following set of parameters (, µw , µr , ε, χ1 , χ2 ) are estimated to fit the model to the data. To
obtain the parameters for household preferences (, µw , µr ), we estimate the consumption share fortp̃t = 1−ϕϕt

 1 −1c̃tc̃2t. The same discussion applies to Figure 3.

20

Figure 3: Equivalent problem.

goods produced in sector 1, ϕt , using nonlinear least squares following Herrendorf et al. (2013):

pt c1tw
−1 −1= ϕt = nw
t 1 + (1/µ − 1)(pt )12
pt ct + ctr
−1 −1+ (1 − nw,t ) 1 + (1/µ − 1)(pt )(33)

15 See Appendix A for details
where nw
t is the working population ratio and pt is the relative price.

of the data used. It is difficult to identify the parameter for the degree of substitution. In fact,
when we jointly estimate (, µw , µr ), we obtain the elasticity of substitution  = 0, which implies
the two goods are perfect complements.16 Therefore we also fix the value of  = {0.25, 0.5, 1.0} foreach and estimate (µw , µr ).
The estimation results are shown in the left panel of Table 3. We find that µw is not significantly
15
When  6= 1, there is also an effect of pt on ϕt . We find such an effect is small in our estimation.  6= 1 also
violates the balanced growth path when pt has a trend in the model.
16
Buera and Kaboski (2009); Herrendorf et al. (2013) find that the elasticity of substitution is almost zero whenusing the value-added data for estimation.

21

different from zero for all values of . We also find that µr is significant and its value is around
0.2–0.3. That is, the elderly spend about 20–30% of their expenditure on hygiene and medical
services. Most importantly, the estimates are consistent with the assumption made (Assumption
3). The left-hand side panel of Figure 4 also shows the fitted values of the consumption share. For
all the values of  and the associated estimates, the fitted values follow the data well. That is, theycapture the upward trend exhibited in the aging industry.
To estimate the parameters for firm technology (ε, χ1 , χ2 ), we first obtain the ratio of MRPK
xt from the relative price pt . That is,xt =χ1 − p̂1−εχ2 − 1 + p̂1−εtt
χ1 − p̂t1−ε χ21 (1−ε)α,where p̂t = (ζt1 /ζt2 )[(1 − τt1 )/(1 − τt2 )]α pt . We assume the term from exogenous wedges s ≡(ζt1 /ζt2 )[(1 − τt1 )/(1 − τt2 )]α is a constant to be estimated. Then, given xt , we have
zt1 /zt2 = ε1− (ε−1)(1−α)  ε−1
ε



.
(ε−1)α(1−ε)α−1ε111−χ +χ x(1−ε)α1−χ1 +χ1 xt(1−ε)α1−χ2 +χ2 xt(34)t(1−ε)α−1

1−χ2 +χ2 xt

The right-hand side panel of Table 3 provides the estimation results. We include the restrictionof ε > 1 so that differentiated goods in the same factor are substitutes and the sectoral production
exhibits decreasing returns to scale. When we jointly estimate (ε, χ1 , χ2 ), we obtain ε = 5.648.
However, the estimate of ε has a large standard error. Therefore, as before, we also fix the valueof ε = {2.0, 4.0, 8.0} and estimate (χ1 , χ2 ). For each value of ε, the steady-state markup 1 + τk =ε/(ε − 1) is 2, 1.33, and 1.2. The estimates of (χ1 , χ2 ) are stable for different values of ε. Whensetting ε = 4, we obtain (χ1 , χ2 ) = (0.300, 0.007), which implies that 30% of firms are borrowers in
sector 1 whereas only 0.7% of firms are borrowers in sector 2. Once again, the estimation results
support the assumption made (Assumption 2). As the balanced growth path (BGP) is obtained
only if  = 1, we use the estimates with  = 1, (µw , µr ) = (0.333, 0.003) in the simulation presented
hereafter. We also use the estimates (ε, χ1 , χ2 ) = (4.0, 0.300, 0.007).

22

Table 3: Estimation results.
Relative TFP: zt1 /zt2 in (34)

Value-added share: ϕt in (33)

µw
µr

(1)

(2)

(3)

(4)

0.034
(0.08)
0.018(2.29)
0.209(3.45)

0.25

0.5

1

ε

0.015
(5.47)
0.239(15.71)

0.011(3.96)
0.272(17.90)0.003(1.13)
0.333(22.08)

χ1
χ2
s

RMSE

.005

.005

.005

.006

(1)

(2)

(3)

(4)

5.648
(1.92)
0.293(5.20)
0.002(0.44)
0.600(17.23)

2.0

4.0

8.0

0.296
(5.22)
0.029(9.67)
0.607(17.84)0.300(5.59)
0.007(4.26)
0.604(18.40)0.264(6.21)
0.000(1.66)
0.595(15.15)

.050

.052

.050

.050

RMSE

Notes: t-values in parentheses. RMSE is the root mean squared error.

1.1
.8

.02

.9

.04

Share
.06

Relative TFP
1

.08

.1

1.2

Figure 4: Fit of estimation.

1970

1980
Data
ε=0.5

1990
Year
ε=0 (est’d)
ε=1.0

2000

2010

1970

ε=0.25

1980

1990
Year

Data
ε=4.0

ε=5.648 (est’d)
ε=8.0

2000

2010

ε=2.0

The other parameters are calibrated. The discount factor for savers and households is set to
β = 0.96 following Hayashi and Prescott (2002), which calibrate a one-sector neoclassical growthmodel to the Japanese economy of the 1980s. Note that a period in the model corresponds to ayear. The credit-to-value ratio is 70%, θ = 0.7, which is consistent with the literature, including
Iacoviello (2005). The capital share α = 0.452 and the depreciation rate δ = 0.081 are calibrated
to match the detrended steady-state values to the data. We use the means of the capital–output

23

and the investment–capital ratios for 1980–2012 as calibration targets.17 βb = 0.649 is set so thatthe relative TFP in the steady state hits the target value of 0.9398, being the mean for 1973–2012(the value in 1973 is normalized to one). Table 4 summarizes the parameters.
Table 4: Parameter values.

4.2

β
θ

Description
discount factor
credit-to-value ratio

Value
.96
.7

Source or target
Hayashi and Prescott (2002)
Iacoviello (2005)


µw
µr
ε

elasticity of intermediate goods
workers bias for sector 1 goods
retirees bias for sector 1 goods
elasticity of final goods

1.0
.000
.333
4.0

BGP restriction

χ1
χ2
δ
α
βb

ratio of borrowers in sector 1
ratio of borrowers in sector 2
depreciation rate
capital sharediscount factor for borrowers

.300
.007
.0812
.4528
.6495

estimated by (33)markup:1 + τk = 1/(1 − ε−1 ) = 1.33
estimated by (34)ĩ/k̃ = 0.0935
k̃/ỹ = 2.4948 and nw = 0.8436
relative TFP: η1 /η2 = 0.9398

Steady state

Table 5 summarizes the detrended steady-state values in both cases (with and without financial
frictions).18 We compute two sets of steady-state values. One is with the working population
ratio nw = 0.909 for the Japanese economy in 1980 and the other is with nw = 0.759 in 2012.
2 )1/(1−α) is set to 1.012, being the mean for
The trend growth rate in sector 2 νt /νt−1 = (ζt2 /ζt−1

1973–2012. In the case without financial frictions, i.e., θ = θ̄ = 1/(ββb ) and βb = β, capital
allocation among firms is efficient, the tightness of collateral constraint is µ = 0 and the ratioof MRPK is x = 1. The (detrended) efficiency wedges are η 1 = η 2 = 1, the capital wedges are(1 + τk1 )−1 = (1 + τk2 )−1 = 1 − ε−1 (when 1 − τti = 1), and the relative price is p̃ = 1. Whilethe efficiency and capital wedges and related variables are independent of the size and structure of
the economy, some aggregate variables and sectoral compositions depend on the size and demand17

The capital–output ratio also depends on the working population ratio given financial frictions, and we set its
value to the mean for 1980–2012.
18
The steady-state values are analytically obtained in Appendix B.2.

24

structure of households, and aggregate capital decreases as the working population ratio and labor
input declines. However, the capital–output ratio is constant across different values of nw in theabsence of financial frictions, as capital allocation between firms and sectors is efficient. At thesame time, a demand shift from sector 2 to 1 arises given the estimate µr > µw , and the preference
wedge (equivalent to the consumption share, pc1 /(pc1 + c2 )) and relative output in both sectors
increases.
In the case with financial frictions, as θ < θ̄ holds in our calibration, only borrowers areconstrained and there is capital misallocation among firms, resulting in a tightness of collateral
constraints of µ = β −βb = 0.307 and a ratio of MRPK of x = 3.133. As a consequence, the sectoral
TFP (the efficiency wedges) in each is less than one, η 1 = 0.939, and η 2 = 0.999, respectively. Notethat η 1 < η 2 given the estimate χ1 > χ2 . Similarly, (1 + τk1 )−1 = 0.708 < 1 − ε−1 , (1 + τk2 )−1 =0.749 < 1 − ε−1 and p̃ = 1.092 > 1, showing that capital allocation between sectors is inefficientcompared to that without financial frictions.19 The values of aggregate capital and relative output
also decrease with financial frictions and capital misallocation. Interestingly, as relative output
increases, the capital–output ratio decreases with financial frictions, as we assume that sector 1 ismore financially constrained and (1 + τk2 )/(1 + τk1 ) > 1 holds.

4.3
4.3.1

Transition dynamics
An example

To demonstrate the transmission mechanism for the effect of the decline in the working population
ratio on sectoral TFP and structural change, we perform a perfect-foresight simulation and observe
the transition dynamics as the labor input permanently declines and the economy migrates tothe new steady state. We assume that the working population ratio declines from 0.909 to 0.759
in period 1, which corresponds to the size of the reduction in the working population ratio theJapanese economy has experienced over recent years.
Figure 5 depicts the transition dynamics for each sector. When the working population ratio
19

The value of the steady-state relative price in the model is close to the mean of the relative price in the datafor 1973–2012 of 1.079, even though this is not a calibration target. As the relative TFP is a calibration target, thecapital wedges are important for pushing the relative price higher.

25

Table 5: Steady-state values.
Description

Value
w/ fric.

nw
µ
x
η1
η2
(1 + τk1 )−1(1 + τk2 )−1p̃
ϕỹ 1 /ỹ 2k̃/ỹworking population ratio
tightness of borrowing constraint
MRPK ratio
efficiency wedge in sector 1
efficiency wedge in sector 2
capital wedge in sector 1
capital wedge in sector 2
relative pricepreference wedge
relative output
capital–output ratio

0.925
0.307
3.133
0.939
0.999
0.708
0.749
1.092
0.028
0.020
2.498

0.759
0.307
3.133
0.939
0.999
0.708
0.749
1.092
0.083
0.062
2.492

w/o fric.
0.925
0
1.000
1.000
1.000
0.750
0.750
1.000
0.028
0.022
2.503

0.759
0
1.000
1.000
1.000
0.750
0.750
1.000
0.083
0.068
2.503

drops in period 1, the collateral constraint becomes tighter as borrowers want to borrow more in theface of low real interest rates (the inverse of the risk-free bond price). The MRPK ratio increases
in the next period as there is a one-period lag for new capital to be installed. The sectoral TFP(the efficiency wedges) also decreases in the following period, and more so in the more constrained
sector (sector 1), as shown in Proposition 1. Note that as the real interest rate moves back to thesteady state, all variables within each sector also revert to their steady-state values. Note that
there is almost no difference in the real interest rate between the case with and without financial
frictions, as there is little feedback from the efficiency wedges to the real interest rate via financial
frictions.

4.3.2

Japanese economy 1973–2012

We simulate the model for the Japanese economy for 1973–2012 using the estimated parameters in
Section 4.1. That is, we feed the sequences of the working population ratio and the sectoral TFP
for each sector into the model and compute the perfect-foresight path by simulating the model andtaking the initial value of the capital–output ratio as given.
Figure 6 illustrates the exogenous path of the working population ratio and sectoral TFP, aswell as the endogenous perfect-foresight path of the relative price and the consumption share in26

Figure 5: Responses of sectoral variables.
nw

0.95

asset price

0.9
0.85

0.96

0.311

0.958

0.31

0.956

0.309

0.954

0.308

0.952

0.8

0.307

0.95
0.75

tightness ofcollateral const.

0

10

20

10

20

0.306

0

1

MRPK

3.3

0

0.945

3.2

0.94

20

2

0.95

3.25

10

1
0.99
0.98
0.97

3.15
3.1

0.935

0

10

20

0.93

0.96
0

10

20

0.95

0

10

20

the simulation. The fit of the model with the data is quite reasonable. The simulated path of
the relative price is close to the data, although it fails to generate the upward trend in the data
toward the end of the sample period.20 As we set  = 1 and the relative price has no effecton the consumption share, the simulated path of consumption share is exactly the same as in theestimation. The model also has a good fit with the capital–output data, as we use its 1973 value andthe mean for 1980–2012 as the initial and the steady-state values for each in the model, respectively.
20

We can rectify this by adding time-varying exogenous capital wedges 1 − τti , as shown in Equation (31).

27

Figure 6: Simulation for the Japanese economy, 1973–2012.
nw

0.95
0.9

1.1

0.85

1

0.8

0.9

0.75

1980

1990

relative TFP

1.2

2000

0.8

2010

1980

consumption share

0.1

1990

2000

2010

relative price
model
data

1.4
0.08
1.2

0.06

1

0.04
0.02

1980

1990

2000

0.8

2010

MRPK

1980

2000

2010

relative output

0.1

3.4

1990

0.08
3.2
0.06
3

2.8

0.04
0.02
1980

1990

2000

2010

1980

1990

1

2000

2010

2000

2010

2

0.95

1
0.99

0.945

0.98
0.94
0.97
0.935
0.93

0.96
1980

1990

2000

0.95

2010

28

1980

1990

Figure 7: Aggregate capital and rate of return.
3.5

capital-output ratio

3

8

2.5

6

2

4

1.5

1980

1990

2000

rate of return

10

2

2010

model
data

1980

1990

2000

2010

Notes: The rate of return is adjusted for corporate tax by multiplying it by 0.5.

Having obtained a good fit of the model with the data, we also evaluate some other endogenous
variables. The endogenous component of sectoral TFP displays a downward trend as both the asset
price (i.e., the capital–output ratio) and the MPRK exhibit upward trends. Sector 1 TFP declines
by 1% from the beginning to the end of the sample period (from 0.945 to 0.935). Recall that thesectoral TFP already falls by 6% in the steady state (shown by the red line). Relative output also
has an upward trend, as does the consumption share.
Finally, we perform a counter-factual simulation to evaluate the role of financial frictions on
sectoral TFP and structural change. Recall that sectoral TFP is decomposed as zti = ζti ηti . zti is
given by the data and ηti is endogenously obtained depending on the MRPK. Therefore, we cantrace out the sequence of ζti = zti /ηti in the model with financial frictions, which can be interpreted
as sectoral TFP in the model without financial frictions. We simulate the model without financial
frictions using zti = ζti as the exogenous sequence of sectoral TFP that we feed into the model andsetting θ = 1/(ββb ) and βb = β.
Figure 8 depicts the relative prices and outputs for the models with and without financial
frictions. As the new sector (sector 1) is more constrained, its efficiency wedge (sectoral TFP) andcapital wedge decrease more. Therefore, the relative price increases and the supply curve shifts
upwards (as shown in Figure 3), which dampens the relative output in the model with financial
frictions. As the endogenous component of sectoral TFP involves additional downward pressure29

owing to demographic change, the gap in the relative price and output widens toward the end of
the sample period.
Figure 8: Relative price and output.
relative price

1.1

0.08

1

0.06

0.9

w/ friction
w/o friction

0.04

0.8

0.02
1980

5

relative output

0.1

1.2

1990

2000

2010

1980

1990

2000

2010

Concluding Remarks

We examined the effects of a decline in the working population ratio by inducing changes in labor
input and the structure of household demand in a two-sector model with financial frictions. We
assumed that firms have differing financial needs and that the new sector in which demand increases
given structural change is more constrained than the old sector in which demand declines. The
original two-sector model with financial frictions is equivalent to a prototype two-sector model withwedges in terms of allocations and prices, while the wedges themselves depend on the degree ofcapital misallocation among firms and the structure of household demand.
We found that the decline in labor input strengthens the collateral constraints of borrowers
and generates capital misallocation and lower sectoral TFP. With respect to the implications forstructural change, as the new sector is more constrained than the old, the new sector’s TFP is also
lower than that in the old sector, and the supply of goods produced in the new sector is much lessthan in the case with no financial frictions, thereby impeding structural change.
We also demonstrated that our theoretical findings for a two-sector economy with endogenous
wedges can explain the actual Japanese data for 1973–2012. We endogenized the wedges andconsidered the role of capital misallocation in structural change to investigate the effects of tech30

nology shocks and structures in our stylized model. We found that financial frictions and capital
misallocation may have indeed impeded structural change.

31References
Arellano, Bai, and Kehoe (2012): “Financial Frictions and Fluctuations in Volatility,” Federal
Reserve Bank of Minneapolis Research Department Staff Report 466.
Buera, F. J. and J. P. Kaboski (2009): “Can Traditional Theories of Structural Change Fit
the Data?” Journal of the European Economic Association, 7, 469–477.
Buera, F. J., J. P. Kaboski, and Y. Shin (2011): “Finance and Development: A Tale of Two
Sectors,” American Economic Review, 101, 1964–2002.
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