Non-regular Workers and the Stagnant Economy
Shingo Umino 1
Graduate School of Economics, Kobe University
Rokko Forum Working Paper Series No. 1201

Abstract
This paper specifically examines features of labor supply heterogeneity in Japanesehouseholds and describes how such a structure affects household expenditure, which has
stagnated during the last two decades. The particular circumstances represent the increaseof non-regular workers but are not necessarily limited to Japan. Non-regular workers aredefinable in many dimensions, but a common feature is that they have quite unstable
contracts of employment. If such labor increases greatly, then one can assess the impact on
the actual economy. Therefore, a general equilibrium model was constructed to explainsome empirical VAR evidence. The model shows that the reactions of aggregate
consumption and housing investment to the shock of increasing non-regular worker ratio
are negative and that they are consistent with empirical results. Housing investment
exhibits greater sensitivity to the shock. Moreover, decreasing output for consumption
goods and housing investment in response to the shock is greater than that decrease of
demand. This paper suggests that employing few non-regular workers is preferred and that
non-regular workers should not be employed for long periods.
Keywords: non-regular workers, collateral constraint, household demand, DSGE
model.
JEL Classification Number: J23, E24, E32.

1

Kobe University, 2-1 Rokko-dai, Nada, Kobe 657-8501 (E-mail: shingo.umino@gmail.com).

1

1. Introduction
Since the bubble era, Japan’s economy has not yet emerged from its long-run slump,which has lasted two decades. The development of non-regular workers is one noticeablefeature that has produced the severely stagnated economy of that period. Figure 1 displays
the transition of the share of non-regular workers among total labor (hereinafter, thenon-regular worker ratio). Actually, the ratio was 17% in 1986 and was 34% in 2008,
doubling over that period. In fact, one in three workers is a non-regular worker. Moreover,Figure 1 shows that, after 1990, the number of employees has remained mostly stable at 50
million, which emphasizes that a rise in the non-regular worker ratio is attributable simply
to an increase in the number of non-regular workers.
In the 1980s, non-regular workers (often wives) were employees working to coverincome that the main supporters (often husbands) earned. This surely meant that the income
earned by non-regular workers was less than that of regular workers. However, during morethan a decade after the bubble burst, circumstances by which the number of non-regular
workers has increased can reflect that non-regular workers also play a role of the main
supporters of their own households. If such households increase, then they are not able tosupport the same amount of consumption as flexibly as regular households might.
In Figure 2, it is readily apparent that the income of non-regular workers is below thatof regular workers. As this figure shows, the medians are roughly estimated as around 0.8
million (Non-regular) and around 3.9 million (Regular) in 2002, and to be around 1.2
million (Non-regular) and around 4.1 million (Regular) in 2007. What is the effect of suchincome inequality on both non-regular workers’ consumption and regular workers’
consumption? Presumably, no much difference exists between them in basic consumption
in support of necessary expenditures (i.e., spending for food or clothing). However,
non-regular workers who earn low income are unable to spend for housing investment or
durable goods (i.e., automobile or home electronics) to the same degree as regular workers
might. Non-regular workers can not afford to consume these additional goods aside fromrequired fundamental consumption 2: unless non-regular workers borrow additional funds
2

In January 2009, the Research Institute of Economy, Trade and Industry (RIETI) in Japan investigatedemployment of non-regular workers, especially dispatched workers, using web questionnaires. The web
survey, ‘Survey on life and job behavior of dispatched workers,’ revealed that non-regular workers who are2from agents such as banks, they are unable to purchase these luxury goods and services.
Actually, a high probability exists that they can not pass a bank’s examination forborrowing because they are non-regular workers and are unable to prove a stable income.
As described above, one might readily infer that increasing in non-regular workers
causes a process of consumption without smoothness. In an economy where a kind ofwedge exists, if some usual policies are taken, then the desirable outcomes will not ever beobtained. Now such recognition is being shared, and studies from an economic perspective
intended to elucidate effects of rising non-regular workers are developing. Many themes
related to the topic of non-regular workers exist to be studied. One approach comprises
three steps. First, available data can be used to confirm the degree of impact of anincreasing non-regular workers on the economy. Second, based upon results obtained in thefirst step, one can build a general equilibrium model in which non-regular workers are
specified. The model can explain the aggregate time-series evidence. Furthermore, it ispossible to ascertain the degree of distortion of the existence of non-regular workers. Third,
it is possible to compare some policies used by government in an economy of non-regular
workers with some policies in an economy of regular workers only. This paper presents a
simple general equilibrium model that reflects the existence of non-regular workers up to
the second step of the approach described above.
Details of the effects of the rise in non-regular workers on the economy must be
considered. This paper presents specific examination of housing investment as a good that
requires the additional funds for purchasing. With respect to the actual Japanese economy,
although the growth rate of real GDP was 1.08% during 1991–2008, the growth rate of realresidential investment was 0.78%. One factor causing this stagnation is the rise of
non-regular workers. Here, a simple mechanism is considered: an increase in the
non-regular worker ratio causes a decline in housing investment as explained below. Ifmany regular workers are fired and an equal number of non-regular workers are hired, thenthey earn income as non-regular workers and consume with plans that forego housing
investment. Therefore, housing investment in the whole economy declines because theshare of non-regular workers increases, even as total employees remain constant: byincreasing the non-regular worker ratio, the spending power in the entire economy falls. An
important factor in this mechanism is that the scale of non-regular workers to all workers is
not negligible. Increasing the number of non-regular workers might push Japan’s economy
not able to save up money smoothly account for more than 70% of all non-regular workers.

3

further into stagnation.
To date, although the definition of non-regular workers has not been clear,
non-regular workers and the causes of increasing non-regular worker employment are
defined simply here. A sharp rise of non-regular workers has occurred not only in Japan but
also in the United States, the United Kingdom, European countries, and Korea(Organization for Economic Co-operation and Development, 2002). Generally, non-regular
workers are defined as workers who are not regular workers. However, studies by Suzuki(1999) point to a no single common definition of non-regular workers accepted worldwide.
Some definitions of non-regular workers exist in Japan because some government
statistics capture non-regular workers 3. Among them, the “Labour Force Survey”, a surveyof households usually residing in Japan, provides wide coverage of non-regular workers.
Based on the Labour Force Survey, the definitions of non-regular workers have threevarieties. First, non-regular workers are those who work fewer hours than regular workers(fewer than 35 hours per week). Second, non-regular workers are workers who are notdesignated as “regular employees” at work 4. Finally, non-regular workers are those workers
who have a job contract that expires within a year. The last definition is the same as thedefinition of ‘temporary workers’ defined by the OECD (Organization for Economic
Co-operation and Development, 2002).
In this paper for Japan’s economy, referring to the three definitions presented above,
non-regular workers are defined as workers who work shorter hours than regular workers
do. Especially, a dynamic general equilibrium model is constructed in which suchnon-regular workers appear at the later part of this paper, and the model built under theempirical evidence of aggregate time-series. For example, the model used for this study
reflects the feature that regular workers work 1.73 times longer than non-regular workers inpoint of official working hours 5. A firm that hires regular workers and non-regular workers
chooses nonscheduled working hours to maximize its profit.
Empirical evidence of the causes of increasing use of non-regular workers has been
widely documented by Cappelli and Neumark (2004), Comin and Mulani (2006), Comin
3

Statistical data on non-regular workers are issued by a few government ministries, for example, the Ministryof Internal Affairs and Communications and the Ministry of Health, Labour and Welfare
4“Non-regular employees” are part-time employees, contract employees, fixed-term employees, andtemporary employees.
5

Based on Labor Force Survey, the average was calculated from 1990Q4 to 2008Q4.

4

and Phillippon (2006), Ono and Sullivan (2006), Organization for Economic Co-operation
and Development (2008), and Vidal and Tigges (2009). These studies have highlighted theswing of corporate performance. Especially, for Japan, Morikawa (2010) and Sano et al.
(2011) showed that the reasons underlying increased use of non-regular workers correspond
not to the industrial level but to the firm level. Furthermore, another factor from the firmlevel is that labor force of non-regular workers is gathered easily and labor costs are low.
As in Autor et al. (2003) and Ikenaga (2009), such a factor causes firms to decrease regular
workers and to hire non-regular workers, which almost work were simplified byinformation technology.
What impact does the increase in non-regular workers have on the real economy?
Actually, many reports in the literature have described that expanding the non-regular
worker ratio has had a negative effect on firm productivity in southern European countries 6(i.e., Sanchez and Toharia, 2000, Dolado and Stucchi, 2008, and Boeri and Garibaldi, 2007).
Oshima (2009) surveys details of the relation between non-regular workers andproductivity.
No theoretical study described in the literature has examined non-regular workers
who play a role as representatives of households. However, some studies specificallyexamine labor supply heterogeneity with housing investment. Eusepi and Preston (2009)
and related studies portray a model comprising employed consumers and unemployed
consumers. The model generates some empirical regularities using U.S. labor market data.
The idea that family members of two types exist in the model economy, which these studies
have highlighted, is adopted here. Moreover, Iacoviello (2005) and Monacelli (2009)
studied a general equilibrium (new Keynesian) model that assumes that some households(borrowers) are subject to borrowing constraints by Kiyotaki and Moore (1997) to purchasehousing or durable goods. This perspective is also adopted here. Adoption of a borrowing
constraint can be justified from results of some empirical studies (Hayashi 1985 and 1987,
Kohara and Horioka 1999) and will add to the borrowers some characteristics as
non-regular workers.
The household types presented in this paper include non-regular workers and regular
workers, not employed and unemployed people. This assumption reflects that the
unemployment rate has remained stable during the past half decade: some non-regular6

From OECD, 15.6% in 1987 → 35.0% in 1995 → 29.3% in 2008 in Spain. 4.8% in 985 → 12.5% in2009 in Italy. 14.4% in 1986 → 22.0% in 2009 in Portugal.

5

workers are able to work for a year; others become unemployed temporarily. If thisconjuncture arises every quarter, then the unemployment rate will be stable. Althoughmany authors have specifically examined the sharp rise of non-regular workers empiricallyand have analyzed some theoretical model with unemployment, no study has introduced
non-regular workers as one household type into a general equilibrium model that can
explain the aggregate time-series evidence.
The paper is organized as follows. Section 2 presents some VAR evidence with the
non-regular worker ratio. Section 3 presents the basic model. Section 4 analyzes its
dynamics. Section 5 concludes the paper.

2. Empirically increasing non-regular worker shock
To assess the impact of a shock caused by increasing non-regular workers, weestimate Japan’s quarterly VAR model specified as
LYt =∑A Y + Bε ,
i

t −i

(1)

t

i =1

where ε t is a vector of contemporaneous disturbances. Vector Yt consists of four
variables: (i) detrended TFP, (ii) detrended non-regular worker ratio (s), (iii) detrended realhousehold consumption (Consumption), and (iv) detrended real housing investment(Housing), which represents real private residential investment. This composition includes
all goods and services which non-regular workers are unable to obtain easily 7. The VAR
system is estimated over sample 1990Q4 – 2008Q4 8. This VAR is used to document the
key relations in the data. Figure 4 presents impulse responses of four variables to four
identified shocks. Dashed lines represent 90-percent bootstrapped confidence bands.
1. A persistent response of the non-regular worker ratio to own shock.
2. To ratio shock, although not significantly, the negative responses of real
aggregate consumption and housing investment.
7

All data except the calculated TFP are available at the Statistics Bureau of the Ministry of Internal Affairs

and Communications and the ESRI of the Cabinet Office
8

TFP has already been detrended linearly. TFP is estimated based upon Kamada and Masuda (2001) and

Kawamoto (2004), who adopted the TANKAN DI. The VAR system features a constant and two lags.

63. The response of housing to a shock is greater than that of consumption; and4. Neither positive nor negative response of the ratio to a positive technology shock.
These results are robust to the specifications of alternative ordering and fewer or
additional lags. The remainder of the paper presents development of a model that is
consistent with these facts.

3. The model
Considering a discrete time, infinite horizon economy, populated by entrepreneurs
and households of two types, this economy comprises a continuum of households in theinterval of (0,1). Two types of households exist, respectively designated as non-regular
workers and regular workers, of measure s and 1 − s . The households (workers) of two
types have heterogeneous preferences by which non-regular workers are more impatientthan regular workers. The term “patient” reflects the assumption that non-regular workers
have lower discount rates than regular workers and firms 9 . Entrepreneurs produce ahomogeneous good, hiring household labor of two types 10. Households consume, work, anddemand housing investment: all households derive utility from consumption of a final goodand from possessing housing services. In addition, retailers and a central bank exist.
Retailers are the source of nominal rigidity. The central bank adjusts the short-term
nominal interest rate.

3.1. Non-regular worker households
As described above, the existence of non-regular workers is identified here in point ofhours worked. Working hours for both non-regular and regular workers are composites of
9For earlier models with heterogeneity in discount rates, see Becker (1980), Kiyotaki and Moore (1997),

Iacoviello (2005), Campbell and Hercowitz (2006), and Monacelli (2009).
10

A non-regular worker is not assumed to be promoted to regular worker or a regular to be demoted to

non-regular worker unfortunately. Especially, the assumption of the non-switch from a non-regular to aregular worker is justified from ’General Survey on Temporary Workers’ Contract 2009/2011’ by Ministry of
Health, Labour and Welfare (in Japanese only).

7scheduled and nonscheduled hours. As the data show, regular workers work 1.73 times aslong as non-regular workers in point of official working hours; then their scheduled hours
are assumed to be constant. For workers of both types, nonscheduled hours are chosen byfirms in view of the corporate performance and are assumed to be varying.
If the assumptions described above are fully adopted, then non-regular worker
households maximize the following utility program:
E 0  β Nt U (c N ,t , C t −1 , h N ,t , H t −1 , LNc ,t , LNh ,t )
 t =0∞∑(2)

U (c N ,t , C t −1 , hN ,t , H t −1 , LNc ,t , LNh,t )

{

}

1+η

N

1+ ε
1+ ε
1
= ln (c N ,t − f c C t −1 ) + j ln (hN ,t − f h H t −1 ) −( LNc ,t ) N + ( LNh,t ) N 1+ε N
1+ηN

Therein, household utility depends on the lagged aggregate consumption and housing andhousing investment, defined as
C t = (1 − s t ) × c R ,t + s t × c N ,t ,H t = (1 − s t ) × hR ,t + s t × hN ,t ,and
LNc ,t = Lc , N + LcN ,t ,
L

N
h ,t

(3)
(4)

= Lh , N + LhN ,tsubject to the sequence of budget constraints (in nominal terms):
Pt c N ,t + Qt (hN ,t − (1 − δ h )hN ,t −1 ) + Rt −1 B N ,t −1 + Ξ hN ,t = B N ,t + WcN ,t LNc ,t + WhN ,t LNh,t ,(5)where E 0 stands for the expectation operator, β N ∈ (0,1) denotes a discount factor, c N ,tsignifies consumption at t , hN ,t denotes the holding of housing, LNc ,t and LNh,trespectively represent total hours worked for consumption goods and housing investment,
Lc , N and Lc , N respectively denote constant scheduled working hours for each sector, LcN ,tand LcN ,t are variable nonscheduled working hours, Qt is the nominal housing price,
B N ,t −1 is the end-of-period t nominal one period debt, Rt −1 is the nominal interest rate on
loan between t − 1 and t , W N ,t represents the nominal wage, and Ξ hN ,t is the nominal
adjustment cost for housing, which is symmetric for each agent.
In real terms, (3) reads
c N ,t + q t (hN ,t − (1 − δ h )hN ,t −1 ) +

Rt −1

πt

bN ,t −1 + ξ hN ,t = bN ,t + wcN ,t LNc ,t + whN ,t LNh,t ,

where

8

(6)

2


φ  h − (1 − δ h )h N ,t −1− δ h  qt h N ,t −1 ,
ξ N ,t = h  N ,t2δ h 
h N ,t −1and ξ N ,t is the real adjustment cost for housing. In addition, q t ≡housing price, π t ≡debt, and wcN ,t ≡

Pt
Pt −1

WcN ,tPt

signifies the gross inflation rate, b N ,t −1 ≡and whN ,t ≡W hN ,t
Pt

(7)
Qt
Pt
B N ,t −1
Pt

stands for the real
denotes the realrespectively represent the real wages in sectors ofconsumption goods and housing investment.
As in Kiyotaki and Moore (1997), a limit is assumed on the obligations of
non-regular workers: if the borrowers deny the call from lenders, then the lenders canrepossess not the expected complete future value of the housing but a fraction of the value.
The borrowers’ assets are equal to lenders’ collections after depreciation and paying a
proportional transaction cost: mEt (qt +1 (1 − δ h )hN ,t ), 0 < m < 1 . In other words, the valuemEt (q t +1 (1 − δ h )hN ,t ) is equal to the value of collateral. Finally, the maximum amount Rt B N ,tthat a creditor can borrow is set as below in real terms:
Rt b N ,t ≤ mEt (qt +1 (1 − δ h .)h N ,t π t +1 ).

(8)

Assuming that the collateral constraint (8) is always satisfied with equality in andaround the steady state, Equation (8) can be expressed in real terms as
Rt b N ,t = mEt (qt +1 (1 − δ h .)h N ,t π t +1 ).

(9)3.2. Regular worker households
Aside from non-regular workers, the economy comprises a type of household thatoffers regular workers. They have already turned up in the dynamic optimization literature
as representative agents. Non-regular workers discount the future more heavily than regular
workers do: regular workers correspond to patient workers characterized in previous
studies.
Moreover, as in previous subsections, regular workers are identified as workers of the
opposite to non-regular workers: the official hours are longer than the non-regular worker
hours.
If the assumptions described above are fully adopted, then regular workers maximize

9the following utility program:
∞




E 0  β Rt U (c R ,t , C t −1 , hR ,t , H t −1 , LRc ,t , LRh ,t )
 t =0∑(10)

U (c R ,t , C t −1 , hR ,t , H t −1 , LRc ,t , LRh,t )= ln (c R ,t − f c C t −1 ) + j ln (hR ,t − f h H t −1 ) −

{

}

1+η

R

1+ε
1+ε
1
( LRc ,t ) R + ( LRh,t ) R 1+ε R ,1+ηR

for which the following are true:
LRc ,t = Lc , R + LcR ,t ,

(11)
(12)

LRh ,t = Lh , R + LhR ,tThose expressions are subject to the sequence of budget constraints (in real terms) as
c R ,t + q t (hR ,t − (1 − δ h )hR ,t −1 ) +

Rt −1

πt

bR ,t −1 + ξ hR ,t = bR ,t + wcR ,t LRc ,t + whR ,t LRh,t + Ft ,

(13)

where
2


φ  h − (1 − δ h )hR ,t −1− δ h  qt hR ,t −1 ,
ξ R ,t = h  R ,t2δ h 
hR ,t −1(14)

for which ξ R,t is the real adjustment cost for housing, Ft denotes lump-sum profits
received from the retailers (described below), and β N < β R . The latter assumption
guarantees an equilibrium in which non-regular workers will hit the borrowing constraint.

3.3. Entrepreneurs of intermediate consumption goods
Entrepreneurs produce intermediate consumption goods, which are differentiated andwhich face perfect competition. They hire workers of two types (non-regular and regular
workers) as labor inputs L N ,t and LR ,t and they have access to a production function in
producing intermediate goods:[( )Yc ,t = Ac ,t LRc ,t

(1− a

c ,t

)

(L ) ]µN ac , t c
c ,t

(15)

and equivalently
a c ,t =wcN ,t LNc ,twcN ,t LNc ,t + wcR ,t LRc ,t,10

where At denotes productivity and obeys the AR(1) process 11, which does not affect the
non-regular worker ratio as a result of empirical examination, parameter µ c is the labor
income share for intermediate goods, a c,t represents the non-regular wage share between
non-regular workers and regular workers in intermediate (consumption) goods market, ands t is the time-varying ratio of non-regular workers and obeys AR(1) process. Finally,
entrepreneurs maximize their own profits as Π t , subject to Equations (15) and (16).
Π c ,t =Yc ,tXt− ( wcR ,t LRc ,t + wcN ,t LNc ,t )3.4. Retailers
To introduce the source of nominal stickiness in the model economy, Bernanke et al.
(1999) is followed, with the assumption that monopolistic competition occurs at the “retail”
level. Final good Yt F is a CES composite of a continuum of mass unity of differentiatedretailers, indexed by z . They purchase intermediate outputs from entrepreneurs at Pt E anduse them as the sole input. Total final goods are the following composite of individual retailgoods: 1
Yt F =  Yt ( z ) (ε −1)/ε dz 0∫−ε/( ε −1)

(16)

,

with ε > 1 . The corresponding price index is given as 1

Pt =  Pt ( z ) (1−ε ) dz 
0



∫

1/(1−ε )(17).

Therefore, each retailer faces an individual demand curve:−ε P ( z)  Yt F .
Yt ( z ) =  t

P
 t 

(18)

The retailer chooses the sales price Pt (z ) , taking as given the demand curve and the priceof wholesale goods, Pt w .
To introduce nominal rigidities, a retailer can adjust its price freely with probability
1 − θ , following Calvo (1983). Letting Pt* ( z ) be the “reset” price set by retailers who areable to revise their prices at period t , and letting Yt* ( z ) be the demand at this price, thenthe retailer chooses a price to maximize the expected discounted profit, given as
11

From empirical evidence presented in previous sections, one assumes that technology is unrelated to the

non-regular worker ratio directly.

11



∞


 Pt* ( z ) − Pt +wk  *Yt + k ( z ),
Pt + k∑θ E Λ 
k

t ,k

t

t =0

(19)

where Λ t ,k ≡ β (c R ,t /c R ,t + k ) is the regular worker household relevant discount factor.
Differentiating the objective with respect to Pt* , the optimal price must satisfy thefollowing condition of∞∑ Pt* ( z ) Pt + k

θ k E t Λ t ,k 

t =0

−


X  *
Yt + k ( z ) = 0,
X t +k (20)

where X t (≡ Pt /Pt w ) is the markup, which equals to X * = ε/(ε − 1) in a steady state. As in
BGG and Iacoviello (2005), this condition states that Pt* equates the expected discounted
marginal revenue to the expected discounted marginal cost. Given that the fraction θ ofretailers do not change their price in period t , the aggregate price evolves according to
Pt = [θPt1−−1ε + (1 − θ ) ′( Pt* )1−ε ]1/(1−ε ) .

(21)

By combining Equations (22) and (23), and then log-linearizing, it is possible to obtain aforward-looking Phillips curve.

3.5. Housing producers
In a competitive flexible price market, new homes are produced with labor only andwithout productivity. The production technology is[( )Yh,t = LRh,t

(1− a

h ,t

)

(L ) ] .
µ
N a h ,t h
h ,t

(22)

Equivalently, the following is useful.
a h ,t =whN ,t LNh ,twhN ,t LNh,t + whR ,t LRh,t.

Housing producers solve the following maximization to hire labor:
Π h,t = qt Yh,t − ( whR ,t LRh,t + whN ,t LNh,t ).

3.6. Central bankMonetary policy is conducted using a simple Taylor-type rule as
1+ γγγ
Rt = ( Rt −1 ) R  π t −1 π (YcF,t −1 /Yc ,t −1 ) x R * 



1−γ

R

ε R ,t ,12(23)

where R * denotes the steady state real interest rate, Yt −F1 is the final output (total demand)by retailer, and Yt −N1 stands for the natural rate of output. In addition, ε R,t is a policy shock
assumed to have zero mean, with variance σ ε .
R

3.7. Market clearing
The market clearing conditions are given by the following:C t = (1 − s t ) × c R ,t + s t × c N ,t ,

(24)
(25)

H t = (1 − s t ) × hR ,t + s t × hN ,t ,YcF,t = C t ,0 = (1 − s t ) × bR ,t + s t × bN ,t ,

(26)
(27)
(28)

YcF,t = Dt × Yc ,t(29)

Yh,t = (1 − s t )(hR ,t − (1 − δ h )hR ,t −1 ) + s t (hN ,t − (1 − δ h )hN ,t −1 ),and finally,−α 1 − θπ tθ −1  1−θ.
Dt = θDt −1π t + (1 − θ ) 1−θ α(30)

In those equations, C t represents the total spending for consumption, Ht stands for the
total spending for housing investment, and Dt denotes price dispersion 12 . Equations(19)–(24) respectively represent the goods market, the total household consumption, theborrowing–lending relation, resource constraint for real estate, the linkage between
wholesale and retail output, and the price dispersion form.

3.8. Deterministic steady state
In the deterministic steady state, inflation π * is assumed as one. Therefore, R *corresponds to the real interest rate. It is equal to the reciprocal of the regular workers’
discount rate 1/β R from their consumption Euler condition. Because of the assumption thatthe regular workers’ discount rate is greater than the non-regular workers’ discount rate,
β N < β R . In this case, it is necessary to verify that the debt of non-regular workers is always
12

See Gertler and Karadi (2010).

13

positive. It is possible to evaluate (8) in the steady state and obtainb N*Y*= m(1 − δ h ) β R { f h Ω 5 R + Ω 1N (Ω 5 N − f c )} ,

(31)

where
Ω1N =

j (1 − β N f h s* )> 0,{1 − β N (1 − δ h ) − ( β R − β N )m(1 − δ h )}(1 − f c s* )(32)

and where Ω 5 R , Ω 5 N > 0 respectively represent the steady state of housing price andconsumption for non-regular workers 13. The steady-state debt for regular workers
always negative −s * b N*
1 − s* Y *

bR*
Y*

is

and corresponds to saving. It is particularly interesting that theamount of saving that regular workers need to prepare for non-regular workers’ loans
depends on the steady-state non-regular worker ratio s * , i.e., if the steady state s * is set
to 0.34, a regular worker saves half the amount which a non-regular worker borrows,
whereas a regular worker must save more than the required amount by a regular worker
when s * > 0.50 .

3.9. Calibration and solution method
Some parameters are calibrated based on the data sample means and other studies.
The steady-state real rate of interest is set as R * = 1.5 . Then, because it is pinned down by
the regular workers’ discount rate, this setting implies that (1/β R ) 4 = 1.015 , and in turn thatβ R = 0.996 . The non-regular worker’s discount rate was set as β N = 0.95 . Next, theparameters η R , η N , e R , and e N , specifying the disutility of labor, were set respectively to
3.00, 2.00, 0.40, and 0.80 14. The non-regular worker “loan-to-value” ratio m is set to 0.50
initially. Finally, as in Iacoviello (2005), the parameters j are set to 0.10.
The existence of non-regular workers can be specified further. When scheduled hours
worked for regular workers in the market of consumption goods Lc , R is valued as 1.28,
from the empirical result that scheduled working hours for regular workers are 1.73 times
as great as those of non-regular workers, non-regular workers’ scheduled hours Lc , N were
set to 0.73 (=1.28/1.73). Similarly, if scheduled hours worked for regular workers in the13

See Appendix for more information.

14

These settings follow Horvath (2000).

14

market of housing Lh, R are valued as 0.13, then non-regular workers’ scheduled hours
Lh, N are 0.08. As economy-wide parameters, an annual depreciation rate for housing ischosen as 0.04 percent: δ h = 0.01 . Furthermore, the habit parameters f c and f h are set
respectively to 0.11 and 0.00.
As firms’ parameters, the income share of consumption goods µ c , and the income
share of housing µ h were set respectively to 0.63, and 0.70. The elasticity α is 30. The
degree of nominal rigidity to generate a frequency of price adjustment of about eightquarters is the probability of not resetting prices θ . Following Sugo and Ueda (2008), whoestimated Japan’s Bayesian DSGE model, θ equals 0.87. Moreover, the elasticity of
substitution of intermediate goods ε is set to 5, implying a steady state mark-up
X * (=εε −1) of 25%. For the steady state ratio of non-regular workers s * , it was set to 0.34,

which results from the data sample mean. Finally, for the Taylor rule, as in Sugo and Ueda
(2008), the following were set: γ x = 0.11 , γ π = 0.60 , and γ R = 0.84 .
The solution methods consist in taking a log-linear approximation of the equilibrium
conditions in the neighborhood of the deterministic steady state. Dynare was used, which
derives the reduced form representation of the DSGE model and which automaticallyprovides stability and eigenvalue analysis.

4. Simulation results
4.1. Baseline responses
It is straightforward to demonstrate the ability to produce an empirically plausible
response to non-regular worker ratio shock. Figures 6 and 7 display the impulse responses
of selected variables to a persistent ratio shock 15 . These variables are selected as
macroeconomic variables described in Section II. Figures show the responses of ten key
variables: aggregate consumption, housing investment, output for consumption, output for
housing investment, inflation, the output gap, nominal interest rate, housing prices, savings,
and borrowing.

15

It is a 10 basis point innovation.

15

4.1.1. Consumption goods
Aggregate consumption (i.e. consumption goods) is examined first. Particularly the
impact elasticity of consumption to a 10-percent increase in the non-regular worker ratio isaround -0.02. This result, in terms of shape, is close to the empirical value. This arises fromthe realization that the ratio shock has persistence.
This picture highlights the reason underlying the success of the model in tracking
down the empirical negative elasticity of spending to ratio. To better understand the result,
it is useful to interpret that the figures exhibit responses of each type of worker (non-regularand regular worker). As described in Section 2, s can relate to the share of non-regular
worker’s wage. Therefore, one can presume that if s goes up, then income for non-regular
worker rises and non-regular worker can consume more consumption goods so that income
for non-regular workers rises. However, such a mechanism by which non-regular workers’
income rises seems not to be at work in the model 16. The top left and right in Figure 8
display the impulse responses of consumption by regular workers (right) and non-regular
workers (left) to the ratio shock. The rise in the non-regular ratio reduces the regular
worker’s consumption and increases the non-regular worker’s consumption. The two
responses go in opposite directions, and for a scale of impact, the latter reaction is muchgreater than the former. Therefore, aggregate consumption declines because the negative
effects of both regular workers and ratio itself are dominant.
Details of the mechanism underlying each worker’s consumption can be discussed.
Therefore, it is useful to reinterpret the linearized optimality condition between the ratio
and consumption. For instance, for regular workers, it can be written ascˆ R ,t = C R , −1 cˆ R ,t −1 + C R , +1 E t cˆ R ,t +1 − C R , +2 E t cˆ R ,t + 2 + C N , −1 cˆ N ,t −1 − C N ,0 cˆ N ,t

+ C N , +1 E t cˆ N ,t +1 − S R , −1 sˆt −1 + S R ,0 sˆt − S R , +1 E t sˆt +1 − R( Rˆ t − E t π t +1 ),where
C R , −1 , C R ,0 , C R , +1 , C R , +2 , C N , −1 , C N ,0 , C N , +1 , S R , −1 , S R ,0 , S R , +1 , R > 0.

This equation clearly illustrates that, keeping consumption in regular and non-regular cases,
immediately after the shock, the effect of expected non-regular worker ratio is negative andlarge. Thereafter, by adding to the effect of past ratio, the negative effect on regular
worker’s consumption expands well. Moreover, this equation is reinterpreted as a demand
equation for consumption goods based on the intertemporal work style, which means that
16

Full details will be explained later in Section 4.2.

16

(33)

the negative sign of the term s t −1 is the memory of a past event, that the positive sign ofthe term st is a relief that a present ratio st is exactly lower than past ratio s t −1 , and thatthe negative sign of the term s t +1 signifies anxiety about an increasing ratio.
Regarding the response of output for consumption goods after shock, it shows thesame characteristics of response as aggregate consumption does (bottom left in Figure 6).
However, the output gap is slightly positive and hump-shaped. Moreover, the reaction of
inflation is sharply negative, but inflation is not negative and the sale price does not fall interms of a deviation from the steady state because the steady state of inflation is assumed tobe 1. From the Taylor rule assumption, the nominal interest rate depends mainly upon theinterest rate inertia (middle left in Figure 7).
The mechanism underlying these results ( π < 1 and π ≈ 1 and x > 0 ) can be inferredby referring to Figure 4, which displays the supply demand relation between retailers andwholesalers (entrepreneurs) 17. Assuming the steady state before shock express a point E in
the figure, the results for both retailers and wholesalers as their reactions to a shock stands
respectively for points M and N. With respect to each response of price and quantity, as
described earlier, because (retail price) inflation is strictly close to 1% but less than 1%, theretail price increases from the steady state price, and from Equation (18), intermediate
goods demanded (final goods supplied) by retailers decline. To generate the positive output
gap, the output by wholesalers decreases more than the retailers’ output. Therefore,
wholesale prices are lower than the steady state price for wholesalers. The mark-up X t( ≡ pt /ptw ) rises. It consistently brings inflation down according to NKPC πˆ t = β R πˆ t −1 − κX̂ t .
4.1.2. Housing investment
The top right area of Figure 6 displays the response of aggregate housing investment
to a ratio shock. The increase in the ratio reduces aggregate housing investment as well as
aggregate consumption. The effect of a ratio shock keeps 1 percent persistently, even at 20
quarters after shock. To ascertain the mechanism behind this result, it is necessary toestimate each response of both regular and non-regular workers to a change in ratio. The
bottom right and left in Figure 8 display a positive reaction of non-regular workers’
housing investment and a negative reaction of regular workers to the shock. Although the17

The goods supplied to households differ from goods produced by retailers. Therefore, a vertical axis in the

figure stands for prices of two kinds.

17

figures in this paper display the responses of model variables until 20 quarters, for instance,
the peak response of non-regular workers’ housing investment reaches 7.33% at 29 quarters
after a shock, and the response of regular workers comes up to -0.16% at 32 quarters. Both
responses persistently maintain a situation in which the variables deviate from the steadystates.
As in the case of aggregate consumption, the demand equation must be shown for
housing investment for a regular worker. Housing investment can be expressed as thefollowing:hˆR ,t = −H c , −1cˆ R ,t −1 − H c ,0 cˆ R ,t + H c , +1cˆ R ,t +1 + H c , +2 cˆ R ,t + 2 − H c , −1cˆ N ,t −1
R

R

R

R

N

+ H c ,0 cˆ N ,t + H c , +1cˆ N ,t +1 + H R , −1 hˆR ,t −1 + H R , +1 hˆR ,t +1 + H N , −1 hˆ N ,t −1
NN− H N ,0 hˆ N ,t + S R , −1 sˆt −1 − S R ,0 sˆt + S R , +1 sˆt +1

(34)

where
H c , −1 , H c ,0 , H c , +1 , H c , +2 , H c , −1 , H c ,0 , H c , +1 , H R , −1 , H R , +1 , H N , −1 ,
R

R

R

R

N

N

N

H N ,0 , S R , −1 , S R ,0 , S R , +1 > 0 .

This equation illustrates clearly that, keeping other terms constant except for the term of theratio, the current term of ratio on hR ,t has a dominant negative effect. Moreover, according
to the characteristic of housing that it has durability, i.e., that it is not completely consumed
in one period, regular workers need not increase housing at the current period after shocks t and are able to support their housing demand from s t −1 and E t s t +1 .
As in the case of aggregate consumption, the positive response of non-regular
workers’ housing demand is apparently caused by a change in their income. In the sector of
housing production, as assumed for simplicity, an increase in ratio can mean that theincome share of regular workers changes negatively. Therefore, non-regular workers
generally earn more from a housing sector and add to housing investment. However, theresults were not what they seem to be 18. The demand for non-regular workers’ housing
investment grows mainly because the housing price decreased. After shock, the non-regular
workers who provide shorter worked hours than regular workers play a more important rolein producing housing, the power of housing production, and its price fall (see the middle
18

I will document the full details later.

18

right in Figure 7). However, interestingly, the fall in price can be reinterpreted as follows.
Declining housing prices stimulate non-regular workers’ housing demand and prevent
aggregate housing demand from falling more than necessary.
Although each response is not compatible because the size of shock in the empiricalmodel is not the same as that of the theoretical model, to compare the differences in theempirical responses of both housing and aggregate consumption with the differences in thetheoretical responses is insightful. In an empirical model, the degree of the response in
housing is 6.25 times as great as that of aggregate consumption. Housing is 6.93 times as
great, in terms of consumption, in the theoretical model. The results are not particularly
different. Consequently, in the part of this paper describing calibration, it seems certain thatthe choices of values in deep parameters are consistent with those of the actual economy.
4.1.3. Saving and borrowing
The bottom right and left in Figure 7 display the responses of negative borrowing (i.e.
saving) by regular workers to a ratio shock (left) and the response of positive borrowing (i.e.
usual borrowing) by non-regular workers (right). Increasing in non-regular workers, regular
workers reduce saving 19. They decrease it from the steady state by more than 6% andremain around 2%, even at 20 quarters. It is sure to be persistent. After the shock,non-regular workers change borrowing to a low level by more than 5%. Furthermore, they
maintain such a low level. From 10 quarters, the response becomes positive. These results
can be interpreted as follows. The increase in non-regular workers is simply equivalent to
the decline in regular workers’ income here. Therefore, if it occurs, then they reduce saving.
Furthermore, non-regular workers are temporarily able to attain self-finance for purchasing
housing without borrowing because of the fall in housing prices, and it is mostly during 10
quarters. Thereafter, when housing prices revert to the steady state and nominal interest
rates fall, they recommence borrowing using housing as collateral.

4.2. Each response in between non-regular and regular

19

When ‘saving’ is expressed as a kind of ‘borrowing,’ the steady state of saving is expressed as a negativesign. Therefore, what the positive response in this figure show is that saving is lower than the steady statelevel.

19

The immediately preceding subsection presented an exploration of the effects of anincreasing ratio shock on some basic variables representing the economy. This subsection
presents an examination of the reaction of each type of worker (non-regular worker or
regular worker) to the shock. Although the demands of consumption and housing by
non-regular workers and regular workers have been described, they are reviewed below.
After a shock, the demand for aggregate consumption declines. Non-regular workers
add to consumption and regular workers decline. Therefore, because of the increase in
non-regular workers who are part-time workers, output for consumption goods declines lessthan demand. A positive output gap occurs, and inflation increases slightly. According tototal housing demand or each demand, the results are similar to those in the case of
consumption goods. Non-regular workers need not turn to borrowing to purchase housing
because they earn constant income irrespective of the shock and housing price fall. Regular
workers, who have declining income, decide to decrease borrowing (see Figures 6–8).
Some discussion of the responses of income for each worker should be made. In themodel, results of both all worked hours and every wage are displayed in Figure 9. Basedupon the assumption of model, an increase in the ratio of non-regular workers means thatthe income of non-regular workers grows up. However, reading the figure, it can be readily
understood that to generate such a mechanism is not easy. Although income for regular
workers declines 20, income for non-regular workers mostly remains unchanged. In the labormarkets of both consumption goods and housing, the decline in worked hours offsets therise in wages.
Moreover, as the figure shows, the changes in labor demand and supply have results
related to the impulse responses. First, the responses of worked hours and wage in labormarket of consumption goods for regular workers are that worked hours decline by 0.02%
and that wages also decline by 0.84%. Figure 5-(i) explains these results. In raising the ratio,
the demand of labor force to regular workers declines: this indicates a leftward shift ofcurve. Furthermore, then, regular workers emphasize working rather than consumption andsupply more worked hours (a rightward shift). Second, the responses of worked hours andwages in the labor market of housing for regular workers are that worked hours rise by
0.06% and that the wage decreases by around 0.79%. Some shifts in Figure 5-(ii) occur for
mostly the same reasons as the case of consumption goods. Finally, the responses of20

In the labor market related to housing, because the increasing rate of worked hours is greater thedecreasing rate of wage, income is lowered.

20

worked hours and wage in labor market of consumption goods and housing for regular
workers are that worked hours decline by 13.0% and 26.9% and that wages rise by 12.7%
and 26.6%. Because housing declines completely, despite the emphasis on non-regular
workers, they reduce their worked hours (a leftward shift) (see Figure 5-(iii)). Firms of bothconsumption goods and housing need not change demand for non-regular workers so thatthey attain minimum cost.

4.3. Comparison of responses in different parameter values
The responses of model variables under the baseline settings were examined. This
subsection, in changing some parameter values, presents some novel implications of themodel.
The chosen parameters, selected for various reasons, are s * , m , and ρ s . First, s *represents the steady-state ratio of non-regular workers to all workers. To revalue thisparameter is equivalent to a change in non-regular workers in the economy. The new valuesof s * are set as 0.17 and 0.51. Values greater than 0.51 are not considered because it is not
feasible that non-regular workers account for more than 50% of all workers in a real
economy. Second, m is the parameter reflecting how non-regular workers’ borrowing isclose to their housing value. The higher m is, the closer their borrowing is to the
maximum limits. However, if m is low, then borrowing is small even though housing isvalued highly. Here m is assumed to be 0.30 and 0.80. Finally, parameter ρ s sets thepersistence in the law of motion of the ratio shock. The model variable has been defined as
the exogenous variable. Therefore, if the definition of st can be loosened, high persistence
is interpreted to be a situation by which non-regular workers have been hired for a longer
time because they increased by more than steady state. Therefore, when ρ s was set for0.30 and 0.50 respectively, non-regular workers have a shorter term of employment.
Figures 10 through 15 portray how model variables respond to the ratio shock underalternative values of the three chosen parameters. First, for s * , Figures 10 and 11 display
the natural and clear result: the fewer the non-regular workers are, the better. The figures ofboth demand and supply of every good particularly illustrate that the smaller the steadystate ratio of non-regular workers is, the smaller the negative deviations are. Next, theresults of m (see Figures 12 and 13) are noteworthy. Iacoviello (2005) emphasized thatthe higher the value of loan-to-value is, the more non-regular workers consume in the21reaction to asset price rising. Therefore, generally speaking, m amplifies some effects ofconsumption (Iacoviello’s “asset price"). Although the sign is opposite to that presented by
Iacoviello, the same results are not found from results of this study. The larger the value ofthe loan-to-value is, the less consumption declines because of the negative effect of theratio shock (and the negative response of asset price). Therefore, as results show, parameterm , which is expected to play a role to increase borrowing and to expand consumption,
contrarily amplifies the negativeness of consumption. Finally, in Figures 14 and 15, when
the persistence of shock process is low, the convergence is naturally rapid or the change tothe shock is small. The salient implications are as follows. To avoid the negative deviationfrom the steady state, the added non-regular workers should be not contracted for
employment for long periods.

5. Conclusions
This paper has explained that an increase in non-regular workers can account for thecurrent stagnated demand in Japan. Use of a dynamic stochastic general equilibrium(DSGE) model yields some policy implications. The key idea is that, by raising the numberof non-regular workers who face borrowing constraints, expenditures on goods that require
external finance such as housing investment decline, which causes stagnated demand inJapan.
By the increase of non-regular workers, results show that expenditures on
consumption and housing decrease, and that housing is more sensitive to a non-regular
workers’ shock than consumption is. These results support the empirically obtained results.
As featured results coming from the model, although income for regular workers declined,against expectations, the non-regular workers’ income was constant. Under suchcircumstances, increasing housing demand of non-regular workers results from a fall in
housing prices.
The model presents three implications as follows: 1) it is better to lower the numberof non-regular workers; 2) even though it is easier to borrow, spending does not increase;and 3) even if non-regular workers are employed, they should not be employed over thelong term.
One limitation of the model is that, for simplicity, the ratio of non-regular workers

22was examined as an exogenous variable. In fact, the variable should be controlled as aproblem of firm optimization.

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25

Table 1: Baseline Parameter Value

Parameters

Descriptions

Value

Reference

discount factor
labor supply aversion
labor supply aversion

0.996
3.000
0.800

Original
Sugo and Ueda (2008)
Sugo and Ueda (2008)

Non-regular workers
βN
discount factor
ηNlabor supply aversion
eN
housing depreciationmloan-to-value

0.950
2.000
0.400
0.500

Original
Sugo and Ueda (2008)
Original
Original

Entrepreneurs & Retailersµc
income shareµhincome share

0.630
0.700

Regular workers

βR
ηR
eR

θ
α
Economy
fc
fh
j

δh

probability fixed priceelasticity of substitution

0.875
30.00

Original
Original
Sugo and Ueda (2008)
Sugo and Ueda (2008)

consumption habit
housing habit
weight on housing services
housing depreciation

0.110
0.000
0.100
0.010

Original
Original
Iacoviello (2005)
Original

0.842
0.606
0.110
0.949
0.900

Sugo and Ueda (2008)
Sugo and Ueda (2008)
Sugo and Ueda (2008)
Sugo and Ueda (2008)
Original

Monetary Policy & Shocks
γR
lagged interest rate
γπ
inflation
γx
output gap
ρA
productivity
ρsnon-regular worker ratio

26

σA
σs
σR

productivity
non-regular worker ratio
monetary policy

27

0.843
0.100
0.066

Sugo and Ueda (2008)
Original
Sugo and Ueda (2008)

Figure 1: Employee by type of employment and non-regular worker ratio, Japan.
Source: Special Survey of the Labour Force Survey, 1984–2008.
Note: Bar graph shows the number of employees by type of employment. The unit
is millions. The charcoal bar denotes regular workers, and the light gray denotes
non-regular workers. The line graph shows the fraction of non-regular workers, for which
the unit is percentage on the right axis. Non-regular workers include part-time workers,
temporary workers, dispatched workers from temporary labor agency, contract employees
or entrusted employees, and others. The regular workers are regular staff or employees.

28

Figure 2: Distribution of Annual Income, Japan.
Source: Employment Status Survey, 2002 and 2007.
Note: The definition of non-regular workers is the same as that in Figure 1. The
vertical axis expresses the number of employees. The unit is millions. The horizontal axis
shows the class of annual income earned by the employees. The unit is millions of yen. The
medians are roughly estimated as around 0.8 million (Non-regular) and around 3.9 million(Regular) in 2002, and to be around 1.2 million (Non-regular) and around 4.1 million(Regular) in 2007.

29

Figure 3: VAR Evidence, Japan.
Note: VAR estimated during 1990Q4 – 2008Q4. The dashed lines represent
90-percent confidence bands. The Choleski ordering of the impulse responses is TFP ,ratio , Consumption , Housing . Coordinate: percent deviation from the baseline. TFP is
calculated based upon Kamada and Masuda (2001) and Kawamoto (2004), who adopted the
TANKAN DI.

30

Figure 4: Diagram of the relation between the entrepreneurs’ production function Yc andthe retailers’ demand function Yc f .

31

Figure 5: Diagram of the relation between the labor supply and labor demand: (i) shows theregular workers market for consumption goods; (ii) shows the regular worker market for
housing investment; and (iii) shows the non-regular worker market for consumption goods
and housing investment.

32

Figure 6: Impulse responses to an increasing ratio shock.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

33

Figure 7: Impulse responses to an increasing ratio shock.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

34

Figure 8: Impulse responses to an increasing ratio shock.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

35

Figure 9: Impulse responses to an increasing ratio shock.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

36

Figure 10: Impulse responses to an increasing ratio shock: effects of varying the steadystate of ratio.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

37

Figure 11: Impulse responses to an increasing ratio shock: effects of varying the steadystate of the ratio.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

38

Figure 12: Impulse responses to an increasing ratio shock: effects of varying‘loan-to-value’.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

39

Figure 13: Impulse responses to an increasing ratio shock: effects of varying‘loan-to-value’.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

40

Figure 14: Impulse responses to an increasing ratio shock: effects of varying degrees of
persistence.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

41

Figure 15: Impulse responses to an increasing ratio shock: effects of varying degrees of
persistence.
Note: Vertical axis: deviation from steady state. Horizontal axis: time horizon inquarters.

42