American Economic Journal: Macroeconomics 2017, 9(3): 116–146
https://doi.org/10.1257/mac.20150109
116
Does Home Production Drive Structural Transformation?
†
By A M, S M, S T*
Using new home production data for the United States, we estimate
a model of structural transformation with a home production sector,
allowing for both non-homotheticity of preferences and differential
productivity growth in each sector. We report two main ndings. First,
the estimation results show that home services have a lower income
elasticity than market services. Second, the slowdown in home labor
productivity, which started in the late 70s, is a key determinant of the
rise of market services. Our counterfactual experiment shows that,
without the slowdown, the share of market services would have been
lower by 7.5 percent in 2010. (JEL D13, J24, L16)
S
ince the early 1990s, a number of studies have incorporated household home
production in a neoclassical framework in order to explain several macroeco-
nomic phenomena.
1
Structural transformation is one of the elds in which research-
ers have recently been discussing the role of home production.
2
While previous
studies in this eld have successfully derived rich implications by modeling home
production, empirical works that assess the model’s ability to explain the data have
been limited. Therefore, an important question to be addressed in this literature is
whether a structural transformation model with a home production sector is able to
account for the actual home production data.
In this paper, we propose and estimate a model of structural transformation with
a home production sector that can account for the movements of the home and
1
These studies include issues on business cycles (Benhabib, Rogerson, and Wright 1991; Greenwood and
Hercowitz 1991), life-cycle labor supply decisions (Ríos-Rull 1993), and scal policy (McGrattan, Rogerson, and
Wright 1997), among others.
2
The structural transformation literature started discussing home production following two seminal papers,
Rogerson (2008) and Ngai and Pissarides (2008).
* Moro: Department of Economics and Business, University of Cagliari, Via Sant’Ignazio 17, 09123,
Cagliari, Italy (email: amoro@unica.it); Moslehi: Department of Economics, Monash University, Building H,
900 Dandenong Road, Cauleld East, VIC 3145, Australia (email: solmaz.moslehi@monash.edu.au); Tanaka:
School of Economics, University of Queensland, Level 6 Colin Clark Building, Blair Dr, QLD 4072, Australia and
CAMA (email: s.tanaka@uq.edu.au). We thank Benjamin Bridgman for providing the home production data for
the United States. We also thank Timo Boppart, Fabio Cerina, Horag Choi, Begoña Domínguez, Chris Edmond,
Miguel León-Ledesma, Sephorah Mangin, Rachel Ngai, Michelle Rendall, Akos Valentinyi, Yuichiro Waki, and
other seminar participants at Carlos III, University of Barcelona, University of Luxembourg, Indiana University,
Kansas City Fed, IMF, University of Melbourne, Monash University, University of Queensland, University of
Tokyo, Keio University, Kyoto University, Hitotsubashi University, University of Warwick, Society for Economic
Dynamics (Warsaw), Conference on Urbanization, Structural Change, and Employment (Hong Kong), Workshop
on Structural Transformation (St. Andrews), Midwest Macro Meetings Fall 2015 (Rochester), Public Economic
Theory (Luxembourg), and Workshop of Australasian Macroeconomics Society (Sydney) for their helpful com-
ments and suggestions. The usual disclaimers apply.
†
Go to https://doi.org/10.1257/mac.20150109 to visit the article page for additional materials and author
disclosure statement(s) or to comment in the online discussion forum.
VOL. 9 NO. 3 117
MORO ET AL.: HOME PRODUCTION AND STRUCTURAL CHANGE
market sector shares in extended total consumption in the United States.
3
In order
to construct the home production data for the estimation, we follow the income
approach recently developed in the literature, and compute the value added of home
production from its input factors and their prices.
4
We then use the estimated model
to study the role of a home production sector in the process of structural transfor-
mation. In particular, we run a counterfactual experiment to quantify the effects of
the slowdown in home labor productivity growth in the United States after the late
1970s, which is documented in Bridgman (2013).
Our framework is based on a multi-sector growth model in which structural trans-
formation is generated through non-homothetic preferences and differential pro-
ductivity growth across sectors, as in Buera and Kaboski (2009). We extend this
model to include a home production sector operated by the household. Since the
inter-temporal and the intra-temporal problems can be solved independently in this
class of growth models with structural transformation, we can rewrite the latter as a
static, consumption choice problem of the household, which depends on the prices
of the three market goods, the implicit price of home produced services, and the
extended total consumption. This last version of the model allows us to estimate
the implied share equations, using the home production data together with the val-
ue-added consumption data for the market sectors.
In the estimation, we explore different household preferences specications. In
particular, we allow for different income elasticities of home and market services
in the household consumption demand, something that has not been considered in
the previous literature.
5
This is motivated by the empirical evidence documented in
Eichengreen and Gupta (2013), which suggests that market services with a home
counterpart could have a different income elasticity from the other services. In our
results, it turns out that this feature of the model is crucial to account for the data.
We highlight two main results. First, we nd that home services have a lower
income elasticity than market services. The estimation results indicate that if the
income elasticities are the same between market and home services, the model
cannot generate the secular decline of the home service share from the late 1940s
onward (see panel A in Figure 1). This result contrasts with previous studies in the
literature, which explain the movement of market and home service shares only
through differences in the rates of technological progress across sectors.
6
Our esti-
mates suggest that the changes in technologies are not enough to account for the
movement of the home and market shares observed in the data.
The second result is obtained by running a counterfactual experiment, in which
we assume the growth rate differential between home labor productivity and market
service labor productivity after 1978 is the same as that in the period 1947–1978. We
nd that in the counterfactual the share of market services in the total consumption
expenditure is 0.80 in 2010, compared to 0.86 in the benchmark estimation, which
3
We dene extended total consumption as the value of market consumption plus the value added of home
production.
4
Our income approach is similar to those in Landefeld, Fraumeni, and Vojtech (2009) and Bridgman (2013).
5
A common assumption in previous works is to assume the same income elasticity for home and market ser-
vices. See, for instance, Rogerson (2008), Ngai and Petrongolo (2013), and Rendall (2015).
6
See Ngai and Pissarides (2008) and Buera and Kaboski (2012b) for examples.
118 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JULY 2017
represents a 7.5 percent decrease. That is, if there were no slowdown in home labor
productivity, the extent of structural change would be considerably lower than the
actual data indicates. This experiment therefore suggests that the home produc-
tion sector can have quantitatively important implications for the structural change
observed in market sectors.
Our paper relates to the literature, started by Rogerson (2008) and Ngai and
Pissarides (2008), that considers home production as a key determinant in the process
of structural transformation. More recent studies in this literature include Buera and
Kaboski (2012a) who focus on differences in skill intensities between home and mar-
ket, Buera and Kaboski (2012b) who model differences in production scale between
home and market, Ngai and Petrongolo (2013) who study the rise of female labor force
participation in the United States, and Rendall (2015) who analyzes the implications
of the difference in the tax system for female labor force participation between the
United States and Germany. As emphasized above, while these studies have derived
rich implications from structural transformation models with a home production sec-
tor, they do not estimate these models using actual home production data.
There are two recent contributions that estimate a model of structural transforma-
tion without a home production sector using the US data. On the one hand, Buera
and Kaboski (2009) estimates a three-sector model using the US data in a gen-
eral equilibrium framework. Herrendorf, Rogerson, and Valentinyi (2013), on the
other hand, considers a partial equilibrium setup, and estimates a three-sector model
using nal consumption expenditure and consumption value-added data since 1947.
Our methodology is close to that of Herrendorf, Rogerson, and Valentinyi (2013).
However, we consider a structural transformation model with a home production
sector, and estimate the model using the value added of home production together
with consumption value-added data for the market sectors.
Finally, our paper is also related to the literature which has developed the income
approach to impute the value of nonmarket activities from input factors and their
market prices. This idea goes back as far as Kendrick (1979). In recent years,
researchers at the US Bureua of Economic Analysis (BEA) have further developed
F 1. H M S S (P A) H L P (P B)
Notes: The consumption value added of the market sectors is calculated based on the data of Herrendorf, Rogerson,
and Valentinyi (2013). The consumption value added of the home sector is calculated by using the income approach
similar to Bridgman (2013). The home labor productivity is obtained by deating the value added of home produc-
tion with the price index for the home sector and then dividing it by hours worked at home. The details of the data
used here are discussed in Section III.
Service
Home
Manufacturing
Agriculture
0
0.2
0.4
0.6
Share in extended
total consumption
1950 1960 1970 1980 1990 2000 2010
Panel A. Home and market sector shares
6
10
14
18
Labor productivity
(unit: 2005 USD per hour)
1950 1960 1970 1980 1990 2000 2010
Panel B. Home labor productivity
VOL. 9 NO. 3 119
MORO ET AL.: HOME PRODUCTION AND STRUCTURAL CHANGE
this approach to construct their Satellite Account for Household Production
(Landefeld and McCulla 2000; Landefeld, Fraumeni, and Vojtech 2009; Bridgman
et al. 2012; and Bridgman 2013). This paper’s strategy to construct the home value
added closely follows these works.
The remainder of the paper is as follows. Section I presents the model; Section II
discusses the estimation procedure; Section III explains the data; Section IV reports the
estimation results, while Section V runs the counterfactual experiment. In SectionVI,
we consider an extension by disaggregating the service sector. In Section VII, we
discuss the implications of the model for hours worked. In Section VIII, we conclude.
I. Model
This section presents a model of structural transformation with a home produc-
tion sector.
A. Setup
Time is discrete. There is a representative household whose objective is to maxi-
mize her utility. There are ve types of goods produced in this economy: four con-
sumption goods (agriculture, manufacturing, market services, and home services)
and one investment good. The household’s preferences are given by
u =
∑
t=0
∞
β
t
ln C
t
,
where β is the subjective discount factor. The composite consumption index C
t
is
dened as
(1) C
t
=
(
∑
i=a, m, s
(
ω
i
)
1
__
σ
(
c
t
i
+
_
c
i
)
σ−1
____
σ
)
σ
____
σ−1
,
where c
t
i
denotes consumption of good i ∈
{
a, m, s
}
. In (1), the parameter ω
i
deter-
mines the weight on each good in the household’s preferences; the parameter
_
c
i
con-
trols non-homotheticity in preferences; and the parameter σ governs the elasticity of
substitution among the three goods. Service consumption is a composite of market
services, c
t
sm
, and home produced services, c
t
sh
, as
(2) c
t
s
=
[
ψ ( c
t
sm
)
γ−1
____
γ
+ (1 − ψ)
(
c
t
sh
+
_
c
sh
)
γ−1
____
γ
]
γ
____
γ−1
.
In (2), the parameter γ governs the elasticity of substitution between market and
home services, and ψ is the share parameter in the service aggregator. Note that we
allow for a different income elasticity between market and home services through
the parameter
_
c
sh
. We provide a discussion of this parameter in Section ID and in
the estimation section.
In our setup, for each period, the household is endowed with
_
l = 1 unit of labor
that she splits into working time in the market, l
t
mk
, paid at wage w
t
, and working
time at home, l
t
sh
. Also, the household holds the capital stock k
t
in the economy, and
120 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JULY 2017
decides how much to rent in the market, k
t
mk
, at rate r
t
, and how much to use in home
production, k
t
sh
. Then, the household’s constraints are given by
(3) p
t
a
c
t
a
+ p
t
m
c
t
m
+ p
t
sm
c
t
sm
+ k
t+1
mk
−
(
1 − δ
)
k
t
mk
+ k
t+1
sh
−
(
1 − δ
)
k
t
sh
= r
t
k
t
mk
+ w
t
l
t
mk
,
l
t
mk
+ l
t
sh
=
_
l ,
where p
t
j
is the price of good j ∈
{
a, m, sm
}
and δ is the depreciation rate. We
normalize the price of the investment goods to be equal to one. The total amount of
capital is dened as
k
t
≡ k
t
mk
+ k
t
sh
.
The household produces home services through the following technology:
c
t
sh
= A
t
sh
(
k
t
sh
)
α
(
l
t
sh
)
1−α
.
On the market production side, there is a perfectly competitive rm in each market
sector j ∈
{
a, m, sm
}
, with technology
Y
t
j
= A
t
j
(
K
t
j
)
α
(
L
t
j
)
1−α
.
Finally, there is also a perfectly competitive rm operating in the investment good
sector, with technology
Y
t
x
= A
t
x
(
K
t
x
)
α
(
L
t
x
)
1−α
.
B. Household’s Problem
Next, we rewrite the previous setup by treating the home production sector
as being operated by a perfectly competitive rm. This allows us to consider the
home production sector as an additional market sector, which helps us to simplify
the problem. Assuming perfect competition in the home sector, we can dene an
implicit price index for the home good as
(4) p
t
sh
≡
r
t
α
w
t
1−α
____________
A
t
sh
α
α
(
1 − α
)
1−α
.
Using the above price, we can show that
(5)
p
t
sh
c
t
sh
= w
t
l
t
sh
+ r
t
k
t
sh
.
