Download The Depressing Effect of Agricultural Institutions on the Prewar

The Depressing Effect of Agricultural Institutions
on the Prewar Japanese Economy
Fumio Hayashi
University of Tokyo and National Bureau of Economic Research
Edward C. Prescott
University of Arizona and Federal Reserve Bank of Minneapolis
Why didn’t the Japanese miracle take place before World War II? The
culprit we identify is a barrier that kept prewar agricultural employment constant. Using a standard neoclassical two-sector growth model,
we show that the barrier-induced sectoral distortion and an ensuring
lack of capital accumulation account well for the depressed output
level. Without the barrier, Japan’s prewar GNP per worker would have
been at least about a half of that of the United States, not about a
third as in the data. The labor barrier existed because, we argue, the
prewar patriarchy forced the son designated as heir to stay in
agriculture.
I.
Introduction
The Japanese miracle, which lifted the Japanese economy from the ashes
of the World War II destruction to the present-day prosperity, and the
“lost decade” of the 1990s, during which the economy ceased to grow,
are well known. Much less so is the decades-long relative stagnation
(relative to the postwar boom) before World War II: for much of the
We thank Serguey Braguinsky, Toni Braun, Steve Davis, John Fernald, Takashi Kurosaki,
Richard Rogerson, Juro Teranishi, David Weinstein, two referees, and particularly the
editor of this Journal for comments on earlier versions of the paper. Shuhei Aoki provided
competent research assistance. Gratefully acknowledged is research support from Grantsin-Aid for Scientific Research, 18203023, administered by the Japanese Ministry of Education and the National Science Foundation, SES 0422539.
[ Journal of Political Economy, 2008, vol. 116, no. 4]
2008 by The University of Chicago. All rights reserved. 0022-3808/2008/11604-0005$10.00
573
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journal of political economy
prewar period of 1885–1940, Japan’s real GNP per worker remained a
third of that of the United States. This paper addresses the question of
why the Japanese miracle did not occur before the war.
An amazing fact about agricultural employment in prewar Japan is
that it was virtually constant at 14 million persons (about 64 percent of
total employment in 1885) throughout the entire prewar period, despite
a very large urban-rural income disparity. There was a persistent and
significant rural-to-urban emigration, but its size was never large enough
to diminish rural population. The constancy strongly suggests that there
was a powerful noneconomic force that prevented people from moving
out of agriculture.
This leads us to ask whether a possible sectoral misallocation of labor
due to this barrier to labor mobility had a quantitatively important effect
on the economic development of prewar Japan. We do so by superimposing the labor barrier on a two-sector neoclassical growth model
with agriculture. The two-sector model itself builds on the long tradition
of modeling the “dual economy” starting with Jorgenson (1961).1 Its
most recent renditions are Echevarria (1997), Robertson (1999), Laitner
(2000), Gollin, Parente, and Rogerson (2002), Hansen and Prescott
(2002), and many others. They examine, as we do in the paper, the
dynamics of capital accumulation when the country starts to devote more
resources outside the decreasing-returns-to-scale technology that is agriculture. They do not consider possible effects of sectoral distortion on
the transition, however.
For its concern on the sectoral distortion, our paper is related to the
recent development accounting literature on international income differences, although our focus is exclusively on Japan in relation to the
United States.2 Vollrath (forthcoming) finds for a number of countries
that the sectoral allocation of labor and capital is inefficient because
their marginal products are not equated across sectors. He finds that
the factor market inefficiency accounts for 90–100 percent of international differences in the overall (economywide) total factor productivity
(TFP). Restuccia, Yang, and Zhu (2008) show that sectoral distortions
in the use of intermediate inputs and labor generate large international
differences in the overall TFP. Our paper is similar to these papers in
that we find a large effect on the overall TFP of a sectoral distortion
(due, in our case, to the labor barrier) for prewar Japan. Unlike these
papers, however, our analysis is dynamic in that we also examine the
effect of the distortion on capital accumulation.
We show that our simple two-sector growth model, when the labor
1
Thus, contrary to the Lewisian tradition of development economics, we suppose that
agricultural workers are paid their marginal, not their average, product.
2
See Caselli (2005) for a survey of the recent burgeoning literature on development
accounting.
agriculture and the prewar japanese economy
575
barrier is superimposed on it, can account for the relative stagnation
of prewar Japan. We then lift the labor barrier to predict what would
have happened to the prewar Japanese economy. This counterfactual
simulation shows that prewar GNP per worker would have been higher
by about 32 percent, which would have placed Japan at close to a half,
not a third, of the United States in terms of per-worker output. The
output gain comes about because an increased overall production efficiency achieved by the removal of the barrier would have sparked an
investment boom. The gain from about a third to a half of the U.S.
GNP, however, is only a part, albeit a significant part, of the catch-up
that took place in the postwar period when the labor barrier crumbled
down. To fully account for the catch-up, we need to incorporate the
rapid postwar TFP growth in manufacturing.
We then argue that this hugely costly labor barrier was self-imposed
by the extended family. That is, the barrier was in place not because of
some legal restriction limiting the extent of emigration, which did not
exist in prewar Japan, but because the parent who is a farmer wished
one of the children to succeed his occupation. Other than describing
the prewar social norm to value family lineage, we do not attempt to
derive the assumed paternalistic preferences from some meta theory à
la Akerlof (1980). Unlike the nonpaternalistic preferences standard in
economics, such a paternalistic preference requiring the child to take
actions against his own economic interests is not self-enforcing. We point
to paternalistic clauses in the Civil Code and other institutional features
of prewar Japan that made it possible for the parent to overcome the
enforcement problem. Our hypothesis explains why the number of farm
households remained constant with a constant family size (which accounts for the constant agricultural employment) before the war and
why agricultural employment dropped drastically after the war when
there was a wholesale revision of the Civil Code.
Having stated our thesis, we acknowledge an alternative view about
the income disparity between agriculture and industry. Caselli and Coleman (2001) view the disparity as a skill premium, not a sign of distortion.
They show, using a two-sector model, that the convergence of agricultural income to nonagricultural income observed for the United States
over a century since 1880 can be explained by an increased occupational
mobility brought about by a decline in the cost of acquiring skills. In
their model, individuals are heterogeneous with respect to the amount
of time required to obtain a ticket to get out of agriculture. So there
is always a measure of marginal individuals who are indifferent between
staying in agriculture and paying the one-time cost in time to move out.
In this view of the world, the counterfactual simulation amounts to
asking what would have happened if the training cost were as low as it
is now. We would claim that this training cost model is less suited to
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journal of political economy
prewar Japan than ours. First, to the extent that the time cost of training
is highly correlated between siblings, it is hard to explain why in each
family one of the siblings remained in agriculture and all others left.
Second, to explain the timing of the postwar exodus out of agriculture,
the model would have to assume that there was a mass of individuals
in the cross-section distribution of the training time and that the decline
in the training cost crossed the threshold precisely when the observed
exodus took place.
The plan of the paper is as follows. The next section, Section II,
describes facts about Japan’s economic development. Section III advances our sectoral misallocation hypothesis and summarizes our findings. This is followed by three sections of elaboration: a presentation
of the two-sector growth model in Section IV, a calibration of the model
in Section V, and a detailed discussion, in Section VI, of simulation
results for both the pattern of sectoral allocation and the behavior of
aggregate variables. The issue of why there existed the barrier in the
first place will be taken up in Section VII. Section VIII briefly states
conclusions and an agenda for future research.
II.
Accounting for Japan’s Economic Development since 1885
A.
The Postwar Miracle and Prewar Stagnation
We start out with a look at aggregate output since 1885. The basic data
source for prewar macro variables for Japan ( Japan proper, excluding
former colonies) is the Long Term Economic Statistics (hereafter LTES),
a consistent system of national income accounts compiled by a group
of Japanese academics affiliated with Hitotsubashi University. The reader
is referred to appendix 1 of Hayashi and Prescott (2006) for how the
annual values of real GNP and other variables are constructed from the
LTES and other sources. Figure 1 shows output per worker (real GNP
divided by working-age population) for Japan and the United States for
1885–2000, with the figures for Japan assumed to be as high as 82
percent of those for the United States in her heyday in 1991.3 The scale
is in logs with a base of 2, so a difference of 1.0 in the log scale represents
a 100 percent difference in levels. The log difference for 1885 is 1.75,
3
As in Hayashi and Prescott (2002), we do not recognize government capital, so GNP
here is given after excluding depreciation on government capital. U.S. real GNP since
1929 is the chained real GNP from the U.S. National Income and Product Accounts. Real
GNP before 1929 is taken from Balke and Gordon (1989). The working-age population
is the population 16 years or older for the United States and 15 or older for Japan until
1945 and 21 years or older for the United States and 20 or older for Japan after 1945.
We assume that the ratio of Japan’s per-worker GNP to that of the United States is 71.2
percent in 1998. This ratio is implied by Maddison’s (2001) estimate of GDP levels in
1990 international purchasing power parity (PPP) dollars, placing Japan’s GDP at 31.9
percent of U.S. GDP for 1998. See his tables A-b and A-j.
agriculture and the prewar japanese economy
577
Fig. 1.—GNP per worker, 1885–2000
which means U.S. per-worker GNP was about 3.4 (p 21.75) times Japan’s
(or Japan’s was about 30 percent of that of the United States) in 1885.
There are three features that would catch anyone’s eye. The first is
the fabulous growth in the post–World War II era, known as the Japanese
miracle. There was a fivefold increase in Japan’s GNP per worker in the
25 years since 1947. The second is the prewar relative stagnation of
several decades: between 1885 and 1940, Japan’s GNP per worker remained at 30–50 percent of the U.S. GNP per worker. The third feature
is the stagnation in the 1990s. We have dealt with Japan’s 1990s elsewhere
(Hayashi and Prescott 2002). The question we address in this paper is
why the Japanese miracle did not take place until after World War II.
B.
Growth Accounting
A very standard way to account for a country’s growth is to define the
(overall or macro) TFP as
TFPt {
Yt
,
K (h t E t)1⫺v
v
t
(1)
where Yt is aggregate output in period t, K t is aggregate capital stock,
E t is employment, h t is average hours worked per employed person (so
h t E t equals total hours worked), and v is capital’s share of aggregate
income. In the growth accounting calculations below, we set v to the
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journal of political economy
TABLE 1
Growth Accounting
Average Annual Growth Rate (%) of
1885–1940
1960–73
Per-Worker
GNP
Yt /Nt
2.1
7.2
TFP Factor
TFP1/(1⫺v)
t
CapitalOutput
Ratio
(Kt /Yt)v/(1⫺v)
Employment
Rate
Et /Nt
Hours Worked
per Worker
ht
2.9
7.3
⫺.6
.8
⫺.4
⫺.7
.2
⫺.2
Note.—Geometric means. Yt p real GNP, Kt p capital stock, Et p employment, Nt p working-age population, and
ht p average hours per employed person; TFPt is defined in eq. (1); v p 1/3.
customary value of 1/3. An easy algebra on this definition yields that
GNP per worker can be decomposed into four factors:
v/(1⫺v)
()
Yt
K
p TFPt1/(1⫺v) # t
Nt
Yt
#
(NE ) # h ,
t
t
(2)
t
where Nt is working-age population. This formula shows that, in the long
run where the capital-output ratio (K t /Yt), the employment rate
(E t /Nt), and hours worked per employed person (h t) are constant, the
trend in GNP per worker (Yt /Nt) is given by the TFP factor TFPt1/(1⫺v).
The power 1/(1 ⫺ v) represents the magnification effect of TFP that an
increase in TFP generates a proportionate increase in the capital stock,
so the capital-output factor, (K t /Yt)v/(1⫺v), represents only the part of
capital accumulation not induced by TFP growth.4 The left side, GNP
per worker, has been graphed in figure 1.
Table 1 reports the average annual growth rate of per-worker GNP
and its four factors shown in (2) for prewar and postwar Japan.5 For
the high-growth era of 1960–73, despite a decline in both the average
hours worked per worker and the employment rate, a high per-worker
GNP growth rate of 7.2 percent is brought about by very high TFP
growth and, less importantly, by a slight increase in the capital-output
ratio: an 0.8 percent growth in (K t /Yt)v/(1⫺v). For the prewar period,
there was no increase in the capital-output ratio: between 1885 and
4
This formula has been adopted by King and Levine (1994), Hayashi and Prescott
(2002), and others. Klenow and Rodriguez-Clare (1997) discuss the advantages and disadvantages of this form of growth accounting against the more standard form of decomposing output growth into TFP, capital growth, and labor growth.
5
We use the deflator for nonagricultural goods to convert nominal capital stock into
real capital stock in calculating K. This is to be consistent with the assumption of the
paper’s model that agricultural goods cannot be used as an investment good. See app. 1
of Hayashi and Prescott (2006) for more details on how we defined real output Y and
the real capital stock K. Employment and hours worked are not adjusted for quality. The
initial year for the postwar period is taken to be 1960 because the capital stock data in
the Japanese national accounts for the early 1950s seem unreliable.
agriculture and the prewar japanese economy
579
Fig. 2.—Japan’s overall TFP factor, 1885–2000
1940, the capital-output ratio declined.6 The much lower TFP growth
before the war than after means that the prewar TFP level was very low.
This is described by the graph of the TFP factor TFPt1/(1⫺v) in figure 2
(for now, ignore the line labeled “model, without barrier”). The postwar
TFP factor lies far above the dotted trend line extrapolated from the
prewar period.
In summary, Japan’s prewar relative stagnation can be accounted for
by the low level of overall TFP and a falling capital-output ratio.
III.
A.
The Basic Idea and Summary of Results
The Sectoral Misallocation Hypothesis
The thesis of this paper is that the labor barrier—a barrier limiting the
extent of rural-to-urban emigration—contributed to Japan’s pre–World
War II stagnation. We were led to this thesis by the following observations. Figure 3 shows that employment in agriculture (here and elsewhere excluding forestry and fishery) was essentially constant at 14 million persons in prewar Japan. This figure strongly suggests that
agricultural employment was constrained to be at least about 14 million.
6
The capital stock in this paper excludes government capital. If the capital stock includes
government capital and GNP includes depreciation on government capital, the capitaloutput ratio still declines, but less steeply. The reason is that the share of government
capital increases rather sharply toward the end of the sample period of 1885–1940 (it is
about a third in 1940).
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journal of political economy
Fig. 3.—Employment in agriculture, 1885–2003
The figure also shows that, in sharp contrast to the prewar era, postwar
Japan witnessed a steep decline in agricultural employment.
Thanks to the labor barrier setting the binding lower bound of 14
million on agricultural employment, there was too much labor tied up
in the decreasing-returns-to-scale technology called agriculture. For reasons explored in Section VII, this barrier ceased to operate after World
War II, which must have contributed at least in part to the rapid increase
in the overall TFP in postwar Japan. Hansen and Prescott (2002) described the industrial revolution as a switch from a decreasing-returnsto-scale (with respect to reproducible inputs) technology (the Malthus
technology) to a constant-returns-to-scale technology (the Solow technology). Our hypothesis can be rephrased as saying that the transition
from Malthus to Solow was inhibited by the barrier to labor mobility.
B.
Main Results
The rest of this paper casts our sectoral misallocation hypothesis for
prewar Japan in a two-sector neoclassical growth model with agriculture
in order to see to what extent the model with the labor barrier can
account for the prewar relative stagnation. The growth model’s generic
features are that (i) the actual path of sectoral TFPs (shown in fig. 4)7
is taken as given and was perfectly foreseen by agents as of 1885, (ii)
7
The sectoral TFPs are calculated for each year using the Cobb-Douglas production
functions to be shown in Sec. IV (or, more precisely, [B1] and [B12] of App. B) with
parameter values given in the calibration of Sec. V.
agriculture and the prewar japanese economy
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Fig. 4.—Sectoral TFPs, 1885–1940 (1885 p 100)
the path of total employment and hours are exogenously given to the
model, and (iii) the sectoral allocation of capital and capital accumulation are endogenous. Additional features meant to make the model
suited for prewar Japan are that (iv) labor mobility is subject to the
labor barrier that sets the lower bound of 14 million for employment
in the agricultural sector, and (v) according to the stringent Engel’s law,
the subsistence level of food was a very high fraction of food consumption in 1885.
As will be shown in Section VI, the exogenous employment assumption can be relaxed with essentially the same results. The exogenous
hours assumption is essential; without it, the labor barrier would lose
its bite because the household could largely overcome the labor barrier
by working far fewer hours in sector 1. Freely choosing hours is not
allowed in the hypothesis we will advance in Section VII that the parent
forces the child to be a full-time farmer.
The paper’s main results are the following.
• Our simple two-sector model accounts for the prewar relative stagnation. The simulation (i.e., the solution path of the model) in
which the labor barrier is imposed tracks the prewar data closely.
This is shown for per-worker GNP in figure 5: the simulation represented by the dotted line labeled “with barrier” does not depart
substantially from the actual except for the post–World War I period, where the model consistently overpredicts output (see below
for more on the overprediction for the interwar period). The lower
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Fig. 5.—GNP per worker, 1885–1940
bound for agricultural employment is binding throughout the prewar period.
• The quantitative effect of the labor barrier is large. The counterfactual simulation—the solution path of the model that does not
impose the labor barrier but still takes the sectoral TFPs as given—
for per-worker GNP is the line labeled “without barrier” in figure
5. Japan’s GNP per worker, which was about a third of the U.S.
level for much of the prewar period, would have been substantially
higher (see table 2 below for more quantitative information) were
it not for the barrier.
• There are two main sources of this big gain in aggregate output.
The first is a production efficiency gain due to the removal of the
barrier. Also shown in figure 2 above is the overall TFP factor
calculated from the counterfactual simulation. It shows that the
removal of the barrier-induced misallocation of labor significantly
raises the whole path of overall TFP.8 The second is an investment
8
Although its level is higher than in the data, the growth rate of the overall TFP without
the barrier is less than in the data because the barrier gets less onerous as the lower bound
gradually falls as a fraction of total employment. The reason why the efficiency gain is
exhausted by 1940 is less obvious and has to do with a PPP comparison between the two
economies, the actual prewar Japanese economy and the counterfactual. The removal of
the barrier expands the production possibility frontier substantially even in 1940, but the
higher relative price of agriculture works to depress real GNP of the counterfactual economy in the PPP calculation. Without the PPP adjustment, real GNP and hence the overall
TFP in the counterfactual are higher by 26 percent. See n. 21 for more details.
agriculture and the prewar japanese economy
583
TABLE 2
Level Accounting for 1885–1940, Actual vs. Counterfactual
Geometric mean of (value
without barrier for year
t)/(its actual value for
year t)
Y/N
TFP1/(1⫺v)
(K/Y)v/(1⫺v)
E/N
h
1.32
1.24
1.04
1
1.02
Note.—See the note to table 1 for definitions of symbols. Because the counterfactual simulation uses actual Et and
Nt, the ratio for the employment rate Et /Nt is unity by construction. Because the means are geometric, the product of
the means for the four factors equals the mean for Y/N: 1.32 p 1.24 # 1.04 # 1 # 1.02.
boom sparked by the increased production efficiency. Figure 6
plots the capital stock per worker, K t /Nt, for the three cases, actual
and simulations with and without the barrier. In the counterfactual
simulation (i.e., without the barrier), the capital stock rises sharply
in the early prewar period when the improvement in overall production efficiency is greatest (see below for our comments on the
interwar capital accumulation).
By way of summarizing, table 2 reports the “level accounting,” comparing actual prewar Japan with a hypothetical prewar Japan without
the barrier predicted by the model. It measures the effect of lifting the
labor barrier on each of the factors in (2) by calculating the prewar
mean of the ratio of the factor from the counterfactual simulation to
the actual value. It shows that the prewar output gain, which is 32 percent
on average, comes from three sources: the improvement in overall efficiency (already shown in fig. 2), a rapid capital accumulation raising
the capital-output ratio, and, less important, a gain in average hours
worked h t . This last piece comes about because the employment share
of agriculture (where hours worked are slightly lower) is lower in the
counterfactual simulation (41 percent of total employment vs. 64 percent in the data for 1885).
Before we turn to model specifics, two caveats should be noted.
• Our sectoral misallocation alone does not account for the low level
of prewar overall TFP described in figure 2. Studies on Japan’s
postwar growth accounting show that the nonagricultural TFP rose
sharply precisely when the overall TFP did in the postwar period.9
With the sharp rise in the sectoral TFPs not taking place until after
9
See a series of work by Dale Jorgenson and his associates. For example, a very detailed
disaggregated study by Nomura (2004), which is unique in its inclusion of the 1960s, shows
(see his table 4-28) that the Japanese-U.S. TFP ratio (defined as the ratio of Japan’s TFP
to that of the United States) for the whole economy increased from 0.487 in 1960 to
0.813 in 2000. There was a large decline in the TFP ratio for agriculture from 1.199 in
1960 to 0.737 in 2000, but there was also a rapid TFP growth in manufacturing. The TFP
ratio for autos, e.g., shot up from 0.680 in 1960 to 1.391 in 2000. See Jorgenson and
Nomura (2007) for the most recent estimates.
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journal of political economy
Fig. 6.—Capital stock per worker, 1885–1940 (1885 p 100)
the war, the removal of the labor barrier alone is not enough to
lift the prewar trend line of overall TFP to the postwar level.
• The model has difficulty tracking the capital stock in the interwar
period. As seen in figure 5, the simulation with the labor barrier
overpredicts interwar output. It comes about because the model
wants to respond to the surge in nonagricultural TFP after World
War I (shown in fig. 4) by raising the capital stock (see fig. 6).
Why the actual capital stock ceased to respond to the TFP surge
after the mid-1920s is a puzzle to us. Perhaps it has to do with the
rapid cartelization in the 1930s.10
IV.
The Two-Sector Model
In this section we present our two-sector growth model. The first sector
is agriculture and the second sector is the rest of the economy. Output
of sector 1 will be referred to as good 1 or food.
A.
Households
There is a stand-in household with Nt working-age members at date t.
The size of the household evolves over time exogenously. The stand-in
10
According to Takahashi (1975), the number of cartels jumped from the pre–World
War I figure of seven to 12 in the 1920s and to 48 after 1930.
agriculture and the prewar japanese economy
585
household’s utility function is
冘
⬁
t
bN
tu(c 1t , c 2t),
(3)
tp0
where cjt is per-member consumption of good j ( j p 1, 2) in period t.
Measure E t of the household work. The household takes total employment E t as given and decides how it is divided between employment
in sector 1 (E 1t) and in sector 2 (E 2t), subject to the labor barrier to be
introduced shortly. If employed in sector j, the member works for h jt
hours per unit period ( j p 1, 2). Hours worked (h 1t , h 2t) are exogenously given to the household. With wjt denoted as the wage rate in
sector j, the household’s labor income is
w 1th 1t E 1t ⫹ w 2th 2t E 2t p [w 1th 1tsEt ⫹ w 2th 2t(1 ⫺ sEt)]E t ,
where sEt { E 1t /E t is the fraction of employment in sector 1.
There are two other sources of income for the household. First, if
Ntk t is the capital stock owned by the household (so k t is the capital
stock per worker), its rental income is rt Ntk t. In contrast to labor, we
assume no barrier to capital mobility between sectors, so the rental rate
rt does not depend on which sector rents capital.11 Second, there is a
rent earned from land, an input to sector 1’s production. The period
budget constraint for the household, then, is
qt Ntc 1t ⫹ Ntc 2t ⫹ Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t p
[w 1th 1tsEt ⫹ w 2th 2t(1 ⫺ sEt)]E t ⫹ rt Ntk t ⫺ t(r
t t ⫺ dt)Ntk t ⫺ pt ,
(4)
where dt is the depreciation rate (allowed to be time dependent), qt is
the relative price of good 1 in terms of good 2, tt is the tax rate on netof-depreciation capital income, and pt is taxes other than the capital
income tax less land rent. The second good is the numeraire. So, for
example, w 1t is the sector 1 wage rate in terms of good 2. Since hours
worked as well as total employment E t are exogenous, the tax on labor
income is not distortionary and is included in pt.
There is a barrier to labor mobility requiring employment in sector
1 to be at least Ē 1t persons:
(the labor barrier)
E 1t ≥ E¯ 1t i.e., E 1t /E t { sEt ≥ ¯sEt { E¯ 1t /E t .
(5)
The issue of why such a barrier existed in prewar Japan is the subject
of Section VII.
⬁
The stand-in household chooses a sequence {sEt , c 1t , c 2t , k t⫹1 }tp0
so as
to maximize its utility (3) subject to the budget constraint (4) and the
labor barrier (5) for t p 0, 1, 2, …. Let bt l⫺1
t be the Lagrange multiplier
11
The rental rate is net of intermediation costs. See below on firms in sector 2.
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journal of political economy
for the period t budget constraint (i.e., l t is the ratio of bt to the Lagrange multiplier). So l t is a measure of the household’s wealth. Let
Z t { w 1th 1t /w 2th 2t be the sectoral income ratio. The first-order condition
with respect to sEt ({ E 1t /E t) is given by
(sectoral employment arbitrage)
Zt {
p ¯sEt
sEt p 1
苸 [s¯Et , 1]
{
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
w 1th 1t
.
w 2th 2t
(6)
That is, the household will set sEt to the minimum possible value of ¯sEt
(i.e., the labor barrier is binding) if the income ratio Z t {
w 1th 1t /w 2th 2t is less than unity, to the maximum possible value of unity
(so nobody will work in agriculture) if it is greater than unity, and to
any value between the minimum and the maximum if there is no income
disparity.
The first-order conditions for (c 1t , c 2t , k t⫹1) are
⭸u(c 1t , c 2t)
q
p t,
⭸c 1t
lt
(Euler equation)
⭸u(c 1t , c 2t)
1
p ,
⭸c 2t
lt
(7)
l t⫹1 p bl t[1 ⫹ (1 ⫺ tt⫹1)(rt⫹1 ⫺ dt⫹1)].
(8)
The first-order conditions for consumption (7) can be solved to obtain
the Frisch demand system:
(Frisch demands)
c 1t p c 1(qt , l t),
c 2t p c 2(qt , l t).
(9)
Finally, the the transversality condition is
lim bt l⫺1
t k t p 0.
t r⬁
B.
(10)
Firms
The production function for sector 1 is
Y1t p TFP1t K 1tv1Lh1t ,
(11)
where TFP1t is the sector’s total factor productivity, K 1t is capital input
(demand for capital services), and L 1t is labor input (total hours worked
demanded) in sector 1. Land is the third input, but since it is constant,
its contribution is submerged in the TFP. Because of the existence of
the fixed factor of production, there are decreasing returns in capital
and labor: v1 ⫹ h ! 1. The first-order conditions, which equate marginal
agriculture and the prewar japanese economy
587
productivities to factor prices, for firms in sector 1 are
rt p v1qtTFP1t K 1tv1⫺1Lh1t ,
w 1t p hqtTFP1t K 1tv1Lh⫺1
1t .
(12)
Production in sector 2 does not require land and exhibits constant
returns to scale:
2
Y2t p TFP2t K 2tv 2L1⫺v
.
2t
(13)
In contrast to sector 1, capital input in sector 2 involves costly financial
intermediation. If the household wishes to rent machines to sector 2,
those machines need to be deposited at a bank. The bank then rents
out those machines to firms in sector 2. This financial intermediation
is costly because the bank incurs a cost, in terms of good 2, of f per
machine for this intermediation service. This means that the rental rate
faced by firms in sector 2 is rt ⫹ f, whereas the rental rate for the household net of the intermediation cost is rt (as assumed in the household
budget constraint [4]). Therefore, the first-order conditions for sector
2 are
rt ⫹ f p v2TFP2t
v 2⫺1
(KL )
2t
,
w 2t p (1 ⫺ v2)TFP2t
2t
v2
(KL )
2t
(14)
2t
There are two reasons for assuming costly intermediation, one having
to do with model calibration and the other with realism. First, the low
capital-output ratio in prewar Japan means a high level of marginal
productivity of capital. For the Euler equation requiring consumption
growth to be equated with the net rate of return from capital, we need
a wedge between the gross return and the net return over and above
depreciation. Second, there is some evidence that prewar intermediation costs were substantial. The long-term data on bank lending rates
compiled by Fujino and Akiyama (1977) show that the average spread
(the difference between the bank lending rate and the time deposit
rate) for 1899–1940 was 4.0 percent.
C.
Market Equilibrium
We assume that the second good can be either consumed or invested.
We also assume that government purchases Gt are on the second good.
The market equilibrium conditions are
(good 1)
(good 2)
Ntc 1t p Y1t ,
Ntc 2t ⫹ [Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t] ⫹ Gt p Y2t ⫺ fK 2t ,
(15)
(16)
588
journal of political economy
(capital services)
K 1t ⫹ K 2t p Ntk t ,
(labor in sector 1)
(17)
L 1t p h 1tsEt E t
(18)
L 2t p h 2t(1 ⫺ sEt)E t .
(19)
(recall sEt { E 1t /E t), and
(labor in sector 2)
In the equilibrium condition for good 2, the supply is Y2t ⫺ fK 2t, not
Y2t , because of the resource dissipation incurred in moving capital from
the household to sector 2.
A competitive equilibrium given the initial per-worker capital stock k 0
and the sequence of exogenous variables {Nt , E t , h 1t , h 2t , TFP1t , TFP2t ,
⬁
dt , Gt , t}t tp0
is a sequence of prices and quantities, {l t , qt , w 1t , w 2t , rt ,
⬁
k t⫹1 , K 1t , K 2t , sEt , L 1t , L 2t}tp0
, satisfying the following conditions:
i. the household’s first-order conditions (6), (8), and (9) and the
transversality condition (10);
ii. the firms’ first-order conditions (12) and (14);
iii. the market-clearing conditions (15)–(19), where Y1t is given by (11)
and Y2t by (13).
Three remarks about the model:
• With the market equilibrium condition for each of the two goods,
the model assumes that food is a nontraded good. The ability of
the model with the barrier to account for the prewar relative stagnation is undiminished even if food is a traded good. This point
will be discussed more fully in Section VI.
• The model does not preclude external lending and borrowing. As
in Hayashi and Prescott (2002), we treat foreign capital (claims on
the rest of the world) as part of the capital stock, so investment
here, Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t , is the sum of domestic investment and
the current account, and qtY1t ⫹ Y2t ⫺ fK 2t is GNP (in terms of good
2), not GDP. This treatment of foreign capital implies an imperfect
mobility of capital in that the rate of return on foreign capital is
not exogenously given to the country.12
• As is standard in the real business cycle models with nondistortionary taxes, the sequence of taxes is not included in the equilib12
Appendix 5 of Hayashi and Prescott (2006) shows that the sector 2 production function
defined over total (domestic plus foreign) capital and labor can be derived from two
technologies, one describing domestic output defined over domestic capital and labor
and the other describing the return from foreign capital. The appendix also shows that
the derived production function is essentially Cobb-Douglas for a particular form of imperfect capital mobility and a Cobb-Douglas production function for domestic output.
agriculture and the prewar japanese economy
589
rium conditions because the amount of the lump-sum tax is endogenously determined so that the government budget constraint
holds period by period. By the Ricardian equivalence, any other
sequence of taxes with the same present value results in the same
competitive equilibrium. This also means that the household budget constraint does not need to be included as part of the equilibrium conditions because it is implied by the market-clearing
conditions, the government budget constraint, and the factor exhaustion condition (that payments to factors of production, including land, sum to output).
D.
Solving the Model: A Summary of Appendix A
The equilibrium conditions i–iii above besides the transversality condition (10) can be reduced to the following five conditions:
(resource constraint)
Ntc 2(qt , l t) ⫹ Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t p
(1 ⫺ w)Y
⫺ sKt)k t ,
t
2t ⫺ fN(1
t
(Euler equation)
{
(20)
[
l t⫹1 p bl t 1 ⫹ (1 ⫺ tt⫹1) v2
Y2t
(1 ⫺ sKt)Ntk t
]}
⫺ f ⫺ dt⫹1 ,
(market equilibrium for good 1)
(21)
Ntqtc 1(qt , l t) p qtY1t ,
(22)
(equality of marginal products of capital)
v1
qtY1t
Y2t
p v2
⫺ f,
sKt Ntk t
(1 ⫺ sKt)Ntk t
(sectoral employment arbitrage)
Zt {
p ¯sEt
sEt p 1
苸 [s¯Et , 1]
{
(23)
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
w 1th 1t
h(qtY1t /sEt E t)
p
,
w 2th 2t
(1 ⫺ v2)[Y2t /(1 ⫺ sEt)E t]
(24)
590
journal of political economy
where sKt { K 1t /(Ntk t), sEt { E 1t /E t , wt { Gt /Y2t , and
Y1t p TFP1t(sKt Ntk t)v1(h 1tsEt E t)h,
Y2t p TFP2t[(1 ⫺ sKt)Ntk t]v 2[h 2t(1 ⫺ sEt)E t]1⫺v 2.
(25)
The first two equations are a set of difference equations in (k t , l t). The
two-equation system also involves the other endogenous variables (qt ,
sKt , sEt), but one can solve the static conditions (22)–(24) for these
variables given (k t , l t). The equilibrium is the solution to this twodimensional dynamical system satisfying the transversality condition.
In standard one-sector optimal growth models, the dynamical system
can be converted to an autonomous system after suitable detrending,
and finding the solution path amounts to locating the saddle path converging to the steady state for the detrended autonomous system. The
solution method we use for our model is essentially the same, but there
are several nontrivial complications.
• The model has two trends, TFP1t and TFP2t . Nevertheless, the dynamical system has a steady state in which (k t , l t) grow at the same
rate whereas (sKt , sEt) remain constant, provided that the utility
function u(c 1 , c 2) is log linear asymptotically as (c 1t , c 2t) get large.
The relative price qt (price of good 1 in terms of good 2) grows
at a different rate, but output value shares (qtY1t /(qtY1t ⫹ Y2t),
Y2t /(qtY1t ⫹ Y2t)) remain constant in the steady state.
• To accommodate Engel’s law in the short run while meeting the
asymptotic requirement of log linearity, we will assume the StoneGeary utility function:
u(c 1 , c 2) p m 1 log (c 1 ⫺ d 1) ⫹ m 2 log (c 2),
d 1 1 0, m 1 ⫹ m 2 p 1,
(26)
where d 1 is the subsistence level of food consumption.13 The associated Frisch demands are
l
c 1(q, l) p d 1 ⫹ m 1 ,
q
c 2(q, l) p m 2 l.
(27)
For the asymptotic log linearity, the subsistence food consumption
has to become unimportant in the long run; namely, the ratio
l/q in the Frisch demand for food has to grow without limit. This
means that the two TFP growth rates must be such that the growth
13
The Stone-Geary utility function is not the only utility function that exhibits Engel’s
law and that is asymptotically log linear. See Browning, Deaton, and Irish (1985) for other
choices of the utility function. We chose Stone-Geary because it is the simplest and the
most popular.
agriculture and the prewar japanese economy
591
rate of (k t , l t) is greater than that of the relative price qt . This
restriction is satisfied in our calibrated model.
• Even under the log-linear utility function, the suitably detrended
system is not autonomous because the lower bound s̄Et as a fraction
of total employment is time varying. However, thanks to population
growth, the lower bound declines to zero and the labor barrier
ceases to be binding in finite time (about 150 years from 1885 in
our simulation).
Appendix A describes in great detail how to deal with these complications and how to apply the shooting algorithm to locate the saddle
path in the detrended dynamical system.
V.
Calibration of the Model and Specification of Exogenous
Variables
To numerically solve the model from 1885 on, we need to calibrate the
model by providing parameter values, specify the path of exogenous
variables, and give an initial condition. The initial capital stock is taken
to be its actual value in 1885. In this section, we describe our calibration
of the model and specification of the path of exogenous variables. A
detailed discussion of how we calculated the annual values of relevant
variables from the LTES and other sources is in appendix 1 of Hayashi
and Prescott (2006).
A.
Model Parameters
As explained in the previous section, we accommodate Engel’s law by
the Stone-Geary utility function (26). The preference parameters of the
model are (m 1 , m 2 , d 1) and the discounting factor b.
Turning to technology parameters, for expositional clarity, we have
ignored intermediate inputs to production, whereas the model we actually solve with and without the labor barrier accommodates them.
With intermediate inputs, the production functions for the two sectors
are
Y1t p TFP1t K 1tv1Lh1t M 1ta1 ,
Y2t p TFP2t K 2tv 2Lh2t2 M 2ta 2 ,
(28)
with v2 ⫹ h2 ⫹ a 2 p 1, where Yjt is now gross output of sector j (j p 1,
2), M 1t is the amount of good 2 used in sector 1, and M 2t is good 1
used in sector 2.14 The model’s technology parameters are the share
14
If each sector uses the other sector’s output as an intermediate input, it is not possible
to write the market equilibrium conditions in terms of value added. Take, e.g., good 1.
The market equilibrium condition is Ntc1t p Y1t ⫺ M2t . The value added of sector 1 is
Y1t ⫺ M1t , not Y1t ⫺ M2t .
592
journal of political economy
parameters (v1 , h, a1 , v2 , a 2) and the intermediation parameter f (the
fraction of capital dissipated in moving capital from the household to
sector 2). Appendix B describes in detail how the model of the text,
which does not recognize intermediate inputs, can be generalized with
the production functions above.
B.
Parameter Values
The choices of parameter values are described here in the text only for
(b, f, d 1). For the rest of the parameters, we follow the standard practice
and use factor shares and expenditure shares; the details are in Appendix C.
• b (discounting factor) and f (proportional cost of intermediation):
Under the Stone-Geary utility function (26), we have c 2t p m 2 l t.
Substituting this and the expression for the marginal product of
capital in (14) into the Euler equation (8), we obtain
b⫺1
(
)
c 2,t⫹1
Y
p 1 ⫹ (1 ⫺ tt⫹1) v2 2,t⫹1 ⫺ f ⫺ dt⫹1 .
c 2t
K 2,t⫹1
(29)
We set b to the standard value of 0.96. The depreciation rate d is
calculated from data for each year t. It increases from 2.8 percent
in 1887 to 5.1 percent in 1940. We take the sample average of both
sides for 1885–1940 and solve for f, which gives a calibrated value
of f p 0.037.
• d 1 (food subsistence level): For the subsistence food level, we follow
the procedure used by Caselli and Coleman (2001). That is, we
choose the value d 1 so that the Engel coefficient qtc 1t /(qtc 1t ⫹ c 2t)
observed in the data for 1885 (of about 44 percent) equals that
predicted by the model with the barrier. The value of d 1 produced
by this procedure is 87 percent of per-worker consumption of food
in 1885.
The value of d 1 does not alter the findings to be reported below since
it affects only the first several years of the solution path.15 The same is
not true for f. We need the value of f as high as 3.7 percent per year
to account for the low prewar capital-output ratio, which is reflected in
the high value of Y2,t⫹1 /K 2,t⫹1 in (29). As reported in the next section,
the model with f p 0 wants a more rapid capital accumulation than
observed in the data, even when the labor barrier is in place.
However, our decision to require the Euler equation to hold on average for the sample period of 1885–1940 does not necessarily constrain
15
For example, the value for Y/N in the “level accounting” of table 2 becomes 1.35 if
d1 is 50 percent of 1885 food consumption.
agriculture and the prewar japanese economy
593
the sample average of Y2 /K 2 from the simulation with the barrier to be
the same as the corresponding average in the data. Since in the model
the Euler equation holds period by period and hence on average, the
way we calibrate f amounts to requiring the sample average of a particular linear combination
b⫺1
c 2,t⫹1
Y2,t⫹1
⫺ v2(1 ⫺ tt⫹1)
c 2t
K 2,t⫹1
to be the same both in the data and in the model. So, there is nothing
in our calibration that forces the sample capital-output ratio for sector
2, let alone the capital-output ratio for the economy as a whole, to be
the same as in the data on average. Table 3 displays our choice of
parameter values.
C.
Time Path of Exogenous Variables
The exogenous variables are Nt (working-age population), E t (aggregate
employment), Ē 1t (lower bound for sector 1 employment E 1t), (h 1t ,
h 2t) (hours worked in two sectors), TFP1t and TFP2t (sectoral TFPs), wt
(share of government expenditure in sector 2’s output), dt (time-varying
depreciation rate), and tt (tax rate on capital income). For these variables except for Ē 1t, we use their actual values for the sample period of
1885–1940. In particular, the actual values of TFP1t and TFP2t are calculated by solving the sectoral production functions for them. To do
that, we need the sectoral capital stocks K 1t and K 2t. Let K˜ 1t and K˜ 2t be
the beginning-of-the-period sectoral capital stocks in the data. We calculate K 1t and K 2t as
K t { K˜ 1t ⫹ K˜ 2t ,
K 1t { sKt K t ,
K 2t { (1 ⫺ sKt)K t ,
(30)
with
K̃1,t⫹1
sKt { ˜
.
K1,t⫹1 ⫹ K˜ 2,t⫹1
Therefore, the sectoral breakdown of the period t capital stock is based
on the sectoral breakdown in the data for period t ⫹ 1 (or at the end
of period t). We do this because in the model the sectoral breakdown
can respond to date t variables including TFP1t and TFP2t .16 The lower
bound Ē1t is set equal to the actual employment in sector 1.
For periods beyond the sample period of 1885–1940, we assume that
16
Use of (K1t , K2t) as defined here instead of (K˜ 1t , K˜ 2t) makes little difference to the
simulation results. The main difference is that in fig. 8 below, the graph of actual sKt is
shifted to the left by 1 year. In the previous version (Hayashi and Prescott 2006), we used
(K˜ 1t , K˜ 2t) rather than (K1t , K2t) in all calculations.
Calibrated Value
87% of per-worker
food consumption
in 1885
.15
.85
.96
.037
.14
.55
.15
.059
1/3
Parameter
d1 (minimum subsistence level for good 1)
m1 (asymptotic consumption share of good 1)
m2 (asymptotic consumption share of good 2)
b (discounting factor)
f (proportional intermediation cost)
v1 (capital share in sector 1 gross output)
h (labor share in sector 1 gross output)
a1 (share of intermediate inputs in sector 1)
a2 (share of intermediate inputs in sector 2)
v2/(1 ⫺ a2) (capital share in sector 2’s value
added)
Comment
Calculated from the sample average of the Engel coefficient
with m1 ⫹ m2 p 1
Calculated from the sample average of the Engel coefficient
with m1 ⫹ m2 p 1
Standard value from the literature
Given b p .96, chosen so that the Euler equation holds on average during the sample period
Calculated from sample averages of relevant input shares
Calculated from sample averages of relevant input shares
Calculated from sample averages of relevant input shares
Calculated from sample averages of relevant input shares
Standard value from the literature
Chosen so that the Engel coefficient for 1885 in the simulation
with the barrier is the same as in the data
TABLE 3
Calibration of the Model
agriculture and the prewar japanese economy
595
TABLE 4
How Exogenous Variables Are Projected into the Future
Exogenous Variable
n (growth factor of aggregate employment and working-age population)
Ē 1t (lower bound for sector 1
employment)
h1, h2 (hours worked)
g1, g2 (TFP growth factors for two
sectors)
w (government share of sector 2
output)
d (depreciation rate)
t (tax rate on capital income)
Its Projection
Set to the geometric mean over
1885–1940 of the growth rate of
working-age population of 1.1%; so
nt p 1.011 for t 1 1940
E¯ 1t p E¯ 1,1940 p 13.5 million persons for
t 1 1940
h1t p h2t p h2,1940 p 62.3 for t 1 1940
Projected growth rates set to their geometric means for 1885–1940 of 0.9%
and 1.7%, respectively; so g1t p 1.009
and g2t p 1.017 for t 1 1940
wt p w1940 p 27.4% for t 1 1940
dt p d1940 p 5.1% for t 1 1940
tt p t1940 p 47.2% for t 1 1940
the projected values are the same as at the end of the sample period,
either in levels or in growth rates. We are thus assuming that in the
prewar period agents did not anticipate the actual development of the
exogenous variables in the postwar period, let alone the disastrous war.
The only exception is h 1t (hours worked in sector 1). Its 1940 value is
59.0 hours, but its projected value is aligned with that of h 2t , at
h 2,1940 p 62.3 hours.17 Table 4 displays the projected values (or the
growth rates thereof) of all the exogenous variables.
VI.
Findings
With the model thus calibrated, the path of exogenous variables specified, and the initial condition given, we can now answer two questions:
How closely does the model track historical data? What would have
happened had there been no labor barrier? The first question is answered by solving the model with the barrier in place, namely, by conducting a simulation with the barrier. The latter question is answered
by solving the model without the labor barrier, namely, by a counterfactual simulation.
As it turns out, to the model’s credit, the lower bound is indeed
binding in the simulation with the barrier. Furthermore, to our eyes,
the model with the barrier also does a good job of tracking not only
17
We do this only to make the discussion of the model with endogenous employment,
to be developed in App. D, more transparent; the steady-state equations for the endogenous employment model get simpler if the long-run values of hours worked in the two
sectors are the same. For the present case of exogenous employment, simulation results
are virtually identical when we set the projected value of h1t at 59.0 hours rather than 62.3
hours.
596
journal of political economy
Fig. 7.—Agriculture’s share of employment, 1885–1940
aggregate variables but also variables describing sectoral resource allocation. This feat is accomplished in spite of the fact, mentioned in
the previous section, that in our calibration the average implied by the
simulation is constrained to equal the corresponding sample average in
the data only for one linear combination of the model variables. On
these bases, our model is a credible one, making it interesting for us
to find out, in the counterfactual simulation, the model’s prediction
when the labor barrier is lifted.
A.
Results about Sectoral Resource Allocation
Simulation results for sEt (sector 1’s share of employment), sKt (sector
1’s share of the capital stock), and qt (the relative price of food in terms
of nonfoods) with and without the labor barrier are displayed in figures
7–9. Figure 7 shows that the constraint setting the lower bound on sector
1 employment is binding throughout the sample period (and for more
than 150 years from 1885). The figure also shows that, without the
barrier, far less labor would have been utilized in agriculture. With
minimum food consumption taking up as much as 87 percent of food
consumption in 1885 and with no option to import food, the country
is on the yoke of Engel’s law. Even so, devoting as high a fraction of
the labor force as observed is by no means an efficient way to deliver
food to the starving population; less labor and more capital is more
efficient. This is why sKt is lower with the labor barrier than without, as
shown in figure 8.
agriculture and the prewar japanese economy
597
Fig. 8.—Agriculture’s share of capital, 1885–1940
Fig. 9.—Relative price of food, 1885–1940 (1934–36 in the data p 1)
For qt (the relative price of food), figure 9 shows that the model with
the labor barrier tracks the observed relative price fairly well until
around 1920. This means that, with the barrier, there would not have
been much trade even if food were tradable. The overprediction of the
food price by the model in the 1920s and 1930s occurs probably because
the country became a significant net importer of food during that pe-
598
journal of political economy
Fig. 10.—Sectoral income ratio w1th1t /w2th2t , 1885–1940
riod.18 The model is not informed of the fact that the country had a
cheaper source of food. Figure 9 also shows, predictably, that food would
have been far more expensive if the labor barrier did not exist. If the
country were allowed to trade food for nonfood, the model would predict a massive movement of labor and capital out of agriculture.
Another interesting variable to look at is the income ratio
w 1th 1t /w 2th 2t. Assuming the Cobb-Douglas technology, it equals the ratio
h(qtY1t /sEt)
(1 ⫺ v2)[Y2t /(1 ⫺ sEt)]
by (24).19 The line labeled “data” in figure 10 is obtained by using actual
values for (Y1t , Y2t , qt , sEt) and the calibrated parameter values in the
calculation of the ratio. (We do not show the ratio implied by the model
without the barrier because it equals unity by construction.) The line
labeled “model, with barrier” uses the model solution for (Y1t , Y2t , qt ,
sEt). Since the labor barrier is binding in the simulation, the difference
between the data and the model for the income ratio is proportional
to that for the output value ratio qtY1t /Y2t. The divergence in the 1920s
and 1930s is mostly due to the corresponding divergence for qt seen in
figure 9.
18
According to the LTES, the net food import ratio as a fraction of domestic food
production was negligible until around 1920. The ratio rises to 6.4 percent in 1920 and
14.1 percent in 1930.
19
This also is the income ratio with intermediate inputs, provided that (Y1t , Y2t) are
value added.
agriculture and the prewar japanese economy
599
The decline in the 1920s and 1930s of the wage income ratio in the
data is not an artifact of the Cobb-Douglas technology. A series of work
utilizing survey data by Ryoshin Minami (collected in Minami [1973])
finds an increasing disparity between manufacturing and agriculture.
For example, figure 10 of Minami’s study shows that the ratio of the
average male wage income for farm laborers on yearly contracts to the
average male wage income in manufacturing for establishments with 30
or more employees falls from slightly below a half in 1902 to less than
a quarter in 1933. For females, the fall is much less pronounced, but
the ratio stays below one.20
B.
Results about Aggregate Variables
⬁
For each simulation, given the solution path {k t , l t , qt , sKt , sEt}tp1885
and
given the path of the exogenous variables, we can calculate the aggregate
capital stock K t (p Ntk t), average hours worked h t (p sEth 1t ⫹ [1 ⫺
sEt]h 2t), real GNP, and the overall TFP (as defined in [1]). Calculation
of real GNP requires some explanation. Since the relative price qt in
the data and from the simulation can and do differ (see fig. 9), we need
to do a PPP calculation to make comparable the real GNP in the data
and from the simulations with or without the barrier. For the base year
of 1935, PPP-adjusted real GNP from the simulation in question is calculated using the Geary-Khamis formula, which for the case of the counterfactual reduces real GNP by about 26 percent.21 Real GNP for other
years is extended from this 1935 value using the chain-type Fisher quantity index using sectoral value added and the relative price from the
simulation.
20
The ratio is based on nominal wage incomes. According to the LTES (see chap. 5 of
vol. 8), it is hard to obtain information on prices in rural areas. Nevertheless, Minami and
Ono (1977) utilize their own estimate of the rural consumer price level to calculate real
wages. Visual inspection of their fig. 1 shows that prices were cheaper in rural areas by
20–25 percent in the 1910s and 1920s, but the price difference shrank since then and
almost vanished by 1935.
21
The formula, when applied to two countries, is as follows. For two countries, x p a,
b, let (Y1x, Y2x, q x) be the outputs (measured in value added) of two sectors and the relative
price (the price of good 1 in terms of good 2) and let P x be the PPP price level. Country
b’s PPP price level, P b, is calculated from the following system of equations:
Pa p
q aY1a ⫹ Y2a
,
(Y1a/v1) ⫹ (Y2a/v2)
Pb p
q bY1b ⫹ Y2b
,
(Y1b/v1) ⫹ (Y2b/v2)
where
Y1a ⫹ Y1b
Y2a ⫹ Y2b
, v2 p a a a
.
a
b b
b
(q Y /P ) ⫹ (q Y1 /P )
(q Y2 /P ) ⫹ (q bY2b/P b)
a
b
This is a system of four equations in four unknowns (P , P , v1, v2). Because the system
is homogeneous, a scalar multiple of a solution is also a solution. So without loss of
generality we can normalize P a p 1 . In the present case, the actual economy is a and the
simulated economy is b. For the counterfactual simulation, P b p 1.26.
v1 p
a
a
1
600
journal of political economy
In Section III we have already commented on the simulation results
about real per-worker GNP (in fig. 5), the overal TFP (in fig. 2), and
capital accumulation (in fig. 6). Our main finding was that the labor
barrier had two depressing effects. First, it prevented the economy’s
factor endowments from being allocated efficiently, thus reducing the
overall production efficiency measured by TFP. Second, this distortion
in factor allocation was a powerful hindrance to capital accumulation.
C.
Alternative Assumptions
Still maintaining the assumption that food is a nontraded good and
that employment is exogenously given, we examined four variations of
the model with the barrier: (i) assume tt (the tax rate on capital income)
to be constant at its sample average and thereafter (ii) assume that the
surge in sector 2’s TFP after 1914 shown in figure 4 did not take place
by setting the growth rate of TFP2t from 1915 on at 1.1 percent (the
average growth rate over the sample period of 1885–1940 and also the
rate used for the projection of TFP2t after 1940); (iii) set f p 0 with
the values of the other parameters kept unchanged; and (iv) assume
the same magnitude of intermediation cost of 3.7 percent for sector 1
as well as for sector 2.
The simulation with the barrier for variation i actually makes the post–
World War I rise in the capital stock shown in figure 6 more pronounced.
This is to be expected because in the data the capital income tax rate
is higher in the latter half of the sample period. For variation ii, the
model with the barrier predicts much less rapid capital accumulation
since World War I (but still more than in the data from around 1925
on). Taken together, the post–World War I rise in capital despite a higher
capital tax rate predicted by the benchmark model shown in figure 6
is indeed due to the TFP surge. The point of variation iii is to underline
the importance of setting f at 3.7 percent rather than at zero. The
simulation with the barrier predicts a far more rapid capital accumulation. The value of K t /Nt predicted by the model with the barrier with
f p 0 is more than 30 percent higher than in the data on average. This
does not occur in variation iv (where f p 3.7 percent not only for sector
2 but also for sector 1 [agriculture]). However, for both variations iii
and iv, agriculture’s share of capital is substantially less (about 20 percent
less) than in the data. This should not be surprising since in either
variation the intermediation cost is the same across sectors (0 percent
in variation iii and 3.7 percent in variation iv), whereas in reality the
intermediation cost would be far less in agriculture with most investment
self-financed.
In the rest of this section, we consider three major alterations of the
benchmark model.
agriculture and the prewar japanese economy
601
22
Tradable food. —Here, we allow the country to trade good 1 (food)
for good 2 without affecting the terms of trade qt . So the market equilibrium condition for good 1 and that for good 2 ([20] and [22] in the
five-equation system) are combined into one single resource constraint,
and qt is now an exogenous variable. In the simulation with the barrier,
the lower bound is binding and the model’s predictions for aggregate
variables such as Y/N and K/N are very similar to those from the benchmark (closed-economy) model. The model also does a very good job
of tracking the income ratio, which is not surprising given that the actual
value of qt is used in the simulation.
The problem with this small-open-economy model lies in the counterfactual simulation. Without the barrier, the model predicts a nearcomplete specialization in nonfoods (agriculture’s employment share
in 1885 is less than 1 percent) and an enormous increase in real GNP,
a 67 percent increase as opposed to 32 percent reported in table 2 for
the closed-economy benchmark. We find this enormous output gain
unlikely; even a relatively small country like prewar Japan would have
affected the terms of trade with such a massive trade volume.
Endogenous employment.—Relaxing the assumption that employment
E t is given to the model requires us to incorporate disutility of labor.
The utility function we tried is the two-sector version of the indivisible
labor specification in Hayashi and Prescott (2002). Its functional form,
borrowed from Cho and Cooley (1994) and shown in Appendix D (see
[D1] and [D19]), is log linear in leisure. Its parameter values are taken
from the same source, except that we rescaled the disutility so that the
steady-state value of the employment rate et { E t /Nt is the same as that
implied by the benchmark model calibration in table 4. Predictions by
this endogenous-employment model, with or without the barrier, are
very similar to those from the benchmark model, for both aggregate
variables and sectoral variables, except for real GNP. Predicted GNP
with the barrier is similar in levels to actual GNP but is more volatile
because of employment volatility that is far greater than in the data (see
App. fig. D2). The calibration of the disutility function of Cho and
Cooley (1994) is designed to match quarterly employment variability in
a stochastic dynamic general equilibrium model. It is not surprising that
the employment variability in our perfect-foresight model is large. To
its credit, this model with barrier captures the downward trend in the
employment rate in data (see App. fig. D1).
Endogenous hours.—There is no technical difficulty in allowing hours
22
A full discussion of this open-economy case is in Hayashi and Prescott (2006). Results
reported here are based on the same calibration as in the benchmark model. In particular,
d1, the minimum food consumption, is 87 percent of per-worker consumption observed
in the data for 1885. The Engel coefficient for 1885 in the simulation with the barrier is
about 45 percent (it is about 44 percent in the data).
602
journal of political economy
to be endogenous in the endogenous-employment model just discussed,
as indicated in Appendix D. The first-order condition for hours dictates
that the ratio of the marginal disutility of work to the wage rate be
equalized across sectors (see [D9] of App. D). However, as long as the
disutility function of hours is the same or similar between the two sectors,
the model is bound to fail because in the data hours worked are similar
but the sector 1 wage rate is only about a third of the sector 2 wage
rate.
This difficulty can be avoided if we drop the assumption, maintained
throughout the paper, that family members are altruistically linked. The
marginal disutility-to-wage equalization across sectors results because the
marginal utility of wealth (l t) is the same for all family members working
in different sectors. We could assume, instead, that the son who goes
to the city severs the tie with the parent household. He gets no inheritance, but with higher wages in the city, he would enjoy more consumption than his siblings in the countryside do. Nevertheless, with
standard balanced growth preferences about consumption and hours,
the predicted difference in hours would be small.23 Finding the equilibrium path would be computationally quite involved, however, because
the model is now essentially an overlapping-generations model with the
number of new households (urban households) endogenously determined. We acknowledge that this is a promising avenue to pursue but
leave it for future research.
Table 5 summarizes the quantitative information referenced in the
above discussion.
VII.
Why Did the Barrier Exist?
In prewar Japan, in contrast to the Edo period preceding it, there was
no restriction imposed by the state on the extent of interregional emigration. It is argued in this section that the labor barrier is self-imposed
by the household head. Our hypothesis consists of two parts. First, we
assume a paternalistic preference that the household head wants one
of the children to succeed him as a full-time farmer. Given the large
income disparity, the child has no incentive to honor the parent’s wish.
The second part of our hypothesis is that the institutions of prewar
Japan including the Civil Code made it possible for the paternalistic
23
Indeed, hours are equalized for all periods in the indivisible-labor model in which
the fixed cost of work does not depend on the employment rate. To see this, consider
the one-sector version of the model in App. D. The constant fixed-cost assumption is that
y(et) p y and y(et) p 0. Set sEt p 0. Then (D7) and the second equation of (D8) determine
h2t independently of the wage rate and the marginal utility of wealth. Set sEt p 1 and do
the same for h1t. If the disutility function v(7) and the fixed cost y are the same between
sectors, we obtain h1t p h2t for all t.
agriculture and the prewar japanese economy
603
TABLE 5
Alternative Assumptions
Model
1
2
3
4
Yes
No
3.7%
No
Yes
3.7%
A. Model
Is food tradable?
Is employment endogenous?
Value of f
No
No
3.7%
No
No
0%
B. Simulation with Barrier Model
Geometric mean of ratio of model to data:
Y/N
K/N
q
E/N
1.04
1.03
1.12
1
1.12
1.34
1.21
1
1.01
1.04
1
1
1.04
1.02
1.18
.98
C. Counterfactual Simulation
Level accounting: geometric mean of (value
without barrier for year t)/(its actual value
for year t) in Yt /Nt p
TFP1/(1⫺v)
(Kt /Yt)v/(1⫺v)(Et /Nt)ht:
t
Y/N
TFP1/(1⫺v)
(K/Y)v/(1⫺v)
E/N
h
1.32
1.24
1.04
1
1.02
NA
NA
NA
NA
NA
1.67
1.56
1.02
1
1.06
1.33
1.24
1.05
1.00
1.02
Note.—See the note to table 1 for the definitions of variables. In models 1, 2 and 3, d1 (minimum food consumption)
is 87 percent of observed per-worker food consumption in 1885. In model 4, the fraction is 62 percent. All four models
assume that hours are exogenous.
preferences to prevail. We do not derive the assumed paternalistic preferences from some meta theory à la Akerlof (1980). Here, we simply
describe the prewar social norm, centered around the notion called ie,
that the assumed preferences are meant to capture.
A.
The Cityward Movement of the Peasant
In prewar Japan, as already emphasized, agricultural employment was
virtually constant at 14 million. Related facts about prewar Japan are
the following.
• The number of farm households (households whose head’s main
occupation is farming) was constant at 5.5 million, and the population in those farm households was constant at 30 million, or
about 5.5 persons per household throughout the prewar era (the
source is LTES). Because there was virtually no migration from the
604
journal of political economy
24
city, the constancy of the number of farm households implies that
the head of the farm household was almost always succeeded by
one of his children upon his death or retirement.25
• All children except for the heir and his spouse left the village. This
follows from the constancy of the number of farm households and
the relatively small household size of 5.5.26
• Primogeniture was prevalent at least in rural areas. Inheritance was
impartible, and the entire estate went to one of the sons (usually
the eldest son), who also succeeded the father’s occupation as a
farmer.27
24
See Takagi (1956) and Taeuber (1958, 126–27, particularly n. 8) for census data and
various other sources on the population supporting the lack of reverse migration from
the city. A classic study on the cityward movement of the peasant by Nojiri (1942) presents
major noncensus evidence. On the basis of voluminous data collected from field work,
he concludes (see sec. 1, chap. 2, of pt. 1) that the incidence of a household head (and
hence the entire household) leaving the village for the city is negligible when compared
to the number of nonhead household members doing the same. A survey cited in Namiki
(1957, sec. 3) reports that in 18 villages, between 1899 and 1916 there were only 21
households whose head changed occupations from agriculture. Since, as shown by these
studies, there was virtually no attrition of farm households and since the number of farm
households was constant, we can conclude that there was no reverse movement of individuals from the city. There was a fair amount of regional variation in the distribution of
farm households, with Hokkaido (the northernmost island previously only sparsely populated) gaining at the expense of the Kinki area (where Kyoto and Osaka are located).
This merely implies that there was migration from one rural area to another.
25
That the occupation as farmer is inherited from one generation to the next is quite
well known in Japanese agricultural economics, but there are no official statistics on social
mobility directly documenting it. There is a survey called the SSM (Social Stratification
and Social Mobility) Survey conducted every 10 years since 1955 by the Institute of Social
Science of the University of Tokyo, which asks the respondent about the father’s occupation
(among other things). Sato (1998, app. 2) reports that about 90 percent (650 in number)
of 732 respondents born between 1896 and 1925 who were currently in agriculture at the
times of the survey replied that their father was in agriculture. The remaining 10 percent
probably entered agriculture after the war. Between 1945 and 1949, when the majority of
the population had difficulty getting enough to eat, agricultural employment increased
from slightly below 14 million to nearly 17 million.
26
The arithmetic is due to Honda (1950) and goes as follows. The infant mortality rate
was such that only four of five children survive into adulthood. Assuming that a generation
is 27 years, a natural increase of four adults occurs in about 200,000 (p 5.5 million/27)
households, and in equally numerous households a natural decrease of two adults (death
of two old parents) occurs every year. That is a natural net annual increase of 400,000
persons (p 800,000 ⫺ 400,000). In each of those 200,000 households, two of the four
adult children succeed their deceased parents and remain in the village. Those two successors are the heir (one of the sons, usually the eldest) and a daughter who came from
a different farm household as his wife. The remaining two children leave the household
well before the death of their parents but not immediately after finishing primary
education.
27
As far as we know, there is no direct prewar evidence for the impartibility for farm
households. The prewar Civil Code stipulates impartible inheritance to be the default
mode; namely, the next head inherited the whole property if the current head died without
leaving a will. In the early postwar period, out of the concern that the new Civil Code,
which stipulates equal division of the estate as the default mode, would result in widespread
subdivision of farmland, a quasi government body conducted a series of surveys on the
inheritance of farmland. The earliest such survey, conducted between January 1948 and
agriculture and the prewar japanese economy
605
• There was a large rural-urban disparity in household income, as
seen already in figure 10.
• The steep postwar decline in agricultural employment after 1955
(see fig. 3) was initiated by young cohorts. In his perceptive essay,
Namiki (1957) noticed that the decline was concentrated in the
14–19 age bracket. His speculation, which was proved correct by
time, was that the youths defecting to the city include eldest sons,
who in the prewar tradition are expected to succeed their fathers’
occupation as farmer.
B.
Why Did Agricultural Employment Remain Constant?
Given the large rural-urban income disparity in prewar Japan, we are
not surprised that household members not designated as heirs left agriculture. The mystery is why the son designated as heir (and his wife)
stayed in agriculture. An explicit calculation of farm and urban incomes
relevant for the peasant contemplating on migration was given by Masui
(1969). He notes that for a son and his prospective wife the comparison
should be between farm labor income for both the son and his wife
combined and urban labor income for the son only because the wife’s
employment opportunity in the city was severely limited in the prewar
era. Furthermore, if the son is the heir, his farm income should also
include imputed rent from the farm property he would eventually inherit. Masui’s calculation for 1923–39 shows that the heir’s farm income,
with wife’s labor income and imputed rent figured in and with an allowance for difference in rural and urban price levels, is less than urban
income for 1928–37.
Besides the issue of why peasants did not leave the village during
those depressed years, three questions can be raised about Masui’s thesis.
First, the heir could sell the inherited farmland and live in the city to
obtain the higher urban income. However, to prevent this, the father
August 1949 with the help of local governments, collected about 33,000 cases of the
inheritance of farmland. Matsumura (1957) reports that one child inherited the entire
farmland in 84.7 percent of those cases. A 1978 survey also asked 5,326 farmers over the
age of 60 about their intention regarding inheritance. Seventy-nine percent of them said
that they would leave the entire farmland to the heir, according to a report by Zenkoku
Nogyo Kaigisho (1979). Therefore, impartible inheritance was the norm even under the
new Civil Code. It would have been more prevalent in the prewar era when the Civil Code
made it the default mode of inheritance. Regarding the succession by eldest son, available
evidence from nongovernment surveys shows that it was less prevalent than might have
been commonly assumed. For example, Tsuburai (1998, table 6) finds that, in the 1965
and 1995 waves of the SSM survey mentioned in n. 25, about 57 percent of those respondents born between 1896 and 1925 who succeeded the father’s occupation as a farmer
(246 persons) were the eldest son. Nojiri (1942) finds that, in his field work data covering
20 villages and about 10,000 farm households, 23 percent of those males who left the
village were eldest sons (see his table 225).
606
journal of political economy
could require the son to remain on the farm until he inherits the land.
By the time his son inherits the estate, it may be too late for him to
start a career in the city.28
Second, there may not have been much to inherit for the heir to a
sharecropper. According to Momose (1990, 149), the right to cultivate
had a property value between 10 percent and 30 percent of the value
of land. Even if the cultivation right is transferable from father to son
(which we do not know is the case), the property value may not have
been large enough to make up for the rural-urban income disparity for
tenant farmers. To the extent that it was not, it is difficult to explain
on purely economic grounds why tenant farmers, constituting about 30–
40 percent of all farm households,29 did not leave agriculture.
Third, as pointed out by Namiki (1957), the land reform instituted
by SCAP (the Supreme Commander of the Allied Powers, namely Douglas MacArthur) in 1951, which transferred land ownership to tenant
farmers, should have made it more attractive for previous tenant farmers
to stay in agriculture in the postwar period. The postwar large-scale
defection to the city took place despite the land reform.
Our hypothesis to explain the constancy of agricultural employment
is an elaboration of Namiki’s (1957) conjecture that the economic forces
favoring migration to the city, which had been held in check by patriarchy in the prewar era, were let loose in the years following the defeat
of Japan. To appreciate his logic, it is necessary to understand the nature
of patriarchy that regulated the behavior of individuals in prewar Japan
through the Civil Code. The distinguishing feature of the prewar Civil
Code (as opposed to the new postwar Civil Code) is its recognition of
the institution called the ie (sometimes translated “house”) and its headship. The ie is “a ‘stem family’—an organization that transcended its
present members through history and spanned generations through the
eldest son” (Ramseyer 1996, 82).30 Vogel (1967, 92–94) describes the ie
in the context of the cityward migration mentioned above:
The ie is a patrilineal organization with rapid segmentation in
each generation. One son, usually the first, inherits all the
family property, including land, home, and ancestral treasures.
Daughters enter their husband’s ie upon marriage, and sons
who do not succeed in their parents’ ie can either be adopted
as heirs in families with no sons or start relatively independent
“branch” lineages of their own ie. . . . Because one son re28
This argument was suggested to us by Andrew Foster.
According to agricultural department tabulations mentioned in Annual Department of
Agriculture Tabulations (various years). The percentage is substantially higher if those owner
farmers who also cultivate someone else’s land are included.
30
For a more detailed description of ie by a Westerner, see Taeuber (1958, chap. 6).
29
agriculture and the prewar japanese economy
607
mained in the rural area and inherited the family property,
the ie was maintained and remained the basic unit of rural
organization. Sometimes it was the first son who migrated to
the city, but in any case the head of the ie has remained remarkably powerful in deciding who would and would not go
to the city.
As we mentioned already, those sons not designated as heirs to the
headship left the village for a good economic reason, and it would also
have been the head’s wish anyway, since the size of the farmland the
family owns (or the family has the right to cultivate) would not have
been enough to support those “excess sons.”31 Why did the heir remain
in the village, and how was he able to find a bride? The power of the
head sanctioned by the prewar Civil Code explains it. According to Oda
(1992, 232), under the code, “the head of the family had the power to
designate the place where family members should live, to control their
choice of marriage-partner and to expel them from the family when
necessary.”32 Takeyoshi Kawashima, a prominent legal scholar in Japan,
notes that the peasant life before the introduction of the Civil Code in
1898 did not quite honor the sort of patriarchy described in the code
(Kawashima 1957, 8–9, 46). He then notes, however (p. 10 and chap.
1, particularly pp. 46–47), that the code, along with the indoctrination
by the government (much like the sort practiced in North Korea today,
we imagine) whereby every schoolchild was required to study a textbook
(called Kyoiku Chokugo; see fig. 11, which is the front page of a textbook
wide in use in 1890) expounding on obedience to the father and to
the emperor, must have had a profound influence, particularly on the
peasant population, as can be surmised, for example, from the decline
31
The annual Department of Agriculture tabulations mentioned in n. 29 show that the
size distribution of land managed by farm households was remarkably equal and stable,
with 50–60 percent concentrated in the 0.5–2.0-hectare bracket. How to feed second and
third sons without subdividing the family plot of land was a major issue in Japanese
agricultural economics in the very early postwar period.
32
Relevant articles of the prewar Civil Code are the following (copied from Ramseyer
[1996, chap. 5]). Article 749: “members of a house may not determine their place of
residence, if the head of the house objects to their choice.” Article 750(a): “In order for
a family member to marry or to enter an adoptive relationship, he or she must obtain
the consent of the family head. Article 750(b): “If a family member marries or enters an
adoptive relationship in violation of the previous subsection, the head may, within one
year of the date of such marriage or adoption, expel such member from the family or
refuse his or her reentry into the family.” Article 772(a) states that until a man and woman
reach the statutory age—30 for men, 25 for women—they could marry only if both of
their parents consented.
608
journal of political economy
Fig. 11.—How children were indoctrinated
of peasant rebellions since the end of the nineteenth century.33 The
heir stayed in the village, and a daughter married into a farm household,
because it was what father wished.
This hypothesis of the constancy of agricultural employment in prewar
Japan also explains its steep postwar decline. A new Constitution was
adopted in 1947, and there was a wholesale revision of the Civil Code
under the direction of SCAP. Article 24 of the new Constitution states
that “With regard to choice of spouse, property rights, inheritance,
33
Ramseyer (1996, chap. 5, secs. 2, 3) argues that the prewar Civil Code did not confer
the head the power to control residence and marriages of the family members. However,
the court cases he cites are not about disputes between the head and the heir, and the
census data he cites for his point that family members did not stay in the family (which
means the head’s threat to expel had no bite) actually reinforce our claim that all the
nonheir siblings left the stem household.
agriculture and the prewar japanese economy
609
choice of domicile, . . . laws shall be enacted from the standpoint of
individual dignity.” The new Civil Code no longer recognizes the ie and
the dictatorial power of the head. School textbooks were rewritten to
fully reflect those changes. It is not surprising at all, then, that the largescale defection to the city since around 1955 was initiated by young
cohorts, who were not subject to the prewar indoctrination of the supremacy of the ie over the individual. Reinforcing the tide to the city
was the fact that the new Civil Code encourages equal division whereas
the old code facilitated (but did not require) primogeniture. Now the
eldest son who inherits the entire estate by the will of his father is
obligated to pay the other siblings a minimum claim (half of what they
would have received under the default mode of inheritance [i.e., equal
division]), which certainly makes it less economically attractive for the
eldest son to stay in the village.
C.
Alternative Explanations?
It was suggested to us that the lack of mechanization in rice production
in prewar Japan could explain the constancy. The introduction of the
tractor started only after 1955, and mechanization of other tasks such
as rice planting and rice reaping did not start until the mid-1960s in
Japan. If the prewar agricultural technology was approximately the Leontief technology with limited substitutability between land area and
labor, it would explain the constancy of agricultural employment. However, this explanation is inconsistent with the well-documented fact that
the rural-urban income disparity was very large in prewar Japan. Furthermore, it is a long tradition of agricultural economics (see, e.g.,
Hayami 1975) to admit substantial substitutability between land, labor,
and capital, as in the Cobb-Douglas production function.
Another possibility is that the barrier may have existed in the city, not
in the countryside, in the form of inadequate urban housing and infrastructure. This, however, does not explain why the scale of the cityward emigration was such that the population left behind in the countryside remained constant. Virtually every nonheir child left for the city.34
VIII.
Conclusion
According to the standard Lewisian theory of development, the supply
curve of industrial labor is horizontal, and the cityward movement of
the peasant is limited only by demand. We argued for prewar Japan that
34
Slums were not prevalent in prewar Japan. The classic account of the underclass by
Yokoyama (1899) estimates that at most 4,000 people lived in three major slums in Tokyo,
a city of about 1.3 million people at that time.
610
journal of political economy
the rural-to-urban migration was limited by supply. Prewar Japan is certainly not the only case in history of a large and persistent rural-urban
income disparity. Even today, the disparity can be observed for a large
number of developing countries.35 Our model of a dual economy may
be applicable to those countries as well. Their per capita income is low
because they have their own version of the labor barrier.
The quantitative implications of our theory are big. Per-worker GNP
of Japan in her heyday was about 82 percent of that of the United States
in 1991 and about 36 percent during the prewar period of 1885–1940.
According to our two-sector model, Japan’s prewar GNP per worker
would have been higher by 32 percent if the labor barrier were absent.
In this sense, our dual economy model accounts for 12 (p 36 # 0.32)
percentage points, or about a quarter, of the U.S.-Japanese gap of 46
(p 82 ⫺ 36) percentage points. This estimate, based on a closedeconomy model, should be taken as a lower bound because in the
counterfactual simulation the country is denied a chance to exploit the
comparative advantage made possible by the release of labor from agriculture. We have argued that the rest of the gap is due mostly to the
rapid postwar TFP growth outside agriculture.
A clear research agenda awaits. To endogenize hours worked, we
could consider an overlapping-generations version of the model in
which family members defecting to the city form households not altruistically linked to their parents. Such a model may help to explain the
low prewar capital accumulation. Turning to substantive issues not fully
addressed in the paper, we could use the model to analyze the postwar
boom and assess the quantitative effect of the release of the pent-up
potential kept back by the prewar barrier. Another important issue is
the sectoral TFP. Japan’s manufacturing TFP went up, once during the
interwar period and another time during the postwar high-growth period. Exploring reasons why the rapid TFP growth took place when it
did is obviously a major future research topic. Hints abound. Hayami
and Ogasawara (1999) and Godo and Hayami (2002) argue that a
threshold level of average educational level was reached in the interwar
period so that foreign advanced technology could be profitably adopted.
Braun, Okada, and Sudou (2005) find a close connection in the postwar
period between U.S. R&D expenditure and Japanese TFP growth 3 years
after. Gordon (2004) documents that the rapid technological catch-up
occurred in postwar Europe as well. Another, perhaps more concrete,
research topic is to explain why the interwar capital accumulation predicted by theory did not occur. We conjectured that the rapid cartelization in the 1930s must have had something to do with it.
35
See, e.g., a documentation by Vollrath (forthcoming) using a database from the International Labor Organization.
agriculture and the prewar japanese economy
611
Appendix A
Details on Solving the Model
As shown in the text, the equilibrium conditions other than the transversality
condition can be reduced to a system of five equations, (20)–(24). This appendix
describes in detail how to solve for the equilibrium path.
Detrending the System
Define two trends by
XYt { TFP2t1/(1⫺v 2)h 2t E t /Nt ,
X Qt { TFP1t⫺1(h 1t E t)⫺h TFP2t(1⫺v1)/(1⫺v 2)(h 2t E t)1⫺v1,
(A1)
and use these trends to deflate (k t , qt):
kt
k˜ t {
,
XYt
q˜ t {
qt
.
X Qt
(A2)
A somewhat tedious algebra yields
qtY1t p Nt XYtq˜ ty˜1t ,
Y2t p Nt XYty˜2t ,
(A3)
where
y˜1t { k˜ tv1sKtv1sEth ,
y˜2t { k˜ tv 2(1 ⫺ sKt)v 2(1 ⫺ sEt)1⫺v 2.
(A4)
The particular trends (XYt , X Qt) above are chosen so that (A3) holds. We look
for a steady state in which l t grows at the same rate as k t . So detrend l t by
XYt :
l
l˜ t { t .
XYt
(A5)
In terms of detrended variables, the five equations (20)–(24) can be written
as
(resource constraint)
Nt⫹1 XY,t⫹1 ˜
k p [1 ⫺ dt ⫺ (1 ⫺ sKt)f]k˜ t
Nt XYt t⫹1
˜
⫹ (1 ⫺ w)y
t 2t ⫺
c 2(q˜ t X Qt , l˜ t XYt)
,
XYt
(A6)
(Euler equation)
{
[
]}
XY,t⫹1 ˜
y˜2,t⫹1
lt⫹1 p bl˜ t 1 ⫹ (1 ⫺ tt⫹1) v2
⫺ f ⫺ dt⫹1 ,
XYt
(1 ⫺ sK,t⫹1)k˜ t⫹1
(A7)
612
journal of political economy
(market equilibrium for good 1)
q˜ tc 1(q˜ t X Qt , l˜ t XYt)
p q˜ ty˜1t ,
XYt /X Qt
(equality of marginal products of capital) v1
q˜ ty˜1t
y˜2t
p v2
⫺ f,
˜
sKtkt
(1 ⫺ sKt)k˜ t
(A8)
(A9)
and
p ¯sEt
(sectoral employment arbitrage) sEt p 1
苸 [s¯Et , 1]
{
Zt {
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
w 1th 1t
h(q˜ ty˜1t /sEt)
p
.
w 2th 2t (1 ⫺ v2)[y˜2t /(1 ⫺ sEt)]
(A10)
This is a dynamical system in two detrended variables (k˜ t , l˜ t) , with two dynamic
equations (the resource constraint [A6] and the Euler equation [A7]) supplemented by three static conditions (A8)–(A10).
Solving for (q˜ t , sKt , sEt) Given (k˜ t , l˜ t)
We now show that, given (k˜ t , l˜ t , XYt , X Qt), we can uniquely determine (q˜ t , sKt ,
sEt) by the static conditions (A8)–(A10), so that the equilibrium conditions reduce to the two-equation dynamical system (A6) and (A7) in two variables
(k˜ t , l˜ t). The graph of (A10), which is a correspondence from income ratio
Z t p w 1th 1t /w 2th 2t to labor share sEt, is the staircase shown in figure A1. This can
be interpreted as the supply curve of sector 1 labor. To derive a demand curve,
we solve (A8) and (A9) for (q˜ t , sKt) given (sEt , k˜ t , l˜ t , XYt , X Qt) and then use these
solved-out values to write Z t p w 1th 1t /w 2th 2t in (A10) as a function of (sEt , k˜ t ,
l˜ t , XYt , X Qt). It is easy to show that the function is strictly decreasing in sEt, so
the graph of Z t p w 1th 1t /w 2th 2t as a function of sEt is downward sloping. This is
the demand curve for sector 1 labor. Three possible cases are drawn in figure
A1. In case A, the demand curve intersects with the vertical portion of the
staircase (the supply curve) at sEt p ¯sEt. In this case, the labor barrier sEt ≥ ¯sEt is
binding. In case B, the intersection is on the horizontal portion of the staircase.
In this case, Z t p 1, so from (A10) we have
(income equalization) Z t p 1,
i.e.,
1p
h(q˜ ty˜1t /sEt)
.
(1 ⫺ v2)[y˜2t /(1 ⫺ sEt)]
(A11)
In the final case, case C, the demand curve intersects with the staircase at
sEt p 1. In either case, given (k˜ t , l˜ t , XYt , X Qt), sEt is uniquely determined. Given
(sEt , k˜ t , l˜ t , XYt , X Qt), (sKt , q˜ t) is uniquely determined by (A8) and (A9), as just
explained.
In case C, sector 1 is so productive that all employment is in agriculture.
Under the calibrated parameter values and the initial conditions specified in
the text about the model, this case does not arise in any period. Assuming that
agriculture and the prewar japanese economy
613
Fig. A1.—The three cases
only case A and case B are relevant, the value of sEt satisfying (A8)–(A10) can
be determined as follows. Notice from the previous paragraph that in case B,
(q˜ t , sKt , sEt) solves (A8), (A9), and Z t p 1. If case C is impossible, then case A
(where the labor barrier sEt ≥ ¯sEt is binding) obtains if and only if the sEt that
solves these three equations is less than s̄Et (this corresponds to point A in fig.
A1). Therefore, to find (q˜ t , sKt , sEt) that solves (A8)–(A10) given (k˜ t , l˜ t , XYt ,
X Qt), we can proceed as follows:
1. Solve (A8), (A9), and (A11) for (q˜ t , sKt , sEt) . If sEt ≥ ¯sEt , then the solution is
found.
2. If sEt ! ¯sEt, then set sEt p ¯sEt and use (A8) and (A9) to solve for (sKt , q˜ t) given
sEt thus determined.
If s̄Et declines to zero as t r ⬁, then the labor barrier ceases to bind in finite
time. So in the steady-state analysis below, the sectoral employment arbitrage
condition (A10) is replaced by the income equalization condition (A11).
The Steady State
By way of summarizing the discussion so far, let x t { (k˜ t , l˜ t) and yt { (q˜ t , sKt ,
sEt), and write the two-equation dynamical system (A6) and (A7) supplemented
by three static conditions (A8)–(A10) as
x t⫹1 p f(x
yt p g t(x t).
t
t , y),
t
(A12)
614
journal of political economy
Here, g is the function described above that determines yt subject to the labor
barrier.
We assume that the share of government purchases and hours worked as well
as the growth rates of the trending exogenous variables eventually become constant: for sufficiently large t,
Nt⫹1 E t⫹1
p
p n,
Nt
Et
TFP1,t⫹1
p g1,
TFP1t
E¯ 1t p E¯ 1 ,
TFP2,t⫹1
p g2,
TFP2t
h 1t p h 1 ,
wt p w,
h 2t p h 2 ,
dt p d,
tt p t.
(A13)
We assume n 1 0, so the lower bound ¯sEt { E¯ 1t /E t goes to zero as t r ⬁. In contrast
to standard real business cycle models, an assumption like (A13) is not enough
to render the detrended dynamical system (A12) autonomous in the long run
for two reasons. First, since XYt and X Qt are not constant, neither c 2(q˜ t X Qt ,
l˜ t XYt)/XYt in (A6) nor c 1(q˜ t X Qt , l˜ t XYt)/(XYt /X Qt) in (A8) may be a stationary (i.e.,
time-invariant) function of (q˜ t , l˜ t). If c 2(q˜ t X Qt , l˜ t XYt)/XYt is nonstationary, then
so is the f function of the dynamical system (A12); and if c 1(q˜ t X Qt ,
l˜ t XYt)/(XYt /X Qt) is nonstationary, then so is the g function of the dynamical
system. Second, even if c 1(q˜ t X Qt , l˜ t XYt)/(XYt /X Qt) in (A8) is stationary, the g
function, which is derived from the static conditions, is still a nonstationary
function of x t p (k˜ t , l˜ t) when the labor barrier is binding with the time-varying
lower bound s̄Et for sector 1’s employment share.
We now seek a set of conditions under which the dynamical system (A12) is
autonomous in the long run. As remarked above, if s̄Et declines to zero, then
for sufficiently large t we can replace the sectoral employment arbitrage condition (A10) by the income equalization condition (A11). Looking at the fiveequation system (A6)–(A9) and (A11) and noting that Nt⫹1 /Nt , XY,t⫹1 /XYt , and
X Q ,t⫹1 /X Qt are constant whereas the levels XYt and X Qt are not in the long run,
one can clearly see that, for the dynamical system to be autonomous, it is nec˜ )/(X /X ) and c (qX
˜ )/X are time-invariant func˜ Qt , lX
˜ Qt , lX
essary that c 1(qX
Yt
Yt
Qt
2
Yt
Yt
˜
˜ l) when XYt and XYt /X Qt grow at constant rates. It is easy to show
tions of (q,
that the only Frisch demand system satisfying this assumption is36
c 1(q, l) p m 1
l
q
(A14)
36
˜ Qt ,
Here is a proof of (A14) (the proof of [A15] is similar). Suppose that c1(qX
˜ )/(X /X ) is a stationary function of (q,
˜ when X p exp (at) and X p exp (bt).
˜ l)
lX
Yt
Yt
Qt
Qt
Yt
Then
˜ a, b).
˜ l,
c1(q˜ exp (at), l˜ exp (bt)) exp [(b ⫺ a)t] p f(q,
This has to hold for any a, b. Set b p 0, differentiate both sides of this equation by t, and
then set a p 0 to obtain
˜
˜
˜ l)
˜ l)
⭸ log c1(q,
1
˜ ⫹ ⭸c1(q,
˜ l)
c1(q,
q˜ p 0, i.e.,
p⫺ .
⭸q˜
⭸q˜
q˜
˜ p A(l)(1/q)
˜
˜ l)
˜ . A similar
This partial differential equation can be solved to yield c1(q,
˜ p B(q)l
˜
˜ p
˜ l)
˜ ˜ . So A(l)(1/q)
˜ p B(q)l
˜ ˜ . Set q˜ p 1 to obtain A(l)
argument gives c1(q,
B(1)l˜ . Define m1 { B(1).
agriculture and the prewar japanese economy
615
and
c 2(q, l) p m 2 l.
(A15)
˜ )/(X /X ) and c (qX
˜ )/X are stationary functions
˜ Qt , lX
˜ Qt , lX
Therefore, c 1(qX
Yt
Yt
Qt
2
Yt
Yt
for any time path (not just exponential paths) of (XYt , X Qt ). The utility function
that generates this demand system is linear logarithmic:
u(c 1 , c 2) p m 1 log (c 1) ⫹ m 2 log (c 2).
The Shooting Algorithm
We now describe a method for finding the solution to the dynamical system
under (A14) and (A15).
i. There is a set over which the dynamical system is autonomous. As explained
already, the labor barrier does not bind if and only if the sEt that solves
(A8), (A9), and (A11) is greater than s̄Et ({ E¯ t /E t). Let At be the set of
˜ such that the labor barrier does not bind. The set depends on t
˜ l)
(k,
because s̄Et is a function of time. Under (A14), none of these three equations
involve the trends, so the g function is stationary over At. Furthermore,
under (A15), the f function is stationary because (A6) no longer involves
the time trends. So the dynamical system is autonomous over At.
ii. Since s̄Et declines with time thanks to a positive employment growth n 1 0,
˜ q,
˜ l,
˜ sK , sE) be the steady state for the
this set At expands with time. Let (k,
autonomous dynamical system. The Inada condition ensures that sE 1 0 (agriculture does not disappear in the long run, thanks to decreasing returns)
˜ is an interior point of
˜ l)
so that, with s̄Et approaching zero as t r ⬁, (k,
At for sufficiently large t.
iii. It is verified numerically for the calibrated parameter values that the eigen˜
˜ l)
values of the two-dimensional linearized system at the steady state (k,
consist of one that is greater than unity and the other that is less than unity
(see App. B). Therefore, the steady state is a saddle point for the autonomous system defined over At. So for sufficiently large t, the solution of
the dynamical system is on the stable saddle path converging to the steady
˜ . The intermediate path leading to the saddle path from a given
˜ l)
state (k,
capital stock k̃0 can then be determined in the usual way, by the shooting
algorithm that takes l˜ 0 as the “jumping variable.” That is, take T large enough
so that the solution is near the steady state. If the initial value l˜ 0 is such
that (k˜ T , l˜ T) is above the saddle path, then adjust the initial value l˜ 0 down;
if (k˜ T , l˜ T) is below the saddle path, adjust the initial value up.
616
journal of political economy
The Stone-Geary Utility Function
To accommodate Engel’s law, we introduce minimum consumption for food:
u(c 1 , c 2) p m 1 log (c 1 ⫺ d 1) ⫹ m 2 log (c 2), d 1 1 0.
(A16)
Now the food demand is given not by (A14) but by
˜
˜ ) p d ⫹ m lXYt
˜ Qt , lX
c 1(qX
Yt
1
1
˜ Qt
qX
or
˜ )
˜ Qt , lX
c 1(qX
X Qt
l˜
Yt
p d1
⫹ m1 .
XYt /X Qt
XYt
q˜
(A17)
The Frisch demand system now consists of (A17) and (A15). Although the f
function remains stationary, the g function is no longer stationary over At thanks
to the existence of the detrended minimum consumption d 1(X Qt /XYt) ; so no˜ plane is the dynamical system (A12) autonomous.
˜ l)
where in the (k,
However, this two-dimensional nonautonomous system can be converted to a
three-dimensional autonomous system.37 Define
z t { X Qt /XYt .
(A18)
By the definition (A1) of trends XYt and X Qt and by the constant-growth assumption (A13), z t for sufficiently large t follows a first-order linear difference
equation
z t⫹1 p
1
z.
g 1 g 2v1/(1⫺v 2)n v1⫹h⫺1 t
(A19)
Add this equation to the two-equation dynamical system to form a three-equation
dynamical system in (k˜ t , l˜ t , z t). Clearly, this augmented system is autonomous
for sufficiently large t when the labor barrier is not binding (because (q˜ t , sKt ,
sEt) is a stationary function of (k˜ t , l˜ t , z t)). Suppose that the parameters of the
model are such that z t r 0 as t r ⬁ (i.e., the trend in per capita output of sector
2 [XYt] grows faster than the trend for the relative price [X Qt ] in the long run),
which is the case in our calibration. Then the detrended minimum consumption
d 1(X Qt /XYt) in (A17) vanishes in the long run, so the steady state is given by
˜ 0), where (k,
˜ is the steady state for the two-dimensional autonomous
˜ l,
˜ l)
(k,
system with d 1 p 0 defined above. Obviously, the eigenvalues for the threedimensional linearized system at this steady state consist of the two eigenvalues
for the two-dimensional system with d 1 p 0 mentioned above and the stable
growth factor for z t (the z t coefficient in [A19]). So the system has two roots
that are less than unity and one that is greater than unity under the calibrated
37
We are grateful to Lars Hansen for suggesting this idea.
agriculture and the prewar japanese economy
617
parameter values. We were able to find the solution by a variant of the shooting
algorithm, with l˜ 0 as the jumping variable.38
Appendix B
Incorporating Intermediate Inputs
In this appendix, we allow each sector to use the output of the other sector as
an intermediate input. For this more general model, we derive a two-equation
dynamical system, compute its steady state, and show that the steady state is a
saddle.
The Equilibrium Conditions
Start with sector 1 (agriculture). If M 1t is the intermediate input from sector 2
to sector 1, the production function for sector 1 is
Y1t p TFP1t K 1tv1Lh1t M 1ta1 .
(B1)
The contribution of land is implicit in this production function, so we have
decreasing returns to scale in capital, labor, and the intermediate input:
v1 ⫹ h ⫹ a1 ! 1.
(B2)
The firms’ first-order conditions with respect to K 1t , L 1t , and M 1t for sector 1
are
rt p v1qtTFP1t K 1tv1⫺1Lh1t M 1ta1 ,
(B3)
a1
w 1t p hqtTFP1t K 1tv1Lh⫺1
1t M 1t ,
(B4)
1 p a1qtTFP1t K 1tv1Lh1t M 1ta1⫺1 .
(B5)
1)
M 1t p a11/(1⫺a1)qt1/(1⫺a1) TFP1t1/(1⫺a1)K 1tv1/(1⫺a1)Lh/(1⫺a
.
1t
(B6)
and
Solving (B5) for M 1t gives
Combining this with (B1) gives
M 1t p a1qtY1t
(B7)
38
For a large T, the algorithm lowers (raises) l˜ 0 if (k˜ T , l˜ T) is above (below) the saddle
path corresponding to zt p 0 for all t. Because convergence to the steady state is slow, we
modified the algorithm as follows. We set T p 60 and examine (k˜ t0⫹T , l˜ t0⫹T), initially for
t0 p 1. If we find l˜ t0 and l˜ t0 such that Fl˜ t0 ⫺ l˜ t0F ! 0.01l˜ and (k˜ t0⫹T , l˜ t0⫹T) is above the
saddle path for l˜ t0 and below it for l˜ t0, then we fix l˜ t0⫹T/2 at the average of the l˜ t0⫹T/2
corresponding to those two l̃t0 ’s and move the initial period forward to t0 p T/2. Starting
from this new initial period t0, we examine (k˜ t0⫹T , l˜ t0⫹T) and do the same procedure to
move the initial date forward by another T/2 periods. This process is repeated until the
distance between the steady state and the solution path thus constructed is less than 0.01.
618
journal of political economy
and
h˜
1t K1tv1L1t
Y1t p qta1/(1⫺a1)TFP
,
˜
(B8)
where
1t { a1a1/(1⫺a1) TFP1t1/(1⫺a1) , v˜ 1 {
TFP
v1
,
1 ⫺ a1
h˜ {
h
.
1 ⫺ a1
(B9)
Substituting (B6) into the marginal productivity conditions (B3) and (B4) yields
h˜
1t K1tv1⫺1L1t
rt p (1 ⫺ a1)v˜ 1qt1/(1⫺a1)TFP
,
˜
˜
h⫺1
1t K1tv1L1t
˜ t1/(1⫺a1)TFP
w 1t p (1 ⫺ a1)hq
.
˜
(B10)
Equation (B8) replaces (11) and (B10) replaces (12). When an amount
M 1t p a1qtY1t of good 2 goes into sector 1, the equilibrium condition for good
2, (16), is now
(good 2) Ntc 2t ⫹ [Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t] ⫹ Gt ⫹ a1qtY1t p Y2t ⫺ fK 2t .
(B11)
In sector 2, if M 2t is the intermediate input from sector 2 to sector 1, the
Cobb-Douglas production function for sector 2 is
Y2t p TFP2t K 2tv 2Lh2t2 M 2ta 2 .
(B12)
The constant-returns-to-scale assumption for sector 2 implies
v2 ⫹ h2 ⫹ a 2 p 1.
(B13)
It is straightforward to derive the following corresponding expressions for sector
2:
M 2t p a 2q⫺1
t Y2t
(B14)
and
v2 1⫺v2
2t K2t
Y2t p qt⫺a 2 /(1⫺a 2)TFP
L2t ,
˜
˜
(B15)
where
ṽ2⫺1
( )
K
2 /(1⫺a 2) rt ⫹ f p (1 ⫺ a 2)v˜ 2q⫺a
TFP2t 2t
t
L 2t
,
ṽ2
( ),
K 2t
2t
w 2t p (1 ⫺ a 2)(1 ⫺ v˜ 2)qt⫺a 2 /(1⫺a 2)TFP
L 2t
(B16)
and
2t { a a2 2 /(1⫺a 2) TFP2t1/(1⫺a 2) , v˜ 2 {
TFP
v2
.
1 ⫺ a2
(B17)
Equation (B15) replaces (13) and (B16) replaces (14). With fraction a 2 of sector
1 output going to the production of good 2, the market equilibrium condition
agriculture and the prewar japanese economy
619
for good 1 is
Ntqtc 1t ⫹ a 2Y2t p qtY1t .
(good 1)
(B18)
The Detrended Dynamical System
With intermediate inputs, the trends X Qt and XYt in (A1) are now
⫺1
(1⫺v1)/(1⫺v2)
1t
2t
X Qt { [TFP
(h 1t E t)⫺h˜ TFP
(h 2t E t)1⫺v1]1/z
˜
˜
˜
(B19)
with
z{
1
a 2(1 ⫺ v˜ 1)
⫹
1 ⫺ a1 (1 ⫺ a 2)(1 ⫺ v˜ 2)
and
2)
1/(1⫺v
XYt p TFP
XQt⫺a 2 /(1⫺a 2)(1⫺v2)(h 2t E t)/Nt .
2t
˜
˜
(B20)
Very tedious algebra shows that the same relation (A3) holds, provided that
y˜1t and y˜2t are now defined as
˜ ˜
y˜1t { q˜ ta1/(1⫺a1)k˜ tv1sKtv1sEth˜ ,
˜
˜
˜
2 /(1⫺a 2) ˜ v2
y˜2t { q˜ ⫺a
kt (1 ⫺ sKt)v2(1 ⫺ sEt)1⫺v2.
t
(B21)
It is then straightforward to show that the five equations corresponding to (A6)–
(A10) are
(resource constraint)
Nt⫹1 XY,t⫹1 ˜
k p
Nt XYt t⫹1
c 2(q˜ t X Qt , l˜ t XYt)
˜
[1 ⫺ dt ⫺ (1 ⫺ sKt)f]k˜ t ⫹ (1 ⫺ w)y
⫺ a1q˜ ty˜1t ,
t 2t ⫺
XYt
(Euler equation)
{
[
bl˜ t 1 ⫹ (1 ⫺ tt⫹1) (1 ⫺ a 2)v˜ 2
(market equilibrium for good 1)
(B22)
XY,t⫹1 ˜
l p
XYt t⫹1
]}
ỹ2,t⫹1
⫺ f ⫺ dt⫹1 ,
k̃t⫹1(1 ⫺ sK,t⫹1)
(B23)
q˜ tc 1(q˜ t X Qt , l˜ t XYt)
⫹ a 2y˜2 p q˜ ty˜1t ,
XYt /X Qt
(B24)
620
journal of political economy
(equality of marginal products of capital)
(1 ⫺ a 2)v˜ 2
q˜ ty˜1t
(1⫺ a1)v˜ 1
p
k̃tsKt
ỹ2t
⫺ f,
(1 ⫺ sKt)k˜ t
(B25)
and
p ¯sEt
(sectoral employment arbitrage) sEt p 1
苸 [s¯Et , 1]
{
Zt {
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
˜ ˜ ty˜1t /sEt)
w 1th 1t
(1 ⫺ a1)h(q
p
.
w 2th 2t (1 ⫺ a 2)(1 ⫺ v˜ 2)[y˜2t /(1 ⫺ sEt)]
(B26)
The Steady State
As in Appendix A for the case without intermediate inputs, we can show that
the detrended dynamical system becomes autonomous in the long run (in which
the labor barrier is not binding) when the utility function is log linear. Assuming,
as in (A13), that the exogenous variables are constant in levels or in growth
rates and dropping the time subscript of the variables of the system, we can
˜ q,
˜ l,
˜ sK ,
derive the following five equations that determine the steady state (k,
sE):
˜˜1
y˜2
l˜
qy
ng p [1 ⫺ d ⫺ (1 ⫺ sK)f] ⫹ (1 ⫺ w) ˜ ⫺ m 2 ˜ ⫺ a1 ˜ ,
k
k
k
{
[
g p b 1 ⫹ (1 ⫺ t) (1 ⫺ a 2)v˜ 2
with g {
]}
ỹ2
⫺f⫺d ,
(1 ⫺ sK)k˜
XY,t⫹1
,
XYt
(B27)
(B28)
˜˜1 ,
m 1l˜ ⫹ a 2y˜2 p qy
(B29)
˜˜
qy
y˜2
(1 ⫺ a1)v˜ 1 ˜1 p (1 ⫺ a 2)v˜ 2
⫺ f,
sKk
(1 ⫺ sK)k˜
(B30)
and
1p
˜ ˜˜1 /sE)
(1 ⫺ a1)h(qy
,
˜
(1 ⫺ a 2)(1 ⫺ v2)[y˜2 /(1 ⫺ sE)]
(B31)
agriculture and the prewar japanese economy
621
where
˜ ˜
y˜1 p q˜ a1/(1⫺a1)k˜ v1sKv1sEh˜ ,
˜
˜
˜
y˜2 p q˜ ⫺a 2 /(1⫺a 2)k˜ v2(1 ⫺ sK)v2(1 ⫺ sE)1⫺v2.
(B32)
This five-equation system can be solved explicitly. For example, the closedform expression for sK is
[(
1⫺d⫹ 1⫺w⫹
sK p
[(
]
m2
r⫹f
a
⫺ f ⫺ ng
m 1 2 (1 ⫺ a 2)v˜ 2
)
]
m
r⫹f
[a ⫹ (m 2 /m 1)]r
1 ⫺ w ⫹ 2 a2
⫺f ⫹ 1
˜
m1
(1 ⫺ a 2)v2
(1 ⫺ a1)v˜ 1
)
,
(B33)
where
r{
(g/b) ⫺ 1
⫹d
1⫺t
(B34)
is the steady-state gross pretax rate of return from capital.
Under the calibrated parameter values, the Jacobian of the mapping from
(k˜ t , l˜ t) to (k˜ t⫹1 , l˜ t⫹1) for the dynamical system is numerically calculated, and its
eigenvalues are (1.19, 0.87). So the steady state is a saddle.
Appendix C
More Details on Calibration
We described in the text the calibration of (b, f, d 1). This appendix covers the
rest of the parameters. The main source of the time-series data used for calibration is the LTES.
The definition of the two sectors.—Sector 1 is agriculture proper as defined in
the LTES (rice, wheat, barley, rye, oats, miscellaneous cereals, potatoes, pulses,
vegetables, fruits and nuts, industrial crops, green manure and forage crops,
sericulture products, livestock and poultry, and straw goods). Sector 2 is the rest
of the economy.
v1, h, a1 (the share parameters for capital, labor, and intermediate input sector 1).—
The share of intermediate inputs in agriculture for each year (call it a1t here)
is reported in the LTES. Its prewar average of 0.146 is our calibrated value of
a1. Gross output of sector 1 is calculated as the sector’s value added (also available
from the LTES) divided by 1 ⫺ a1t . Table J-5 of Yamada and Hayami (1979)
(reproduced as table 2-11 of Hayami [1975]) has gross output factor shares in
agriculture for selected years. Their capital cost, however, ignores depreciation.
We construct capital cost from the LTES.39 The ratio of this capital cost to sector
39
The LTES has gross investment and the capital stock by asset type for agriculture.
From this we can calculate the implicit depreciation rates and the user cost of capital (we
assumed a real rate of return of 5 percent when calculating the user cost). See app. 1 of
Hayashi and Prescott (2006) for more details.
622
journal of political economy
1 gross output just described has no clear trend. The average over 1886–1940
is 0.144, which is our calibrated value of v1 . The average of the Yamada-Hayami
estimate of labor share is adjusted to reflect the difference in the capital cost
estimate between theirs and ours. This produces h p 0.545 (so land rent’s share
is 1 ⫺ 0.146 ⫺ 0.144 ⫺ 0.545 p 0.165). The labor share of value added, therefore,
is 0.545/(1 ⫺ 0.146) p 0.638.
a 2 (the share of intermediate inputs in sector 2).—The difference between the sum
of gross output and net imports and domestic consumption equals the amount
of good 1 used in sector 2. Let x be the prewar average of
(gross output of good 1 ⫹ net imports of good 1 ⫺ consumption of good 1) # qt
.
value added in sector 2 ⫹ fK 2t
This x should be an estimate of a 2 /(1 ⫺ a 2) because the denominator equals
1 ⫺ a 2 times gross output in sector 2. The calibrated value of a 2 is x/(1 ⫹ x).
v2 (capital’s share in sector 2’s gross output).—With intermediate inputs, this v2
divided by 1 ⫺ a 2 is capital’s share in value added. The LTES has no income
accounts, so this parameter cannot be estimated from the LTES. There is an
estimate of capital’s share in value added for the prewar private nonagricultural
sector by Minami and Ono (1978). It rises from 39.4 percent for 1896 to 54.2
percent for 1940. They note, however, that the capital share does not show a
trend in prewar United States, Canada, and the United Kingdom. A trend is
absent in Ohkawa and Rosovsky (1973, table 17), whose capital share estimate
for 1908–38 is between 33.5 percent and 50.2 percent. Our view is that there is
no definitive evidence in favor of a trend in capital share. So we set v2 /(1 ⫺
a 2) to the customary value of 1/3. Under constant returns to scale for sector 2,
labor’s share in value added is 2/3.40
m 1, m 2 (expenditure shares in the Stone-Geary utility function [26]).—Under the
Stone-Geary utility function, the Frisch demand system is c 1t p d 1 ⫹ m 1(l t /qt) and
c 2t p m 2 l t , which imply
m 1 (c 1t ⫺ d 1)qt
p
.
m2
c 2t
We choose the value of (m 1 , m 2) so that m 1 /m 2 equals the prewar average of this
and m 1 ⫹ m 2 p 1.
Appendix D
Endogenizing Employment
The exogenous-employment model in the text assumes that employment is given
to the model. This appendix presents a model with endogenous employment.
40
If h2 is labor’s share in gross output in sector 2, the constant-returns-to-scale assumption
is that a2 ⫹ v2 ⫹ h2 p 1. So
v2
h2
⫹
p 1.
1 ⫺ a2 1 ⫺ a2
Labor’s share in value added equals h2/(1 ⫺ a2).
agriculture and the prewar japanese economy
623
It also displays additional marginal conditions that could be imposed if hours
worked were endogenous. Unless otherwise indicated, the notation is the same
as in the text.
The Indivisible Labor Model
In Hayashi and Prescott (2002), we considered an indivisible labor model of
Rogerson (1988) with hours as well as employment endogenous. A two-sector
extension of the stand-in household’s objective function in that model is
冘
⬁
t
bN
t{u(c 1t , c 2t) ⫺ [sE g(h 1t , et) ⫹ (1 ⫺ sEt)g(h 2t , et)]et},
(D1)
tp0
where et { E t /Nt is the employment rate and g(h jt , et) is the disutility from working
h jt hours in sector j (j p 1, 2). If the employment rate et did not enter the
disutility function g, this would be the natural two-sector extension of the indivisible labor model. That is, et Nt members of the household work. Fraction
sEt of them work in sector 1, each working h 1t hours per week, and the remaining
fraction work in sector 2 for h 2t hours. The term [sE g(h 1t , et) ⫹ (1 ⫺ sEt)g(h 2t ,
et)]et in (D1) is then the average disutility from working. Here, the disutility
function g involves not only hours but also the employment rate because we
follow Cho and Cooley (1994) and allow the fixed cost of working to depend
on the employment rate. Their specification of the disutility function g(h, e) is
g(h, e) p v(h) ⫹ y(e), v(0) p 0.
(D2)
The fixed cost of working is the disutility at h p 0 , which equals y(e) . The average
disutility becomes
[sE g(h 1t , et) ⫹ (1 ⫺ sEt)g(h 2t , et)]et p [sEv(h 1t) ⫹ (1 ⫺ sEt)v(h 2t)]et ⫹ y(et)et .
(D3)
We assume that the fixed cost is a function of the employment rate for two
reasons. First, as Cho and Cooley (1994) argue, if the fixed cost represents the
commuting cost, it should depend on the number of days worked, which varies
with the employment rate. Second, in our simulation the equilibrium employment rate exceeds unity for a number of periods if the fixed cost is specified
to be a constant.
We now turn to the budget constraint. In order to recognize its distortionary
effect when employment is endogenous, the labor income tax must be explicitly
incorporated. With tWt denoting the tax rate, the household’s period budget
constraint is (note that E t p et Nt)
qt Ntc 1t ⫹ Ntc 2t ⫹ Nt⫹1k t⫹1 ⫺ (1 ⫺ dt)Ntk t p
(1 ⫺ tWt)[w 1th 1tsEt ⫹ w 2th 2t(1 ⫺ sEt)]et Nt ⫹ rt Ntk t ⫺ t(r
t t ⫺ dt)Ntk t ⫺ pt .
(D4)
In contrast to the period budget constraint (4) of the text, pt now excludes the
tax on labor income.
In the exogenous-employment model of the text, the household’s first-order
conditions are the sectoral employment arbitrage condition (6), the Euler equation (8), and the Frisch demands (9). With endogenous employment, the sec-
624
journal of political economy
toral employment arbitrage condition should be modified, and there is an additional first-order condition corresponding to the employment rate et. Let
bt /l t be the Lagrange multiplier for the period budget constraint. Then the
sectoral employment arbitrage equation becomes
p ¯sEt
sEt p 1
苸 [s¯Et , 1]
{
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
(D5)
where Z t , which was the income ratio w 1th 1t /w 2th 2t in the exogenous-employment
model, is now generalized as
Zt {
(1 ⫺ tWt)w 1th 1t ⫺ l t[v(h 1t) ⫹ y(et)]
.
(1 ⫺ tWt)w 2th 2t ⫺ l t[v(h 2t) ⫹ y(et)]
(D6)
The first-order condition for the employment rate et ({ E t /Nt) is
sEtv(h 1t) ⫹ (1 ⫺ sEt)v(h 2t) ⫹ [y(et) ⫹ y(e
t)et] p
1 ⫺ tWt
[sEtw 1th 1t ⫹ (1 ⫺ sEt)w 2th 2t].
lt
(D7)
If Hours Were Endogenous . . .
If hours were endogenous, then we would have the following additional marginal
conditions, which are the first-order conditions for hours:
v (h 1t) p
1
(1 ⫺ tWt)w 1t ,
lt
v (h 2t) p
1
(1 ⫺ tWt)w 2t .
lt
(D8)
Taking the ratio of these two equations, we obtain
v (h 1t) w 1t
p
,
v (h 2t) w 2t
(D9)
which indicates that the relative hours worked, h 1t /h 2t , responds to the relative
wage w 1t /w 2t .
Market Equilibrium Conditions
With endogenous employment (but with exogenous hours), the definition of
equilibrium in the text is modified as follows. A competitive equilibrium given the
initial per-worker capital stock k 0 and the sequence of exogenous variables
⬁
{Nt , h 1t , h 2t , TFP1t , TFP2t , dt , Gt , tt , tWt}tp0
is a sequence of prices and quantities,
⬁
{l t , qt , w 1t , w 2t , rt , k t⫹1 , K 1t , K 2t , sEt , L 1t , L 2t , et}tp0
, satisfying conditions i, ii, and
iii shown in the text, except that in condition i the sectoral employment arbitrage
condition (6) is now (D5) and the employment rate first-order condition (D7)
is added.
agriculture and the prewar japanese economy
625
Incorporating Intermediate Inputs
Intermediate inputs can be incorporated into these equilibrium conditions as
indicated in Appendix B. The set of equilibrium conditions are those listed in
the first subsection of Appendix B (including the definitions [B8] and [B15]
of (Y1t , Y2t)) and the employment rate first-order condition, with the sectoral
employment arbitrage condition modified as indicated above.
The Detrended Dynamical System with Endogenous Employment and Intermediate
Inputs
Define two trends, X Qt and XYt, as
⫺1
(1⫺v1)/(1⫺v2)
1t
2t
X Qt { [TFP
(h 1t Nt)⫺h˜ TFP
(h 2t Nt)1⫺v1]1/z
˜
˜
˜
(D10)
with
z{
1
a 2(1 ⫺ v˜ 1)
⫹
,
1 ⫺ a1 (1 ⫺ a 2)(1 ⫺ v˜ 2)
and
1/(1⫺v2) ⫺a 2 /(1⫺a 2)(1⫺v2)
2t
XYt p TFP
XQt
h 2t .
˜
˜
(D11)
Define detrended variables as
lt
l˜ t {
,
XYt
kt
k˜ t {
,
XYt
q˜ t {
qt
.
X Qt
(D12)
Very tedious algebra yields
qtY1t p Nt XYtq˜ ty˜1t ,
Y2t p Nt XYty˜2t ,
(D13)
where (Y1t , Y2t) are as defined in (B8) and (B15) and
y˜1t { q˜ ta1/(1⫺a1)k˜ tv1sKtv1sEth˜ eth˜ ,
˜
˜
˜
˜
˜
˜
2 /(1⫺a 2) ˜ v2
y˜2t { q˜ ⫺a
kt (1 ⫺ sKt)v2(1 ⫺ sEt)1⫺v2et1⫺v2 .
t
(D14)
As shown in Appendix B, under exogenous employment, the detrended dynamical system with intermediate inputs has two dynamic equations in (k˜ t , l˜ t),
the resource constraint (B22) and the Euler equation (B23). Given (k˜ t , l˜ t), we
can determine (q˜ t , sKt , sEt) by the static conditions (B24)–(B26). Under endogenous employment (but with exogenous hours), the dynamical system is still in
the same two variables (k˜ t , l˜ t), but there is one more variable, namely, the
employment rate et, determined by the static conditions. It is easy to show that
the two dynamic equations and the first two of the three static conditions remain
the same in appearance, provided that (y˜1t , y˜2t) are now defined by (D14). When
we use this definition of (y˜1t , y˜2t) and recall that Z t is now defined by (D6), the
626
journal of political economy
sectoral employment arbitrage equation (the third static condition) is
p ¯sEt
(sectoral employment arbitrage) sEt p 1
苸 [s¯Et , 1]
{
if Z t ! 1,
if Zt 1 1,
if Zt p 1,
(D15)
with
Zt p
˜ ˜ ty˜1t /sEtet) ⫺ l˜ t[v(h 1t) ⫹ y(et)]
(1 ⫺ tWt)(1 ⫺ a1)h(q
.
(1 ⫺ tWt)(1 ⫺ a 2)(1 ⫺ v˜ 2)[y˜2t /(1 ⫺ sEt)et] ⫺ l˜ t[v(h 2t) ⫹ y(et)]
The fourth static condition is given by the employment rate first-order condition, which, written in terms of the detrended variables, is
(employment first-order condition)
sEtv(h 1t) ⫹ (1 ⫺ sEt)v(h 2t) ⫹ [y(et) ⫹ y(e
t)et] p
[
]
1 ⫺ tWt
q˜ ty˜1t
y˜2t
˜
˜l sEt(1 ⫺ a1)h˜ sEtet ⫹ (1 ⫺ sEt)(1 ⫺ a 2)(1 ⫺ v2) (1 ⫺ sEt)et .
t
(D16)
In summary, under endogenous employment, the detrended dynamical system
has two dynamic equations, (B22) and (B23), in (k˜ t , l˜ t). The four static conditions determining (q˜ t , sKt , sEt , et) given (k˜ t , l˜ t) are (B24), (B25), (D15), and
(D16).
The Steady State
The five steady-state equations for the case of exogenous employment and with
intermediate inputs were derived in Appendix B (see the five equations [B27]–
[B31]). Derivation of the steady-state equations, which are six in number, under
endogenous employment proceeds the same way. The first four of them are the
same as those in Appendix B, provided that (y˜1 , y 2) are now defined as
˜ ˜
y˜1 { q˜ a1/(1⫺a1)k˜ v1sKv1sEh˜ eh˜ ,
˜
˜
˜
˜
y˜2 { q˜ ⫺a 2 /(1⫺a 2)k˜ v2(1 ⫺ sK)v2(1 ⫺ sE)1⫺v2e 1⫺v2.
(D17)
The fifth equation, which is the steady-state version of Z t p 1 , where Z t is as in
(D15), reduces to the fifth equation for the exogenous-employment case (B31),
because in the long run h 1t p h 2t p h and v(h 1t) ⫹ y(et) p v(h 2t) ⫹ y(et) if h 1t p
h 2t p h. The sixth steady-state condition is just the steady-state version of the
employment first-order condition (D16):
sEv(h) ⫹ (1 ⫺ sE)v(h) ⫹ [y(e) ⫹ y(e)e]
p
[
]
˜˜1
1 ⫺ tW
qy
y˜2
˜
˜l sE(1 ⫺ a1)h˜ sE e ⫹ (1 ⫺ sE)(1 ⫺ a 2)(1 ⫺ v2) (1 ⫺ sE)e ,
(D18)
where t W is the long-run value of t Wt. These six equations, (B27)–(B31) and
agriculture and the prewar japanese economy
627
˜ q,
˜ l,
˜ sK , sE ,
(D18), can be solved for the six-dimensional steady-state vector (k,
e).
Calibration
For the parameters besides those for the disutility function g(h, e) p v(h) ⫹
y(e) and d 1 (the subsistence level), their values are chosen as summarized in
table 4 of the text. The value of minimum food consumption d 1 is chosen so
that the predicted Engel coefficient in the simulation with the barrier equals
the observed coefficient for 1885. This procedure results in the calibrated value
of d 1 p 62 percent of actual food consumption in 1885. The projected paths
of the exogenous variables other than the employment rate are also the same
as in the exogenous-employment case and are given in table 4.41 In particular,
the steady-state value of hours worked is h 1t p h 2t p h with h p 62.3 hours per
week.
For the employment rate et { E t /Nt, we assumed for the exogenous-employment model of the text that et p e 1940 for t 1 1940 (this is so because the projected
growth rate of the population Nt and that of employment E t are assumed to be
the same [at 1.1 percent per year]). To complete the calibration for the
endogenous-employment model, we need to parameterize and calibrate the
disutility function.
We do this so that the implied steady-state value of et equals what is assumed
in the exogenous-employment case as the long-run value (which is e 1940 in the
data). This is accomplished in two steps. Looking at the six steady-state equations
just derived, we note that the first five do not involve v(7) and y(7). The first step
˜ q,
˜ l,
˜ sK , sE), assuming that the steady-state employment rate
is to solve for (k,
equals its 1940 value (i.e., e p e 1940 ).42 The second step is to specify v(7) and
y(7) so that the sixth steady-state equation (D18) (the employment first-order
˜ q,
˜ l,
˜ sK , sE) from the first step and for e p e 1940.
condition) holds for the (k,
To carry out the latter step, we first need to parameterize the two functions
v(7) and y(7) comprising the disutility function. We use one of the specifications
41
There is an additional exogenous variable, which is the tax rate on labor income
tWt . Appendix 1 of Hayashi and Prescott (2006) describes the data source for calculating
direct taxes on persons. There, in calculating the tax on capital, we assumed that 10
percent of the direct tax on persons is a capital income tax. We therefore assume that
the rest is the wage tax for each year. Labor income for each year is calculated as
v1 # (gross output of sector 1) ⫹
(
)
v2
# (value added for sector 2),
1 ⫺ a2
where the values of v1 and v2/(1 ⫺ a2) are as specified in table 4 of the text. The wage
tax rate tWt is calculated as the ratio of the wage tax for year t to wage income for year t.
The projection of the wage tax is that tWt p tW,1940 for t p 1941, 1942, ….
42
The (sK , sE) thus obtained are the same as in the exogenous-employment model; but
˜ q)
˜ l,
˜ thus obtained are not, because the trend levels are different (compare [D10]
the (k,
and [D11] with [B19] and [B20]). After we adjust for the difference in trend levels, the
˜ q)
˜ l,
˜ are the same across the two models.
steady-state values of (k,
628
journal of political economy
Fig. D1.—Employment rate, 1885–1940
Fig. D2.—GNP per worker, 1885–1940, employment endogenously determined
entertained by Cho and Cooley (1994):
( hT) , y(e ) p 1 ⫹b j e ,
h
b
g(h , e ) p ⫺a 7 log (1 ⫺ ) ⫹
e ,
T
1⫹j
v(h t) p ⫺a 7 log 1 ⫺
so
t
t
t
t
j
t
t
j
t
(D19)
agriculture and the prewar japanese economy
629
where T here is time endowment. So the average disutility becomes
[sE g(h 1t , et) ⫹ (1 ⫺ sEt)g(h 2t , et)]et p
[ ( )
⫺a 7 sE log 1 ⫺
(
)]
h 1t
h 2t
b
⫹ (1 ⫺ sEt) log 1 ⫺
et ⫹
et1⫹j .
T
T
1⫹j
(D20)
We choose this particular specification because when the fixed cost of work is
set at zero, it reduces to the log-linear specification used by Hansen (1985) and
a number of other researchers.
The calibration by Cho and Cooley (1994) for this parameterized disutility
function is that (a, b, j) p (1.5, 0.45, 1.6). Since our two-good specification of
the utility from consumption is different from Cho and Cooley’s one-good specification, we rescale this parameterized disutility. That is, in the above parameterized disutility function, we set b p (0.45/1.5) 7 a and solve the sixth steady˜ q,
˜ l,
˜ sK , sE) obtained from the first step described
state equation for a given (k,
above and given e p e 1940. The value of a thus calibrated is a p 2.1 (so b p
0.64). We assume T p 24 # 7 hours.
Simulation Results
A quantitative summary of simulation results for the present case of endogenous
employment and intermediate inputs is in table 5 of the text. Here, we display
two figures. One, figure D1, plots the employment rate et in the data and in two
simulations. The other, figure D2, is the endogenous-employment version of
figure 5 of the text. Compared to the exogenous-employment case, the model
fits less well for GNP; but this is not surprising because in the exogenousemployment case the employment rate is set at its actual level. We do not show
the endogenous-employment version of figure 6 (about capital accumulation)
because it looks almost the same.
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