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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$10.00 573 574 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 576 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 578 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). 580 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 581 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 582 journal of political economy 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. 584 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. 586 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. References Akerlof, George. 1980. “A Theory of Social Custom, of Which Unemployment May Be One Consequence.” Q.J.E. 94 (June): 749–75. Balke, Nathan, and Robert J. Gordon. 1989. “The Estimation of Prewar Gross National Product: Methodology and New Evidence.” J.P.E. 97 (February): 38– 92. Braun, Anton, Toshihiro Okada, and Nao Sudou. 2005. “U.S. R&D and Japanese Medium Cycles.” Manuscript, Dept. Econ., Univ. Tokyo. Browning, Martin, Angus Deaton, and Margaret Irish. 1985. “A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle.” Econometrica 53 (May): 503–43. Caselli, Francesco. 2005. “Accounting for Cross-Country Income Differences.” In Handbook of Economic Growth, vol. 1B, edited by Philippe Aghion and Steven Durlauf. Amsterdam: Elsevier. Caselli, Francesco, and Wilbur Coleman II. 2001. “The U.S. Structural Transformation and Regional Convergence: A Reinterpretation.” J.P.E. 109 (June): 584–616. 630 journal of political economy Cho, J.-O., and T. F. Cooley. 1994. “Employment and Hours over the Business Cycle.” J. Econ. Dynamics and Control 18 (March): 411–32. Echevarria, Cristina. 1997. “Changes in Sectoral Composition Associated with Economic Growth.” Internat. Econ. Rev. 38 (May): 431–52. Fujino, S., and R. Akiyama. 1977. “Security Prices and the Rates of Interest in Japan: 1874–1975.” Report no. 7, Documentation Center Japanese Econ. Statis., Inst. Econ. Res., Hitotsubashi Univ. Godo, Yoshihisa, and Yujiro Hayami. 2002. “Catching Up in Education in the Economic Catch-up of Japan with the United States, 1890–1990.” Econ. Development and Cultural Change 50 (July): 960–78. Gollin, Douglas, Stephen Parente, and Richard Rogerson. 2002. “Structural Transformation and Cross-Country Income Differences.” Manuscript, Dept. Econ., Univ. Illinois. Gordon, Robert J. 2004. “Two Centuries of Economic Growth: Europe Chasing the American Frontier.” Working Paper no. 10662 (June), NBER, Cambridge, MA. Hansen, Gary. 1985. “Indivisible Labor and the Business Cycle.” J. Monetary Econ. 16 (November): 309–27. Hansen, Gary, and Edward C. Prescott. 2002. “From Malthus to Solow.” A.E.R. 92 (September): 1205–17. Hayami, Yujiro. 1975. A Century of Agricultural Growth in Japan. Tokyo: Univ. Tokyo Press. Hayami, Yujiro, and Junichi Ogasawara. 1999. “Changes in the Sources of Modern Economic Growth: Japan Compared with the United States.” J. Japanese and Internat. Econ. 13 (March): 1–21. Hayashi, Fumio, and Edward C. Prescott. 2002. “The 1990s in Japan: A Lost Decade.” Rev. Econ. Dynamics 5 (February): 206–35. ———. 2006. “The Depressing Effect of Agricultural Institutions on the Prewar Japanese Economy.” Working Paper no. 12081 (March), NBER, Cambridge, MA. Honda, Tatsuo. 1950. “Nihon jinko mondai no shiteki kaiseki” [A historical analysis of the population problem in Japan]. Kikan Jinko Mondai Kenkyu 6 (2): 1–29. Jorgenson, Dale W. 1961. “The Development of a Dual Economy.” Econ. J. 71 ( June): 309–34. Jorgenson, Dale W., and Koji Nomura. 2007. “The Industry Origins of the USJapan Productivity Gap.” Manuscript, Dept. Econ., Harvard Univ. Kawashima, Takeyoshi. 1957. Ideorogi to shite no kazokuseido [The family as an ideology]. Tokyo: Iwanami Shoten. King, Robert G., and Ross Levine. 1994. “Capital Fundamentalism, Economic Development, and Economic Growth.” Carnegie-Rochester Conf. Ser. Public Policy 40 ( June): 259–92. Klenow, Peter J., and Andrés Rodriguez-Clare. 1997. “The Neoclassical Revival in Growth Economics: Has It Gone Too Far?” In NBER Macroeconomics Annual, edited by Ben S. Bernanke and Julio Rotemberg. Cambridge, MA: MIT Press. Laitner, John. 2000. “Structural Change and Economic Growth.” Rev. Econ. Studies 67 ( July): 545–61. Maddison, Angus. 2001. The World Economy: A Millennial Perspective. Paris: Development Centre Studies, Organization for Economic Cooperation and Development. Masui, Yukio. 1969. “The Supply Price of Labor: Farm Family Workers.” In Agriculture and Economic Growth: Japan’s Experience, edited by K. Ohkawa, B. F. agriculture and the prewar japanese economy 631 Johnston, and H. Kaneda. Tokyo: Univ. Tokyo Press; Princeton, NJ: Princeton Univ. Press, 1970. Matsumura, Katsujiro. 1957. Nochi sozoku ni kansuru kenkyu [A study of the inheritance of the farmland]. Tokyo: Noson Seisaku Kenkyusitsu. Minami, Ryoshin. 1973. The Turning Point in Economic Development: Japan’s Experience. Tokyo: Kinokuniya Bookstore. Minami, Ryoshin, and A. Ono. 1977. “Senzenki Nihon no kajo rodo” [Surplus labor in prewar Japan]. Keizai Kenkyu 28 (2): 156–66. ———. 1978. “Bunpairitsu no susei to hendo” [Trends and fluctuations in factor income shares]. Keizai Kenkyu 29 (3): 230–42. Momose, Takashi. 1990. Jiten Showa senzenki no Nihon [A dictionary on Japan in the prewar Showa era]. Tokyo: Yoshikawa Kobunkan. Namiki, Shokichi. 1957. “Sengo ni okeru nogyo jinko no hoju mondai” [The problem of recruiting farm population in the postwar period]. Nogyo Sogo Kenkyu 12 (1): 89–139. Nojiri, Shigeo. 1942. Nomin rison no jisshoteki kenkyu [An empirical study of farm exodus]. Tokyo: Iwanami Shoten. Nomura, K. 2004. Measurement of Capital and Productivity in Japan. Tokyo: Keio Univ. Press. Oda, Hiroshi. 1992. Japanese Law. London: Butterworths. Ohkawa, Kazushi, and H. Rosovsky. 1973. Japanese Economic Growth. Stanford, CA: Stanford Univ. Press. Ramseyer, J. Mark. 1996. Odd Markets in Japanese History. New York: Cambridge Univ. Press. Restuccia, Diego, Dennis Tao Yang, and Xiaodong Zhu. 2008. “Agriculture and Aggregate Productivity: A Quantitative Cross-Country Analysis.” J. Monetary Econ. 55 (March): 234–50. Robertson, Peter. 1999. “Economic Growth and the Return to Capital in Developing Economies.” Oxford Econ. Papers 51 (October): 577–94. Rogerson, Richard. 1988. “Indivisible Labor, Lotteries and Equilibrium.” J. Monetary Econ. 21 ( January): 3–16. Sato, Toshiki. 1998. “20 seiki Nihon no ‘kaiso’ to ido” [Social stratification and mobility in twentieth-century Japan]. In Kindai Nihon no ido to kaiso: 1896– 1995 [Social mobility and stratification in modern Japan: 1896–1995], edited by Toshiki Sato. Tokyo: Univ. Tokyo. Taeuber, Irene. 1958. The Population of Japan. Princeton, NJ: Princeton Univ. Press. Takagi, Naofumi. 1956. “Senzen sengo ni okeru noson jinko no toshi shuchu ni kansuru toukeiteki kosatsu” [A statistical study of migration from rural to urban areas in the prewar and postwar periods]. In Nogyo ni okeru seizai sitsugyo [Hidden unemployment in agriculture], edited by S. Tohata. Tokyo: Nihon Hyoronsha. Takahashi, Kamekichi. 1975. “Nihon keizai tosei ron” [Economic controls in Japan]. In Kindai Nihon keizai shi yoran [Handbook of modern Japanese economic history], edited by Y. Ando. Tokyo: Univ. Tokyo Press. Tsuburai, Kaoru. 1998. “Rino to rison no keiryo bunseki” [A quantitative analysis of peasants leaving the village]. In Kindai Nihon no ido to kaiso: 1896–1995 [Social mobility and stratification in modern Japan: 1896–1995], edited by Toshiki Sato. Tokyo: Univ. Tokyo. Vogel, Ezra. 1967. “Kinship Structure, Migration to the City, and Modernization.” In Aspects of Social Change in Modern Japan, edited by R. Dore. Princeton, NJ: Princeton Univ. Press. 632 journal of political economy Vollrath, Dietrich. Forthcoming. “How Important Are Dual Economy Effects for Aggregate Productivity?” J. Development Econ. Yamada, S., and Y. Hayami. 1979. “Agricultural Growth in Japan, 1880–1970.” In Agricultural Growth in Japan, Taiwan, Korea, and the Philippines, edited by Y. Hayami and V. W. Ruttan. Honolulu: Univ. Press Hawaii. Yokoyama, Gennosuke. [1899] 1985. Nihon no kaso shakai [The underclass society in Japan]. Reprint. Tokyo: Iwanami Shoten. Zenkoku Nogyo Kaigisho. 1979. Nochi sozoku no iko to jittai ni kansuru chosakekka [Report on the intention and the practice of farmland inheritance]. Research Report no. 141 (March). Tokyo: Zenkoku Nogyo Kaigisho.