Depopulation and importance of agriculture in Japan: Implications from the overlapping generations and general equilibrium growth accounting model

Kinugasa, Tomoko; Yamagucki, Mitoshi Article Depopulation and importance of agriculture in Japan: Implications from the overlapping generations and general equilibrium growth accounting model Economics & Finance Research Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Kinugasa, Tomoko; Yamagucki, Mitoshi (2013) : Depopulation and importance of agriculture in Japan: Implications from the overlapping generations and general equilibrium growth accounting model, Economics & Finance Research, ISSN 2164-9499, Taylor & Francis, Abingdon, Vol. 1, Iss. 1, pp. 60-74, https://doi.org/10.1080/21649480.2013.862734 This Version is available at: https://hdl.handle.net/10419/147691 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/3.0/ Economics & Finance Research, 2013 Vol. 1, 60–74, http://dx.doi.org/10.1080/21649480.2013.862734 Depopulation and importance of agriculture in Japan: implications from the overlapping generations and general equilibrium growth accounting model Tomoko Kinugasa∗and MitoshiYamaguchi Graduate School of Economics, Kobe University, 2–1 Rokkodai-cho, Nada-ku, Kobe, 657–8501, Japan We investigate the effects of demographic change on agriculture and nonagriculture in Japan whileconsideringcapitalaccumulationandtotalpopulationandlabour.Combiningtheoverlapping generations model with the three generations and general equilibrium growth accounting models, we simulate the effect of demographic change on agricultural and nonagricultural inputs and outputs. Our simulation analyses show that demographic change greatly influenced agriculture and nonagriculture through capital accumulation although the influences of total populationand labour werenot negligible.Remarkable demographic dividendslikethedecline of young dependents and increase of adult longevity greatly influenced capital accumulation in Japan in the 1950s to the 1990s, which decreased the importance of agriculture. In the future, aggregate capital in Japan will presumably decrease due to a decline of the working age population, which may result in the disappearance of the advantages of nonagriculture and an increase of the importance of agriculture. I. Introduction This study investigates the effects of demographic change on industrial structure in Japan considering capital accumulation, labour force, and total population. Simulation analyses using Growth Rate Multipliers (GRMs) and an Overlapping Generations (OLGs) model indicate a rapid demographic change after World War II; for example, decreased fertility and increased adult longevity stimulated capital accumulation, which increased the importance of nonagriculture. After World War II, Japan experienced a remarkable demographic transition. At the beginning of the twentieth century, both fertility and mortality were high; however, mortality (especially adult mortality) declined rapidly. Subsequently, fertility began to decline. Fertility declined rapidly in the 1960s and 1970s, and is low today. Moreover, the population started to decline in 2005, and it is expected that it will continue to decline in the future. The effects of depopulation on the economy are controversial. A decrease in population can increase per capita income ∗Corresponding author. E-mail: [email protected] 1For example, Lewis (1954),Ranis and Fei (1961),Jorgenson (1961),Kelley et al. (1972). if other conditions do not change, however, it may decrease the labour force and the possibility of innovation. High life expectancy in Japan, also a characteristic of the country, is the highest in the world. Higher life expectancy may encourage capital accumulation, which is considered a positive aspect of population aging. Consideration of agriculture is essential when we discuss the development of a country. Agriculture is fundamental to human activity.Malthus(1798)statedthattherelationship betweenpopulation and agriculture is important. Extensive research has attempted to explain economic development in relation to agriculture using a dual economy model.1The dual economy model assumes two sectors: the agricultural and the nonagricultural sectors. The agricultural sector is traditional, self-sufficient, and characterized by low productivity. The nonagricultural sector is modern, profitable, and highly productive. According to the dual economy model, it is necessary to have a technical change in agriculture at the onset of economic development, to move labour and capital into the nonagricultural sector. © 2013 TheAuthor(s). Published by Taylor & Francis. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted. Depopulation and importance of agriculture in Japan 61 Yamaguchi’s (1972, 1973, 1982, 2001) dual economy model was noteworthy in that it distinguished between changes in population and labour force. The author established a general equilibrium growth accounting model. In this study, we developed a new model that can capture the agricultural and nonagricultural distortion problemsbased onTemple(2005) and Hayashi and Prescott (2008). The model analyses the effects of eight exogenous variables, including agricultural and nonagricultural technologies, total population, total labour, aggregate capital stock, land, demand shifter of agricultural products, and wage gap between the agricultural and nonagricultural sectors, on eight endogenous variables, including agricultural and nonagricultural outputs, labour and capital, relative prices of agricultural and nonagricultural products, and per capita income. It is also important to consider the working and saving behaviour of people when we discuss the effects of demographics on economic growth.A considerable volume of research has attempted to examinethe economic implicationsofdemographictransition.During a demographic transition, the young dependency rate decreases, while the share of the working-age population increases. This stage is called the ‘first demographic dividend.’ Bloom and Williamson (1998), Bloom et al. (2000), and Kelley and Schmidt (2001, 2005) found that changes in age structure result in changes in the labour force, thus significantly contributing to economic growth. Demographic changes also influence saving behaviour. According to the lifecycle hypothesis, individuals save when they are young and employed and spend their savings after retirement (Modigliani and Brumberg, 1954;Tobin, 1967). Changes in the young dependency ratiocouldalterage-earningandconsumptionprofiles.Inparticular, a higher young dependency ratio can result in increased consumption at a younger age (Mason, 1981, 1987; Higgins andWilliamson, 1997). The concept of the ‘second demographic dividend’has also been attracting the attention of population economists. Increased adult longevity can increase the savings of prime-age adults, resulting in capital accumulation (Lee et al., 2001;Kinugasa and Mason, 2007; Mason and Kinugasa, 2008). Capital accumulation significantly contributes to economic growth. In many developed countries, including Japan, the first demographic dividend has already disappeared.Declininggrowthof thelabourforcecansuppresseconomic growth. On the other hand, the second demographic dividend could stillcontinueindevelopedcountriesinthefuture.The life expectancies of old people are gradually increasing and many developed countries may still have opportunities for economic development. (Mason, 2007;Ogawa, 2007;Mason and Kinugasa, 2008). The research discussed above does not analyse the effects of demographicchangeonindustrializationintermsofcapitalaccumulation. Kinugasa andYamaguchi (2008) combined the OLG model of Kinugasa and Mason (2007) and the general equilibrium growth accounting model ofYamaguchi (1982, 2001). Kinugasa andYamaguchianalysedtheeffectsofchangesinthenumberofchildrenand adult longevity on capital accumulation, and examined how capital, which is influenced by the demographic change, affects agricultural and nonagricultural inputs and outputs. Their simulation analysis with Japanese data showed that a rapid decline in the number of 2In our theory, we do not consider linkage of demographic variables and treat different demographic variables, such as an increase in labour force, a decrease in the number of children/an increase in adult longevity, and an increase in population independently, because to consider these connections in theory would over-complicate the discussion. However, we use real data for three demographic variables, and the interrelationship between these demographic variables is incorporated in the simulation analysis; we would like to deal with these issues in future research. 3Henceforth, the importance of agriculture (nonagriculture) implies the relative importance of agriculture (nonagriculture) with respect to nonagriculture (agriculture). children and an increase in adult longevity stimulated capital accumulation, which increased the importance of nonagriculture from the 1960s to 1990s. In this research, we develop the analyses of Kinugasa and Yamaguchi (2008) in the following four points and investigate the effects of demographic change on agriculture and nonagriculture from a broader perspective. First, we consider the effects of demographic change on per capita income and industrial structure, in terms of labour force and total population, as well as capital accumulation. Second, we estimate the effects of demographic change not only in the past and the present but also in the future. Third, we use the model that can consider the distortion problem as stated above. Fourth, we consider domestic capital and capitaldepreciation,whichtheresearchofKinugasaandYamaguchi (2008) did not consider. Our findings regarding the relationships between demographic change, capital accumulation, and importance of agriculture are summarized by the flowcharts presented in Fig. 1.2In this figure, a broad arrowhead indicates that the effect is strong, a thin arrowhead indicates that the effect is weak, and a dashed arrowhead indicates that the effect appears after a while. Fig. 1(a) presents the relationship from the 1950s to 1990s. According to our OLG model, Japan experienced a rapid decline in the number of children and a rapid increase in adult longevity during the period, which stimulated capital accumulation. Moreover, the labour force increased rapidly because the working-age population increased, and this also stimulated capital accumulation. According to the results from the GRMs of the general equilibrium growth accounting model, capital accumulation stimulated industrialization; that is, it decreased the importance of agriculture.3The analysis using GRMs also indicates that an increase in labour force decreased the importance of agriculture and increased per capita income. Increased per capita income also increased capital accumulation according to the OLG model, which further decreased the importance of agriculture according to the general equilibrium growth accounting model. From the 1950s to 1990s, the population growth rate was also high, which increased the importance of agriculture according to the general equilibrium growth accounting model. Fig. 1(b) describes the outlook for Japan. It is expected that the number of children will decrease and adult longevity will increase gradually, which will encourage capital accumulation and, as a result, increase the importance of nonagriculture slightly. According to our OLG model, a decline in the labour force will decrease capital accumulation to a large extent, which will make agriculture more important. The general equilibrium growth accounting model implies that a decrease in the labour force will directly increase the importance of agriculture. The model also indicates that a decrease in capital accumulation caused by a decrease in the labour force will decrease per capita income, and this will further decrease capital accumulation. The population will continue to decrease in Japan in the future, and this may increase the importance of nonagriculture according to Malthus’s law as indicated in the general equilibrium growth accounting model. However, this effect will not be large. To sum up, in Japan, the importance of agriculture will increase in the future considering the demographic situation. 62 T. Kinugasa and M. Yamaguchi (a) Japanese experience from the 1950s to 1990s (b) Outlook for Japan Increase in capital accumulation Decrease in labour force (working-age population) OLG OLG GRM GRM GRM OLG GRM Decrease in population Increase in importance of nonagriculture Increase in importance of agriculture Increase in per capita income Increase in capital accumulation Decrease in number of children Increase in adult longevity Decrease in number of children Increase in adult longevity Increase in labour force (working-age population) OLG OLG GRM GRM GRM OLG GRM Increase in population Increase in importance of agriculture Increase in importance of nonagriculture Increase in per capita income Fig. 1. Outline of relationships between demographic change, capital accumulation, and importance of agriculture. Note: ‘OLG’ indicates the Overlapping Generations model. ‘GRM’ indicates the Growth Rate Multiplier in general equilibrium growth accounting model. The remainder of this article is organized as follows: The general equilibrium growth accounting model established by Yamaguchi (1982, 2001) is introduced in Section II. Section II also describes howtotalpopulation,labour, andcapitalinfluenceendogenousvariables such as agricultural and nonagricultural outputs and inputs. Section III describes the OLG model, which considers three generations, and explains the effects of demographic change, such as 4Our model combines two different kinds of models. Therefore, the models might not be entirely consistent. An OLG model is used to calculate the growth rate of aggregate capital. Although simulated growth in aggregate capital is obtained in the discrete OLG model, we multiply the simulated growth rate of capital based on the discrete OLG model with a growth rate multiplier of the continuous general equilibrium growth accounting model. However, the model’s implication would not be remarkably influenced given the inconsistency. Moreover, our OLG model with three periods is a necessary assumption in the discussion on the effects of various demographic variables, such as the number of children and adult and child mortality, on the economy. changes in present and past fertility and adult longevity, on capital accumulation. Moreover, this section also examines the influence of present and past fertility and adult longevity on aggregate capital. Based on the models described in Sections II and III, and using Japanese data, we simulate the effects of demographic change on agricultural and nonagricultural outputs and inputs in Section IV.4 Section Vpresents the conclusion. Depopulation and importance of agriculture in Japan 63 II. General Equilibrium Growth Accounting Model The Computable General Equilibrium (hereafter CGE) model has prevailed since 1975. However, Ezaki (1984) evaluated that Yamaguchi (1969, 1972, 1973, 1982) made the bridge (i.e. Yamaguchi is the first person who applied the theoretical general equilibriumgrowthmodeltoCGEmodelintheworld)tothepresent CGE model. More accurately, Kelley et al. (1972) and Kelley and Williamson (1971, 1974) also began to build the bridge to the present CGE model in the early 1970s. Kelley and Williamson (1971) published a CGE model similar to the present CGE model. However, although the Yamaguchi model is a CGE model, this is also a general equilibrium growth accounting model with endogenousvariablespreciselycoincidingwith actual values.In this sense, Yamaguchimodels are also growthaccountingmodels and are completelydifferentfromKelleyandWilliamsonandotherpresentCGE models. Since the beginning of the 1970s, Yamaguchi (1973) evaluated the Kelley–Williamson model very highly. However, he criticized the following three points of their works. First, the Stone-Geary model is the ideal model for a demand system and is used in many recent studies, including Kelley–Williamson works. However, not enough research exists for this model to adopt the rigorous sectoral differences of parameters between agriculture and nonagriculture. Second, population and labour were treated as a single variableintheirmodel.Yamaguchigreatlycriticizedtheirtreatment. Although it took a long time to consider Yamaguchi’s criticism, Bloom and Williamson (1998) finally recognized this importance and used labour and population independently. Mason (2005, 2007) and Mason and Kinugasa (2008) found the first and second dividend by treating labour and population independently. These are very important findings in population studies. Recentresearchesoneconomicdevelopment,whichmustbeconsidered in our study, are in the following three areas. The first area is the agricultural-nonagricultural distortion problem. Hayashi and Prescott (2008) consider that the labour barrier existed because the pre-war patriarchy forced the son designated as the heir to remain in agriculture. Moreover, Temple (2005) pointed out the problem of distortion,i.e.outputlossesassociatedwithfactormisallocationand aggregate growth in the presence of factor market distortion.Therefore, we considered the problem of distortion and assume imperfect competition in both labour and capital markets (m1,m2,m3,m4, Nw, and Nrin our model described in Appendix 1 and Table A1). The second area is the reconfirmation that agriculture is the centre of development (Gollin et al., 2002), although this conclusion may be reversed when we consider the international situation (Matsuyama,1992).Inother words,twoopposing opinionsforagriculture exist. Gollin et al. (2002) believe that agriculture is very important and must occupy the central topic of development. On theother hand, Matsuyama,for example,opposes this thinking with respect to international trade.As the third area, Temple (2005) evaluates that the two-sector model is still important in the research of development. Therefore, we use the two-sector model in this study. 5See alsoYamaguchi and Binswanger (1975) andYamaguchi and Kennedy (1984a, 1984b). 6This model is further explained inAppendix 1. 7The exogenous variables are agricultural technical growth (TA), nonagricultural technical growth (TM), population (Q), total labour force (L), aggregate capital (K), land (B), demand shifter of agricultural products (a), and wage gap between the agricultural and nonagricultural sectors (mW). The endogenous variables are agricultural output (YA), nonagricultural output (YM), agricultural labour (LA), nonagricultural labour (LM), agricultural capital (KA), nonagricultural capital (KM), relative prices of agricultural goods and nonagricultural products (P), and income (E). Here, aggregate capital refers to domestic capital. 8These findings are valid for the entire analysis period except for 1945. Japan was at war in 1945; hence, this year can be considered an exception. Laitner (2000) (on page 546) suggest that while an unusual thrift may lead to a high income level (as shown in Solow’s framework), causality can run the other way: a higher standard of living can lead to a higher measured savings rate. In our study, we calculate how population, labour, and capital stock influence income levels and sectoral outputs through savings. In this study, we explain the extension of the growth accounting general equilibrium model (as stated above, we assume imperfect competition, i.e. the distortion problem in our model here) of Yamaguchi (1982, 2001).5The authors considered a two-sector economy consisting of agricultural and nonagricultural sectors and established a general equilibrium growth accounting model.6Further, they calculated the effects of eight exogenous variables on eight endogenous variables.7Each effect is referred to as a GRM, which reflects the percentage increase of an endogenous variable given a 1% increase in a certain exogenous variable. GRMs are expressed by aligning endogenous and exogenous variables; for example, YAKis the effect of a 1% increase in aggregate capital on agricultural output. Yamaguchi and colleagues also calculated the contributions of exogenous variables to endogenous variables by multiplying the GRMs and the growth rates of the exogenous variables. Table 1presents the GRMs with respect to capital, labour, and population. This table shows that aggregate capital (K) has the following effects on the endogenous variables.8An increase in aggregate capital increases both agricultural and nonagricultural outputs;however,ithasalargereffectonnonagriculturaloutputthan onagriculturaloutput,(YMK>YAK>0).Moreover,anincreasein aggregatecapitalhasapositiveeffectonbothagriculturaland nonagricultural capital, and its effect on nonagricultural capital is larger than that on agricultural capital, (KMK>KAK>0). An increase in aggregate capital decreases agricultural labour, but increases nonagricultural labour (LAK<0, LMK>0). These findings imply that capital accumulation induces growth in both agricultural and nonagricultural sectors; however, it has a greater positive effect on nonagricultural growth. Therefore, capital accumulation is likely to accelerate industrialization. Moreover, an increase in aggregate capital increases per capita income (EK >0). Growth in the labour force can also increase the importance of nonagriculture. Growth in total labour increases both agricultural andnonagriculturaloutput and labour, butincreases nonagricultural output and labour more than the corresponding agricultural output and labour (YML>YAL>0,LML>LAL>0).An increase in the labour force increases nonagricultural capital, but decreases agricultural capital (KAL<0, KML>0). It is also confirmed that an increase in the labour force increases per capita income (EL >0). Malthus’s law holds for the effects of population growth on endogenous variables. An increase in population increases agricultural inputs and outputs and decreases nonagricultural inputs and outputs (YAQ>0, YMQ<0, KAQ>0, KMQ<0, LAQ>0, LMQ<0).Moreover,anincreaseinpopulationdecreasespercapita income (EQ <0). To sum up, increases in capital and labour decrease the importance of agriculture and increase the importance of nonagriculture. 64 T. Kinugasa and M. Yamaguchi Table 1. GRMs for aggregate capital, labour, and population YAKY MKK AKK MKL AKL MKEKY ALY MLK ALK MLL ALL MLELY AQY MQK AQK MQL AQL MQEQ 1890 0.10 0.30 0.96 1.03 −0.02 0.05 0.22 0.48 0.88 −0.14 0.09 0.92 1.16 0.73 0.09 −0.22 0.22 −0.14 0.12 −0.25 −1.10 1895 0.10 0.33 0.96 1.02 −0.02 0.04 0.25 0.49 0.81 −0.12 0.07 0.93 1.13 0.71 0.08 −0.19 0.21 −0.12 0.11 −0.22 −1.10 1900 0.09 0.37 0.97 1.01 −0.02 0.03 0.29 0.51 0.75 −0.12 0.06 0.94 1.12 0.68 0.08 −0.17 0.21 −0.11 0.11 −0.21 −1.10 1905 0.09 0.41 0.95 1.02 −0.03 0.05 0.33 0.48 0.76 −0.18 0.08 0.90 1.17 0.69 0.13 −0.24 0.32 −0.14 0.17 −0.29 −1.15 1910 0.09 0.42 0.94 1.02 −0.03 0.05 0.34 0.48 0.75 −0.19 0.07 0.90 1.16 0.68 0.13 −0.22 0.33 −0.12 0.17 −0.28 −1.14 1915 0.09 0.51 0.94 1.02 −0.03 0.04 0.42 0.47 0.62 −0.18 0.06 0.90 1.14 0.59 0.14 −0.18 0.34 −0.10 0.19 −0.25 −1.11 1920 0.09 0.41 0.94 1.01 −0.03 0.04 0.34 0.46 0.71 −0.20 0.04 0.88 1.12 0.66 0.16 −0.17 0.35 −0.08 0.21 −0.22 −1.09 1925 0.08 0.40 0.94 1.01 −0.03 0.03 0.33 0.49 0.71 −0.22 0.04 0.87 1.12 0.66 0.17 −0.15 0.36 −0.06 0.22 −0.20 −1.08 1930 0.10 0.46 0.97 1.01 −0.02 0.02 0.42 0.51 0.63 −0.21 0.03 0.87 1.11 0.61 0.17 −0.12 0.34 −0.05 0.21 −0.18 −1.09 1935 0.11 0.51 0.96 1.01 −0.03 0.02 0.46 0.46 0.56 −0.20 0.02 0.88 1.10 0.55 0.17 −0.11 0.35 −0.04 0.22 −0.17 −1.07 1940 0.09 0.55 0.97 1.00 −0.02 0.01 0.49 0.46 0.51 −0.20 0.02 0.87 1.09 0.50 0.17 −0.09 0.36 −0.04 0.24 −0.16 −1.06 1945 0.11 0.53 1.02 1.00 0.01 −0.01 0.47 0.49 0.50 −0.14 0.02 0.91 1.07 0.50 0.11 −0.07 0.24 −0.03 0.15 −0.12 −1.04 1950 0.09 0.55 0.97 1.00 −0.02 0.01 0.48 0.46 0.52 −0.20 0.02 0.88 1.10 0.51 0.16 −0.10 0.37 −0.04 0.22 −0.18 −1.06 1955 0.08 0.30 0.92 1.01 −0.05 0.03 0.27 0.47 0.82 −0.32 0.03 0.78 1.13 0.77 0.28 −0.16 0.49 −0.05 0.34 −0.20 −1.09 1960 0.09 0.37 0.93 1.01 −0.06 0.02 0.34 0.42 0.72 −0.27 0.02 0.79 1.09 0.69 0.26 −0.11 0.47 −0.04 0.36 −0.15 −1.08 1965 0.11 0.32 0.92 1.01 −0.06 0.02 0.31 0.42 0.74 −0.27 0.02 0.78 1.07 0.72 0.29 −0.09 0.44 −0.03 0.37 −0.11 −1.06 1970 0.10 0.32 0.93 1.01 −0.06 0.02 0.31 0.42 0.74 −0.27 0.02 0.78 1.07 0.72 0.29 −0.09 0.44 −0.03 0.37 −0.11 −1.06 1975 0.11 0.37 0.92 1.00 −0.05 0.03 0.31 0.42 0.74 −0.27 0.02 0.78 1.07 0.72 0.29 −0.09 0.44 −0.03 0.37 −0.11 −1.06 1980 0.10 0.32 0.94 1.00 −0.06 0.01 0.31 0.42 0.73 −0.28 0.02 0.76 1.06 0.72 0.30 −0.08 0.46 −0.02 0.38 −0.09 −1.05 1985 0.11 0.40 0.92 1.01 −0.05 0.02 0.31 0.41 0.73 −0.28 0.01 0.76 1.06 0.73 0.30 −0.08 0.46 −0.02 0.38 −0.09 −1.05 1990 0.10 0.32 0.91 1.00 −0.07 0.01 0.31 0.41 0.72 −0.29 0.01 0.74 1.05 0.72 0.31 −0.07 0.47 −0.02 0.39 −0.08 −1.04 1995 0.09 0.35 0.93 1.01 −0.06 0.02 0.31 0.40 0.72 −0.29 0.01 0.75 1.05 0.70 0.31 −0.07 0.48 −0.01 0.39 −0.08 −1.04 2000 0.11 0.32 0.92 1.01 −0.06 0.02 0.31 0.40 0.74 −0.30 0.01 0.74 1.03 0.72 0.32 −0.07 0.48 −0.01 0.40 −0.07 −1.04 Note: The data from columns YAKto EK are adopted fromYamaguchi (1982, 2001). New values from columns YALto EQ are estimated by using the data ofYamada and Hayami (1972),Minami and Ono (1978),Ohkawa (1972), and Ohkawa and Shinohara (1979). Depopulation and importance of agriculture in Japan 65 Table 2. Equations with respect to the OLG model Vt=λ1c1−θ 1,t 1−θ+λ2qt 1+ρ c1−θ 2,t+1 1−θ+κn1−ε tλ0c1−θ 0,t 1−θ(1) wtAt(1−νnt)=c1,t+ntc0,t+qt 1+rt+1c2,t+1(2) s1,t=qt(λ2/(λ1(1+ρ)))1/θ (1+rt+1)1/θ−1(1−νnt)Atwt 1+(κλ0/λ1)1/θ n1−ε/θ t+qt(λ2/(λ1(1+ρ)))1/θ (1+rt+1)1/θ−1(3) Wt+1=Kt+1+Ft+1=s1,tN1,t(4) Kt+1=dt+1s1,tptnt−1N1,t−1(5) ˙ Kt=Kt−Kt−1 Kt−1(6) An increase in the population increases the importance of agriculture.Aggregatecapitalandlabour positivelyaffectpercapita income, and total population negatively affects per capita income. III. Demographic Change and Capital Accumulation in the OLG Model This section presents an OLG model to investigate the effects of demographic change on capital accumulation. Table 2presents key equations in our OLG model. Our model is similar to Kinugasa and Yamaguchi (2008), although it considers international capital flow. The OLG model considers the existence of different generations at the same time.We assume that there are three generations: children, prime-age adults, and elderly. Child age, prime age, and old age are set at age zero, one, and two, respectively. Children are considered to be dependent and not employed. Prime-age adults take care of childrenand work, and savetoconsume in theirold age.The elderly are retired and spend the savings they accumulate in their prime-age years.9Not all children survive to prime-age and not all prime-age adults survive after retirement. The utility function of a prime-age adult is expressed in Equation 1 of Table 2. Prime-age adults at time t decide on their present consumption for themselves and their children, and their consumptioninthefuture maximizes the lifetime utilityasshownin Equation 1 of Table 2. In the equation, c1,t,c2,t+1, and c0,trepresent the consumption of prime-age adults, the elderly, and the dependent children, respectively. qtis the survival rate of prime-age adults until old age and is used as a measure of adult longevity. Prime-age adults decide c1,t,c2,t+1, and c0,t. The parameter κimplies the rate at which parents discount the utility of children, and it is assumed that 0 ≤κ≤1. It is also assumed that ε>0, so that the marginal utility with respect to the number of children declines according to the number of children. The parameters λ0,λ1, and λ2reflect the relative importance of consumption for children, prime-age, and post-retirement, respectively. ρis the discount rate; that is, the rate 9For simplicity, we assume that there are neither bequests nor transfers from children to parents. 10 In this research, we assume that (1/θ) > 1. An increase in the interest rate will increase savings by prime-age adult sif (1/θ) > 1. On the other hand, an increase in the interest rate will decrease savings by prime-age adults if (1/θ) < 1. 11 In this model, availability of insurance against longevity risk is assumed. A consumer purchases an annuity at the beginning of age 2 if insurance companies are risk neutral and annuity markets are perfect. The rate of return for the surviving elderly is ((1 +rt+1)/qt), where rt+1is the riskless interest rate on savings. The return with regard to annuities is ((1 +rt+1)/qt). Since returns on insurance are higher than on regular notes, individuals restrict their savings to insurance. After retirement, the elderly consume the proceeds of their savings. See Yaari (1965) and Blanchard (1985) for details. of time preference. The intertemporal elasticity of substitution is givenby(1/θ).10 Prime-age adults obtain wage income Atwtper unit of labour, where Atis the level of technology and wtis the wage per effective worker. The total time available for a prime-age adult is one unit. νunits of time need to be spent to nurture one child, and prime-ageadults with n children workfor(1-νn) units of time.They allocatetheirearningstotheirownconsumption,tothatoftheirchildren, and to savings. Therefore, their budget constraint is given by: c1,t+ntc0,t+s1,t=Atwt(1−νnt), where s1,trepresents savings by prime-age adults.After retirement, the elderly consume the proceeds from their savings. Thus, the budget constraint of the elderly is:11 c2,t+1=(1+rt+1)s1,t/qt.Accordingtothebudgetconstraints of prime-age adults and the elderly, the lifetime budget constraint faced by prime-age adults is derived as shown in Equation 2 of Table 2. Consumers determine their children’s consumption and their own consumption in prime-age and post-retirement, thus maximizing life utility as given in Equation 1 under the lifetime budget constraint given in Equation 2. Savings by prime-age adults is calculated as shown in Equation 3 inTable 2based on theutilitymaximizationproblem. In Equation 3, ∂s1,t/∂qt>0 holds, and the savings of prime-age adults increase if the adult survival rate increases. Intuitively, if consumers are aware that they will live longer, they are more likely to have higher savings in preparation for old age. Equation 3 also implies ∂s1,t/∂nt<0ifθ>ε. Savings by prime-age adults decreases with an increase in the number of children as long as θ>ε. Moreover, expenditure on children correspondingly increases with an increase in the number of children, while the wage income of prime-age adults decreases because raising children requires the expenditure of time.Therefore, higher fertility decreases savings by prime-age adults. Based on the individual utility maximization problem, aggregate capital is determined as detailed inAppendix 2. The aggregate capital at t+1, Wt+1, is given by Equation 4 in Table 2, where Kis the domestic capital and Fis the foreign capital. From Equation 4, 66 T. Kinugasa and M. Yamaguchi the total savings of prime-age adults at time tformulates the aggregate capital in the next period.12 Higher savings of prime-age adults result in higher capital accumulation. In this context, the number of prime-age adults at time t is expressed as N1,t=ptN0,t−1= ptnt−1N1,t−1, where ptis the survival rate of children. Therefore, Equation4can berewrittenasWt+1=s1,tptnt−1N1,t−1.Weassume that the ratio of domestic capital to aggregate capital, dt, is exogenous, and domestic capital at time t is given by Kt+1=dt+1Wt+1. Then, we obtain Equation 5 as shown in Table 2. The growth rate of domestic capital ˙ Ktis defined as shown in Equation 6 of Table 2. According to Equations 5 and 6, the effect of an increase in adult longevity at time t on the growth rate of domestic capital at time t+1isgivenby∂˙ Kt+1/∂qt= dt+1(∂s1,t/∂qt)ptnt−1N1,t−1/Kt>0.Thisindicatesthatanincrease inadultlongevityattimetincreasesthegrowthrateofdomesticcapitalattimet+1givenanincreaseinthesavingsof prime-age adults at time t.13 In this model, an increase in adult longevity at time t does not influence the growth rate of domestic capital at the same time. The effect of an increase in the number of children at time t on the growth rate of capital at time t+1is∂˙ Kt+1/∂nt= dt+1(∂s1,t/∂nt)/Kt<0. The number of children at time t decreases domestic capital at time t+1. If the number of children increases at time t, prime-age adults save less during the same period; thus, less capital is accumulated at time t+1. On the other hand, the growth rate of capital at time tis not affected by the number of children at the same time. The influence of the number of children at time t on the growth rate of capital at time t+2 is expressed as ∂˙ Kt+2/∂nt= (dt+1s1,tptN1,t−dt+1(∂s1,t/∂nt)ptnt−1N1,t−1)/K2 t+1>0.Thenumber of children at time t increases the number of prime-age adults who can accumulate wealth at time t+1, which results in a higher capital growth at time t+2. Moreover, less capital is accumulated at time t+1, which gives rise to a higher growth rate of capital at time t+2. Therefore, the growth rate of aggregate capital increases at time t+2 if fertility increases at time t. To sum up, an increase in fertility prevents capital accumulation in the short run. As children grow, the increase in the prime-age population stimulates capital accumulation. According to the OLG model, a typical demographic transition such as declining fertility and mortality may either increase or decreasethegrowthof aggregatecapitalstock.Therefore, a detailed simulation analysis would be helpful to precisely investigate the effect of demographic change. In the next section, we set the values for the parameters to simulate the influence of demographic change on capital accumulation in Japan. 12 Because the model assumes only one period of working life and wealth is not accumulated across generations, the economy’s aggregate capital stock at time tis equal to the flow of savings at time t−1. This is a typical assumption in the OLG model with two or three generations as Higgins (1994) and Kinugasa and Mason (2007) did. This might be problematic; however, to overcome this problem, we need to set up an OLG model with many generations, which will over-complicate our model. The characteristic of our overlapping generations model is that it considers consumption for children and different survival rates for adults and children. 13 We can calculate the effect of adult longevity at time ton growth of capital at time t+1 as: ∂˙ Kt+2/∂qt=−dt+1(∂s1,t/∂qt)ptnt−1Kt+2/K2 t+1<0. An increase in adult longevity at time t decreases the growth in capital at time t+2 because of the increase in the numerator. This and ∂˙ Kt+1/∂qt>0 imply that a continuing increase of adult longevity increases the rate of capital accumulation. 14 In this research, many variables such as demographic variables and land are assumed to be exogenous. We need further discussion regarding the determinants of these variables; however, our discussion would become over-complicated if we regard these variables endogenously. 15 Appendix 2 describes how to calculate child and adult survival indices. 16 The labour force and population growth rates in the 1970s were exceptional.The population growth rate increased primarily because of an increased fertility rate during the second baby boom, and the growth in the labour force declined, primarily because of an increase in unemployment during the second oil crisis. 17 According to the data, the growth of the labour force is higher than that of population in 2025, probably because the death rate of first baby-boomers born from 1947 to 1950 will become high. IV. Simulation Analysis using Japanese Data In this section, we estimate the effects of demographic change on capital and agricultural and nonagricultural inputs and output in the past, present, and future. The simulation method is detailed in Appendix 3. First, growth in aggregate capital is simulated using data from the number of children per adult, and adult and child longevities based on the OLG model in Section III. Then, the sums of contributions of simulated aggregate capital, population, and labour to agricultural and nonagricultural inputs and outputs are calculated.14 Fig.2showsgraphsofdemographicvariablessuchasthenumber of children per adult, the child survival index, and the adult survival index,15 and growths in population and labour from 1890 to 2025. Thenumberofchildrenperadultincreasedmoderatelyfrom1890to 1935, and began to decline rapidly in 1965.The number of children declined rapidly from 1965 to 1980. Since the 1990s, the number of children per adult has decreased gradually, and it is expected to decrease continuously in the future. The child survival index did not change significantly before the World War II and increased considerably in 1950. Since then, Japan’s child survival index has been close to 100%, and this figure is expected to remain high in Japan. A significant increase in the adult survival index was not seen until around 1950. Adult longevity increased rapidly from the 1950s to 1990s. Since 1990, it has continued to increase and is estimated to increase gradually in the future. From Fig. 2(b), labour force growth rate was much lower than the population growth rate, primarily because of a high fertility rate. After the World War II, the growth rate of the labour force increased sharply and was greater than the population growth rate from 1950 to 1995.16 Japan had a high cyclical population growth rate from 1890 to 1970. Since 1970, the population growth has slowed, and became negative around 2005. Growth rates of the population and labour force are estimated to continuously decrease in the future. Furthermore, it is expected that the labour force growth rate will be lower than the population growth rate until 2020.17 The period in which labour force growth was greater than the population growth may be the period in which Japan benefited from the ‘first demographic dividend,’ as mentioned in Section I. It is likely that Japan had a great opportunity to use the first demographic dividend during the high economic growth period after the war. However, the first dividend has not been effective since 2000. Fig. 3presents the simulation results for the effects of demographic change on agricultural and nonagricultural outputs and inputs considering changes in labour, total population, and capi- Depopulation and importance of agriculture in Japan 67 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 (a) (b) 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 p, q n Number of children and adult and child survival indices Number of children per prime-age adult Child survival index Adult survival index –1 –0.5 0 0.5 1 1.5 2 2.5 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 % Growth rates of labour and population Labour Population Fig. 2. Demographic changes in Japan tal accumulation18 (The data are taken from Yamada and Hayami (1972),Minami and Ono (1978),Ohkawa (1972), Ohkawa and Sinohara (1979), Ohkawa et al. (1966) and others). The effects of demographic change on agricultural inputs and outputs are calculated as the sum of the products of GRM and the growth rate of relatedexogenousvariables.Forexample,thecontributionofdemographic change to agricultural output is calculated as YAK·˙ ˆ K+ YAL·˙ L+YAQ·˙ Q, and the contribution of demographic change to nonagricultural capital is calculated as KMK·˙ ˆ K+KML·˙ L+ KMQ·˙ Q, where ˙ ˆ Kis the simulated growth in domestic capital based on our OLG model (Equation 6 in Table 2). The results are illustrated in Fig. 3(a). We also calculate the contribution of demographic change to agricultural and nonagricultural inputs and outputs when we do not consider the effects of demographic change on aggregate capital and only the effects of growths of population 18 The research of Kinugasa and Yamaguchi (2008) did not consider domestic capital and capital depreciation. A detailed explanation is given in Appendix 3. 19 When we do not consider the effects of demographic change on aggregate capital, we do not use an OLG model. We calculate the contributions of demographic change to agricultural and nonagricultural output and input based only on GRM. and labour are considered. In this case, the contribution of demographic changes on agricultural output is YAL·˙ L+YAQ·˙ Q, and the contribution of demographic changes to nonagricultural capital is KML·˙ L+KMQ·˙ Q.19 The results are presented in Fig. 3(b). Fig. 3(a) shows that demographic change significantly contributedtoincreases in both agriculturalandnonagricultural capital. The contribution of demographic change to nonagricultural capital was slightly more than the contribution to agricultural capital until 1955, and it was much more than the contribution to agricultural capital from 1960 to 1970. Demographic change positively influenced agricultural and nonagricultural output from 1890 to 2000, and the effect of demographic change on nonagricultural output was much larger than that on agricultural output from 1930 to 1985. Demographic characteristics in Japan seem to have had an insignificant effect on agricultural and nonagricultural labour compared with outputs and capital in both sectors throughout the period, but 74 T. Kinugasa and M. Yamaguchi analysis, we consider capital depreciation assuming that capital is depreciated 5% a year, and 1 unit of capital becomes 0.77 unit in 5 years. Regarding demographic variables, population data are from Japan Statistical Yearbook. Labour force data are obtained from Ohkawa and Shinohara (1979) (from 1890 to 1950), ‘Historical Statistics of Japan’ (from 1950 to 2000), and Cabinet Office in Japan (2004) (from 2005 to 2025).Adult and child survival rates are calculated using the life table from the Health and Welfare Statistics Association in Japan (from 1890 to 2000) and estimated life table from National Institute of Population and Social Security Research in Japan (from 2005 to 2025). The adult survival index is defined as 89 x=60 Lx/59 x=30 Lx, where Lxis number of years lived between the exact age xand the exact age x+1.25 The child survival index is defined as 59 x=30 Lx/29 x=0Lx. For the number of children per adult, we divide the population aged 0–29 by that aged 30–59. The data are obtained from the Historical Statistics of Japan from the Statistics Bureau and the Statistical Research and Training Institute in Japan (from 1890 to 2000) and from National Institute of Population and Social Security Research in Japan (from 2005 to 2025). When we calculate contribution of demographic change to agricultural and nonagricultural inputs and outputs, we use GRMs presented in Table 1.Yamaguchi (1982, 2001) calculates these from 1880to1965,whereaswerecalculatethemfrom1970to2000.After 2005, we assume that GRMs are constant at the values of 2000. Appendix 4 Table A1. Definitions of variables and parameters Variables Definitions Parameters Definitions (i) Definition of growth accounting model Parameters YAAgricultural output ηPrice elasticity of agricultural products YMNonagricultural output ζIncome elasticity of agricultural products LAAgricultural labour αShare of agricultural labour in agricultural output LMNonagricultural labour βShare of agricultural capital in agricultural output KAAgricultural capital γShare of nonagricultural labour in nonagricultural output KMNonagricultural capital δShare of nonagricultural capital in nonagricultural output PRelative prices of agricultural and nonagricultural products lAShare of agricultural labour in total labour PConsumer price index lMShare of nonagricultural labour in total labour EIncome per capita kAShare of agricultural capital in total capital wAAgricultural wage kMShare of nonagricultural capital in total capital wMNonagricultural wage χShare of agricultural income in total income rAAgricultural interest rate rMNonagricultural interest rate TAAgricultural technical growth TMNonagricultural technical growth LTotal labour force BLand (i)’s Variables Continued from (i) of left side aDemand shifter of agricultural products m1Distortion of agricultural labour mwWage gap between agricultural and nonagricultural sectors m2Distortion of nonagricultural labour Nw=mwm2/m1m3Distortion of agricultural capital Nr=mrm4/m3m4Distortion of nonagricultural capital (ii) Definition of OLG Model Parameters c0Consumption of children λ0Relative importance of consumption in childhood c1Consumption of prime-age adults λ1Relative importance of consumption in prime age c2Consumption of the elderly λ2Relative importance of consumption in old age nNumber of children per prime-age adult κThe rate at which parents discount the utility of children qAdult longevity (adult survival rate) ε(See the explanation in Section III) s1Saving of prime age adults ρDiscount rate AThe level of technology of the whole economy θReciprocal of intertemporal elasticity of substitution wWage νTime taken to raise one child rInterest rate ξDepreciation rate SGross national saving WAggregate capital KDomestic capital FForeign capital N0Number of children N1Number of prime-age adults N2Number of the elderly pChild survival rate dRatio of domestic capital to aggregate capital Note: In Section III, variables are expressed using subscripts of time. For example, c0,tis the consumption of children at time t.