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

Figures & data

Fig. 1. Outline of relationships between demographic change, capital accumulation, and importance of agriculture.\newline {\rm Note: ‘OLG’ indicates the Overlapping Generations model. ‘GRM’ indicates the Growth Rate Multiplier in general equilibrium growth accounting model.}

Table 1.  GRMs for aggregate capital, labour, and population

	YAK	YMK	KAK	KMK	LAK	LMK	EK	YAL	YML	KAL	KML	LAL	LML	EL	YAQ	YMQ	KAQ	KMQ	LAQ	LMQ	EQ
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 Y_AK to EK are adopted from Yamaguchi (1982, 2001). New values from columns Y_AL to EQ are estimated by using the data of Yamada and Hayami (1972), Minami and Ono (1978), Ohkawa (1972), and Ohkawa and Shinohara (1979).

Table 2.  Equations with respect to the OLG model

	(1)
	(2)
	(3)
	(4)
	(5)
	(6)

Fig. 2. Demographic changes in Japan

Fig. 3. Simulated contributions of demographic changes to agricultural and nonagricultural inputs and outputs and per capita income

Fig. 4. Simulated changes in importance of agriculture in terms of output, capital, and labour

Table A1. Definitions of variables and parameters

Variables	Definitions	Parameters	Definitions
(i)	Definition of growth accounting model	Parameters
YA	Agricultural output	η	Price elasticity of agricultural products
YM	Nonagricultural output	ζ	Income elasticity of agricultural products
LA	Agricultural labour	α	Share of agricultural labour in agricultural output
LM	Nonagricultural labour	β	Share of agricultural capital in agricultural output
KA	Agricultural capital	γ	Share of nonagricultural labour in nonagricultural output
KM	Nonagricultural capital	δ	Share of nonagricultural capital in nonagricultural output
P	Relative prices of agricultural and nonagricultural products	lA	Share of agricultural labour in total labour
P^′	Consumer price index	lM	Share of nonagricultural labour in total labour
E	Income per capita	kA	Share of agricultural capital in total capital
wA	Agricultural wage	kM	Share of nonagricultural capital in total capital
wM	Nonagricultural wage	χ	Share of agricultural income in total income
rA	Agricultural interest rate
rM	Nonagricultural interest rate
TA	Agricultural technical growth
TM	Nonagricultural technical growth
L	Total labour force
B	Land	(i)’s Variables	Continued from (i) of left side
a	Demand shifter of agricultural products	m1	Distortion of agricultural labour
mw	Wage gap between agricultural and nonagricultural sectors	m2	Distortion of nonagricultural labour
Nw		m3	Distortion of agricultural capital
Nr		m4	Distortion of nonagricultural capital
(ii)	Definition of OLG Model	Parameters
c0	Consumption of children	λ0	Relative importance of consumption in childhood
c1	Consumption of prime-age adults	λ1	Relative importance of consumption in prime age
c2	Consumption of the elderly	λ2	Relative importance of consumption in old age
n	Number of children per prime-age adult	κ	The rate at which parents discount the utility of children
q	Adult longevity (adult survival rate)	ϵ	(See the explanation in Section III)
s1	Saving of prime age adults	ρ	Discount rate
A	The level of technology of the whole economy	θ	Reciprocal of intertemporal elasticity of substitution
w	Wage	ν	Time taken to raise one child
r	Interest rate	ξ	Depreciation rate
S	Gross national saving
W	Aggregate capital
K	Domestic capital
F	Foreign capital
N0	Number of children
N1	Number of prime-age adults
N2	Number of the elderly
p	Child survival rate
d	Ratio of domestic capital to aggregate capital

Note: In Section III, variables are expressed using subscripts of time. For example, c_{0, t} is the consumption of children at time t.

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