Impact of changes in the labor force and innovative agro-based food industry clusters on primary and food–beverage industries, and regional economies in Japan’s depopulating society

Abstract

Demographic changes such as a decline in the labor force population and increase in an elderly population in Japan since 2000 have not been uniform across regions. These population dynamics restrain regional Japanese industries and impede the growth of regional economies. The period from 2005 to 2030 can be divided into two periods according to the degree of depopulation: mild depopulation period (2005–2015) and rapid depopulation period (2015–2030). This demographic change has a significant impact on primary and food–beverage industries. The domestic supply of primary and food–beverage industries under mild depopulation declined from 2000 until 2015. Therefore, in this paper, we evaluate the impacts of the decline in labor force, domestic market, and total-factor productivity (TFP) on primary and food–beverage industries, and regional economies during these periods. As a countermeasure to the rapid decline in population and TFP for 2015–2030, policies for demand-side consumption tax reduction and supply-side innovative agro-based food industry clusters were proposed, and their economic effects empirically analyzed using the four-region computable general equilibrium (4SCGE) model. We found that the long-term sustainable economic development of primary and food–beverage industries, and regional economies under rapid depopulation requires a demand-side consumption tax reduction policy to stimulate short-term domestic demand as well as a supply-side innovative agro-based food industry cluster policy to expand long-term domestic production.

Appendix 1: Structure of the four spatial CGE (4SCGE) model

While the overview for the 4SCGE model is explained in Sect. 3, we explain further the core blocks of this model below (Fig. 5). The 4SCGE model comprises 25 agents in the four regions, 21 commodity markets, and the two production factor markets of labor and capital. Furthermore, we add the two agents such as the central government and overseas sector. Furthermore, we assume that labor and capital total endowments are exogenously fixed, and no transfers outside the region, although both labor and capital can move among industries within the region. In addition, we make unemployment endogenous and social security benefits to the household sector endogenous in the 4SCGE model. Specifically, concerning the former we incorporated the following Eqs. (1) and (2) of a Phillips curve-type formula into the 4SCGE model.²⁸

$$ \mathop \sum \limits_{\alpha \in A} PL^{o} \, \cdot \,L_{a}^{o} + \overline{{LW^{o} }} \, \cdot \,ER = PL^{o} \, \cdot \,\left( {\overline{{LS^{o} }} - UNEMP^{o} } \right), $$

(1)

$$ \left( {\frac{{PL^{o} \, \cdot \,PCINEDX^{o} }}{{PLZ^{o} \, \cdot \,PCINEDXZ^{o} }} - 1} \right) = phillips^{o} \left( {\frac{{UNEMP^{o} /\overline{{LS^{o} }} }}{{UNEMPZ^{o} /\overline{{lS^{o} }} }} - 1} \right), $$

(2)

where ${UNEMP^{o}} \left( {UNEMPZ^{o} } \right)$ and ${PCINDEX^{o}} \left( {PCINDEXZ^{o} } \right)$ represent the unemployment (initial unemployment) and consumer commodity price index of the Laspeyres formula (initial consumer price index) of region o respectively, ${phillips^{o}}$ represents a Phillips parameter, ${L_{a}^{o}}$ and ${PL^{o}} \left( {PLZ^{o} } \right)$ represent the labor and wage rate (initial wage rate) respectively, and $\overline{{LS^{o} }}$,${\overline{{LW^{o} }}}$ and ER represent the labor endowment (exogenous), labor demand from the rest of world (exogenous), and exchange rate respectively. Therefore, in order to conduct simulation of the depopulation society in the Sect. 4 using this 4SCGE model, we will decrease $\overline{{LS^{o} }}$ as the decline in the population aged 20–64 group. In additional, we will change $\overline{{KS^{o} }}$ as the capital endowment in region o

$$ \mathop \sum \limits_{\alpha \in A} PK^{o} \, \cdot \,K_{a}^{o} + \overline{{KW^{o} }} \, \cdot \,ER = PK^{o} \, \cdot \,\overline{{KS^{o} }} , $$

(3)

where $K_{a}^{o}$ represents the capital demand by production sector a of region o, $PK^{o}$ represents the return to capital in region o,and $\overline{{KW^{o} }}$ represents the capital demand in region o from ROW in foreign currency. Then, we explain the structure of the following blocks in the 4SCGE model: the domestic production block in the case of Southern Kanto as an example, the savings-and-investment block, the trade block, and the regional government block.

The domestic production block has the nested structure of production shown in Fig. 6. Each production sector ${\text{a}}\left( {a \in A} \right)$ in region ${\text{o}}\left( {o \in S} \right)$ is assumed to produce $XD_{a}^{o}$ of 1 commodity ${\text{c}}\left( {c \in C} \right)$ and to maximize their profits and face a multi-level production function. In level 1 (A1), an industry in sector a constrained by the Leontief technology takes the production function using each intermediate input good $XC_{ca}^{o}$ aggregated from 20 commodities $\left( {c \ne t} \right)$ except transport $\left( { = t} \right)$ and the added value $KLT_{a}^{o}$. Since the producer price $PD_{a}^{o}$ of sector a in region o holds true for the “zero profit condition,” it follows that income equals production costs. In level 2 (A2) on the right, we arrive at the intermediate goods aggregated for the 20 commodities from the composite commodity according to the Armington assumption $XX_{ca}^{do}$ input from origin $d\left( {d \in R} \right)$ in region d to destination $\left( {o \in S} \right)$ in region o, under the constraint of constant returns to scale CES technology, and the o intra-regional composite commodity according to the Armington assumption $XX_{ca}^{oo}$. In addition, we arrive at $PXC_{ca}^{o}$, the price of the intermediate goods aggregated from sector a in region o, by the income definition, considering the zero profit condition for intermediate goods. As the 4SCGE model is inter-regional model, we will distinguish transport industry from other industries. Conversely, in Level 3(A3), the added-value portion consists of three levels. In Level 1 (A3-1), we derive $KLT_{a}^{o}$ from the labor ${ }L_{a}^{o}$ and the capital-transport bundle by the firms $\left( {KT_{a}^{o} } \right)$ from sector a of the destination region o under the constraint of constant returns-to-scale CES technology. Furthermore, in Level 2 (A3-2), we derive $KT_{a}^{o}$ from the capital ${ }K_{a}^{o}$ and transport industry dealing with the production factor $XC_{a}^{o}$ under the constraint of constant returns-to-scale CES technology. In Level 3 (A3-3), we derive $XC_{ta}^{o}$ by the same method of (A2). Then, each price level of $PKLT_{a}^{o}$ and $PKT_{a}^{o}$ holds true for the zero-profit condition. Since the return to capital $PK^{o}$ and wage rate $PL^{o}$ for the destination region o can move between industries within region.

Therefore, in order to conduct simulation of the TFP (productivity) in the Sect. 4 using this 4SCGE model, we will raise the efficiency parameters $\left( {aF2_{a}^{o} } \right)$ for each CES-type production function between labor $(L_{a}^{o} )$ and the capital-transport bundle $\left( {KT_{a}^{o} } \right)$ on the level (A3-1) in Fig. 6 as shown by Eqs. (4)–(6),

$$ KT_{a}^{o} = \gamma F2_{a}^{{o^{{\sigma F2_{a} }} }} \, \cdot \,PKT_{a}^{{o^{{ - \sigma F2_{a} }} }} \left( {\gamma F2_{a}^{{o^{{\sigma F2_{a} }} }} \, \cdot \,PKT_{a}^{{o^{{\left( {1 - \sigma F2_{a} } \right)}} }} + \left( {1 - \gamma F2_{a} } \right)^{{\sigma F2_{a} }} \, \cdot \,PL^{{o^{{\left( {1 - \sigma F2_{a} } \right)}} }} } \right)^{{\frac{{\sigma F2_{a} }}{{1 - \sigma F2_{a} }}}} \, \cdot \,\left( {\frac{{KLT_{a}^{o} }}{{aF2_{a}^{o} }}} \right), $$

(4)

$$ L_{a}^{o} = \left( {1 - \gamma F2_{a}^{o} } \right)^{{\sigma F2_{a} }} \, \cdot \,PL_{a}^{{o^{{ - \sigma F2_{a} }} }} \left( {\gamma F2_{a}^{{o^{{\sigma F2_{a} }} }} \, \cdot \,PKT_{a}^{{o^{{\left( {1 - \sigma F2_{a} } \right)}} }} + \left( {1 - \gamma F2_{a} } \right)^{{\sigma F2_{a} }} \, \cdot \,PL^{{o^{{\left( {1 - \sigma F2_{a} } \right)}} }} } \right)^{{\frac{{\sigma F2_{a} }}{{1 - \sigma F2_{a} }}}} \, \cdot \,\left( {\frac{{KLT_{a}^{o} }}{{aF2_{a}^{o} }}} \right), $$

(5)

$$ PKLT_{a}^{o} \, \cdot \,KLT_{a}^{o} = PL^{o} \, \cdot \,L_{a}^{o} + PKT_{a}^{o} \, \cdot \,KT_{a}^{o} , $$

(6)

where ${\upsigma }F2_{a}$ represents elasticity of substitution between labor and capital-transport bundle in the CES function of sector a and ${\upgamma }F2_{a}^{o}$ represents CES distribution parameter in the production function of sector a in region o.²⁹ In additional, in order to conduct simulation of change in the indirect tax in the Sect. 4 using this 4SCGE model, we will change in indirect tax $\left( {tp_{c}^{d} } \right)$ as shown by Eq. (7):

$$ \left( {1 + tp_{c}^{d} - sp_{c}^{d} } \right)FD_{c}^{d} \, \cdot \,XD_{c}^{d} = PE_{c}^{d} \, \cdot \,E_{c}^{d} + PDD_{c}^{d} \, \cdot \,XDD_{c}^{d} , $$

(7)

where $sp_{c}^{d}$ represents the production subsidies rate of production sector a On the other hand, the structure of production on the level (A1) is shown by Eqs. (8)–(10):

$$ KLT_{a}^{o} = b_{a}^{o} \, \cdot \,XD_{a}^{o} = \frac{{XD_{a}^{o} }}{{aFI_{a}^{o} }}, $$

(8)

$$ XC_{ca}^{o} = io_{ca}^{o} \, \cdot \,XD_{a}^{o} \;\;c \ne t, $$

(9)

$$ PD_{a}^{o} \, \cdot \,XD_{a}^{o} = PKLT_{a}^{o} \, \cdot \,KLT_{a}^{o} + \mathop \sum \limits_{c \in C,c \ne t} PXC_{ca}^{o} \, \cdot \,XC_{ca}^{o} . $$

(10)

The structure of production on the level (A2 and A3-3) in Fig. 6 is shown by Eqs. (11) and (12).

$$ XX_{ca}^{do} = \left[ {\frac{1}{{\beta_{{XX_{ca}^{do} }} }}\, \cdot \,\frac{{P_{c}^{d} }}{{PXC_{ca}^{o} }}} \right]^{{ - \sigma R_{c} }} \, \cdot \,XC_{ca}^{o} , $$

(11)

$$ PXC_{ca}^{o} \, \cdot \,XC_{ca}^{o} = \mathop \sum \limits_{d \in R} P_{c}^{d} \, \cdot \,XX_{ca}^{do} , $$

(12)

where ${\upsigma }R_{c}$ represents the inter-regional elasticity of substitution for intermediate goods c in the CES function and $\beta_{{XX_{ca}^{do} }}$ represents the shift parameter in the CES function of demand as intermediate input or production factor to production sector a in region o of composite commodity c being produced in region d.

Finally, the structure of production on the level (A3-2) is shown by Eqs. (13)–(15):

$$ K_{a}^{o} = \gamma F3_{a}^{{o}{\sigma F3_{a} }} vPK_{a}^{{o^{{ - \sigma F3_{a} }} }} \left( {\gamma F3_{a}^{{o^{{\sigma F3_{a} }} }} \, \cdot \,PK_{{}}^{{o^{{\left( {1 - \sigma F3_{a} } \right)}} }} + \left( {1 - \gamma F3_{a} } \right)^{{\sigma F3_{a} }} \, \cdot \,PXC_{ta}^{{o}{\left( {1 - \sigma F3_{a} } \right)}} } \right)^{{\frac{{\sigma F3_{a} }}{{1 - \sigma F3_{a} }}}} \, \cdot \,\left( {\frac{{KT_{a}^{o} }}{{aF3_{a}^{o} }}} \right), $$

(13)

$$ XC_{a}^{o} = \left( {1 - \gamma F3_{a}^{o} } \right)^{{\sigma F3_{a} }} \, \cdot \,PXC_{ta}^{{o^{{ - \sigma F3_{a} }} }} \left( {\gamma F3_{a}^{{o^{{\sigma F3_{a} }} }} \, \cdot \,PK_{{}}^{{o^{{\left( {1 - \sigma F3_{a} } \right)}} }} + \left( {1 - \gamma F3_{a} } \right)^{{\sigma F3_{a} }} \, \cdot \,PXC_{ta}^{{o}{\left( {1 - \sigma F3_{a} } \right)}} } \right)^{{\frac{{\sigma F3_{a} }}{{1 - \sigma F3_{a} }}}} \, \cdot \,\left( {\frac{{KT_{a}^{o} }}{{aF3_{a}^{o} }}} \right), $$

(14)

$$ PKT_{a}^{o} \, \cdot \,KT_{a}^{o} = PK^{o} \, \cdot \,K_{a}^{o} + PXC_{ta}^{o} \, \cdot \,XC_{ta}^{o} , $$

(15)

where ${\upsigma }F3_{a}$ represents the elasticity of substitution between capital and transport in the CES function of sector, ${\text{a}}F3_{a}^{o}$ represents the efficiency parameter in the production function of sector a in region o, and ${\upgamma }F3_{a}^{o}$ represents the CES distribution parameter in the production function of secr a in region o. In the household block, we have formulated the behavior maximizing the level of household utility $UH^{o}$ (Fig. 7). At level 1 (B1), households in the destination region o maximize the linear-homogeneous Cobb–Douglas utility function for the goods $HC_{c}^{o}$ aggregated under the budgetary constraints $CBUD^{o}$. In addition, at level 2 (B2), we derive the aggregated goods from the composite commodity according to the Armington assumption $XH_{c}^{do}$ imported from region d in origin region ${\text{d}} \in {\text{R}}$ to destination ${\text{o}} \in {\text{S}}$ in region ${\text{o}}$ under the constant returns to scale CES technology constraint and the intra-regional o composite commodity according to the Armington assumption $XH_{c}^{oo}$. In addition, we arrive at the price $PHC_{c}^{o}$ of the aggregated commodities c, by the income definition, taking account of the zero profit condition for such goods. Household income comprises employment income, capital income, social security benefits, property income, and receipts from other current transfers. In addition, the household budget $CBUD^{o}$ comprises payments of income tax from household income, household savings, social contributions, and payments from property income and other current transfers. Furthermore, household savings is calculated from household income, assuming a fixed propensity to save. The savings and investment block has the same structure as the household block. The 4SCGE model is closed to prior savings, and in terms of investment, an agent called a “bank” allots savings $S^{o}$ to investment demand $IC_{c}^{o}$ from 21 commodities in accordance with the linear-homogeneous Cobb–Douglas utility function. The savings as shown by Eq. (16) include the savings of household $SH^{o}$, company $SN^{o}$, regional government $SLG^{o}$, and central government $SCG^{o}$, in addition to income transfers $SDB^{o}$ to offset inter-regional current account balances and overseas savings $SF^{o}$ to offset a region’s external current account balances.³⁰ On the other hand, the 4SCGE model treats each region’s external current account deficit (foreign savings) as an exogenous variable, and we do not regard this as a problem because the exchange rate is deemed to be an endogenous variable. In addition, at level 2 (C2), we arrive at the aggregated commodities $IC_{c}^{o}$ from the composite commodity according to the Armington assumption $XI_{c}^{do}$ imported from region d in origin region $d \in R$ to region o destination $o \in S$ under the constant returns to scale CES technology constraint and the intra-regional o composite commodity according to the Armington assumption $XI_{c}^{oo}$. In addition, we arrive at $PCI_{c}^{o}$ the price of the aggregated commodities c, by the income definition, taking account of the zero profit condition for such commodities (Fig. 8):

$$ S^{o} = SH^{o} + SN^{o} + SLG^{o} + SCG^{o} + SDB^{o} + SF^{o} \, \cdot \,ER. $$

(16)

Although the trade sector includes exports and imports between each region and the foreign sector, trade also occurs through imports and exports among the four regions (Fig. 9). Specifically, the structure incorporated into the 4SCGE model allocates products produced in region for the domestic market and for export, with being derived by solving the problem of sales maximization under the constraint of the constant elasticity of transformation function. In addition, for the composite commodity according to the Armington assumption, which is the composite commodity for domestic supply comprising producer goods for the domestic market and imported goods, this part is derived by solving the constrained optimization problem by minimizing its total costs subject to the CES function constraint. The 4SCGE model fixes the foreign-currency denominated international price and, in the trade balance, it sets net overseas transfers of labor $\overline{{NLW^{o} }}$ and net overseas transfers of capital $\overline{{NLK^{o} }}$ as exogenous variables for foreign savings $SF^{o}$ in region o, whereas the sum of property and transfer incomes $BOP^{o}$ and the common exchange rate for the regions are set as endogenous variables. Thus, we must take the following point into consideration. The exchange rate that is changed by the trade balances of the Southern Kanto has an impact on the price for the composite commodity in the other three regions. Then, the current account between four regions as shown in Fig. 9 is given as the following inter-regional trade equations.

Here, we explain the relationship between regional and central governments. The central government itself does not engage in spending. Instead, its function is to reallocate the taxes it collects to the regional governments of the four regions, as well as to create savings by taking a fixed proportion of the tax revenue and allocating it to the savings sector of the four regions. Meanwhile, the regional governments in the four regions have budgets that contain the difference between the revenues generated from tax receipts and local allocation tax grants, etc. and the subsidies disbursed to each production sector. These budgets are then multiplied by a fixed ratio to create savings, and expenditures comprise social security benefits to the household sector and transfers to other institutional sectors and the like. Concerning the latter, we incorporated the following Eq. (17) in order to reflect an increasing aging population. That is, the allowance to the household sector from local government ($TEGH^{o}$ in region o) is composed of income compensation to the unemployed person and social security expenditures (exogenous ${ }\overline{{TEPS^{o} }}$) such as pension benefits that are tied to price changes.

$$ TEGH^{o} = trep^{o} \left( {PL^{o} \, \cdot \,UNEMP^{o} } \right) + PCINDEX^{o} \, \cdot \,\overline{{TEPS^{o} }} , $$

(17)

where ${trep}^{o}$ represents the replacement rate in region $o.$ Therefore, in order to conduct simulation of aging society in the Sect. 4 using this 4SCGE model, we will raise $\overline{{TEPS^{o} }}$ as the increase in the population aged 65 and over group. In the market equilibrium conditions block, equilibrium conditions for the 21 markets are given a set formula. In the system of equations we have described above, one of the equations becomes redundant due to Walras' law. We must therefore select one of the goods’ price as the Numéraire. In this case, the wage rate of Regions Other Than Kanto was selected and fixed. Finally, we estimated the function parameters for each block with a calibration method using the four-regional SAM data with 2005 as the benchmark year and referenced the values used in GTAP 9 for the elasticity of substitution for labor and capital in the production sector and the elasticity of substitution for the CES-type (Armington) function of the trade sector for estimating the function parameters requires that one of the parameters must depend on an external database. Furthermore, referencing previous studies, we set the inter-regional elasticity of substitution for the production sector, the inter-regional elasticity of substitution for the household and investment sectors, and the elasticity of substitution of the CET-type function for the trade sector. These are summarized in Table 12 (Table 13).

Table 12 Elasticity of substitution by type of production activity

Table 13 Setting efficiency parameter at 2005 and 2015