Assessments of ICT Policy Options: The Framework of Input–Output Table Linked with Intangible Knowledge Stock

Abstract

The 21st century marks the prosperity of cyber systems that drastically reshaped the social economy structure. Confronting the hyper-aging society with shrinking population in Japan, rapid development of ICT/IoT has contributed to social economic change nowadays while evaluating the effectiveness of policy options thus becomes an urgent task for stakeholders. A new type of social economic development with technology substitute of labor deserves more attention to accommodate technology improvement in the society. In order to capture the structural change, we develop a CGE model applying Japan’s input–output table from 1995 to 2011 with the disaggregation of 95 sectors. In this model, the capital stock has been distinguished into tangible and intangible capital to better interpret the R&D capital formation and its spillover effect for technology realizations. Based on the mechanism, a user-friendly application called SPIAS-e was developed for policy option evaluation. Finally, the chapter demonstrated simulation results of STI policy options scenarios on how new service platform with ICT would be affected by R&D investments and technological improvement.

Appendixes

1.1 Appendix 1: SPIAS-e Architecture

SPIAS-e is a Web-based system consisting of (1) economic model module by Java languages and (2) front-end/visualization module by Python 3.x Language. The data are stored in MySQL (compatible MariaDB) Database and running in Linux/Windows OS environment.

Initially, user could set policy parameter (a) R&D expenditure in six categories for both public and private sectors and (b) short-term and long-term sectoral productivity (classified in Table 3) through Web browser and other exogenous variables are stored in csv format. After initialization, front-end modules call economic model module in parallel with policy parameter.

In the simulation process, economic model module stores macro-data into MySQL database, and front-end module fetches yearly GDP data. After completion of economic simulation, economic model module returns simulated endogenous and exogenous variables (listed in Appendix 2) and those are stored into MySQL DB (Fig. 9).

Table 3 Sector classification

Table 4 Breakdown of value add

Fig. 9

Structure and illustration of MySQL DB

1.2 Appendix 2: List of Variables

Variable Subscripts

• a(1, …, 5): age range

  1: 15–19, 2: 20–34, 3: 35–5, 4: 51–64, 5: over 65.

• i, j (1, …, 93): Product

• o(1, …, 3): Category of intra-firm activity

  1: Main products, 2: Intra-firm ICT activity, 3: Intra-firm R&D activity.

Agriculture and fishery, mining, software, information management and service, Internet, other service, intra-firm ICT activity including two kinds of product, the public R&D activity without occupation classification

• s(M, F): M: male, F: female

• t (1, …, T): period

• θ(1, …,5): R&D classification of purpose.

  Public R&D activity is classified into five sectors as well as private R&D sector.

Exogenous Variables

• a ^DINVK _ij : j-sector, o = 1 (main products) nominal input share of i-capital goods

• a ^MINVK _ij : j-sector, o = 1 (main products) nominal input share of i-capital goods

• a ^DINVKITE _ij : j-sector, o = 2 (intra-firm ICT activity) nominal input share of i-capital goods

• a ^MINVKITE _ij : j-sector, o = 2 (intra-firm ICT activity) nominal input share of i-capital goods

• a ^DINVKRDE _ij : j-sector, o = 2 (intra-firm ICT activity) nominal input share of i-capital goods

• a ^MINVKRDE _ij : j-sector, o = 2 (intra-firm ICT activity) nominal input share of i-capital goods

• e: Exchange rate (¥/$)

• h^*: Regular working hour

• IM ^CIF _i : Import

• Kj^GNθt: Intangible capital stock of public R&D activity in t-period (classified in θ purpose)

• LC_j: Current compensation

• LC_SEYj: Self-employed income

• LC_FWYj: Income of family worker

• LC^R: Income of oversea employee

• N^t: Population

• PC^R: Net asset income from oversea

• P^BCTtBC ^t _T : Nominal household expenditure in t-period

• P ^Ex _i Ex_i: Export (final demand block)

• P^GCC^G: Government expenditure

• P^GDEPGDEP_T: Social cost depreciation

• P^GII^G: Public tangible capital formation (excluding R&D investment)

• P ^INVKG _j KG_j: Public R&D activity investment (Classified in θ purpose)

• P ^INVKGθ _j K_j: Public tangible capital formation R&D activity (Classified in θ purpose)

• P ^INVKNθ _j KNG_j: Public intangible capital formation R&D activity (Classified in θ purpose)

• P ^INVKNGt _θ KNG ^t _θ : Public nominal R&D investment in t-period (Classified in θ purpose)

• P ^INVKNEt _θ KNE ^t _θ : Private nominal R&D investment in t-period (Classified in θ purpose)

• P ^M _i M_i: Import (final demand block)

• P ^m _i : Price of intermediate import goods of i-sector

• P ^mt+1 _j : Price of import goods from j-sector

• P ^MIT _j : Price function of aggregate intermediate import goods of intra-firm ICT activity in j-sector

• P ^MRD _j : Price function of aggregate intermediate import goods of intra-firm R&D activity in j-sector

• P ^Z _T Z_T: Net capital stock

• r^*: Average interest rate in capital market

• SS^GP: Personal social insurance premium by age

• SS^PG: Personal social insurance payment by age

• T^M: Custom tax, tariff

• TRC^PG: Capital transfer from private to public

• TRC^RP: Capital transfer from oversea to individual

• TRE^GP: Net current transfer from public to individual

• TRE^GR: Net current transfer from public to oversea

• TRE^PR: Net current transfer from individual to oversea

• TRE^RG: Net capital transfer from oversea to public

• TRE^RP: Net capital transfer from oversea to individual

• W: World trade volume

• weight ^Et* _j : Cost share of employee wage on j-sector at the start of t-period

• weight ^SEFWt* _j : Cost share of self-employed and family worker wage on j-sector at the start of t-period

• X ^{* t+1} _j : Assumed demand of j-sector

• Y: Assumed gross output

• Z: Net capital stock (nominal)

• δ_j: Capital depreciation on main products of j-sector

• δ ^KIT _j : Capital depreciation on intra-firm ICT activity of j-sector

• δ ^KPE _j : Capital depreciation on intra-firm R&D activity of j-sector

• δ ^KN _j : Intangible Capital depreciation of j-sector

• τ^C: Consumption tax rate

• τ^I: Net indirect tax rate

• τ^K: Capital income tax rate (investment revenue tax rate) on tangible capital (main product)

• τ^KIT: Capital income tax rate (investment revenue tax rate) on tangible capital (intra-firm ICT activity)

• τ^KPE: Capital income tax rate (investment revenue tax rate) on tangible capital (intra-firm R&D activity)

• τ^KN: Capital income tax rate (investment revenue tax rate) on intangible capital (main product)

• τ^SKPIN: Capital income tax rate (investment revenue tax rate) on intangible capital (intra-firm ICT activity)

• τ^KNE: Capital income tax rate (investment revenue tax rate) on intangible capital (intra-firm R&D activity)

• τ^L: Personal income tax rate

• τ ^M _i : Custom tax, tariff rate

• τ^P: Fixed asset tax rate

• τ^PKN: Fixed asset tax rate on tangible capital (main products)

• τ^PIT: Fixed asset tax rate on tangible capital (intra-firm ICT activity)

• τ^PPE: Fixed asset tax rate on tangible capital (intra-firm R&D activity)

Endogenous Variables

• a ^d _ij : Input share of nominal domestic intermediate i-goods on j-sector at the beginning

• a ^m _ij : Input share of nominal import intermediate i-goods on j-sector at the beginning

• a ^DD _j : Input share of nominal domestic intermediate goods on j-sector at the beginning

• a ^MM _j : Input share of nominal import intermediate goods on j-sector at the beginning

• a ^d* _ij : Input coefficient of intermediate input on domestic goods

• a ^m* _ij : Input coefficient of intermediate input on import goods

• AN^t: Labor force

• AN ^t _as : Labor force by age (a = 1, …, 5), gender (Survey on employment structure¹)

• Labor force = Employed person + Job seeker (among unemployed person)

• Employed person = Full-time employee + Part-time employee

• Unemployed person = Work applicant (job seeker) + Non-work applicant

• BC_j: Household expenditure

• BS_j: Capital cost of j-sector

• C ^* _j : Long-term cost function of j-sector

• C ^L* _j : Total employment cost of j-sector

• DEP_j: Capital depreciation provision of j-sector

• DEP ^KITE _j : Tangible capital depreciation provision on intra-firm ICT activity of j-sector

• DEP ^KNITE _j : Intangible capital depreciation provision on intra-firm ICT activity of j-sector

• DEP ^KNRDE _j : Tangible capital depreciation provision on intra-firm R&D activity of j-sector

• DEP ^KRDE _j : Intangible capital depreciation provision on intra-firm R&D activity of j-sector

• DEP ^PK _j : Tangible capital depreciation provision of j-sector

• DIV_j: Dividends of j-sector

• ED ^t _jas : Demand for employment of j-sector by age, gender in t-year

• ES ^t _as : Supply of employment by age, gender in t-year²

• FW ^t _as : Family workers by age and gender in t-year

• g(·): Formula of technology improvement

• h_j: Working hours on j-sector

• h_j: Actual working hour

• INVK_j: Tangible capital formation on j-sector (real)

• INVKN_j: Intangible capital formation on j-sector (real)

• IY ^t _jSEFW : Self-employed, family worker income per person

• K_j: Tangible capital stock of main product of j-sector is endogenous at the start of time period as long-term selection. In the main product sectors, the tangible capital stock is endogenous. From tangible capital to capital service, the capital stock ratio is following the assumption of SK ^t _j = K ^t _j

• KC_j: Capital revenue

• KG_j: Sectoral public tangible capital stock, public R&D sectors (j = 82–86)

• KPI_j: Private R&D on tangible capital stock of j-sector

• KNG^θt, KNPI^θt: Intangible public and private capital stock on R&D sector (by θ purpose) at the start of t-period

• KNITE_j: Intangible capital stock of intra-firm ICT activity of j-sector

• KNRDE_j: Intangible capital stock of intra-firm R&D activity of j-sector

• KNPI_j: Private intangible capital stock of intra-firm R&D activity of j-sector

• L_j: Number of employment in j-sector

• LITE_j: Number of ICT-related employment in j-sector

• LRDE_j: Number of R&D-related employment in j-sector

• L ^* _j : Labor input of j-sector predetermined by long-term production block

• MITE: Aggregate of domestic and import intermediate goods of intra-firm ICT activity

• MNE: Aggregate of domestic and import intermediate goods of intra-firm R&D activity

• MR_j: Marginal short-term income of j-sector

• N_as: Population by age (a = 0, 1,…, 5) and gender (s = M, F)

• P: Current price level

• P^BCT: Price of household expenditure

• P ^C _T : Price function of aggregate consumption goods

• P ^d _j : Price of domestic goods of j-sector in current period

• P ^dc _i : Price after consumption tax

• P ^DMt _ij : Price of good and service determined by the equilibrium of short-term good and service market. In the assumption of competitive input–output table, the import price P ^mt _i of i-sector is set as exogenous variable.

• P^Et: Aggregate price of employed labor service by gender and age of current period. The price of labor service is determined by the technology choice of the next time period as well as the equilibrium of labor market; with the technology choice, the price of labor service is predetermined at the start of current period.

• P ^Et _j : Labor service price employed in j-sector at current period, predetermined endogenously. The price gaps exist in sectors such as agriculture, mining, manufacturing (main product, organizational, ICT activity, intra-firm R&D activity), energy, service (main product, organization, ICT activity, intra-firm R&D activity), public, private R&D.

• P ^Et _jas : Wage by age (a = 1,…, 5) and gender (s = M, F) of j-sector

• P ^INVK _j : Price of capital investment good of tangible capital formation of j-sector. Aggregated from the share weight of investment price (aggregate price of domestic and import good) in the matrix of tangible capital. The price of investment good of tangible capital formation of public R&D j-sector () and private R&D sector is also calculated according to share weight of tangible capital matrix, as well as determined by the short-term equilibrium of good and service market.

• P ^INVKIT _j : Price of capital investment good in tangible capital formation of intra-firm ICT activity of j-sector

• P ^INVKPE _j : Price of capital investment good in tangible capital formation of intra-firm R&D activity of j-sector

• P_j^INVKNE, P_j^INVKNGθt, P_j^INVKNPIt: Price of intangible capital investment good of price intra-firm R&D activity, public R&D sector (θ), private R&D sector (θ), determined by short-term equilibrium of goods and service market.

• P ^DIT _j : Aggregate price function of domestic intermediate goods of intra-firm ICT activity of j-sector

• P ^DRD _j : Aggregate price function of domestic intermediate goods of intra-firm R&D activity of j-sector

• P ^MIT _j : Aggregate price function of import intermediate goods of intra-firm ICT activity of j-sector

• P ^MRD _j : Aggregate price function of import intermediate goods of intra-firm R&D activity of j-sector

• P ^DMIT _j : Aggregate price function of intermediate input of intra-firm ICT activity of j-sector

• P ^DMRD _j : Aggregate price function of intermediate input of intra-firm R&D activity of j-sector

• P ^L _j : Price of labor service of j-sector

• P ^LIT _j : Price of labor service of intra-firm ICT activity of j-sector

• P ^LNG* _j : Price of labor service predetermined by long-term production block of j-sector

• P ^LRD _j : Price of labor service of intra-firm R&D activity of j-sector

• P ^mc _i : Import price after consumption tax

• P ^Mt _j : Price of intermediate good determined by the process of short-term equilibrium in goods and service market of j-sector in current period

• P ^Set _j : Average income per employer of j-sector in current period

• P ^Set _j : Average income per family worker of j-sector in current period

• P ^SEFWt* _j : Price of labor service per employer or family worker of j-sector in t-year (IY ^t _{jSEFW /} h^*)

• P ^SK _j : Price of tangible capital service of j-sector

• P ^SKt _j , P ^SKGθt _j , P ^SKPIθt _j : Price of tangible capital service of j-sector. The price is derived from the tangible capital investment price, function of rate of return/depreciation of capital. Among them, the price of tangible capital service of public R&D sector (θ) and private R&D sector (θ) is corresponded with special purpose R&D activity (θ).

• P ^SKIPI _j : Price of tangible capital service in private R&D of j-sector

• P ^SKIT _j : Price of tangible capital service of intra-firm ICT activity of j-sector

• P ^SKK _j : Price of tangible capital service input (SK_j+ SKPE_j) of j-sector

• P ^SKNE _j : Price of intangible capital service in intra-firm R&D of j-sector

• P ^SKNEt _θ , P ^SNGt, _θ P ^SKNPIt _θ : Price of intangible capital service of intra-firm R&D activity, public R&D sector (θ), and private R&D sector (θ). With the respect to the intangible capital stock in the different R&D activity, the capital service price is derived from the intangible capital investment price, function of rate of return/depreciation of capital.

• P ^SKNG _j : Price of intangible capital service in public R&D of j-sector

• P ^SKNPI _j : Price of intangible capital service in private R&D of j-sector

• P ^SKPE _j : Price of tangible capital service of intra-firm R&D activity of j-sector

• Q_j: Potential output of j-sector in the period

• r ^K _j : Rate of capital return on tangible capital (main products and organizational activity)

• r ^KIT _j : Rate of capital return on tangible capital (intra-firm ICT activity)

• r ^KNE _j : Rate of capital return on tangible capital (intra-firm R&D activity)

• r ^KPI _j : Rate of capital return on private R&D tangible capital

• r ^KNPI _j : Rate of capital return on private R&D intangible capital

• r ^KG _j : Rate of capital return on public R&D tangible capital

• r ^KNG _j : Rate of capital return on public R&D intangible capital

• r ^KN _j : Rate of capital return on intangible capital (main product and organizational activity)

• r ^SKPINN _j : Rate of capital return on intangible capital (intra-firm ICT activity)

• S^G: Public saving

• S^P: Private gross saving

• S^PN: Private net saving

• SE ^t _as : Number of employer by age and gender in t-year

• SK_j: Tangible capital service of j-sector

• SKG_j: Tangible capital service of public R&D of j-sector

• SKI_j: Tangible capital service of private R&D of j-sector

• SKK_j: Tangible capital service input of j-sector (SK_j+ SKPE_j)

• SKITE_j: Tangible capital service of intra-firm ICT activity of j-sector

• SKNE_j: Intangible capital service of intra-firm R&D activity of j-sector

• SKNITE_j: Intangible capital service of intra-firm ICT activity of j-sector

• SKNRDE_j: Intangible capital service of intra-firm R&D of j-sector

• SKPE_j: Tangible capital service of intra-firm R&D of j-sector

• SKNG_j: Intangible capital service of public R&D of j-sector

• T^C: Consumption tax revenue

• T^G: Gross tax revenue on public sector

• T^I: Net indirect tax revenue

• T^K: Capital income tax revenue

• T^L: Personal tax revenue

• T^P: Tax revenue on fixed asset

• v ^K _j : Cost share function on capital

• v ^L _j : Cost share function on labor

• v ^M _j : Cost share function on intermediate input

• v ^X _j : Cost share function on output

• X_j: Output of j-sector

• x ^DINVK _ij : Domestic capital investment in original product tangible capital formation of j-sector

• x ^MINVK _ij : Import capital investment in original product tangible capital formation of j-sector

• x ^DINVKIT _ij : Domestic capital investment in intra-firm ICT activity tangible capital formation of j-sector

• x ^MINVKIT _ij : Import capital investment in intra-firm ICT activity tangible capital formation of j-sector

• x ^DINVKPE _ij : Domestic capital investment in intra-firm R&D activity tangible capital formation of j-sector

• x ^MINVKPE _ij : Import capital investment in intra-firm R&D activity tangible capital formation of j-sector

• Y: Personal disposable income

• Y ^t _jFW : Income per person of family worker of j-sector at the start of t-year

• Y ^t _jSE : Income per person of employer of j-sector at the start of t-year

• YE ^t _j : Total employer income of j-sector in t-year

• YSEFW ^t _j : Income of employer and family workers of j-sector in t-year

• ΔBP^R: Current gap from oversea (nominal)

• ΔIS^G: Fiscal gap of government (nominal)

• ΔIS^P: Gap on national saving

• λ_ANas^t: Ratio labor force of age and gender over total labor force in t-year

• λ ^t _ANas = Labor force of age and gender (AN ^t _as )/Total labor force (AN^t)

• λ ^t _ESas : Ratio of employment by age and gender in t-year

• λ ^t _SEas : Ratio of employer by age and gender in t-year³

• λ ^t _SEas = Number of employer (SE ^t _as )/ labor force (AN ^t _as )

• λ ^t _FWas : Ratio of family workers by age and gender in t-year

• λ ^t _FWas = Family workers (FW ^t _as )/Total labor force (AN ^t _as )

  Supply of employment = Employed person + Job seeker

• μ ^t _ESas : Rate of employed person by age and gender (ES ^t) _as /Labor force by age and gender (AN ^t _as )

1.3 Appendix 3: Model Formula Structure

The formula structure of the model is derived as follows:

Goods and service demand market ( t -period)

j-sector domestic goods and production

$$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right]\left[ {\left( {\sum\limits_{{\left( {i \ne j} \right)}} {P_{i}^{d} a_{ij}^{d} } + \sum\limits_{i} {P_{i}^{m} a_{ij}^{m} } } \right)} \right. \\ & \quad + \left. {\left[ {L_{j} P_{j}^{L} P_{j}^{L0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} K_{j}^{bj} KNITE_{j}^{cj} KNRDE_{j}^{dj} KNG_{\theta }^{ej} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

(1)

• Intra-firm ICT activity

  $$\begin{aligned} & P_{j}^{d} \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right]\left[ {\left( {\sum\limits_{{\left( {i \ne j} \right)}} {P_{i}^{d} a_{ij}^{d} } + \sum\limits_{i} {P_{i}^{m} a_{ij}^{m} } } \right)} \right. \\ & \quad + \left. {\left[ {LITE_{j} P_{j}^{LITE} P_{j}^{LITE0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} KITE_{j}^{bj} KNITE_{j}^{cj} KNG_{{\left( {\theta = 1} \right)}}^{dj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (2)

• Intra-firm R&D activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right] \cdot \left[ {\sum\limits_{{\left( {i \ne j} \right)}} {\left( {P_{i}^{d} a_{ij}^{d} + P_{i}^{m} a_{ij}^{m} } \right)} } \right. \\ & \quad + \left. {\left[ {LRDE_{j} P_{j}^{LN} P_{j}^{LN0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} KRDE_{j}^{bj} KNRDE_{j}^{cj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (3)

• Private sector R&D activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right]\left[ {\sum\limits_{{\left( {i \ne j} \right)}} {\left( {P_{i}^{d} a_{ij}^{d} + P_{i}^{m} a_{ij}^{m} } \right)} } \right. \\ & \quad + \left. {\left[ {LRDE_{j} P_{j}^{L} P_{j}^{L0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} KPI_{j}^{bj} KNPI_{j}^{cj} KNRDE_{j}^{dj} KNG_{\theta }^{ej} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (4)

• Public R&D activity

  $$\begin{aligned} P_{j}^{d} & = C_{j} /X_{j} = \left[ {\left\{ {\left( {1 + \tau_{j}^{I} } \right)/\left( {1 - \left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} } \right)} \right\}} \right] \cdot \left[ {\sum\limits_{{\left( {i \ne j} \right)}} {P_{i}^{d} a_{ij}^{d} + \sum\limits_{i} {P_{i}^{m} a_{ij}^{m} } } } \right. \\ & \quad + \left. {\left( {LNG_{j} h_{j} P_{j}^{LNGt} P_{j}^{LNG0} + KG_{j}^{t} P_{j}^{SKGt} P_{j}^{SKG0} + KNG_{j}^{t} P_{j}^{SKNGt} P_{j}^{SKNG0} } \right)/X_{j} } \right] \\ \end{aligned}$$

  (5)

• ICT activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right]\left[ {\left( {\sum\limits_{{\left( {i \ne j} \right)}} {P_{i}^{d} a_{ij}^{d} + \sum\limits_{i} {P_{i}^{m} a_{ij}^{m} } } } \right)} \right. \\ & \quad + \left. {\left[ {L_{j} P_{j}^{L} P_{j}^{L0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} K_{j}^{bj} KNRDE_{j}^{cj} KNRDE_{j}^{dj} KNG_{\theta }^{dj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (6)

• ICT R&D activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right] \cdot \left[ {\sum\limits_{{\left( {i \ne j} \right)}} {\left( {P_{i}^{d} a_{ij}^{d} + P_{i}^{m} a_{ij}^{m} } \right)} } \right. \\ & \quad + \left[ {LRDE_{j} P_{j}^{LN} P_{j}^{LN0} } \right./\left. {\left\{ {\alpha_{j} \left( {a_{j} KRDE_{j}^{bj} KNRDE_{j}^{cj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} \\ \end{aligned}$$

  (7)

• Other product activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma _{j}^{s} } \right)\left( {1 + \tau _{j}^{I} } \right)} \right\}/\left\{ {\gamma _{j}^{s} \left( {\left( {1 + \tau _{j}^{I} } \right)a_{{jj}}^{d} - 1} \right)} \right\}} \right] \cdot \left[ {\left( {\sum\limits_{{\left( {i \ne j} \right)}} {P_{i}^{d} a_{{ij}}^{d} + \sum\limits_{i} {P_{i}^{m} a_{{ij}}^{m} } } } \right)} \right. \\ & \quad \left. { + \left[ {L_{j} P_{j}^{L} P_{j}^{{L0}} } \right./\left. {\left\{ {\alpha _{j} \left( {a_{j} K_{j}^{{bj}} KNRDE_{j}^{{cj}} KNG_{\theta }^{{dj}} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (8)

• Other R&D activity

  $$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} - \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\left\{ {\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right\}} \right] \cdot \left[ {\sum\limits_{{\left( {i \ne j} \right)}} {\left( {P_{i}^{d} a_{ij}^{d} + P_{i}^{m} a_{ij}^{m} } \right)} } \right. \\ & \quad + \left. {\left[ {{{LN_{j} P_{j}^{LN} P_{j}^{LN0} } \mathord{\left/ {\vphantom {{LN_{j} P_{j}^{LN} P_{j}^{LN0} } {\left\{ {\alpha_{j} \left( {a_{j} KRDE_{j}^{bj} KNRDE_{j}^{cj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}}}} \right. \kern-0pt} {\left\{ {\alpha_{j} \left( {a_{j} KRDE_{j}^{bj} KNRDE_{j}^{cj} h^{{*\left( {1 - \alpha j} \right)}} } \right)^{{\left( {1/\alpha j} \right)}} } \right\}}}} \right] \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

  (9)

Value-added block

Labor income

$$YE_{j}^{t} = E_{j}^{t} h_{j} P_{j}^{Et} P_{j}^{E0}$$

(10)

$$YSEFW_{j}^{t} = IY_{jSEFW}^{t} \left( {SE_{j}^{t} + FW_{j}^{t} } \right)$$

(11)

Capital income

$$BS_{j}^{t} + DEP_{j} = P_{j}^{d} X_{j} /\left( {1 + \tau_{j}^{I} } \right){-}\Sigma_{i} P^{d}_{i} a_{ij}^{d} X_{j} {-}\Sigma_{i} P_{i}^{m} a_{ij}^{d} X_{j} {-}BC_{j} - LC_{j}$$

(12)

$$P_{j}^{SK} = (1{-}\tau^{K} )r_{j}^{K} P_{j}^{INVKt - 1} + \delta_{j} P_{j}^{INVKt} {-}\left( {P_{j}^{INVKt} {-}P_{j}^{INVKt - 1} } \right) + \tau^{P} P_{j}^{INVKt - 1}$$

(13)

$$P_{j}^{SKITt} = \left( {1{-}\tau^{KIT} } \right)r_{j}^{K} P_{j}^{INVKITt - 1} + \delta_{j} P_{j}^{INVKITt} - \left( {P_{j}^{INVKITt} {-}P_{j}^{INVKITt - 1} } \right) + \tau^{PIT} P_{j}^{INVKITt - 1}$$

(14)

$$P_{j}^{SKPEt} = \left( {1{-}\tau^{KPE} } \right)r_{j}^{K} P_{j}^{INVKPEt - 1} + \delta_{j} P_{j}^{INVKPEt} - \left( {P_{j}^{INVKPEt} {-}P_{j}^{INVKPEt - 1} } \right) + \tau^{PPE} P_{j}^{INVKPEt - 1}$$

(15)

$$P_{j}^{SKN} = (1 \, {-}\tau^{K} )r_{j}^{KN} P_{j}^{INVKNt - 1} + \delta_{j}^{KN} P_{j}^{INVKNt} {-}\left( {P_{j}^{INVKNt} {-}P_{j}^{INVKNt - 1} } \right) + \tau^{P} P_{j}^{INVKNt - 1}$$

(16)

$$\begin{aligned} P_{j}^{SKPINt} & = \left( {1{-}\tau^{SKPIN} } \right)r_{j}^{SKPINN} P_{j}^{INVSKPISNt - 1} + \delta_{j}^{KN} P_{j}^{INVSKPINt} - \left( {P_{j}^{INVSKPINt} - P_{j}^{INVSKPINt} } \right) \\ & \quad + \tau^{SKPIN} P_{j}^{INVSKPINt - 1} \\ \end{aligned}$$

(17)

$$P_{j}^{SKNE} = \left( {1{-}\tau^{K} } \right)r_{j}^{KNE} P_{j}^{INVKNEt - 1} + \delta_{j}^{KNE} P_{j}^{INVKNEt} {-}\left( {P_{j}^{INVKNEt} {-}P_{j}^{INVKNEt - 1} } \right) + \tau^{P} P_{j}^{INVKNEt - 1}$$

(18)

$$\begin{aligned} BS_{j} & = SK_{j} P_{j}^{SK} + SKN_{j} P_{j}^{SKN} + SKNE_{j} P_{j}^{SKE} \\ & = K_{j} \left\{ {\left( {1{-}\tau^{K} } \right)r_{j}^{K} P_{j}^{INVKt - 1} + \delta_{j} P_{j}^{INVKt} {-}\left( {P_{j}^{INVKt} {-}P_{j}^{INVKt - 1} } \right) + \tau^{P} P_{j}^{INVKt - 1} } \right\} \\ & \quad + KN_{j} \left\{ {\left( {1{-}\tau^{K} } \right)r_{j}^{KN} P_{j}^{INVKNt - 1} + \delta_{j}^{KN} P_{j}^{INVKNt} {-}\left( {P_{j}^{INVKNt} {-}P_{j}^{INVKNt - 1} } \right) + \tau^{P} P_{j}^{INVKNt - 1} } \right\} \\ & \quad + KNE_{j} \left\{ {\left( {1{-}\tau^{K} } \right)r_{j}^{KNE} P_{j}^{INVKNEt - 1} + \delta_{j}^{KNE} P_{j}^{INVKNEt} {-}\left( {P_{j}^{INVKNEt} {-}P_{j}^{INVKNEt - 1} } \right) + \tau^{P} P_{j}^{INVKNEt} } \right\} \\ \end{aligned}$$

(19)

Sectoral capital depreciation

$$DEP_{j}^{INVK} = \delta_{j} P^{INVK} K_{j}$$

(20)

$$DEP_{j}^{INVKN} = \delta_{j} P^{INVKN} KN_{j}$$

(21)

$$DEP_{j}^{INVKNE} = \delta_{j} P^{INVKNE} KNE_{j}$$

(22)

$$DEP_{j}^{{INVK{\text{G}}}} = \delta_{j} P^{INVKG} KG_{j}$$

(23)

$$DEP_{j}^{INVKGN} = \delta_{j} P^{INVKGN} KGN_{j}$$

(24)

Sectoral dividends

$$DIV_{j} = \left( {1 - \tau^{K} } \right)BS_{j} - \tau^{P} P_{j}^{INVK} K_{j} - \tau^{P} P_{j}^{INVKN} KN_{j} - \tau^{P} P_{j}^{INVKNE} KNE_{j}$$

(25)

Individual disposable income

$$\begin{aligned} Y & = \left( {1 - \tau^{L} } \right)\Sigma_{j} \left( {LC_{j} + LC_{SEYj} + LC_{FWYj} } \right) + \left( {1 - \tau^{L} } \right)LC^{R} \\ & \quad + \Sigma_{j\varepsilon } DIV_{j} + \left( {1 - \tau^{P} } \right)PC^{R} + TRE^{GP} {-}TRE^{PR} + SS^{GP} {-}SS^{PG} + TRC^{RP} {-}TRC^{PG} \\ \end{aligned}$$

(26)

Gross saving and net saving

$$S^{P} = \left( {Y{-}TRC^{RP} + TRC^{PG} } \right) - P^{C} C$$

(27)

$$S^{PN} = S^{P} {-}\Sigma_{(j\varepsilon IND)} DEP_{j}^{P}$$

(28)

$$\begin{aligned} \Delta IS^{P} & = S^{P} - \left( {\sum\limits_{j} {P_{j}^{INVK} INVK_{j} } + \sum\limits_{j} {P_{j}^{INVKN} + INVKN_{j} } + \sum\limits_{j} {P_{j}^{INVKNE} INVKNE_{j} } } \right) \\ & \quad - Z + TRC^{RP} + TRC^{PG} = \Delta BP^{R} \Delta IS^{G} \\ \end{aligned}$$

(29)

Government block

$$T^{L} = \tau^{L} \left\{ {\sum\limits_{j} {\left( {LC_{j} + LC_{SEYj} + LC_{FWYj} } \right)} + LC^{R} } \right\}$$

(30)

$$T^{K} = \tau^{K} \sum\limits_{j} {KC_{j} }$$

(31)

$$T^{P} = \tau^{P} \left( {\sum\limits_{j} {P_{j}^{INVK} } K_{j} + PC^{R} } \right)$$

(32)

$$T^{I} = \sum\limits_{j} {\left\{ {\left( {\tau_{j}^{I} /\left( {1 + \tau_{j}^{I} } \right)P_{j}^{d} X_{j} } \right)} \right\}}$$

(33)

$$T^{C} = \left( {1 + \tau^{C} } \right)\sum\limits_{i} {P_{i}^{C} C_{i} }$$

(34)

$$T^{M} = \sum\limits_{i} {\tau_{i}^{M} IM_{i}^{CIF} }$$

(35)

$$T^{G} = T^{L} + T^{K} + T^{P} + T^{I} + T^{C} + T^{M}$$

(36)

$$S^{G} = T^{G} - TRE^{GP} - TRE^{GR} - P^{GC} C^{G} - SS^{GP} + SS^{PG}$$

(37)

$$\Delta IS^{G} = S^{G} + TRC^{PG} + TRC^{RG} - \left( {P^{GI} I^{G} + \sum\limits_{{j = 82{-}86}} {P_{j}^{INVK} } INVK_{j} + \sum\limits_{{j = 82{-}86}} {P_{j}^{INVKN} } INVKN_{j} } \right)$$

(38)

Product

$$X_{i} = \sum\limits_{j} {a_{ij}^{d} } X_{j} + BC_{T} + CK_{i} + GC_{T} + GDEP_{T}$$

(39)

$$\varvec{X} = \left[ {\varvec{I} - \varvec{A}_{\varvec{d}} } \right]^{ - 1} \varvec{F}_{\varvec{d}}$$

(40)

Product calculation

$$\begin{aligned} X_{i} & = \sum\limits_{j} {a_{ij}^{d} X_{j} } + BC_{T} + CK_{i} + GC_{T} + GDEP_{T} + INVKG_{i} + INVKGN_{i} \\ & \quad + INVK_{i} + INVKITE_{i} + INVKRDE_{i} + INVKPI_{i} + INVKN_{i} + INVKNITE_{i} \\ & \quad + INVKNRDE_{i} + INVKNPI_{i} + Z_{T} + EX_{i} + M_{i} \\ \end{aligned}$$

(41)

$$\varvec{X} = \left[ {\varvec{I} - \varvec{A}_{\varvec{d}} } \right]^{ - 1} \varvec{F}_{\varvec{d}}$$

(42)

Long-term product block

Price function of intermediate goods

$$\ln P_{j}^{DIT} = \Sigma_{i} a_{j}^{dIT} \ln P_{i}^{d}$$

(43)

$$\ln P_{j}^{DRD} = \, \Sigma_{i} a_{ij}^{dRD} \ln P_{i}^{d}$$

(44)

$$\ln P_{j}^{MIT} = \Sigma_{i} a_{ij}^{mIT} \ln P_{i}^{m}$$

(45)

$$\ln P_{j}^{MRD} = \Sigma_{i} a_{ij}^{mRD} \ln P_{i}^{m}$$

(46)

$$\ln P_{j}^{DMIT} = a_{j}^{DDIT} \ln P_{j}^{DIT} + a_{j}^{MMIT} \ln P_{j}^{MIT}$$

(47)

$$\ln P_{j}^{DMRD} = a_{j}^{DDRD} \ln P_{j}^{DRD} + a_{j}^{MMRD} \ln P_{j}^{MRD}$$

(48)

Price function of aggregate tangible capital and intangible investment goods

$$\ln P_{j}^{INVK} = \Sigma_{i} a_{i}^{DINVK} \ln P_{i}^{d} + \Sigma_{i} a_{ij}^{MINVK} \ln P_{i}^{m}$$

(49)

$$\ln P_{j}^{INVKIT} = \Sigma_{i} a_{i}^{DINVKIT} \ln P_{i}^{d} + \Sigma_{i} a_{ij}^{MINVKIT} \ln P_{i}^{m}$$

(50)

$$\ln P_{j}^{INVKPE} = \Sigma_{i} a_{i}^{DINVKPE} \ln P_{i}^{d} + \Sigma_{i} a_{ij}^{MINVKPE} \ln P_{i}^{m}$$

(51)

$$a_{ij}^{DINVK} = P_{i}^{d} x_{ij}^{DINVK} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVK} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVK} } \right)$$

(52)

$$a_{ij}^{MINVK} = P_{i}^{m} x_{ij}^{MINVK} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVK} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVK} } \right)$$

(53)

$$a_{ij}^{DINVKIT} = P_{i}^{d} x_{ij}^{DINVKIT} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVKIT} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVKIT} } \right)$$

(54)

$$a_{ij}^{MINVKIT} = P_{i}^{m} x_{ij}^{MINVKIT} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVKIT} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVKIT} } \right)$$

(55)

$$a_{ij}^{DINVKPE} = P_{i}^{d} x_{ij}^{DINVKPE} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVKPE} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVKPE} } \right)$$

(56)

$$a_{ij}^{MINVKPE} = P_{i}^{m} x_{ij}^{MINVKPE} /\left( {\Sigma_{i} P_{i}^{d} x_{ij}^{DINVKPE} + \Sigma_{i} P_{i}^{m} x_{ij}^{MINVKPE} } \right)$$

(57)

Price function of aggregate labor service

$$P_{j}^{Lt + 1} = F\left( {P_{j}^{L} ,P_{j}^{LNPE} ,P_{j}^{LNG} ,P_{j}^{LNPI} } \right)$$

(58)

Long-term cost function

$$\begin{aligned} & \ln {\text{C}}_{j}^{*ITE} \\ & = \alpha_{j}^{ITE0} + \sum\limits_{k} {\alpha_{j}^{ITEk} } \ln P_{j}^{k*} + \alpha_{j}^{ITEx} \ln X_{j}^{*} + \alpha_{j}^{ITEt} g\left( {KNG_{{j\left( {j = 83} \right)}}^{t} } \right) + \left( {1/2} \right)\sum\limits_{k} {\sum\limits_{l} {\ln \beta_{j}^{ITEkl} } } \ln P_{j}^{k*} \ln P_{j}^{l*} \\ & \quad + \sum\limits_{k} {\beta^{ITEkx} } \ln P_{j}^{k*} \ln X_{j}^{*} + \sum\limits_{k} {\beta_{j}^{ITEkt} } \ln P_{j}^{k*} g\left( {KNG_{{j\left( {j = 83} \right)}}^{t} ,P\text{-Index}\left( k \right)} \right) \\ \end{aligned}$$

(59)

$$\begin{aligned} & \ln {\text{C}}_{j}^{RDE*} \\ & = \alpha_{j}^{RDE0} + \sum\limits_{k} {\alpha_{j}^{RDEk} } { \ln }P_{j}^{k*} + \alpha_{j}^{RDEx} { \ln }X_{j}^{*} + \beta_{j}^{RDEt} g\left( {KNG_{j}^{t} } \right) + \left( {1/2} \right)\sum\limits_{k} {\sum\limits_{l} {{ \ln }\beta_{j}^{RDEkl} } } { \ln }P_{j}^{k*} { \ln }P_{j}^{l*} + \sum\limits_{k} {\beta^{RDEkx} } { \ln }P_{j}^{k*} { \ln }X_{j}^{*} \\ & + \sum\limits_{k} {\beta_{j}^{RDEkt} } { \ln }P_{j}^{k*} g\left( {KNG_{j}^{t} ,P\text{-Index}\left( k \right)} \right) \\ \end{aligned}$$

(60)

$$\ln {\text{C}}_{j}^{*} = \alpha_{j}^{0} + \sum\limits_{k} {\alpha_{j}^{k} } { \ln }P_{j}^{k*} + \alpha_{j}^{x} { \ln }X_{j}^{*} + \alpha_{j}^{t} g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right) + \left( {1/2} \right)\sum\limits_{k} {\sum\limits_{l} {{ \ln }\beta_{j}^{kl} } } { \ln }P_{j}^{k*} { \ln }P_{j}^{l*} + \sum\limits_{k} {\beta^{kx} } { \ln }P_{j}^{k*} { \ln }X_{j}^{*} + \sum\limits_{k} {\beta_{j}^{kt} } { \ln }P_{j}^{k*} g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right)$$

(61)

Function of technology improvement

$$g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right) = \mu_{j} (SKNG_{\theta }^{t} \text{ + }SKNE_{j}^{t} )/\{ 1 + \mu_{j} (SKNG_{\theta }^{t} + SKNE_{j}^{t} )\}$$

(62)

Share function

$$v_{j}^{K} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{k*} = a_{j}^{k} + \sum\limits_{i} {\beta_{j}^{ki} } \ln P_{j}^{i*} + \beta_{j}^{kX} \ln X_{j}^{*} + \beta_{j}^{kT} g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right)$$

(63)

$$v_{j}^{L} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{L*} = a_{j}^{L} + \sum\limits_{i} {\beta_{j}^{Li} } \ln P_{j}^{i*} + \beta_{j}^{LX} \ln X_{j}^{*} + \beta_{j}^{LT} g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right)$$

(64)

$$v_{j}^{M} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{M*} = a_{j}^{M} + \sum\limits_{i} {\beta_{j}^{Mi} } { \ln }P_{j}^{i} + \beta_{j}^{MX} { \ln }X_{j}^{*} + \beta_{j}^{kT} g\left( {SKNG_{\theta }^{t} ,SKNE_{j}^{t} } \right)\text{(}i = K,L,M\text{)}$$

(65)

$$v_{j}^{X} = \partial \,\ln C_{j}^{*} /\partial \,\ln \,X_{j}^{k*} = \alpha_{j}^{X} + \Sigma_{i} \beta_{j}^{kX} \ln P_{j}^{i} + \beta_{j}^{XX} \ln X_{j}^{*} + \beta_{j}^{XT} g\left( {K^{GNt + 1} } \right)$$

(66)

Output

$$K_{j}^{*} = v_{j}^{K} \left( {C_{j}^{*} /\left( {P_{j}^{K*} P_{j}^{K0} } \right)} \right)\left( {j = 1, \ldots ,n} \right)$$

(67)

$$L_{j}^{*} = v_{j}^{L} \left( {C_{j}^{*} /\left( {P_{j}^{L*} P_{j}^{L0} } \right)} \right)/h_{j}^{*} \left( {j = 1, \ldots ,n} \right)$$

(68)

$$a_{ij}^{d} = V_{ij}^{d} P_{j}^{d} /P_{i}^{d} \quad \left( {i,j = 1, \ldots ,n} \right)$$

(69)

$$a_{ij}^{m} = V_{ij}^{m} P_{j}^{d} /P_{i}^{m} \quad \left( {i,j = 1, \ldots ,n} \right)$$

(70)

Current rate of return

$$r_{j}^{K} = \left[ {\frac{{BS_{j} - \left\{ {\left\{ {\begin{array}{*{20}c} {K_{j} \left\{ {\delta_{j} P_{j}^{INVKt} - \left( {P_{j}^{INVKt} - P_{j}^{INVKt - 1} } \right) + \tau^{P} P^{INVKt - 1} } \right\}} \\ { + KRDE_{j} \left\{ {\delta_{j}^{KRDE} P_{j}^{INVKRDEt} - \left( {P_{j}^{INVKRDEt} - P_{j}^{INVKRDEt - 1} } \right) + \tau^{PKRDE} P^{INVKRDEt - 1} } \right\}} \\ { + KITE_{j} \left\{ {\delta_{j}^{KITE} P_{j}^{INVKITEt} - \left( {P_{j}^{INVKITEt} - P_{j}^{INVKITEt - 1} } \right) + \tau^{PKITE} P^{INVKITEt - 1} } \right\}} \\ { + KN_{j} \left\{ {\delta_{j}^{KN} P_{j}^{INVKNt} - \left( {P_{j}^{INVKNt} - P_{j}^{INVKNt - 1} } \right) + \tau^{PKN} P^{INVKNt - 1} } \right\}} \\ { + KNRDE_{j} \left\{ {\delta_{j}^{KNRDE} P_{j}^{INVKNRDEt} - \left( {P_{j}^{INVKNRDEt} - P_{j}^{INVKNRDEt - 1} } \right) + \tau^{PKNRDE} P^{INVKNRDEt - 1} } \right\}} \\ { + KNITE_{j} \left\{ {\delta_{j}^{KNITE} P_{j}^{INVKNITEt} - \left( {P_{j}^{INVKNITEt} - P_{j}^{INVKNITEt - 1} } \right) + \tau^{PKNITE} P^{INVKNITEt - 1} } \right\}} \\ \end{array} } \right\}} \right\}}}{{\begin{array}{*{20}c} {K_{j} \left( {1 - \tau^{K} } \right)P_{j}^{INVKt - 1} } \\ { + KRDE_{j} \left( {1 - \tau^{KRDE} } \right)P_{j}^{INVKRDEt - 1} } \\ { + KITE_{j} \left( {1 - \tau^{KITE} } \right)P_{j}^{INVKITEt - 1} } \\ { + KN_{j} \left( {1 - \tau^{KN} } \right)P_{j}^{INVKNt - 1} } \\ { + KNRDE_{j} \left( {1 - \tau^{KNRDE} } \right)P_{j}^{INVKRDEt - 1} } \\ { + KNITE_{j} \left( {1 - \tau^{KNITE} } \right)P_{j}^{INVKNITEt - 1} } \\ \end{array} }}} \right]$$

(71)

Expected rate of return of next period

$$r_{j}^{*K} = f\left( {r,r_{j}^{K} } \right)$$

(72)

Price function of aggregate capital service

$$PSK_{j}^{t} = F\left( {P_{j}^{SKt} \cdot P_{j}^{SKNPlt} } \right)$$

(73)

$$P_{j}^{SKt} = \left( {1 - \tau^{K} } \right)r_{j}^{K} P_{J}^{INVKt - 1} + \delta_{j} P_{j}^{INVKt} - \left( {P_{j}^{INVKt} - P_{j}^{INVKt - 1} } \right) + \tau^{P} P^{INVKt - 1}$$

(74)

$$P_{j}^{SKITEt} = \left( {1 - \tau^{KITE} } \right)r_{j}^{K} P_{J}^{INVKITEt - 1} + \delta_{j} P_{j}^{INVKITEt} - \left( {P_{j}^{INVKITEt} - P_{j}^{INVKITEt - 1} } \right) + \tau^{PITE} P^{INVKITEt - 1}$$

(75)

$$P_{j}^{SKRDEt} = \left( {1 - \tau^{KRDE} } \right)r_{j}^{KRDE} P_{J}^{INVKRDEt - 1} + \delta_{j} P_{j}^{INVKRDEt} - \left( {P_{j}^{INVKRDEt} - P_{j}^{INVKRDEt - 1} } \right) + \tau^{PRDE} P^{INVRDEt - 1}$$

(76)

$$P_{j}^{SKNt} = \left( {1 - \tau^{KN} } \right)r_{j}^{K} P_{J}^{INVKNt - 1} + \delta_{j} P_{j}^{INVKNt} - \left( {P_{j}^{INVKNt} - P_{j}^{INVKNt - 1} } \right) + \tau^{PKN} P^{INVKNt - 1}$$

(77)

$$P_{j}^{SKNITEt} = \left( {1 - \tau^{KNITE} } \right)r_{j}^{KNITE} P_{J}^{INVKNITEt - 1} + \delta_{j}^{KNITE} P_{j}^{INVKNITEt} - \left( {P_{j}^{INVKNITEt} - P_{j}^{INVKNITEt - 1} } \right) + \tau^{PKNITE} P^{INVKNITEt - 1}$$

(78)

$$P_{j}^{SKNRDEt} = \left( {1 - \tau^{KNRDE} } \right)r_{j}^{KNRDE} P_{J}^{INVKNRDEt - 1} + \delta_{j}^{KNRDE} P_{j}^{INVKNRDEt} - \left( {P_{j}^{INVKNRDEt} - P_{j}^{INVKNRDEt - 1} } \right) + \tau^{PSKNRDE} P^{INVSKNRDEt - 1}$$

(79)

Capital cost

$$\begin{aligned} BSj & = SKjPSKj + SKPEjPSKPEj + SKITjPSKITj + SKNEjPSKNEj \\ & = K_{j} \left\{ {(1{-}\tau^{K} )r_{j}^{K} P_{j}^{INVKt - 1} + \delta_{j} P_{j}^{INVKt} - \left( {P_{j}^{INVKt} {-}P_{j}^{INVKt - 1} } \right) + \tau^{P} P^{INVKt - 1} } \right\} \\ & \quad + KPE_{j} \left\{ {\left( {1{-}\tau^{KPE} } \right)r_{j}^{K} P_{j}^{INVKPEt - 1} + \delta_{j}^{KPE} P_{j}^{INVKPEt} - \left( {P_{j}^{INVKPEt} {-}P_{j}^{INVKPEt - 1} } \right) + \tau^{PKPE} P^{IKVKPEt - 1} } \right\} \\ & \quad + KIT_{j} \left\{ {\left( {1{-}\tau^{KIT} } \right)r_{j}^{K} P_{j}^{INVKITt - 1} + \delta_{j}^{KIT} P_{j}^{INVKITt} - \left( {P_{j}^{INVKITt} {-}P_{j}^{INVKITt - 1} } \right) + \tau^{PKIT} P^{IKVKITt - 1} } \right\} \\ & \quad + KNE_{j} \left\{ {\left( {1{-}\tau^{KNE} } \right)r_{j}^{K} P_{j}^{INVKNEt - 1} + \delta_{j}^{KNE} P_{j}^{INVKNEt} - \left( {P_{j}^{INVKNEt} {-}P_{j}^{INVKNEt - 1} + \tau^{PKNE} P^{INVKNEt - 1} } \right)} \right\} \\ \end{aligned}$$

(80)

Short-term supply of goods and service

j-sector product

$$\begin{aligned} C_{j} & = P_{j}^{d} X_{j} = \left( {1 + \tau_{j}^{I} } \right)\left\{ {\Sigma _{i} P_{i}^{d} a_{ij}^{d} X_{j} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} X_{j} + L_{j} h_{j} P_{j}^{Et} P_{j}^{E0} } \right. \\ & \quad \left. { + IY_{jSEFW}^{t} \text{(}SE_{j}^{t} + FW_{j}^{t} ) + \left( {K_{j}^{t} + KPE_{j}^{t} } \right)P_{j}^{SKKt} P_{j}^{SKK0} } \right\} \\ \end{aligned}$$

(81)

$$P_{j}^{d} X_{j} /P = \alpha_{j}^{s} Y + \beta_{j}^{s} W + \gamma_{j}^{s} \left( {P_{j}^{d} /P} \right) + \eta_{j}^{s}$$

(82)

$$MR_{j} = - \, P_{j}^{d} \left( {\gamma_{j}^{s} /\left( {X_{j} {-}\gamma_{j}^{s} } \right)} \right)$$

(83)

$$X_{j} = Q_{j} h_{j}^{*} \left( {h_{j} /h_{j}^{*} } \right)^{\alpha j}$$

(84)

$$Q_{j} = a_{j} \left( {K_{j} + KPE_{j} } \right)^{bj} KNE_{j}^{cj} KNG_{\theta }^{dj}$$

(85)

$$h_{j} = \left( {X_{j} /a_{j} \left( {K_{j} + KPE_{j} } \right)^{bj} KNE_{j}^{cj} KN_{\theta }^{dj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)}$$

(86)

$$\begin{aligned} P_{j}^{d} & = \left[ {\left\{ {\left( {X_{j} {-}\gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right] \cdot \left[ {\left( {\Sigma _{(i \ne j)} P_{i}^{d} a_{ij}^{d} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} } \right)} \right. \\ & \quad + \{ L_{j} P^{L}_{j} P^{L0}_{j} /\left\{ {\alpha_{j} \left( {a_{j} \left( {K_{j} + KPE_{j} } \right)^{bj} KNE_{j}^{cj} KN_{\theta }^{dj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)} } \right\} \cdot \left. {X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

(87)

Intra-firm ICT activity

$$C_{j} = P_{j}^{d} X_{j} = \left( {1 \, + \tau_{j}^{I} } \right)\{\Sigma _{i} P_{i}^{d} a_{ij}^{d} X_{j} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} X_{j} + (LIT_{j} h_{j} P_{j}^{LITt} P_{j}^{LIT0} + KIT_{j}^{t} P_{j}^{SKITt} P_{j}^{SKIT0} \}$$

(88)

$$P_{j}^{d} X_{j} /P = \alpha_{j}^{s} Y + \beta_{j}^{s} W + \gamma_{j}^{s} \left( {P_{j}^{d} /P} \right) + \eta_{j}^{s}$$

(89)

$$MR_{j} = - \, P_{j}^{d} \left( {\gamma_{j}^{s} /\left( {X_{j} {-}\gamma_{j}^{s} } \right)} \right)$$

(90)

$$X_{j} = Q_{j} h_{j}^{*} \left( {h_{j} /h_{j}^{*} } \right)^{\alpha j}$$

(91)

$$Q_{j} = a_{j} KIT^{bj} KNG_{(\theta = 1)}^{dj}$$

(92)

$$h_{j} = \left( { \, X_{j} /a_{j} KIT_{j}^{bj} KNG_{j}^{cj} \,_{(\theta = 1)}^{dj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)}$$

(93)

$$\begin{aligned} P^{d}_{j} & = \left[ {\left\{ {\left( {X_{j} {-} \, \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right] \cdot \left[ {\left( {\Sigma _{(i \ne j)} P_{i}^{d} a_{jj}^{d} +\Sigma _{i} P_{i}^{m} a_{jj}^{m} } \right)} \right. \\ & \left. {\quad + \{ LIT_{j} P_{j}^{LIT} P_{j}^{LIT0} /\left\{ {\alpha_{j} \left( {a_{j} KIT_{j}^{bj} KNG_{j(\theta = 1)}^{cj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)} } \right\} \cdot X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

(94)

Intra-firm R&D activity

$$\begin{aligned} C_{j} & = P_{j}^{d} X_{j} = \left( {1 + \tau_{j}^{I} } \right)\left\{ {\Sigma _{i} P_{i}^{d} a_{ij}^{d} X_{j} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} X_{j} + LN_{j} h_{j} P_{j}^{Et} P_{j}^{E0} } \right. \\ & \quad \left. { + \, IY_{jSEFW}^{t} \left( {SE_{j}^{t} + FW_{j}^{t} } \right) + KPE_{j}^{t} P_{j}^{SKPEt} P_{j}^{SKPE0} + KNE_{j}^{t} P_{j}^{SKNEt} P_{j}^{SKNE0} } \right\} \\ \end{aligned}$$

(95)

$$X_{j} = Q_{j} h_{j}^{*} \left( {h_{j} /h_{j}^{*} } \right)^{\alpha j}$$

(96)

$$Q_{j} = a_{j} KNE_{j}^{bj}$$

(97)

$$h_{j} = \left( {X_{j} /a_{j} KNE_{j}^{bj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)}$$

(98)

$$\begin{aligned} & P_{j}^{d} = \left[ {\left\{ {\left( {X_{j} {-} \, \gamma_{j}^{s} } \right)\left( {1 + \tau_{j}^{I} } \right)} \right\}/\gamma_{j}^{s} \left( {\left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} - 1} \right)} \right. \\ & \quad \left. { \cdot \left[ {\Sigma_{(i \ne j)} \left( {P_{i}^{d} a_{ij}^{d} + P_{i}^{m} a_{ij}^{m} } \right) + \left\{ {LN_{j} P_{j}^{LN} P_{j}^{LN0} /\alpha_{j} \left( {a_{j} KNE_{j}^{b} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)} } \right\}} \right]X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} a} \right] \\ \end{aligned}$$

(99)

Private R&D activity (STI category)

$$\begin{aligned} C_{j} & = P_{j}^{d} X_{j} = \left( {1 + \tau_{j}^{I} } \right)\left\{ {\Sigma _{i} P_{i}^{d} a_{ij}^{d} X_{j} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} X_{j} + E_{j} h_{j} P_{j}^{Et} P_{j}^{E0} } \right. \\ & \quad + \, \left. {IY_{jSEFW}^{t} \left( {SE_{j}^{t} + FW_{j}^{t} } \right) + KPI_{j}^{t} P_{j}^{SKPIt} P_{j}^{SKPI0} + KNPI_{j}^{t} P_{j}^{SKNPIt} P_{j}^{SKNPI0} } \right\} \\ \end{aligned}$$

(100)

$$X_{j} = Q_{j} h_{j}^{*} \left( {h_{j} /h_{j}^{*} } \right)^{\alpha j}$$

(101)

$$Q_{j} = a_{j} KPI_{j}^{bj} KNPI_{j}^{dj}$$

(102)

$$h_{j} = \left( {X_{j} /a_{j} KPI_{j}^{bj} KNPI_{j}^{dj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)}$$

(103)

$$\begin{aligned} & P_{j}^{d} = \left[ {\left\{ {\left( {X_{j} {-} \, \gamma_{j}^{s} } \right)\left( {1 + \tau^{I}_{j} } \right)} \right\}/\gamma^{s}_{j} \left( {\left( {1 + \tau^{I}_{j} } \right)a^{d}_{jj} - 1} \right)} \right. \\ & \quad \cdot \left. {\left[ {_{(i \ne j)} \left( {P^{d}_{i} a^{d}_{ij} + P^{m}_{i} a^{m}_{ij} } \right) \, + \, \left\{ {E_{j} P^{E}_{j} P^{E0}_{j} /\alpha_{j} \left( {a_{j} KPI_{j}^{bj} KNPI_{j}^{dj} h^{*(1 - \alpha j)} } \right)^{(1/\alpha j)} } \right\}} \right] \, X_{j}^{{\left( {1 - \alpha j} \right)/\alpha j}} } \right] \\ \end{aligned}$$

(104)

Public R&D sector (STI category)

$$\begin{aligned} C_{j} & = P_{j}^{d} X_{j} = \left( {1 + \tau_{j}^{I} } \right)\{\Sigma _{i} P_{i}^{d} a_{ij}^{d} X_{j} +\Sigma _{i} P_{i}^{m} a_{ij}^{m} X_{j} \\ & \quad + \, \left( {LN_{j}^{G} h_{j} P_{j}^{LNGt} P_{j}^{LNG0} + KG_{j}^{t} P_{j}^{SKGt} P_{j}^{SKG0} + KNG_{j}^{t} P_{j}^{SKNGt} P_{j}^{SKNG0} } \right) \\ \end{aligned}$$

(105)

$$\begin{aligned} P_{j}^{d} & = C_{j} /X_{j} = \left\{ {\left( {1 + \tau_{j}^{I} } \right)/\left( {1 - \left( {1 + \tau_{j}^{I} } \right)a_{jj}^{d} } \right)} \right\} \cdot \left[ {\Sigma_{(i \ne j)} P_{i}^{d} a_{ij}^{d} + \Sigma_{i} P_{i}^{m} a_{ij}^{m} + (LN_{j}^{G} h_{j} P_{j}^{LNGt} P_{j}^{LNG0} + } \right. \, \\ & \quad \left. { + KG_{j}^{t} P_{j}^{SKGt} P_{j}^{SKG0} + KNG_{j}^{t} P_{j}^{SKNGt} P_{j}^{SKNG0} )/X_{j} } \right] \\ \end{aligned}$$

(106)

Labor block

Labor force

$$AN_{as}^{t + 1} =\uplambda_{ANas}^{t + 1} \times N_{as}^{t + 1}$$

(107)

$$SE_{as}^{t + 1} =\uplambda_{SEas}^{t + 1} \times AN_{as}^{t + 1}$$

(108)

$$FW_{as}^{t + 1} = \lambda_{FWeas}^{t + 1} \times AN_{as}^{t + 1}$$

(109)

$$ES_{as}^{t + 1} = \left( {1 - \lambda_{SEas}^{t + 1} - \lambda_{FWeas}^{t + 1} } \right) \times AN_{as}^{t + 1}$$

(110)

$$ES_{as}^{t} =\uplambda_{ESas}^{t} \times ES_{as}^{t} (a = 1, \ldots ,5),\left( {s = M,F} \right){\text{ while }}\lambda_{ESas}^{t} = 1 - \lambda_{SEas}^{t} - \lambda_{FWeas}^{t}$$

(111)

Price of labor service

$$P^{Et} =\Sigma _{j}\Sigma _{a}\Sigma _{s} {\text{weight}}_{jas}^{t} P_{jas}^{Et}$$

(112)

$${\text{weight}}_{jas}^{t} = P_{jas}^{Et} ED_{jas}^{t} /\Sigma _{j}\Sigma _{a}\Sigma _{s} P_{jas}^{Et} ED_{jas}^{t}$$

(113)

$$P_{j}^{SEFWt*} = IY_{jSEFW}^{t} /h^{*} = F\left( {P^{Et} *} \right)$$

(114)

Labor wage

$$\begin{aligned} \ln C_{j}^{*} & = \alpha_{j}^{0} + \Sigma_{k} \alpha_{j}^{k} \ln P_{j}^{k*} + \alpha_{j}^{x} \ln X_{j}^{*} + \alpha_{j}^{t} g\left( {K_{j}^{GNt + 1} } \right) + \left( {1/2} \right)\Sigma_{k} \Sigma_{l} \ln \beta_{j}^{kl} \ln P_{j}^{k*} \ln P_{j}^{l*} \\ & \quad + \Sigma_{k} \ln P_{j}^{k*} \ln X_{j}^{*} + \Sigma_{k} \beta_{j}^{kt} \ln P_{j}^{k*} g(K^{GNt + 1} ) \\ \end{aligned}$$

(115)

$$v_{j}^{L} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{Lt*} = \alpha_{j}^{L} + \Sigma_{l} \beta_{j}^{Ll} \ln P_{j}^{l*} + \beta_{j}^{LX} \ln X*_{j} + \beta_{j}^{Lx} g(K^{GNt + 1} )$$

(116)

$$P_{j}^{Lt*} = weight_{j}^{Et*} P_{j}^{Et*} + weight_{j}^{SEFEt*} P_{j}^{SEFWt*}$$

(117)

$$C_{j}^{L*} = v_{j}^{L} \times C_{j}^{*}$$

(118)

Wage gap of labor service by gender, age, and occupation

$$P_{jaso}^{Et + 1*} = \theta_{Jaso}^{Et + 1*} P^{Et*}$$

(119)

Determinant of wage and employment level in the next period

$$v_{j}^{L} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{L*} = \alpha_{j}^{L} + \Sigma_{i} \beta_{j}^{Li} \ln P_{j}^{i} + \beta_{j}^{LX} \ln X_{j}^{*} + \beta_{j}^{LT} g\left( {SK^{GNt + 1} } \right)$$

(120)

$$P_{j}^{Lt + 1*} = P_{j}^{Lt}$$

(121)

$$P_{j}^{Et + 1*} = P_{j}^{Et}$$

(122)

$$P_{j}^{SEFWt + 1*} = P_{j}^{SEFWt}$$

(123)

$$P_{j}^{SKt*} = P_{j}^{SKt\blacktriangle }$$

(124)

$$P_{j}^{DMt*} = P_{j}^{DMt\blacktriangle }$$

(125)

$$ED_{jas}^{t + 1*} = v_{jas}^{L*} \times Y_{jE}^{*t + 1} /(P_{jas}^{Et + 1*} \cdot h^{*} )$$

(126)

Formula of occupation and industry

$$\begin{aligned} \ln C_{j}^{*} & = \alpha_{j}^{0} + \Sigma_{k} \alpha_{j}^{k} \ln P_{j}^{k*} + \alpha_{j}^{x} \ln X_{j}^{*} + \alpha_{j}^{t} g\left( {K_{j}^{GNt + 1} } \right) + \left( {1/2} \right)\Sigma_{k} \Sigma_{l} \ln \beta_{j}^{kl} \ln P_{j}^{k*} \ln P_{j}^{l*} \\ & \quad + \Sigma_{k} \ln P_{j}^{k*} \ln X_{j}^{*} + \Sigma_{k} \beta_{j}^{kt} \ln P_{j}^{k*} g\left( {K^{GNt + 1} } \right) \\ \end{aligned}$$

(127)

$$P_{j}^{SKt*} = \Sigma_{o} weight_{j}^{ot} P_{j}^{oSKt}$$

(128)

$${\text{weight}}_{j}^{ot} = P_{j}^{oSKt} SK_{j}^{ot} /\Sigma_{o} P_{j}^{oSKt} SK_{j}^{ot}$$

(129)

$$P_{j}^{SKNt*} = \Sigma_{o} {\text{weight}}_{j}^{ot} P_{j}^{oSKNt}$$

(130)

$${\text{weight}}_{j}^{ot} = P_{j}^{oSKNt} SKN_{j}^{oNt} /\Sigma_{o} P_{j}^{oSKNt} SKN_{j}^{oNt}$$

(131)

$$P_{j}^{Mt} = \Sigma_{o} {\text{weight}}_{j}^{ot} P_{j}^{oMt*}$$

(132)

$${\text{weight}}_{j}^{ot} = P_{j}^{oM*} M_{j}^{oMt} /\Sigma_{o} P_{j}^{oM*} M_{j}^{oMt}$$

(133)

$$P_{j}^{Lt*} = \Sigma_{o} {\text{weight}}_{j}^{ot} P_{j}^{oLt*}$$

(134)

$${\text{weight}}_{j}^{ot} = P_{j}^{oL*} L_{j}^{oLt} /\Sigma_{o} P_{j}^{oLt*} L_{j}^{oLt}$$

(135)

$$v_{j}^{L} = \partial \,\ln C_{j}^{*} /\partial \,\ln P_{j}^{Lt*} = \alpha_{j}^{L} + \Sigma_{l} \beta_{j}^{Ll} \ln P_{j}^{l*} + \beta_{j}^{LX} \ln X*_{j} + \, \beta_{j}^{Lx} g\left( {K^{GNt + 1} } \right)$$

(136)

$$ED_{as}^{t + 1*} = \Sigma_{j} ED_{jas}^{t + 1*}$$

(137)

Optimal capital stock in t  + 1 period

$$INVK_{j} = K_{j}^{*} - \left( {1 - \delta_{j}^{K} } \right)K_{j}$$

(138)

$$INVKITE_{j} = KITE_{j}^{*} - \left( {1 - \delta^{KITE} } \right)KITE_{j}$$

(139)

$$INVKRDE_{j} = KRDE_{j}^{*} - \left( {1 - \delta^{KRDE} } \right)KRDE_{j}$$

(140)

$$INVKPI_{j} = KPI_{j}^{*} - \left( {1 - \delta_{j}^{KPI} } \right)KPI_{j}$$

(141)

$$INVKN_{j} = KN_{j}^{*} - \left( {1 - \delta_{j}^{KN} } \right)KN_{j}$$

(142)

$$INVKNITE_{j} = KNITE_{j}^{*} - \left( {1 - \delta^{KNITE} } \right)KNITE_{j}$$

(143)

$$INVKNRDE_{j} = KNRDE_{j}^{*} - \left( {1 - \delta^{KNRDE} } \right)KNRDE_{j}$$

(144)

$$INVKNPI_{j} = KNPI_{j}^{*} - \left( {1 - \delta_{j}^{KNPI} } \right)KNPI_{j}$$

(145)

Investment demand

$$INVK_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVK} P_{j}^{INVK} INVK_{j} }}{{P_{i}^{d} }}$$

(146)

$$INVKITE_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKITE} P_{j}^{INVKITE} INVKITE_{j} }}{{P_{i}^{d} }}$$

(147)

$$INVKRDE_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKRDE} P_{j}^{INVKRDE} INVKRDE_{j} }}{{P_{i}^{d} }}$$

(148)

$$INVKPI_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKPI} P_{j}^{INVKPI} INVKPI_{j} }}{{P_{i}^{d} }}$$

(149)

$$INVKN_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKN} P_{j}^{INVKN} INVKN_{j} }}{{P_{i}^{d} }}$$

(150)

$$INVKNITE_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKNITE} P_{j}^{INVKNITE} INVKNITE_{j} }}{{P_{i}^{d} }}$$

(151)

$$INVKNRDE_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKNRDE} P_{j}^{INVKNRDE} INVKNRDE_{j} }}{{P_{i}^{d} }}$$

(152)

$$INVKNPI_{i} = \frac{{\mathop \sum \nolimits_{j \in IND} \omega_{ij}^{INVKNPI} P_{j}^{INVKNPI} INVKNPI_{j} }}{{P_{i}^{d} }}$$

(153)

Foreign block

$$\Delta IS^{R} = \Sigma_{(\varepsilon \,IND)} P_{i}^{d} Ex_{i} {-}\Sigma_{(I\,\varepsilon \,IND)} \left( {1 - \tau_{i}^{M} } \right)IM_{i}^{CIF} + LC^{R} + PC^{R} {-}TRE^{GR} {-}TRE^{PR}$$

(154)

$$\Delta B^{R} = \Delta IS^{R} + TRC^{RC} + TRC^{RP}$$

(155)

Final demand block

$$P_{i}^{dc} = (1 + \tau^{C} )P_{i}^{d}$$

(156)

$$P_{i}^{mc} = (1 + \tau^{C} )P_{i}^{m}$$

(157)

$$\ln P_{T}^{C} = \Sigma_{i} \alpha_{i}^{dC} \ln P_{i}^{dc} + \Sigma_{i} \alpha_{i}^{mC} \ln P_{i}^{mc}$$

(158)

$$C_{T} = \alpha_{c} + \beta_{c} (Y/P_{T}^{C} )$$

(159)

$$\begin{aligned} F^{D} & = BC^{T} + C^{T} + GC^{T} + GDEP^{T} + INVKG^{T} + INVK^{T} \\ & \quad + INVKGN^{T } + INVKVN^{T} + INVKNE^{T} + Z^{T} \\ \end{aligned}$$

(160)

$$X^{D} = \left( {I{-}A + M^{D} } \right)^{ - 1} (F^{D} + E^{T} )$$

(161)