6. Appendix¶
6.1. NTA Variables in MicroWELT:¶
- Private Consumption Education (CFE)
- Private Consumption Health (CFH)
- Private Consumption other than Education and Health (CFX)
- Public Consumption Education (CGE)
- Public Consumption Health (CGH)
- Public Consumption other than Education and Health (CGX)
- Public Transfers Pensions, Inflows (TGSOAI)
- Public Transfers Other Cash Inflows (TGXCI)
- Public Transfers Other In-Kind Inflows (TGXII)
- Public Transfers Education Inflows (TGEI)
- Public Transfers Health Inflows (TGHI)
- Public Transfers Outflows (TGO)
- Net Interhousehold Transfers (TFB)
- Net Intrahousehold Transfers (TFW)
- Private Saving (SF)
- Public Saving (SG)
- Labor Income (LY)
- Private Asset Income (YAF)
- Public Asset Income (YAG)
6.2. Calculation of the Support Ratio and the Impact Index for a closed economy:¶
Variables:
- yl(x) Average labor income age x
- yk(x) Average capital income age x
- P(x) Population age x
- i(x) Average savings age x
- s(x) Saving rate age x - constant
- c(x) Average Consumption age x (reference values for calculation of N) - reference
- L Labor
- K Capital
- I Saving
- S Saving rate
- C Consumption
- r Interest rate
- w Wage
- Yl Labor Income
- YK Capital Income
- Y Total Income Yl+Yk
- α Alpha – constant
- N Effective Consumers (population-weighted base-year consumption)
- l(x) Average labor age x – constant
- k(x) Average capital age x – constant
Cobb Douglas production function:
- Y = L^α K^(1- α)
- Y = wL + rK
- w = αY / L
- r = (1- α) Y / K
- Yl = wL = αY
- Yk = rK = (1- α)Y
Known:
- yl(x) NTA data of reference year
- yk(x) NTA data of reference year
- i(x) NTA data of reference year
- c(x) NTA data of reference year
- P(x) NTA data of reference year
- r parameter for reference year (used also to estimate stock from capital income flow)
Calculated for initial year:
- Yl = ∑ yl(x) * P(x)
- Yk = ∑ yk(x) * P(x)
- Y = Yl + Yk
- α = Yl / Y
- K = Yk / r
- L = ( Y / K^(1- α))^(1/α)
- w = Yl / L
- s(x) = i(x) / (yl(x) + ykx))
- l(x) = yl (x) / w
- k(x) = yk (x) / r
- N = ∑ cl(x) * P(x)
Simulation: calculate for an updated population by age P(x)
- L = ∑ l(x)* P(x)
- K = ∑ k(x)* P(x)
- Y = L^α K^(1- α)
- Yl = αY
- YK = (1- α)Y
- w = αY / L
- r = (1- α) Y / K
- N = ∑ c(x) * P(x)
- yl(x) = w * l(x)
- yk(x) = r * k(x)
- C = ∑ (1-s(x)) * (yl(x) + yk(x) ) * P(x)
Indices
- SR = L / N Support Ratio
- IMP = C / N Impact Index