Key sector analysis for a subnational region with leakages

Abstract

Key sector analyses have a long and rich history. However, almost all the previous analyses were conducted only within an input–output (IO) framework for a national economy. The present study (1) performs the analysis for a subnational (or regional) economy suffering severe leakages of industries’ revenues due to a large amount of imports and a large fraction of factor income earned by non-residents, and (2) extends the previous IO-based analyses to an analysis within a social accounting matrix (SAM) model and, further, to a multi-regional SAM (MRSAM) model. Comparing the results from the three alternative models shows that the key sectors identified with the alternative models are considerably different. This finding points to the necessity of using SAM-based models for an accurate key sector analysis and offers valuable implications for regional policymakers whose main interest is identifying the industries that they target for the economic development of their regions.

Appendices

Appendix 1

See Tables 4, 5 and 6.

Table 4 Industry aggregation scheme for Alaska SAM model

Table 5 Social accounting matrix for Alaska

Table 6 Simplified schematic representation of a three-region MRSAM

Appendix 2: Detailed descriptions of the structures of SAM and MRSAM models

• 1. SAM model

The SAM model in Eq. (4) can be expressed alternatively as:

$$ \left[ {\begin{array}{*{20}c} Q \\ C \\ V \\ {\text{IBT}} \\ H \\ {\text{SG}} \\ \end{array} } \right] = \left( {I - S} \right)^{ - 1} \left[ {\begin{array}{*{20}c} {\text{eq}} \\ {\text{ec}} \\ {\text{ev}} \\ {\text{et}} \\ {\text{eh}} \\ {\text{eg}} \\ \end{array} } \right], $$

(B.1)

where Q = vector of industry output (endogenous), C = vector of commodity output (endogenous), V = vector of total primary factor payments (endogenous), IBT = indirect business tax payments (endogenous), H = vector of total household income (endogenous), SG = total state and local government revenue (endogenous), eq = vector of exogenous demand for industry output, ec = vector of exogenous demand for commodity output, ev = vector of exogenous factor payments, et = exogenous indirect business tax payments, eh = vector of exogenous federal transfers to households, eg = federal transfers to state and local government.

In Equation (B.1), vectors Q, C, V, IBT, H, and SG contain elements that are endogenous variables. Vectors eq, ec, ev, et, eh, and eg have elements that are exogenous variables. Nonzero elements are included in the vectors ec, eh, and eg. Vector ec is the final demand vector whose elements are investment demand, federal government demand, and export demand. Elements of eh include federal government transfers to households and capital income inflow from outside of Alaska. The components of eg include (1) federal government transfers, (2) revenue from, for example, investments, leases, and trusts, and (3) non-Alaska residents’ tax payments. The elements in vectors ec, eh, and eg constitute injections of income or revenue into the state’s economy. Leakages of income transpire via payments to non-resident factor owners (non-resident factor income), tax payments to the federal government, savings, and imports of commodities.

• 2. MRSAM model

As mentioned, the MRSAM model can be also represented by Eq. (4):

$$ T = \left( {I - S} \right)^{ - 1} K. $$

where $T = \left[ {\begin{array}{*{20}c} {t_{1} } \\ {t_{2} } \\ {t_{3} } \\ \end{array} } \right]$, $S = \left[ {\begin{array}{*{20}c} {Z_{11} z_{12} z_{13} } \\ {z_{21} Z_{22} z_{23} } \\ {z_{31} z_{32} Z_{33} } \\ \end{array} } \right]$, and $K = \left[ {\begin{array}{*{20}c} {k_{1} } \\ {k_{2} } \\ {k_{3} } \\ \end{array} } \right]$.

Here S is now the matrix of direct MRSAM coefficients and $\left( {I - S} \right)^{ - 1}$ is now called the MRSAM multiplier matrix or the matrix of MRSAM inverse coefficients. t_r and k_r denote the column vectors of endogenous and exogenous accounts, respectively, for region r; Z_rr is the submatrix containing coefficients representing the intra-regional transactions; and z_rs is the submatrix containing coefficients representing inter-regional transactions. All the coefficients in Z_rr and z_rs are derived by dividing the elements in the columns in the MRSAM by the column totals.

t_r is a column vector for region r comprising the following endogenous sub-vectors:

• Q_r = vector of regional industry output.

• C_r= vector of regional commodity output.

• V_r = vector of total primary factor payments.

• IBT_r = indirect business tax payments.

• H_r = vector of total household income.

• SG_r = total state and local government revenue.

Z_rr for region r is:

$$ Z_{rr} = \left[ {\begin{array}{*{20}c} 0 & {M_{r} } & 0 & 0 & 0 & 0 \\ {U_{r} } & 0 & 0 & 0 & {{\text{CS}}_{r} } & {{\text{GD}}_{r} } \\ {V_{r} } & 0 & 0 & 0 & 0 & 0 \\ {{\text{IBT}}_{r} } & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & {F_{r} } & 0 & 0 & {{\text{STR}}_{r} } \\ 0 & 0 & {{\text{SF}}_{r} } & {{\text{BTS}}_{r} } & {{\text{HTX}}_{r} } & {{\text{IGT}}_{r} } \\ \end{array} } \right], $$

(B.2)

where U_r= matrix of coefficients showing the use of commodities by industries in production, V_r= matrix of primary factor payments coefficients, IBT_r = matrix of indirect business tax coefficients, M_r= market share matrix (i.e., elements in make matrix divided by total output), F_r = matrix of factor payment to household coefficients, SF_r = matrix of state and local factor tax coefficients, BTS_r = matrix of state and local indirect business tax coefficients, CS_r = matrix of household consumption coefficients, HTX_r = matrix of state and local government direct household tax coefficients, GD_r = matrix of state and local government demand coefficients, STR_r = matrix of state and local government transfer coefficients, IGT_r = matrix of intergovernmental transfers.

z_rs is:

$$ z_{rs} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & {{\text{IM}}_{rs} } & 0 & 0 & 0 & 0 \\ 0 & 0 & {{\text{LK}}_{rs} } & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} } \right], $$

(B.3)

where IM_rs is the matrix of imports from region r to s and LK_rs is the matrix of leakage of factor income from region s to region r. k_r is the column vector consisting of the following exogenous sub-vectors:

• eq_r = vector of exogenous demand for regional industry output.

• ec_r = vector of exogenous demand for regional commodity output.

• ev_r = vector of exogenous factor payments.

• et_r = exogenous indirect business tax payments.

• eh_r = vector of exogenous federal transfers to households.

• eg_r = federal transfers to state and local government.