Create an output coefficient matrix

Create an output-coefficient matrix from a symmetric input–output table or a use table. Output coefficients can be interpreted as the market shares of products in total output (row-wise normalization).

Usage

output_coefficient_matrix_create(data_table, total = "tfu", digits = NULL)

Arguments

data_table

A symmetric input–output table, use table, margins, or tax table retrieved by iotable_get(). If you request total = "tfu" (total final use), you must supply a full table from iotable_get() because the TFU column is in the second quadrant.

total

Which total to use for normalization. Use "total" (or the present table variant name, e.g. "CPA_TOTAL") for output by product, or "tfu" / "total_final_use" / "final_demand" for total final use. Default: "tfu".

digits

Integer number of decimal places for rounding. Default NULL (no rounding).

Value

A data.frame whose first column is the key (product labels) and the remaining columns form the output-coefficient matrix. Column order follows the input.

Details

Let \(Z\) be the inter-industry flow block and \(x\) the vector of product output (or, for final-demand shares, total final use). The output-coefficient matrix \(B\) is defined row-wise as \(b_{ij} = z_{ij} / x_i\). In practice, zeros in the denominator can make equations unsolvable; this function replaces zeros with a small epsilon (1e-6) to avoid division by zero.

Eurostat, Manual of Supply, Use and Input-Output Tables (e.g., pp. 495, 507) describes output coefficients and the Ghosh framework you may use these with.

See also

Other analytic object functions: ghosh_inverse_create(), input_flow_get(), leontief_inverse_create(), leontief_matrix_create()

Examples

data_table <- iotable_get()
output_coefficient_matrix_create(
  data_table = data_table,
  total = "tfu",
  digits = 4
)
#>              iotables_row agriculture_group industry_group construction
#> 1       agriculture_group            0.0258         0.5803       0.0000
#> 2          industry_group            0.0073         0.2822       0.0594
#> 3            construction            0.0017         0.0299       0.0158
#> 4             trade_group            0.0066         0.1346       0.0263
#> 5 business_services_group            0.0053         0.1388       0.0448
#> 6    other_services_group            0.0030         0.0294       0.0034
#>   trade_group business_services_group other_services_group
#> 1      0.0138                  0.0162               0.0174
#> 2      0.0381                  0.0111               0.0281
#> 3      0.0216                  0.0955               0.0373
#> 4      0.1378                  0.0201               0.0389
#> 5      0.0950                  0.2790               0.0494
#> 6      0.0221                  0.0296               0.0434