Create Ghosh inverse from output coefficients
Source:R/ghosh_inverse_create.R
ghosh_inverse_create.RdCompute the Ghosh inverse from an output-coefficient matrix.
Arguments
- output_coefficients_matrix
A technology-coefficient matrix created by
output_coefficient_matrix_create().- digits
Optional integer precision for rounding. Default
NULL(no rounding).
Value
A data.frame with the original key column and the Ghosh inverse in the
remaining columns. If digits is provided, values are rounded.
Details
The Ghosh inverse is defined as \(G = (I - B)^{-1}\), where \(B\) is
the output-coefficient matrix created by
output_coefficient_matrix_create().
See the United Nations Handbook on Supply and Use Tables and Input–Output Tables with Extensions and Applications (2018, Rev. 1), pp. 622–639 (PDF).
For the analogous inverse based on input coefficients, see
leontief_inverse_create().
See also
Other analytic object functions:
input_flow_get(),
leontief_inverse_create(),
leontief_matrix_create(),
output_coefficient_matrix_create()
Examples
# Minimal example
om <- output_coefficient_matrix_create(iotable_get())
ghosh_inverse_create(om)
#> iotables_row agriculture_group industry_group construction
#> 1 agriculture_group 1.033872798 0.86116467 0.05605892
#> 2 industry_group 0.011782944 1.42917800 0.09013694
#> 3 construction 0.003700754 0.08389383 1.02893808
#> 4 trade_group 0.010318967 0.24265216 0.04839848
#> 5 business_services_group 0.011680549 0.32284302 0.08879096
#> 6 other_services_group 0.004271007 0.06261891 0.01050767
#> trade_group business_services_group other_services_group
#> 1 0.06255558 0.04771125 0.05126741
#> 2 0.07103604 0.03825762 0.05061124
#> 3 0.04635583 0.14107965 0.05179948
#> 4 1.17840037 0.04560652 0.05948028
#> 5 0.17460288 1.41256213 0.09323763
#> 6 0.03512252 0.04657745 1.05149484
# Using the Germany 1995 benchmark table (Eurostat manual)
# data(germany_1995)
# om_de <- output_coefficient_matrix_create(germany_1995)
# ghosh_inverse_create(om_de)