Germany 1990

Creating technical indicators

Technical indicators assume constant returns to scale and fixed relationship of all inputs to each industry. With these conditions the technical input coefficients show how much input products, labour or capital is required to produce a unit of industry output.

60. \(a_{ij}\) = \(z_{ij}\) / \(x_j\) [technical input coefficients]

The helper function primary_input_get() selects a row from the SIOT and brings it to a conforming form. The input_indicator_create() creates the vector of technical input coefficients.

de_emp <- primary_input_get ( data_table,
                              primary_input = "employment_domestic_total" )

de_emp_indicator <- input_indicator_create ( 
    data_table  = data_table,
    input_vector = "employment_domestic_total")

print ( tidyr::gather( de_emp_indicator, indicators, values, !!2:ncol(de_emp_indicator))[,-1] )
#>                indicators      values
#> 1       agriculture_group 0.024960146
#> 2          industry_group 0.007764168
#> 3            construction 0.013175574
#> 4             trade_group 0.017129483
#> 5 business_services_group 0.006148852
#> 6    other_services_group 0.020054311

Often we want to analyze the effect of growing domestic demand on some natural units, such as employment or \(CO_2\) emissions. The only difficulty is that we need data that is aggregated / disaggregated precisely with the same industry breakup as our SIOT table.

European employment statistics have greater detail than our tables, so employment statistics must be aggregated to conform the 60 (61, 62) columns of the SIOT. There is a difference in the columns based on how national statistics offices treat imputed real estate income and household production, and trade margins. Czech SIOTs are smaller than most SIOTS because they do not have these columns and rows.

In another vignette we will show examples on how to work with these real-life data. For the sake of following the calculations, we are continuing with the simplified 1990 German data.

Creating income indicators

The input coefficients for value added are created with input_indicator_create().

de_gva <- primary_input_get ( data_table,
                              primary_input = "gva") 

de_gva_indicator  <- input_indicator_create( 
    data_table  = data_table,
    input_vector = "gva")

print( tidyr::gather(de_gva_indicator, indicators, values,!!2:ncol(de_gva_indicator))[,-1]  ) 
#>                indicators    values
#> 1       agriculture_group 0.4933728
#> 2          industry_group 0.3659488
#> 3            construction 0.4707703
#> 4             trade_group 0.5766124
#> 5 business_services_group 0.5999044
#> 6    other_services_group 0.7172413

This is equal to the equation on page 495 of the Eurostat Manual. The results above can be checked on the bottom of page 498.

44. \(w_{ij}\) = \(W_{j}\) / \(x_j\) [input coefficients for value added]

You can create a matrix of input indicators, or direct effects on (final) demand with direct_supply_effects_create(). The function by default creates input requirements for final demand. With the code below it re-creates the Table 15.14 of the Eurostat manual.

direct_effects_de <- coefficient_matrix_create(data_table  = data_table, 
                                               total       = 'output', 
                                             return_part = 'primary_inputs')
print ( direct_effects_de[1:6,1:4])
#>                 iotables_row agriculture_group industry_group construction
#> 7                      total        0.41528126    0.482855094  0.468258104
#> 8                    imports        0.06665908    0.145169837  0.054668860
#> 9   intermediate_consumption        0.50662719    0.634051171  0.529229742
#> 10    compensation_employees        0.21366431    0.274644586  0.320916427
#> 11        net_tax_production       -0.04582100    0.001349766  0.003920914
#> 12 consumption_fixed_capital        0.17925302    0.059075674  0.023859352

The ‘total’ row above is labelled as Domestic goods and services in the Eurostat Manual. The table can be found on p498.

Income multipliers

The SIOTs contain (with various breakups) three types of income:

• Employee wages, which is usually a proxy for all household income.

• Gross operating surplus, which is a form of corporate sector income.

• Taxes that are the income of government.

These together make gross value added (GVA). If you are working with SIOTs that use basic prices, then GVA = GDP at producers’ prices, or basic prices.

The GVA multiplier shows the additional gross value created in the economy if demand for the industry products is growing with unity. The wage multiplier (not shown here) shows the increase in household income.

The following equation is used to work with different income effects and multipliers:

63. Z = B(I-A)^-1

B = vector of input coefficients for wages or GVA or taxes.

Z = direct and indirect requirements for wages (or other income)

The indicator shows that manufacturing has the lowest, and other services has the highest gross value added component. This is hardly surprising, because manufacturing needs a lot of materials and imported components. When the demand for manufacturing in the domestic economy is growing by 1 unit, the gross value added is 0.3659488.

You can check these values against the Table 15.16 of the Eurostat Manual on page 501 (row 10).

You can recreate the whole matrix, when the data data permits, with input_multipliers_create() as shown here. Alternatively, you can create your own custom multipliers with multiplier_create() as shown in the following example.

input_reqr <- coefficient_matrix_create(
    data_table  = iotable_get (), 
    total       = 'output', 
    return_part = 'primary_inputs') 

multipliers <- input_multipliers_create(
  input_requirements = input_reqr,
  inverse = I_de)

knitr::kable(multipliers, digits= 4)

You can check these results against the Table 15.16 on p501 of the Eurostat manual. the label ‘total’ refers to domestic intermediaries. The ordering of the rows is different from the Manual.

These multipliers are Type-I multipliers. The type-I GVA multiplier shows the total effect in the domestic economy. The initial extra demand creates new orders in the backward linking industries, offers new product to build on in the forward-linking industry and creates new corporate and employee income that can be spent. Type-II multipliers will be introduced in a forthcoming vignette [not yet available.]

Employment multipliers

The E matrix contains the input coefficients for labor (created by input_indicator_create()). The following matrix equation defines the employment multipliers.

64. Z = E(I-A)^-1

The multiplier_create() function performs the matrix multiplication, after handling many exceptions and problems with real-life data, such as different missing columns and rows in the national variations of the standard European table.

Please send a bug report on Github if you run into further real-life problems.

de_emp_indicator <- input_indicator_create (
  data_table = data_table, 
  input = 'employment_domestic_total') 

employment_multipliers <- multiplier_create ( 
  input_vector    = de_emp_indicator,
  Im              = I_de,
  multiplier_name = "employment_multiplier", 
  digits = 4 )

print (tidyr::gather(employment_multipliers,
              multipliers, values, !!2:ncol(employment_multipliers))[-1])
#>               multipliers values
#> 1       agriculture_group 0.0665
#> 2          industry_group 0.0574
#> 3            construction 0.0625
#> 4             trade_group 0.0548
#> 5 business_services_group 0.0423
#> 6    other_services_group 0.0431

You can check against page 501 that these values are correct and on page 501 that the highest employment multiplier is indeed \(z_i\) = 0.0665, the employment multiplier of agriculture.

For working with real-life, current employment data, there is a helper function to retrieve and process Eurostat employment statistics to a SIOT-conforming vector employment_get(). This function will be explained in a separate vignette.

Output multipliers

Output multipliers and forward linkages are calculated with the help of output coefficients for product as defined on p486 and p495 of the the Eurostat Manual. The Eurostat Manual uses the definition of output at basic prices to define output coefficients which is no longer part of SNA as of SNA2010.

5. \(b_{ij}\) = \(X_{ij}\) / \(x_i\) [also (45) output coefficients for products / intermediates].

\(x_i\): output of sector i

de_input_coeff <- input_coefficient_matrix_create( 
                         data_table = iotable_get(), 
                         digits = 4)
                           
output_multipliers <- output_multiplier_create ( 
                        input_coefficient_matrix = de_input_coeff )

print (tidyr::gather(output_multipliers, multipliers, values)[-1,])
#>               multipliers           values
#> 2       agriculture_group 1.70492243301356
#> 3          industry_group  1.8414208680286
#> 4            construction 1.81374666684297
#> 5             trade_group 1.60371174683177
#> 6 business_services_group 1.59497385374824
#> 7    other_services_group 1.37837464728208

These multipliers can be checked against the Table 15.15 on p500 of the Eurostat Manual.

Backward linkages

de_coeff <- input_coefficient_matrix_create( iotable_get(), digits = 4)
I_de <- leontieff_inverse_create ( de_coeff )

de_bw <- backward_linkages(I_de)
print (tidyr::gather(de_bw, backward_linkages, values)[-1,])
#> Warning: attributes are not identical across measure variables;
#> they will be dropped
#>         backward_linkages           values
#> 2       agriculture_group 1.70492243301356
#> 3          industry_group  1.8414208680286
#> 4            construction 1.81374666684297
#> 5             trade_group 1.60371174683177
#> 6 business_services_group 1.59497385374824
#> 7    other_services_group 1.37837464728208

You can check the results against Table 15.19 on page 506 of the Eurostat Manual.

Manufacturing has the highest backward linkages, and other services the least. An increased demand for manufacturing usually effects supplier industries. Service industry usually have a high labor input, and their main effect is increased spending of the wages earned in the services.

Forward linkages

Forward linkages show the strength of the new business opportunities when industry i starts to increase its production. Whereas backward linkages show the increased demand of the suppliers in industry i, forward linkages show the increased availability of inputs for other industries that rely on industry i as a supplier.

de_out <- output_coefficient_matrix_create ( 
  data_table, "final_demand", digits = 4
  )
                                    
forward_linkages ( output_coefficient_matrix = de_out )
#>              iotables_row forward_linkages
#> 1       agriculture_group         2.112754
#> 2          industry_group         1.690891
#> 3            construction         1.355896
#> 4             trade_group         1.584989
#> 5 business_services_group         2.104036
#> 6    other_services_group         1.210504

You can check forward linkages against the Table 15.20 of Eurostat Manual on page 507.