Análise de Insumo-produto: teoria e aplicações no R

Análise do impacto de investimento usando a matriz insumo-produto.

Código construído com base em

Vale,V.A. e Perobelli, F. S. (2020), Análise de Insumo-produto: teoria e aplicações no R, Curitiba, PR: Edição Independente, 2020. Disponível em (NEDUR) http://www.nedur.ufpr.br/portal/publicacoes/livros/ip-r/ e LATES https://www.ufjf.br/lates/publicacoes/livros/ip-r/.

Passos iniciais

# Definição do Diretório de Trabalho 
  #setwd("C:/Users/R-VALE/Insumo-Produto")
# Verificar o diretório de trabalho
  #getwd()
# Remover todos objetos do Environment
  #rm(list = ls())

   install.packages("openxlsx")
   install.packages("flextable")
   install.packages("knitr")
   install.packages("kableExtra")
   install.packages("dplyr")
   install.packages("ggplot2")
   install.packages("scales")
   install.packages("ggrepel")
   install.packages("tibble")
   install.packages("gridExtra")

  # Leitura dos pacotes
  library(openxlsx)
  library(knitr) 
  library(kableExtra)
  library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:kableExtra':
## 
##     group_rows

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

  library(ggplot2)
  library(scales)
  library(ggrepel)
  library(tibble)
  library(gridExtra)

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

  library(flextable)

## 
## Attaching package: 'flextable'

## The following objects are masked from 'package:kableExtra':
## 
##     as_image, footnote

Base de Dados

Descrição

Matriz de Insumo-Produto (MIP) 2015 do Brasil disponibilizada pelo IBGE com abertura para 12 atividades produtivas (setores). Os cálculos podem ser facilmente replicados com outras matrizes de insumo-produto, inclusive com a MIP brasileira com 67 atividades produtivas.

Importando dados

    # Importando doados com o pacote openxls
    Z = read.xlsx("MIP2015_12s.xlsx", sheet = "Z", colNames = FALSE) # Consumo intermediário 
    y = read.xlsx("MIP2015_12s.xlsx", sheet = "y", colNames = FALSE) # Demanda final
    x = read.xlsx("MIP2015_12s.xlsx", sheet = "x", colNames = FALSE) # VB da Produção (VBP)
    v = read.xlsx("MIP2015_12s.xlsx", sheet = "v", colNames = FALSE) # Valor adicionado
    r = read.xlsx("MIP2015_12s.xlsx", sheet = "r", colNames = FALSE) # Remunerações
    e = read.xlsx("MIP2015_12s.xlsx", sheet = "e", colNames = FALSE) # Pessoal ocupado
    c = read.xlsx("MIP2015_12s.xlsx", sheet = "c", colNames = FALSE) # Consumo das famílias
    sp = read.xlsx("MIP2015_12s.xlsx", sheet = "sp", colNames = FALSE) # Setor de Pagamentos
    Setores = read.xlsx("MIP2015_12s.xlsx", sheet = "set", colNames = FALSE) # Setores

Preparação dos Objetos

# Classe dos objetos
    
    class(Z) # Verificar classe do objeto Z

## [1] "data.frame"

    class(y) # Verificar classe do objeto y

## [1] "data.frame"

    # Mudar classe dos objetos
    Z = data.matrix(Z) # Consumo intermediário
    y = data.matrix(y) # Demanda final
    x = data.matrix(x) # Valor Bruto da Produção
    x = as.vector(x)   # Valor Bruto da Produção
    v = data.matrix(v) # Valor adicionado
    r = data.matrix(r) # Remunerações
    e = data.matrix(e) # Pessoal ocupado
    c = data.matrix(c) # Consumo das famílas
    sp = data.matrix(sp) # Setor de Pagamentos

Exportando dados

    # Salvar base de dados no formato RData
    save(Z, y, x, v, r, e, c, sp, Setores, file = "MIP2015_12s.RData")
    
    # Importação de dados no formato RData
    load("MIP2015_12s.RData")

Insumo-Produto

Modelo aberto

    A = Z %*% diag(1 / x) # Matriz de coeficientes técnicos
    A # Matriz de coeficientes técnicos

##            [,1]         [,2]         [,3]         [,4]        [,5]         [,6]
## 1  4.053431e-02 0.0005246369 0.0764492534 0.0004633725 0.002559273 0.0091478919
## 2  1.102888e-03 0.0544009633 0.0420777813 0.0149135188 0.011187753 0.0001890271
## 3  2.064230e-01 0.1108945052 0.2730694834 0.0759925493 0.205220303 0.0573808439
## 4  2.330124e-02 0.0108076054 0.0154556049 0.2757595679 0.001162759 0.0175890682
## 5  5.926945e-04 0.0125710963 0.0009171252 0.0127611368 0.093540153 0.0010353060
## 6  5.939513e-02 0.0312098980 0.0789023217 0.0201625275 0.057717650 0.0275047815
## 7  1.999363e-02 0.0837831375 0.0493231465 0.0186085348 0.011904719 0.0503422095
## 8  2.015810e-04 0.0038789881 0.0056297325 0.0065432923 0.002253644 0.0131079208
## 9  1.525339e-02 0.0222417825 0.0175588983 0.0216950729 0.014284850 0.0235984415
## 10 3.645757e-05 0.0013583593 0.0018308430 0.0042946036 0.001680581 0.0338135746
## 11 3.691960e-03 0.0929645727 0.0458518255 0.0506329264 0.023313871 0.0799177956
## 12 7.414102e-04 0.0048640577 0.0027987040 0.0045944450 0.001172534 0.0041072929
##            [,7]         [,8]         [,9]        [,10]        [,11]
## 1  0.0005683193 0.0002397377 6.256554e-05 5.501254e-05 0.0043313175
## 2  0.0002836057 0.0002885543 7.855493e-05 6.278740e-04 0.0002062247
## 3  0.1825349810 0.0279488999 9.685629e-03 9.289329e-03 0.0711063547
## 4  0.0057399609 0.0072395728 4.112766e-03 1.259522e-03 0.0166493955
## 5  0.0031402527 0.0163693755 2.982811e-03 2.920853e-03 0.0035603285
## 6  0.0469936940 0.0249873104 5.934150e-03 3.260666e-03 0.0321010426
## 7  0.1125305307 0.0096395434 1.421525e-02 8.538736e-04 0.0183127869
## 8  0.0076419524 0.1209578864 3.927254e-02 1.419554e-03 0.0379995553
## 9  0.0247778800 0.0291164305 1.240729e-01 3.790436e-02 0.0170013436
## 10 0.0067321513 0.0122305450 9.615042e-03 2.742154e-03 0.0174985177
## 11 0.0576725848 0.1405865936 1.018015e-01 7.998258e-03 0.0903391523
## 12 0.0038896420 0.0063169808 4.482879e-03 3.771107e-04 0.0041638989
##           [,12]
## 1  0.0015679301
## 2  0.0002943657
## 3  0.0258993452
## 4  0.0172561462
## 5  0.0139242494
## 6  0.0133143660
## 7  0.0117725258
## 8  0.0173315988
## 9  0.0446279563
## 10 0.0036050269
## 11 0.0782021425
## 12 0.0034693898

    n = length(x) # Número de setores
    I = diag(n) # Matriz identidade
    I # Matriz identidade

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
##  [1,]    1    0    0    0    0    0    0    0    0     0     0     0
##  [2,]    0    1    0    0    0    0    0    0    0     0     0     0
##  [3,]    0    0    1    0    0    0    0    0    0     0     0     0
##  [4,]    0    0    0    1    0    0    0    0    0     0     0     0
##  [5,]    0    0    0    0    1    0    0    0    0     0     0     0
##  [6,]    0    0    0    0    0    1    0    0    0     0     0     0
##  [7,]    0    0    0    0    0    0    1    0    0     0     0     0
##  [8,]    0    0    0    0    0    0    0    1    0     0     0     0
##  [9,]    0    0    0    0    0    0    0    0    1     0     0     0
## [10,]    0    0    0    0    0    0    0    0    0     1     0     0
## [11,]    0    0    0    0    0    0    0    0    0     0     1     0
## [12,]    0    0    0    0    0    0    0    0    0     0     0     1

    B = solve(I - A) # Matriz inversa de Leontief
    B # Matriz inversa de Leontief

##                 1           2           3          4           5           6
##  [1,] 1.070422587 0.020220639 0.119541085 0.01695088 0.032572083 0.020604755
##  [2,] 0.017117985 1.068456656 0.066637159 0.03073724 0.029213540 0.006456716
##  [3,] 0.338341626 0.228313297 1.475314987 0.19010756 0.354863612 0.125413219
##  [4,] 0.046079029 0.028026440 0.043749839 1.39072595 0.015664875 0.032800699
##  [5,] 0.002713328 0.017113531 0.004714078 0.02154187 1.105148396 0.003373673
##  [6,] 0.098930568 0.067164118 0.139921088 0.05446153 0.102701710 1.049128186
##  [7,] 0.052696808 0.122595743 0.103237504 0.04969012 0.046313509 0.071664588
##  [8,] 0.008162795 0.016809713 0.020076865 0.01991403 0.011802612 0.024247868
##  [9,] 0.032710787 0.042425099 0.044850572 0.04621991 0.033160500 0.039227220
## [10,] 0.005778595 0.008308725 0.011105795 0.01120964 0.008089475 0.039152423
## [11,] 0.043049349 0.144534269 0.111835546 0.10775512 0.068080015 0.114687333
## [12,] 0.003040183 0.007680536 0.006544965 0.00834081 0.003651577 0.005982250
##                 7           8           9           10          11          12
##  [1,] 0.027928857 0.008637801 0.004569083 0.0017161391 0.016687791 0.007821476
##  [2,] 0.015300439 0.004881639 0.002445668 0.0016108868 0.007044501 0.004034943
##  [3,] 0.324263851 0.086666173 0.045038597 0.0188388377 0.137938888 0.067116259
##  [4,] 0.022581877 0.020132759 0.012474430 0.0031276448 0.032043358 0.029658522
##  [5,] 0.006093483 0.022494708 0.005937902 0.0036518813 0.006546596 0.017247958
##  [6,] 0.089774219 0.047266968 0.019363532 0.0064763712 0.054238044 0.027236678
##  [7,] 1.155888289 0.026338243 0.026436167 0.0038121827 0.037013131 0.023482726
##  [8,] 0.020720816 1.150184985 0.058744055 0.0046578953 0.052660116 0.028402123
##  [9,] 0.046931531 0.048274077 1.150137925 0.0448298029 0.031618875 0.058561901
## [10,] 0.014228941 0.020123836 0.015366774 1.0038390836 0.023276126 0.007794733
## [11,] 0.109769989 0.196536643 0.145252952 0.0168317906 1.128525475 0.107207543
## [12,] 0.006805594 0.009027533 0.006548314 0.0008037355 0.006157929 1.004950809

    # Visualização de elementos específicos da matriz A e B
    A[1, 1]

##          1 
## 0.04053431

    A[2, 1]

##           2 
## 0.001102888

    B[1, 1]

##        1 
## 1.070423

    B[2, 1]

##          1 
## 0.01711798

Modelo fechado

    hc = c / sum(r) # Coeficientes de consumo
    hr = r / x # Coeficientes de remuneração do trabalho (renda)
    hr = t(hr) # Coeficientes de remuneração do trabalho (renda) transposto
    AF = matrix(NA, ncol = n + 1, nrow = n + 1)  # Criação da matriz A do modelo fechado
    AF = rbind(cbind(A, hc), cbind(hr, 0)) # Matriz de coeficientes técnicos
    AF # Matriz de coeficientes técnicos

##                                                                                
## 1  4.053431e-02 0.0005246369 0.0764492534 0.0004633725 0.002559273 0.0091478919
## 2  1.102888e-03 0.0544009633 0.0420777813 0.0149135188 0.011187753 0.0001890271
## 3  2.064230e-01 0.1108945052 0.2730694834 0.0759925493 0.205220303 0.0573808439
## 4  2.330124e-02 0.0108076054 0.0154556049 0.2757595679 0.001162759 0.0175890682
## 5  5.926945e-04 0.0125710963 0.0009171252 0.0127611368 0.093540153 0.0010353060
## 6  5.939513e-02 0.0312098980 0.0789023217 0.0201625275 0.057717650 0.0275047815
## 7  1.999363e-02 0.0837831375 0.0493231465 0.0186085348 0.011904719 0.0503422095
## 8  2.015810e-04 0.0038789881 0.0056297325 0.0065432923 0.002253644 0.0131079208
## 9  1.525339e-02 0.0222417825 0.0175588983 0.0216950729 0.014284850 0.0235984415
## 10 3.645757e-05 0.0013583593 0.0018308430 0.0042946036 0.001680581 0.0338135746
## 11 3.691960e-03 0.0929645727 0.0458518255 0.0506329264 0.023313871 0.0799177956
## 12 7.414102e-04 0.0048640577 0.0027987040 0.0045944450 0.001172534 0.0041072929
## X1 1.040461e-01 0.1258418946 0.1418226807 0.1017991459 0.200233114 0.3131173559
##                                                                    
## 1  0.0005683193 0.0002397377 6.256554e-05 5.501254e-05 0.0043313175
## 2  0.0002836057 0.0002885543 7.855493e-05 6.278740e-04 0.0002062247
## 3  0.1825349810 0.0279488999 9.685629e-03 9.289329e-03 0.0711063547
## 4  0.0057399609 0.0072395728 4.112766e-03 1.259522e-03 0.0166493955
## 5  0.0031402527 0.0163693755 2.982811e-03 2.920853e-03 0.0035603285
## 6  0.0469936940 0.0249873104 5.934150e-03 3.260666e-03 0.0321010426
## 7  0.1125305307 0.0096395434 1.421525e-02 8.538736e-04 0.0183127869
## 8  0.0076419524 0.1209578864 3.927254e-02 1.419554e-03 0.0379995553
## 9  0.0247778800 0.0291164305 1.240729e-01 3.790436e-02 0.0170013436
## 10 0.0067321513 0.0122305450 9.615042e-03 2.742154e-03 0.0174985177
## 11 0.0576725848 0.1405865936 1.018015e-01 7.998258e-03 0.0903391523
## 12 0.0038896420 0.0063169808 4.482879e-03 3.771107e-04 0.0041638989
## X1 0.2599952119 0.2322935748 2.492869e-01 1.229647e-02 0.3610414874
##                           X1
## 1  0.0015679301 0.0355377729
## 2  0.0002943657 0.0005673371
## 3  0.0258993452 0.3091105074
## 4  0.0172561462 0.0385672335
## 5  0.0139242494 0.0005120007
## 6  0.0133143660 0.2160913501
## 7  0.0117725258 0.0482781193
## 8  0.0173315988 0.0381995070
## 9  0.0446279563 0.0976598582
## 10 0.0036050269 0.1686937659
## 11 0.0782021425 0.2283419503
## 12 0.0034693898 0.0106970178
## X1 0.6605820953 0.0000000000

    IF = diag(n + 1) # Matriz identidade (n+1)x(n+1)
    IF # Matriz identidade (n+1)x(n+1)

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0
##  [2,]    0    1    0    0    0    0    0    0    0     0     0     0     0
##  [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0
##  [4,]    0    0    0    1    0    0    0    0    0     0     0     0     0
##  [5,]    0    0    0    0    1    0    0    0    0     0     0     0     0
##  [6,]    0    0    0    0    0    1    0    0    0     0     0     0     0
##  [7,]    0    0    0    0    0    0    1    0    0     0     0     0     0
##  [8,]    0    0    0    0    0    0    0    1    0     0     0     0     0
##  [9,]    0    0    0    0    0    0    0    0    1     0     0     0     0
## [10,]    0    0    0    0    0    0    0    0    0     1     0     0     0
## [11,]    0    0    0    0    0    0    0    0    0     0     1     0     0
## [12,]    0    0    0    0    0    0    0    0    0     0     0     1     0
## [13,]    0    0    0    0    0    0    0    0    0     0     0     0     1

    BF = solve(IF - AF) # Matriz inversa de Leontief no modelo fechado
    BF # Matriz inversa de Leontief

##              1          2           3          4          5           6
##    1.106383315 0.06533606 0.174707114 0.05743221 0.08710409 0.085750406
##    0.028557533 1.08280843 0.084186149 0.04361484 0.04656084 0.027180346
##    0.571976599 0.52142584 1.833725801 0.45311264 0.70915521 0.548661110
##    0.082336886 0.07351463 0.099371683 1.43154176 0.07064746 0.098484622
##    0.005924269 0.02114190 0.009639865 0.02515645 1.11001757 0.009190542
##    0.222689713 0.22242922 0.329775437 0.19377837 0.29037406 1.273327484
##    0.102629922 0.18524057 0.179838057 0.10590029 0.12203369 0.162122302
##    0.039910157 0.05663915 0.068779326 0.05565234 0.05994533 0.081760680
##    0.098099729 0.12446042 0.145161342 0.11982885 0.13231840 0.157684365
##    0.084925565 0.10760452 0.132522250 0.10030612 0.12811049 0.182533305
##    0.190256231 0.32921631 0.337660206 0.27346729 0.29130927 0.381364029
##    0.010261235 0.01673989 0.017622515 0.01646962 0.01460181 0.019063746
## X1 0.416046161 0.52196102 0.638241105 0.46834707 0.63090580 0.753699921
##             7          8          9          10         11         12
##    0.09467580 0.06855661 0.06170450 0.007481185 0.08967488 0.12149546
##    0.03653346 0.02394255 0.02062114 0.003444819 0.03026259 0.04019603
##    0.75791528 0.47595554 0.41624440 0.056294042 0.61213216 0.80565017
##    0.08988033 0.08054665 0.07008193 0.008940325 0.10563351 0.14427174
##    0.01205333 0.02784487 0.01103954 0.004166644 0.01306363 0.02739793
##    0.31948439 0.25347804 0.21599553 0.026316826 0.30542370 0.41844663
##    1.24856948 0.10953825 0.10577130 0.011817213 0.13835903 0.18132424
##    0.07964731 1.20308336 0.10918516 0.009747476 0.11709561 0.12875741
##    0.16830038 0.15722703 1.25402971 0.055312635 0.16433444 0.26526020
##    0.16113416 0.15200081 0.14111770 1.016527535 0.18391544 0.25798297
##    0.38300166 0.44181702 0.37913938 0.040431271 1.42730144 0.57253717
##    0.02020864 0.02105946 0.01802132 0.001961379 0.02081401 1.02777698
## X1 0.77222605 0.69322818 0.66102582 0.066698465 0.84442106 1.31514643
##            X1
##    0.15040265
##    0.04784493
##    0.97715814
##    0.15164536
##    0.01342948
##    0.51761196
##    0.20884095
##    0.13278061
##    0.27348361
##    0.33102539
##    0.61568010
##    0.03020143
## X1 1.74007722

    # Visualização de elementos específicosda matriz B
    BF[1, 1]

## [1] 1.106383

Modelo pelo lado da oferta

    F = diag(1 / x) %*% Z # Matriz de coeficientes técnicos pelo lado da oferta
    F # Matriz de coeficientes técnicos pelo lado da oferta

##                 X1           X2          X3           X4           X5
##  [1,] 4.053431e-02 0.0002855602 0.443377883 0.0003132171 0.0033802953
##  [2,] 2.026249e-03 0.0544009633 0.448347591 0.0185206635 0.0271482680
##  [3,] 3.559241e-02 0.0104075383 0.273069483 0.0088569751 0.0467366500
##  [4,] 3.447179e-02 0.0087026810 0.132608572 0.2757595679 0.0022720223
##  [5,] 4.487381e-04 0.0051805264 0.004027090 0.0065308020 0.0935401535
##  [6,] 2.583138e-02 0.0073880179 0.199015719 0.0059273009 0.0331545772
##  [7,] 1.893793e-02 0.0431952694 0.270951993 0.0119142899 0.0148935413
##  [8,] 2.753559e-04 0.0028840446 0.044599839 0.0060416597 0.0040660068
##  [9,] 1.270817e-02 0.0100861417 0.084842752 0.0122177999 0.0157191993
## [10,] 3.196997e-05 0.0006483476 0.009311215 0.0025456152 0.0019464890
## [11,] 1.202181e-03 0.0164766530 0.086590482 0.0111445096 0.0100268650
## [12,] 2.938671e-04 0.0010493730 0.006433542 0.0012309506 0.0006138409
##                X6           X7           X8           X9          X10
##  [1,] 0.021034113 0.0006000005 0.0001755059 0.0000750963 6.273461e-05
##  [2,] 0.000798525 0.0005500921 0.0003881003 0.0001732280 1.315465e-03
##  [3,] 0.022749368 0.0332280251 0.0035279237 0.0020045197 1.826540e-03
##  [4,] 0.059831629 0.0089650548 0.0078406668 0.0073030138 2.124889e-03
##  [5,] 0.001802328 0.0025100696 0.0090729669 0.0027106343 2.521838e-03
##  [6,] 0.027504782 0.0215772258 0.0079555751 0.0030976950 1.617144e-03
##  [7,] 0.109641823 0.1125305307 0.0066842473 0.0161613882 9.223164e-04
##  [8,] 0.041170083 0.0110206771 0.1209578864 0.0643897912 2.211272e-03
##  [9,] 0.045206742 0.0217941560 0.0177586558 0.1240729036 3.601235e-02
## [10,] 0.068178704 0.0062325755 0.0078515525 0.0101201963 2.742154e-03
## [11,] 0.059835569 0.0198262860 0.0335128918 0.0397878317 2.969981e-03
## [12,] 0.003743271 0.0016276507 0.0018329777 0.0021327142 1.704538e-04
##               X11         X12
##  [1,] 0.013301704 0.003955800
##  [2,] 0.001163561 0.001364445
##  [3,] 0.037652593 0.011266671
##  [4,] 0.075643312 0.064407471
##  [5,] 0.008278264 0.026597534
##  [6,] 0.042874909 0.014609149
##  [7,] 0.053269975 0.028133131
##  [8,] 0.159408148 0.059729791
##  [9,] 0.043499794 0.093806153
## [10,] 0.047124092 0.007975733
## [11,] 0.090339152 0.064244953
## [12,] 0.005068504 0.003469390

    G = solve(I - F) # Matriz inversa de Ghosh
    G # Matriz inversa de Ghosh

##            [,1]        [,2]       [,3]        [,4]        [,5]        [,6]
## X1  1.070422587 0.011006105 0.69329484 0.011457967 0.043021303 0.047377336
## X2  0.031449509 1.068456656 0.71003291 0.038171677 0.070889750 0.027275710
## X3  0.058338419 0.021427386 1.47531499 0.022157145 0.080816255 0.049721671
## X4  0.068169190 0.022567920 0.37537215 1.390725949 0.030609046 0.111576078
## X5  0.002054302 0.007052456 0.02069948 0.011024541 1.105148396 0.005873110
## X6  0.043025638 0.015899113 0.35292366 0.016010389 0.058994637 1.049128186
## X7  0.049914314 0.063205512 0.56712536 0.031814566 0.057941071 0.156080478
## X8  0.011150225 0.012498095 0.15905284 0.018387351 0.021294180 0.076159045
## X9  0.027252585 0.019238816 0.21671325 0.026029209 0.036490164 0.075146269
## X10 0.005067301 0.003965771 0.05648133 0.006644482 0.009369423 0.078943486
## X11 0.014017783 0.025616651 0.21119974 0.023717333 0.029279956 0.085868007
## X12 0.001205014 0.001657001 0.01504529 0.002234682 0.001911661 0.005452054
##            [,7]        [,8]        [,9]       [,10]       [,11]      [,12]
## X1  0.029485762 0.006323513 0.005484188 0.001957032 0.051249084 0.01973315
## X2  0.029677295 0.006565717 0.005393144 0.003374984 0.039746486 0.01870278
## X3  0.059027849 0.010939667 0.009321104 0.003704238 0.073042091 0.02919675
## X4  0.035269885 0.021804360 0.022150770 0.005276522 0.145582809 0.11069855
## X5  0.004870649 0.012468023 0.005396079 0.003153001 0.015221757 0.03294635
## X6  0.041219969 0.015049075 0.010107987 0.003211989 0.072441609 0.02988537
## X7  1.155888289 0.018263451 0.030055404 0.004117750 0.107667313 0.05611732
## X8  0.029882078 1.150184985 0.096314565 0.007255711 0.220909208 0.09788208
## X9  0.041280090 0.029443263 1.150137925 0.042592100 0.080900345 0.12309474
## X10 0.013173047 0.012918750 0.016174113 1.003839084 0.062683382 0.01724501
## X11 0.037735975 0.046850209 0.056770276 0.006250123 1.128525475 0.08807359
## X12 0.002847853 0.002619490 0.003115338 0.000363288 0.007495736 1.00495081

Insumo-Produto

Multiplicadores

Multiplicadores de produção

MP = colSums(B)
MP

##        1        2        3        4        5        6        7        8 
## 1.719044 1.771649 2.147529 1.947655 1.811262 1.532739 1.840288 1.640565 
##        9       10       11       12 
## 1.492315 1.110196 1.533751 1.383516

MPT = colSums(BF[, 1:n])
MPT

##        1        2        3        4        5        6        7        8 
## 2.959997 3.328518 4.051231 3.344608 3.693084 3.780823 4.143630 3.708278 
##        9       10       11       12 
## 3.463977 1.309140 4.052431 5.306243

MPTT = colSums(BF[1:n, 1:n])
MPTT

##        1        2        3        4        5        6        7        8 
## 2.543951 2.806557 3.412990 2.876261 3.062178 3.027123 3.371404 3.015050 
##        9       10       11       12 
## 2.802952 1.242441 3.208010 3.991097

MultProd= cbind(Setores, MP, MPT, MPTT)
MultProd = as.data.frame(MultProd)
colnames(MultProd) = c("Setores", "MP", "MPT", "MPTT")

MultProd$MP = as.numeric(as.character(MultProd$MP))
MultProd$MPT = as.numeric(as.character(MultProd$MPT))
MultProd$MPTT = as.numeric(as.character(MultProd$MPTT))

flextable(MultProd) #%>%

Setores	MP	MPT	MPTT
Agro	1.719044	2.959997	2.543951
Ind.Extr	1.771649	3.328518	2.806557
Ind.Tran	2.147529	4.051231	3.412990
SIUP	1.947655	3.344608	2.876261
Cons	1.811262	3.693084	3.062178
Com	1.532739	3.780823	3.027123
Transp	1.840288	4.143630	3.371404
Info	1.640565	3.708278	3.015050
Finan	1.492315	3.463977	2.802952
Imob	1.110196	1.309140	1.242441
Otrs.Serv	1.533751	4.052431	3.208010
Adm	1.383516	5.306243	3.991097

#align(align = "center", part = "all" ) #%>%
#set_caption(caption = "Multiplicadores de Produção")
#%>%
#footnote(value = as_paragraph("Fonte: elaboração própria com dados da MIP do IBGE (2015)."), #ref_symbols = "")

kable(MultProd, caption = "Multiplicadores de Produção", align = "lccc") %>%
kable_styling(bootstrap_options = "striped", full_width = FALSE) #%>%

Multiplicadores de Produção
Setores	MP	MPT	MPTT
Agro	1.719044	2.959997	2.543951
Ind.Extr	1.771649	3.328518	2.806557
Ind.Tran	2.147530	4.051231	3.412990
SIUP	1.947655	3.344608	2.876261
Cons	1.811262	3.693084	3.062178
Com	1.532739	3.780823	3.027123
Transp	1.840288	4.143630	3.371404
Info	1.640565	3.708278	3.015050
Finan	1.492315	3.463977	2.802952
Imob	1.110196	1.309140	1.242441
Otrs.Serv	1.533751	4.052431	3.208010
Adm	1.383516	5.306243	3.991097

#footnote(general = "elaboração própria com dados da MIP do IBGE (2015).",
#general_title = "Fonte:", footnote_as_chunk = TRUE, title_format = c("bold"))

# Multiplicador Total de Produção do Setor 1:
# Efeito Total no modelo fechado
format(round(sum(BF[,1]), digits = 4), nsmall = 4)

## [1] "2.9600"

# Efeito Total no modelo aberto
format(round(sum(B[,1]), digits = 4), nsmall = 4)

## [1] "1.7190"

# Efeito Induzido
format(round(sum(BF[,1]) - sum(B[,1]), digits = 4), nsmall = 4)

## [1] "1.2410"

# Efeito Direto
format(round(sum(A[,1]), digits = 4), nsmall = 4)

## [1] "0.3713"

# Efeito Indireto
format(round(sum(B[,1]) - sum(A[,1]), digits = 4), nsmall = 4)

## [1] "1.3478"

#Multiplicador Total de Produção Truncado do Setor 1:
# Efeito Total no modelo fechado
format(round(sum(BF[1:n,1]), digits = 4), nsmall = 4)

## [1] "2.5440"

# Efeito Total no modelo aberto
format(round(sum(B[,1]), digits = 4), nsmall = 4)

## [1] "1.7190"

# Efeito Induzido
format(round(sum(BF[1:n,1]) - sum(B[,1]), digits = 4), nsmall = 4)

## [1] "0.8249"

# Efeito Direto
format(round(sum(A[,1]), digits = 4), nsmall = 4)

## [1] "0.3713"

# Efeito Indireto
format(round(sum(B[,1]) - sum(A[,1]), digits = 4), nsmall = 4)

## [1] "1.3478"

ggplot(MultProd, aes(x = factor(Setores, levels = unique(Setores)), y = MP)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Simples de Produção") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015)."
) +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MP, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0, 2.5),
breaks = seq(from = 0.0, to = 2.5, by = 0.5))

ggplot(MultProd, aes(x = factor(Setores, levels = unique(Setores)), y = MPT)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Totais de Produção") +
labs(subtitle = "2015",caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MPT, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0, 5.5),
breaks = seq(from = 0.0, to = 5.5, by = 0.5))

ggplot(MultProd, aes(x = factor(Setores, levels = unique(Setores)), y = MPTT)) +
geom_col() +
theme_bw() +
theme(plot.background = element_rect(fill = "#e6f2ff", colour = "#e6f2ff")) +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Totais de Produção Truncados") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MPTT, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0, 4.5),
breaks = seq(from = 0.0, to = 4.5, by = 0.5))

ce = e / x
ce = as.vector(ce)

Cehat = diag(ce)

E = Cehat %*% B

ME = colSums(E)

ME

##         1         2         3         4         5         6         7         8 
## 34.101037  8.451915 15.374493  8.348028 21.242773 22.473178 17.071567 10.674351 
##         9        10        11        12 
##  6.687006  1.560459 26.034161 13.211106

MEI = ME / ce

MEI

##        1        2        3        4        5        6        7        8 
## 1.242638 7.658824 3.806716 3.987779 1.554648 1.310717 1.827595 2.771608 
##        9       10       11       12 
## 3.202383 2.042665 1.264451 1.428829

EF = Cehat %*% BF[1:n, 1:n]

MET = colSums(EF)

MET = colSums(EF)

MEII = MET / ce

MEII

##         1         2         3         4         5         6         7         8 
##  1.536640 16.831101  6.871265  8.326354  2.450048  2.163178  3.430779  6.262196 
##         9        10        11        12 
##  9.341304  3.735805  2.059785  4.187166

MultEmp = cbind(Setores, ME, MEI, MET, MEII)
MultEmp = as.data.frame(MultEmp)
colnames(MultEmp) = c("Setores", "ME", "MEI", "MET", "MEII")

MultEmp$ME = as.numeric(as.character(MultEmp$ME))
MultEmp$MEI = as.numeric(as.character(MultEmp$MEI))
MultEmp$MET = as.numeric(as.character(MultEmp$MET))
MultEmp$MEII = as.numeric(as.character(MultEmp$MEII))

flextable(MultEmp) # %>%

Setores	ME	MEI	MET	MEII
Agro	34.101037	1.242638	42.169181	1.536640
Ind.Extr	8.451915	7.658824	18.574004	16.831101
Ind.Tran	15.374493	3.806716	27.751536	6.871265
SIUP	8.348028	3.987779	17.430413	8.326354
Cons	21.242773	1.554648	33.477565	2.450048
Com	22.473178	1.310717	37.089247	2.163178
Transp	17.071567	1.827595	32.046902	3.430779
Info	10.674351	2.771608	24.117726	6.262196
Finan	6.687006	3.202383	19.505899	9.341304
Imob	1.560459	2.042665	2.853904	3.735805
Otrs.Serv	26.034161	1.264451	42.409532	2.059785
Adm	13.211106	1.428829	38.714983	4.187166

#align(align = "center", part = "all" ) %>%
#set_caption(caption = "Multiplicadores de Emprego") %>%
#footnote(value = as_paragraph(c("Fonte: elaboração própria com dados da MIP do IBGE (2015).", #"Nota: ME e MET por 1.000.000 R$.")),
#ref_symbols = c("", ""))

flextable(MultEmp) #%>%

Setores	ME	MEI	MET	MEII
Agro	34.101037	1.242638	42.169181	1.536640
Ind.Extr	8.451915	7.658824	18.574004	16.831101
Ind.Tran	15.374493	3.806716	27.751536	6.871265
SIUP	8.348028	3.987779	17.430413	8.326354
Cons	21.242773	1.554648	33.477565	2.450048
Com	22.473178	1.310717	37.089247	2.163178
Transp	17.071567	1.827595	32.046902	3.430779
Info	10.674351	2.771608	24.117726	6.262196
Finan	6.687006	3.202383	19.505899	9.341304
Imob	1.560459	2.042665	2.853904	3.735805
Otrs.Serv	26.034161	1.264451	42.409532	2.059785
Adm	13.211106	1.428829	38.714983	4.187166

#align(align = "center", part = "all" ) %>%
#set_caption(caption = "Multiplicadores de Emprego") %>%
#footnote(value = as_paragraph(c("Fonte: elaboração própria com dados da MIP do IBGE (2015).", #"Nota: ME e MET por 1.000.000 R$.")),
#ref_symbols = c("", ""))

kable(MultEmp, caption = "Multiplicadores de Emprego", align = "lcccc") #%>%

Multiplicadores de Emprego
Setores	ME	MEI	MET	MEII
Agro	34.101037	1.242638	42.169181	1.536640
Ind.Extr	8.451915	7.658824	18.574004	16.831101
Ind.Tran	15.374493	3.806716	27.751535	6.871265
SIUP	8.348028	3.987779	17.430413	8.326354
Cons	21.242773	1.554648	33.477565	2.450048
Com	22.473178	1.310717	37.089247	2.163178
Transp	17.071567	1.827595	32.046902	3.430779
Info	10.674351	2.771608	24.117726	6.262196
Finan	6.687006	3.202383	19.505899	9.341304
Imob	1.560459	2.042665	2.853904	3.735805
Otrs.Serv	26.034161	1.264451	42.409532	2.059785
Adm	13.211106	1.428829	38.714983	4.187166

#kable_styling(bootstrap_options = "striped", full_width = FALSE) %>%
#footnote(general = "elaboração própria com dados da MIP do IBGE (2015).",
#general_title = "Fonte:",
#alphabet = "ME e MET por 1,000,000 R$.",
#alphabet_title = "Nota:",
#footnote_as_chunk = TRUE, title_format = c("bold"))

Interpretações

Os Multiplicadores de Emprego do Setor 1 (Agro), por exemplo, podem ser interpretados como: - Multiplicador Simples de Emprego (ME): uma variação de demanda de R$1.000.000 no Setor 1 (Agro) gera 34,101 empregos na economia. - Multiplicador de Emprego (Tipo I) (MEI): para cada emprego gerado diretamente no Setor 1 (Agro), tem-se um efeito multiplicador de 1,2426 na economia. - Multiplicador Total de Emprego Truncado (MET): uma variação de demanda de R$1.000.000 no Setor 1 (Agro) gera 42,1692 empregos na economia, incluindo o efeito induzido (apenas nos 𝑛𝑛 setores produtivos). - Multiplicador de Emprego (Tipo II) (MEII): para cada emprego gerado diretamente no Setor 1 (Agro), tem-se um efeito multiplicador de 1,5366 na economia, incluindo o efeito induzido (apenas nos 𝑛𝑛 setores produtivos).

Multiplicadores Simples de Emprego

ggplot(MultEmp, aes(x = factor(Setores, levels = unique(Setores)), y = ME)
) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Simples de Emprego") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).\nNota: por 1,000,000 R$.") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(ME, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,35),
breaks = seq(from = 0.0, to = 35.0, by = 5))

Multiplicadores de Emprego (Tipo I)

ggplot(MultEmp, aes(x = factor(Setores, levels = unique(Setores)), y = MEI
)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores de Emprego (Tipo I)") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MEI, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,8),
breaks = seq(from = 0.0, to = 8, by = 1))

Multiplicadores Totais de Emprego (truncados)

ggplot(MultEmp, aes(x = factor(Setores, levels = unique(Setores)), y = MET
)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Totais de Emprego (truncados)") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015
).\nNota: por 1,000,000 R$.") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MET, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,45),
breaks = seq(from = 0, to = 45, by = 5))

Multiplicadores de Emprego (Tipo II)

ggplot(MultEmp, aes(x = factor(Setores, levels = unique(Setores)), y = MEII)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores de Emprego (Tipo II)") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MEII, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,20),
breaks = seq(from = 0, to = 20, by = 5))

Multiplicadores de Renda

cr = r / x
cr = as.vector(cr)

Crhat = diag(cr)

R = Crhat %*% B

MR = colSums(R)

MR

##          1          2          3          4          5          6          7 
## 0.23909638 0.29996428 0.36678896 0.26915304 0.36257345 0.43314165 0.44378838 
##          8          9         10         11         12 
## 0.39838932 0.37988304 0.03833075 0.48527792 0.75579774

MRI = MR / cr

MRI

##        1        2        3        4        5        6        7        8 
## 2.297985 2.383660 2.586250 2.643962 1.810757 1.383320 1.706910 1.715025 
##        9       10       11       12 
## 1.523879 3.117216 1.344106 1.144139

RF = Crhat %*% BF[1:n, 1:n]

MRT = colSums(RF)
MRT

##          1          2          3          4          5          6          7 
## 0.41604616 0.52196102 0.63824110 0.46834707 0.63090580 0.75369992 0.77222605 
##          8          9         10         11         12 
## 0.69322818 0.66102582 0.06669846 0.84442106 1.31514643

MRII = MRT / cr
MRII

##        1        2        3        4        5        6        7        8 
## 3.998671 4.147752 4.500275 4.600697 3.150856 2.407084 2.970155 2.984276 
##        9       10       11       12 
## 2.651667 5.424196 2.338848 1.990890

MultRen = cbind(Setores, MR, MRI, MRT, MRII)
MultRen = as.data.frame(MultRen)
colnames(MultRen) = c("Setores", "MR", "MRI", "MRT", "MRII")

MultRen$MR = as.numeric(as.character(MultRen$MR))
MultRen$MRI = as.numeric(as.character(MultRen$MRI))
MultRen$MRT = as.numeric(as.character(MultRen$MRT))
MultRen$MRII = as.numeric(as.character(MultRen$MRII))

flextable(MultRen)

Setores	MR	MRI	MRT	MRII
Agro	0.23909638	2.297985	0.41604616	3.998671
Ind.Extr	0.29996428	2.383660	0.52196102	4.147752
Ind.Tran	0.36678896	2.586250	0.63824110	4.500275
SIUP	0.26915304	2.643962	0.46834707	4.600697
Cons	0.36257345	1.810757	0.63090580	3.150856
Com	0.43314165	1.383320	0.75369992	2.407084
Transp	0.44378838	1.706910	0.77222605	2.970155
Info	0.39838932	1.715025	0.69322818	2.984276
Finan	0.37988304	1.523879	0.66102582	2.651667
Imob	0.03833075	3.117216	0.06669846	5.424196
Otrs.Serv	0.48527792	1.344106	0.84442106	2.338848
Adm	0.75579774	1.144139	1.31514643	1.990890

#%>%
#align(align = "center", part = "all" ) %>%
#set_caption(caption = "Multiplicadores de Renda") %>%
#footnote(value = as_paragraph("Fonte: elaboração própria com dados da MIP do IBGE (2015)."),
#ref_symbols = "")

kable(MultRen, caption = "Multiplicadores de Renda", align = "lcccc") %>% kable_styling(bootstrap_options = "striped", full_width = FALSE)

Multiplicadores de Renda
Setores	MR	MRI	MRT	MRII
Agro	0.2390964	2.297985	0.4160462	3.998670
Ind.Extr	0.2999643	2.383660	0.5219610	4.147752
Ind.Tran	0.3667890	2.586250	0.6382411	4.500275
SIUP	0.2691530	2.643962	0.4683471	4.600697
Cons	0.3625734	1.810757	0.6309058	3.150856
Com	0.4331417	1.383320	0.7536999	2.407084
Transp	0.4437884	1.706910	0.7722261	2.970155
Info	0.3983893	1.715025	0.6932282	2.984276
Finan	0.3798830	1.523879	0.6610258	2.651667
Imob	0.0383307	3.117215	0.0666985	5.424196
Otrs.Serv	0.4852779	1.344106	0.8444211	2.338848
Adm	0.7557977	1.144139	1.3151464	1.990890

#%>%
#footnote(general = "elaboração própria com dados da MIP do IBGE (2015).",
#general_title = "Fonte:",
#footnote_as_chunk = TRUE, title_format = c("bold"))

Interpretações

Os Multiplicadores de Renda do Setor 1 (Agro), por exemplo, podem ser interpretados como: - Multiplicador Simples de Renda (MR): uma variação de demanda de R$1,00 no Setor 1 (Agro) gera R$0,2391 de renda na economia. - Multiplicador de Renda (Tipo I) (MRI): para cada unidade de renda gerada diretamente no Setor 1 (Agro), tem-se um efeito multiplicador de R$2,298 na economia. - Multiplicador Total de Renda Truncado (MRT): uma variação de demanda de R$1,00 no Setor 1 (Agro) gera R$0,416 de renda na economia, incluindo o efeito induzido (apenas nos 𝑛𝑛 setores produtivos). - Multiplicador de Renda (Tipo II) (MRII): para cada unidade de renda gerada diretamente no Setor 1 (Agro), tem-se um efeito multiplicador de R$3,9987 na economia, incluindo o efeito induzido (apenas nos 𝑛𝑛 setores produtivos).

Multiplicadores Simples de Renda

ggplot(MultRen, aes(x = factor(Setores, levels = unique(Setores)), y = MR)
) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Simples de Renda") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MR, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,1),
breaks = seq(from = 0, to = 1, by = 0.25))

Multiplicadores de Renda (Tipo I)

ggplot(MultRen, aes(x = factor(Setores, levels = unique(Setores)), y = MRI)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores de Renda (Tipo I)") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MRI, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,3.5),
breaks = seq(from = 0, to = 3.5, by = 0.5))

Multiplicadores Totais de Renda (truncados)

ggplot(MultRen, aes(x = factor(Setores, levels = unique(Setores)), y = MRT)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores Totais de Renda (truncados)") +
labs(subtitle = "2015",
caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MRT, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,1.5),
breaks = seq(from = 0, to = 1.5, by = 0.25))

Multiplicadores de Renda (Tipo II)

ggplot(MultRen, aes(x = factor(Setores, levels = unique(Setores)), y = MRII)) +
geom_col() +
theme_bw() +
xlab("Setores") +
ylab(" ") +
ggtitle("Multiplicadores de Renda (Tipo II)") +
labs(subtitle = "2015", caption = "Fonte: elaboração própria com dados da MIP do IBGE (2015).") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5),
plot.caption = element_text(hjust = 0)) +
geom_text(aes(label = round(MRII, digits = 2)), vjust = -0.5, size = 3) +
scale_y_continuous(labels = scales::number_format(accuracy = 0.01),
limits = c(0,6),
breaks = seq(from = 0, to = 6, by = 0.5))

MIP

2026-01-06

Análise de Insumo-produto: teoria e aplicações no R

Passos iniciais

Base de Dados

Descrição

Importando dados

Preparação dos Objetos

Exportando dados

Insumo-Produto

Modelo aberto

Modelo fechado

Modelo pelo lado da oferta

Insumo-Produto

Multiplicadores

Multiplicadores de produção

Interpretações

Multiplicadores Simples de Emprego

Multiplicadores de Emprego (Tipo I)

Multiplicadores Totais de Emprego (truncados)

Multiplicadores de Emprego (Tipo II)

Multiplicadores de Renda

Interpretações

Multiplicadores Simples de Renda

Multiplicadores de Renda (Tipo I)

Multiplicadores Totais de Renda (truncados)