Econometria: exemplo_soja_apostila

Abstract

This is an undergrad student level exercise for class use. We analyse soy data, 117 observations.

Licença

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

License: CC BY-SA 4.0

Citação

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Econometria: exemplo_soja_apostila. Campo Grande-MS,Brasil: RStudio/Rpubs, 2020. Disponível em http://rpubs.com/amrofi/exemplo_soja_apostila.

1 Exercício

Sabendo que a variável dependente Qsoja é a quantidade produzida de soja, a variável FERTILIZANTE é a quantidade utilizada de fertilizantes, a variável TRATOR é o número de horas-máquina utilizadas, e MO é a quantidade de mão-de-obra em número de pessoas.

Pede-se:

1. Quais os parâmetros significativos a 10% de significância? Explique e mostre seus valores.
   
2. Sabendo que o desejável numa função de produção é que o aumento no uso de insumos leve a uma produção maior, o resultado é coerente com a teoria econômica? Justifique sua resposta.
   
3. Qual a hipótese nula no teste de significância global do modelo? Qual a probabilidade de erro desse teste para essa regressão?

library(readxl)
# library(foreign)
# dados <- read_excel("soja_apostila.xlsx", 
#                     sheet = "dados")
dados<-structure(list(OBS = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 
45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 
77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 
107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117), QSOJA = c(436.631327347, 
373.648319403, 394.422208122, 343.569529223, 303.766149519, 301.164159253, 
288.948162961, 330.653425923, 312.790481897, 326.337437514, 393.924244131, 
472.095484821, 506.519816219, 351.622349614, 381.683735178, 383.16244294, 
411.039886175, 393.721292241, 434.570723074, 433.61603289, 397.521061235, 
392.667303139, 388.161060061, 370.962499467, 392.989989558, 364.608287145, 
346.432408617, 418.249947335, 406.403616915, 335.565654517, 372.389277147, 
355.138034335, 350.368666514, 333.22912698, 331.404160354, 350.215587437, 
347.930917294, 429.353837601, 312.648633868, 320.1290397, 367.600375264, 
370.58115319, 318.293875369, 360.716491231, 344.127888634, 348.460445231, 
339.909909323, 355.115806958, 333.991242698, 324.352196839, 326.362748629, 
337.522873509, 326.439134587, 315.883680773, 309.389262881, 309.992167966, 
294.858595183, 319.126938705, 321.075126328, 324.617110436, 326.498169984, 
323.024096765, 306.607962724, 316.685380598, 306.63234033, 347.051171678, 
281.018277888, 306.438241825, 310.158071775, 308.554712739, 317.988817729, 
309.3024648, 301.907326808, 293.695986672, 286.246007121, 284.741951642, 
281.541824884, 276.076484065, 225.250102468, 221.579142339, 222.819046328, 
210.465091286, 204.579726173, 210.208100729, 214.619137203, 249.68373735, 
234.056997721, 237.782743552, 247.783594823, 243.326935015, 250.517759798, 
245.477283956, 242.547637962, 235.139515392, 246.077631412, 300.660379261, 
311.547314244, 311.592498254, 311.661546245, 313.521069724, 324.623216411, 
325.219601572, 316.051963666, 315.23510561, 313.039404973, 311.256344161, 
314.759829619, 319.859862035, 315.86486682, 313.067146865, 305.235250016, 
299.911393983, 292.819273066, 288.374750217, 282.574142328, 280.040196223, 
272.093598783), FERTILIZANTE = c(19.0271541214, 17.896131535, 
16.7816326404, 13.4907436954, 9.8792199643, 9.47578570764, 11.3642792008, 
15.1279345194, 15.3328667597, 12.851502126, 11.5137639555, 12.855099231, 
13.0130463524, 13.4551480743, 14.3478259384, 13.4461834272, 12.8505836532, 
11.878680085, 8.97428388969, 11.2853667097, 10.3459526645, 10.1678109845, 
12.599515057, 18.0635955859, 22.5905514861, 27.0789975599, 25.8933999151, 
24.670302157, 22.3482879799, 23.0661021802, 23.46202603, 23.3742807993, 
23.6293106114, 21.5085651347, 20.4244350802, 18.8640383209, 18.2649424041, 
16.1258445984, 15.3872613296, 15.7475620647, 14.8983557849, 18.5713738614, 
19.782502768, 19.9334418708, 20.8217736318, 20.2664704198, 18.7039332243, 
16.9397047639, 15.2224405941, 15.3900606317, 15.4866979181, 14.1888364722, 
17.5057959027, 18.4499760981, 18.0443380567, 18.7653974258, 17.733992169, 
14.4708212634, 19.1906127545, 23.6107568782, 22.4809389477, 19.9623501966, 
24.292193006, 23.7774100871, 20.902854945, 17.6135324226, 18.2422805406, 
18.4963907183, 20.1887054098, 17.2164566133, 18.2228548842, 17.63412, 
17.3651340732, 21.165752859, 20.6546570465, 20.5382250175, 20.2625821575, 
20.0316705895, 19.6747891284, 19.2320746157, 19.1556951795, 18.6659751037, 
18.2573530021, 18.0250472242, 18.2220357618, 18.1808546614, 17.9427350427, 
17.8936494922, 17.5782913467, 17.4452921577, 17.4075434149, 17.287132673, 
17.0010026609, 16.7956796708, 16.6141444443, 16.6135183413, 16.5922588804, 
22.0744924554, 22.0123280182, 21.8207871467, 21.4818658909, 21.3918043526, 
21.1455500396, 21.0219803014, 20.9587175263, 20.8135574015, 22.8749876176, 
22.8850270408, 22.7508743781, 22.6733292656, 22.4866071739, 22.3322073706, 
22.1375395445, 22.1331443789, 22.081593902, 22.1113459316, 22.0611011027
), TRATOR = c(3.1712177231, 2.9130726375, 2.79693877341, 2.89345709284, 
3.09884379577, 3.55341964037, 3.9774977203, 4.86255038122, 5.27067294863, 
5.29179499304, 4.38619579258, 3.61549665871, 3.18096688613, 3.31203644906, 
3.58695648459, 3.36154585679, 2.79360514201, 3.25443289999, 2.69228516691, 
2.90195143963, 2.95598647557, 2.98255788878, 3.23987530037, 3.18769333868, 
3.80472446082, 4.16599962459, 4.25644930111, 3.65485957882, 3.42843054238, 
3.56476124603, 4.10585455524, 4.23376550096, 4.21951975203, 4.45534563505, 
4.22104991658, 3.77280766418, 4.05887608981, 4.35397804157, 3.71858815465, 
3.9194002239, 3.86253116707, 3.4489694314, 3.40698658782, 3.10590838452, 
3.40719932157, 3.89739815766, 3.58705568686, 3.06139242721, 2.56377946849, 
3.27038788423, 3.61356284755, 2.9212310384, 3.72808616447, 4.09999468846, 
4.00985290148, 3.12756623763, 3.66502504826, 3.61770531584, 2.74151610779, 
3.07966394064, 2.24809389477, 2.21803891073, 3.23895906746, 3.26939388698, 
2.71737114285, 3.52270648453, 2.63499607808, 2.84559857204, 3.02830581147, 
2.75463305812, 3.79642810087, 3.673775, 4.3412835183, 4.23315057181, 
5.50790854573, 5.47686000466, 5.40335524199, 6.67722352984, 6.5582630428, 
6.41069153856, 6.3852317265, 6.22199170124, 6.08578433403, 6.00834907473, 
6.07401192061, 6.06028488713, 5.98091168091, 5.96454983075, 5.85943044889, 
5.8150973859, 5.80251447164, 5.76237755766, 5.66700088697, 5.59855989028, 
5.53804814809, 5.53783944709, 5.53075296013, 5.51862311384, 5.50308200454, 
5.45519678667, 5.37046647273, 5.34795108814, 5.28638750989, 5.25549507535, 
5.23967938158, 5.20338935039, 5.19886082219, 5.20114250927, 5.17065326775, 
5.15302937855, 5.11059253952, 5.07550167513, 6.03751078486, 6.03631210335, 
6.02225288236, 6.03036707224, 6.01666393711), MO = c(0.0680761131536, 
0.0680761131536, 0.0680761131536, 0.0680761131536, 0.0715237353179, 
0.0833559863149, 0.0985723372523, 0.111410334113, 0.114487135409, 
0.102686021888, 0.121305727388, 0.123194700963, 0.113382190903, 
0.0988435877764, 0.0807663035114, 0.0622686351567, 0.083800394246, 
0.0765243736067, 0.0574877668834, 0.0653655605136, 0.0725099376921, 
0.0780548956575, 0.0806568955951, 0.0816669323964, 0.0822771664653, 
0.0801052294483, 0.0750435658726, 0.0703103611476, 0.0796030780377, 
0.0830484524405, 0.093584156327, 0.100913962297, 0.108669511694, 
0.111606408158, 0.118828985067, 0.120133794043, 0.118234214897, 
0.105740298613, 0.093457488034, 0.0841934657141, 0.0798233440708, 
0.0747407520408, 0.0708495225001, 0.0672990598108, 0.0611103807825, 
0.055394759321, 0.0660366632049, 0.0689438046948, 0.0669589093824, 
0.0638618759693, 0.0596771157157, 0.0549263770463, 0.073413760912, 
0.0823331322263, 0.0834334103063, 0.079906745817, 0.0716246518416, 
0.0633701381158, 0.0934971222594, 0.104075531949, 0.100833255886, 
0.0930097649901, 0.0813417334974, 0.0695736926403, 0.21049581374, 
0.261260874072, 0.258725366517, 0.236599269382, 0.206871841743, 
0.167746823366, 0.126327870706, 0.114329213918, 0.104788717578, 
0.0945762804116, 0.0848737411962, 0.0770183438155, 0.0741085180759, 
0.071409196083, 0.0683152400292, 0.0649972892104, 0.0629654795252, 
0.0596274204703, 0.0578149511733, 0.0565786204537, 0.0566907779257, 
0.0560576352059, 0.0548250237417, 0.0541779942959, 0.0539450091897, 
0.0542532433056, 0.0548506857575, 0.0551811677564, 0.0549659731863, 
0.0549918545222, 0.0547197615699, 0.0550399709491, 0.0552913982385, 
0.0554912883605, 0.0556552669895, 0.0554884433151, 0.0541104333052, 
0.0533695807757, 0.0522471298894, 0.0514366981903, 0.0507783150735, 
0.049926520817, 0.049902565317, 0.0499439709453, 0.0496705879533, 
0.0495206123279, 0.0491319590269, 0.0488136373605, 0.0483839405954, 
0.0483701426115, 0.0482533012199, 0.0483141284115, 0.0482001633184
)), row.names = c(NA, -117L), class = c("tbl_df", "tbl", "data.frame"
))
attach(dados)
# QSOJA = quantidade produzida de soja; 
# FERTILIZANTE = quantidade utilizada de fertilizantes, 
# TRATOR = número de horas-máquina utilizadas, e 
# MO = quantidade de mão-de-obra em número de pessoas 
dados

1.1 Estimação

1.1.1 PASSO 1: estimar o modelo

# 
regressao1<-lm(QSOJA~FERTILIZANTE+TRATOR+MO)
summary(regressao1)

## 
## Call:
## lm(formula = QSOJA ~ FERTILIZANTE + TRATOR + MO)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -66.714 -33.171   1.768  24.894 149.637 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   494.9657    25.5723  19.356  < 2e-16 ***
## FERTILIZANTE   -0.5535     1.0589  -0.523   0.6022    
## TRATOR        -33.6899     3.7410  -9.006 6.09e-15 ***
## MO           -209.1407   107.8926  -1.938   0.0551 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.51 on 113 degrees of freedom
## Multiple R-squared:  0.4651, Adjusted R-squared:  0.4509 
## F-statistic: 32.75 on 3 and 113 DF,  p-value: 2.608e-15

library(stargazer)

## 
## Please cite as:

##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.

##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer

stargazer(list(regressao1),type="text",style="all" )

## 
## =======================================================
##                             Dependent variable:        
##                     -----------------------------------
##                                    QSOJA               
## -------------------------------------------------------
## FERTILIZANTE                      -0.554               
##                                   (1.059)              
##                                 t = -0.523             
##                                  p = 0.603             
## TRATOR                          -33.690***             
##                                   (3.741)              
##                                 t = -9.006             
##                                  p = 0.000             
## MO                               -209.141*             
##                                  (107.893)             
##                                 t = -1.938             
##                                  p = 0.056             
## Constant                        494.966***             
##                                  (25.572)              
##                                 t = 19.356             
##                                  p = 0.000             
## -------------------------------------------------------
## Observations                        117                
## R2                                 0.465               
## Adjusted R2                        0.451               
## Residual Std. Error          41.506 (df = 113)         
## F Statistic         32.753*** (df = 3; 113) (p = 0.000)
## =======================================================
## Note:                       *p<0.1; **p<0.05; ***p<0.01

1.1.2 PASSO 2: obtencao dos valores ajustados

1.1.3 PASSO 3: colocar valores ajustados ao quadrado e ao cubo e a quarta potencias

Utilizaremos o recurso I(fitted(regressao1)) para gerar automaticamente e já estimar a regressão de teste

# 
reg_RESET_3<-lm(QSOJA~FERTILIZANTE+TRATOR+MO+I(fitted(regressao1)^2)+
                  I(fitted(regressao1)^3)+I(fitted(regressao1)^4),data=dados)

reg_RESET<-lm(QSOJA~FERTILIZANTE+TRATOR+MO+
                I(fitted(regressao1)^2)+I(fitted(regressao1)^3),data=dados)
results<-stargazer(list(regressao1,reg_RESET_3),type="text",style="all" )

## 
## ==============================================================================================
##                                                  Dependent variable:                          
##                        -----------------------------------------------------------------------
##                                                         QSOJA                                 
##                                        (1)                                 (2)                
## ----------------------------------------------------------------------------------------------
## FERTILIZANTE                         -0.554                             304.130**             
##                                      (1.059)                            (135.047)             
##                                    t = -0.523                           t = 2.252             
##                                     p = 0.603                           p = 0.027             
## TRATOR                             -33.690***                         18,591.290**            
##                                      (3.741)                           (8,231.767)            
##                                    t = -9.006                           t = 2.258             
##                                     p = 0.000                           p = 0.026             
## MO                                  -209.141*                         115,237.700**           
##                                     (107.893)                         (51,069.360)            
##                                    t = -1.938                           t = 2.256             
##                                     p = 0.056                           p = 0.027             
## I(fitted(regressao1)2)                                                   2.665**              
##                                                                          (1.165)              
##                                                                         t = 2.287             
##                                                                         p = 0.025             
## I(fitted(regressao1)3)                                                  -0.006**              
##                                                                          (0.002)              
##                                                                        t = -2.300             
##                                                                         p = 0.024             
## I(fitted(regressao1)4)                                                  0.00000**             
##                                                                         (0.00000)             
##                                                                         t = 2.303             
##                                                                         p = 0.024             
## Constant                           494.966***                        -230,604.700**           
##                                     (25.572)                          (101,861.300)           
##                                    t = 19.356                          t = -2.264             
##                                     p = 0.000                           p = 0.026             
## ----------------------------------------------------------------------------------------------
## Observations                           117                                 117                
## R2                                    0.465                               0.532               
## Adjusted R2                           0.451                               0.507               
## Residual Std. Error             41.506 (df = 113)                   39.331 (df = 110)         
## F Statistic            32.753*** (df = 3; 113) (p = 0.000) 20.879*** (df = 6; 110) (p = 0.000)
## ==============================================================================================
## Note:                                                              *p<0.1; **p<0.05; ***p<0.01

1.1.4 PASSOS 4 A 6: calcular estatisticas de teste

# RESET: H0: o modelo esta bem especificado, ou H0: COEFICIENTES incluindo "fitted" sao nulos
library(car)

## Carregando pacotes exigidos: carData

# RESETH0<-c("I(fitted(regressao1)^2)","I(fitted(regressao1)^3)",
#         "I(fitted(regressao1)^4)")
RESETH0<-c("I(fitted(regressao1)^2)","I(fitted(regressao1)^3)")
Tabela_RESET<-linearHypothesis(reg_RESET,RESETH0)
# outra alternativa é usar a linha abaixo com o matchCoefs
#Tabela_RESET<-linearHypothesis(reg_RESET, matchCoefs(reg_RESET,"fitted"))
Tabela_RESET

1.1.5 RESET pelo comando resettest da library(lmtest)

library(lmtest)

## Carregando pacotes exigidos: zoo

## 
## Anexando pacote: 'zoo'

## Os seguintes objetos são mascarados por 'package:base':
## 
##     as.Date, as.Date.numeric

TesteRESET<-resettest(regressao1, power = 2:3) # default é power = 2:3
TesteRESET

## 
##  RESET test
## 
## data:  regressao1
## RESET = 5.0746, df1 = 2, df2 = 111, p-value = 0.007783

#alterando as potencias
TesteRESET.power<-resettest(regressao1, power = 2:4)
TesteRESET.power

## 
##  RESET test
## 
## data:  regressao1
## RESET = 5.2816, df1 = 3, df2 = 110, p-value = 0.001932

1.1.6 fazendo os criterios de informacao de Akaike e Schwarz

regressao1$AIC <- AIC(regressao1)
regressao1$BIC <- BIC(regressao1)


#mostrando os valores de AIC e SIC
library(stargazer)
star.1 <- stargazer(regressao1,
                    title="Título: Resultado da Regressão",
                    align=TRUE,
                    type = "text", style = "all",
                    keep.stat=c("aic","bic","rsq", "adj.rsq","n")
)

## 
## Título: Resultado da Regressão
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                QSOJA           
## -----------------------------------------------
## FERTILIZANTE                  -0.554           
##                               (1.059)          
##                             t = -0.523         
##                              p = 0.603         
## TRATOR                      -33.690***         
##                               (3.741)          
##                             t = -9.006         
##                              p = 0.000         
## MO                           -209.141*         
##                              (107.893)         
##                             t = -1.938         
##                              p = 0.056         
## Constant                    494.966***         
##                              (25.572)          
##                             t = 19.356         
##                              p = 0.000         
## -----------------------------------------------
## Observations                    117            
## R2                             0.465           
## Adjusted R2                    0.451           
## Akaike Inf. Crit.            1,209.807         
## Bayesian Inf. Crit.          1,223.617         
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01