Ejercicio 3 Modelos con indicadores del banco mundial

Regina Enríquez Chapa A01721435

Maximiliano Carvajal A01552179

Guillermo Cazares Cruz A01283709

library(WDI)
library(wbstats)
library(tidyverse)

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## v lubridate 1.9.3     v tidyr     1.3.0
## v purrr     1.0.1     
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library(gplots)

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## Attaching package: 'gplots'
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library(plm)

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## Attaching package: 'plm'
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Tarea 2. Gráficas de Heterogeneidad (5 puntos)

climate_change <- wb_data(country=c("MX","NO","FI","SE","DK"), indicator=c("EN.ATM.CO2E.KT","EG.FEC.RNEW.ZS","SP.URB.TOTL.IN.ZS","AG.LND.AGRI.ZS"), start_date=1950, end_date = 2020)

climate_change_periodic <- subset(climate_change, date == 1990 | date == 2000 | date == 2010 | date == 2020)

climate_change_periodic <- pdata.frame(climate_change_periodic, index = c("country","date"))

Heterogeneidad entre países y años

plotmeans(EG.FEC.RNEW.ZS ~ country, data = climate_change_periodic, xlab = "Países", ylab = "Consumo de energía renovable (%)", main = "Heterogeneidad entre países", mean.labels = FALSE)

plotmeans(EG.FEC.RNEW.ZS ~ date, data = climate_change_periodic, xlab = "Años", ylab = "Consumo de energía renovable (%)", main = "Heterogeneidad entre años", mean.labels = FALSE)

Ejercicio 3. Modelos con Indicadores del Banco Mundial (10 puntos)

Variables:

• EG.FEC.RNEW.ZS = Consumo de energía renovable (%)
• EN.ATM.CO2E.KT = Emisiones de CO2 (toneladas métricas per cápita)
• SP.URB.TOTL.IN.ZS = Población Urbana (%)
• AG.LND.AGRI.ZS = Tierras agrícolas (% del área de tierra)

Modelo 1. Regresión agrupada (pooled)

pooled <- plm(EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS, data = climate_change_periodic, model = "pooling")

summary(pooled)

## Pooling Model
## 
## Call:
## plm(formula = EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + 
##     AG.LND.AGRI.ZS, data = climate_change_periodic, model = "pooling")
## 
## Balanced Panel: n = 5, T = 4, N = 20
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -21.0579  -9.1215   1.5252   8.3077  19.4014 
## 
## Coefficients:
##                      Estimate  Std. Error t-value Pr(>|t|)   
## (Intercept)        6.6920e+01  5.2745e+01  1.2688 0.222678   
## EN.ATM.CO2E.KT    -4.8978e-05  2.5891e-05 -1.8917 0.076779 . 
## SP.URB.TOTL.IN.ZS -1.9257e-01  6.3960e-01 -0.3011 0.767230   
## AG.LND.AGRI.ZS    -4.3226e-01  1.1559e-01 -3.7396 0.001786 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7001.9
## Residual Sum of Squares: 2093.7
## R-Squared:      0.70098
## Adj. R-Squared: 0.64492
## F-statistic: 12.5029 on 3 and 16 DF, p-value: 0.00018278

Modelo 2. Efectos fijos within

within <- plm(EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS, data = climate_change_periodic, model = "within")

summary(within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + 
##     AG.LND.AGRI.ZS, data = climate_change_periodic, model = "within")
## 
## Balanced Panel: n = 5, T = 4, N = 20
## 
## Residuals:
##    Min. 1st Qu.  Median 3rd Qu.    Max. 
## -9.4665 -4.4639 -1.4433  5.8039 13.0689 
## 
## Coefficients:
##                      Estimate  Std. Error t-value Pr(>|t|)  
## EN.ATM.CO2E.KT    -1.2809e-04  5.6772e-05 -2.2562  0.04351 *
## SP.URB.TOTL.IN.ZS  1.3931e+00  7.3104e-01  1.9057  0.08093 .
## AG.LND.AGRI.ZS    -1.6306e+00  1.7146e+00 -0.9510  0.36036  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1268.4
## Residual Sum of Squares: 691.09
## R-Squared:      0.45515
## Adj. R-Squared: 0.13732
## F-statistic: 3.34148 on 3 and 12 DF, p-value: 0.055906

Prueba pF

pFtest(within,pooled)

## 
##  F test for individual effects
## 
## data:  EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS
## F = 6.0886, df1 = 4, df2 = 12, p-value = 0.006492
## alternative hypothesis: significant effects

Son muy diferentes, no se pueden intercambiar.

Modelo 3. Efectos aleatorios método walhus

walhus <- plm(EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", random.method = "walhus")

summary(walhus)

## Oneway (individual) effect Random Effect Model 
##    (Wallace-Hussain's transformation)
## 
## Call:
## plm(formula = EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + 
##     AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", 
##     random.method = "walhus")
## 
## Balanced Panel: n = 5, T = 4, N = 20
## 
## Effects:
##                  var std.dev share
## idiosyncratic 79.485   8.915 0.759
## individual    25.200   5.020 0.241
## theta: 0.336
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -16.1471  -8.5619   1.2411   5.9506  17.9110 
## 
## Coefficients:
##                      Estimate  Std. Error z-value  Pr(>|z|)    
## (Intercept)        2.4120e+01  5.1083e+01  0.4722 0.6367978    
## EN.ATM.CO2E.KT    -4.0618e-05  2.8544e-05 -1.4230 0.1547456    
## SP.URB.TOTL.IN.ZS  3.3143e-01  6.1918e-01  0.5353 0.5924661    
## AG.LND.AGRI.ZS    -4.6303e-01  1.4025e-01 -3.3015 0.0009617 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    3796.2
## Residual Sum of Squares: 1521.1
## R-Squared:      0.59931
## Adj. R-Squared: 0.52418
## Chisq: 23.9313 on 3 DF, p-value: 2.5819e-05

Modelo 4. Efectos aleatorios método amemiya

amemiya <- plm(EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", random.method = "amemiya")

summary(amemiya)

## Oneway (individual) effect Random Effect Model 
##    (Amemiya's transformation)
## 
## Call:
## plm(formula = EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + 
##     AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", 
##     random.method = "amemiya")
## 
## Balanced Panel: n = 5, T = 4, N = 20
## 
## Effects:
##                    var  std.dev share
## idiosyncratic   46.073    6.788 0.028
## individual    1624.149   40.301 0.972
## theta: 0.9161
## 
## Residuals:
##    Min. 1st Qu.  Median 3rd Qu.    Max. 
## -8.8523 -4.7937 -1.7098  5.8322 13.9319 
## 
## Coefficients:
##                      Estimate  Std. Error z-value Pr(>|z|)  
## (Intercept)       -6.1390e+01  5.6670e+01 -1.0833  0.27868  
## EN.ATM.CO2E.KT    -1.1019e-04  4.8273e-05 -2.2825  0.02246 *
## SP.URB.TOTL.IN.ZS  1.4989e+00  5.9081e-01  2.5370  0.01118 *
## AG.LND.AGRI.ZS    -5.3496e-01  6.3082e-01 -0.8480  0.39641  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1308.8
## Residual Sum of Squares: 761.35
## R-Squared:      0.41828
## Adj. R-Squared: 0.3092
## Chisq: 11.5045 on 3 DF, p-value: 0.0092885

Modelo 5. Efectos aleatorios método nerlove

nerlove <- plm(EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", random.method = "nerlove")

summary(nerlove)

## Oneway (individual) effect Random Effect Model 
##    (Nerlove's transformation)
## 
## Call:
## plm(formula = EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + 
##     AG.LND.AGRI.ZS, data = climate_change_periodic, model = "random", 
##     random.method = "nerlove")
## 
## Balanced Panel: n = 5, T = 4, N = 20
## 
## Effects:
##                    var  std.dev share
## idiosyncratic   34.555    5.878 0.017
## individual    2044.584   45.217 0.983
## theta: 0.9351
## 
## Residuals:
##    Min. 1st Qu.  Median 3rd Qu.    Max. 
## -8.1316 -5.3145 -1.5510  5.8629 14.0382 
## 
## Coefficients:
##                      Estimate  Std. Error z-value Pr(>|z|)  
## (Intercept)       -5.9767e+01  6.1306e+01 -0.9749  0.32961  
## EN.ATM.CO2E.KT    -1.1558e-04  4.8847e-05 -2.3661  0.01798 *
## SP.URB.TOTL.IN.ZS  1.5195e+00  5.9493e-01  2.5541  0.01065 *
## AG.LND.AGRI.ZS    -6.3356e-01  7.6253e-01 -0.8309  0.40605  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1292.5
## Residual Sum of Squares: 743.06
## R-Squared:      0.42511
## Adj. R-Squared: 0.31732
## Chisq: 11.8314 on 3 DF, p-value: 0.0079835

Prueba de Hausman

phtest(amemiya,within)

## 
##  Hausman Test
## 
## data:  EG.FEC.RNEW.ZS ~ EN.ATM.CO2E.KT + SP.URB.TOTL.IN.ZS + AG.LND.AGRI.ZS
## chisq = 0.73372, df = 3, p-value = 0.8652
## alternative hypothesis: one model is inconsistent

Debido a la r cuadrada ajustada, el modelo seleccionado es el de efectos aleatorios por el método amemiya.