Datos_panel_ACT1

Actividad

Instalar paquete y Llamar librerías

#install.packages("WDI")
library(WDI)
#install.packages("wbstats")
library(wbstats)
#install.packages("tidyverse")
library(tidyverse)
#install.packages("plm") #Realiza modelos lineales para datos de panel
library(plm)
#install.packages("gplots")
library(gplots)

Obtener Información

gdp <- wb_data(country=c("MX","US","CA"), indicator=c("NY.GDP.PCAP.CD","SM.POP.NETM"), start_date = 1950, end_date = 2025)
#View(gdp)

Generar conjunto de datos de panel

Panel_1 <- select(gdp, country, date, NY.GDP.PCAP.CD, SM.POP.NETM)
Panel_1 <- subset(Panel_1, date == 1960 | date == 1970 | date == 1980 | date == 1990 | date == 2000 | date == 2010 | date == 2020)

Panel_1 <- pdata.frame(Panel_1, index = c("country","date"))
Panel_1

##                          country date NY.GDP.PCAP.CD SM.POP.NETM
## Canada-1960               Canada 1960      2264.9485       49694
## Canada-1970               Canada 1970      4135.8215      304627
## Canada-1980               Canada 1980     11208.2027      122743
## Canada-1990               Canada 1990     21525.8611      181461
## Canada-2000               Canada 2000     24271.0021      201727
## Canada-2010               Canada 2010     47560.6666      225369
## Canada-2020               Canada 2020     43537.8393      256592
## Mexico-1960               Mexico 1960       355.0752      -85591
## Mexico-1970               Mexico 1970       699.0068     -164100
## Mexico-1980               Mexico 1980      3054.6216     -252177
## Mexico-1990               Mexico 1990      3154.4692     -321764
## Mexico-2000               Mexico 2000      7524.0271     -356433
## Mexico-2010               Mexico 2010      9728.8008      -40845
## Mexico-2020               Mexico 2020      8841.2708     -147456
## United States-1960 United States 1960      3002.0893      422708
## United States-1970 United States 1970      5234.2967      744902
## United States-1980 United States 1980     12574.7915      595916
## United States-1990 United States 1990     23888.6000     1084720
## United States-2000 United States 2000     36329.9703     1248392
## United States-2010 United States 2010     48642.6312     1594453
## United States-2020 United States 2020     64401.5074      329769

Obtener Información2

gdp2 <- wb_data(country=c("FR","DE","PL"), indicator=c("NY.GDP.PCAP.KD.ZG","AG.PRD.CROP.XD"), start_date = 1950, end_date = 2010)
#View(gdp2)

Generar conjunto de datos de panel

Panel_2 <- select(gdp2, country, date, NY.GDP.PCAP.KD.ZG, AG.PRD.CROP.XD)
Panel_2 <- subset(Panel_2, date == 1960 | date == 1970 | date == 1980 | date == 1990 | date == 2000 | date == 2010)

Panel_2 <- pdata.frame(Panel_2, index = c("country","date"))
Panel_2

##              country date NY.GDP.PCAP.KD.ZG AG.PRD.CROP.XD
## France-1960   France 1960                NA             NA
## France-1970   France 1970          5.238215          83.98
## France-1980   France 1980          1.134990          91.14
## France-1990   France 1990          2.268451          98.60
## France-2000   France 2000          3.428690         103.98
## France-2010   France 2010          1.498725          98.02
## Germany-1960 Germany 1960                NA             NA
## Germany-1970 Germany 1970          4.754088          88.75
## Germany-1980 Germany 1980          1.198694          81.32
## Germany-1990 Germany 1990          4.351639          89.56
## Germany-2000 Germany 2000          2.738012         101.29
## Germany-2010 Germany 2010          4.306441          91.64
## Poland-1960   Poland 1960                NA             NA
## Poland-1970   Poland 1970                NA         122.69
## Poland-1980   Poland 1980                NA          89.00
## Poland-1990   Poland 1990                NA         128.14
## Poland-2000   Poland 2000          5.755023         101.87
## Poland-2010   Poland 2010          3.464009          88.29

---

Paso 1 Generar conjunto de datos de panel

#Obtener información de varios países 
#gdp <- wb_data(country=c("MX","US","CA"), indicator=c("NY.GDP.PCAP.CD","SM.POP.NETM"), start_date = 1950, end_date = 2025)
#View(gdp)

#Generar conjunto de datos panel
#Panel_1 <- select(gdp, country, date, NY.GDP.PCAP.CD, SM.POP.NETM)
#Panel_1 <- subset(Panel_1, date == 1960 | date == 1970 | date == 1980 | date == 1990 | date == 2000 | date == 2010 #| date == 2020)

#Panel_1 <- pdata.frame(Panel_1, index = c("country","date"))
#Panel_1

#NO CORRER

Paso 2: Prueba de Heterogeneidad

plotmeans(NY.GDP.PCAP.CD ~ country, main= "Prueba de heterogenidad entre paises para el PIB", data= Panel_1)

# Si la linea sale casi horizontal, hay poca o nula heterogenidad, por lo que no hay diferencias sistematicas que ajustar. 

#Si la linea sale quebrada, sube y baja, hay mucha Heterogenidad, por lo que hay que ajustar. (Buscamos esta linea quebarada para utilizar ya sea los modelos fijos o aleatorios)

#plotmeans(SM.POP.NETM ~ country, main= "Prueba de heterogenidad entre paises para la migracion neta", data= Panel_1)

Paso 3: Prueba de efectos fijos y aleatorios

#Modelo 1. Regresión agrupada (pooled)
#Asume que no hay heterogeneidad observada
pooled <- plm(NY.GDP.PCAP.CD ~ SM.POP.NETM, Panel_1, model="pooling")
summary(pooled)

## Pooling Model
## 
## Call:
## plm(formula = NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "pooling")
## 
## Balanced Panel: n = 3, T = 7, N = 21
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -21506.0 -10924.8  -3728.9   5274.5  45389.3 
## 
## Coefficients:
##               Estimate Std. Error t-value Pr(>|t|)   
## (Intercept) 1.2873e+04 4.2134e+03  3.0553 0.006511 **
## SM.POP.NETM 1.8616e-02 7.2324e-03  2.5740 0.018588 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7259500000
## Residual Sum of Squares: 5382600000
## R-Squared:      0.25855
## Adj. R-Squared: 0.21952
## F-statistic: 6.62533 on 1 and 19 DF, p-value: 0.018588

#Modelo 2. Efectos fijos (within)
#Cuando las diferencias no observadas son constantes en el tiempo
within <- plm(NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "within" )
summary(within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "within")
## 
## Balanced Panel: n = 3, T = 7, N = 21
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -20886.56  -9903.27   -403.03   3407.39  44059.72 
## 
## Coefficients:
##             Estimate Std. Error t-value Pr(>|t|)
## SM.POP.NETM 0.013921   0.014345  0.9705   0.3454
## 
## Total Sum of Squares:    5256100000
## Residual Sum of Squares: 4980200000
## R-Squared:      0.052492
## Adj. R-Squared: -0.11471
## F-statistic: 0.94181 on 1 and 17 DF, p-value: 0.34542

#Prueba F
pFtest(within, pooled)

## 
##  F test for individual effects
## 
## data:  NY.GDP.PCAP.CD ~ SM.POP.NETM
## F = 0.68685, df1 = 2, df2 = 17, p-value = 0.5166
## alternative hypothesis: significant effects

# Si p-value < 0.05 se prefiere el modelo de efectos fijos.

#Modelo 3. Efectos Aleatorios
#Cuando las diferencias no observadas son aleatorias

#Método walhus
walhus <- plm(NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", random.method = "walhus")
summary(walhus)

## Oneway (individual) effect Random Effect Model 
##    (Wallace-Hussain's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", 
##     random.method = "walhus")
## 
## Balanced Panel: n = 3, T = 7, N = 21
## 
## Effects:
##                     var   std.dev share
## idiosyncratic 278418900     16686     1
## individual            0         0     0
## theta: 0
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -21506.0 -10924.8  -3728.9   5274.5  45389.3 
## 
## Coefficients:
##               Estimate Std. Error z-value Pr(>|z|)   
## (Intercept) 1.2873e+04 4.2134e+03  3.0553 0.002248 **
## SM.POP.NETM 1.8616e-02 7.2324e-03  2.5740 0.010054 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7259500000
## Residual Sum of Squares: 5382600000
## R-Squared:      0.25855
## Adj. R-Squared: 0.21952
## Chisq: 6.62533 on 1 DF, p-value: 0.010054

#Método amemiya
amemiya <- plm(NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", random.method = "amemiya")
summary(amemiya)

## Oneway (individual) effect Random Effect Model 
##    (Amemiya's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", 
##     random.method = "amemiya")
## 
## Balanced Panel: n = 3, T = 7, N = 21
## 
## Effects:
##                     var   std.dev share
## idiosyncratic 276675480     16634     1
## individual            0         0     0
## theta: 0
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -21506.0 -10924.8  -3728.9   5274.5  45389.3 
## 
## Coefficients:
##               Estimate Std. Error z-value Pr(>|z|)   
## (Intercept) 1.2873e+04 4.2134e+03  3.0553 0.002248 **
## SM.POP.NETM 1.8616e-02 7.2324e-03  2.5740 0.010054 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    7259500000
## Residual Sum of Squares: 5382600000
## R-Squared:      0.25855
## Adj. R-Squared: 0.21952
## Chisq: 6.62533 on 1 DF, p-value: 0.010054

#Método nerlove
nerlove <- plm(NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", random.method = "nerlove")
summary(nerlove)

## Oneway (individual) effect Random Effect Model 
##    (Nerlove's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.CD ~ SM.POP.NETM, data = Panel_1, model = "random", 
##     random.method = "nerlove")
## 
## Balanced Panel: n = 3, T = 7, N = 21
## 
## Effects:
##                     var   std.dev share
## idiosyncratic 237150411     15400 0.864
## individual     37271843      6105 0.136
## theta: 0.31
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -20850.0  -9773.4  -2826.2   3450.7  45608.0 
## 
## Coefficients:
##               Estimate Std. Error z-value Pr(>|z|)  
## (Intercept) 1.3174e+04 5.8290e+03  2.2601  0.02382 *
## SM.POP.NETM 1.7563e-02 9.0595e-03  1.9386  0.05255 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    6.21e+09
## Residual Sum of Squares: 5184500000
## R-Squared:      0.16513
## Adj. R-Squared: 0.12119
## Chisq: 3.75814 on 1 DF, p-value: 0.052551

#Comparar la r2 ajustada de los 3 métodos y elegir el que tenga el mayor. 

phtest(walhus, within)

## 
##  Hausman Test
## 
## data:  NY.GDP.PCAP.CD ~ SM.POP.NETM
## chisq = 0.14364, df = 1, p-value = 0.7047
## alternative hypothesis: one model is inconsistent

# si el valor de p-value es < 0.05 usamos Efectos fijos

Paso 2: Prueba de Heterogeneidad (Ejercicio personal)

plotmeans(NY.GDP.PCAP.KD.ZG ~ country, main= "Prueba de heterogenidad entre paises para el PIB", data= Panel_2)

# Si la linea sale casi horizontal, hay poca o nula heterogenidad, por lo que no hay diferencias sistematicas que ajustar. 

#Si la linea sale quebrada, sube y baja, hay mucha Heterogenidad, por lo que hay que ajustar. (Buscamos esta linea quebarada para utilizar ya sea los modelos fijos o aleatorios)

#plotmeans(AG.PRD.CROP.XD ~ country, main= "Prueba de heterogenidad entre paises para la producción agrearia", data= Panel_2)

# "NY.GDP.PCAP.KD.ZG","AG.PRD.CROP.XD"

Paso 3: Prueba de efectos fijos y aleatorios (Ejercicio personal)

#Modelo 1. Regresión agrupada (pooled)
#Asume que no hay heterogeneidad observada
pooled2 <- plm(NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, Panel_2, model="pooling")
summary(pooled2)

## Pooling Model
## 
## Call:
## plm(formula = NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, 
##     model = "pooling")
## 
## Unbalanced Panel: n = 3, T = 2-5, N = 12
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.200286 -1.292837  0.088143  1.125158  2.370490 
## 
## Coefficients:
##                 Estimate Std. Error t-value Pr(>|t|)
## (Intercept)    2.9168926  6.3610858  0.4586   0.6564
## AG.PRD.CROP.XD 0.0045906  0.0680542  0.0675   0.9475
## 
## Total Sum of Squares:    27.764
## Residual Sum of Squares: 27.751
## R-Squared:      0.0004548
## Adj. R-Squared: -0.0995
## F-statistic: 0.0045501 on 1 and 10 DF, p-value: 0.94755

#Modelo 2. Efectos fijos (within)
#Cuando las diferencias no observadas son constantes en el tiempo
within2 <- plm(NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, model = "within" )
summary(within2)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, 
##     model = "within")
## 
## Unbalanced Panel: n = 3, T = 2-5, N = 12
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.171680 -1.115609  0.068295  0.937140  2.645126 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## AG.PRD.CROP.XD 0.010814   0.072255  0.1497   0.8847
## 
## Total Sum of Squares:    22.496
## Residual Sum of Squares: 22.433
## R-Squared:      0.002792
## Adj. R-Squared: -0.37116
## F-statistic: 0.0223984 on 1 and 8 DF, p-value: 0.88474

#Prueba F
pFtest(within2, pooled2)

## 
##  F test for individual effects
## 
## data:  NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD
## F = 0.94824, df1 = 2, df2 = 8, p-value = 0.427
## alternative hypothesis: significant effects

# Si p-value < 0.05 se prefiere el modelo de efectos fijos y elegimos de los siguiente método aleatorios.

#Modelo 3. Efectos Aleatorios
#Cuando las diferencias no observadas son aleatorias

#Método walhus
walhus2 <- plm(NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, model = "random", random.method = "walhus")
summary(walhus2)

## Oneway (individual) effect Random Effect Model 
##    (Wallace-Hussain's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, 
##     model = "random", random.method = "walhus")
## 
## Unbalanced Panel: n = 3, T = 2-5, N = 12
## 
## Effects:
##                    var  std.dev share
## idiosyncratic 2.770499 1.664482 0.998
## individual    0.006575 0.081085 0.002
## theta:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.002365 0.005881 0.005881 0.005295 0.005881 0.005881 
## 
## Residuals:
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -2.197746 -1.291179  0.086712 -0.000738  1.123339  2.364997 
## 
## Coefficients:
##                 Estimate Std. Error z-value Pr(>|z|)
## (Intercept)    2.9071350  6.3604207  0.4571   0.6476
## AG.PRD.CROP.XD 0.0047111  0.0680437  0.0692   0.9448
## 
## Total Sum of Squares:    27.784
## Residual Sum of Squares: 27.711
## R-Squared:      0.0048655
## Adj. R-Squared: -0.094648
## Chisq: 0.00479378 on 1 DF, p-value: 0.9448

#Método amemiya
amemiya2 <- plm(NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, model = "random", random.method = "amemiya")
summary(amemiya2)

## Oneway (individual) effect Random Effect Model 
##    (Amemiya's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, 
##     model = "random", random.method = "amemiya")
## 
## Unbalanced Panel: n = 3, T = 2-5, N = 12
## 
## Effects:
##                 var std.dev share
## idiosyncratic 2.804   1.675     1
## individual    0.000   0.000     0
## theta:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0       0       0       0       0       0 
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -2.200286 -1.292837  0.088143  1.125158  2.370490 
## 
## Coefficients:
##                 Estimate Std. Error z-value Pr(>|z|)
## (Intercept)    2.9168926  6.3610858  0.4586   0.6466
## AG.PRD.CROP.XD 0.0045906  0.0680542  0.0675   0.9462
## 
## Total Sum of Squares:    27.764
## Residual Sum of Squares: 27.751
## R-Squared:      0.0004548
## Adj. R-Squared: -0.0995
## Chisq: 0.0045501 on 1 DF, p-value: 0.94622

#Método nerlove
nerlove2 <- plm(NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, model = "random", random.method = "nerlove")
summary(nerlove2)

## Oneway (individual) effect Random Effect Model 
##    (Nerlove's transformation)
## 
## Call:
## plm(formula = NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD, data = Panel_2, 
##     model = "random", random.method = "nerlove")
## 
## Unbalanced Panel: n = 3, T = 2-5, N = 12
## 
## Effects:
##                  var std.dev share
## idiosyncratic 1.8694  1.3673 0.737
## individual    0.6677  0.8171 0.263
## theta:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2362  0.4009  0.4009  0.3734  0.4009  0.4009 
## 
## Residuals:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -2.1573 -1.1315 -0.0249 -0.0395  1.0150  2.1772 
## 
## Coefficients:
##                Estimate Std. Error z-value Pr(>|z|)
## (Intercept)    2.519123   6.274084  0.4015   0.6880
## AG.PRD.CROP.XD 0.010119   0.066739  0.1516   0.8795
## 
## Total Sum of Squares:    27.647
## Residual Sum of Squares: 24.98
## R-Squared:      0.15769
## Adj. R-Squared: 0.073459
## Chisq: 0.0229902 on 1 DF, p-value: 0.87948

#Comparar la r2 ajustada de los 3 métodos y elegir el que tenga el mayor. 

phtest(walhus2, within2)

## 
##  Hausman Test
## 
## data:  NY.GDP.PCAP.KD.ZG ~ AG.PRD.CROP.XD
## chisq = 0.063028, df = 1, p-value = 0.8018
## alternative hypothesis: one model is inconsistent

# si el valor de p-value es < 0.05 usamos Efectos fijos