Actividad1

Ejercicio 1. Modelo Econométrico

Actividad 1: Ejemplo modelo económico y econométrico

¿Qué factores afectan a la plusvalía de una propiedad?

M^2 (Construcción) - Metros cuadrados de construcción de la propiedad

M^2 (Terreno) - Metros cuadrados de terreno de la propiedad

Antigüedad - Años que tiene la propiedad

Municipio - Neighborhood index

Modelo Económico Plusvalía = f(M^2 Construcción, M^2 Terreno, Antigüedad, Municipio)

Modelo econométrico: plusvalía = B0 + B1* M^2 Construcción + B2 * M^2 Terreno + B3 * Antigüedad +B4 * Municipio + u

Actividad 2. Good to Great

¿Debe una empresa que lo hace bien, buscar ser sobresaliente? Claro, siempre se tiene que buscar ser mejor. La empresa tiene que ir incrementando los objetivos que se plantea para poder llegar a un nivel superior del que se encuentra. Esto no solo se busca para beneficiar a los altos mandos, si no a los mismos empleados, añadiendo incentivos que ellos valoren y así todos salir beneficiados. Buscando subir de hacerlo bien a nivel sobresaliente se mejora también la calidad de vida.

Instalar paquetes y librerías

#install.packages("WDI")
library(WDI)
#install.packages("wbstats")
library(wbstats)
#install.packages("tidyverse")
library(tidyverse)
#install.packages("plm") #Paquete para realizar modelos lineales para datos de panel
library(plm)
#install.packages("gplots")
library(gplots)
#install.packages("readxl")
library(readxl)
#install.packages("lmtest")
library(lmtest)

# 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)
panel_1 <- gdp |>
  dplyr::select(country, date, NY.GDP.PCAP.CD, SM.POP.NETM) |>
  dplyr::mutate(date = as.integer(date)) |>
  dplyr::filter(date %in% c(1960, 1970, 1980, 1990, 2000, 2010, 2020))

panel_1 <- plm::pdata.frame(panel_1, index = c("country", "date"))
View(panel_1)  # usar solo en sesión interactiva

# Paso 2. Prueba de heterogeneidad

plotmeans(NY.GDP.PCAP.CD ~ country, main= "Prueba de heterogeneidad entre países para el PIB", data=panel_1)

plotmeans(SM.POP.NETM ~ country, main= "Prueba de heterogeneidad entre países para la Migración Neta", data=panel_1)

#Si la línea sale casi horizontal, hay poca o nula heterogeneidad, por lo que no hay diferencias sistemáticas que ajustar.
#Si la línea sale quebrada, sube y baja, hay mucha heterogeneidad, por lo que si hay diferencias sitemáticas que ajustar.

Paso 3. Pruebas 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, data = 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 la 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
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 el 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

#Este código compara la r2 ajustada de los 3 métodos y elegir el que tenga la 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 p-value es <.05 usamos efectos fijos(within)

Ejercicio 3 . Panel en Equipos

# Obtener información de varios países
le <- wb_data(country=c("BR", "JP", "SA"), indicator=c("SP.DYN.LE00.IN", "SP.DYN.IMRT.IN"), start_date=1950, end_date=2025)

#Generar conjunto de datos de panel
panel_2 <- select(le, country, date, SP.DYN.LE00.IN, SP.DYN.IMRT.IN)
panel_2 <- subset(panel_2, date == 1960 | date == 1970 | date == 1980 | date == 1990 | date == 2000 | date == 2010 | date == 2020)
panel_2 <- pdata.frame(panel_2, index=c("country", "date"))

# Prueba de heterogeneidad
plotmeans(SP.DYN.LE00.IN ~ country, main="Prueba de Heterogeneidad entre países para Esperanza de Vida", data=panel_2)

plotmeans(SP.DYN.IMRT.IN ~ country, main="Prueba de Heterogeneidad entre países para Mortalidad Infantil", data=panel_2)

Ejercicio 3.1 Panel en Equipos

# Modelo 1. Regresión agrupada (pooled)
# Asume que no hay heterogeneidad observada (si la línea esta derecha y no quebrada)
pooled <- plm(SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN , data = panel_2, model = "pooling")
summary(pooled)

## Pooling Model
## 
## Call:
## plm(formula = SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN, data = panel_2, 
##     model = "pooling")
## 
## Unbalanced Panel: n = 3, T = 5-7, N = 19
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -4.38143 -1.48349 -0.75575  1.45971  6.34152 
## 
## Coefficients:
##                 Estimate Std. Error t-value  Pr(>|t|)    
## (Intercept)    78.604999   0.882384  89.082 < 2.2e-16 ***
## SP.DYN.IMRT.IN -0.214735   0.017766 -12.087 9.008e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1303.7
## Residual Sum of Squares: 135.89
## R-Squared:      0.89577
## Adj. R-Squared: 0.88964
## F-statistic: 146.098 on 1 and 17 DF, p-value: 9.0076e-10

# Modelo 2. Efectos Fijos
# Cuando las diferencias no observadas son constantes en el tiempo
within <- plm(SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN , data = panel_2, model = "within")
summary(within)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN, data = panel_2, 
##     model = "within")
## 
## Unbalanced Panel: n = 3, T = 5-7, N = 19
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -5.64597 -1.10959  0.08486  1.07060  5.56936 
## 
## Coefficients:
##                 Estimate Std. Error t-value  Pr(>|t|)    
## SP.DYN.IMRT.IN -0.197520   0.022151 -8.9168 2.209e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    764.69
## Residual Sum of Squares: 121.37
## R-Squared:      0.84129
## Adj. R-Squared: 0.80954
## F-statistic: 79.5093 on 1 and 15 DF, p-value: 2.2086e-07

# Prueba 
pFtest(within, pooled)

## 
##  F test for individual effects
## 
## data:  SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN
## F = 0.89749, df1 = 2, df2 = 15, p-value = 0.4284
## alternative hypothesis: significant effects

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

# Modelo 3. Efectos aleatorios 
#Cuando las diferenciasno observadas son aleatorias

# Método Walhus
walhus <- plm(SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN , data = panel_2, model = "random", random.method="walhus")
summary(walhus)

## Oneway (individual) effect Random Effect Model 
##    (Wallace-Hussain's transformation)
## 
## Call:
## plm(formula = SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN, data = panel_2, 
##     model = "random", random.method = "walhus")
## 
## Unbalanced Panel: n = 3, T = 5-7, N = 19
## 
## Effects:
##                 var std.dev share
## idiosyncratic 8.275   2.877     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. 
## -4.38143 -1.48349 -0.75575  1.45971  6.34152 
## 
## Coefficients:
##                 Estimate Std. Error z-value  Pr(>|z|)    
## (Intercept)    78.604999   0.882384  89.082 < 2.2e-16 ***
## SP.DYN.IMRT.IN -0.214735   0.017766 -12.087 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1303.7
## Residual Sum of Squares: 135.89
## R-Squared:      0.89577
## Adj. R-Squared: 0.88964
## Chisq: 146.098 on 1 DF, p-value: < 2.22e-16

# Método amemiya
amemiya <- plm(SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN , data = panel_2, model = "random", random.method="amemiya")
summary(amemiya)

## Oneway (individual) effect Random Effect Model 
##    (Amemiya's transformation)
## 
## Call:
## plm(formula = SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN, data = panel_2, 
##     model = "random", random.method = "amemiya")
## 
## Unbalanced Panel: n = 3, T = 5-7, N = 19
## 
## Effects:
##                  var std.dev share
## idiosyncratic 8.0912  2.8445 0.985
## individual    0.1206  0.3473 0.015
## theta:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.03531 0.04187 0.04843 0.04498 0.04843 0.04843 
## 
## Residuals:
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -4.420983 -1.445524 -0.720421  0.000804  1.422388  6.333348 
## 
## Coefficients:
##                 Estimate Std. Error z-value  Pr(>|z|)    
## (Intercept)    78.566380   0.908529  86.477 < 2.2e-16 ***
## SP.DYN.IMRT.IN -0.213638   0.018004 -11.866 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1256.5
## Residual Sum of Squares: 134.96
## R-Squared:      0.89259
## Adj. R-Squared: 0.88628
## Chisq: 140.809 on 1 DF, p-value: < 2.22e-16

# Método nerlove
nerlove <- plm(SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN , data = panel_2, model = "random", random.method="nerlove")
summary(nerlove)

## Oneway (individual) effect Random Effect Model 
##    (Nerlove's transformation)
## 
## Call:
## plm(formula = SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN, data = panel_2, 
##     model = "random", random.method = "nerlove")
## 
## Unbalanced Panel: n = 3, T = 5-7, N = 19
## 
## Effects:
##                 var std.dev share
## idiosyncratic 6.388   2.527 0.786
## individual    1.739   1.319 0.214
## theta:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3492  0.3813  0.4134  0.3965  0.4134  0.4134 
## 
## Residuals:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -4.81067 -1.28907 -0.44860  0.00389  1.13099  6.18509 
## 
## Coefficients:
##                Estimate Std. Error z-value  Pr(>|z|)    
## (Intercept)    78.27119    1.23232  63.515 < 2.2e-16 ***
## SP.DYN.IMRT.IN -0.20520    0.01962 -10.459 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1028.9
## Residual Sum of Squares: 127.81
## R-Squared:      0.87579
## Adj. R-Squared: 0.86849
## Chisq: 109.381 on 1 DF, p-value: < 2.22e-16

#Comparar la R^2 ajustada de los 3 métodos y elegir el que tenga el mayor.

phtest(walhus, within)

## 
##  Hausman Test
## 
## data:  SP.DYN.LE00.IN ~ SP.DYN.IMRT.IN
## chisq = 1.693, df = 1, p-value = 0.1932
## alternative hypothesis: one model is inconsistent

#Si el p-value es <0.05, usamos Efectos Fijos (within)

Aplicación de Shiny

Aplicación de Shiny

Actividad 1. Patentes

Contexto

El entorno de negocios en el que las organizaciones se desarrollan es cada vez más dinámico por lo que las empresas enfrentan constantemente el reto de mantenerse al día y superar los nuevos retos que el ambiente presenta. La innovación es una de las mejores formas que las empresas tienen para conseguirlo. De acuerdo con el artículo “Innovation in business: What it is and why is so important” ´publicado en el Harvard Business Review la innovación presenta tres grandes ventajas para las empresas: les permite adaptarse, promueve el crecimiento y además les ayuda a diferenciarse de su competencia generando ventajas competitivas.

Se proporcionan datos sobre patentes en distintas empresas a lo largo de 10 años

Importar la base de datos

patentes <- read_excel("C:\\Users\\serva\\Downloads\\PATENT 3.xls")

## Importar la base de datos

summary(patentes)

##      cusip            merger           employ            return       
##  Min.   :   800   Min.   :0.0000   Min.   :  0.085   Min.   :-73.022  
##  1st Qu.:368514   1st Qu.:0.0000   1st Qu.:  1.227   1st Qu.:  5.128  
##  Median :501116   Median :0.0000   Median :  3.842   Median :  7.585  
##  Mean   :514536   Mean   :0.0177   Mean   : 18.826   Mean   :  8.003  
##  3rd Qu.:754688   3rd Qu.:0.0000   3rd Qu.: 15.442   3rd Qu.: 10.501  
##  Max.   :878555   Max.   :1.0000   Max.   :506.531   Max.   : 48.675  
##                                    NA's   :21        NA's   :8        
##     patents         patentsg           stckpr              rnd           
##  Min.   :  0.0   Min.   :   0.00   Min.   :  0.1875   Min.   :   0.0000  
##  1st Qu.:  1.0   1st Qu.:   1.00   1st Qu.:  7.6250   1st Qu.:   0.6847  
##  Median :  3.0   Median :   4.00   Median : 16.5000   Median :   2.1456  
##  Mean   : 22.9   Mean   :  27.14   Mean   : 22.6270   Mean   :  29.3398  
##  3rd Qu.: 15.0   3rd Qu.:  19.00   3rd Qu.: 29.2500   3rd Qu.:  11.9168  
##  Max.   :906.0   Max.   :1063.00   Max.   :402.0000   Max.   :1719.3535  
##                                    NA's   :2                             
##     rndeflt             rndstck              sales                sic      
##  Min.   :   0.0000   Min.   :   0.1253   Min.   :    1.222   Min.   :2000  
##  1st Qu.:   0.4788   1st Qu.:   5.1520   1st Qu.:   52.995   1st Qu.:2890  
##  Median :   1.4764   Median :  13.3532   Median :  174.065   Median :3531  
##  Mean   :  19.7238   Mean   : 163.8234   Mean   : 1219.601   Mean   :3333  
##  3rd Qu.:   8.7527   3rd Qu.:  74.5625   3rd Qu.:  728.964   3rd Qu.:3661  
##  Max.   :1000.7876   Max.   :9755.3516   Max.   :44224.000   Max.   :9997  
##                      NA's   :157         NA's   :3                         
##       year     
##  Min.   :2012  
##  1st Qu.:2014  
##  Median :2016  
##  Mean   :2016  
##  3rd Qu.:2019  
##  Max.   :2021  
## 

str(patentes)

## tibble [2,260 × 13] (S3: tbl_df/tbl/data.frame)
##  $ cusip   : num [1:2260] 800 800 800 800 800 800 800 800 800 800 ...
##  $ merger  : num [1:2260] 0 0 0 0 0 0 0 0 0 0 ...
##  $ employ  : num [1:2260] 9.85 12.32 12.2 11.84 12.99 ...
##  $ return  : num [1:2260] 5.82 5.69 4.42 5.28 4.91 ...
##  $ patents : num [1:2260] 22 34 31 32 40 60 57 77 38 5 ...
##  $ patentsg: num [1:2260] 24 32 30 34 28 33 53 47 64 70 ...
##  $ stckpr  : num [1:2260] 47.6 57.9 33 38.5 35.1 ...
##  $ rnd     : num [1:2260] 2.56 3.1 3.27 3.24 3.78 ...
##  $ rndeflt : num [1:2260] 2.56 2.91 2.8 2.52 2.78 ...
##  $ rndstck : num [1:2260] 16.2 17.4 19.6 21.9 23.1 ...
##  $ sales   : num [1:2260] 344 436 535 567 631 ...
##  $ sic     : num [1:2260] 3740 3740 3740 3740 3740 3740 3740 3740 3740 3740 ...
##  $ year    : num [1:2260] 2012 2013 2014 2015 2016 ...

sum(is.na(patentes)) #NA's en la base de datos

## [1] 191

sapply(patentes, function(x) sum (is.na(x))) #NA's por variables

##    cusip   merger   employ   return  patents patentsg   stckpr      rnd 
##        0        0       21        8        0        0        2        0 
##  rndeflt  rndstck    sales      sic     year 
##        0      157        3        0        0

patentes$employ[is.na(patentes$employ)] <- mean(patentes$employ, na.rm=TRUE)
patentes$return[is.na(patentes$return)] <- mean(patentes$return, na.rm=TRUE)
patentes$stckpr[is.na(patentes$stckpr)] <- mean(patentes$stckpr, na.rm=TRUE)
patentes$rndstck[is.na(patentes$rndstck)] <- mean(patentes$rndstck, na.rm=TRUE)
patentes$sales[is.na(patentes$sales)] <- mean(patentes$sales, na.rm=TRUE)
summary(patentes)

##      cusip            merger           employ            return       
##  Min.   :   800   Min.   :0.0000   Min.   :  0.085   Min.   :-73.022  
##  1st Qu.:368514   1st Qu.:0.0000   1st Qu.:  1.242   1st Qu.:  5.139  
##  Median :501116   Median :0.0000   Median :  3.893   Median :  7.601  
##  Mean   :514536   Mean   :0.0177   Mean   : 18.826   Mean   :  8.003  
##  3rd Qu.:754688   3rd Qu.:0.0000   3rd Qu.: 16.034   3rd Qu.: 10.473  
##  Max.   :878555   Max.   :1.0000   Max.   :506.531   Max.   : 48.675  
##     patents         patentsg           stckpr              rnd           
##  Min.   :  0.0   Min.   :   0.00   Min.   :  0.1875   Min.   :   0.0000  
##  1st Qu.:  1.0   1st Qu.:   1.00   1st Qu.:  7.6250   1st Qu.:   0.6847  
##  Median :  3.0   Median :   4.00   Median : 16.5000   Median :   2.1456  
##  Mean   : 22.9   Mean   :  27.14   Mean   : 22.6270   Mean   :  29.3398  
##  3rd Qu.: 15.0   3rd Qu.:  19.00   3rd Qu.: 29.2500   3rd Qu.:  11.9168  
##  Max.   :906.0   Max.   :1063.00   Max.   :402.0000   Max.   :1719.3535  
##     rndeflt             rndstck              sales                sic      
##  Min.   :   0.0000   Min.   :   0.1253   Min.   :    1.222   Min.   :2000  
##  1st Qu.:   0.4788   1st Qu.:   5.5882   1st Qu.:   53.204   1st Qu.:2890  
##  Median :   1.4764   Median :  16.2341   Median :  174.283   Median :3531  
##  Mean   :  19.7238   Mean   : 163.8234   Mean   : 1219.601   Mean   :3333  
##  3rd Qu.:   8.7527   3rd Qu.: 119.1048   3rd Qu.:  743.422   3rd Qu.:3661  
##  Max.   :1000.7876   Max.   :9755.3516   Max.   :44224.000   Max.   :9997  
##       year     
##  Min.   :2012  
##  1st Qu.:2014  
##  Median :2016  
##  Mean   :2016  
##  3rd Qu.:2019  
##  Max.   :2021

sum(is.na(patentes)) #NA's en la base de datos

## [1] 0

boxplot(patentes$cusip, horizontal = TRUE)

boxplot(patentes$merger, horizontal = TRUE)

boxplot(patentes$employ, horizontal = TRUE)

boxplot(patentes$return, horizontal = TRUE)

boxplot(patentes$patents, horizontal = TRUE)

boxplot(patentes$patentsg, horizontal = TRUE)

boxplot(patentes$stckpr, horizontal = TRUE)

boxplot(patentes$rnd, horizontal = TRUE)

boxplot(patentes$rndeflt, horizontal = TRUE)

boxplot(patentes$rndstck, horizontal = TRUE)

boxplot(patentes$sales, horizontal = TRUE)

boxplot(patentes$sic, horizontal = TRUE)

boxplot(patentes$year, horizontal = TRUE)

patentes$year <- patentes$year - 40
summary(patentes)

##      cusip            merger           employ            return       
##  Min.   :   800   Min.   :0.0000   Min.   :  0.085   Min.   :-73.022  
##  1st Qu.:368514   1st Qu.:0.0000   1st Qu.:  1.242   1st Qu.:  5.139  
##  Median :501116   Median :0.0000   Median :  3.893   Median :  7.601  
##  Mean   :514536   Mean   :0.0177   Mean   : 18.826   Mean   :  8.003  
##  3rd Qu.:754688   3rd Qu.:0.0000   3rd Qu.: 16.034   3rd Qu.: 10.473  
##  Max.   :878555   Max.   :1.0000   Max.   :506.531   Max.   : 48.675  
##     patents         patentsg           stckpr              rnd           
##  Min.   :  0.0   Min.   :   0.00   Min.   :  0.1875   Min.   :   0.0000  
##  1st Qu.:  1.0   1st Qu.:   1.00   1st Qu.:  7.6250   1st Qu.:   0.6847  
##  Median :  3.0   Median :   4.00   Median : 16.5000   Median :   2.1456  
##  Mean   : 22.9   Mean   :  27.14   Mean   : 22.6270   Mean   :  29.3398  
##  3rd Qu.: 15.0   3rd Qu.:  19.00   3rd Qu.: 29.2500   3rd Qu.:  11.9168  
##  Max.   :906.0   Max.   :1063.00   Max.   :402.0000   Max.   :1719.3535  
##     rndeflt             rndstck              sales                sic      
##  Min.   :   0.0000   Min.   :   0.1253   Min.   :    1.222   Min.   :2000  
##  1st Qu.:   0.4788   1st Qu.:   5.5882   1st Qu.:   53.204   1st Qu.:2890  
##  Median :   1.4764   Median :  16.2341   Median :  174.283   Median :3531  
##  Mean   :  19.7238   Mean   : 163.8234   Mean   : 1219.601   Mean   :3333  
##  3rd Qu.:   8.7527   3rd Qu.: 119.1048   3rd Qu.:  743.422   3rd Qu.:3661  
##  Max.   :1000.7876   Max.   :9755.3516   Max.   :44224.000   Max.   :9997  
##       year     
##  Min.   :1972  
##  1st Qu.:1974  
##  Median :1976  
##  Mean   :1976  
##  3rd Qu.:1979  
##  Max.   :1981

Entender base de datos

1. Generar Conjunto de Datos de Panel

# Obtener información de varios países
panel_patentes <- pdata.frame(patentes, index =  c("cusip", "year"))

Paso 2. Prueba de heterogeneidad

plotmeans(patents ~ cusip, main= "Prueba de heterogeneidad entre empresas para sus patentes", data=panel_patentes)

#Como la línea sale quebrada, sube y baja, hay mucha heterogeneidad, por lo que hay que ajustar.

Paso 3. Pruebas de Efectos Fijos y Aleatorios

#Modelo 1. Regresión agrupada (pooled)
#Asume que no hay heterogeneidad observada
pooled_patentes <- plm(patents ~ merger + employ + return + stckpr + rnd + sales + sic, data = panel_patentes, model="pooling")
summary(pooled_patentes)

## Pooling Model
## 
## Call:
## plm(formula = patents ~ merger + employ + return + stckpr + rnd + 
##     sales + sic, data = panel_patentes, model = "pooling")
## 
## Balanced Panel: n = 226, T = 10, N = 2260
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -320.36212  -10.01555    0.94472    7.40861  433.86316 
## 
## Coefficients:
##                Estimate  Std. Error t-value  Pr(>|t|)    
## (Intercept) -4.1831e-01  5.2757e+00 -0.0793   0.93681    
## merger      -1.1612e+01  7.2433e+00 -1.6031   0.10905    
## employ       1.3683e+00  4.1969e-02 32.6040 < 2.2e-16 ***
## return      -4.3505e-03  1.8155e-01 -0.0240   0.98088    
## stckpr       6.5137e-01  4.3139e-02 15.0994 < 2.2e-16 ***
## rnd         -1.3853e-01  1.6106e-02 -8.6007 < 2.2e-16 ***
## sales       -3.2049e-03  4.6962e-04 -6.8246  1.13e-11 ***
## sic         -2.6894e-03  1.4820e-03 -1.8146   0.06972 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    10998000
## Residual Sum of Squares: 4600300
## R-Squared:      0.58173
## Adj. R-Squared: 0.58043
## F-statistic: 447.437 on 7 and 2252 DF, p-value: < 2.22e-16

#Modelo 2. Efectos Fijos (within)
# Cuando la diferencias no observadas son constantes en el tiempo
within_patentes <- plm(patents ~ merger + employ + return + stckpr + rnd + sales + sic, data = panel_patentes, model= "within")
summary(within_patentes)

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = patents ~ merger + employ + return + stckpr + rnd + 
##     sales + sic, data = panel_patentes, model = "within")
## 
## Balanced Panel: n = 226, T = 10, N = 2260
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -497.22898   -1.64569   -0.19669    1.64341  184.49423 
## 
## Coefficients:
##           Estimate  Std. Error  t-value  Pr(>|t|)    
## merger  3.30904770  4.16313684   0.7948   0.42680    
## employ  0.11963128  0.07052503   1.6963   0.08998 .  
## return -0.07056694  0.10867769  -0.6493   0.51620    
## stckpr -0.01107952  0.03242512  -0.3417   0.73262    
## rnd    -0.19889614  0.01443066 -13.7829 < 2.2e-16 ***
## sales  -0.00309052  0.00041525  -7.4426 1.451e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1091400
## Residual Sum of Squares: 819280
## R-Squared:      0.24935
## Adj. R-Squared: 0.16385
## F-statistic: 112.278 on 6 and 2028 DF, p-value: < 2.22e-16

#Prueba
pFtest(within_patentes, pooled_patentes)

## 
##  F test for individual effects
## 
## data:  patents ~ merger + employ + return + stckpr + rnd + sales + sic
## F = 41.782, df1 = 224, df2 = 2028, p-value < 2.2e-16
## alternative hypothesis: significant effects

#Como el p-value es menor a 0.05 se avanza

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

#Método Walhus
walhus_patentes <- plm(patents ~ merger + employ + return + stckpr + rnd + sales + sic, data = panel_patentes, model="random",
random.method="walhus")
summary(walhus_patentes)

## Oneway (individual) effect Random Effect Model 
##    (Wallace-Hussain's transformation)
## 
## Call:
## plm(formula = patents ~ merger + employ + return + stckpr + rnd + 
##     sales + sic, data = panel_patentes, model = "random", random.method = "walhus")
## 
## Balanced Panel: n = 226, T = 10, N = 2260
## 
## Effects:
##                   var std.dev share
## idiosyncratic  555.26   23.56 0.273
## individual    1480.26   38.47 0.727
## theta: 0.8099
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -433.72438   -3.89667   -1.76198    0.78484  211.91016 
## 
## Coefficients:
##                Estimate  Std. Error z-value  Pr(>|z|)    
## (Intercept) 11.84397257 12.78087032  0.9267    0.3541    
## merger       4.47647107  4.51685216  0.9911    0.3217    
## employ       1.10525428  0.04853786 22.7710 < 2.2e-16 ***
## return      -0.12920955  0.11762230 -1.0985    0.2720    
## stckpr       0.17097726  0.03355374  5.0956 3.476e-07 ***
## rnd         -0.14575073  0.01469317 -9.9196 < 2.2e-16 ***
## sales       -0.00393738  0.00042854 -9.1880 < 2.2e-16 ***
## sic         -0.00107515  0.00376075 -0.2859    0.7750    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1449600
## Residual Sum of Squares: 1098300
## R-Squared:      0.24236
## Adj. R-Squared: 0.24
## Chisq: 720.388 on 7 DF, p-value: < 2.22e-16

#Método amemiya
amemiya_patentes <- plm(patents ~ merger + employ + return + stckpr + rnd + sales + sic, data = panel_patentes, model="random",
random.method="amemiya")
summary(amemiya_patentes)

## Oneway (individual) effect Random Effect Model 
##    (Amemiya's transformation)
## 
## Call:
## plm(formula = patents ~ merger + employ + return + stckpr + rnd + 
##     sales + sic, data = panel_patentes, model = "random", random.method = "amemiya")
## 
## Balanced Panel: n = 226, T = 10, N = 2260
## 
## Effects:
##                   var std.dev share
## idiosyncratic  402.79   20.07 0.051
## individual    7483.44   86.51 0.949
## theta: 0.9268
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -454.59697   -2.99704   -1.65272    0.59741  193.17353 
## 
## Coefficients:
##                Estimate  Std. Error  z-value  Pr(>|z|)    
## (Intercept)  8.58107091 29.77947247   0.2882    0.7732    
## merger       3.91351453  4.11354681   0.9514    0.3414    
## employ       0.49060426  0.06153621   7.9726 1.554e-15 ***
## return      -0.09427795  0.10733800  -0.8783    0.3798    
## stckpr       0.04660332  0.03163610   1.4731    0.1407    
## rnd         -0.17995961  0.01406835 -12.7918 < 2.2e-16 ***
## sales       -0.00342554  0.00040647  -8.4275 < 2.2e-16 ***
## sic          0.00425278  0.00877425   0.4847    0.6279    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1144500
## Residual Sum of Squares: 891720
## R-Squared:      0.22085
## Adj. R-Squared: 0.21842
## Chisq: 638.312 on 7 DF, p-value: < 2.22e-16

#Método nerlove
nerlove_patentes <- plm(patents ~ merger + employ + return + stckpr + rnd + sales + sic, data = panel_patentes, model="random",
random.method="nerlove")
summary(nerlove_patentes)

## Oneway (individual) effect Random Effect Model 
##    (Nerlove's transformation)
## 
## Call:
## plm(formula = patents ~ merger + employ + return + stckpr + rnd + 
##     sales + sic, data = panel_patentes, model = "random", random.method = "nerlove")
## 
## Balanced Panel: n = 226, T = 10, N = 2260
## 
## Effects:
##                   var std.dev share
## idiosyncratic  362.51   19.04 0.046
## individual    7557.16   86.93 0.954
## theta: 0.9309
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -455.94828   -2.93752   -1.60035    0.62863  192.36375 
## 
## Coefficients:
##                Estimate  Std. Error  z-value  Pr(>|z|)    
## (Intercept)  8.38498937 31.41700295   0.2669    0.7896    
## merger       3.86675065  4.09938561   0.9433    0.3456    
## employ       0.46018862  0.06203371   7.4184 1.186e-13 ***
## return      -0.09236163  0.10697310  -0.8634    0.3879    
## stckpr       0.04167663  0.03156299   1.3204    0.1867    
## rnd         -0.18153379  0.01403810 -12.9315 < 2.2e-16 ***
## sales       -0.00339833  0.00040545  -8.3816 < 2.2e-16 ***
## sic          0.00451640  0.00925634   0.4879    0.6256    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1138700
## Residual Sum of Squares: 885220
## R-Squared:      0.22262
## Adj. R-Squared: 0.22021
## Chisq: 644.925 on 7 DF, p-value: < 2.22e-16

#Este código compara la r2 ajustada de los 3 métodos y elegir el que tenga la mayor.
phtest(walhus_patentes, within_patentes)

## 
##  Hausman Test
## 
## data:  patents ~ merger + employ + return + stckpr + rnd + sales + sic
## chisq = 352.48, df = 6, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistent

#Si el p-value es <.05 usamos efectos fijos(within)

#Por lo tanto nos quedamos con el modelo de efectos fijos (within)

Paso 4. Pruebas de Heterocedasticidad y Autocrrelación Serial

#Prueba de Heterocedasticidad
bptest(within_patentes)

## 
##  studentized Breusch-Pagan test
## 
## data:  within_patentes
## BP = 1447.6, df = 7, p-value < 2.2e-16

#Si el p-value es >0.05, hay heterocedasticidad en los residuos (problema detectado)

#Prueba de Autocorrelación Serial
pwartest(within_patentes)

## 
##  Wooldridge's test for serial correlation in FE panels
## 
## data:  within_patentes
## F = 104.29, df1 = 1, df2 = 2032, p-value < 2.2e-16
## alternative hypothesis: serial correlation

#Si el p-value <0.05, hay autocorrelación serial en los errores (problema detectado)

#Modelo de corrección con Errores Estándar Robustos
coeficientes_corregidos <- coeftest(within_patentes, vcov=vcovHC(within_patentes, type = "HC0"))
solo_coeficientes <- coeficientes_corregidos[,1]

Paso 5. Generar Pronósticos y Evaluar Modelo

datos_de_prueba <- data.frame(meger = 0, employ = 10, return = 6, stckpr = 48, rnd = 3, sales = 344)
prediccion <- sum(solo_coeficientes*datos_de_prueba)
prediccion

## [1] -1.418735

Conclusiones

En conclusión este ejercicio nos permite generar pronósticos en bases de datos con panel, tomando en cuenta los tratamientos.