Actividad Repaso

Librerías y carga de datos

Instalar paquetes y llamar librerías

library(readxl)
library(dplyr)
library(tidyr)
library(ggplot2)
library(corrplot)
library(stringr)
library(plm)
library(psych)
library(ggthemes)
library(caret)
library(glmnet)
library(car)
library(regclass)
library(lmtest)
library(mctest)
library(caret)
library(lubridate)
library(forecast)
library(tseries)
library(urca)
library(reshape2)

Carga de datasets

exports <- read_excel("inegi_exports_dataset.xlsx", 
    sheet = "exports")
ts_exports <- read_excel("~/Proyecto R/CONCENTRACION/inegi_exports_dataset.xlsx", 
    sheet = "ts")
data <- read_excel("inegi_exports_dataset.xlsx", 
    sheet = "data")
fdi <- read_excel("inegi_exports_dataset.xlsx", 
    sheet = "fdi")

Limpieza y tratamiento inicial de datos

Diseño y composicion del dataset tipo panel

exports <- exports %>%
  mutate(state = str_trim(state))

fdi <- fdi %>%
  mutate(state = str_trim(state))

data <- data %>%
  mutate(state = str_trim(state))

# EXPORTS
exports_long <- exports %>%
  pivot_longer(
    cols = starts_with("exports_"),
    names_to = "year",
    values_to = "real_exports"
  ) %>%
  mutate(
    year = str_extract(year, "\\d{4}") %>% as.numeric()
  ) %>%
  select(state, region, year, real_exports)

# FDI
fdi_long <- fdi %>%
  pivot_longer(
    cols = starts_with("fdi_"),
    names_to = "year",
    values_to = "fdi"
  ) %>%
  mutate(
    year = str_extract(year, "\\d{4}") %>% as.numeric()
  ) %>%
  select(state, region, year, fdi)

# Verificar duplicados en exports
dup_exports <- exports_long %>%
  count(state, year) %>%
  filter(n > 1)

# Verificar duplicados en fdi
dup_fdi <- fdi_long %>%
  count(state, year) %>%
  filter(n > 1)

# Verificar duplicados en base principal
dup_data <- data %>%
  count(state, year) %>%
  filter(n > 1)

# Si cualquiera tiene filas, hay problema estructural
print(dup_exports)

## # A tibble: 0 × 3
## # ℹ 3 variables: state <chr>, year <dbl>, n <int>

print(dup_fdi)

## # A tibble: 0 × 3
## # ℹ 3 variables: state <chr>, year <dbl>, n <int>

print(dup_data)

## # A tibble: 0 × 3
## # ℹ 3 variables: state <chr>, year <dbl>, n <int>

ts_exports_annual <- ts_exports %>%
  mutate(
    year = substr(date, 1, 4) %>% as.numeric()
  ) %>%
  group_by(year) %>%
  summarise(
    ts_exports = sum(ts_exports, na.rm = TRUE),
    .groups = "drop"
  )

panel_data <- data %>%
  left_join(exports_long, by = c("state", "year")) %>%
  left_join(fdi_long %>% select(-region), 
            by = c("state", "year")) %>%
  left_join(ts_exports_annual, by = "year")

Variables de estudio:

Para propósitos de este análisis nos enfocaremos en las siguientes variables clave:

• real_exports: total de exportaciones no procedentes del petroleo o sus derivados a valor del dinero del 2018.
• fdi: Inversión extranjera directa con un valor del dinero relativo a 2018.
• year: año en el que sucedió el evento.
• real_public_investment: Inversión pública por la población del estado.
• state: Estado de la república.
• border_distance: distrancia entre la capital del estado y la frontera con Estados Unidos más cercana.

Estadística Descriptiva

psych::describe(panel_data)

##                           vars   n         mean           sd      median
## state*                       1 288        16.50         9.25       16.50
## year                         2 288      2019.00         2.59     2019.00
## pop_density                  3 288       308.82      1063.93       65.02
## gdp_per_capita_2018          4 288      1986.91      1062.05     1788.31
## lq_primary                   5 288         1.06         0.88        0.84
## lq_secondary                 6 288         1.00         0.38        0.97
## lq_tertiary                  7 288         1.00         0.09        1.00
## average_daily_salary         8 288       332.49        46.96      324.12
## real_public_investment_pc    9 288       627.38       446.39      506.42
## border_economic_activity    10 288        -1.77         0.87       -1.99
## crime_rate                  11 256        27.43        23.99       18.36
## college_education           12 256         0.25         0.05        0.25
## exchange_rate               13 256        19.49         1.05       19.72
## border_distance             14 256       704.92       274.27      751.64
## inpc                        15 256       105.17        11.77      104.47
## region*                     16 256         4.09         1.51        4.00
## real_exports                17 256 228822083.78 274331648.02 97535120.79
## fdi                         18 256     18535.61     26141.08    10478.15
## ts_exports                  19 288   7822529.33    606507.99  7997670.57
##                                trimmed          mad        min          max
## state*                           16.50        11.86       1.00 3.200000e+01
## year                           2019.00         2.97    2015.00 2.023000e+03
## pop_density                      96.05        67.14       9.60 6.233410e+03
## gdp_per_capita_2018            1831.36       728.79     603.71 8.216560e+03
## lq_primary                        0.92         0.64       0.01 4.630000e+00
## lq_secondary                      0.97         0.45       0.37 1.990000e+00
## lq_tertiary                       1.00         0.10       0.79 1.180000e+00
## average_daily_salary            328.56        43.29     249.97 5.057300e+02
## real_public_investment_pc       570.97       384.18       4.14 2.423360e+03
## border_economic_activity         -1.92         0.26      -2.77 2.530000e+00
## crime_rate                       23.29        14.07       1.98 1.169500e+02
## college_education                 0.25         0.05       0.15 4.400000e-01
## exchange_rate                    19.66         0.85      17.07 2.052000e+01
## border_distance                 720.83       223.45       8.83 1.252660e+03
## inpc                            104.54        13.82      89.05 1.264800e+02
## region*                           4.16         1.48       1.00 6.000000e+00
## real_exports              178098052.86 136535980.71  268782.64 1.163117e+09
## fdi                           13034.20     11111.04   -7412.68 1.712389e+05
## ts_exports                  7860733.19    558612.44 6535587.76 8.792925e+06
##                                  range  skew kurtosis          se
## state*                    3.100000e+01  0.00    -1.21        0.55
## year                      8.000000e+00  0.00    -1.24        0.15
## pop_density               6.223810e+03  5.20    25.70       62.69
## gdp_per_capita_2018       7.612850e+03  2.49     9.25       62.58
## lq_primary                4.620000e+00  1.46     1.96        0.05
## lq_secondary              1.620000e+00  0.42    -0.58        0.02
## lq_tertiary               4.000000e-01 -0.13    -0.57        0.01
## average_daily_salary      2.557600e+02  0.83     0.55        2.77
## real_public_investment_pc 2.419220e+03  1.32     2.08       26.30
## border_economic_activity  5.300000e+00  3.60    14.55        0.05
## crime_rate                1.149700e+02  1.50     1.66        1.50
## college_education         2.900000e-01  0.50     0.37        0.00
## exchange_rate             3.450000e+00 -1.29     0.80        0.07
## border_distance           1.243830e+03 -0.54     0.04       17.14
## inpc                      3.743000e+01  0.36    -0.86        0.74
## region*                   5.000000e+00 -0.32    -1.14        0.09
## real_exports              1.162848e+09  1.38     0.99 17145728.00
## fdi                       1.786516e+05  3.26    12.47     1633.82
## ts_exports                2.257337e+06 -0.56     0.08    35738.83

panel_data$region <- as.factor(panel_data$region)
panel_data$state <- as.factor(panel_data$state)
summary(panel_data)

##                  state          year       pop_density      
##  Aguascalientes     :  9   Min.   :2015   Min.   :   9.601  
##  Baja California    :  9   1st Qu.:2017   1st Qu.:  42.067  
##  Baja California Sur:  9   Median :2019   Median :  65.017  
##  Campeche           :  9   Mean   :2019   Mean   : 308.816  
##  Chiapas            :  9   3rd Qu.:2021   3rd Qu.: 161.291  
##  Chihuahua          :  9   Max.   :2023   Max.   :6233.409  
##  (Other)            :234                                    
##  gdp_per_capita_2018   lq_primary       lq_secondary     lq_tertiary    
##  Min.   : 603.7      Min.   :0.01493   Min.   :0.3685   Min.   :0.7867  
##  1st Qu.:1307.2      1st Qu.:0.43199   1st Qu.:0.6470   1st Qu.:0.9360  
##  Median :1788.3      Median :0.83619   Median :0.9693   Median :0.9993  
##  Mean   :1986.9      Mean   :1.05887   Mean   :0.9969   Mean   :0.9973  
##  3rd Qu.:2314.7      3rd Qu.:1.32423   3rd Qu.:1.2569   3rd Qu.:1.0669  
##  Max.   :8216.6      Max.   :4.63480   Max.   :1.9911   Max.   :1.1847  
##                                                                         
##  average_daily_salary real_public_investment_pc border_economic_activity
##  Min.   :250.0        Min.   :   4.139          Min.   :-2.772          
##  1st Qu.:297.5        1st Qu.: 289.064          1st Qu.:-2.137          
##  Median :324.1        Median : 506.424          Median :-1.985          
##  Mean   :332.5        Mean   : 627.380          Mean   :-1.765          
##  3rd Qu.:360.2        3rd Qu.: 879.463          3rd Qu.:-1.791          
##  Max.   :505.7        Max.   :2423.360          Max.   : 2.530          
##                                                                         
##    crime_rate      college_education exchange_rate   border_distance  
##  Min.   :  1.984   Min.   :0.1453    Min.   :17.07   Min.   :   8.83  
##  1st Qu.: 10.560   1st Qu.:0.2077    1st Qu.:19.16   1st Qu.: 613.26  
##  Median : 18.355   Median :0.2460    Median :19.72   Median : 751.64  
##  Mean   : 27.433   Mean   :0.2482    Mean   :19.49   Mean   : 704.92  
##  3rd Qu.: 37.002   3rd Qu.:0.2798    3rd Qu.:20.20   3rd Qu.: 875.76  
##  Max.   :116.950   Max.   :0.4376    Max.   :20.52   Max.   :1252.66  
##  NA's   :32        NA's   :32        NA's   :32      NA's   :32       
##       inpc                       region    real_exports            fdi        
##  Min.   : 89.05   CdMx              : 8   Min.   :2.688e+05   Min.   : -7413  
##  1st Qu.: 96.71   Centro_Sur_Oriente:48   1st Qu.:2.152e+07   1st Qu.:  4048  
##  Median :104.47   Noreste           :32   Median :9.754e+07   Median : 10478  
##  Mean   :105.17   Noroeste          :48   Mean   :2.288e+08   Mean   : 18536  
##  3rd Qu.:111.28   Occidente_Bajio   :64   3rd Qu.:3.502e+08   3rd Qu.: 22572  
##  Max.   :126.48   Sur               :56   Max.   :1.163e+09   Max.   :171239  
##  NA's   :32       NA's              :32   NA's   :32          NA's   :32      
##    ts_exports     
##  Min.   :6535588  
##  1st Qu.:7588156  
##  Median :7997671  
##  Mean   :7822529  
##  3rd Qu.:8098039  
##  Max.   :8792925  
## 

Resultados

El análisis descriptivo arrojó los siguientes resultados:

• real_exports:

• Media: 228822083.78
  

• Mediana: 97535120.79

• Máximo: 1163116946.59
  

• Mínimo: 268782.64

• Desviación estándar: 274331648.02

• fdi:

• Media: 18535.61
  

• Mediana: 10478.15
  

• Máximo: 171238.91
  

• Mínimo: -7412.68

• Desviación estándar: 26141.08

• year:

• Media: 2019.50
  

• Mediana: 2019.50

• Máximo: 2023.00
  

• Mínimo: 2016.00

• Desviación estándar: 2.30

• real_public_investment_pc:

• Media: 599.27
  

• Mediana: 483.94
  

• Máximo: 2423.36
  

• Mínimo: 4.14

• Desviación estándar: 423.74

• border_distance:

• Media: 704.92
  

• Mediana: 751.64
  

• Máximo: 1252.66
  

• Mínimo: 8.83

• Desviación estándar: 274.34

Interpretaciones

• real_exports: La media es mucho mayor que la mediana, lo que indica que pocos estados exportan montos muy altos y elevan el promedio.

• fdi: Existe mucha variación entre estados y algunos concentran grandes montos de inversión, mientras que otros incluso presentan valores negativos.

• year: Los datos están distribuidos de forma uniforme entre 2016 y 2023, lo que confirma un panel balanceado en el tiempo.

• real_public_investment_pc: Hay diferencias importantes entre estados en inversión pública por habitante, con algunos valores considerablemente más altos que el resto.

• real_public_investment_pc: Hay diferencias importantes entre estados en inversión pública por habitante, con algunos valores considerablemente más altos que el resto.

• border_distance: La distancia a la frontera varía bastante entre estados, aunque la mayoría se concentra en distancias intermedias o altas.

Variable de mayor dispersión: real_exports.

panel_data <- panel_data[-(1:32), , drop = FALSE]
str(panel_data)

## tibble [256 × 19] (S3: tbl_df/tbl/data.frame)
##  $ state                    : Factor w/ 32 levels "Aguascalientes",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ year                     : num [1:256] 2016 2016 2016 2016 2016 ...
##  $ pop_density              : num [1:256] 235.01 50.85 9.79 14.92 70.76 ...
##  $ gdp_per_capita_2018      : num [1:256] 2329 2281 2254 7731 713 ...
##  $ lq_primary               : num [1:256] 0.403 0.845 0.599 0.486 0.731 ...
##  $ lq_secondary             : num [1:256] 1.191 1.508 0.651 0.709 0.965 ...
##  $ lq_tertiary              : num [1:256] 0.992 0.866 1.097 1.091 1.024 ...
##  $ average_daily_salary     : num [1:256] 314 333 318 424 307 ...
##  $ real_public_investment_pc: num [1:256] 1027 275 1360 887 1022 ...
##  $ border_economic_activity : num [1:256] -1.85 2.42 -2.16 -2.15 -2.36 ...
##  $ crime_rate               : num [1:256] 3.71 31.68 32.89 10.84 10.64 ...
##  $ college_education        : num [1:256] 0.249 0.258 0.287 0.229 0.146 ...
##  $ exchange_rate            : num [1:256] 20.5 20.5 20.5 20.5 20.5 ...
##  $ border_distance          : num [1:256] 625.59 8.83 800.32 978.33 1111.82 ...
##  $ inpc                     : num [1:256] 92 92 92 92 92 ...
##  $ region                   : Factor w/ 6 levels "CdMx","Centro_Sur_Oriente",..: 5 4 4 6 6 4 1 3 5 4 ...
##  $ real_exports             : num [1:256] 1.75e+08 8.03e+08 5.30e+06 2.12e+08 1.31e+07 ...
##  $ fdi                      : num [1:256] 13225 33796 11420 3162 3091 ...
##  $ ts_exports               : num [1:256] 7399443 7399443 7399443 7399443 7399443 ...

Visualizacion de los Datos

Histogramas

variables <- c("year","real_public_investment_pc","fdi","real_exports","border_distance","inpc")

panel_data %>%
  pivot_longer(cols = all_of(variables), names_to = "variable", values_to = "valor") %>%
  ggplot(aes(x = valor)) +
  geom_histogram(bins = 20) +
  facet_wrap(~ variable, scales = "free") +
  labs(title = "Distribucion de variables clave",
       x = "Valor de exportaciones", y = "Frecuencia") +
  theme_fivethirtyeight()

## Interpretación de histogramas

En términos generales, la mayoría de las variables presentan distribuciones asimétricas (sesgo positivo).
fdi, real_exports y real_public_investment_pc muestran una clara asimetría a la derecha: la mayor parte de las observaciones se concentran en valores bajos o medios, pero existen algunos valores muy altos que alargan la cola derecha.
inpc y year son relativamente más simétricas y estables.

Respecto a los outliers, las colas largas en los histogramas, evidencian valores atípicos principalmente en:
* fdi * real_exports * real_public_investment

Boxplots

panel_data %>%
  pivot_longer(cols = all_of(variables), names_to = "variable", values_to = "valor") %>%
  ggplot(aes(x = region, y = valor)) +
  geom_boxplot(outlier.alpha = 0.6) +
  facet_wrap(~ variable, scales = "free_y") +
  labs(title = "Dispersion de variables clave por region (boxplots)",
       x = "Region", y = "Valor de exportaciones") +
  theme_fivethirtyeight() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Interpretación de los boxplots

Observando los boxplots:

• La región Norte muestra la mayor dispersión, especialmente en real_exports y fdi, ya que tiene cajas más amplias y valores más extremos.
• La región Sur presenta la menor dispersión, con cajas más compactas y menor variabilidad en exportaciones.

¿Es relevante la región?

Sí. La región parece ser una variable relevante para analizar el desempeño exportador de México, ya que existen diferencias claras en niveles y dispersión de exportaciones entre regiones, particularmente entre el Norte y el Sur.

Matriz de Correlacion

corr_mat <- panel_data %>%
  select(all_of(variables)) %>%
  cor(use = "complete.obs")

corr_df <- melt(corr_mat)

ggplot(corr_df, aes(Var1, Var2, fill = value)) +
  geom_tile(color = "white") +
  geom_text(aes(label = round(value, 2)), size = 3) +
  scale_fill_gradient2(low = "#3B4CC0",
                       mid = "white",
                       high = "#B40426",
                       midpoint = 0,
                       limits = c(-1,1),
                       name = "Correlacion") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        panel.grid = element_blank()) +
  labs(title = "Matriz de correlacion: Variables Clave",
       x = NULL, y = NULL)

Interpretación de la Matriz de Correlacion

Las variables con mayor correlación son:

• year e inpc (0.98): correlación positiva muy fuerte.
• real_exports y border_distance (-0.75): correlación negativa fuerte.

Las variables con menor correlación (cercanas a cero) son:

• real_exports y year (0.03)
• real_exports e inpc (0.03)
• real_public_investment_pc y border_distance (0.05)
• fdi y year (-0.06)

Gráficos de dispersion

scatter_data <- panel_data %>%
  select(real_exports, all_of(variables)) %>%
  pivot_longer(
    cols = -real_exports,
    names_to = "variable",
    values_to = "value"
  )

ggplot(scatter_data, aes(x = value, y = real_exports)) +
  geom_point(alpha = 0.5, color = "#2C3E50") +
  geom_smooth(method = "lm", se = FALSE, color = "#E74C3C") +
  facet_wrap(~ variable, scales = "free_x")

Interpretación de gráficos de dispersión

A simple vista y similar a lo observado en la matriz de correlación, la única variable con la que parece tener una correlación los suficientement fuerte o significativa es con border_distance.

Preguntas clave

1. ¿Qué tan relevante es la distancia a la frontera con Estados Unidos en el crecimiento futuro de las exportaciones estatales?
2. ¿En qué medida la inversión extranjera directa (fdi) impulsa el desempeño exportador de los estados en los próximos años?
   
3. ¿La estabilidad de precios (inpc) influye directamente en la evolución de las exportaciones?

Hipótesis

Hipótesis 1: Los estados con menor distancia a la frontera con Estados Unidos presentan mayores niveles y tasas de crecimiento en sus exportaciones en comparación con estados más alejados.

Hipótesis 2: Un mayor flujo de inversión extranjera directa (fdi) se asocia positivamente con un mejor desempeño exportador estatal en los próximos años.

Hipótesis 3: Una mayor estabilidad de precios (menor variabilidad en el inpc) favorece el crecimiento sostenido de las exportaciones estatales.

Modelos de regresion (MLRM, MLRM + log(), LASSO)

Modelo base de regresion lineal múltiple (1 explicativa + 1 control)

modelo_base <- lm(real_exports ~ fdi + inpc, data = panel_data)
rmse_base <- sqrt(mean(residuals(modelo_base)^2, na.rm = TRUE))
summary(modelo_base)

## 
## Call:
## lm(formula = real_exports ~ fdi + inpc, data = panel_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -681702219 -162790837 -107996862  103162435  878848333 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.285e+07  1.800e+08   0.238    0.812    
## fdi         3.163e+03  6.784e+02   4.662 5.41e-06 ***
## inpc        1.189e+06  1.656e+06   0.718    0.473    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 265600000 on 221 degrees of freedom
##   (32 observations deleted due to missingness)
## Multiple R-squared:  0.09038,    Adjusted R-squared:  0.08215 
## F-statistic: 10.98 on 2 and 221 DF,  p-value: 2.844e-05

rmse_base

## [1] 263766989

MLRM con 2–4 controles (explicativa + controles)

modelo_full <- lm(real_exports ~ state + fdi + real_public_investment_pc + border_distance + inpc + year, data = panel_data)
rmse_full <- sqrt(mean(residuals(modelo_full)^2, na.rm = TRUE))
summary(modelo_full)

## 
## Call:
## lm(formula = real_exports ~ state + fdi + real_public_investment_pc + 
##     border_distance + inpc + year, data = panel_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -103824886  -11651720    1555925    9832202  124781237 
## 
## Coefficients: (1 not defined because of singularities)
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                2.223e+10  1.085e+10   2.049 0.041873 *  
## stateBaja California       5.945e+08  1.677e+07  35.438  < 2e-16 ***
## stateBaja California Sur  -1.824e+08  1.566e+07 -11.649  < 2e-16 ***
## stateCampeche              7.464e+07  1.613e+07   4.626 6.91e-06 ***
## stateChiapas              -1.689e+08  1.605e+07 -10.522  < 2e-16 ***
## stateChihuahua             8.353e+08  1.683e+07  49.641  < 2e-16 ***
## stateCiudad de Mexico     -1.443e+08  3.300e+07  -4.372 2.03e-05 ***
## stateCoahuila              6.636e+08  1.619e+07  40.985  < 2e-16 ***
## stateColima               -1.733e+08  1.609e+07 -10.772  < 2e-16 ***
## stateDurango              -1.432e+08  1.578e+07  -9.076  < 2e-16 ***
## stateGuanajuato            2.860e+08  1.625e+07  17.601  < 2e-16 ***
## stateGuerrero             -1.669e+08  1.619e+07 -10.307  < 2e-16 ***
## stateHidalgo              -1.444e+08  1.617e+07  -8.936 3.73e-16 ***
## stateJalisco               2.071e+08  1.670e+07  12.402  < 2e-16 ***
## stateMexico                1.508e+08  1.760e+07   8.571 3.71e-15 ***
## stateMichoacan            -1.066e+08  1.629e+07  -6.541 5.63e-10 ***
## stateMorelos              -1.221e+08  1.598e+07  -7.638 1.08e-12 ***
## stateNayarit              -1.796e+08  1.603e+07 -11.206  < 2e-16 ***
## stateNuevo Leon            5.409e+08  2.066e+07  26.178  < 2e-16 ***
## stateOaxaca               -1.668e+08  1.621e+07 -10.291  < 2e-16 ***
## statePuebla                9.566e+07  1.609e+07   5.946 1.32e-08 ***
## stateQueretaro             4.235e+07  1.569e+07   2.700 0.007572 ** 
## stateQuintana Roo         -1.820e+08  1.608e+07 -11.319  < 2e-16 ***
## stateSan Luis Potosi       7.217e+07  1.572e+07   4.590 8.09e-06 ***
## stateSinaloa              -1.496e+08  1.568e+07  -9.545  < 2e-16 ***
## stateSonora                1.722e+08  1.600e+07  10.765  < 2e-16 ***
## stateTabasco              -6.202e+07  1.600e+07  -3.877 0.000146 ***
## stateTamaulipas            3.374e+08  1.582e+07  21.326  < 2e-16 ***
## stateTlaxcala             -1.576e+08  1.585e+07  -9.942  < 2e-16 ***
## stateVeracruz             -6.757e+07  1.628e+07  -4.150 5.04e-05 ***
## stateYucatan              -1.591e+08  1.661e+07  -9.577  < 2e-16 ***
## stateZacatecas            -1.209e+08  1.600e+07  -7.555 1.77e-12 ***
## fdi                        1.605e+01  2.431e+02   0.066 0.947425    
## real_public_investment_pc  1.159e+04  7.000e+03   1.656 0.099357 .  
## border_distance                   NA         NA      NA       NA    
## inpc                       2.922e+06  9.961e+05   2.934 0.003764 ** 
## year                      -1.108e+07  5.426e+06  -2.042 0.042558 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29280000 on 188 degrees of freedom
##   (32 observations deleted due to missingness)
## Multiple R-squared:  0.9906, Adjusted R-squared:  0.9888 
## F-statistic: 565.7 on 35 and 188 DF,  p-value: < 2.2e-16

rmse_full

## [1] 26821007

MLRM con escala logarítmica con 2–4 controles (explicativa + controles)

modelo_log <- lm(real_exports ~ state + log(1+fdi) + log(real_public_investment_pc) + log(border_distance) + log(inpc) + year, data = panel_data)
rmse_log <- sqrt(mean(residuals(modelo_log)^2, na.rm = TRUE))
summary(modelo_log)

## 
## Call:
## lm(formula = real_exports ~ state + log(1 + fdi) + log(real_public_investment_pc) + 
##     log(border_distance) + log(inpc) + year, data = panel_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -105020500  -11490402     866747   10714873  127159981 
## 
## Coefficients: (1 not defined because of singularities)
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     2.758e+10  1.274e+10   2.164  0.03174 *  
## stateBaja California            5.933e+08  1.665e+07  35.626  < 2e-16 ***
## stateBaja California Sur       -1.807e+08  1.595e+07 -11.328  < 2e-16 ***
## stateCampeche                   7.702e+07  1.615e+07   4.768 3.76e-06 ***
## stateChiapas                   -1.710e+08  1.628e+07 -10.506  < 2e-16 ***
## stateChihuahua                  8.341e+08  1.668e+07  49.994  < 2e-16 ***
## stateCiudad de Mexico          -1.399e+08  1.707e+07  -8.200 3.92e-14 ***
## stateCoahuila                   6.639e+08  1.603e+07  41.412  < 2e-16 ***
## stateColima                    -1.755e+08  1.731e+07 -10.139  < 2e-16 ***
## stateDurango                   -1.432e+08  1.591e+07  -9.001 2.69e-16 ***
## stateGuanajuato                 2.848e+08  1.613e+07  17.652  < 2e-16 ***
## stateGuerrero                  -1.695e+08  1.620e+07 -10.461  < 2e-16 ***
## stateHidalgo                   -1.460e+08  1.637e+07  -8.920 4.49e-16 ***
## stateJalisco                    2.066e+08  1.625e+07  12.708  < 2e-16 ***
## stateMexico                     1.529e+08  1.628e+07   9.392  < 2e-16 ***
## stateMichoacan                 -1.087e+08  1.643e+07  -6.621 3.76e-10 ***
## stateMorelos                   -1.237e+08  1.616e+07  -7.652 1.06e-12 ***
## stateNayarit                   -1.822e+08  1.612e+07 -11.303  < 2e-16 ***
## stateNuevo Leon                 5.428e+08  1.782e+07  30.457  < 2e-16 ***
## stateOaxaca                    -1.692e+08  1.692e+07 -10.002  < 2e-16 ***
## statePuebla                     9.486e+07  1.631e+07   5.815 2.62e-08 ***
## stateQueretaro                  4.382e+07  1.596e+07   2.746  0.00662 ** 
## stateQuintana Roo              -1.845e+08  1.608e+07 -11.475  < 2e-16 ***
## stateSan Luis Potosi            7.171e+07  1.591e+07   4.508 1.16e-05 ***
## stateSinaloa                   -1.492e+08  1.584e+07  -9.419  < 2e-16 ***
## stateSonora                     1.705e+08  1.611e+07  10.582  < 2e-16 ***
## stateTabasco                   -6.451e+07  1.609e+07  -4.009 8.85e-05 ***
## stateTamaulipas                 3.379e+08  1.597e+07  21.154  < 2e-16 ***
## stateTlaxcala                  -1.591e+08  1.604e+07  -9.918  < 2e-16 ***
## stateVeracruz                  -6.971e+07  1.650e+07  -4.224 3.76e-05 ***
## stateYucatan                   -1.588e+08  1.776e+07  -8.941 3.94e-16 ***
## stateZacatecas                 -1.253e+08  1.671e+07  -7.496 2.65e-12 ***
## log(1 + fdi)                   -4.755e+05  2.401e+06  -0.198  0.84324    
## log(real_public_investment_pc)  4.486e+06  3.502e+06   1.281  0.20179    
## log(border_distance)                   NA         NA      NA       NA    
## log(inpc)                       3.782e+08  1.333e+08   2.837  0.00507 ** 
## year                           -1.445e+07  6.614e+06  -2.185  0.03013 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29630000 on 185 degrees of freedom
##   (35 observations deleted due to missingness)
## Multiple R-squared:  0.9904, Adjusted R-squared:  0.9886 
## F-statistic: 548.1 on 35 and 185 DF,  p-value: < 2.2e-16

rmse_log

## [1] 27112395

LASSO

set.seed(123)
idx <- createDataPartition(panel_data$real_exports, p = 0.75, list = FALSE)
train_data <- panel_data[idx, ]
test_data  <- panel_data[-idx, ]

# --- TRAIN: x e y alineados (mismas filas) ---
mf_train <- model.frame(real_exports ~ ., data = train_data, na.action = na.omit)
y_train  <- model.response(mf_train)
x_train  <- model.matrix(real_exports ~ ., data = mf_train)[, -1]

# --- TEST: x e y alineados (mismas filas) ---
mf_test <- model.frame(real_exports ~ ., data = test_data, na.action = na.omit)
y_test  <- model.response(mf_test)
x_test  <- model.matrix(real_exports ~ ., data = mf_test)[, -1]

set.seed(123)
cv_lasso <- cv.glmnet(x_train, y_train, alpha = 1)
lasso_model <- glmnet(x_train, y_train, alpha = 1, lambda = cv_lasso$lambda.min)

pred_lasso <- as.vector(predict(lasso_model, newx = x_test))

RMSE_lasso <- RMSE(pred_lasso, y_test)
R2_lasso   <- R2(pred_lasso, y_test)

RMSE_lasso

## [1] 32077848

R2_lasso

## [1] 0.9858817

coef(lasso_model)

## 53 x 1 sparse Matrix of class "dgCMatrix"
##                                      s0
## (Intercept)                2.434832e+10
## stateBaja California       1.646669e+08
## stateBaja California Sur  -9.417562e+07
## stateCampeche              1.740530e+08
## stateChiapas               .           
## stateChihuahua             7.184962e+08
## stateCiudad de Mexico     -1.519623e+08
## stateCoahuila              5.336884e+08
## stateColima               -1.150422e+07
## stateDurango              -8.313408e+07
## stateGuanajuato            3.148007e+08
## stateGuerrero             -1.339583e+07
## stateHidalgo              -1.034491e+08
## stateJalisco               2.590956e+08
## stateMexico                2.084174e+08
## stateMichoacan            -3.059761e+07
## stateMorelos              -4.885840e+07
## stateNayarit              -5.774609e+07
## stateNuevo Leon            3.214024e+08
## stateOaxaca               -7.960520e+06
## statePuebla                1.724382e+08
## stateQueretaro             2.445335e+07
## stateQuintana Roo          6.838772e+07
## stateSan Luis Potosi       .           
## stateSinaloa              -3.404641e+07
## stateSonora                5.810535e+07
## stateTabasco               7.354367e+07
## stateTamaulipas            1.734331e+08
## stateTlaxcala             -1.107964e+08
## stateVeracruz             -3.546283e+07
## stateYucatan              -4.593071e+07
## stateZacatecas            -1.023260e+08
## year                      -1.221207e+07
## pop_density                .           
## gdp_per_capita_2018       -5.817087e+03
## lq_primary                -7.187881e+06
## lq_secondary               2.631034e+07
## lq_tertiary                .           
## average_daily_salary       5.493408e+05
## real_public_investment_pc  4.211319e+03
## border_economic_activity   6.272532e+07
## crime_rate                -1.670094e+05
## college_education         -1.463661e+07
## exchange_rate              2.700079e+06
## border_distance           -2.245104e+05
## inpc                       .           
## regionCentro_Sur_Oriente   .           
## regionNoreste              2.964960e+07
## regionNoroeste             .           
## regionOccidente_Bajio      .           
## regionSur                  .           
## fdi                        1.080623e+02
## ts_exports                 6.138800e+01

Tabla Comparativa de los Modelos

resultados <- data.frame(
  Regression_Model = c("a) Modelo Base", "b) Modelo Full", "c) Modelo log", "d) LASSO"),
  Adjusted_R2      = c(summary(modelo_base)$adj.r.squared,
                       summary(modelo_full)$adj.r.squared,
                       summary(modelo_log)$adj.r.squared,
                       R2_lasso),
  RMSE             = c(rmse_base, rmse_full, rmse_log, RMSE_lasso)
)

resultados

##   Regression_Model Adjusted_R2      RMSE
## 1   a) Modelo Base  0.08214863 263766989
## 2   b) Modelo Full  0.98884381  26821007
## 3    c) Modelo log  0.98864172  27112395
## 4         d) LASSO  0.98588168  32077848

Diagnosticos

Multicolinealidad

VIF(modelo_base)

##      fdi     inpc 
## 1.002812 1.002812

Heterocedasticidad

bptest(modelo_base)

## 
##  studentized Breusch-Pagan test
## 
## data:  modelo_base
## BP = 43.961, df = 2, p-value = 2.845e-10

bptest(modelo_full)

## 
##  studentized Breusch-Pagan test
## 
## data:  modelo_full
## BP = 76.177, df = 35, p-value = 6.952e-05

bptest(modelo_log)

## 
##  studentized Breusch-Pagan test
## 
## data:  modelo_log
## BP = 72.379, df = 35, p-value = 0.0002069

Normalidad de Residuales

hist(modelo_base$residuals,xlab="Residuales estimados de la regresion", main="Distribucion de Residuales en Modelo Base", col="lightgreen", border="white")

hist(modelo_full$residuals,xlab="Residuales estimados de la regresion", main="Distribucion de Residuales en Modelo Full", col="lightgreen", border="white")

hist(modelo_log$residuals,xlab="Residuales estimados de la regresion", main="Distribucion de Residuales en Modelo logaritmico", col="lightgreen", border="white")

library(tseries)

# Jarque-Bera test
jb_test_base <- jarque.bera.test(modelo_base$residuals)
jb_test_base

## 
##  Jarque Bera Test
## 
## data:  modelo_base$residuals
## X-squared = 64.302, df = 2, p-value = 1.088e-14

jb_test_full <- jarque.bera.test(modelo_full$residuals)
jb_test_full

## 
##  Jarque Bera Test
## 
## data:  modelo_full$residuals
## X-squared = 141.43, df = 2, p-value < 2.2e-16

jb_test_log <- jarque.bera.test(modelo_log$residuals)
jb_test_log

## 
##  Jarque Bera Test
## 
## data:  modelo_log$residuals
## X-squared = 148.02, df = 2, p-value < 2.2e-16

AIC(modelo_base, modelo_full, modelo_log)

##             df      AIC
## modelo_base  4 9330.663
## modelo_full 37 8372.588
## modelo_log  37 8266.223

Análisis de series del tiempo

Limpieza de datos

ts_df <- ts_exports %>%
  mutate(
    year  = as.integer(substr(date, 1, 4)),
    month = as.integer(substr(date, 6, 7)),
    date_m = as.Date(paste0(year, "-", month, "-01"))
  ) %>%
  arrange(date_m)

Visualización de series del tiempo

p_ts <- ggplot(ts_df, aes(x = date_m, y = ts_exports)) +
  geom_line() +
  theme_minimal() +
  labs(
    title = "Exportaciones a traves del tiempo",
    x = "Date",
    y = "ts_exports"
  )

p_ts

Descomposicion de series del tiempo

ts_y <- ts(
  ts_df$ts_exports,
  start = c(min(ts_df$year), min(ts_df$month[ts_df$year == min(ts_df$year)])),
  frequency = 12
)

decomp_classic <- decompose(ts_y, type = "additive")
plot(decomp_classic)

Test de estacionariedad y autocorrelacion serial

adf_level  <- tseries::adf.test(ts_y)
adf_level

## 
##  Augmented Dickey-Fuller Test
## 
## data:  ts_y
## Dickey-Fuller = -2.7908, Lag order = 7, p-value = 0.2433
## alternative hypothesis: stationary

Acf(ts_y, main = "ACF: ts_exports")

Pacf(ts_y, main = "PACF: ts_exports")

ts_y_d1 <- diff(ts_y, differences = 1)

modelo_arma <- Arima(
  ts_y_d1,
  order = c(1,0,1),
  include.constant = FALSE
)

summary(modelo_arma)

## Series: ts_y_d1 
## ARIMA(1,0,1) with zero mean 
## 
## Coefficients:
##          ar1      ma1
##       0.1397  -0.7685
## s.e.  0.0648   0.0388
## 
## sigma^2 = 1.969e+09:  log likelihood = -4931.87
## AIC=9869.73   AICc=9869.79   BIC=9881.76
## 
## Training set error measures:
##                    ME     RMSE      MAE      MPE     MAPE      MASE
## Training set 6095.921 44259.69 28757.12 11.34027 211.5769 0.8993409
##                      ACF1
## Training set -0.005080321

checkresiduals(modelo_arma)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,0,1) with zero mean
## Q* = 195.82, df = 22, p-value < 2.2e-16
## 
## Model df: 2.   Total lags used: 24

modelo_arima <- Arima(
  ts_y,
  order = c(1,1,1),
  include.constant = TRUE
)

summary(modelo_arima)

## Series: ts_y 
## ARIMA(1,1,1) with drift 
## 
## Coefficients:
##          ar1      ma1      drift
##       0.1647  -0.8148  1652.2861
## s.e.  0.0649   0.0382   485.8929
## 
## sigma^2 = 1.928e+09:  log likelihood = -4927.24
## AIC=9862.47   AICc=9862.57   BIC=9878.51
## 
## Training set error measures:
##                    ME     RMSE      MAE        MPE     MAPE      MASE
## Training set 1.093527 43697.63 28231.01 -0.9572928 7.338796 0.6850747
##                    ACF1
## Training set 0.01418405

checkresiduals(modelo_arima)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,1) with drift
## Q* = 185.54, df = 22, p-value < 2.2e-16
## 
## Model df: 2.   Total lags used: 24

modelo_sarima <- Arima(
  ts_y,
  order = c(1,1,1),
  seasonal = c(1,1,1),
  include.constant = TRUE
)

summary(modelo_sarima)

## Series: ts_y 
## ARIMA(1,1,1)(1,1,1)[12] 
## 
## Coefficients:
##          ar1      ma1    sar1     sma1
##       0.1122  -0.7140  0.0104  -0.8390
## s.e.  0.0757   0.0523  0.0585   0.0306
## 
## sigma^2 = 1.369e+09:  log likelihood = -4720.77
## AIC=9451.55   AICc=9451.7   BIC=9471.44
## 
## Training set error measures:
##                     ME     RMSE      MAE        MPE    MAPE      MASE
## Training set -97.56791 36215.02 22759.48 -0.4223074 5.68124 0.5522986
##                    ACF1
## Training set 0.01070795

checkresiduals(modelo_sarima)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,1)(1,1,1)[12]
## Q* = 150.49, df = 20, p-value < 2.2e-16
## 
## Model df: 4.   Total lags used: 24

library(forecast)

fc_5 <- forecast(modelo_sarima, h = (5*12))

fc_5

##          Point Forecast    Lo 80     Hi 80    Lo 95     Hi 95
## Jan 2026       626786.3 579376.6  674196.0 554279.4  699293.1
## Feb 2026       701484.9 650453.8  752516.0 623439.6  779530.2
## Mar 2026       770569.9 717184.5  823955.3 688924.0  852215.8
## Apr 2026       714768.1 659228.2  770308.0 629827.1  799709.0
## May 2026       727821.7 670218.5  785424.9 639725.2  815918.3
## Jun 2026       738255.1 678661.1  797849.1 647114.0  829396.3
## Jul 2026       731630.7 670110.4  793150.9 637543.6  825717.8
## Aug 2026       751347.6 687959.6  814735.6 654404.1  848291.1
## Sep 2026       749738.1 684535.9  814940.3 650019.9  849456.3
## Oct 2026       802541.5 735574.2  869508.8 700123.8  904959.2
## Nov 2026       753991.8 685304.7  822678.9 648943.9  859039.6
## Dec 2026       762075.9 691711.0  832440.7 654462.1  869689.6
## Jan 2027       643327.4 569173.6  717481.2 529919.0  756735.8
## Feb 2027       718024.4 641595.3  794453.5 601136.1  834912.6
## Mar 2027       786930.0 708418.7  865441.3 666857.4  907002.7
## Apr 2027       731014.2 650488.3  811540.1 607860.4  854168.0
## May 2027       744186.0 661696.1  826675.9 618028.6  870343.4
## Jun 2027       755060.9 670652.9  839468.8 625970.0  884151.7
## Jul 2027       748059.9 661776.4  834343.3 616100.8  880019.0
## Aug 2027       768174.3 680055.3  856293.2 633407.9  902940.6
## Sep 2027       766603.5 676686.5  856520.6 629087.3  904119.8
## Oct 2027       818583.8 726904.0  910263.7 678371.6  958796.1
## Nov 2027       770978.1 677568.7  864387.5 628120.7  913835.5
## Dec 2027       778723.7 683616.2  873831.2 633269.3  924178.1
## Jan 2028       659963.4 561468.0  758458.8 509327.7  810599.2
## Feb 2028       734660.4 633958.2  835362.5 580649.8  888671.0
## Mar 2028       803564.2 700807.6  906320.7 646411.6  960716.7
## Apr 2028       747647.2 642888.0  852406.4 587431.8  907862.6
## May 2028       760820.2 654097.1  867543.3 597601.3  924039.0
## Jun 2028       771699.6 663048.3  880350.9 605531.7  937867.5
## Jul 2028       764694.7 654148.8  875240.6 595629.3  933760.1
## Aug 2028       784813.2 672404.6  897221.8 612899.1  956727.3
## Sep 2028       783242.9 669002.0  897483.8 608526.5  957959.3
## Oct 2028       835214.7 719170.4  951258.9 657740.3 1012689.1
## Nov 2028       787618.7 669798.7  905438.8 607428.5  967809.0
## Dec 2028       795360.8 675791.4  914930.3 612495.1  978226.5
## Jan 2029       676600.4 553775.0  799425.8 488755.2  864445.6
## Feb 2029       751297.4 626253.3  876341.5 560059.0  942535.8
## Mar 2029       820201.1 693072.1  947330.2 625774.0 1014628.3
## Apr 2029       764284.1 635114.1  893454.2 566735.6  961832.7
## May 2029       777457.2 646279.0  908635.3 576837.5  978076.8
## Jun 2029       788336.6 655180.8  921492.4 584692.4  991980.9
## Jul 2029       781331.7 646227.2  916436.2 574707.2  987956.2
## Aug 2029       801450.3 664424.7  938475.8 591887.8 1011012.7
## Sep 2029       799879.9 660960.0  938799.9 587420.2 1012339.7
## Oct 2029       851851.6 711062.7  992640.5 636533.5 1067169.7
## Nov 2029       804255.8 661622.4  946889.2 586116.9 1022394.7
## Dec 2029       811997.8 667543.5  956452.1 591074.1 1032921.6
## Jan 2030       693237.4 545582.1  840892.7 467418.1  919056.7
## Feb 2030       767934.4 618018.5  917850.3 538657.8  997210.9
## Mar 2030       836838.1 684783.2  988893.1 604290.2 1069386.1
## Apr 2030       780921.1 626766.5  935075.8 545161.9 1016680.4
## May 2030       794094.2 637869.0  950319.3 555168.4 1033019.9
## Jun 2030       804973.6 646705.3  963242.0 562923.0 1047024.3
## Jul 2030       797968.7 637683.1  958254.3 552833.0 1043104.4
## Aug 2030       818087.3 655809.5  980365.0 569904.9 1066269.6
## Sep 2030       816516.9 652271.2  980762.6 565324.8 1067709.0
## Oct 2030       868488.6 702298.3 1034679.0 614322.4 1122654.8
## Nov 2030       820892.8 652780.3  989005.3 563786.9 1077998.7
## Dec 2030       828634.8 658621.9  998647.8 568622.5 1088647.2

autoplot(fc_5) +
  theme_minimal() +
  labs(
    title = "SARIMA Forecast: Proximos 5 periodos",
    x = "Time",
    y = "ts_exports"
  )