Introducción

El modelo estándar IS-LM se expresa teóricamente como

Mercado de Bienes y Servicios \[\begin{align} Y&=C+I+G \\ C&=C_0+cYd\equiv C_0+c(Y-Tx_0) \\ I&=I_0-bi \\ G&=G_0 \end{align}\]

Mercado Monetario \[\begin{align} M_d&=kY-hi\\ \frac{M_s}{P}&=M_0\\ \end{align}\]

library(ggplot2)
library(readxl)
library(corrplot)
library(dplyr)
library(fBasics)
library(ggthemes)
library(zoo)
library(xts)
library(PerformanceAnalytics)

# base <- read_excel('') Llama la base de datos ajustando la dirección de ubicación dentro de ''
# En este caso ajustado en R se ha asignado a  "base"

class(base)

## [1] "tbl_df"     "tbl"        "data.frame"

options(scipen = 999) # Amplitud de cifras
head(base)

## # A tibble: 6 x 15
##   TIME     PIB     CP      I     CG     DM    IVA     YD   TIN     M4
##   <chr>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl>  <dbl>
## 1 1999~ 1.26e7 8.19e6 2.72e6 1.62e6 1.54e8 13790. 1.25e7  22.2 2.09e9
## 2 2000~ 1.27e7 8.00e6 2.93e6 1.67e6 1.53e8 14857. 1.27e7  18.6 2.18e9
## 3 2000~ 1.30e7 8.33e6 2.78e6 1.68e6 1.61e8 15162. 1.30e7  18.2 2.27e9
## 4 2000~ 1.30e7 8.46e6 2.87e6 1.63e6 1.60e8 15755. 1.30e7  15.6 2.35e9
## 5 2000~ 1.30e7 8.80e6 2.70e6 1.65e6 1.82e8 17428. 1.30e7  14.5 2.43e9
## 6 2001~ 1.28e7 8.33e6 2.71e6 1.61e6 1.78e8 17740. 1.28e7  18.5 2.50e9
## # ... with 5 more variables: OM <dbl>, M3 <dbl>, M2 <dbl>, M1 <dbl>,
## #   IM <dbl>

tail(base)

## # A tibble: 6 x 15
##   TIME     PIB     CP      I     CG     DM    IVA     YD   TIN       M4
##   <chr>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl>    <dbl>
## 1 2017~ 1.78e7 1.17e7 3.87e6 2.12e6 1.37e9 66878. 1.77e7  6.63  1.50e10
## 2 2017~ 1.81e7 1.20e7 3.83e6 2.13e6 1.37e9 66440. 1.81e7  7.04  1.52e10
## 3 2017~ 1.79e7 1.22e7 3.82e6 2.08e6 1.36e9 79219. 1.79e7  7.2   1.56e10
## 4 2017~ 1.87e7 1.26e7 3.97e6 2.17e6 1.44e9 59479. 1.87e7  7.27  1.60e10
## 5 2018~ 1.80e7 1.20e7 3.96e6 2.14e6 1.49e9 78183. 1.79e7  7.65 NA      
## 6 2018~ 1.86e7 1.23e7 3.93e6 2.20e6 1.51e9 75472. 1.85e7  7.76 NA      
## # ... with 5 more variables: OM <dbl>, M3 <dbl>, M2 <dbl>, M1 <dbl>,
## #   IM <dbl>

Los datos son de temporalidad trimestral.

• PIB\(_n\) = Y
• CP = Consumo Privado
• CG = Consumo de Gobierno
• I = Inversión
• DM = Demanda Monetaria
• TIN= Tasa de Interés Nominal

DF<-data.frame(base)
class(DF)

## [1] "data.frame"

dim(DF)

## [1] 75 15

# Expresamos como temporalidad expresado en R
DF$TIME=as.yearqtr(DF$TIME, format = "%Y/%q") #ZOO LIBRARY

ggplot(DF,aes(DF$TIME,DF$PIB))+geom_line(colour="blue")+
  geom_point(colour="#53005E",size=0.9)+xlab("")+ylab("PIB")+
  scale_x_yearqtr(format="%YQ%q", n=12)

  ggplot(DF,aes(DF$TIME,DF$CP))+
  geom_line(colour="red")+geom_point(colour="red",size=0.9)+
  xlab("")+
  ylab("CONSUMO")+
  scale_x_yearqtr(format="%YQ%q", n=12)

par(mfrow=c(1,2))       #1 FILA Y 2 COLUMNA

#PerformanceAnalytics
chart.TimeSeries(ts(DF$TIN,frequency = 4,start = c(1999,04)) , colorset= "gray",lwd=3,main="TASA DE INTERÉS",
                 auto.grid = FALSE)
chart.TimeSeries(ts(DF$I,frequency = 4,start = c(1999,04)) , colorset= "black",lwd=2,main="INVERSIÓN",
                 auto.grid = FALSE)

Statistical Analysis

#Extraer una base que solo se necesita con determinadas variables
DF1<-select(DF,-TIME,-M4,-M2,-M3,-IM,-M1,-OM)     #dplyr LIBRARY

summary(DF1)

basicStats(DF1[1:3])  #fBasics LIBRARY, se puede selecionar toda la base

#Matriz de Correlación
cor(DF1))

corrplot(cor(DF1))

Econometric Model

# Extructura de matriz
YD.M <- as.matrix(cbind(1,DF$YD))
CP.M <- as.matrix(DF$CP)

#Como:  solve(t(YD.M)%*%YD.M)%*%t(YD.M)%*%CP.M indica: sistema es computacionalmente singular: número de condición recíproco = 5.88086e-17

beta <- solve(t(YD.M)%*%YD.M,tol=5.88086e-17)%*%t(YD.M)%*%CP.M
beta                                                  #Parametros de estimacion

##              [,1]
## [1,] 656871.89054
## [2,]      0.63127

REG.C = lm(DF$CP ~ DF$YD, data=DF)
summary(REG.C)

## 
## Call:
## lm(formula = DF$CP ~ DF$YD, data = DF)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -685149 -118608   -1718  138445  401428 
## 
## Coefficients:
##                 Estimate   Std. Error t value             Pr(>|t|)    
## (Intercept) 656871.89054 221741.85484   2.962              0.00412 ** 
## DF$YD            0.63127      0.01464  43.125 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 223100 on 73 degrees of freedom
## Multiple R-squared:  0.9622, Adjusted R-squared:  0.9617 
## F-statistic:  1860 on 1 and 73 DF,  p-value: < 0.00000000000000022

# Respecto los parametros

REG.C$coefficients[1]

## (Intercept) 
##    656871.9

REG.C$coefficients[2]

##   DF$YD 
## 0.63127

REG.INV = lm(DF$I ~ DF$TIN, data=DF)
summary(REG.INV)

## 
## Call:
## lm(formula = DF$I ~ DF$TIN, data = DF)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -884948 -145503   -7866  262379  636342 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  3915028      90010  43.496 < 0.0000000000000002 ***
## DF$TIN        -77746      10058  -7.729      0.0000000000453 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 365300 on 73 degrees of freedom
## Multiple R-squared:  0.4501, Adjusted R-squared:  0.4425 
## F-statistic: 59.74 on 1 and 73 DF,  p-value: 0.00000000004534

REG.DM = lm(DF$DM ~ DF$PIB+DF$TIN - 1, data=DF)
summary(REG.DM)

## 
## Call:
## lm(formula = DF$DM ~ DF$PIB + DF$TIN - 1, data = DF)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -336300410 -169215579  -82240193  108974542  667646382 
## 
## Coefficients:
##             Estimate    Std. Error t value             Pr(>|t|)    
## DF$PIB        64.497         3.329  19.376 < 0.0000000000000002 ***
## DF$TIN -44044584.593   5649862.998  -7.796      0.0000000000341 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 236800000 on 73 degrees of freedom
## Multiple R-squared:  0.895,  Adjusted R-squared:  0.8922 
## F-statistic: 311.2 on 2 and 73 DF,  p-value: < 0.00000000000000022

Mathematical Adjustment

Numéricamente las ecuaciones se estructuran como \[\begin{align} Y&=C+I+G_0\\ C&=656\,\, 871.891+0.631(Y-Tx)\\ I&=3 \,\,915 \,\,027.957-77 \,\,746.449 \,i\\ G_0&=1\,\,827\,\,433.512\\ Tx_0&=39\,\,074.621\\ Md&=64.497\,Y-44\,\,044\,\,584.593\,i\\ M_0&=608\,\,659\,\,845.209 \end{align}\]

Por lo que: \[\begin{align} Y-C-I&=G_0\\ cY-C&=cTx-C_0\\ I+bi&=I_0\\ kY+hi&=M_0 \end{align}\]

De acuerdo a una estructura matricial

\[\begin{equation} \left[ \begin{array}{crrr} 1&-1&-1&0\\ c&-1&0&0\\ 0&0&1&b\\ k&0&0&-h\\ \end{array}\right] \left[\begin{array}{c} Y\\ C\\ I\\ i \\ \end{array} \right] = \left[\begin{array}{c} G_0\\ cTx-C_0\\ I_0\\ M_0\\\end{array}\right] \equiv {\bf{\Omega\Gamma=A}} \end{equation}\]

Resolviendo para \(\bf{\Gamma}\)

\[\bf{\Gamma=\Omega^{-1}A}\]

Conforme los cálculos necesarios de \(\bf{\Omega}\). El determinante:

\[|{\bf{\Omega}}| = h-ch + bk\]

El cofactor de \({\bf{\Omega}}\) es:

\[\begin{equation} \text{Cof} ({\bf{\Omega}})= \left[ \begin{array}{cccc} h & -h & h & b \\ ch & -h-b k & ch & cb \\ -b k & b k & h-ch & b-cb \\ k & -k & k & c-1 \\ \end{array} \right] \end{equation}\]

Así:

\[\begin{equation} {\bf{\Omega^{-1}}}= \left[ \begin{array}{cccc} \displaystyle\frac{h}{h-ch+bk} & \displaystyle-\frac{h}{h-ch+bk} &\displaystyle \frac{h}{h-ch+bk} & \displaystyle\frac{b}{h-ch+bk} \\ \displaystyle\frac{c h}{h-ch+bk} & \displaystyle\frac{-h-b k}{h-ch+bk} & \displaystyle\frac{c h}{h-ch+bk} & \displaystyle\frac{c b}{h-ch+bk} \\ \displaystyle -\frac{b k}{h-ch+bk} & \displaystyle\frac{b k}{h-ch+bk} & \displaystyle\frac{h-c h}{h-ch+bk} & \displaystyle\frac{b-c b}{h-ch+bk} \\ \displaystyle \frac{k}{h-ch+bk} & \displaystyle-\frac{k}{h-ch+bk} & \displaystyle\frac{k}{h-ch+bk} & \displaystyle\frac{c-1}{h-ch+bk} \\ \end{array} \right] \end{equation}\]

Los resultado de comportamiento general se vinculan en los equilibrios como:

\[\begin{align} Y^*&=\frac{h}{h-ch+bk}G_0-\frac{h}{h-ch+bk}(cTx-C_0)+\frac{h}{h-ch+bk} I_0+\frac{b}{h-ch+bk}M_0\\ C^*&=\frac{c h}{h-ch+bk} G_0+\frac{-h-b k}{h-ch+bk} (cTx-C_0)+\frac{c h}{h-ch+bk} I_0+\frac{c b}{h-ch+bk} M_0\\ I^*&=-\frac{b k}{h-ch+bk} G_0+\frac{b k}{h-ch+bk} (cTx-C_0)+\frac{h-c h}{h-ch+bk} I_0 +\frac{b-c b}{h-ch+bk} M_0\\ i^*&=\frac{k}{h-ch+bk} G_0 -\frac{k}{h-ch+bk} (cTx-C_0) +\frac{k}{h-ch+bk} I_0 +\frac{c-1}{h-ch+bk} M_0 \end{align}\]

La función de demanda agregada es:
\[\begin{align} Y=DA\therefore DA=(C_0-cTx+I_0+G_0-b\,i^*)+[1-(1-c)]Y \end{align}\]

En la función IS, \(Y\) tiene una relación inversa en \(i\), es decir:

\[\begin{equation} Y=\left(1-c\right)^{-1}(C_0-cTx+I_0+G_0-b\,i)\equiv Y=\Theta_0-\Theta_1\,i \end{equation}\]

En la función LM, \(Y\) tiene una relación directa en \(i\), es decir:

\[\begin{equation} Y=(k)^{-1}(M_0+h\,i)\equiv Y=\Pi_0+\Pi_1\,i \end{equation}\]

# Se ajustan los valores
Co=lm(DF$CP ~ DF$YD, data=DF)$coefficients[1]
c=lm(DF$CP ~ DF$YD, data=DF)$coefficients[2]
Io=lm(DF$I ~ DF$TIN, data=DF)$coefficients[1]
b=-(lm(DF$I ~ DF$TIN, data=DF)$coefficients[2])
k=lm(DF$DM ~ DF$PIB+DF$TIN - 1, data=DF)$coefficients[1]
h=-(lm(DF$DM ~ DF$PIB+DF$TIN - 1, data=DF)$coefficients[2])
g=mean(DF$CG)
tx=mean(DF$IVA)
mo=mean(DF$DM)

# Incorporación de la matriz y el vector

# Arreglo inicial
value.omega=c(1,-1,-1,0,c,-1,0,0,0,0,1,b,k,0,0,-h)
value.a=c(g,c*tx-Co,Io,mo)

# Arreglo final
omega <- t(matrix(value.omega,4,4))
a<-matrix(value.a,4,1)

gamma<-inv(omega)%*%a   #Gamma=Inversa(Omega)*A
gamma

##                [,1]
## [1,] 15435968.51685
## [2,] 10376468.37729
## [3,]  3232066.62716
## [4,]        8.78447

Ingreso_Equilibrio=gamma[1]
Consumo_Equilibrio=gamma[2]
Inversion_Equilibrio=gamma[3]
Tasa_Equilibrio=gamma[4]

### Definimos la función consumo
consumo.f=function(Yd){
    Co + c*Yd
}

ggplot(data.frame(Yd = c(-1000, 10000)), aes(x = Yd)) +
        stat_function(fun = consumo.f)+ylab('Consumo')

# Mediante la base directa
ggplot(DF, aes(DF$YD, DF$CP)) +
  geom_point() + geom_smooth(method='lm',col="red") + ggtitle('Función Consumo') + 
  ylab('Consumo')+xlab('Ingreso Disponible')

### Definimos la función Inversión

inversion.f=function(i){
    lm(DF$I ~ DF$TIN, data=DF)$coefficients[1]-(-(lm(DF$I ~ DF$TIN, data=DF)$coefficients[2]))*i   # I=Io-b*i 
}

# Graficamos

ggplot(data.frame(i = c(0, 15)), aes(x = i)) +
    stat_function(fun = inversion.f,color="red",size=0.8)+
          ylab('Inversión') + 
        geom_segment(aes(x = 0, y = gamma[3], xend = gamma[4], yend =gamma[3]),linetype="dotted",   #Nivel I
                size=0.65) +
        geom_segment(aes(x = gamma[4], y = 0, xend = gamma[4], yend = gamma[3]),linetype="dotted",  #Nivel i
                size=0.65) +
        annotate("text", x=gamma[4]+0.55, y=gamma[3]+129990, label="Equilibrio",size=2.8)+          #Equilibrio
        annotate("text", x=0.6, y=gamma[3]+90000, label="3232066.63",size=2.3)  +                   #I*
        annotate("text", x=gamma[4]+0.28, y=60000, label="8.78",size=1.8)  +                        #i*
        labs(title="Función Inversión")+
        geom_point(aes(x=gamma[4], y=gamma[3]), colour="blue")

### Definimos la función DM= k*Y-h*i
demandaM.f=function(i){
    (lm(DF$DM ~ DF$PIB+DF$TIN - 1, data=DF)$coefficients[1])*gamma[1]-  
    (-lm(DF$DM ~ DF$PIB+DF$TIN - 1, data=DF)$coefficients[2])*i
}                                                                      

ggplot(data.frame(i = c(-0.5,23)), aes(x = i)) +
      stat_function(fun = demandaM.f,size=0.8,color="blue")+
        ylab('Demanda monetaria')+
        geom_segment(aes(x = 0, y = mean(DF$DM), xend = gamma[4], yend =mean(DF$DM)),linetype="dotted",  #Nivel DM
                size=0.65) +
        geom_segment(aes(x = gamma[4], y = 0, xend = gamma[4], yend = mean(DF$DM)),linetype="dotted",  #Nivel i
                size=0.65) +
        annotate("text", x=gamma[4]+1, y=mean(DF$DM)+mean(DF$DM)/25, label="Equilibrio",size=2.8)+    #Equilibrio
        annotate("text", x=1.4,y=mean(DF$DM)+mean(DF$DM)/18,label='608659845.209',size=2.3)  +        #DM*
        annotate("text", x=gamma[4]+0.5, y=10000000,label="8.78",size=1.8) +                          #i*
        labs(title="Demanda Monetaria")+
        geom_point(aes(x=gamma[4], y=mean(DF$DM)), colour="red")

La función de demanda agregaga se establece que: \(DA=Y\), por lo que:

\[DA=(C_0-cTx+I_0+G_0-b\,i^*)+[1-(1-c)]Y\]

es decir \(DA(Y)\) y como \(OA=DA\), se ajusta la denominada linea de 45° que representa la \(OA\).

### Se definine las funciones DEMANDA Y OFERTA AGREGADA

demanda.f <- function(Y) {
    (Co-c*tx+Io+g-b*gamma[4])+(1-(1-c))*Y
}


oferta.f <- function(Y) {
    Y
}

# Se grafica

ggplot(data.frame(Y = c(10, gamma[1]+gamma[1]/3)), aes(x = Y))+
    stat_function(fun=demanda.f,geom="line",size=0.8,aes(colour = "Demanda Agregada"))+
    stat_function(fun=oferta.f,geom="line",size=0.8,aes(colour = "Oferta Agregada"))+
        ylab("Demanda y Oferta Agregada")+
        geom_segment(aes(x = 0, y = gamma[1], xend = gamma[1],                  #line DM/OM*
                         yend = gamma[1]),linetype="dotted",size=0.65) +
        geom_segment(aes(x = gamma[1], y = 0, xend = gamma[1],                  # line Y*
                         yend = gamma[1]),linetype="dotted",size=0.65) +
        annotate("text", x=gamma[1]+gamma[1]/15, y=gamma[1]-gamma[1]/60, label="Equilibrio",size=2.8)+  # equilibrio
        annotate("text", x=1000000, y=gamma[1]+gamma[1]/29, label="15435968.517",size=2.3)  +           # Text DA-OA
        annotate("text", x=gamma[1]+gamma[1]/14, y=400000, label="15435968.517",size=2.3)     +         # Text Y
        labs(title = "Equilibiro DA/OA")+
        geom_point(aes(x=gamma[1], y=gamma[1]), colour="red")+
        scale_colour_manual('',values = c("purple", "orange"))+
        theme(legend.position = c(0.9,0.4),legend.background=element_rect(fill = NA),
              legend.key = element_rect(fill = NA, color = NA))

Para el gráfico de Equilibrio del Mercado Monetario, la función de Demanda se conoce que

\[M_d=kY-hi\]

como la representación gráfica es tal que \(i(Moneda)\), entonces:

\[i=\frac{kY}{h}-\frac{1}{h}M_d\]

por lo que \(DM=OM\).

# Mercado Monetario: Equilibrio

DEMANDAm.f <- function(Moneda) {
    (k*gamma[1])/h-Moneda/h           #Como Moneda=k*Y-h*i : i=(k*Y)/h-Moneda/h
}


ggplot(data.frame(Moneda = c(0, 1000000000)), aes(x = Moneda)) +
        stat_function(fun = DEMANDAm.f,size=0.8,aes(colour='Demanda Monetaria'))+
            ylab('i') +
            geom_segment(aes(x = 0, y = gamma[4], xend =mean(DF$DM),                                      # i*
                             yend = gamma[4]),linetype="dotted",size=0.65) + 
            geom_vline(xintercept = mean(DF$DM),color = "aquamarine2", size=0.8) + 
            annotate("text", x=mean(DF$DM)+mean(DF$DM)/12, y=gamma[4]+0.3, label="Equilibrio",size=2.8) + # Equilibrio
            annotate("text", x=20000000, y=gamma[4]+0.5, label="8.78",size=2.3) +                         #text i* 
            annotate("text", x=mean(DF$DM)+mean(DF$DM)/7, y=0.3, label="Oferta Monetaria = 608659845.209",size=2.3) +       #texto DM*
            labs(title = "Mercado Monetario: Equilibrio")+
            geom_point(aes(x=mean(DF$DM), y=gamma[4]), colour="red")+
            scale_colour_manual('',values = c("coral4"))+
            theme(legend.position = c(0.9,0.4),legend.background=element_rect(fill = NA),
                  legend.key = element_rect(fill = NA, color = NA))

Como la función simplificada de la IS es

\[\begin{equation} Y=\Theta_0-\Theta_1\,i \end{equation}\]

y la función LM

\[\begin{equation} Y=\Pi_0+\Pi_1\,i \end{equation}\]

La representación gráfica del modelo se expresa tal que \(i(Y)\), por lo tanto:

\[\begin{align} i_{IS}&=\frac{\Theta_0}{\Theta_1}-\frac{1}{\Theta_1}Y\\ i_{LM}&=\frac{\Pi_0}{\Pi_1}+\frac{1}{\Pi_1}Y \end{align}\]

IS.f <- function(Y) {
                     (Co-c*tx+Io+mean(DF$CG))/b-((1-c)/b)*Y
}


LM.f <- function(Y) {
                     (-mean(DF$DM))/h+(k/h)*Y
}

IS_LM.plot <- ggplot(data.frame(Y = c(0, 21000000)), aes(x = Y)) +
    stat_function(fun = IS.f,size=0.8,aes(color="IS"))+                             # Función IS
    stat_function(fun = LM.f,size=0.8,aes(color="LM"))+                     # Función LM
        ylab("Nivel de Interés")+xlab("Nivel de ingreso")+ 
        geom_segment(aes(x = gamma[1], y = 0, xend = gamma[1],                        #linea  Y*
                         yend = gamma[4]),linetype="dotted",size=0.65)+
        geom_segment(aes(x = 0, y = gamma[4], xend =gamma[1],                         #linea i*
                             yend = gamma[4]),linetype="dotted",size=0.65) +
        annotate("text", x=400000, y=gamma[4]+2, label="8.78",size=2.3) +             #Text i*
        annotate("text", x=gamma[1], y=-1, label="15435968.517",size=2.3) +           #Text Y*
        annotate("text", x=gamma[1]+gamma[1]/13, y=gamma[4]-0.7, label="Equilibrio",  #Equilibrio
                 size=2.8) + 
        geom_point(aes(x=gamma[1], y=gamma[4]), colour="red") +
        labs(title="Equilibrio IS-LM") +
        theme(plot.title = element_text(hjust=0.5))+
        scale_colour_manual('',values = c("darkgreen", "salmon2"))+
        theme(legend.position = c(0.9,0.6),legend.background=element_rect(fill = NA),
              legend.key = element_rect(fill = NA, color = NA))

IS_LM.plot

Extensión

ggplot(data = DF, aes(DF$CP, DF$YD)) + 
  geom_point(size=0.8,alpha=0.5) + 
  geom_smooth(method = 'lm', aes(colour="A"),se=F,size=0.58) + 
  geom_smooth(method = 'loess', aes(colour="B"),se=F,size=0.58) +
  scale_colour_manual(name="", values=c("lightcoral", "cyan3"),labels = c("OLS", "LOESS"))+
  labs(title='OLS vs LOESS Consumption Function Estimation')+
  xlab('Ingreso Disponible')+
  ylab('Consumo')

# Create a new theme
theme_bluewhite <- function (base_size = 11, base_family = "") {
    theme_bw() %+replace% 
    theme(
      panel.grid.major  = element_line(color = "white"),
      panel.background = element_rect(fill = "honeydew1"),
      panel.border = element_rect(color = "honeydew1", fill = NA),
      axis.line = element_line(color = "honeydew1"),
      axis.ticks = element_line(color = "honeydew1"),
      axis.text = element_text(color = "lightblue4")
      )
}

OLS <- lm(DF$CP ~ DF$TIME, data = DF)
CP.OLS <- transform(DF$CP, Fitted = fitted(OLS))

UNDER_OVER.OLS <-ggplot(CP.OLS, aes(DF$TIME, DF$CP)) + 
              geom_point(color="cyan3",size=0.8) + 
              geom_smooth(method = "lm",size=0.5,colour="black",se=F) +
              geom_segment(aes(x = DF$TIME, y = DF$CP,xend = DF$TIME, yend = Fitted),colour="lightcoral")+
              scale_x_yearqtr(format="%YQ%q", n=12)+
              xlab("Tiempo")+
              ylab("Consumo")+
              labs(title="Underestimation and Overestimation via OLS Consumption")+
              theme_bluewhite()

UNDER_OVER.OLS

ggplot(data = DF, aes(DF$TIME, DF$CP)) + 
  geom_point(size=0.8,alpha=0.7)  + 
  geom_smooth(method = 'loess',se=T,size=0.6) +
  labs(title='LOESS Consumption Time Estimation')+
  xlab('Tiempo')+
  ylab('Consumo')+
  scale_x_yearqtr(format="%YQ%q", n=12)+
  theme_economist() + scale_fill_economist()+
  theme(plot.title = element_text(hjust=0.5))