Assignment_IV_Sastre_Paola(1).R

#*************************************************************
#### Advanced Econometrics - Assignment 4 #####
##   Paola Sastre Dordelly
#*************************************************************
####MARKETING CAMPAING OPTIMIZATION####

### 0. HOUSEKEEPING ####
#***********************

## 0.1 Clear session ####
rm(list = ls())    # clear workspace
if(!is.null(dev.list())) dev.off() # Clear previous plots
cat("\014")        # clear command window

## 0.2 Read the files ####
setwd("~/Desktop/Econometría:Assignments")
data1<-read.csv("marketing_data.csv")
data2<-read.csv("pricing_data.csv")
sales<-data1$s
google_exp<-data.frame(data1$g)
youtube_exp<-data.frame(data1$y)


# 1.1 Plot the available data on sales with the google search expenditures
# and again the sales but this time with the youtube expenditures.
# Estimating the parameters of the nonlinear dynamic time-varying parameter model
# yields to the following maximum likelihood parameter estimates.

mu       <-0.617
epsilon1 <- 2.88
epsilon2  <- 9.51
delta1   <- 0.27
delta2   <- 0.60
alpha1   <- 0.203
alpha2   <- 0.065
beta1    <- 0.949
beta2    <- 0.95

adstock_google<-data.frame(
  google_exp,
  sales
)

adstock_youtube<-data.frame(
  youtube_exp,
  sales
)

T<-length(google_exp$data1.g)
## Plot observed data and forecast
google_plot <- ggplot()  +
  geom_point(data = adstock_google, aes(x = sales, y = google_exp), color = "black")+
  labs(title="Google Expenditures") +xlab("") + ylab("")
google_plot+ scale_x_discrete(labels=c('s-2','s-1','s','s+1','s+2','s+3','s+4','s+5','s+6','s+7','s+8','s+9','s+10'))

google_plot

## Plot observed data and forecast
youtube_plot <- ggplot()  +
  geom_point(data = adstock_youtube, aes(x = sales, y = youtube_exp), color = "red")
youtube_plot+labs(title="Youtube Expenditures") +xlab("sales") + ylab("Euros spent")

# 2. Plot the filtered adstock generated by marketing on Google search
# and Youtube.

# 2.1 adstock google 
T<-2443
adstock_google  <- matrix(c(0:0), T, 1) 
adstock_google [1] <- google_exp[1,1];     
for (t in 1:T){ 
  adstock_google[t+1] = beta1*adstock_google[t]+alpha1*google_exp[t+1,1]
}
adstock_google_df<-as.data.frame(adstock_google)

# 2.1.1.adstock google plot
gads_plot <- ggplot()  +
  geom_line(data = adstock_google_df, aes(x = (1:2444), y = adstock_google), color = "blue")
gads_plot+labs(title="Adstock generated by marketing Google") +xlab("") + ylab("")


# 2.2 adstock youtube
adstock_youtube  <- matrix(c(0:0), T, 1) 
adstock_youtube [1] <- youtube_exp[1,1];     
for (t in 1:T){ 
  adstock_youtube[t+1] = beta2*adstock_youtube[t]+alpha2*youtube_exp[t+1,1]
} 
adstock_youtube_df<-as.data.frame(adstock_youtube)
# 2.2.1 adstock youtube plot
yads_plot <- ggplot()  +
  geom_line(data = adstock_youtube_df, aes(x = (1:2444), y = adstock_youtube), color = "red")
yads_plot+labs(title="Adstock generated by marketing youtube") +xlab("") + ylab("")

# 2.3 both plots
gyads_plot <- ggplot()  +
  geom_line(data = adstock_google_df, aes(x = (1:2444), y = adstock_google), color = "blue")+
  geom_line(data = adstock_youtube_df, aes(x = (1:2444), y = adstock_youtube), color = "red")
gyads_plot+labs(title="Adstock generated by Marketing: Google and Youtube ") +xlab("Observed hours") + ylab("sales")


#filtered adstock?
N<-10

# 3. Use the fitted model to plot impulse response functions for both
# the adstock and sales volume generated by spending 100 euros with marketing
# on Youtube on a given hour

## 3.1 Parameter Values
s = 10 # Set shock time s
x0 = 0 # Set origin value
e = 100 # Set shock size e
h = 40 # Set steps ahead


## 3.2 Generate Innovations
eps <- matrix(0, s+h, N)

for (t in 1:(s+h)){
  eps[t,] = 0.1*rnorm(N)
}    # Generate N values of epsilon_T+1

## 3.3 Generate IRF
IRF <- matrix(0, s+h+1, N)
IRF[1:s-1,] = x0*matrix(1, s-1, N)
IRF[s,] = (x0+e)*matrix(1, 1 , N)

for (t in (s+1):(s+h)) {

  IRF[t] <- mu+(epsilon1*adstock_google[t]^delta1)+(epsilon2*adstock_youtube[t]^delta2)
}

# 3.4 Calculate point forecasts (conditional mean) and confidence bounds (5 and
# 95 percentiles) recursively
IRF_hat = matrix(0, (s+h), 1)
upper_bound = matrix(0, (s+h),1)
lower_bound= matrix(0, (s+h),1)

#x_hat[1] = x_T
#upper_bound[1]= x_T
#lower_bound[1]= x_T
for (t in 1:(s+h)) {
  IRF_hat[t] = mean(IRF[t,])
  upper_bound[t] = quantile(IRF_hat[t,],.90)
  lower_bound[t] = quantile(IRF_hat[t,],.10)
  
}


# 3.5 Plot Data

IRF_hatt <- data.frame(
  h_ax = 1:(h+s),
  IRF_hat = IRF_hat
)

lower_b <- data.frame(
  h_ax = 1:(h+s),
  low_b = lower_bound
)

upper_b <- data.frame(
  h_ax = 1:(h+s),
  upp_b = upper_bound 
)

p1 = ggplot() + 
  geom_line(data = lower_b, aes(x = h_ax, y = low_b), color = "red") +
  geom_line(data = upper_b,aes(x = h_ax, y = upp_b),color = "red") +
  geom_line(data = IRF_hatt, aes(x = h_ax, y = IRF_hat), color = "black")

p1 + scale_x_discrete(labels=c('s-2','s-1','s','s+1','s+2','s+3','s+4','s+5','s+6','s+7','s+8','s+9','s+10'))


####DYNAMIC PRICING####
# ***********************

# A retailer of electronic products has called upon you to help design a data-driven procedure
# for optimizing the prices for their products. The activity of this company consists
# essentially of buying consumer electronics (e.g. cell phones, laptops, etc.) from large manufacturers
# (Apple, Samsung, etc.) and selling these products directly to consumers both
# online and on their shops

# 1. Plot the available data on sales, prices, acquisition costs and marketing
# expenditures.

M<-length(data2$s)

sales_plot <- ggplot()  +
  geom_line(data = data2, aes(x = 1:M, y = data2$s), color = "black")+
  labs(title="De-seasonnalized sales") +xlab("Time") + ylab("")
sales_plot

price_plot <- ggplot()  +  
  geom_line(data = data2, aes(x = 1:M, y = data2$p), color = "red")+
  labs(title="Selling price") +xlab("Time") + ylab("")
price_plot

marketing_plot<- ggplot()  + 
  geom_line(data = data2, aes(x = 1:M, y = data2$m), color = "dark blue")+
  labs(title="Marketing expenditures") +xlab("Time") + ylab("")
marketing_plot

cost_plot<- ggplot()  + 
  geom_line(data = data2, aes(x = 1:M, y = data2$c), color = "orange")+
  labs(title="Acquisition Costs") +xlab("Time") + ylab("")
cost_plot

names(data2)
sales<-data2$s
price<-data2$p
cost<-data2$c
marketing<-data2$m

# 2. Run a simple regression of sales st on prices pt, and report the estimates

# 2.1 Simple OLS regression
Model1<-lm(sales~price)
Model1
stargazer(Model1, type = "text")

# 3. Concerned about simultaneity, you have decided to use costs as an
# instrument variable. Run a regression of prices pt on costs ct,
# and use predicted price hat(p_t) to find the structural-causal relation between sales and
# prices,
# Consider the parameter estimates for both the instrumental regression and the
# simple regression in (1). What is the causal impact of an increase in price pt on
# expected sales st?
  
# 3.1 2SLS with package
# independent ~ endogenous variable | instrumental variable
ivreg<-ivreg(sales~price|cost)
summary(ivreg)

# check the 2SLS because of negative R2
# 2SLS
Model2<-lm(price~cost)
summary(Model2)
p_hat<-fitted(Model2)

Model3<-lm(sales~p_hat)
summary(Model3)

# 4. Compare the R2 obtained for the regression in (1) with that obtained
# in (2). Which model is best?
# Answered above.