larasantak/RTutorSomethingToTalkAbout
RTutor problem set SomethingToTalkAbout

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In larasantak/RTutorSomethingToTalkAbout: RTutor problem set SomethingToTalkAbout 

user.name = '' # set to your user name

# To check your problem set, run the 
# RStudio Addin 'Check Problemset'

# Alternatively run the following lines
library(RTutor)
ps.dir = getwd() # directory of this file
ps.file = 'SomethingToTalkAbout.Rmd' # name of this file
check.problem.set('SomethingToTalkAbout', ps.dir, ps.file, user.name=user.name, reset=FALSE)

Something To Talk About:

Social Spillovers in Movie Consumption

Author: Lara Santak

Hey there! Welcome to this interactive problem set. If you are interested in improving your R coding skills, getting an introduction to a basic machine learning algorithm (LASSO), and learn something about the relationship between moviegoing and weather, keep ongoing. You should have some basic knowledge of linear regression. As well be familiar with the package dplyr.

This problem set is part of my bachelor’s thesis at Ulm University. It is based on the paper Something to Talk About: Social Spillovers in Movie Consumption, which was published in the Journal of Political Economy in 2016.

The paper, data, and some more information can be found here. Further, in the problem set, we will refer to it as paper.

Exercise Content

0 - How to solve the problem set

1 - Motivation

2 - Data

3 - Recap Linear Regression

4 - Empirical Model

5 - Moviegoing Summer

6 - LASSO

7 - First Stage Results

7 - Second Stage Results

9 - Conclusion

Exercise 0 -- How to solve the problem set

If this is your first RTutor Problem Set, you can find some instructions in exercise 0. If you have already solved a problem set, you can start with exercise no. 1.

In this problem set, you will find from time to time some code chunks. The first chunk is usually already active. On the top you find five buttons:

If you start a new exercise, your code chunk might not already be active. Then you can press the button edit.

You have to solve previous code blocks to run the current chunk. Nevertheless, you can always start chunks in a new exercise. Previous exercises do not have to be addressed. But they are recommended to do.

Exercise 1 -- Motivation

Have you ever wondered why you watch a particular movie? Sometimes you might have been anticipating a certain one like one of the Harry Potter movies or a newly filmed favorite book of yours. Other times you might have just gone to a movie theater and decided on the film there, or a friend told you about a specific one. As you can already see, there might be several factors that contribute to moviegoing behavior. The economic term that drives consumers to consume something is called demand. First, let us define the term demand:

"In economics, demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given period of time."

(O’Sullivan and Sheffrin, 2003, p. 79)

Usually, we have fixed prices in theaters for all movies. The price cannot be a driver for demand. The economic definition of demand might not describe it for moviegoing very well. Therefore we are interested in other effects on demand.

One of the effects might be the weather. If the weather is harsh, for example, it rains, viewership might increase due to the fact that movies are watched indoors. The weather has several attributes like temperature, precipitation, and a combination of both, like snow or hail. Adding the weather into account results in having a broad set of instruments for different weather occurrences. Some variables might explain each other so that we might have redundant variables. In total, our model with all-weather variables might be overfitted and too complicated. That means it would work well with the given data since it is perfectly molded to the data at hand. But the model might not work as good with new data. Hand-picking variables might be a good idea first, but it is hard to find the crucial variables. Therefore we will introduce a variable selection method called LASSO, which helps us to select the essential variables for our model.

Another aspect of demand might be how and if others consume a particular good. A consumer might have more utility from a specific good if others demand or consume it (Becker 1991). In our case of moviegoing people might be influenced to watch a movie, just because others around them have seen it. In this case, so-called learning effects, where a consumer learns from others’ decisions, drive demand (Young 2009). This research is mainly theoretical, because of the difficulties to divide causal from noncausal effects in a social group setting (Manski 1993). We will discuss this at the end of the problem set.

Exercise 2 -- Data

Let’s start with our analysis by getting to know our data:

Our first data set comes from Box Office Mojo, owned by Internet Movie Database (IMDb). It contains national box office data with total US tickets sales by day from 2002 till 2012. Our data set is called data_movies.dta. The ending .dta implicates a stata file. This data and all the following data can be downloaded with the paper.

R cannot read stata files by default. Therefore we need our first package, called haven. If you haven’t worked with haven, you will find additional information in the infobox.

info("haven") # Run this line (Strg-Enter) to show info

Load the package haven with the command library(). Then use the function read_dta() to read our data set data_movies.dta and store it in the variable data. If you need some help, take a look at the info box above or press hint.

# Load the package haven
# Read in our data "data_movies.dta" and save it as data

Overview of our data

When reading in new data, it is always useful to first take a look at the data before doing any analyses.

Display the first ten rows of the data set data. The function head() displays the head of an object like a vector, table, data frame, etc. The first argument should be our data set. To display ten rows, insert the number of rows as the second argument. For the function to run successfully, remove the underscores. 

# Fill in the arguments to see the first 10 rows of our data.
head(___, ___)

As you can see, we have two variables with date in the name and not readable date format. We can fix this by using the package lubridate and the function as_date(). Since our data is stata format and has a different origin date than R, we need to set ‘origin = "1960-01-01" ‘. Uncomment the first three rows and display the first ten rows as above.

#library(lubridate)
#data$date <- as_date(data$date, origin = "1960-01-01")
#data$sat_date <- as_date(data$sat_date, origin = "1960-01-01")

# display again the first ten rows of our data

Now you can see the first ten rows of our data with readable dates. If you cannot see all columns use the scrollbar at the bottom of the table. Some variables which are irrelevant for this exercise have already been dropped. In the first column title, you find the title for each movie. Next, you see in the column production_budget the production budget for each film. The next three columns are date variables. opening_sat_date contains the opening date of movies, later we will find out more about all three date variables. dow stands for "day of week" with each weekday being an integer. wkintheaters gives us the week after release for each observation, so in the week of release it equals $1$ and in the last week in movies $6$. Each movie_id is just an indicator number for each movie title. tickets contains the viewership (sold tickets) for each date and movie in millions.

This data set includes movies released in the US that have not been terminated in the first six weeks. First, we want to find out more about our variable, production_budget.

An easy way to find out more is to get some summary statistics of a variable. This can be done with the library skimr and the function skim_without_charts(). To only look at the variable production_budget, we can use the $-command (data$production_budget). To get better readable results use the function print() around the function skim_without_charts(). 

# Load the package skimr

# use the function skim_without_charts() to get summary statistics of the variable production budget

In the first section Data Summary, we find the name, number of rows, and number of columns of our variable. As we can see, we have 24855 rows and one column, because we only looked at one variable. Also, the frequency of different column types is listed. Since we have one column overall, we see that our production budget has the type numeric. In the section Variable type: numeric we find for our (single) numeric variable summary statistics. n_missing stands for the number of missing values and complete_rate for the relation of missing and not-missing values (with n_missing == 0 implicates complete_rate == 1). Next, we find the mean, standard error, quantiles, and histograms with the distribution.

Now we take a look at the allocation of production budgets over time in our data. Therefore we need the package ggplot2. We want to create a plot with the production budget over time. On our x-axis, we use the variable opening_sat_date and on our y-axis production_budget. It contains for each movie the date of the Saturday, where it has been released. First, we load the package ggplot2, then insert the correct variables for the x- and y-axis, save it under the name plot_pb and print out the plot (this may take a while): 

# Load the package ggplot2:
library(ggplot2)

# Fill in the arguments to plot our data
plot_pb <- ggplot(data = data) +
  geom_point( aes(x = ___, y = ___), na.rm = TRUE, size = 0.5 ) +
    labs(x= "date of opening Saturday", y = "production budget in dollar" )

# Print out the plot (nothing to do here)
plot_pb

Most movies have a production budget below 100 million dollars. Since 2006 we have some films which largely exceed 200 million dollars as a production budget. At the end of 2009, we have an enormous outlier with a production budget of over 400 million. Later in this exercise, we will find out the title of the outlier. Maybe you already can guess the movie! Especially movies with higher production budgets seem to be around imaginary horizontal lines, once in the middle of the year and once at the end of the year.

Let’s check if this is true and draw some vertical lines in our graph. We draw for each year one line at the first of June in red and at the first of December in yellow. ggplot2 allows us to draw vertical lines with geom_vline(), this just can be added to the plot plot_pb with a +. We also need the package lubridate in order to transform our dates from strings to readable dates. This can be done with the function as_date(). Just press check in order to see the new plot: 

library(lubridate)
plot_pb +
  geom_vline(
    xintercept = c(
      as_date("2002-06-01"),
      as_date("2003-06-01"),
      as_date("2004-06-01"),
      as_date("2005-06-01"),
      as_date("2006-06-01"),
      as_date("2007-06-01"),
      as_date("2008-06-01"),
      as_date("2009-06-01"),
      as_date("2010-06-01"),
      as_date("2011-06-01"),
      as_date("2012-06-01")
    ),
    colour = "red"
  )+
  geom_vline(
    xintercept = c(
      as_date("2002-12-01"),
      as_date("2003-12-01"),
      as_date("2004-12-01"),
      as_date("2005-12-01"),
      as_date("2006-12-01"),
      as_date("2007-12-01"),
      as_date("2008-12-01"),
      as_date("2009-12-01"),
      as_date("2010-12-01"),
      as_date("2011-12-01"),
      as_date("2012-12-01")
    ),
    colour = "yellow"
  )

As we can see, a lot of movies with higher production budgets are lingering around the horizontal lines we just have drawn. Einav (2012) explains this pattern because bigger movies are released when seasonal demand is the highest.
Therefore demand increases even more in those seasons. There are two seasons for high-budget movies. One at the beginning of summer with the 4th of July as one of the key holidays. The other one in the winter holiday season with holidays like Thanksgiving and Christmas.

As mentioned earlier, at the end of 2009, we have one enormous outlier. Maybe you already have an idea which movie this could be. So let us figure out which movie has the highest and which movie has the lowest production budget.

For the next task, we need from the package dplyr the pipe %>% and the function slice(). Further, we also need the functions which.max() and which.min() from base R. If you need further information, check the following infoboxes.

info("dplyr: Piping (%>%), slice()") # Run this line (Strg-Enter) to show info

info("which.max(), which.min()") # Run this line (Strg-Enter) to show info

Load the package dplyr and use the pipe %>% and slice() to get the minimum and maximum rows of production budget. Because this is the first task with dplyr just press check: 

library(dplyr)
data %>%
  slice(which.max(production_budget), which.min(production_budget))

You can now see each movie with the highest and lowest production budget in our data one observation. Let us have our first quiz! (Just type in the answer below. The answer is case sensitive.)

! addonquizEx2-1

We found out a few things about the variable production budget. Let us get back to analyzing our entire data set. One important thing to know is how many observation does our data set contain. This can easily be done by just counting the number of rows in our data set with nrow(), just give it a try and use the pipe %>%: 

# Enter your code here.

! addonquizEx2-2

Let’s find out if our number of observations match our number of movies. With the command n_distinct() you get the number of distinct values of a variable. Just plug in the variable title (data$title) without the pipe: 

# Enter your code here.

! addonquizEx2-3

Now, look at the two numbers. What does this implicate for our data? Try to figure out the quiz below. In case you need to do some calculations here is a code chunk:

# Delete all arguments and press check to continue.

! addonquizEx2-4

Data for one movie

The number of observations is a lot higher than the number of movies. This is because of the way the data is structured. Let us take a look at the data of the movie "Avatar". We need to filter our data set for the movie title "Avatar". This can be done by using the function filter() and the condition title == "Avatar". Uncomment the given line and add the missing function and argument: 

# avatar <- data %>%

How many observations does our new data set Avatar contain? (The needed function has already been used, also use the pipe %>%.) 

# Enter your code here.

! addonquizEx2-5

Let’s take a deeper look at our data set avatar. We only keep the columns date, sat_date, opening_sat_date, gross, dow, wkintheaters and tickets. This can be done with the dplyr function select(). The code is already entered, just press check:

avatar <- avatar %>%
  arrange(date) %>%
  select( opening_sat_date, date, wkintheaters, dow, sat_date, tickets, gross)

Now we want to display the entire data set. Since we now have 18 observations in our data set, just use head() and specify the number of output rows. Just try it:

# Use head() to look at the 18 observations.

As in Dahl and Della-Vigna (2009), we only look at viewership on weekends, since weekend sales contain the majority of ticket sales.

opening_sat_date is for all observations the same. This contains the Saturday when the movie is first in theaters.
date includes the date of each observation. The next variable is wkintheaters (weeks in theaters), which indicates how long the movie has already been in theaters for each observation. As you can see we have for each week three observations, since we only look at weekends. dow stands for "day of week". 5 stands for Fridays 6 for Saturdays and 0 for Sundays. sat_date is the Saturday of each week. tickets are the sold tickets in a million for each day, and gross is the gross for each day.

Gross

As explained above, the gross for each movie is not available in our data. The gross is given for each day. So if we want to find out which movie had the biggest gross, we have to start with some calculations. Therefore, we have to sum up the gross for each day and by each movie: We use our original data data again. We need to group our data with group_by() for each movie and sum the gross across those groups. We save our data in the variable gross. Just press check to get the results:

gross <- data %>%
  group_by(title) %>%
  summarise( gross = sum(gross), opening_sat_date = mean(opening_sat_date))

Take a look at the first 15 rows of our new calculated data, use head() and $15$ as second argument:

# Look at the first 15 rows of gross

We have for each movie the first date in theaters and the accumulated gross overall weekends.

! addonquizEx2-6

Now we want to take a look at the top 10 movies with the biggest gross. We can just arrange our data from above with arrange(). Since we want a decreasing order, we have to write a - in front of our variable. Afterward, we want to display the top 10 movies. 

# Rearrange the data gross by rearranging the variable gross in descending order

# take a look at the first ten rows

! addonquizEx2-7

Let us take a look at the gross overtime of our entire data set by making a new plot. For each movie, we want to have one data point. Unfortunately, we have three date variables.

! addonquizEx2-8

Fill in the correct variables for the x- and y-axis:

plot_gross <- ggplot(data = gross) +
  geom_point( aes(x = ___, y = ___), na.rm = TRUE, size = 0.5)

plot_gross

As done above, lets add some lines for seasonality. Just press check:

plot_gross +
  geom_vline(
    xintercept = c(
      as_date("2002-06-01"),
      as_date("2003-06-01"),
      as_date("2004-06-01"),
      as_date("2005-06-01"),
      as_date("2006-06-01"),
      as_date("2007-06-01"),
      as_date("2008-06-01"),
      as_date("2009-06-01"),
      as_date("2010-06-01"),
      as_date("2011-06-01"),
      as_date("2012-06-01")
    ),
    colour = "red"
  )+
  geom_vline(
    xintercept = c(
      as_date("2002-12-01"),
      as_date("2003-12-01"),
      as_date("2004-12-01"),
      as_date("2005-12-01"),
      as_date("2006-12-01"),
      as_date("2007-12-01"),
      as_date("2008-12-01"),
      as_date("2009-12-01"),
      as_date("2010-12-01"),
      as_date("2011-12-01"),
      as_date("2012-12-01")
    ),
    colour = "yellow"
  )

As we can see again, a lot of movies with a high gross are lingering around those vertical lines. As previously explained, due to seasonal effects.

Average Daily Weekend Audiences

Let us visualize our data in some more figures. We want to plot the average daily audience against weeks in theaters, first by movie, then by weekend release. On our x-axis, we want weeks in theaters, and overall, on our y-axis, we want average daily audiences by each movie. We need to calculate the averages for tickets by movie and week in theaters. Therefore we need to group the data by the latter two. After that, we want average values for each week. Thus we repeat the step, but only for the group wkintheaters.

To get average audiences by movies, we first need to calculate the means over tickets per movie_id and week in theaters. To understand what is happening, we select the movie with movie_id == 1. We only select variables, which are important in this task. Just press check:

movie_1 <- data %>%
  filter(movie_id ==1) %>%
  select(date, wkintheaters, tickets)

head(movie_1,18)

For the movie with the movie_id == 1, we see all observations. As we can see again, we have three observations per week. wkintheaters tells us in which week after release we are. In the next step, we want to calculate the average tickets for each different week. Therefore we need to group the data by each value of wkintheaters and calculate the mean of the belonging tickets measures and save it in a new variable called avg_tickets_week. Just press check:

movie_1 <- movie_1 %>%
  group_by(wkintheaters) %>%
  mutate(avg_ticktes_week = mean(tickets)) 

head(movie_1,18)

As you can see, we calculated the average ticket sales per week for the movie with the movie_id == 1 and saved it in the variable the avg_tickets_week. Now we want to calculate the means for all the movies in our data. Therefore, we are doing the same with the entire data set. Just press check:

avg_audiences <- data %>%
  group_by(wkintheaters) %>% 
  summarise( avg_tickets_week = mean(tickets))

head(avg_audiences)

The table shows the average audiences for each week. Let us visualize this in a plot. Just press check:

 ggplot( data = avg_audiences) +
    geom_line( aes(x = wkintheaters, y = avg_tickets_week), linetype = "dashed") +
    geom_point( aes(x = wkintheaters, y = avg_tickets_week)) +
    labs(title = "A. by Movie", x= "Week in Theaters", y = "Average Daily Audience (1,000,000s)" )

The plot shows the average daily ticket sales for each of the six weekends in theaters across 1381 movies in our sample. During opening weekend, regular average ticket sales are exceeding 1 Million. In the following weeks, it drops approximately exponentially. We will further investigate this drop in later exercises.

Exercise 3 -- Recap Regression

In this chapter, we take a look at linear regression, ordinary least squares, and the f-statistic. This is a small recap to refresh your knowledge. It also discusses briefly ordinary least squares which you will need later. If you need a more detailed introduction or more mathematical details, see Kenndy (2008) or Wooldridge (2016).

Linear Regression

When creating a model with linear regression, we have $n$ explanatory variables $x_n$ and one response variable $y$. Response variables usually have some kind of relationship to one or more explanatory variables. This relationship can be examined by using a linear regression model: $$ y = \beta_0 + \sum_{i=1}^n x_{i}\beta_{i} + \epsilon.$$ $\beta = (\beta_1, ..., \beta_n)$ are our regression weights and $\beta_0$ is our y-intercept. $\epsilon$ is independent and normally distributed (cf. Wooldridge (2016), pp. 61-63).

Let us look at some data and inspect the case for one explanatory variable. We now take a look at the relationship of sold tickets and gross.

First load the data tickets_gross.dta and display with head() part of the data:

library(haven)

# As in Exercise 2 save our data "tickts_gross.dta" in a variable data with read_dta()
# uncomment the next line and add the needed commands
#data <- 

# Display the first rows of data 
head(data)

For each movie and date, we have an observation with tickets and gross. Our date is in a numeric variable (therefore the dates are not readable). tickets are in a million tickets.

In the next step we want to visualize gross by tickets. Therefore we plot a ggplot with tickets on the x- axis and gross on the y-axis. We save our plot in the variable plot_tickets_gross. Fill in below the variables for x and y:

library(ggplot2)
ggplot(data = data) +
  geom_point( aes( x= ___, y = ___))

We already can tell with more sold tickets the gross increases. So let us figure out how much. Therefore we need to run a linear regression on this data. In this case, x is our tickets and y our response variable.

Use lm() to run a linear regression with tickets being our explanatory variable and gross our response variable and save it in the variable my_lm. In the infobox, you find some information on how to use lm().

info("Code Example with lm()") # Run this line (Strg-Enter) to show info

# uncomment the next line and add the missing parts
#my_lm <-

Let's get with summary() some information about our linear regression, Just press check:

 summary(my_lm)

First, we see our formula with gross ~ tickets and the used data set. Next, we get some statistics about our residuals. We will find out more about the residuals later.

The next part is called coefficients. First, we look at the column Estimate. The first number in the column is the y-intercept, and the second one is the slope of our linear regression. Our line, therefore, has the form:

$$y_i = -15309 + 6957491 x_i $$

! addonquizEx3-1



! addonquizEx3-2



It is a little bit unhandy to calculate in a million tickets. Therefore, we want to know the average increase in the gross by one more sold ticket. Use the chunk below to make some calculations if needed.

# Enter your code here.

! addonquizEx3-3



Lets add this regression line to our plot plot_tickets_gross. ggplot2 has with geom_smooth() a function which adds the linear regression line. In geom_smooth() we need the method = lm. Just press check:

ggplot(data = data, aes( x= tickets, y = gross)) +
  geom_point()+
  geom_smooth( method = 'lm')

Now you can see our regression line in our plot with $y_i = -15309 + 6957491 x_i$.



Ordinary Least Squares

Now you might wonder how $(\beta, \beta_0)$ has been calculated. There are a lot of ways. The most common approach, which is also used in the function lm() from above, is ordinary least squares (OLS).

The idea is to minimize the difference between observed and predicted values. Since this could be positive and negative values, we use squares of the differences. This means we have to minimize the following function (cf. Wooldridge (2016), p. 64-66):

$$\sum_{i=1}^{n}(y_i - \beta_0 - \beta_1x_{i1} - ... - \beta_p x_{ip})^2 \rightarrow min_{\beta_0, \beta_1,...,\beta_p}$$

F-statistic - Overall Significance of the Regression

The f-statistic tests the hypothesis if none of the explanatory variables affect the regression. That means all of our coefficients are zero (cf. Wooldridge (2016), p. 135):

$$H_0: \beta_1 = \beta_2 = ... = \beta_n = 0$$

Rejecting $H_0$ means that at least one of the coefficients is, not zero.

lm() also calculates the f-statistic. Retake a look at our regression output: (The f-statistic can be found in the last row)

# Enter your code here.

To find out if our f-statistic is meaningful, we can calculate a critical value. If the f-statistic is more substantial than our critical value, we can dismiss our $H_0$.

To calculate our critical value, we need the function qf().In the first argument, we give the confidence interval for our f-statistic. Next, we specify our degrees of freedom (DF), which you can find in the f-statistic in our regression output.

What is the critical value for our regression above with a confidence interval of 99%? Just press check.

qf(.99, 1, 28248)

! addonquizEx3-6



! addonquizEx3-7



The previous theory and more mathematical details can be found in Wooldridge (2006, chapter 4).

Exercise 4 -- Empirical Model

In Exercise 2, you already saw that movie releases are not constant. According to Einav (2007), this is mainly due to two factors: First, demand depends on seasons. Moviegoing is just more prevalent when the weather is not so ideal. For example, ticket sales tend to be higher during winter due to cold, rainy, or snowy weather. The second factor is the supply of good quality movies. For example, Christmas is the prime time for movie releases. Therefore more high budget movies are released around this time.

We aim to find unexpected higher or lower ticket sales in our data. For example, if ticket sales on a specific day are unusually high, compared to other years, we want the difference between the expected number of ticket sales and real ticket sales on this day. This is called abnormal viewership. Therefore, the seasonal effects have to be factored out. For example, around Christmas, ticket sales are high every year. This is a seasonal effect that we want to factor out to be able to get abnormal viewership.

In our data, we have variables for each year, each week of the year, day of the week, and holidays, which are our indicators for seasons.

To manipulate our data accordingly, we need to read in a new data set data_emp.dta. It has already been transformed. It only contains relevant variables for this exercise. Since we only work with one data set in this exercise, we will call it data. Just press check:

library(haven)
data <- read_dta("data_emp.dta")

As always, we should first take a look at our data and see what it contains. Let us look at the variable names with colnames(). Just press check:

colnames(data)

The data set also contains the already known variables tickets (in a million), date, and opening_sat_date. The rest of the variables are indicator variables. For every observation, we have a date variable, which has been split up in indicator variables. The variables starting with "ww" are indicators for the week of the year; the variables beginning with yy indicates the year. This means yy1 stands for 2002 and yy11 for 2012. The variables starting with h are holiday indicators. All these variables are either 0 or 1, 0 if it is false for one observation, and one if true. The last two variables should be already familiar. dow stands for day of the week and can be 5, 6, or 0, which indicates Friday, Saturday, or Sunday. wk1 is an indicator variable if the movie is one week in theaters. We will need this later.

info("Holiday variables") # Run this line (Strg-Enter) to show info

Now let us plot ticket sales against date, just press check:

library(lubridate)
data <- data %>%
  mutate(date = as_date(date, origin = "1960-01-01"))

library(ggplot2)
ggplot(data = data, aes(date, tickets)) +
  geom_point(size = 0.5, colour = "red")  +
  xlab("year")

The plot shows data points for each movie on each day of the weekend. The majority of movies are between 0 - 1.5 million sold tickets per day. However, there are a lot of movies, with more than 1.5 million sold tickets. This plot does not show, if those higher ticket sales are due to seasonal effects or if they are unexpected high on that certain day compared to that day in other years. It seems like most of the higher data points are around the same time every year so that seasonality may have a high effect. As explained earlier, for example, around Christmas, ticket sales tend to be higher every year. To find abnormal viewership, we need to take into account that our sold tickets on each day, may depend on the day itself. Therefore we have to correct our tickets for influences, which occur by date. We use the date indicator variables that were explained earlier.

Empirical Method

Abnormal Viewership

In our empirical method, we need to factor out seasonality. Therefore we denote $v_{tj}$ as viewership on date $t$ and $j$ as a week in theaters. For now, we will look at opening weekends. Therefore we set $j=1$. Our viewership or sold tickets in opening weekends is then $v_{t1}$. Now we denote the indicators for the day of the week, each week, each year, and holidays as $F’ _t$.

We want to create a variable with the column names for $F’ _t$. Therefore, we select our indicator variables with select() and save the names of the variables with colnames() in a variable f_t. Just press check:

f_t <- data %>%
  select(starts_with("ww"),
         starts_with("yy"),
         starts_with("h"),
         starts_with("dow")) %>%
  colnames()

To factor out seasonality, we first have to run a regression to determine how much ticket sales are influenced by it. Our regression formula is

$$v_{t1}=\beta_0 + F'_t \beta_1 + \epsilon.$$

Writing the regression formula by hand with all the weeks, years, and holidays would be tedious. Therefore we just let R write it for us and save it as a formula. The formula is saved under reg_formula. Just press check to run the chunk, at the end the formula will be printed:

reg_formular <-
  as.formula(paste("tickets", paste(f_t, collapse = "+"), sep = " ~ "))

print(reg_formular)

Now, run the regression with lm() and save it as my_lm:

my_lm <- lm(reg_formular, data = data)

For this task, we are not interested in the estimates of our regressions, but we are interested in the predicted also called fitted values in the lm-object. We add those values to our data with the variable name fit.

data$fit <- my_lm$fitted.values

Now we take the plot from above and add the predicted values:

ggplot(data = data)  +
  geom_point(aes(x = date, y = tickets), size = 0.5, colour = "red")+
  geom_point(aes(x = date, y = fit),size= 1, colour = "blue")+
  scale_x_date(date_labels = "%Y")  +
  xlab("year")

We now have predicted ticket sales for each date according to season and holiday (in blue). We denote the predicted values with $\widehat{v}{t1}$. As we can see, we have a lot of actual data points that are much higher or lower than the predicted values. This means the difference between those points is not explained by seasonality. We call this difference abnormal viewership ${v_abn}{t1}$. (Remember, we are only looking at tickets in the first week in theaters!) Abnormal viewership is our residual values. That can be calculated by

$${v_abn}{t1} = v{t1} - \widehat{v}_{t1}.$$ In an lm-object are residuals already saved. We are saving the residuals of my_lm to our data. Just press check:

data$res <- my_lm$residuals

Our aim is it to get abnormal viewership’s by date, that means for each date we need the biggest difference between realized and predicted values. Therefore we group our data by date and save the largest residual for each date in a new variable called abn_tickets_wk1:

data <- data %>%
  group_by(date) %>%
  mutate(abn_tickets_wk1 = max(res)) %>%
  ungroup()

Now plot our new variable abn_tickets_wk1:

ggplot(data = data) +
  geom_point(aes(x = date, y = abn_tickets_wk1), size = 0.5) +
  ylab("abnormal viewership") +
  xlab("year")

The plot shows abnormal viewership for each date. Next, you find some questions about the plot and abnormal viewership.

Are the following statements true or false?

! addonquizEx4-1



! addonquizEx4-2



Questions:

! addonquizEx4-3



! addonquizEx4-4



! addonquizEx4-5



Weather Shocks

Now we want to do the same for weather variables. Our weather data is from the US National Weather Service. It contains percentages of theaters experiencing certain weather on a national level. The weather measures include different temperatures, precipitation, and combined measures of precipitation and temperature, such as snow. Temperature measures are divided into 5° Fahrenheit dummies (2.8° Celsius). Precipitation measures are divided into 0.25-inch dummies (0,635 cm).

As mentioned above, we create new weather variables called "weather shocks" for the weather, which occurs unexpectedly. $w_k$ is our variable for each of our weather measures. As done above, we have the following regression for each weather measure:

$$w_{tk} = \delta_k + F’_t \beta_1 + \epsilon$$ $t$ is the index for the date, and $k$ is an index for each weather measure. $ F’ _t$ is our indicator variable for the day of the week, each week of the year, year, and holidays.

We predict our weather measures and denote it with $\widehat{w_{tk}}$.

Our weather shocks are now defined as $$w_shock_{tk} = w_{tk} - \widehat{w}_{tk}.$$

Question:

If you need a hint, you find an info box below the question.

We look at one temperature range: temperature between 5° and 10° Fahrenheit. At one day, the weather shock variable has a value higher than zero for this range.

! addonquizEx4-6



We pass on calculating all these variables in the problem set. They have already been created and will be introduced in the next exercise.

Our tickets and weather variables are now only showing abnormal effects. Further, we will only use abnormal viewership/ticket sales and weather shocks.

After doing an analysis of our weather shock variables we will select the most influencal variables. We will perform a first stage analysis. (Exercise 7) $$ {v_abn}{t1} = \eta + \sum{i=1}^{n}\xi_i * w_shock_{tki} + \epsilon $$ With i being the number of selected weather shocks.

Next, we will perform a second stage analysis to estimate the influence of abnormal viewership in the first week on abnormal viewership in the following weeks with $j>1$ for each subsequent week. (Exercise 8)

$$ {v_abn}{tj} = \mu_t + \theta_t * \widehat{{v_abn}}{t-7(j-1)} + \epsilon $$

Exercise 5 -- Moviegoing Summer

In this exercise, we want to get familiar with some of the weather shock variables. We are going to analyze some typical summer variables - the temperature range between 60° and 95° Fahrenheit (about 15.6° till 35° Celsius). For this exercise, we need to read in the data_summer.dta. It only contains observations for the first week with abnormal viewership, as calculated in exercise 3 and seven "summer" temperature variables.

library(haven)
data <- read_dta("data_summer.dta")

Let’s take a look at our data with head().

head(data)

The first column, abn_tickets_wk1 is the abnormal ticket sales in the first week from exercise 3. A number around zero for one day means that the ticket sales are as expected for that day, after factoring out seasonality. A positive number means that ticket sales are unexpectedly high. A negative number of ticket sales means they are unexpected low on that day.
The other seven columns are our temperature data in 5° degree increments from 60° till 95° Fahrenheit. Each variable ends with a 0 for Sunday. Due to large moviegoing during day time. temperature_shock_60_0 stands for the temperature increment between 60° and 65° Fahrenheit. If the number in this increment is high, more theaters than expected are in this temperature range on that day. Each temperature variable may influence abnormal ticket sales.

To find out to which degree this is the case for, we are going to run regressions for each temperature as the independent variable and abnormal ticket sales as a dependent variable:

$${tickets_abn} = \alpha + \beta* {temperature_increment} + \epsilon$$ Just press check to run all seven regressions.

lm_1 <- lm(abn_tickets_wk1 ~ temperature_shock_60_0, data = data)
lm_2 <- lm(abn_tickets_wk1 ~ temperature_shock_65_0, data = data)
lm_3 <- lm(abn_tickets_wk1 ~ temperature_shock_70_0, data = data)
lm_4 <- lm(abn_tickets_wk1 ~ temperature_shock_75_0, data = data)
lm_5 <- lm(abn_tickets_wk1 ~ temperature_shock_80_0, data = data)
lm_6 <- lm(abn_tickets_wk1 ~ temperature_shock_85_0, data = data)
lm_7 <- lm(abn_tickets_wk1 ~ temperature_shock_90_0, data = data)

Instead of looking at each regression and comparing regression tables, we are using the library dotwhisker to get the results in a graph. The graph we are plotting is a so-called coefplot. It shows with a dot the estimate of the coefficients, and the whiskers are by the default the 95% confidence interval. Further information you find here. Just press check to create the plot:

library(dotwhisker)


dwplot(
  list(lm_1, lm_2, lm_3, lm_4, lm_5, lm_6, lm_7),
  vline = geom_vline(
    xintercept = 0 ,
    colour = "grey30",
    linetype = "dotted")) %>%
  relabel_predictors(
    c(temperature_shock_60_0 = "60-65",
      temperature_shock_65_0 = "65-70",
      temperature_shock_70_0 = "70-75",
      temperature_shock_75_0 = "75-80",
      temperature_shock_80_0 = "80-85",
      temperature_shock_85_0 = "85-90",
      temperature_shock_90_0 = "90-95")) +
  ylab("Residual Temperature Range( Degrees F, levels)") +
  xlab("Residual Opening Daily Ticket Sales (1,000,000)") +
  theme(legend.position = "none")

In this plot, we can see how unexpected temperatures in 5° intervals from 60° till 95° Fahrenheit influence ticket sales. Sudden high and low temperatures influence ticket sales positively. Unexpected temperatures between 70° till 85° Fahrenheit (21.1° - 29,4° Celsius) effect ticket sales negatively. In absolute values, the most prominent influence has the range 75° till 80° Fahrenheit (23.9° - 26.7° Celsius).

We want to take a closer look at this range by plotting all data points in one plot. We also add a regression line:

library(ggplot2)
ggplot(data = data, aes(x=temperature_shock_75_0, y = abn_tickets_wk1)) +
  geom_point(size = 0.25) + 
  geom_smooth(method='lm', se = FALSE) +
    xlab("Residual % Theaters at 75-80 degrees") +
    ylab("Residual Ticket Sales (1,000,000s)")

summary(lm_4)

The plot has on the x-axis the percentage of theaters, which are unexpected in the 75° to 80° range. On the y-axis is abnormal viewership. The blue line is our regression. Below the plot, you have a regression output with further details.

Question:

If you need a hint, you find an info box below the question.

! addonquizEx5-1



info("Hint") # Run this line (Strg-Enter) to show info



Exercise 6 -- Variable Selection Method

Weather shocks influence abnormal viewership, as we have seen. But there is a catch: Including all our weather measures into our model is tempting, but we have too many different variables for the entire US. It might cause us to overfit by keeping all variables or underfit by selecting too few or nonrelevant variables. Therefore we want to find the most important variable which predicts abnormal viewership in the first week:

LASSO - Least Absolute Shrinkage and Selection Operator

LASSO stands for Least Absolute Shrinkage and Selection Operator. It is a regression method used in statistics and machine learning. It can help to improve the prediction and interpretability of the produced model. That is done by variable selection and regularization. LASSO uses regularization to penalize features. It can automatically set coefficients of features to zero. So if the feature is not relevant, it does not influence our model. Therefore we have an algorithm for variable selection. LASSO is very similar to OLS with some modifications to the error function (cf. Dangeti (2017), pp. 75-77):

Error function - OLS:

Remember in exercise 3 we took a look at least squares. In order to get a good regression line we minimize the following :

$$\sum_{i=1}^{n}(y_i - \beta_0 - \beta_1x_{i1} - ... - \beta_p x_{ip})^2 \rightarrow min_{\beta_0, \beta_1,...,\beta_p}$$

Error function - LASSO:

LASSO in the case of least squares uses the same function, but adds a penalty term (cf. Dangeti (2017), pp. 75-77):

$$\sum_{i=1}^{n}(y_i - \beta_0 - \beta_1x_{i1} - ... - \beta_p x_{ip})^2+ \lambda \sum_{i=1}^{n} |\beta_i| \rightarrow min_{\beta_0, \beta_1,...,\beta_p}$$

$\lambda$ is a so-called tuning parameter (cf. Dangeti (2017), pp. 75-77). As you can see, setting $\lambda$ to $0$ produces the same error function as for ordinary least squares.
Increasing the tuning parameter $\lambda$ results in more impact of the penalty term. With more influence of the penalty term, the number of variables for our model gets reduced because insignificant parameters are set to zero by minimizing the absolute values of the parameters.

Start with loading data_lasso.dta. It only includes the variables we need for our LASSO. Press check:

library(haven)
data <- read_dta("data_lasso.dta")

Let us take a look at the variable names in our data set with colnames():

# Take a look at the variable names in our data set with `colnames()`

The data contains a variable with the name abn_tickets_wk1, which contains abnormal viewership for week 1. The other variables are weather shock variables, containing percentages of theaters unexpectedly experiencing certain weather. The temperature_shock variables are divided into 5° Fahrenheit dummies (2.8° Celsius). We have two variables for rain and snow shocks each, called rain_shock and snow_shock. The remaining variables are variables for unexpected precipitation divided into 0.25-inch dummies (0,635 cm). Each variable ends with a 6 for Saturday or 0 for Sunday.

All variables were calculated in exercise 4.

Now we load the package glmnet, which already has a function for LASSO:

#Load the package glmnet


info("glmnet and LASSO") # Run this line (Strg-Enter) to show info

First, we need to create a model. Therefore we create a x-variable with model.matrix() containing a formula. Our response variable gets saved in another variable $y$. Just press check:

# predictors
x <- model.matrix(abn_tickets_wk1 ~., data)[,-1]

# outcome
y <- data$abn_tickets_wk1

In the next step, we are going to create our model with the function glmnet. The first argument of glmnet() is the created model matrix x; the second argument is our vector y. glmnet supports different regression analysis methods. With alpha = 1 as our third argument, LASSO is used. To get results with more and more variables set to zero, LASSO is calculated with a vector of different values of $\lambda’ s$. Higher values of lambda set more variables to zero. By default, the number of distinct values of $\lambda$ (nlambda) is set to 100. In our case, this is not sufficient. Therefore we specify the forth argument as nlambda = 300.

model <- glmnet(x, y, alpha = 1, nlambda = 300)

Now we have created a glmnet-object. We can plot the coefficients of the model with plot():

plot(model, xvar = "lambda")

The lower x-axis shows the logarithm of our lambda values. It increases from left to right. The y-axis shows the coefficient values. Each line in the plot stands for one coefficient of a weather shock variable. So the plot shows the development of the coefficients for each variable when $\lambda$ is increased.
The upper x-axis shows the number of variables that have coefficient values higher than zero. This number is called the degree of freedom (= df).

When $\lambda = 0$, we have the ordinary least square regression from chapter 3, because the penalty term has no impact. That means no weather shock variable is excluded, so all variables are used in the regression. The number of degrees of freedom is the number of different weather shock variables.
When lambda is increased, more and more coefficient values of not so important weather shock variables are set to zero, and the degree of freedom is reduced. That can be seen in the plot, with one line after another going to zero.

Questions:

! addonquizEx6-1



! addonquizEx6-2



! addonquizEx6-3



Our next aim is to select the essential weather shock variables. Therefore we take a look at the five highest lambda values with corresponding degrees of freedom. The lambdas and corresponding degrees of freedom are saved in a table called output. Just press check to save the table and print the first five lines:

output <- data.frame("df" =model$df, "lambda" = model$lambda)
head(output, 5)

In the column lambda, you now see the ten highest $\lambda’s$ and the corresponding degrees of freedom in the column df.

Selecting the most important weather shock variable

To get the most important variable, we have to select a lambda with the corresponding degree of freedom, which equals one. In our case, this is the second lambda in our table output.

The function coef() displays all coefficients of our model. Specifying our lambda allows us to get a coefficient output for all-weather shocks for this lambda. Therefore, we set $\lambda$ with s=output$lambda[2]. Just press check to get the coefficients of all-weather shocks for the second-highest lambda:

coef(model, s=output$lambda[2])

Each weather shock with a . next to it was set to zero and therefore eliminated from our model. As expected, we have one variable with a coefficient next to it. This variable is called temperature_shock_50_6. That is the temperature range between 50° and 55° on a Saturday. In the next exercise, we will take a closer look at the influence of this variable on abnormal viewership.

Selecting the second most important weather shock variable

Now we want our algorithm to select the second most crucial weather shock variable. 

# Fill in the correct column to get the first and second most important weather shock variable
coef(model, s=output$lambda[___])

! addonquizEx6-4



LASSO Results paper

Our results differ from the results in the paper. The first and second variables were selected in reverse order. We used the standard LASSO-algorithm given by the glmnet package, but the paper used a different LASSO-Algorithm. It is modified to predict better instrumental variables of a model with linear instrumental variables. In exercise 8, we will get to know instrumental variables.

With both algorithms, we have similar results. By selecting two variables, we even get the same instruments.

Exercise 7 -- First Stage Results

In this exercise, we analyze the impact of our LASSO selected weather variables from exercise 6 on abnormal viewership and compare our different variables. We are analyzing our LASSO selected variables and the selected variables of the paper.

LASSO Results

In Exercise 6, LASSO selected temperature_shock_50_6 first and temperature_shock_75_0 as second variable. The order of the selected variables was reversed in the paper, due to a slightly different algorithm.

As always, we first need to load our data set. This time we need to load data_first_stage.dta. It has already been altered for this exercise. Just press check:

library(haven)
data <- read_dta("data_first_stage.dta")

Take a look at the data set with head():

# Enter your code here.

Our data contains only our abnormal tickets for week one and the two selected temperature shock variables and our date variable in numeric format.

For the rest of the problem set, we need a new function to run our regression. It is called felm() from the package lfe. felm() is an extension for lm(). For this exercise, we need to be able to calculate clustered standard errors. In the next exercise, we need another attribute of this function.

First Stage Results: One Variable

Our Results

In exercise 6, our first variable selected by our Lasso regression was the temperature range between 50° and 55° Fahrenheit. felm() has several applications. Two of them we don’t need right now. Our standard errors are supposed to be clustered by date. Therefore we have to insert after our regression |0|0| date. Just press check to look at the results:

library(lfe)
reg_o1 <- felm(abn_tickets_wk1 ~ temperature_shock_50_6 |0|0| date, data = data)

summary(reg_o1)

These are our results for our first selected variable with LASSO. We get the following model: $$ abnormal _ viewership = 0 + 3.905* temp_{50-55}$$

As you can see, the felm() output is very similar to lm(). For $R^2$ and the f-statistic, we have each an added column for the projected model.


! addonquizEx7-1


In the paper, a different LASSO algorithm was used and therefore had different results. Let us look at the model of the paper. First, run the regression for the single variable in the paper.

Paper

reg_p1 <- felm(abn_tickets_wk1 ~ temperature_shock_75_0|0|0| date, data = data)

Now we need to compare our two models:

Comparison

We want to write both regression results in one table. Therefore we need the function stargazer() from the stargazer package. Just press check to get the results:

library(stargazer)
stargazer(reg_o1,reg_p1,
          omit = c("Constant"),
          type = "html",
          column.labels = c( "Our Results", "Results Paper"),
          omit.stat = c("all"))

Our LASSO picked a variable with a positive effect and the LASSO algorithm of the paper, one with negative effects. Both variables have a p-value below 0.01 (***), which indicates that their relationship to abnormal viewership is highly significant. In parenthesis, the standard error clustered on the date level is lower than in the paper’s model.

Now we want to calculate the f-statistic and add it to our table. Therefore we need to extract the f-statistic from our summary statistic. Just press check again to get the results.

fstat_1<- c(summary(reg_o1)$P.fstat[5], summary(reg_p1)$P.fstat[5]) %>%
  round(digits = 3)

stargazer(reg_o1,  reg_p1,
          omit = c("Constant"),
          type = "html",
          column.labels = c( "Our Results", "Results Paper"),
          add.lines = list(c("f-statistic", fstat_1 )),
          omit.stat = c("all"))

So what is the critical value for our f-statistic? That can be done with the function qf(). In the first argument, we give the desired percentile. In this case, we want the 99% - percentile. Next, we specify our degrees of freedom df1 and df2, which are 1 and 1669. Give it a try:

# Enter your code here.

! addonquizEx7-2



First Stage Results: Two Variables

In exercise 6, we selected not only one variable with LASSO but two, which are conveniently the same in the paper and exercise 6.

reg_2 <- felm(abn_tickets_wk1 ~ temperature_shock_50_6 + temperature_shock_75_0 |0|0| date, data = data)
fstat_2 <- c(summary(reg_2)$P.fstat[5]) %>%
  round(digits = 3)

stargazer(reg_2,
          omit = c("Constant"),
          type = "html",
          add.lines = list(c("f-statistic", fstat_2 )),
          omit.stat = c("all"))

Again both variables have a p-value below 0.01 (***), which indicates that their relationship to abnormal viewership is highly significant. In parenthesis, you find once more the clustered standard error on the date level.

What is the critical value for the f-statistic, when we have two variables?

# Enter your code here.

! addonquizEx7-3



All Results

Let us add all the results in one table to get a better overview:

# Enter your code here.

All our models can reject the f-statistic and have a significant relationship between the analyzed weather shock and abnormal viewership in week one. Therefore, we can continue our second stage analysis in the next exercise.

Exercise 8 -- Second Stage Results

One of the key interests in the paper was how moviegoing behavior is influenced. So far, we have only looked at the data to determine how moviegoing behavior is influenced in the first week after release. Now we want to take a look at how the following weeks are influenced by the first week of moviegoing behavior. First, we need to load our data set. Just press check:

library(haven)
data <- read_dta("data_second_stage.dta")

Take a look with head() at our data. Just press check:

head(data)

Additional to our variable for abnormal viewership in the first week (abn_tickets_wk1), we have variables for all following weeks. abn_tickets_wk2_to_6 contains the accumulated abnormal viewership of week two till six. We have the two temperature shocks from the last two exercises, our usual date variable, and indicator variables for the week in theaters.

In this case, our ticket sales for the opening weekend are not our independent variable but our dependent variable. We run a regression in the form of: $$ abnormal _ viewership {i} = \beta_0 + \beta_1* abnormal _ viewership {1} + \epsilon $$ $i$ indicates week two till six and overall ticket sales for all weeks. Now we rerun a regular regression with felm(). Again we cluster at the date level and filter the data for each week with subset =. Press check to view a table of all regression results:

library(lfe)

ols_p_2 <- felm(abn_tickets_wk2 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk2 ==1)

ols_p_3 <- felm(abn_tickets_wk3 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk3 ==1)

ols_p_4 <- felm(abn_tickets_wk4 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk4 ==1)

ols_p_5 <- felm(abn_tickets_wk5 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk5 ==1)

ols_p_6 <- felm(abn_tickets_wk6 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk6 ==1)

ols_p_7 <- felm(abn_tickets_wk2_to_6 ~ abn_tickets_wk1 |0|0| date ,
     data = data, subset = wk1 ==1)


stargazer(ols_p_2, ols_p_3 ,ols_p_4, ols_p_5, ols_p_6 ,ols_p_7, type = "html", 
          omit = c("Constant"),
          omit.stat = c("all"))

For each regression, we have a column. The last column is the accumulated abnormal viewership of weeks two to six.

In our table, we find each dependent variable’s value of the coefficient of ticket sales, its clustered standard errors in parentheses below, and the p-value. As we can see, all relationships are highly significant below the 1% level. As always our ticket sales are in millions.

Questions:

! addonquizEx8 - 1



! addonquizEx8 - 2



As we have seen in our previous exercises, other variables influence our ticket sales opening weekend. Right now, these variables are included in our error term and therefore correlate with our explanatory variable. We assume no correlation between the explanatory variable and the error term for our regression with ordinary least squares. This problem is called endogeneity(cf. Kennedy, 2008, chapter 9, p. 139).

To solve for endogeneity, we have to use instrumental variables. An instrumental variable should be uncorrelated with the error term and correlated with the explanatory variable for which it is used as an instrument (cf. Kennedy, 2008, chapter 9, pp. 139 - 144). As we have seen in exercise 7, our LASSO selected variables are connected with our abnormal viewership in the first week. So these will be used as instruments. The instruments should be able to explain some variation of our abnormal viewership and help reduce the correlation between the explanatory variable and error term.

$$ {v_abn}{t1} = \mu_t + \theta_t * \widehat{{v_abn}}{t-7(j-1)} + \epsilon $$ $\widehat{{v_abn}}_{t-7(j-1)}$ is our predicted abnormal viewership by our weather shock, as done in the first stage. $t$ is the date and for each week with $j>1$.

Instrumental Variables (IV) can be implementer with felm(). The formula has now the form: y ~ x | 0 | IV | cluster. Our first instrument is the variable temperature_shock_50_6, which we obtained in exercise 6. Therefore we regress abn_tickets_wk1 ~ temperature_shock_50_6. With clustering at our date level and having only one explanatory variable the formula is: y ~ 1 | 0 |(abn_tickets_wk1 ~ temperature_shock_50_6)| date. For y, we need for each week a different variable with abnormal viewership.

Everything has been filled in in advance. In the end, a table will be computed. Just press check:

iv_l_2 <- felm(abn_tickets_wk2 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_50_6)| date ,
     data = data, subset = wk2 ==1)
iv_l_3 <- felm(abn_tickets_wk3 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_50_6)| date ,
     data = data, subset = wk3 ==1)
iv_l_4 <- felm(abn_tickets_wk4 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_50_6)| date ,
     data = data, subset = wk4 ==1)
iv_l_5 <- felm(abn_tickets_wk5 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_50_6)| date ,
     data = data, subset = wk5 ==1)
iv_l_6 <- felm(abn_tickets_wk6 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_50_6)| date ,
     data = data, subset = wk6 ==1)
iv_l_n <- felm(abn_tickets_wk2_to_6 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_50_6)| date ,
     data = data, subset = wk1 ==1)


stargazer(iv_l_2, iv_l_3, iv_l_4, iv_l_5, iv_l_6, iv_l_n,
          type = "html", 
          omit = c("Constant"),
          omit.stat = c("all"))

In the table, you see the results of our instrumental variable estimation with the temperature range from 50° to 55° Fahrenheit as an instrument. Our LASSO-algorithm estimated this instrument in exercise 6.

Question:

! addonquizEx8 - 4



Now we want to do the same for our variable, which was selected in the paper:

iv_lp_2 <- felm(abn_tickets_wk2 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0)| date ,
     data = data, subset = wk2 ==1)
iv_lp_3 <- felm(abn_tickets_wk3 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0)| date ,
     data = data, subset = wk3 ==1)
iv_lp_4 <- felm(abn_tickets_wk4 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0)| date ,
     data = data, subset = wk4 ==1)
iv_lp_5 <- felm(abn_tickets_wk5 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0)| date ,
     data = data, subset = wk5 ==1)
iv_lp_6 <- felm(abn_tickets_wk6 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0)| date ,
     data = data, subset = wk6 ==1)
iv_lp_n <- felm(abn_tickets_wk2_to_6 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0)| date ,
     data = data, subset = wk1 ==1)

stargazer(iv_lp_2, iv_lp_3, iv_lp_4, iv_lp_5, iv_lp_6, iv_lp_n, type = "html", 
          omit = c("Constant"),
          omit.stat = c("all"))

Question:

! addonquizEx8 - 5



In our last case, we use those two variables, which our LASSO chose and was also chosen in the paper.

iv_l2_2 <- felm(abn_tickets_wk2 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk2 ==1)
iv_l2_3 <- felm(abn_tickets_wk3 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk3 ==1)
iv_l2_4 <- felm(abn_tickets_wk4 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk4 ==1)
iv_l2_5 <- felm(abn_tickets_wk5 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk5 ==1)
iv_l2_6 <- felm(abn_tickets_wk6 ~ 1|0|(abn_tickets_wk1 ~ temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk6 ==1)
iv_l2_n <- felm(abn_tickets_wk2_to_6 ~ 1|0|(abn_tickets_wk1 ~temperature_shock_75_0 + temperature_shock_50_6)| date ,
     data = data, subset = wk1 ==1)


stargazer(iv_l2_2, iv_l2_3, iv_l2_4, iv_l2_5, iv_l2_6, iv_l2_n, type = "html", 
          omit = c("Constant"),
          omit.stat = c("all"))

Question:

! addonquizEx8 - 6



! addonquizEx8 - 7



In total, our results are very similar for each instrument.

! addonquizEx8 - 8



Learning vs. Network Externalities

In the paper were similar results found on the local level. That could be due to a "learning effect". Therefore, the paper examines the effects of movie quality and prior knowledge, only to find the results unchanged. There might still be a learning effect, but the paper finds no further evidence for learning due to private information like movie quality. In the first week, our weather shocks impact viewership in the next weeks, a so-called social spillover effect. That might be since viewership knows that others have seen the movie and value the shared experience by knowing that others have seen the movie. That is called network externalities.

Exercise 9 -- Conclusion

! addonquizEx9 - 1



! addonquizEx9 - 2



In this problem set, we analyzed the effect of weather shocks on moviegoing behavior. Since our weather data has a lot of instruments, we implemented a LASSO algorithm for variable selection. Using the basic LASSO algorithm provided by the package glmnet, we get slightly different results, as found in the paper. In the paper, a modified LASSO algorithm, adapted to select optimal instruments, was used.

With our and from the paper LASSO-selected instruments, we perform a first stage analysis for opening weekend viewership. We find that all instruments are reliable. Conducting the second stage analysis, we find similar results for all selected instruments: Viewership in subsequent weeks were in total a little bit larger than at the opening weekend. That means the efffect of abnormal viewership of opening weekends more than doubled in the following weeks.

In this problem set, we only replicated the essential parts of the paper. Therefore you find additional robustness checks, local analysis, and proxies for qualities in the paper itself.

Overall our results stay the same. That indicates that the observed effect takes place on a local level. That moviegoing is driven by either some unknown learning effects or the value of shared experiences, so-called network externalities.

Here you can see the collected awards, in total there are eigth awards:

awards()

Exercise References -- References

Bibliography

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