In rotterp/RTutorOnlineDisclosure: RTutor problem set RTutorOnlineDisclosure

Information Asymmetry and Online Disclosure: An interactive analysis with R

Author: Patrick Rotter

< ignore

library(restorepoint)
# facilitates error detection
#set.restore.point.options(display.restore.point=TRUE)

library(RTutor)
library(yaml)
#library(restorepoint)
setwd("C:/Users/patri/Google Drive/UNI/90_Thesis/Bachelor/OnlineDisclosure")
ps.name = "RTutorOnlineDisclosure"; sol.file = paste0(ps.name,"_sol.Rmd")
libs = c("ggplot2", "devtools", "foreign", "gridExtra", "dplyr", "dplyrExtras", "data.table", "lfe", "stargazer", "regtools","svgdiagram", "fitdistrplus", "logspline")
#name.rmd.chunks(sol.file) # set auto chunk names in this file
create.ps(sol.file=sol.file, ps.name=ps.name, user.name="YOUR_NAME",libs=libs, stop.when.finished=FALSE,extra.code.file="init.R",var.txt.file = "variables.txt",addons="quiz",use.memoise=TRUE)

# This function creates a skeleton for your problem set package
rtutor.package.skel(sol.file=sol.file, ps.name=ps.name,libs=libs,
    pkg.name="RTutorOnlineDisclosure",   # Name of the problem set package
    pkg.parent.dir = "C:/Users/patri/Google Drive/UNI/90_Thesis/Bachelor/OnlineDisclosure", # Parent directory
    author="Patrick Rotter", # Your name
    github.user="rotterp",     # Your github user name
    extra.code.file="init.R", # name of extra.code.file
    var.txt.file="variables.txt",    # name of var.txt.file
    overwrite=TRUE  # Do you want to override if package directory exists?
  )

show.shiny.ps(ps.name, load.sav=FALSE,  sample.solution=TRUE, is.solved=FALSE, catch.errors=TRUE, launch.browser=TRUE)
stop.without.error()

>

This problem set analyses information asymmetries between a sellers and possible bidders in used good auctions. It sheds some light upon how to prevent information asymmetries by disclosing as much information as possible online. The entire problem set is developed from the paper "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors", written by Gregory Lewis, published in 2011 in the American Economic Review 101(4). You may download the paper from aeaweb.org/articles?id=10.1257/aer.101.4.1535 to get more detailed information. On the same webpage, the whole dataset utilized for the initial analysis in the paper, as well as the Stata Code are provided. This problem set uses a condensed version of the original data, which may be downloaded here: github.com/rotterp/RTutorOnlineDisclosure

Concerning the problem set, there is no need for solving the exercises in a given order. Yet I highly advise you to do so, as exercises become trickier and challenging or may expect some previously gained knowledge to solve them. A plethora of tasks will already be solved to circumvent repetitive assignments. Also, keep in mind, that you won't need any R knowledge at all, although some basic statistics software or programming knowledge may be of advantage.

Exercise Content

1. Overview

2. Descriptive Statistics

3. Hedonic Regression Model

3A. Hedonic Regressions A

3B. Hedonic Regressions B

1. Endogeneity

2. Online Disclosure and its Costs

5A. Linear Fixed Effects Regression with IV

5B. OLS and IV

1. Text Coefficients

2. Conclusion

3. References

4. Appendix

Exercise 1 -- Overview

This problem set analyses the effect of asymmetric information, adverse selection and online disclosure in the automobile market. Therefore, online auctions hosted by eBay Motors back in the time the largest market place for second-hand cars in the US were analysed. It is puzzling, that the whole business seemed to run well and thus one could probably assume, that information asymmetries had little to no effect on the trading volume. Even though we probably would have suspected them to do so, as there was no way to inspect the good pre-buying. The latter sentence is perfectly resembling the findings of Akerlof (1970) and his so-called 'Lemons problem'. Akerlof stated two possible outcomes in the event of a seller having better information about the quality of her product sold than a hypothetical buyer: firstly, if the asymmetry prevails high quality cars won't be sold anymore and the volume of transactions will drop below the social optimum. Secondly the inefficiency must vanish, e.g. a third-party could intervene and guarantee for quality with a certificate. Bond (1982) tested Akerlof's findings with used and new trucks. He found, that by controlling for age and mileage on maintenance, there seemed to be no difference between used and new trucks sold. Thus, his findings showed no support for Akerlof's first statement. Yet his results could support Akerlof's second thesis, meaning that either there was another institution involved, or the information asymmetry was eliminated otherwise. The paper of Gregory Lewis tries to shed light on the fact, why obvious information asymmetries - concerning for example the condition of the car, which can only be judged ex post - seem to be neglectable small. To show this, the paper utilizes the amount of photos posted by the seller as a proxy of quality and information. Videlicet due to describing the cars condition very diligently in the listing via text and the usage of certain key phrases, like rust, dents or scratches, the information asymmetry vanishes. If the latter plays indeed a role, disclosing information online is almost as good as inspecting the car personally and the overall good performance of the automobile market can be explained, the author argues.

Moreover, it is also quite easy to auction off cars on eBay Motors, as listings are easily created and only a small fee is taken by eBay. This makes auctioning off cars on eBay Motors very convenient, as all a possible seller must do is enlist his car. He doesn't need to show somebody around or even worry about his car being properly advertised. Furthermore, creating a nice auction can also be easily simplified by using third-party software applications like "carad", "auction123" or "eBizAutos". Other than that, you are also free to create your own template of choice. Even though creating a custom template is more time consuming, chances are high, it is also more rewarding in return. As disclosing your private information as a seller seems to be a huge aspect and eBay lets you do so by providing photos or text describing the condition of your car for a minimum fee, we will also try to elaborate on disclosing costs. Especially, whether they play a role when listing cars. Nevertheless, for now we assume that, if a seller describes his car as precisely as possible information asymmetries should be neglectable small. Thus, they do not intervene with the result of the auction. Yet this means contracts have to be valid and disclosure costs should be appropriate, otherwise the market won't be efficient. Both latter conditions hold true, as there is little to no difference entering a contract online or personally and an additional photo cost approximately US\$ $0.15$.

The results of the paper support the evidence, that photos provided by the seller appears to be significant covariates regarding the price and online disclosure indeed seems to influence the degree of disclosure. And thus, on the auction price itself. We will elaborate on this in more detail in later exercises of this problem set.

Let's first dig into our dataset. We will be utilizing the same data for the entirety of this problem set. The data cleanedebay.Rds is just an extract of the original data used by the author of the paper. Yet it comprises all variables needed. In fact, the data holds $67$ variables and $106,559$ observations of finished second-hand car auctions from March to October 2006. Before we can work on it, we have to load the data into our environment. If you are completely new to either programming or statistical software, feel free to always refer to the info boxes, which contain step-by-step instructions on analysing our data. In addition, you may always consult the hint button inside a task for further tips and tricks. If, however, you seem to be unable to solve a given task, just refer to the solution button, which will present you the code needed to solve the task. Whenever you're done with a given task procced with check.

< info "readRDS()"

The function readRDS() is a powerful base R function. It is a fast way to read .Rds files in R. We assign the output to our variable data. In future tasks, we will only have to refer to this variable, when using our data. The readRDS() function is pretty simple and for our purpose takes a single argument only. In quotation marks we state the name of our file cleanedebay.Rds. You may also adapt this argument to fit a full path ('C://.../'), if you stored the data to a different location on your personal computer.

If you want to learn more about which types of output files may be generated in R, have a look at this tutorial: sthda.com/english/wiki/saving-data-into-r-data-format-rds-and-rdata.

# Assign our data set to the variable 'data'
data = readRDS("cleanedebay.Rds")

>

To get you started, the first task will be rather simple. Please proceed with edit and then enter your code.

Task: Use the function readRDS() to read in the downloaded data set cleanedebay.Rds. After having read in the file, we want to assign the latter function to the variable data. To check whether you did everything right, proceed with check.

For any further advice, press the hint button. This will provide you with either additional information about your given task, or parts of the solution. If, however, you seem to be unable to solve the task with the provided information, proceed with solution. This will paste the solution code in your command line. You may then confirm with check.

#< task
# Enter your Code below

#>
data = readRDS("cleanedebay.Rds")
#< hint
display("The solution is given by the info box above.")
#>

< award "opening bid"

You successfully solved your first task, let's treat this as your opening bid. As we all know opening the auction with a bid is far off from being an auction winner. To receive the winning bid, you must solve all tasks. Good Luck!

>

We have now successfully loaded the data from our flat file to R and can start working with it. This exercise will focus on showing you how to operate on the data.frame data, as well as which variables data contains. This is a pure introduction with a little twist in the end, showing you that not everything is as obvious as it might seem at first glance. The goal for this exercise is to acquaint yourself with the dataset and not analysing it. We shift the analysing and deducing part to the following exercises.

Let's look at the basic structure. In our dataset, a row corresponds to a single auction, while each column corresponds to a variable for this specific auction. Our variables are containing relevant information like our winning bid, the total number of bids, the carmodel and so on. To get an overview of all variables we utilize a function called glimpse() from the dplyr package. Packages are mostly user contributed content, with useful functions.

< info "glimpse()"

The function glimpse(), which is part of the dplyr package, is the first non-base function we are going to utilize in this problem set. Thus, we have to load the package dplyr first, we can do so using library(dplyr). Note that this time there is no assignment to a variable made, which results in our output being printed to console. The function glimpse() will give us a neat overview over all variables contained in the applied dataset. It takes data as an argument and its output is a formatted table with the generic datatype of each variable, as well as an excerpt of example data for each respective variable.

library(dplyr)

# glimpse(dat)

For further information about glimpse() you may want to head over to cran.r-project.org/web/packages/dplyr/index.html.

>

Task: Use the function glimpse() to get a rough overview over all variables in the dataset.

#< task
# Enter your Code here
#>
glimpse(data)
#< hint
display("Check the info box above, the solution is already given.")
#>

This is quite a nice and convenient way, to acquaint yourself with the dataset data at hand. As we already know, the dataset contains a total of $106,559$ auctions and $67$ variables. Let's have a look at our first variable membersince. Next to the name of the variable, there is a <fctr> statement. This means our variable membersince was erroneously interpreted as a factor variable. Factor variables are categorical variables which hold limited values for example 1-3, while each value corresponds to another distinct meaning. We can easily conclude though, that a date format seems more appropriate for this variable. So you could correct this by referring as.Date(data$membersince, format = "%b-%d-%y") if you're within the US or Great Britain to adapt the data type. Yet this is not important for this problem set and therefore completely optional. There are other variables of interest we want to get to know right away though:

Some of the more important variables are part of this table, yet there are many other self-explaining variables like trans,model, bookvalue and so on, which we will be utilizing at later stages of this problem set.

Variables	Meaning
n	Total number of unique bidders.
numbids	Total number of bids.
photos	Total number of photos
software	Corresponds to the software utilized to create the listing. For example 'ebayhosting' means, that no third-party application was used.
biddyX	Total bid amount in US$ in descending order, which means that biddy1 equals the highest bid of the auction.
relist	Factor variable, which takes either '1' or '0' as a value. A value of '1' corresponds to the car being relisted at least once, while a '0' signals, that it is the first attempt to sell the car

Other than this table, you may have a look at the whole dataset in table format at any point of time, if you click on data, or change the actual tab from 1 to Data Explorer. You will soon notice though, that as our dataset comprises $67$ variables and $106,559$ observations, the glimpse() function in the latter exercise provides a very good overview already. Nevertheless, any datasets and subsets of data, which we are going to use for the remainder of the problem set can be accessed by the Data Explorer. So, don't hesitate to look there occasionally. If you are uncertain about a variable's meaning, you may also consult the Data Explorer: if you hover over a column name, a tooltip with additional information about the respective variable will be shown.

Now let's dig deeper into data. For sub setting our dataset of any kind we're going to stick to the dplyr package, which is very convenient to work with. For dplyr starters take a look at the info box below, which explains in detail how to subset our data.frame data.

< info "dplyr"

The dplyr package offers a variety of possibilities to subset data. However, we are going stick with the simplest syntax. Let's start by selecting specific columns of our dataset. The following commands will select a subset of your data.frame data, which contains only the variables sellername, biddy1 and sell. The result will be the eBay alias of the seller, the winning bid and information with regards to if the car has been sold, as there might have been a reserve. You can check this for yourself, including the variable reserve.

library(dplyr)

# select(dat, highbiddername, biddy1, sell)

Other than that, we can also subset our data by rows matching certain criteria. The following code will take all columns and identify those auctions with cars, which have never been listed before, starting with an initial startbid of over US\$ $10,000$ and cars with manual transmissions only. The latter being very unlikely in the US, as automatic transmissions are highly more probable. We are separating all our conditions with an & operator, this means these criteria must be met. At a later point of this problem set you will be introduced to the pipe operator | which corresponds to an OR-statement, meaning not all our conditions have to hold true.

library(dplyr)

# filter(data, startbid > 10000 & trans == "Manual" & relist == 0)

The following code will introduce you to the famous pipe operator syntax %>% utilized by dplyr. Please don't get confused with the pipe operator |, well known in informatics overall. They just share their name, as both work completely different. The latter notation allows you to start with your data.frame data and then narrow it down further with other dplyr functions. The given code basically looks for every observation which is a relisted collectible car, meaning by the paper's definition it has been produced before 1980. On this subset of data, it looks for the age column and then groups the results by model and year. If you run this code, you will notice that Camaros from all years, seem to be real shelf warmers.

library(dplyr)

# data %>%
# filter(collectible == 1 & relist == 1) %>%
# group_by(model, year) %>%
# select(age) 

Finally we extend the syntax from above with an arrange statement, to do this, we first ungroup() and use arrange(-age) afterwards. The code below will order the now ungrouped subset descending by age. If you want to order ascending, removing the '-' is sufficient. Our results can be interpreted as follows: The oldest collectible cars which have been enlisted were 53 years old.

library(dplyr)

# data %>%
# filter(collectible == 1 & relist == 1) %>%
# group_by(model, year) %>%
# select(age) %>%
# ungroup() %>%
# arrange(-age)

For further information have a look at the introduction vignette: cran.rstudio.com/web/packages/dplyr/vignettes/introduction.html.

Note, that the same steps as above could have been achieved by the data.table package. Yet the 'call by value' feature of data.tables might be a bit puzzling at first, so for starters we are sticking to the simpler alternative, using dplyr. If you want to acquaint yourself with another syntax, there is another vignette, you might want to have a look at: rawgit.com/wiki/Rdatatable/data.table/vignettes/datatable-keys-fast-subset.html.

>

In the following tasks, we are going to have a closer look at certain excerpt of our data. In fact, we want to know more about Honda Civics fulfilling certain conditions. This will make you familiar with dplyr, so you can do the data manipulation part on your own from exercise 2 on. Furthermore, we want to have a look at the relation of our winning bid, the amount of photos and the overall condition of the Civic and see if we can already deduce something.

Task: Subset data to match the following criteria: The model we are looking for is a Honda Civic, built between 2000 and 2002. All cars matching the previous condition were sold on first attempt. Furthermore, the odometer holds between $30.000$ and $35.000$ miles and the seller posted photos. To make it easier, parts of the code are already given.

#< task
filter(data, model == "Civic" & is.na(photos) == FALSE & miles >= 30000 & miles <= 35000)
#>
filter(data, relist == 0 & sell == 1 & is.na(photos) == FALSE & year >= 2000 & year <= 2002 & miles >= 30000 & miles <= 35000 & model == "Civic")
#< hint
display("Check the info box above and be aware of, that 'startbid <= 1000' will limit the observations to those having a starting bid less or equal to 1000 US$.")
#>

These are still quite a few of observations, and due to the many variables, there is still not much information gained. Let's try to narrow our observations down further, by selecting only certain variables. Keep in mind, dent_group, scratch_group, as well as rust_group are categorical variables based on dummy variables from the original mined data. You can read more about this topic in the paper itself. Following values are possible:

Group	Value	Meaning
rust_group	0	The seller did not mention rust in his description. This is the omitted value and won't be part of our statistics.
rust_group	1	Corresponds to a negation of rust, i.e. the seller stated there is no rust, or something similar.
rust_group	2	Positively qualified mention, i. e. the seller stated there is very little to no rust, or something similar.
rust_group	3	Unqualified mention, neither good, nor bad. For example the seller stated the word rust, but didn't provide more information.
rust_group	4	Negatively qualified mention, i.e. the seller stated there is lots of rust.

The other groups behave accordingly to the explanation above.

Task: Select all of the following columns from data: dent_group, scratch_group, rust_group, as well as biddy1, which equals the highest bid, photos, model, year, miles, age, text and n. n is the total number of bidders, who participated in the auction.

#< task
# Enter your code here
#>
select(data, model, year, biddy1, photos, text, miles, n, age, dent_group, scratch_group, rust_group)
#< hint
display("The info box above should give you a reasonably good idea how to solve this task.")
#>

Did you notice the difference between this and the previous task? This time, we are back to using our complete dataset data, with only a handful of variables we are interested in, but other than recently we didn't use any conditions on our auctions to narrow down our results. Thus, we get model, year, miles, age, text and n, as well as the groups for every single auction. To put it in other words, it is still not clearly structured, as we either have too many variables at hand, or too many observations. To tackle this problem, let's now put both those statements together and extend the syntax a little bit, by grouping and ordering our results. This will return a small table containing interesting information.

Task: Using the results of the previous two tasks, we now want to extend the code further. Please extend the select() and filter() statements from previously to order our resulting table descending by biddy1, which again equals the highest bid.

#< task
# Extend the code below
data %>%
  filter(relist == 0 & sell == 1 & is.na(photos) == FALSE & year >= 2000 & year <= 2002 & miles >= 30000 & miles <= 35000 & model == "Civic") %>%
  select(model, year, biddy1, photos, text, miles, n, age, dent_group, scratch_group, rust_group)
#>
  data %>%
    filter(relist == 0 & sell == 1 & is.na(photos) == FALSE & year >= 2000 & year <= 2002 & miles >= 30000 & miles <= 35000 & model == "Civic") %>%
    select(model, year, biddy1, photos, text, miles, n, age, dent_group, scratch_group, rust_group) %>%
    arrange(-biddy1)
#< hint
display("Copy & paste the following statement: data %>% 
        filter(relist == 0 & sell == 1 & is.na(photos) == FALSE & year >= 2000 & yea <= 2002 & miles >= 30000 & miles <= 35000 & model == \"Civic\") %>%
        select(model, year, biddy1, photos, text, miles, n, age, dent_group, scratch_group, rust_group) %>%
        arrange(-biddy1)")
#>

< award "dplyr rookie"

You know have basic knowledge how to work on data the dplyr way! Congratulations!

>

Let's first summarise our results: we are looking for Honda Civics, built between 2000 and 2002, with $30,000$ to $35,000$ miles on the odometer. These cars must be sold on first attempt, which is a possible proxy for filtering out any effects of possible buyers bidding in multiple auctions. If we take a closer look at our resulting table, first off, we can identify, that for this subset of our dataset, neither dents, nor scrapes and the occurrence of rust seem to have an influence on the highest bid, as all groups have a value of $0$. We remember though, that the paper suggested photos as a way of measuring the amount of online disclosure. All cars should be virtually identical in their condition, as the deviation in age and miles is minimal in this scenario. Nevertheless, the number of bidders could also play a role and indeed, the range of bidders from auction to auction is quite different. If we compare auction 4 with auction 3 the amount of photos and the total miles is almost identical, yet in auction 4 only a single bidder took part, while on the other hand in auction 3 a total of 7 unique bidders took part in the auction. We will examine the number of bidders as a possible reason to explain for a higher price at a later stage in this problem set in more detail. For now, let's come back to our photos, if we compare auction 1 to auction 5, the winning bid in auction 5 with US\$ $7800$ is much lower than the US\$ $9100$. Comparing only those two auctions, the difference in photos posted by the seller is quite striking, so we could assume that photos indeed play a huge role in explaining the difference in the winning bid as well. Keep in mind, each respective car should be homogenous, as it differs just slightly in its age and miles. This leads us to our final task of this exercise, or rather first quiz of our problem set.

< quiz "Understanding your data A"

question: 1. Based on the previous table, can we conclude, that photos influence the actual bid amount? sc: - yes - no* success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

< quiz "Understanding your data B"

question: 2. Could the number of unique bidders n, for example due to missing competition be a possible variable in explaining biddy1? sc: - yes* - no success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

Summary

We cannot yet deduce from our table above, that photos seem to have a significant effect on the amount our bidders are willing to pay, the sample size is just too small and the data was gained by filtering very strictly for a good example. Even though it doesn't support our hypothesis from the overview. It is also very important to note, that it doesn't decline it either. And indeed, there seems to be a link between the amount of photos posted by the seller and the highest bid. Yet this could also be due to higher participation in this auction, or other omitted variables and thus endogeneity. We will have a look on regression prerequisites and answering the latter questions in the following exercises.

Exercise 2 -- Descriptive statistics

Task: The first task of the exercise will almost every time be the same, as it is necessary to load the dataset in each exercise. The following chunk of code resembles the readRDS() statement from exercise 1 and is already given to you.

Please proceed with edit and immediately check afterwards to proceed with the following task.

#< task
data = readRDS("cleanedebay.Rds")
#>

Before introducing the hedonic regression model and starting with the regressions, we want to first gain some more information about the cars being auctioned off on eBay Motors. The result of this exercise will resemble a table from the paper which will give some nice insights into the overall condition of the cars for the whole sample, as well as possible differences between private sellers and professional dealers. Moreover, during this exercise, you will acquaint yourself with most of the needed variables for our future regressions, which makes summary statistics a perfect start for understanding the underlying data.

To skip repetitive tasks without gaining further knowledge, the second exercise has been solved already. We want to drop most of our unnecessary variables at this point and store our resulting ones in a data.frame to the variable dat. Operating on subsets of data will speed up the processing and calculating part in R by quite a margin, as we drop unnecessary variables. In further exercises we will also learn new ways to do this, e.g. we can use felm() to subset data in accordance to our analysis.

Task: Following code will restrict our data stored in the variable dat to the important variables for this exercise. Please confirm with check to solve this and proceed with the next task.

#< task
dat <- select(data, dealer, miles, age, trans, warranty, options, photos, relist, sellfdback, negpct, minbid, posbid, sell, biddy1, rust, rust_negation, scratch, scratch_negation, dent, dent_negation)
#>

The variable dat holds the same number of auctions as data from the previous exercise, yet we do not have all our $67$ variables anymore, instead we are going to stick to just $20$ variables. This will speed up plotting our data as well as making it easier to calculate summary statistics, as we do not want to calculate summary statistics for each variable in cleanedebay.TXT. To get you started, the first exercise is again rather easy and introduces you to some additional basic R functions. Let's start with the function mean(). To learn more about mean(), please check the info box below.

< info "mean()"

The function mean() will take mostly any format as a valid data and will then proceed to calculate the arithmetic mean of this variable. Keep in mind if you give a data.frame you have to specify the variable, which you want to calculate the mean of. To get access to a single variable of a data.frame it is best to you use the '$ notation', data\$age will return a vector of age and its generic datatype.

Do not forget to enable na.rm = TRUE as second parameter, as otherwise no mean will be calculated if it happens, that you are missing data for certain observations.

# mean(dat$age, na.rm = TRUE)

To get a good overview regarding basic R statistics, have a look at cran.r-project.org/doc/contrib/Torfs+Brauer-Short-R-Intro.pdf. for a very short introduction to basic R. You may also find information concerning other useful functions like max(), min(), summary() and so on if you head over there.

>

Task: Referring to dat as our new underlying dataset, calculate the mean of sell.

#< task
# Add your code below
#>
mean(dat$sell, na.rm = TRUE)
#< hint
display("Check the info box above for further advice.")
#>

Our result of the previous task is $0.2842463$, but how do we interpret this? If you have taken a close look at the variable sell during the first exercise, you will have noticed, that sell takes only two different values, $0$ and $1$. Thus the mean() function calculates a percentage in favour of $1$. This means, over all values of sell, we currently have ~$28.4\%$ chance of sell being $1$. This only works though, as R interprets the data type of our variable sell in our Rds file cleanedebay.Rds. You may verify this, either through the usage of the function class() or you can look the variable sell up, after having used glimpse(). Due to being an integer, R recognizes the values as being numeric and calculates a mean. If sell was set as a factor instead, R would not do this. Remember, the variable sell holds the information if the car has been sold in this auction, a value of $1$ corresponds to the car having been sold, a value of $0$ corresponds to an unsuccessful auction. Hence, if we know, how both values are distributed, the mean equals the percentage, how many cars have been sold.

First, let's verify that our result is indeed correct and sell is indeed a integer, using another R base function.

Task: Take a look at the possible values, the variable sell may take, using the function unique().

#< task
# Add your code below
#>
unique(dat$sell)
#< hint
display("Check the infobox above for further advice.")
#>

We see, there are indeed just two values the variable sell takes. Let's now try to answer the following question, please be aware, that multiple solutions might be correct.

< quiz "basic statistical knowledge"

question: Based on your previous task, what are we save to say about the variable sell and mean(sell)? mc: - A total of 28.4% of all cars have been sold. - A total of 28.4% of all cars have not been sold. - Approximately 28,000 cars have been sold. - Approximately 28,000 cars have not been sold. - The variable sell indicates that more than 2/3 of all auctions are unsuccessful, resulting in no car being sold in our analysis period. success: Congratulations, everything was correct! failure: Unfortunately, this was wrong. Try again!

>

It is quite striking, that most auctions seem to not payoff for the seller, so one could assume as our sample is limited in time, there might be a lot of relisted cars in our sample, but in fact only about $22.6\%$ of the cars are being relisted, and this value is not yet adjusted for multiple relisting. Thus, the data is very small and no analysis was conducted to find out, whether changes of the latter might result in a car being sold. Let's now proceed with gaining some more information about our data, without referring to multiple mean() functions. There are quite a lot of possibilities to choose from, yet to show our result in a nicely formatted table, we want to make use of the package stargazer. As data explorers are lazy, I provided you with a function called tab.summary(). Check the info box below, which will introduce you to stargazer. Afterwards there are more tasks, to get to know the data.

< info "stargazer()"

The function stargazer(), which is part of the package stargazer creates nicely formatted outputs from regressions or simple statistics in either LaTeX, HTML or ASCII format. As we are going to utilize stargazer() for all subsequent regressions as well, it is nice to get an inkling in regards to the possibilities this function offers.

# library(stargazer)
#
# stargazer(data,
#           title = "Summary statistics",
#           align=TRUE,
#           type = "text",
#           style = "aer",
#           digits = 2,
#           digits.extra = 0,
#           df = FALSE,
#           report = "vct*",
#           star.cutoffs = c(0.05, 0.01, 0.001),
#           object.names = TRUE,
#           model.numbers = FALSE,
#           omit.summary.stat = c("n", "max", "min", "sd"),
#           omit.stat = c("adj.rsq", "f", "ser")
#           )

Do not worry, you won't need to remember the options for stargazer, in fact, please use the function tab.summary(), which takes as argument one or more data.frames. This will make it much easier for you. You may have a look at the syntax of tab.summary() below

tab.summary = function(.dat1, .dat2=NULL, .digits = 2){

  library(stargazer)

  stargazer(data.frame(.dat1),
            data.frame(.dat2),
            title = "Summary statistics",
            align=TRUE,
            type = "text", 
            style = "aer",  
            digits = .digits,
            digits.extra = 0,
            df = FALSE,
            report = "vct*",
            star.cutoffs = c(0.05, 0.01, 0.001),
            object.names = TRUE,
            model.numbers = FALSE,
            omit.summary.stat = c("n", "max", "min", "sd"),
            omit.stat = c("adj.rsq", "f", "ser") 
  )
}

To apply the function tab.summary(), see the following example, which creates a table for dat1 and dat2, specified in the parenthesis of tab.summary()

#   tab.summary(dat1, dat2)

For more information regarding stargazer, have a look at cran.r-project.org/web/packages/stargazer/stargazer.pdf. for the stargazer vignette.

>

Let's now put our newly gained knowledge to the test.

Task: The code below will create a nicely formatted table for our subsetted data of the first task of this exercise. The code has already been provided, so you just need to proceed with check.

#< task
# Proceed with check
tab.summary(dat)
#>
#< hint
display("Just proceed with check, as the code is already given to you.")
#>

Let's summarise our findings as following: the average car's odometer posts about $90,180$ miles, which is equivalent to approximately $145,130$ kilometres. Cars furthermore are on average around $16$ years old and only $19\%$ are still under warranty Furthermore, on average there are around $17$ photos complementing the listing. The variable minbid means that the minimum bid is around $52\%$ of the book value and for $85\%$ of all cars, there was at least one bidder taking part in the auction. The variables rust, scratch and dent mean that, for example in $19\%$ of all our listings the phrase rust was used and in more than half of these cases, any appearance of rust was negated by the seller.

< quiz "Quick check"

question: Based on our previous table with results, which answers are correct? mc: - In 16% of all auctions, the word dent was used. - In more than half of the auctions, the word dent was used and the seller negated any existence of dents. - On average a car being auctioned off has about 5 features, like AC, radio, etc. - We can only tell, if dents are mentioned in a positive or negative way. success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

This quiz was a little bit challenging. Nevertheless, it is important for you to understand. From the latter statistic alone, we cannot tell, how our cars' overall conditions look like, as we would have to look at the rust_group, dent_group and scratch_group variables instead. For the moment, we can only identify positive mentions, but not how bad the dents are. It could just be a very minor dent for example. We will have a closer look at this in a later exercise, where we are going to interpret with the help of our predefined groups.

Let's now divide our dataset in private sellers and dealers and look if there are obvious changes regarding the cars' conditions.

Task: Please adapt the code, with your previous knowledge of the first exercise in a way that as a result we have a single table, displaying the same statistics for professional dealers and private sellers separately.

#< task
# tab.summary()
#>
tab.summary(filter(dat, dealer == 0), filter(dat, dealer == 1))
#< hint
display("For further advice check the stargazer() info box.")
#>

The interpretation is identical to before, most noticeably, private sellers seem to offer older cars, which also results in more miles Furthermore if a car is being auctioned off by a private seller, the car is less likely to be under warranty and the amount of photos provided by private parties is also significantly smaller. Yet there are so many factors coming into play, that we cannot distinguish for now, which ones are more important to us than others. In the next exercise, we are going to estimate which variables account for changes in our winning bid biddy1, which is our most important goal for this problem set.

To foster your understanding of this exercise let's calculate some easy maths.

< quiz "Spotting differences"

parts: - question: 1. What is the average highest bid, a private seller receives for his car? answer: 9173 roundto: 0.01 success: Congratulations, all your answers are correct! failure: Unfortunately, not all answers were correct. - question: 2. Comparing dealers to private sellers, what is the difference in photos provided? answer: 9 roundto: 0.01

>

< award "Keen eye"

You seem to have a proper power of observation. Keep this up for the entirety of the problem set.

>

To finish this exercise, we want to visually analyse our core issues, before we head into our regression model. To do so, let's recap our results shortly. We will use a vector of possible covariates to explain our winning bid biddy1. In the following exercise, we will have a look at two of them, namely miles and photos. While only photos will foster our understanding of our core issue regarding online disclosure and information asymmetry, it's nice to see as a comparison how the total amount of miles influences our winning bid. It is only natural to assume, that a high amount of miles will lower the return of the seller, but how does the amount of information disclosed influence the latter?

Task: The solution is already given to you. Please proceed with edit and immediately check afterwards. Even though the following code chunk is quite long, it should also be fairly easy to read and understand. We are going to create a new variable called mgroup which groups our miles in intervals. This is easily done with the help of the cut() function.
We repeat this step for our photos and afterwards we create two plots, both having our logarithmic winning bid biddy1 on the ordinate axis and miles and photos respectively on the abscissa.

#< task
dat$mgroup <- cut(dat$miles, 
                  breaks = c(0, 50000, 100000, 150000, 200000, 250000, 300000, 350000, 400000, 450000, Inf), 
                  labels = c("[0,50k]", "(50k,100k]", "(100k,150k]", "(150k,200k]", "(200k,250k]", 
                             "(250k,300k]", "(300k,350k]", "(350k,400k]", "(400k,450k]", "(450k,inf)"),
                  right = FALSE)

dat$pgroup <- cut(dat$photos, 
                  breaks = c(0, 5, 10, 15, 20, 25, 30, 35, Inf), 
                  labels = c("[0,5]", "(5,10]", "(10,15]", "(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,inf)"),
                  right = FALSE)
#>

Task: The solution is already given to you. Please proceed with edit and immediately check afterwards. The following code will create the first plot, showing how our winning bid behaves conforming to our miles intervals. Remember the intervals are increasing in steps of $50,000$ miles.

#< task
library(ggplot2)

ggplot(dat, aes(mgroup, log(biddy1))) +
  geom_bar(aes(fill = as.factor(mgroup)), position = "dodge", stat="identity") +
  labs(title = "Plotting winning bid on miles") + 
  labs(x = "miles", y = expression("log " * biddy[1])) +
  theme_bw(base_family = "Helvetica") +
  theme(legend.position = "none", axis.text.x = element_text(size  = 10, angle = 45, hjust = 1, vjust = 1)) 
#>

We see that miles behave as expected, the more miles, the lower the winning bid becomes, yet it is easy to spot, that there is quite some noise to this, as vehicles with a high mileage - to be more exact in our case more than $350,000$ miles - are sold at exceptionally high price. This is largely due to a very big outlier and the amount of collectible cars in this group.

Task: The solution is already given to you. Please proceed with edit and immediately check afterwards. The following code will create the second plot, showing how our winning bid behaves conforming to our photo intervals. Remember the intervals are increasing in steps of five.

#< task
ggplot(dat, aes(pgroup, log(biddy1))) +
  geom_bar(aes(fill = as.factor(pgroup)), position = "dodge", stat="identity") +
  labs(title = "Plotting winning bid on photos") + 
  labs(x = "photos", y = expression("log " * biddy[1])) +
  theme_bw(base_family = "Helvetica") +
  theme(legend.position = "none", axis.text.x = element_text(size  = 10, angle = 45, hjust = 1, vjust = 1))  
#>

For the second plot the result might be puzzling at first sight, and there is no obvious explanation for this. We see that our winning bid increases with the amount of photos provided by our seller, yet upon reaching a value of 4, which is equivalent to $20$ photos posted, the winning bid seems to go back to our previous level. It would be rational to expect the winning bid biddy1 to stagnate at some point, as you can only show your car's condition up to a certain extent. Nevertheless, this doesn't seem to be the case here, as more photos seem to lower the price again. This could either be due to the seller providing too many photos and thus eventually depicting the bad condition of his car in exact detail, or be car related. It's impossible to say.

Summary

We see there seems to be quite a difference regarding the cars' conditions. The second-hand cars from dealers, do not only have less miles, they also seem to provide substantially more photos. Also, on average, they receive a higher winning bid. Participation appears to be alike in both settings, while cars under warranty are much more probable for dealers, private sellers usually relist less and have a higher chance of selling the car.

Aside from that, it's difficult to pinpoint what exactly drives our price for now, as there are too many variables at stake we didn't take in consideration.

Exercise 3 -- Hedonic regression model

Before heading further into the analysis of our data, let's first look at our literature. The paper is based in parts on Milgrom (1981) as well as Grossman and Hart (1980). In these papers, they deduct a disclosure model in which it's always best to fully disclose all possible information. As lacking information, should be treated negatively. This indeed makes sense, as if there is no information provided by the seller in the listing, a possible buyer will probably neglect to bid. This is caused by the lack of information available in regards to the car's condition, which is being sold. Due to this one-way information asymmetry for the bidder, he will completely abandon the auction, or lower his own maximum bid amount. Another possible solution to this, would be a scenario, in which a possible bidder asks questions and therefore forces the seller to disclose more information about certain topics, he didn't disclose in the first place. Keep in mind, all information provided by the seller may be regarded as part of the contract. If the car violates its description, the bidder might resign from the contract.

We therefore follow their model and suggest the seller to disclose all information and thus no information asymmetry should prevail.

To start of our regressions, it's time to introduce our hedonic regression model in accordance with Sopranzetti (2015). Our model looks as follows:

$$p_t \textrm{ is the price in auction t, or in other words, the winning bid } biddy_1$$

$$x_t \textrm{ is a vector with the cars characteristics from the listing}$$

$$\beta \textrm{ is the coefficient of regression}$$

$$t \textrm{ is a single auction}$$

$$\epsilon_t \textrm{ is the error term}$$

$$log(p_t) = x_t * \beta + \epsilon_t$$

Or explicitly in matrix notation, dropping the t indices:

$$log(biddy_1) = \begin{pmatrix}log(miles)\ photos\ photos^{2}\ options\ log(sellfdback)\ negpct \end{pmatrix} \cdot \beta + \varepsilon$$

This is basically the standard linear model, yet attempting to remove 'hedonic' features - which a consumer might prefer - from the price of the car. If one looks at pricing regressions, hedonic regression models are likely to be used, as this enables statistical modelling based on product characteristics - like warranty, age of the car, overall condition and so on - alone, unbiased by personal preferences. In the case of our model $x_t$ will be our vector comprising a set of features at time t, extracted from the listing.

Next we want to fit our variables to a linear model and start with our regressions.

Exercise 3A -- Hedonic Regressions

We introduced our hedonic regression model in exercise 3, yet for your convenience, I'll provide it in this exercise as well.

$$log(biddy_1) = x_t \cdot \beta + \varepsilon_t$$

$$log(biddy_1) = \begin{pmatrix} log(miles) \ photos \ {photos}^2 \ options \ log(sellfdback) \ negpct \end{pmatrix} \cdot \beta + \varepsilon$$

Before we start with our regressions, please have a look at the info box below for further technical prerequisites in regards to performing linear fixed effects regression in R. To observe fixed effects, we are following in parts Arellano (2004), which is a good guide, when working with panel data in econometrics.

< info "felm() - part 1"

The felm() function is part of the lfe package and an abbreviation for fixed effects linear model. It is used to extract linear group fixed effects. In exercise 3 we got acquainted to our model: $log(p_t) = x_t * \beta + \epsilon_t$. Our goal is now to apply the latter formula utilizing the felm() function. Following our model we want to regress the logarithm of our price in auction t, $log(p_t)$, on a vector of car characteristics in auction t, $x_t$, which we will refer to as covariates. There are also some fixed effects, which we want to project out. For now, our fixed effects are carmodel, year and week. We will learn more about fixed effects later in exercise 3. Finally, there is also a possibility to cluster standard errors and to apply instruments to your linear regression. Last but not least, felm() has an integrated parameter, which allows us to subset our data utilized by the function, according to match a criteria we defined.

As we will come back to instrumental variable regression at a later point in this problem set, we are going to put a $0$ in our formula instead. This way felm() can correctly call the formula to not implement any instruments for our regression.

# library(lfe)

# felm(logp_t ~ x_t | fixed_effects | 0 | clustered_se , data=data, subset = c(variable == value))

For more information, have a look at cran.r-project.org/web/packages/lfe/lfe.pdf for the lfe vignette.

>

< info "I()"

The I() is a R base function, which takes a single object, in our case any factor variable, being part of our dataset data. To understand what the function does, we must clarify the term formula. In R a formula is a generic function which consists for the remainder of our problem set of 2 parts: a left-hand side (LHS) and a right-hand side (RHS), separated by a ~ statement. By looking at the above info box carefully, the following syntax might seem familiar to you already:

#   logp_t ~ x_t | fixed_effects | 0 | clustered_se

The whole statement is referred to as a formula - meaning the LHS p_t is regressed by the RHS x_t. Moreover | fixed_effects | 0 | clustered_se is also part of the formula. In this case, the pipe operator |, is not an 'OR' statement, as it might be in most of the other cases. This time it is applied to separate our different parts of the formula.

Let's come back to I(). If the function I() is applied inside a formula, it will treat the variables 'as is', meaning they are evaluated as they are and thus they are not being interpreted as part of the formula but as arithmetical operators instead. To illustrate this, we split up our vector x_t. The I(photos^2/100) will calculate the photos squared divided by 100 and put this value inside our formula.

#   logp_t ~ log(miles) + photos + I(photos^2/100) | fixed_effects | 0 | clustered_se

For more information, have a look at cran.r-project.org/doc/manuals/r-release/R-intro.pdf.

>

At this point we encounter the same situation as previously. We must load our dataset cleanedebay.TXT first. As this task is identical to the previous ones, the solution is already given to you.

Task: The following chunk of code resembles the readRDS() statement from exercise 1 and is already stated. Please proceed with edit and immediately check afterwards to solve the next task.

#< task
data = readRDS("cleanedebay.Rds")
#>

You are now ready to work with the felm() function on your own. Please proceed to conduct your first regression of this problem set.

Task: Using a call to the function felm() perform a simple linear regression. As this will be the first regression of this problem set, parts of the code are provided. Please use the previously defined vector x_t as your covariates. This means you must use the following variables: miles, photos, $photos^2$, options, negpct and sellfdback. Keep in mind, you might have to apply a logarithm for some of the variables and/or make use of the I() function.

#< task
# Adapt and uncomment the code below
#felm(log(biddy1) ~ ..., data = data)
#>
felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback), data = data)
#< hint
display("felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback), data = data) and proceed with check.")
#>

< award "First Regression modelled in R!"

Congratulations, you successfully solved your first regression of this problem set. Keep this up!

>

Let's have a quick look at our results: this first regression is still not completely modelled since we only want to get a feeling for the hedonic regression model. If we look at our covariates though, it is easily to spot, that our logarithmic miles seem to be the strongest coefficient. The magnitude of the coefficient and the negative sign imply the following: the more miles the car has on the odometer, the lower the price. This result fosters the intuition that miles are probably the first and most important thing a possible buyer has a look at, when deciding upon buying a car.

< quiz "Interpreting regression results 1"

question: Based on the previous regression, is the negative sign of negpct expected? mc: - yes* - no success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

We would expect any negative feedback a seller has received in earlier auctions to be a somewhat negative indicator concerning this seller. Thus, a possible bidder limits his bids, to avoid additional risk. To put this in an economic context: the seller probably auctioned off goods before and trivialised the poor condition his good was in, to jack up the price.

< award "Understanding regression results 1"

You now have a rough understanding of our first regression. In the following exercise, we will extend this model to our so-called base model which we will then use as our underlying regression model for most of our regressions in the whole problem set.

>

As for now, our results are only digits and it may still be somewhat troubling to identify the link between our winning bid biddy1 and our covariates, we want to show them graphically.

Task: The code is already given, so you just need to proceed with check. This chunk will create some nice plots, showing the relations in a more comprehensive way.

#< task
logdata <- filter(data, sellfdback >= 0, is.na(photos)==FALSE, is.na(negpct)==FALSE, is.na(biddy1)==FALSE)
ggplot(logdata, aes(miles, felm(log(biddy1)~log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback), data = logdata)$residuals)) + 
  geom_point(aes(color = felm(log(biddy1)~log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback), data = logdata)$residuals)) + 
  labs(title = "Plotting residuals on miles") + 
  labs(x = "miles", y = expression("log " * biddy[1])) +
  scale_x_continuous(labels = c("0", "100k", "200k", "300k", "400k", "500k")) +
  coord_cartesian(xlim = c(0,450000)) +
  theme_bw(base_family = "Avenir") +
  theme(legend.position = "none", axis.text.x = element_text(size  = 10, angle = 45, hjust = 1, vjust = 1))
#>

We can see that there seems to be no significant over- or underestimation. In fact, our data is well distributed, if we consider, that we expect less bids for absurd high amounts of miles on the odometer. Nevertheless, we can get an even smoother result, if we account for fixed effects. This means, there are variables, which are not yet part of our regression, indicating an over- or underestimation. To segregate them from our error term, we use a fixed effects regression where the fixed effect is within a specific carmodel, year and week. We will do this in conjunction with clustered standard errors to arrive at our final version of our base model.

Task: Extend the previous regression with our fixed effects, defined in task 4. It is basically the same formula as previously, yet the results are different, as we are going to project out fixed effects for carmodel, year and week. Assign the result to a variable called rega.

#< task
# Add your code below

#>
rega <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week, data = data)
#< hint
display("Check the info box felm() for further advice.")
#>

Now there is only one additional adjustment needed, before we achieve our base model: we extend our previous regressions with clustered standard errors by sellername, whilst still projecting out fixed effects for carmodel, year and week.

< quiz "Estimating regression results 1"

question: What do you think, which version of our base model has higher standard errors, clustered or non-clustered? mc: - clustered* - non-clustered success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

Task: The following task will store the base model to a variable called reg1 and compare the resulting standard errors from the clustered and non-clustered version of the base model. Just proceed with check, as the solution is already given to you.

#< task
# Proceed with check to look out regression results.
reg1 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data)

se.summary(rega$se, reg1$cse)
#>

We may conclude, that for the clustered version, standard errors seem to be much higher than for the non-clustered one. But what's the reasoning behind? There could be heteroskedasticity in our regression model, which means the variance of our error term $\epsilon_t$ is not constant. Yet we cannot directly observe our error term $\epsilon_t$, as this is the idiosyncratic taste of a bidder. Nevertheless, assuming heteroskedasticity is indeed a valid assumption, as a professional dealer is very likely to sell akin cars: if he has lots of expertise selling caravans, he most likely will not sell a muscle car all of a sudden, as he doesn't know this business very well. Heteroskedasticity thus will cause inconsistent standard errors. To tackle the latter problem, we clustered our standard errors by sellername, which concerning our data set, is the unique alias of the persona selling the car. A broader spectrum of heteroskedasticity is covered in Williams, Richard (2015).

Task: Let's now take a closer look at our regression results of our final base model, stored in the variable reg1. To do this, we apply the function summary(). Just proceed with check.

#< task
summary(reg1)
#>

Before interpreting our results, let's quickly recall our model as following:

$$log(p_t) = x_t * \beta + \epsilon_t$$

We want to regress the logarithmic value of our winning bid biddy1 on as-is, as well as on logarithmic values. This means our interpretation is somewhat different regarding which covariate we consider. Albeit the interpretation differs from logarithmic to non-logarithmic variables, both have one thing in common: we will always interpret our results under a ceteris paribus assumption, which means, we pick one variable of the right-hand side to explain the change in our winning bid biddy1, whilst holding each other covariates constant. For example, an increase of miles by $1\%$ - remember miles is a logarithmic value: log(miles) - causes our winning bid to decrease by $0.13\%$. This means, we can read our values as-is and the coefficient of $-0.1302630$ may be interpreted as elasticity. This leads us to our non-logarithmic variables. These must be interpreted differently, as we have to calculate our percentage. To do this, we insert our coefficient in this formula: $([exp(coefficient)-1]100)\%$. Choosing photos for example, will yield an interpretation like this: posting a single additional photo, results in an increase of the winning bid by around $([exp(0.0197524)-1]100)\% = approx. 2\%$.

< quiz "Interpreting statistical results"

question: Based on your previous task, what is the correct statement? mc: - An increase in seller feedback by 1% will decrease the winning bid by 0.009%* - An increase in seller feedback by 1% will decrease the winning bid by 0.9% - An increase in seller feedback by 1% will decrease the winning bid by US$ 0.915 success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

< award "Understanding regression results 2"

Congratulations, you know have deeper knowledge how to interpret our results and thus how our winning bid is influenced by our covariates!

>

Let's now focus on our other hedonic regressions in part B, which will include a view on our fixed effects, as well as a summary for the whole exercise.

Exercise 3B -- Hedonic Regressions

As already stated, in part B of exercise 3 we are going to focus on additional hedonic regressions. Each regression will always resemble our base model, as we are just going to adapt our previous version introduced in part A. We will conduct a total of 5 additional regressions, most of them make up a new task, yet also concerning future regressions, some tasks may contain multiple regressions, as some changes are very minor.

Analogous to previously, we are interested in the relationship of our logarithmic winning bid biddy1 and our current proxy of information disclosed by the seller photos. Here our base model is given as a reminder:

$$log(p_t) = log(biddy_1)$$

$$x_t = log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback)$$

$$fixed_effects = carmodel + year + week$$

$$clustered_se = sellername$$

Before we can start, we again must load our dataset cleanedebay.TXT. The task is identical to the previous ones; the solution is already given to you.

Task: The following chunk of code resembles the readRDS() statement from exercise 1 and is already given. Please proceed with edit and immediately check afterwards to solve the next task.

#< task
data = readRDS("cleanedebay.Rds")
#>

Task: Utilizing the base model, assign 2 regressions with a call to the function felm() to the variables reg2 and reg3. We want to divide both regressions in private sellers and professional dealers. Contrary to previous exercises, this time you need to subset our data. Please utilize the parameter subset in the felm() function and assign the regressions in this order: First private sellers, second professional dealers.

#< task_notest
# Regression for reg1 (full sample)
reg1 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data)
# Regression for reg2 (private sellers only sample)
# ...
# Regression for reg3 (professional dealers only sample)
# ...
#>
reg1 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data)
reg2 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data, subset = c(dealer==0))
reg3 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data, subset = c(dealer==1))
#< hint
display("Just adapt reg1 and set the 'subset' parameter to c(dealer==0) and c(dealer==1).")
#>

Let's now have a look at our results from our previous regressions, including reg1 from part A.

Task: The following chunk shows a nicely formatted table with our regression results. Keep in mind that all regressions are in line with our base model, they are only analysing a different subset of data.

#< task
reg.summary1(reg1, reg2, reg3)
#>

What can be seen from the table above, is that all coefficients are highly significant and have mostly the expected sign. It is a little bit awkward, that the logarithmic feedback of the seller seems to have a negative impact, meaning the more feedback a seller received, the lower the price. There is no obvious explanation for this, yet it is reassuring that negpct still has a negative sign, as already discussed in the previous exercise.

Overall, considering the private sellers sample only, the coefficient of photos seems to be stronger compared to the dealer sample. As digits alone might be confusing, we want to visually represent our covariates of reg1 with the help of an effect plot.

Task: The following chunk shows a bar plot containing all our independent variables of reg1 to illustrate their effect on log(biddy1). We manipulated our regression results from reg1, as effectplot() doesn't support quadratic terms and logarithmic values natively. The solution is already given, just press check to proceed.

#< task
library(regtools)

# Manipulate our data set and reassign it to a new variable called logdata
data %>%
  filter(sellfdback >= 0, is.na(photos)==FALSE, is.na(negpct)==FALSE, is.na(biddy1)==FALSE, miles >= 0) %>%
  mutate(logmiles = log(miles), logsellfdback = log(sellfdback)) -> logdata

# Rerun our regression and omit the quadratic term (photos^2) 
reg1_omit <- felm(log(biddy1) ~ logmiles + photos + options + negpct + logsellfdback | carmodel + year + week | 0 | sellername, data = logdata)

# Plot the effects on log(biddy1)
effectplot(reg1_omit, ylab = expression("Effect on log " * biddy[1]), xlab = "Explanatory Variables")
#>

We see that, even though log(miles) account for the most variance in log(biddy1), our proxy of online disclosure photos and options are also important for explaining variation in price. Furthermore, note the difference between our variables used in our regression. As we would expect both photos and options to be positive and thus reward the seller with a higher price.

To finish this exercise, we want to conduct another three hedonic regressions, all of them being extensions of our base model.

Task: Conduct our base model regression for the collectible sample only. To avoid repetitive task, the solution is already given. Please proceed with check.

#< task
reg4 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week | 0 | sellername, data = data, subset = c(collectible==1))

# Show regression results
summary(reg4)
#>

We see slight changes in our covariates for the collectible sample: all coefficients are still significant, yet the coefficient of photos reached its peak. It's also new, that the options variable seems to play a huge role compared to miles and photos. This is indeed very interesting as it suggests, that possible buyers for collectible cars are mostly interested in additional features like air-condition and less interested in miles. While the latter seems perfectly fine, as a collectible car is unlikely to be actively driven anyway, the first one is quite puzzling.

< quiz "Possible reasons for strong options"

question: What is a likely possible reason for options being such an important factor? mc: - Even vehicles on display are driven from time to time. - In cars before 1980 an air-condition and other features were built in every time. - Sellers listed frequently less options for collectible cars.* success: Great, all answers are correct! failure: Not all answers correct. Try again.

>

The last statement is in fact true, as the variation in options concerning collectible cars, is not as volatile as non-collectible cars. This could be due to the fact, that options are not a crucial part, when selling collector's item.

Let's now proceed with implementing new covariate to extend our basic hedonic regression model. We want to implement our first control variable bookvalue. This is basically a new subsample of our dataset data with newer cars, where book value data was available. In the latter regression, we observed the strongest relationship between photos and our logarithmic winning bid biddy1. This is mostly due to older cars being more homogenous, as newer cars have many different features to opt for. Following this what relationship would you expect for the bookvalue sample:

< quiz "The relation between biddy1 and photos becomes ..."

question: What relationships would you expect for the book value sample? mc: - Relation between biddy1 and photos becomes weaker compared to the collectible sample. - Relation between biddy1 and photos becomes stronger compared to the collectible sample. - Relation between biddy1 and bookvalue becomes will be very strong. - Relation between biddy1 and bookvalue becomes will be very low. success: Great, all answers are correct! failure: Not all answers correct. Try again.

>

Knowing the solution, let's first perform our regression to validate and afterwards proceed with our economic reasoning.

Task: The following chunk extends our base model regression and adds another covariate of the logarithmic book value. Furthermore, the result of this regression is printed. The solution is already given to you. Please proceed with check.

#< task
reg5 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + log(bookvalue) | carmodel + year + week | 0 | sellername, data = data)

# Show regression results
summary(reg5)
#>

And indeed as expected, the relationship between photos and biddy1 is not as strong anymore. This is likely due to the cars being relatively new with less heterogeneity. On the other hand, the relationship between biddy1 and bookvalue is strong. This is expected, as the winning bid is somewhat tied to the bookvalue of a car. If there was a huge gap, one would either expect to only bid - given auctions are underprized - in auctions, or not bid at all. Moreover we are going to utilize the book value sample to illustrate the extent of our fixed effects for different car models. Remember we deliberately projected out fixed effects for carmodel. year and week. We will see, that especially for the carmodel the fixed effect is quite large; thus, we will only plot the carmodel fixed effects in task 7 of this exercise.

Our last regression for this exercise includes possible interactions between age and warranty. We already argued that photos seem to have a greater impact, the older a car becomes. One would also expect photos to have a lower impact for cars, which are still under warranty, as this will give the buyer some additional insurance. Unfortunately, there is no significant relation between the interaction of photos and warranty, which means we have no statistical support for this thesis. Nonetheless we want to take a quick look at this regression:

Task: Extend our base model regression for 3 new covariates: The multiplier of age and photos, the warranty and the multiplier of warranty and photos. Store the result of the function felm() to a variable called reg6 and print it.

#< task
# Add your code below
#>
reg6 <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + I(age * photos) + warranty + I(warranty * photos) | carmodel + year + week | 0 | sellername, data = data)

# Show regression results
summary(reg6)
#< hint
display("You will need to use the function I().")
#>

Having a look at our results, we may conclude that there is indeed a significant interaction between age and photos, which supports our assumptions made in previous tasks.

Task: To sum up all of our regressions, including reg1 from part A of the exercise, we again utilize a wrapper function based on the stargazer package, to create a nicely formatted output table. The code is already provided, so you just need to proceed with edit and check. If you have a closer look at the code you will see that we use a wrapper function called reg.summary2(). If you want to have a look inside this function, check the init.R file in the problem set's folder.

#< task
# Proceed with check to look out regression results.
reg.summary2(reg1, reg2, reg3, reg4, reg5, reg6)
#>

This table is a summary of all our regressions conducted in exercise 3. As we have already discussed the results in detail before, this is more a nice overview about all our previously conducted regressions. We can see that our covariates used in our regression vary regarding different samples and/or other sets of covariates. We can see this if we compare reg2, the private seller sample with reg5, the bookvalue sample.

Task: The following chunk shows two bar plots illustrating the effect on our dependant variables on log(biddy1). We again manipulate our regression results as effectplot() doesn't support quadratic terms and logarithmic values. The solution is already given to you, just press check to proceed.

#< task
# Manipulate our data set and reassign it to a new variable called logdata
logdata %>%
  filter(bookvalue >= 0) %>%
  mutate(logbookvalue = log(bookvalue)) -> logdata

# Rerun our regressions and omit the quadratic term (photos^2) 
reg_private <- felm(log(biddy1) ~ logmiles + photos + options + negpct + logsellfdback | carmodel + year + week | 0 | sellername, data = logdata, subset = c(dealer==0))
reg_bookval <- felm(log(biddy1) ~ logmiles + photos + options + negpct + logsellfdback + logbookvalue | carmodel + year + week | 0 | sellername, data = logdata)

# Plot the effects on log(biddy1)
effectplots(reg_private, reg_bookval)
#>

We can see that, if we add log(bookvalue) to our regression, all of our other covariates lose power to explain variation in log(biddy1). This is expected as the winning bid and thus the selling price should be somewhat tied to the bookvalue. If we compare our other regressions, it is also expected that with regards to private sellers, for which no additional information is available, photos take a more important role in assessing the condition of the good sold. The same applies to the collectible car sample. For very old cars bookvalue is not a proper measure to explain the price. Whilst the condition of a collector's item - which may be conveyed via photos - is more important.

To end this exercise, we'll have a closer look at the fixed effects of our carmodel, which we deliberately projected out of our base model. This should shed some light on the extent of our fixed effects for different car models.

Task: Just proceed check, as the code is already given.

#< task
# Fixed Effects
setDF(getfe(reg5)) %>%
  group_by(fe) %>%
  summarise(mean = mean(effect))

# Plot of Fixed effects for the carmodel
setDF(getfe(reg5)) %>%
  filter(fe == "carmodel") %>%
  summarise(mean = mean(effect), sd = sd(effect), upper = 0, lower = 0) %>%
  mutate(upper = mean+qnorm(0.975)*sd/sqrt(nrow(filter(setDF(getfe(reg5)), fe == "carmodel"))), 
         lower = mean-qnorm(0.975)*sd/sqrt(nrow(filter(setDF(getfe(reg5)), fe == "carmodel")))) -> fix_car

fix_car_e <- dplyr::select(filter(setDF(getfe(reg5)), fe == "carmodel"), effect)

ggplot(fix_car_e, aes(0, effect)) + 
  geom_point(aes(color = effect), size = 4, alpha = 1/2) + 
  labs(title = "Fixed Effects for 'carmodel'") + 
  labs(x = "", y = "Fixed Effect") +
  theme_bw(base_family = "Avenir") +
  geom_errorbar(colour = "grey", aes(x=0, ymin = rep(as.numeric(fix_car$lower),52), ymax = rep(as.numeric(fix_car$upper),52)), size = 1, alpha = 0.25)
#>

Having a look at the error bar, we can easily identify that the projected out fixed effects for carmodel vary quite a lot. The error bar illustrates the upper and lower bound of the confidence intervall. The darker a value becomes, the more often it appears to have this value, meaning darker spots are observations, which are lying on top of each other. It is also worth noting that the effect is not weak at all with a median value of $5.418$.

Exercise 4 -- Endogeneity

So far, we have seen that all our regression results were highly significant at the 1 percent significance level. This means there is a $1\%$ probability of rejecting the null hypothesis, given it is true. Keep in mind our null hypothesis in this case would be: none of our covariates chosen has a significant effect on the logarithmic winning bid log(biddy1). Our R squared is also respectably high, so we may expect to have found a proper fit explaining the variance in our dependant variable with our covariates chosen.

Now, we want to proceed with some robustness checks - in the paper the author also elaborates on the possibility of a selection bias, due to a tobit regression. This will ensure that the sample is indeed a proper representative population and not some selections of individual listings, which may cause the effects described in the previous exercises. We nevertheless skip this, as the results were positive, which means no selection bias was found by the author and our conclusions are correct. In this exercise, we want to put emphasis on various possibilities for endogeneity to occur. For example, omitted variables, which is our true focal point for this exercise.

Keep in mind, our base model regression looks as follows:

$$log(p_t) = x_t * \beta + \epsilon_t$$

$$log(p_t) = log(biddy_1)$$

$$x_t = log(miles) + photos + photos^2 + options + negpct + log(sellfdback)$$

$$fixed_effects = carmodel + year + week$$

$$clustered_se = sellername$$

The logarithmic miles seem to explain most of our logarithmic price logp_t, which is perfectly rationally explained as a vehicle's main purpose are the means of transportation. The miles therefore are a perfect proxy for evaluating a car's condition in a sense of how intensively it has been battered already. The more usage the car has experienced in the past, the less utility we expect it to yield in the future. Also, take in mind, that the maintenance costs of cars rise with the miles on the odometer. For our purpose, though, we want to examine the connection between photos and logp_t, which was strong. Recall that we argued: if a seller provides enough photos in his listing to convey the car's actual condition, the apparent information asymmetry - keep in mind a possible buyer most likely doesn't have the opportunity to inspect the car pre-bidding - should disappear. This strong relationship between photos and log(biddy1) could also be due to an omitted variable - this means, the variable is currently not part of our set of explanatory variables in our regression - influencing the photos posted by the seller. This would be very unfortunate, yet there are many scenarios to think of. The author for example argues, that the amount of photos posted could vary widely across the participation. And indeed, it is a valid assumption to think that bidders will upload more photos, if there is more competition. If nobody is interested in the listing anyways, why would he put additional effort in uploading more photos. To tackle this problem, we take the same regression, yet we add another covariate, the number of bidders n to control for the latter scenario.

As previously, we must load our dataset cleanedebay.TXT first, to work on the data.

Task: The following chunk of code resembles the readRDS() statement from exercise 1 and is already given. Please proceed with edit and immediately check afterwards to solve the next task.

#< task
data = readRDS("cleanedebay.Rds")
#>

Task: The following regression extends our base model from exercise 3 to include a control variable for the number of total bidders n. Press check to proceed.

#< task
# Proceed with check to look out regression results
regb <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week + n | 0 | sellername, data = data)

# Show regression results
summary(regb)
#>

We may conclude, that even after controlling for the overall participation of bidders, the provided photos have a strong effect on the winning bid biddy1. This supports the thesis, that the amount of photos posted does not depend on the overall participation of bidders.

Another possibility would be, that possible bidders prefer dealers to private sellers. As dealers have lower disclosure costs, they may put up more photos at the same price. Thus, the link between the winning bid biddy1 and photos could be biased, if possible buyers prefer dealers. To gain more information regarding this scenario, we subset our data to a professional dealer only sample and introduce a fixed effect for each dealer.

To make this more interesting, this time I'll provide you with the results of the regression, before we perform it. You may want to test yourself with the following quiz:

Coefficient	Estimated value	Clustered standard error	T-statistic
photos	0.0186181	0.0023702	7.855

< quiz "Understanding regression results 3"

question: Utilizing the regression results in the table above, is the relationship between log(biddy1) and photos significant? sc: - yes* - no success: Awesome! You got it right. failure: Try again.

>

The results will reveal support towards the fact, that the strong and significant relation between photos and log(biddy1) persists, even after controlling for the upper scenario. Thus, sellers seem to vary the amount of photos provided with each car. This also implies, that sellers are very specific concerning their photos and do not tend to upload just a sheer amount of photos arbitrarily.

Task: The code is already given to you. All you need to do is to proceed with check.

#< task
# Proceed with check to look out regression results
regc <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) | carmodel + year + week + sellername | 0 | sellername, data = data, subset = c(dealer == 1))

# Show regression results
summary(regc)
#>

< quiz "Arriving at the correct conclusion"

question: Given both tasks in this exercise yield no endogeneity, can we conclude there is no other possibility for an omitted variable? sc: - yes - no* success: Awesome! You got it right. failure: Try again.

>

< award "Perfect Awareness"

You didn't get tricked by the recent question, even though we showed other regressions supporting our recent results from exercise 3, we cannot rule out the possibility of other causes for endogeneity. It is always best to remember: as long as there is a econometric story, there may as well be other variables involved, which account for a change of our winning bid and/or our set of explanatory variables.

>

Task: This task is optional and completely up to you. In statistics, there is no such thing as the only one 'solution' - if your model fits the data and given there is some econometric reasoning to support your thesis, it makes perfect sense to introduce another set of covariates. If you want to try other versions of our previous regressions, feel free to perform a regression to your liking and test it.

#< task
# You may enter your code here

#>
#< hint
display("You may try anything you want, this exercise is completely optional and there is no solution!")
#>

Exercise 5 -- Online Disclosure and its Costs

In this exercise, we want to shift emphasis on the following question: how does the amount of online disclosure relate to its cost. By now we know that disclosure is an important factor with regards to receiving a higher winning bid. This is expected to be each seller's ultimate joint goal. All our results are in line with our disclosure model: it's always best to disclose as much information as possible to raise returns on auctions. Yet disclosing information may also be expensive and probably not as worthwhile, as each listing has a fee attached to create it. Furthermore, there also costs involved to set up the listing. Dealers have a clear advantage, as they mostly utilize a ready-to-use template. Hence setting up new auctions becomes easy. Templates require very little adjustments concerning individual car specific features only. Private sellers on the other hand are most likely expected to sell a single car and not more, as for them it is a onetime event, not to occur twice within the next years. Thus, those sellers should have quite high costs related to online disclosure, as they are most likely neither familiar with the business, nor familiar with setting up listings; and for certain won't be using any listing software like "carad", "auction123" or "eBizAutos". This circumstance makes it very difficult to observe their behaviour, respectively to assess their disclosure costs. Thus, we again restrict our data set to professional dealers only. Keep in mind by the paper's definition a dealer is a seller, who sold more than one car. Dealers therefore have an incentive to use professional listing software, as this will lower their listing costs considerably, rendering the high initial costs to set everything up negligibly small.

In regards to this exercise, we are interested in the following questions:

• Do dealers, who switch to professional listing software put up significantly more photos than previously?
• Do disclosure costs influence our level of disclosure significantly?

To approach the first question, we are leaving our base model for a moment: with the help of our previously gained knowledge about regressions, we will perform a new regression model; this time using photos as independent variable and our software as additional covariate. Most of the other former covariates will stay on the right-hand side. To make this more interesting and in view of the plethora of regressions we've already conducted, you will do part A of this exercise on your own. In part B on the other hand, I'm going to lead you through the whole exercise, explaining iv regression and the reasoning behind in a rather easy and convenient way with the help of path models.

Exercise 5A -- Linear Fixed Effects Regression with IV

The tasks of this exercise are meant to be challenging, but not insoluble. If, however, you appear to be unable to proceed - or you're having problems even though you are certain you entered the right solution - just resort to the solution button. Nevertheless, I highly encourage you to try everything yourself and always refer to the hints first.

We want to conduct a regression as follows:

$$\textrm{photos} = \beta_0 + \beta_1 \cdot \textrm{software} + \beta_2 \cdot \textrm{log(miles)} + \beta_3 \cdot \textrm{options} + \beta_4 \cdot \textrm{log(sellfdback)} + \beta_5 \cdot \textrm{negpct} + \varepsilon$$

$$\textrm{Fixed effects for carmodel, year, week and sellername}$$

$$\textrm{Clustered standard errors by seller}$$

< quiz "Estimating our regression results 2"

question: Given our regression model, which of the following statements would we expect? sc: - There is a reason, why the relationship between seller feedback and photos could be positive. - Our relationship between logarithmic miles and photos will be negative. - One would expect a professional dealer to provide significantly less photos, if he resorts to third-party software like 'carad'. - There is a significant and strong positive relationship between utilized software and photos. - Any relationship between third-party software and photos will be significantly negative. success: Awesome! You got it right. failure: Try again.

>

Your assumptions were correct: A seller with a high feedback puts up significantly more photos and the relationship between software and photos is significant and positive. We will elaborate on both statements at later stages. Please keep in mind, that the level of difficulty will grow with the tasks. Yet all tasks should already be familiar to you, such that you can directly proceed with the next task.

Task: Utilizing a call to the function readRDS(), load the dataset cleanedebay.Rds and assign the result to a variable called data.

#< task
data = readRDS("cleanedebay.Rds")
#>

Task: Using a call to the function select() to drop all columns except those contained in our regression model as well as dealer and the number of bidders n. If you are uncertain which variables you might have to use, you may always use glimpse() to have a precise view at each individual variable in your dataset data. Reassign the result to the variable dat. When you are done, please proceed with check.

#< task
# Enter your code below
#>
dat <- select(data, biddy1, photos, software, miles, options, sellfdback, negpct, carmodel, year, week, sellername, dealer, n)
#< hint
display("We did this already in a previous exercise.")
#>

The variable dat is now a data.frame() with $106,559$ auctions and $12$ columns. All our columns are somehow part of our regression, if you do not know how to apply them, you may always have a look at the regression we want to conduct. This should be quite telling.

Before the next task, please acquaint yourself with another powerful R base function: C()

< info "C()"

The function C() is a R base function, which combines arguments: in our case we will need to pass three arguments to this function. 'C' is short for Concatenation, it will combine each argument you pass, coerce it to a common data type and then return this object. We need C() to set our factor level for our software, as otherwise our factor level will not match.

# C(object, contrasts, number_of_contrasts)

You may have a look at our variable software contained in data with the following chunk:

# class(dat$software)
# levels(dat$software)

The function class() returns the data type, which will be "factor". This means our variable software is a categorical variable, which may only take certain values. Those values are referred to as "levels".

The function levels() returns a character vector with all values the variable software may take. If you run the previous chunk, the result will be "auction123", "carad", "eBizAutos" and "ebayhosting". This is also the order you need to remember, for setting up the reference level. The following chunk shows you the code you need, to change the reference level of a categorical variable. You will only need to adjust 'factor_variable' and 'desired_reference_lvl_as_number'. Please leave the rest unchanged. E.g. if you set base = 1, your reference level will be "auction123".

# C(factor_variable, contr.treatment, base = desired_reference_lvl_as_number)

Analogous to I(), you may apply the function C() in a formula as follows:

# dependent_variable ~ C(independent_variable, ...) + independent_variable2 + ... + independent_variableN

For more information, have a look at cran.r-project.org/doc/manuals/r-release/R-intro.pdf.

>

Task: Using a call to the function felm(), perform a linear regression in accordance to our regression model with fixed effects and clustered standard errors. Do not forget to subset our data to match dealers and auctions with non-zero bidders only. Set the reference level for our categorical variable software to ebayhosting.

If you are uncertain which variables you might have to use, you may always use glimpse() to have a precise view at each individual variable in your dataset dat. Assign the result to a variable called reg. When you are done, please proceed with check.

#< task
# Enter your code below
#>
reg <- felm(photos ~ C(software, contr.treatment, base = 4) + log(miles) + options + log(sellfdback) + negpct | carmodel + year + week + sellername | 0 | sellername, data = dat, subset = c(dealer == 1 & n > 0))
#< hint
display("The function C() takes three arguments, consult the info box above for further help. To subset your data by the means of multiple conditions, utilize the "&" operator between conditions.")
#>

< award "Lone Warrior 1"

Awesome! You did this regression all by yourself, even though it was complex. For the remainder of this exercise we are going analyse our results.

>

Task: Using a call to the function summary(), show the results of reg, so we can start analysing them. When you are done, please proceed with check.

#< task
# Enter your code below
#>
summary(reg)
#< hint
display("We did this already in a previous exercise.")
#>

Keep in mind, this is the first time we don't have a log-linear regression model. This time we regressed our total of photos provided. And indeed, the link between software and photos in the listing seems to be strong. In average, if a dealer changes to a professional listing software he uploads up to $10$ additional photos. Every other coefficient has the expected sign, as miles and a negative feedback lower the overall amount of photos. This makes sense: if the car has been worn down already, it is not as worthwhile to provide lots of photos, as the miles are the strongest link to the winning bid. Thus, if an odometer states many miles, the winning bid won't be as high. From a seller's perspective, one would tend to avoid additional costs, neglecting how small they might be. As photos are our proxy for disclosing information, we would also expect a positive sign from our seller feedback, as the seller most likely has disclosed as many information as possible in regards to the car's condition in the past, which made him earn that positive feedback.

< quiz "Linear Regression with Categorical Variables"

parts: - question: 1. Which coefficient is insignificant? choices: - miles - options - sellfdback - negpct* multiple: FALSE success: Awesome, this is correct! failure: Try again. - question: 2. If a seller swaps from ebayhosting to the carad listing software, how much additional photos is he expected to post? answer: 9 roundto: 0.12970

>

< award "Lone Warrior 2"

Awesome! You mastered all previous steps on your own, albeit those tasks where somewhat repetitive, they still served their purpose in solidifying your recent R and statistic acquirements.

>

Task: We can also spot the relation between photos and the seller's utilized software easily with the means of another graph. Please proceed with check, as the solution is already given.

#< task
ggplot(filter(dat, sellfdback >= 0, is.na(photos)==FALSE, is.na(negpct)==FALSE, is.na(biddy1)==FALSE), aes(software, photos)) +
  geom_bar(aes(fill = as.factor(software)), position = "dodge", stat="identity") +
  labs(title = "Plotting photos on software") + 
  labs(x = "software", y = "photos") +
  theme_bw(base_family = "Helvetica") +
  theme(legend.position = "none", axis.text.x = element_text(size  = 10, angle = 45, hjust = 1, vjust = 1))
#>

It's easy to spot the difference in using a professional listing software, where it's just 'drag&drop' to add additional photos and the standard eBay website. Using a third-party tool seems to boost the amount of photos posted quite substantially.

Exercise 5B -- OLS and IV

Now that we've seen a strong positive relationship between photos and software, we could possibly use software as an instrument in our regression. Yet in this circumstance, software needs to be uncorrelated with our error term $\epsilon$. There is no certain proof, and even the author states that it is per se not 'testable', if our upgrade in software is caused by selection on quality or influence of a nicely looking listing. Yet, to proceed we are going to assume both latter conditions are false, which renders software as a valid instrument for photos.

Let's first have a look at the difference between our ols and iv regression. Utilizing a path model should help you to understand the relationships between dependant variable and covariates in our regression. There are observed (rose) and unobserved (cyan) variables in our analysis. Solid arrows are causal relations being part of our actual regression model. Dotted arrows on the other hand, are possible causal relations, which could be present, yet we do not have a proxy to observe them in our actual model.

Let's put our ols regression model in a path model and have a look:

Our ultimate goal is to find support for our disclosure model's thesis: fully disclosing every information maximizes the winning bid. Until now we used photos as a proxy for our level of disclosure: if a seller posted significantly more photos than others, this should also cause higher bids on his item in return. As our disclosure model suggests, it's always best to disclose everything, to prevent any information asymmetry to occur in the first place. So, we basically want to estimate our winning bid biddy1 with the amount of photos, miles and other important covariates of interest like options, the seller's feedback and so on.

If we come back to exercise 4 and concern ourselves with endogeneity, we find many possibilities for endogeneity here as well. For example, given a car enthusiast, who kept his car in a tidy state compared to others, who would probably care less. As his car is in a splendid condition, it will yield a higher return when sold. Yet the photos of the car, the seller provides will most likely go up as well, as the car lover wants to disclose every information possible and if every detail is in proper state, why not disclose just all of it? This is a problem of endogeneity though, as we expect photos to have a positive effect on the winning bid biddy1. As a result, we cannot clearly distinguish which effect accounts for the shift in price and how strong they actually are, when observed individually. For further understanding I provided a path model for our hypothetical thesis as well, yet we may never forget, that there are numerous other possible reasons for endogeneity to think of.

< quiz "Understanding endogeneity"

question: Given our hypothetical scenario above and our positive coefficient from earlier. Do we tend to over- or underestimate the effect of photos and winning bid? mc: - overestimate* - underestimate success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

Our objective now, based on the previous paragraph is to find a good instrument for our proxy of online disclosure photos. And as we have already shown, photos are correlated with the seller's utilized software. This means, that the utilized software could as well explain our change in the winning bid biddy1 and thus amount of photos would not play a role as huge as expected in the first place. Aside from that, there could be other covariates, we did not yet account for distorting our initial result and therefore weaken the link between biddy1 and photos. The alternatives are endless; thus, we cannot control for everything and even our data is limited. Nevertheless, we can discuss what would happen to those variables and think of other possibilities, which would cause a wrong relationship between our variables biddy1 and photos.

< quiz "Guessing the likelihood of other variables"

question: What are possible candidates for instrumenting photos? mc: - trans - year - pctfdback - pwrseller - n* success: Congratulations, this is correct! failure: Unfortunately, this was wrong. Try again!

>

A possible way to tackle such endogeneity problems would be to implement control variables, which we did in a previous exercise by adding the overall number of bidders n as part of the regression. We saw that a higher participation in the auction didn't seem to be the reason for higher bids.

For this exercise, we want to stick to software as our instrument though. As ols doesn't account for omitted variables it will cause a bias to occur. If photos and software are positively correlated, our distribution would not be centred around the true population, in fact, an upward bias would occur, as photos gets additional power from software, since software isn't observed. Thus, our estimated coefficient will shift upwards.

To tackle this eventuality, we use software as an instrument for photos. This will eliminate any variance due to the influence of unobservable variables, as we are estimating a coefficient for photos first. The latter statement will only hold, if we have found a good instrument for photos though, meaning in our case software has indeed significant explanatory power towards photos and is uncorrelated with the error term our main regression. Put differently, in our graphic you can see a causal relation between the utilized software to create the listing, while the link between other unobserved factors and photos got separated.

To illustrate this, we are going to simplify our path model to the possible endogenous parts. Depicted on the left is the part of our previous ols model, whilst on the right hand side, the link between other unobserved factors and estimated change in photos is separated due to iv estimation.

To tackle a scenario such as the latter, we introduce an instrumental variable. When one refers to an iv regression, he will first regress the values of our endogenous variable photos on our suspected instrument software, this is also called first stage least squares, as overall we are going to conduct a two stage least squares estimation instead of a simple ordinary least squares (ols) regression. In the second stage, having already estimated our estimator for photos, we will only add the variance of photos, as the variance can be explained by our instrument - given software is indeed a valid instrument. This will take variation in software by seller into account, whilst excluding any other variation due to other excluded variables. Yet this will only not 'back-fire', if our software is independent from our winning bid biddy1.

Now, that we discussed our models, let's again summarise, what we are going to do: We want to conduct an 'instrumental variable regression' this time. To be more precise, we are going to use the utilized software for creating the listing as an instrument for photos, to check for possible endogeneity. So, we assume our software is correlated with the amount of photos but uncorrelated to the winning bid biddy1 and the error term in our regression.

If you want to understand how to implement an iv regression in felm() check the info box below, otherwise proceed.

< info "felm() - part 2"

By this point we already acquainted ourselves to the felm() function. For now, we always ignored the iv part in our formula, setting it manually to $0$. Yet now we want to use software as an instrument for our 'endogenous' variable photos.

Previously our formula looked like this:

# logp_t ~ x_t | fixed_effects | 0 | clustered_se

Now we substitute our $0$ with a second formula. It is important to use parenthesis in this case, as the 'OR' operator, the so-called pipe: '|' will always be compiled at higher priority than the formula separator '~'. Our formula therefore needs to look like this: (endogenous_var ~ instrument).

# logp_t ~ x_t | fixed_effects | (endogenous_var ~ instrument) | clustered_se

The felm() function stays aside from passing a different formula untouched:

# library(lfe)

# felm(logp_t ~ x_t | fixed_effects | (endogenous_var ~ instrument) | clustered_se , data=data, subset = c(variable == value))

For more information, have a look at cran.r-project.org/web/packages/lfe/lfe.pdf for the lfe vignette.

>

Having learnt how an iv regression with the help of felm() is conducted, let's now directly head to our regressions. We start with the simple ols regression and include the iv regression in the second task. Keep in mind, that both regressions look pretty similar, the only difference is in the iv part of the felm(y ~ covariates | fixed_effects | instrumental_variable_regression | clustered_by) function.

We again have to load our dataset cleanedebay.TXT, the task is identical to the previous ones, the solution is already given to you.

Task: The following chunk of code resembles the readRDS() statement from exercise 1 and is already given. Please proceed with edit and immediately check afterwards to solve the next task.

#< task
data = readRDS("cleanedebay.Rds")
#>

Task: Using a call to the function felm() perform a linear regression and assign the result to a variable called ols. Keep in mind that as we are only observing dealers, we must add sellername to our list of fixed effects to project those out as well. As the solution is already given to you, please confirm with check.

#< task
ols <- felm(log(biddy1) ~ log(miles) + photos + options + log(sellfdback) + negpct | carmodel + year + week + sellername | 0 | sellername, data = data, subset = c(dealer == 1))

# Show regression results
summary(ols)
#>

As both, the ols regression and the iv regression are closely tied together, we are going to skip the analysis of ols now and first conduct the second regression, before we'll have a look at both regression results in detail.

Task: Using a call to the function felm(), perform a linear regression and assign the result to a variable called iv. Keep in mind that as we are only observing dealers, we must add sellername to our list of fixed effects to project those out as well. In accordance to our regression model, we perform an iv regression on photos, utilizing software as an instrument and cluster standard errors by sellername. As the solution is already given to you, please confirm with check.

#< task
iv <- felm(log(biddy1) ~ log(miles) + options + log(sellfdback) + negpct | carmodel + year + week + sellername | (photos ~ software) | sellername, data = data, subset = c(dealer == 1))
#>

Task: Let's now compare our regression results stored in the variables ols and iv. To do so refer to the function reg.summary3(). As the solution is already given to you, please proceed with check.

#< task
reg.summary3(ols, iv)
#>

At first glance, both regression results seem to be yielding almost the same results, yet having a closer look, we see that the feedback a seller gained from previous actions, is not significant anymore. Indeed, only the logarithmic miles and options seem to play a role in explaining the winning bid biddy1. Our goal was to have a look if software is an appropriate instrument for photos, as we assumed due to our previous results. Yet upon seeing our results, photos is only significant, when observing the ols regression and insignificant, when observing the iv regression. This renders software as a weak instrument and supports the thesis, that software is not suited to explain photos. Which also points to the fact that disclosure costs indeed seem to affect our price.

Exercise 6 -- Text Coefficients

For this exercise, we're are going to focus on another measure of determining online disclosure. The description of the listing itself should also reveal quite a lot of information to a possible buyer. Analogous to the photos provided within a selling, the description itself may also be enforced by a contract, which means, to avoid any legal actions taken by a disappointed buyer, a seller also mustn't lie regarding the vehicle's condition. Hence, he basically has two options to choose from, to not disclose any information at all or to disclose everything willingly. The latter being the better option as our disclosure model says we must disclose everything possible. Yet if the car is in a bad condition and no person would buy it, the seller could be better off disclosing nothing, which makes it impossible for the buyer to enforce ex post legal actions based on the description alone.

We have already seen our groups of text coefficients in the first exercise, so let's take a closer look again:

The data available with the paper was mined from eBay Motors and all necessary text was extracted via pattern matching by the author. The algorithm was looking at which index a variable of interest, in our case rust, scratch and dent appeared. Afterwards within a $50$ words interval before and after the variable was mentioned, the most mentioned words were extracted and used to identify qualifiers like 'many', 'much' and so on. Using this knowledge, he categorized each variable in pre-defined groups.

group	value	meaning
rust_group	0	The seller did not mention the variable in his description. This is the omitted value and won't be part of our statistics
rust_group	1	Corresponds to a negation of our variable.
rust_group	2	Positively qualified mention
rust_group	3	Unqualified mention, neither good, nor bad.
rust_group	4	Negatively qualified mention of our variable

< quiz "Understanding the categorical variable rust_group"

parts: - question: 1. Which group does the following description belong to 'There's quite a lot of rust on the bonnet'? choices: - 0 - 1 - 2 - 3 - 4 multiple: FALSE success: Awesome, this is correct! failure: Try again. - question: 2. Which group does the following description belong to 'The car is still in a super good condition'? choices: - 0 - 1 - 2 - 3 - 4 multiple: FALSE

>

Even though the second statement is clearly a positively qualified mention, there is no reference regarding any of our variables. So, this a 'group = 0' scenario, in which the variable of interested wasn't mentioned at all in the description.

We are going to extend our basic regression model introduced in exercise 3.

$$log(biddy_1) = \beta_0 + \beta_1 \cdot \textrm{log(miles)} + \beta_2 \cdot \textrm{photos} + \beta_3 \cdot \textrm{photos}^2 + \beta_4 \cdot \textrm{options} + \beta_5 \cdot \textrm{log(sellfdback)} + \beta_6 \cdot \textrm{negpct} + \begin{pmatrix} scratch_group \ dent_group \ rust_group \end{pmatrix} \cdot \beta_{7,8,9} + \varepsilon$$

$$\textrm{Fixed effects for carmodel, year and week}$$ $$\textrm{Clustered standard errors by seller}$$

< quiz "Estimating our regression results 3"

question: Given our regression model, which of the following statements would we expect? sc: - There is a significant and strong positive relationship between log(biddy1) and the absence of dents, rust and scratches. - We cannot tell if Few scratches/dents/rust are considered positive. - Few dents will be significantly positive. - No rust will always yield a significant negative relationship with log(biddy1) - The worse the extent of scratches/dents/rust becomes, the more negative the coefficient should become.* success: Awesome! You got it right. failure: Try again.

>

< award "Estimation Expert"

Awesome! You did well estimating the regression results. We really cannot tell, how a possible bidder evaluates the occurrence of little scratches, rust and dents. As this is also very car specific. Concerning a very old car for example, a buyer might be more forgiving, than if it is a new car. Moreover, we will see that only one of the two other statements will hold true. Nevertheless, both are valid assumptions.

>

Let's now examine the link between our logarithmic winning bid log(biddy1) and our groups. We again clustered all regressions into a single task, respective code chunk, as all our regressions are very identical and this is just to add some diversity. The statement will create a nice table, like those we have already seen before in other tasks.

We again must load our dataset cleanedebay.TXT, the task is identical to the previous ones, the solution is already given to you.

Task: The following chunk of code resembles the readRDS() statement from exercise 1 and is already given. Please proceed with edit and immediately check afterwards to solve the next task.

#< task
data = readRDS("cleanedebay.Rds")
#>

Task: The code below will include the groups in our regressions from exercise 3. The first regression will take the whole sample, the second and third regression will be for private sellers and dealers only and the last regression will also include the bookvalue of the respective cars. Afterwards we have a look at the summary of those regressions and shortly interpret them. As the regressions are basically just extended versions from earlier, the code is already given to you, just proceed with check.

#< task
# Please proceed with enter, as the code is already given to you

regbasemod <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + scratch_group + dent_group + rust_group | carmodel + year + week | 0 | sellername, data = data)

regprivate <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + scratch_group + dent_group + rust_group | carmodel + year + week | 0 | sellername, data = data, subset = c(dealer == 0))

regdealers <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + scratch_group + dent_group + rust_group | carmodel + year + week | 0 | sellername, data = data, subset = c(dealer == 1))

regbookval <- felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + log(bookvalue) + scratch_group + dent_group + rust_group | carmodel + year + week | 0 | sellername, data = data)

reg.summary4(regbasemod, 
             regprivate, 
             regdealers, 
             regbookval)
#>

Having a look at our results, we may conclude, that the findings are somewhat puzzling. Neither No dents, nor No rust is significant over all regressions. Yet No scratches is significant in both our base model and our private seller sample. Remember the base model resembles our full sample. This could be due to private sellers lacking any other sources of information for possible buyers. Imagine a professional seller on the other hand, aside from car-specific information like photos and the text in the listing itself to disclose information, there are numerous other possibilities like a webpage, seller reputation, ...

Nevertheless, it is a little bit reassuring, that most of the puzzling coefficients with a supposed 'wrong' sign, for example No dents in the private seller sample, are hardly significant. As we would not expect an absence of dents to come along with a lower winning bid log(biddy1). Another plus is the decreasing numbers as the condition gets worse. We can easily spot this in the base model. No rust is not significant so we skip this, but from Few rust to Lot of rust our coefficient decreases from $-0.246$ to $-0.429$, which is absolutely expected as a car in worse condition should be not as valuable.

Exercise 7 -- Conclusion

We were interested in information asymmetries and how they relate to online disclosure in eBay Motor auctions. At our disposal was a data set containing original data mined from eBay Motors, which enabled us to perform various regressions to determine the driver is for our winning bid biddy1. Remember, we started with a very select example of Honda Civics and I suggested that there might be a link between the amount of photos a seller posted and the highest bid biddy1 the respective auction achieves. After this brief introduction, we calculated some more descriptive statistics and headed to our first regressions. Our so-called basic model was a hedonic regression model, which tried to explain the price per specific car features. We saw that the amount of photos seemed to be indeed a good candidate explaining our variation in the bid amount. Yet as expected the miles on the odometer are - and will probably always be - the most driving covariate in all auctions. Afterwards we were considering the robustness of our findings: possibly there are other candidates who would make good variates as well, yet our previous results held strong. In a final attempt to explain our price we started to have a look at certain text coefficients in the listing itself. We examined a relation between scratches, rust and dents, yet our results were mostly not significant and we therefore didn't proceed with a further analysis.

We found out that a seller posting a single additional photo expects a higher payoff of roughly $2\%$. As an additional photo costs US\$ $0.15$, it is highly recommended to disclose as much information as possible to your bidders. The link between photos and our winning bid biddy1 was robust in all our findings and supports our utilized disclosure model from Milgrom, Paul (1981) and Grossmann, S.J. and Hart, O.D. (1980). Also, worth noting is, that there are many other works concerning themselves with disclosure of information. For example, Jovanovic (1982) also supports the disclosure thesis, as his results support the idea, that even more than the socially optimal amount of information is disclosed - yet his findings are very restricted, as his results do not allow for false statements being made. All in all the level of disclosure seems to play an important role, when considering used-good markets and should always be considered by a seller.

Task: To show all your achievements, proceed with edit and then check. Regarding the whole problem set, a total of $10$ awards could be obtained.

#< task_notest
awards(as.html = TRUE)
#>

Exercise 8 -- References

R and Packages in R

• R Core Team (2015): foreign. "Read Data Stored by Minitab, S, SAS, SPSS, Stata, Systat, Weka, dBase, ...", R package version 0.8-63 http://cran.r-project.org/package=foreign
• R Development Core Team (2016): R. "A language and environment for statistical computing, R Foundation for Statistical Computing", Vienna, Austria. http://www.r-project.org
• Gaure, S. (2016): lfe. "Linear Group Fixed Effects", R package version 2.5-1998 http://cran.r-project.org/web/packages/lfe/index.html
• Hlavac, Marek (2015): stargazer. "Well-Formatted Regression and Summary Statistics Tables", R package version 5.2. http://CRAN.R-project.org/package=stargazer
• Kranz, S. (2015): RTutor. "Creating R problem sets with automatic assessment of student's solutions", R package version 2015.12.16 https://github.com/skranz/RTutor
• Wickham, H. and Francois, R. (2016): dplyr. "A Grammar of Data Manipulation", R package version 0.5.0 http://cran.r-project.org/web/packages/dplyr/index.html
• Wickham, H. and RStudio. (2016): dtplyr. "Data Table Back-End for 'dplyr'", R package version 0.0.1 https://cran.r-project.org/web/packages/dtplyr/index.html
• Dowle, M. and Srinivasan, A. (2016): data.table. "Extension of data.frame", R package version 1.9.6 https://cran.r-project.org/web/packages/data.table/index.html
• Oehlschlägel, J. (2015): bit64. "A S3 Class for Vectors of 64bit Integers", R package version 0.9-5 https://cran.r-project.org/web/packages/bit64/index.html
• Wickham, H., Chang, W. (2016): ggplot2. "An Implementation of the Grammar of Graphics", R package version 2.2.1 http://cran.r-project.org/web/packages/ggplot2/index.html
• Delignette-Muller, M.L. and Dutang, C. (2015): fitdistrplus. "An R Package for Fitting Distributions", R package version 1.0-8 http://www.jstatsoft.org/v64/i04/.
• Kooperberg, C. (2016): logspline. "Routines for the logspline density estimation", R package version 2.1.9 https://cran.r-project.org/web/packages/logspline/index.html
• Kranz, S. (2016): svgdiagram. "Create svg files from graphviz .gv files.", R package version 0.1.0 https://github.com/skranz/svgdiagram
• Matloff, N. (2016): regtools. "Regression Tools", R package version 0.2 https://cran.r-project.org/web/packages/regtools/index.html
• Auguie, B. and Antonov, A. (2016): gridExtra. "Miscellaneous Functions for 'Grid' Graphics", R package version 2.2.1 https://cran.r-project.org/web/packages/gridExtra/index.html

Bibliography

• Lewis, Gregory. 2011. "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors." American Economic Review, 101(4): 1535-46
• Milgrom, Paul R. 1981. "Good News and Bad News: Representation Theorems and Applications." The Bell Journal of Economics, Vol. 12, No. 2.: 380-391.
• Grossman, S.J. and Hart, O.D. 1980 "Disclosure Laws and Takeover Bids" The Journal of Finance, Vol. 35, No. 2, Papers and Proceedings Thirty-Eighth Annual Meeting American Finance Association, Atlanta, Georgia: 323-334.
• Grossman, S.J. 1981. "The Informational Role of Warranties and Private Disclosure About Product Quality." Journal of Law and Economics, 24(3): 461-83.
• Sopranzetti, B.J. 2015. "Hedonic Regression Models" Springer New York, 2119-2134
• Akerlof, George A. 1970. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism.", Quarterly Journal of Economics, 84(3): 488-500.
• Grossman, Sanford J. and Oliver D. Hart. 1980. "Disclosure Laws and Takeover Bids." Journal of Finance, 35(2): 323-34.
• Bond, Eric W. 1982. "A Direct Test of The 'Lemons' Model: The Market for Used Pickup Trucks." American Economic Review, 72(4): 836-40.
• Genesove, David. 1993. "Adverse Selection in the Wholesale Used Car Market." Journal of Political Economy, 101(4): 644-65.
• Jovanovic, Boyan. 1982. "Truthful Disclosure of Information." Bell Journal of Economics, 13(1): 36-44.
• Lewis, Gregory. 2011. "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors: Dataset." American Economic Review. http://www.aeaweb.org/articles.php?doi=10.1257/aer.101.4.1535.
• Williams, Richard. 2015: "Heteroskedasticity", University of Notre Dame. https://www3.nd.edu/~rwilliam/stats2/l25.pdf
• Arellano, Manuel. 2004: "Panel Data Econometrics" Oxford.
• Wickham, Hadley. (2009). "ggplot2: Elegant Graphics for Data Analysis". Springer. ISBN: 978-0-387-98140-6

Exercise 9 -- Appendix

Task: Support for the assumption, that fixed effects for the variable carmodel are indeed normally distributed as assumed earlier in this problem set. First load the data and perform the regression. Then plot actual distribution and compare. Please proceed with edit and immediately check afterwards.

#< task
library(fitdistrplus)
library(logspline)
library(lfe)
library(data.table)
library(dplyr)

# Read the data
data = readRDS("cleanedebay.Rds")

# Perform Regression
fix_eff <- setDF(getfe(felm(log(biddy1) ~ log(miles) + photos + I(photos^2/100) + options + negpct + log(sellfdback) + log(bookvalue) | 
                            carmodel + year + week | 0 | sellername, data = data)))
filter(fix_eff, fe == "carmodel") -> fix_eff

# Show plot
descdist(as.numeric(fix_eff$effect), discrete = FALSE)
norm <- fitdist(as.numeric(fix_eff$effect), "norm")
plot(norm)
#>

rotterp/RTutorOnlineDisclosure documentation built on May 27, 2019, 11:42 p.m.