Download Lecture 2 (Brian Quistorff)

Lecture 2
Multiple Prices, Econometrics & Modeling Demand Curves
Econ 404
Jacob LaRiviere & Brian Quistorff
Broad Agenda
• Introductions
• Homework 1
• Section 1: Competition & Direct Price Discrimination
• [Break]
• Section 2: Indirect price discrimination
• [Empirical Setup & Break]
• Section 3: Intro to Demand Modelling
2
Homework 1
• Collect Homework
• Discuss:
• Deviations from “Law of one price”
• Confusing aspects of markets
3
Section 1: Agenda
• Bargaining with perfect information
• Bargaining with uncertainty
• Single price vs. Segmentation
• Value-based pricing for segmentation
• Direct price discrimination
• Discussion: Ethics of segmentation
4
Bargaining with complete information
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
We both know all this
P=0
Seller walks away
P=20
P=10
Buyer walks away
Bargaining region
5
Bargaining and outside options
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
Competitor price for the same good is 15
P=0
Seller walks away
P=10
Bargaining region
P=20
Buyer walks away
Competitor gets sale
6
Bargaining and outside options
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
Competitor has a good that I like less: vc = 15, 𝑝𝑐 = 12
P=0
Seller walks away
P=20
P=10
Bargaining region
Buyer walks away
Prefer to buy the
cheaper, less
preferred good from
the competitor
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What price will be set?
Economic theory says  if both sides know each other’s values and costs,
some deal will be made. It does not say what price will be set.
Bargaining power: factors that determine how much of the surplus each side
gets from a transaction.
P=0
Seller walks away
P=20
P=10
Bargaining region
Buyer walks away
8
Threat points in bargaining
“threat points”: the outcomes if one party walks away
• If my threat point is bad, bargaining breakdown is very bad for me.
• What is my outside option if we don’t make a deal?
Ex. A factory negotiating with employees over wages.
• Each employee’s threat point is to quit, which may lead to financial troubles for them.
For the factory, having one less employee is probably not that big a deal. Bargaining
“alone”, the factory has most of the bargaining power.
• Unions allow workers to bargain together. Now the threat point is to strike, meaning
the factory is shut down, at least in the short-run.
9
Bargaining with uncertainty
My value for a good: v1 ~𝑈 10,20 (equal chance of any value 10 to 20)
You own the good and value it at: v2 ~𝑈 5,15
Myerson Satterthwaite Theorem:
there is no mechanism that
guarantees a transaction will be
made when 𝐯𝟏 >𝐯𝟐
Idea: the seller doesn’t know the
buyers valuation, wants to increase
price and may in advertently price
buyer out of market.
Buyer has no credible way of
conveying they have a low value
5
15
20
10
My value is probably above
yours, but maybe not
10
Why can’t we overcome Myerson-Satterthwaite?
Trusted intermediary: we both tell a third party our true values, if buyer’s value
exceeds sellers, then price is set as halfway between the two values.
• E.g. I say 15, you say 10  price = 12.5
• Problem: we both do not have an incentive to be fully truthful. You want to lie a bit to
increase price, I want to lie a bit to reduce price
Repeated play: we both agree to always be honest with each other and “split
the surplus” each “round” of play.
• Will only work if we know the distributions of each other’s values. Idea, if the buyer is
really uniformly U(10,20), then there should be an equal number of 20’s as 10’s, etc.
• Often we won’t know the distributions and have an incentive to like (“long con”)
11
Bargaining and elasticity
Low elasticity  minimal ability to switch to competing products/technologies
With low elasticity  margins are high. In other words, the firm captures a lot
of the “surplus” of the transaction.
With high elasticities (more competitive markets)  margins are low.
Consumer’s capture most of the surplus of transactions.
12
One price versus multiple prices
A firm charges a uniform price if it sets the same price for every unit of output
sold.
While the firm captures profits due to an optimal uniform pricing policy, it
does not receive the consumer surplus or dead-weight loss associated with
this policy.
The firm can overcome this by charging more than one price for its product.
A firm price discriminates if it charges more than one price for the same good
or service.
13
The inefficiency of a single price
• Customers “in the DWL triangle” could
have been profitably served, but are
“priced out” of the market
• To serve these customers with a single
price, the firm has to discount all units to
this price. Loses more money on the
intensive margin than it makes up by
serving more customers.
• Customers cannot credibly reveal their
value is below the set price, but above
costs, e.g. Myerson-Satterthwaite theorem
14
Economic Value to the Customer (EVC)
The maximum price a customer would be willing
to pay assuming she is fully informed about the
product’s benefits as compared to the closest
competitor’s product and price
Goal: Generate an accurate value proposition
15
Price discrimination as “value based pricing”
Goal: charge different prices based on differential value to the customer
For higher value customers, firm can charge a higher prices and still “share in
the surplus”
Allows firm to serve more of the demand curve by tailoring prices to the value
a customer gets from the good
Also, it sounds better than “discrimination”
16
Using EVC
• EVC = Reference Price + Differentiation value
• After Calculating EVC managers have to take strategic decisions about
how far below EVC they price.
• EVC Analysis can be used as
• To guide pricing
• As a diagnostic tool for underperforming products
17
Segmentation Basics
• Reference price will vary across customers, because “next best alternative” differs
• Differentiation value will vary across customers, because usage scenarios and
intrinsic valuations differ
• Segmentation tries to cluster customers into a smaller number of well-defined
“types”
• Pricing strategy targets these types with different products, features and offers
18
Strategic assessment of whether firm should
move from one-price to multiple price strategy
Does my product offering have differentiation value? i.e.
it is not totally “commodified”
Can I identify 2+ customer value profiles who
theoretically have different EVCs for my product?
Can I empirically identify these segments?
Can I actually implement a pricing strategy based on
these segments?
19
20
Hypothetical EVC profiles for radiology
EVC
6400
5800
Defense Systems
Radiology Imaging Labs
4400
Hospitals
3900
Ambulatory Facilities
3500
2800
Slide credit: Catherine Tucker
Doctors
Animal Hospitals
Millions of $ of market potential
21
We can reorganize value profiles to construct a
demand curve
EVC
6400
5800
4400
3900
3500
2800
Defense
Systems
Radiology
Labs
Ambulatory
Hospitals Facilities
Doctors
Animal Doctors
Millions of $ of market potential
Slide credit: Catherine Tucker
22
How can we effectively charge a different
price to these segments?
23
Three forms of price discrimination
• Direct (aka “3rd degree”)
• Different prices based on customer characteristics
• Has to be observable and legal
• Product-based or “indirect” (aka “2nd degree”)
• Offer multiple versions to all and allow consumers to “self select
• Examples: bundling, versioning (“good, better, best”), quantity discounts
• Perfect (aka “1st degree”)
• Charge each consumer her WTP.
24
Perfect Price Discrimination
• Theoretical standard: charge everyone their willingness
to pay, provided this exceeds costs
• In practice, impossible to achieve.
• View this as a benchmark
25
26
Dell 512 MB Memory Module
Part Number A 019 3405, July 2005
Mar 2005 July 2005
June 2006
Large Business
$289.99
$334.99
$294.95
GSA/DOD
$266.21
$334.99
$294.95
Home
$275.49
$267.99
$265.45
Small Business
$246.49
$267.99
$265.45
Slide credit: Preston McAfee
27
Direct Price Discrimination
• AKA customer value-based pricing
• Charge based on customer characteristics
• Student, elderly, enterprise
• Location, e.g. zone pricing
• Tied into other purchases
• Problem: Arbitrage
• Ex. How can you prevent doctors from buying as if they were a vet?
• Sometimes mechanisms exist to verifiably link customers to segment, like
a .edu email address, often you cannot
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Implementation of customer-based
segmentation is challenging
Unambiguous indicator of group membership
Product must not be tradable across group members
Group membership must correlate with EVC
Must be legal
Must be acceptable
29
Illegal Discrimination
In the US, the follow are “Protected Classes”:
•
•
•
•
•
•
•
•
Race/Color, Religion
National Origin/Citizenship
Age (40+)
Sex (and somewhat gender and sexual orientation)
Familial status/pregnancy
Disability
Veteran
Genetic Information
30
Fuzzy Matching of Protected Classes
• Advertisers now often know
customers very well (e.g. on Facebook)
• Legality?
31
Segmentation Ethics
Discuss in groups
• What are the distributional consequences of segmentation?
• What if firm can segment into high & low value customers? How are
segments, the firm, and others are affected? Reactions?
• What about other types of segmentation?
• Should businesses avoid some types of segmentation?
32
Indirect Price Discrimination
• Offer different options and let customers decide.
• Tailor options to value determines choice
• Called “screening”
• Solves arbitrage by “self-selection”
33
Methods
• Coupons/rebates
• Quantity discounts & two-part tariffs
• Timing
• Payment models (up-front, pay-as-you-go, etc.)
• Multiple versions with different features offered to all
• “Damaged” goods
• Branding
• Warranties
34
Coupons and Rebates
• Coupons and rebates are used by those with a low value of
time
• Value of time correlated with price sensitivity
35
List prices versus realized prices
• ARPU: average revenue per unit, or average prices. If sales team has pricing
discretion, these will tend to differ
• A common sales scheme:
• List price: the starting point for negotiations
• Floor price: the absolute rock bottom price the salesperson cannot go below
• Incentive compensation = f(total sales, ARPU). Example:
• Commission = .1*(Q*ARPU - Floor). Sales person gets 10% the revenue that is in excess of the
floor price.
• Sales person has two incentives: close deals (want to offer lower price) and keep prices high
(increases commissions if sale will still be made)
36
Quantity Discounts
• For a single product, quantity discounts work by correlation of
family size and price sensitivity
• Large families usually have tighter budgets than single people
• When selling multiple products, quantity discounts work in
different ways
• Customer may be unlikely you have a high valuation for many products
• “Additional products” get a low price that is not offered widely.
• Also works due to budget concerns---if I am near your budget (high quantity), you get more price sensitive
37
NY Times ad rates uses quantity discounts
Color
US ½ page: 133K
US Full page would be 266K, but is
actually 214K, or about 20% off.
Same 20% discount applies
internationally
B/W
½ page: 97K
Full page would be 196K, but is
actually 178K, or about 10% off
In other markets, discount is 20%
38
Do NY Times ad rates make sense?
• Lower per square inch price for large units
• Large ads are more disruptive to the newspaper, so arguably have “super linear costs” (e.g. a
whole page is a bigger disruption, harder to fit than 2 half page ads)
• Can always split a whole page into two half pages ads, so cost of half page ad is *at most*, ½
the cost of the whole, and maybe less
• How can we explain this:
• Values: 2 half pages more desirable than one whole page? Maybe, but maybe the opposite.
• Price sensitivity: Advertisers that can afford a whole page are *more* price sensitive?
Unlikely.
• Market power: there are more competitors for whole page ads, so the NY Times has lower
margins. Very unlikely.
• Market thickness: lots of demand for half page ads, limited, but some demand for whole
page ads (“too expensive”). Maybe.
• It’s a mistake. Maybe.
39
Payment models: two part tariff
Definition: A firm charges a two part tariff if it charges a per
unit fee, p, plus a lump sum fee (paid whether or not a
positive number of units is consumed), F.
This, effectively, charges demanders of a low quantity a
different average price than demanders of a high quantity.
Example: hook-up charge plus usage fee for a telephone,
club membership, etc.
This is a form of indirect price discrimination because it does
not rely on knowledge of customer valuations or group
membership.
40
Example:
P
All customers are identical and have demand
• P = 100 – Q
100
• MC = AC = 10
• What type of payment scheme makes sense?
4050
10
41
90 100
Q
What is the optimal two-part tariff?
Two steps:
(1) maximize the benefits to the consumers by charging p = MC = 10.
(2) capture this benefit by setting F = consumer benefits = 4050.
(3) Goal is to extract maximum revenue from each customer
In essence, the firm maximizes the size of the "pie", then sets the lump sum fee so
as to capture the entire "pie" for itself.
The total surplus captured!
42
Two-part tariffs with multiple types
Often better to charge the surplus of the
lower type consumer (A) and set a higher
price, 𝑝𝑚
In general, prices will be shaded up from
marginal cost because the entry fee will not
equal “high types” surplus (I can now raise
price on them a bit)
Figure source: Wikipedia
43
Examples of two-part tariffs
Phone contracts
• Monthly fee + usage charges (some included usage for “free” as well)
Cover charges
• Fee to get in + prices to drink/eat
Clubs
• Membership fee + usage fee (e.g. per visit, to play golf, etc.), also used for rentals, e.g. Zipcar
• May allow options with no membership, e.g. daily use, to appeal to travelers or causal users
44
Timing
Price sensitive
customers wait for
a good deal
45
Timing
Not all products
show this much
variation.
46
Timing
Flash sales
47
Why timing can work
• Two sets of consumers, “shoppers” (price comparers) and “loyals” (show up and
buy)
• if firm knows rivals’ price, wants to undercut it slightly
• at low prices, would rather have high price sold only to loyal customers
• leads to randomization and price cycles
• Price sensitive customers will wait, die-hards want it now
• Hardbacks vs. paperbacks
• Video on demand prices start at high “purchase only” price and drop to low rental price over time
• The distribution of customers into “shoppers” vs. “loyals” or patient vs.
impatient can vary by product or over time
• For laptops/tv’s vs. headphones, we should see less price variation for the higher priced goods
• Supermarkets run sales on goods valued by price sensitive shoppers (milk, paper towels, cola, diapers) or when people are
likely to be “looking around” (Thanksgiving turkeys, Super Bowl chips, etc.)
• Price competition is highest during peak holiday shopping period
48
Payment models
Pay-as-you-go
• Can overcome budget constraints. Ex. “go phone”
• Can also help with the “sticker shock” of a big upfront price and
expand market
49
Product based price discrimination
• The demand curve reminds of us of our missed pricing and
segmentation opportunities
• Product-based segmentation success rests on identifying key
differentiation value to distort and persuading customers of the
fairness of the segmentation.
50
Product based price discrimination
• Different versions in a product class
• Includes product attributes, included add-ons and bundling
51
Necessary conditions for product-based
customer segmentation
Correlation of attribute with EVC
Distortion (altering products)
Compensation
52
Ex. Capacity
(note: 16GB flash memory cost about $15
at the time, 3G chips cost much less than
$130)
53
Identifying the right kind of feature
Not Integral to the brand
Features that customer segments have
widely differing values
We’ll discuss how to use conjoint and
statistical methods
54
Damaged goods: intentional reduction in the value of the
product in order to price discriminate
• Amazon “super saver” free shipping (7-10 days)
• Hold
thethis
itemreduction
in the warehouse
forcomes
a few days
Note:
in value
at a positive
• Copied
bythe
many
online
retailers, price
sensitive
consumers willing to wait,
cost to
firm.
Producing
a piece
of hardware
some people pay for “standard”
with fewer features is a different, but related,
• IBM LaserPrinter E
concept.
• Added
chips to slow processing
• Sony 74, 60 minute mini-discs
• differ by instructions on disc
• Throttling of internet speeds when there is no congestion
55
Sharp DV740U Missing Button
56
Sharp DV740U Missing Button
57
Tracking shows that FedEx holds 2-day delivery
packages at distribution centers to reduce chance
they arrive in 1 day (intentional delays)
58
Due to increased routing complexity, it actually
costs FedEx to reduce the quality of the service…
why is this profitable?
59
Pushes high value of speed customers into one day
who would otherwise risk two-day
Differentiation to justify price differences
Note the arrow
60
Question: would this make sense if there were only
the following two types of customers?
1. Those that absolutely need overnight
2. Those that only require it arrives in 2-days
61
Answer, no. It only makes sense if there are three (or more) types,
those that:
1. Absolutely require overnight
2. Desire a good chance at overnight delivery
3. Just want delivery within 2-days.
The intentional delay strategy tries to drive group 2 to purchase costly
overnight shipping, which is paired with an “overnight guarantee”
62
Takeaway
The success of a damaged good strategy depends
critically on the types of consumers in the
marketplace and their relative frequency
63
Branding
64
Branding
65
Branding
• Especially common in consumer packaged goods
• Premium brands vs. “low end”
• Often the products are very similar
• Legal issues
• Selling exact same product with different claims can be illegal
• E.g. selling same contact lens, but different recommended usage times,
was deemed fraudulent
• Can create a perception of competition and differentiation when
there in reality it is quite limited
66
Break & Empirical Setup in R
• Download & Install R – cran.rstudio.com
• Download & Install RStudio Desktop (Open Source) – rstudio.com
• Open Rstudio
•
•
•
•
•
Tools -> Install packages: “knitr, rmarkdown, dplyr, reshape2, ggplot2, formatR”
File -> New File -> R Markdown
Put Title & Author, then OK
Save file “<somewhere>/<foo>.Rmd”
Knit
67
Intro to modeling a
demand curve
68
Goal: measure “slope and shifters”
• Slope/elasticity: what is the response in terms of quantity sold to
price changes (this may be different at various price levels)
• Shifters: factors that shift the demand curve. E.g. seasonal
components, promotional activity, etc.
• It’s possible that external factors will change the slope as well. For
instance, for holiday shopping, people buy more consumer goods
overall, but are also more price sensitive due to holiday shopping
budget and when buying stuff for other people one cares more
about price than the “perfect fit” (relatively speaking)
69
Using logs
• Recall:
𝑦 = 𝑎𝑥
ln 𝑦 = ln 𝑎 + ln 𝑥
𝑦 = 𝑎𝑥 𝑟
ln 𝑦 = ln 𝑎 + r ∗ ln 𝑥
𝑦 = 𝑒𝑥
ln 𝑦 = 𝑥 ∗ ln 𝑒 = 𝑥 ∗ 1 = 𝑥
70
Find elasticity two ways
𝑦 = 𝑎𝑥 𝑟
𝑦 = 𝑎𝑥 𝑟
𝑑𝑦
= 𝑟𝑎𝑥 𝑟−1
𝑑𝑥
ln 𝑦 = ln 𝑎 + 𝑟 ∗ ln(𝑥)
𝑑𝑦 𝑥 𝑟𝑎𝑥 𝑟
∗ =
=𝑟
𝑟
𝑑𝑥 𝑦
𝑎𝑥
Elasticity
𝑑𝑙𝑛(𝑦)
=𝑟
𝑑𝑙𝑛(𝑥)
For small changes,
gives the elasticity too
71
More generally
𝑑𝑦
𝑑𝑙𝑛(𝑦)
𝑑𝑦 𝑥
𝑦
=
=
= elasticity
𝑑𝑙𝑛(𝑥) 𝑑𝑥 𝑑𝑥 𝑦
𝑥
72
Constant elasticity demand curve
𝛾 𝑥′𝛽
𝑞=𝑝 𝑒
ln 𝑞 = 𝛾 ∗ ln 𝑝 + 𝑥 ′ 𝛽
Even if this function is correct, in practice there will be noise in the data
ln 𝑞 = 𝛾 ∗ ln 𝑝 + 𝑥 ′ 𝛽 + error
R-squared and related measures tell you how much of the data is “explained by the
model” vs. in the error term
73
Constant elasticity demand curve
• Simple functional form, gives a useful baseline
• Elasticity may often be constant in the “relevant range” of prices
• Statistical tests should be used to see if different functional forms
provide better fit to the data
74
Empirics Outline
1) Value Based Pricing
2) Isolating Value Empirically
3) Causality and Elasticity
After this section you will know….
…why “causal inference” is so important for pricing.
Running Example (Assignment): OJ
Data: 83 Chicago-area stores
At weekly level:
• Sales (“log move”)
• Average sales price
• Whether advertised (“feat”)
At store level:
• Various demographics of the shoppers
Data taken from:
“Determinants of Store-Level Price Elasticity” Stephen J. Hoch, Byung-Do
Kim, Alan L. Montgomery and Peter E. Rossi
Journal of Marketing Research Vol. 32, No. 1 (Feb., 1995), pp. 17-29
Data available here:
http://www.jacoblariviere.com/uw-econ-404/
77
Data
Log of quantity sold
each week
Price is not logged
Demographics of
shoppers by store
We’ll study 3 brands,
“dominicks” is the
store’s brand
1 if advertised that week
by that store, 0 if not
78
79
80
81
82
Who cares?
Value of Inference
84
Value of Inference
85
Value of Inference
86
Value of Inference
87
88
…why “causal inference” is so important for pricing.
Terminology
• 𝑋: features/explanatory variables
• 𝑦: outcome/dependent variable
example: Price
example: Quantity
Goal: model outcomes as a function of features.
Terminology cont.
𝑋: 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑠.
𝑦: outcomes
91
Estimating equations
𝑌 =𝑓 𝑋 +𝜖
ln 𝑄 = 𝛼 + ln 𝑋 + 𝜖
log 𝑚𝑜𝑣𝑒𝑖𝑡 = 𝛼 + log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 + 𝜖𝑖𝑡
𝜖𝑖 is called the error term.
Note: Outcome on horizontal axis.
92
𝛽 gives the slope
Recall: Linear regression
𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜖𝑖
𝛼
𝑦𝑖 = 𝛼 + 𝑥𝑖
𝑦−𝑦
2
𝛼
gives the intercept
93
How does this work intuitively?
Assume 𝛼 = 0
min𝛽 y − y 2 = y − 𝑥
= y 2 − 2 𝑥𝑦 + ( 𝑥)2
→ −2𝑥𝑦 + 2 𝑥 2 = 0
𝑥 2 = 𝑥𝑦
𝑥𝑦
= 2
𝑥
𝜷 = 𝑋′𝑋
−1
(𝑋 ′ 𝑌)
94
2
OK… Now lets take this to our data.
Will show output from R
NOTE: ln 𝑄 = 𝛼 + 𝛽 ln 𝑝
𝛽 is % change in Q for a 1% change in P
Basic OJ Regression
ln 𝑄 = 𝛼 + 𝛽 ln 𝑝 + 𝜖, Dominicks==1
Coefficients:
(Intercept)
log(price)
Estimate Std. Error t value
10.95468 0.02424 451.87
-3.37753 0.04238 -79.69
Pr(>|t|)
<2e-16 ***
<2e-16 ***
96
Interpretation of Coefficients
ln(𝑄𝑖𝑡 ) = 𝛼 + ln 𝑃𝑖𝑡 𝛽 + 1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑𝑖𝑡 𝛾 + ln 𝑃𝑖𝑡 ∗ 1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑𝑖𝑡 𝜙 + 𝜖𝑖𝑡
%Δ𝑄
𝛽=
= 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐼𝐹 𝑛𝑜𝑡 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑
% Δ𝑃
𝛾 = %Δ𝑄 𝑖𝑓 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑
%Δ𝑄
𝜙+𝛽 =
= 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐼𝐹 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑
% Δ𝑃
97
Expand Regression
ln 𝑄 = 𝛼 + 𝛽 ln 𝑝 + 𝜖, Dominicks==1
Coefficients:
(Intercept)
log(price)
Estimate Std. Error t value
10.95468 0.02424 451.87
-3.37753 0.04238 -79.69
Pr(>|t|)
<2e-16 ***
<2e-16 ***
ln 𝑄 = 𝛼 + 𝛽 ln 𝑝 + 𝛾1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 + 𝜙 ln 𝑝 ∗ 1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 + 𝜖, Dominicks==1
Coefficients:
(Intercept)
log(price)
featured
log(p)*feat
Estimate
10.40658
-2.77415
1.09441
-0.47055
Std. Error
0.02852
0.04742
0.04654
0.09049
t value
364.89
-58.50
23.52
-5.20
Pr(>|t|)
< 2e-16 ***
< 2e-16 ***
< 2e-16 ***
2.04e-07 ***
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Why appear price sensitive when featured?
• Normally featured items on sale.
• Some of the “featured/display” effect is attributed to “elasticity”.
• Display & pricing decisions are not random.
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This randomization question is a big deal.
In an experiment, treatment is randomly assigned
Unbiased Demand Estimation
What you’d like is some data on prices and sales, while everything else is “held constant”
This is why experiments are terrific.
Price changes often correlated with other changes in the environment; everything else not held constant.
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Christmas is bad for econometrics
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Endogeneity
• Omitted Variable
• Simultaneity
• Reverse Causality
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Validity
Random events can come from lots of sources: experimental variation, nature (“quasi-experimental” variation),
arbitrary cutoffs in eligibility for a program, rollouts, etc…
This is really important for policy: policy changes often occur is isolation of other changes.
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- As a result, knowing causal relationships rather than correlations is extra important.
This randomization question is a big deal.
In an experiment, treatment is randomly assigned
If you don’t adequately control for the environment there could be
“Omitted Variable Bias”
Omitted Variable Bias
𝑐𝑜𝑣 𝜖𝑖 , 𝑥𝑖
> 0 → biased up, positive selection (innately talented goes to more school)
= 0 → Unbiased (this could be a fluke though!)
< 0 → biased down, negative selection (innately untalented school stuff)
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We’d like to enforce that the random component unobserved by econometrician
has no correlation/covariance with the independent variables. This isolates the
treatment effect from the selection bias.
The cleanest way to do this is with an experimental design because it
provides the right counterfactual to
compare the treated group to.
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So far we’ve only focused on own price elasticity
What about substitution?
How would you find what substitutes for Minute Maid?
For the purposes of the assignment
• Assume the store randomly changes the price of various brands of
orange juice, and then chooses to pair the price change with
advertising or not (so advertising and price can be correlated)
• Start by assuming a constant elasticity of demand function
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Linear Regression in R
regoutput = glm(y ~ var1 + var2 + … + varK, data=df)
Formula to estimate, y is
the LHS, the RHS is a linear
function of the vars
The data frame that
contains the variables in
the estimating equation
regoutput is an object with many useful outputs
Summary(regoutput) prints the coefficients and basic diagnostics
Coef(regoutput) gives a vector of the coefficients
Fitted.values(regoutput) gives a vector of the fitted values of y
Predict(regoutput, newdata=mynewdata) predicts new values for “scenarios” given
in new data sets
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Using R for the Assignment
oj <- read.csv("C:/Users/<name>/Econ404/oj.csv")
reg1 = glm(logmove ~ log(price)+ vars, data=oj)
reg2 = glm(logmove ~ log(price)*var1*var2, data=oj)
The second specification will create additive and multiplicative terms of each variable.
In the assignment, you will estimate and interpret models of this type
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Start for graphing
• Basic graphing using ggplot2
ggplot(oj, aes(logmove, price)) + geom_point(aes(color =
factor(brand)))
• aes stands for “aesthetic”
• See cheat sheet for more examples.
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