1. Lecture 2 Multiple Prices, Econometrics & Modeling Demand Curves
Jacob LaRiviere & Brian Quistorff

2. 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

3. Homework 1 Collect Homework Discuss:
Deviations from “Law of one price”
Confusing aspects of markets

4. 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

5. 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
P=10
P=20
Seller walks away
Buyer walks away
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination
Bargaining region

6. 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
P=10
P=20
Seller walks away
Buyer walks away
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination
Bargaining region
Competitor gets sale

7. 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: v c =15, 𝑝 𝑐 =12
P=0
P=10
P=20
Seller walks away
Buyer walks away
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination
Bargaining region
Prefer to buy the cheaper, less preferred good from the competitor

8. 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.
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination
P=10
P=0
P=20
Bargaining region
Seller walks away
Buyer walks away

9. 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.
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination

10. Bargaining with uncertainty
My value for a good: v 1 ~𝑈 10,20 (equal chance of any value 10 to 20)
You own the good and value it at: v 2 ~𝑈 5,15
Myerson Satterthwaite Theorem: there is no mechanism that guarantees a transaction will be made when 𝐯 𝟏 > 𝐯 𝟐
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
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination 10 20
My value is probably above yours, but maybe not

11. 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”)
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination

12. 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.
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination

13. 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.

14. 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

15. 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

16. 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”
Can be converted into a markup formula
Often used to justify a “constant markup” policy
but it doesn’t justify that, since elasticity changes from market to market
In markets with less elastic demand, price higher. This is known as price discrimination

17. 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

18. 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

19. 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?

20. Example of commodified products
Actual commodities (oil, corn, orange juice…)
Packaging (cardboard, …)
Apt management
Trucking
When a competitive market exists, don’t do it internally, use the market.

21. Hypothetical EVC profiles for radiology
6400
Defense Systems
5800
Radiology Imaging Labs
Hospitals
4400
Ambulatory Facilities
3900
3500
Doctors
2800
Animal Hospitals
Millions of $ of market potential
Slide credit: Catherine Tucker

22. We can reorganize value profiles to construct a demand curve
EVC
6400
A single price could “price out” independent doctors and vets
5800
4400
3900
3500
Defense
Systems
Radiology
Labs
2800
Ambulatory
Facilities
Animal Doctors
Hospitals
Doctors
Millions of $ of market potential
Slide credit: Catherine Tucker

23. How can we effectively charge a different price to these segments?

24. 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.
Likely to increase quite dramatically with increased computational power

25. 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
Solves arbitrage problem by letting consumers choose
quantity discounts: Shoe, buy one get one free

26. Ex. of Direct: Pharmaceutical pricing varies widely by customer attributes
Hospital size
Urban/rural
Office visit vs. hospital
Location of pharmacy
All differing by country
Patient type: child, adult, senior

27. Dell 512 MB Memory Module Part Number A 019 3405, July 2005 Mar 2005
June 2006
Large Business
$289.99
$334.99
$294.95
GSA/DOD
$266.21
Home
$275.49
$267.99
$265.45
Small Business
$246.49
Slide credit: Preston McAfee

28. 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 address, often you cannot
Likely to increase quite dramatically with increased computational power

29. 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

30. 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

31. Fuzzy Matching of Protected Classes
Advertisers now often know customers very well (e.g. on Facebook)
Legality?

32. 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?

33. Indirect Price Discrimination
Offer different options and let customers decide.
Tailor options to value determines choice
Called “screening”
Solves arbitrage by “self-selection”
Solves arbitrage problem by letting consumers choose
quantity discounts: Shoe, buy one get one free

34. 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
quantity discounts: Shoe, buy one get one free

35. Coupons and Rebates
Coupons and rebates are used by those with a low value of time
Value of time correlated with price sensitivity

36. 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)
NYT quantity discount is always 1/6. But probably there should be a full page surcharge, and different discounts depending on the type of firm buying that section.

37. 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

38. 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%
NYT quantity discount is always 1/6. But probably there should be a full page surcharge, and different discounts depending on the type of firm buying that section.

39. 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.
NYT quantity discount is always 1/6. But probably there should be a full page surcharge, and different discounts depending on the type of firm buying that section.

40. 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.

41. Example: All customers are identical and have demand P = 100 – Q P
MC = AC = 10
What type of payment scheme makes sense? P
100
4050 10 Q 90
100

42. 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!

43. Two-part tariffs with multiple types
Often better to charge the surplus of the lower type consumer (A) and set a higher price, 𝑝 𝑚
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

44. 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

45. Timing
Price sensitive customers wait for a good deal

46. Timing
Not all products show this much variation.

47. Timing
Flash sales

48. 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
This slide is much too busy

49. 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

50. 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.

51. Product based price discrimination
Different versions in a product class
Includes product attributes, included add-ons and bundling

52. Necessary conditions for product-based customer segmentation
Correlation of attribute with EVC
Distortion (altering products)
Compensation
What is compensation? ROI?
You offer your customers a menu products at different prices. Customers choose which price to pay based on the product’s observable characteristics.
Incentive Compatibility
You need to make sure those with high valuations won’t pretend to be low valuation people and keep surplus
Make sure they just prefer the product they should prefer
Individual Rationality
You need to make sure that the choice for those with low valuations is not so crummy they don’t buy
Firm Rationality
Costs of providing two products and maintaining price fences does not exceed value captured.
One Price:
IC: Diff_H-P_H>EVC_L-P_L
IR: Diff_L-P_L>Outside Option
Costs of maintaining fences<Profits of fences
Up to this point, we have outside our firm for the closest competitive offering.
Relative to a competing brand, we can adjust P and Vus
In segmented pricing, the reference brand is a product from our menu of offers.
In segmented pricing, we can adjust P, RefP and DVus
However, we often have to adjust DVus downwards for low types and lower the price accordingly.
Unless we do this our high Types will just purchase the low Type good.
We impose costs on our low-types to make them reveal their low valuations – but then have to lower our price accordingly.

53. Ex. Capacity
(note: 16GB flash memory cost about $15 at the time, 3G chips cost much less than $130)
Costs are roughtly $15 for flash, $20 for 3G chip. This is a really nice example of engineering price discrimination

54. 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

55. Damaged goods: intentional reduction in the value of the product in order to price discriminate
Amazon “super saver” free shipping (7-10 days)
Hold the item in the warehouse for a few days
Copied by many online retailers, price sensitive consumers willing to wait, some people pay for “standard”
IBM LaserPrinter E
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
Note: this reduction in value comes at a positive cost to the firm. Producing a piece of hardware with fewer features is a different, but related, concept.

56. Sharp DV740U Missing Button
Makes it possible to play a European disc and output to a US TV

57. Sharp DV740U Missing Button
Makes it possible to play a European disc and output to a US TV

58. Tracking shows that FedEx holds 2-day delivery packages at distribution centers to reduce chance they arrive in 1 day (intentional delays)

59. Due to increased routing complexity, it actually costs FedEx to reduce the quality of the service… why is this profitable?

60. Differentiation to justify price differences
Pushes high value of speed customers into one day who would otherwise risk two-day
Differentiation to justify price differences
Note the arrow
No, need a third type that would accept a risk of arrival in 2 days for a lower price

61. 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

62. 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”

63. Takeaway
The success of a damaged good strategy depends critically on the types of consumers in the marketplace and their relative frequency

64. Branding
vs.
vs.
Same underlying network and corporate parent, but different stores, different branding, different plans and different prices!

65. Branding

66. Branding Especially common in consumer packaged goods Legal issues
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

67. 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

68. Intro to modeling a demand curve

69. 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)

70. Using logs Recall: 𝑦=𝑎𝑥 ln 𝑦 = ln 𝑎 + ln 𝑥 𝑦=𝑎 𝑥 𝑟
ln 𝑦 = ln 𝑎 + r∗ln 𝑥
𝑦= 𝑒 𝑥
ln 𝑦 =𝑥∗ ln 𝑒 =𝑥∗1=𝑥

71. Find elasticity two ways
𝑦=𝑎 𝑥 𝑟 𝑑𝑦 𝑑𝑥 =𝑟𝑎 𝑥 𝑟−1 𝑑𝑦 𝑑𝑥 ∗ 𝑥 𝑦 = 𝑟𝑎 𝑥 𝑟 𝑎 𝑥 𝑟 =𝑟
𝑦=𝑎 𝑥 𝑟
ln 𝑦 = ln 𝑎 +𝑟∗ln⁡(𝑥)
𝑑𝑙𝑛(𝑦) 𝑑𝑙𝑛(𝑥) =𝑟
For small changes, gives the elasticity too
Elasticity

72. More generally
𝑑𝑙𝑛(𝑦) 𝑑𝑙𝑛(𝑥) = 𝑑𝑦 𝑦 𝑑𝑥 𝑥 = 𝑑𝑦 𝑑𝑥 𝑥 𝑦 =elasticity

73. Constant elasticity demand curve
𝑞= 𝑝 𝛾 𝑒 𝑥 ′ 𝛽
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

74. 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

75. Empirics Outline Value Based Pricing Isolating Value Empirically
Causality and Elasticity

76. After this section you will know….
…why “causal inference” is so important for pricing.

77. 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
Data available here:

78. 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

83. Who cares?

84. Value of Inference
Primary value of inference is informing decisions.

85. Value of Inference
Primary value of inference is informing decisions.

86. Value of Inference
Primary value of inference is informing decisions.

87. Value of Inference
Primary value of inference is informing decisions.

88. Dominick’s OJ: What happens if we add precision to this
What is expected lift in sales/profits for a 10% discount?
This is a question about elasticities…

89. …why “causal inference” is so important for pricing.

90. Terminology 𝑋: features/explanatory variables example: Price
𝑦: outcome/dependent variable example: Quantity
Goal: model outcomes as a function of features.
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

91. Terminology cont. 𝑋:𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑠. 𝑦:outcomes Feature 1 Obs 1 Obs 1
11/6/2017 4:14 AM
Terminology cont.
𝑋:𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑠.
𝑦:outcomes
Feature 1
Obs 1
Obs 1
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

92. Estimating equations 𝑌=𝑓 𝑋 +𝜖 ln 𝑄 =𝛼+ ln 𝑋 +𝜖
11/6/2017 4:14 AM
Estimating equations
𝑌=𝑓 𝑋 +𝜖
ln 𝑄 =𝛼+ ln 𝑋 +𝜖
log 𝑚𝑜𝑣 𝑒 𝑖𝑡 =𝛼+ log 𝑝𝑟𝑖𝑐 𝑒 𝑖𝑡 + 𝜖 𝑖𝑡
𝜖 𝑖 is called the error term.
Note: Outcome on horizontal axis.
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

93. Recall: Linear regression
11/6/2017 4:14 AM
𝛽 gives the slope
Recall: Linear regression
𝑦 𝑖 =𝛼+𝛽 𝑥 𝑖 + 𝜖 𝑖
Ordinary least squares will find the 𝛼 and 𝛽 to minimized the squared distance between the fitted line and the observations
𝑦 𝑖 = 𝛼 + 𝛽 𝑥 𝑖
Minimizes 𝑦 −𝑦 2 𝛼
gives the intercept
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

94. How does this work intuitively?
11/6/2017 4:14 AM
How does this work intuitively?
Assume 𝛼=0
min 𝛽 y− y 2 = y−𝛽𝑥 2
= y 2 −2𝛽𝑥𝑦+ (𝛽𝑥) 2
→−2𝑥𝑦+ 2 𝛽 𝑥 2 =0
𝛽 𝑥 2 =𝑥𝑦
𝛽 = 𝑥𝑦 𝑥 2
𝜷 = 𝑋 ′ 𝑋 −1 ( 𝑋 ′ 𝑌)
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

95. 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

96. Basic OJ Regression
ln 𝑄 =𝛼+𝛽 ln 𝑝 +𝜖 , Dominicks==1
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) <2e-16 ***
log(price) <2e-16 ***

97. Interpretation of Coefficients
ln⁡(𝑄 𝑖𝑡 )=𝛼+ ln 𝑃 𝑖𝑡 𝛽+1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑑 𝑖𝑡 𝛾+ ln 𝑃 𝑖𝑡 ∗1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑑 𝑖𝑡 𝜙+ 𝜖 𝑖𝑡
𝛽= %Δ𝑄 % Δ𝑃 =𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐼𝐹 𝑛𝑜𝑡 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑
𝛾=%Δ𝑄 𝑖𝑓 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑
𝜙+𝛽= %Δ𝑄 % Δ𝑃 =𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐼𝐹 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑

98. ln 𝑄 =𝛼+𝛽 ln 𝑝 +𝛾1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 +𝜙 ln 𝑝 ∗1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 +𝜖 , Dominicks==1
Expand Regression
ln 𝑄 =𝛼+𝛽 ln 𝑝 +𝜖 , Dominicks==1
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) <2e-16 ***
log(price) <2e-16 ***
ln 𝑄 =𝛼+𝛽 ln 𝑝 +𝛾1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 +𝜙 ln 𝑝 ∗1 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑑 +𝜖 , Dominicks==1
(Intercept) < 2e-16 ***
log(price) < 2e-16 ***
featured < 2e-16 ***
log(p)*feat e-07 ***

99. 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.

100. Why these outliers?
Random or not?

101. Why these outliers?
Random or not?

102. This randomization question is a big deal.
In an experiment, treatment is randomly assigned

103. 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.
example insight from book
airlines leading example

104. Christmas is bad for econometrics
Prices
example insight from book
airlines leading example
Sales

105. Endogeneity
Omitted Variable
Simultaneity
Reverse Causality

106. 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.
- As a result, knowing causal relationships rather than correlations is extra important.

107. 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”

108. Omitted Variable Bias 𝑦𝑖=𝛼+ 𝑥 𝑖 𝛽+𝜖𝑖
plim 𝛽 𝑂𝐿𝑆=𝛽+ 𝐶𝑜𝑣 𝜖𝑖, 𝑥 𝑖 𝑉𝑎𝑟( 𝑥 𝑖 )
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)

109. 𝑦𝑖=𝛼+ 𝑥 𝑖 𝛽+𝜖𝑖
𝑝𝑙𝑖𝑚 𝛽 𝑂𝐿𝑆=𝛽+ 𝐶𝑜𝑣 𝜖𝑖, 𝑥 𝑖 𝑉𝑎𝑟( 𝑥 𝑖 )
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.

110. 𝑦𝑖=𝛼+ 𝑥 𝑖 𝛽+𝜖𝑖
Alternative view following Angrist and Pischke textbook. 𝑥 𝑖 - Is a binary variable representing “treatment” NOTE: treated could be extra year of educating, more advertising impressions, etc… Outcome for treated – Outcome for untreated = [Outcome for treated – Outcome for treated if not treated] + [Outcome for treated if not treated – Outcome for untreated] = Impact of Treatment on Treated (TOT) Selection Bias

111. So far we’ve only focused on own price elasticity
What about substitution?
How would you find what substitutes for Minute Maid?

112. 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

113. Linear Regression in R
regoutput = glm(y ~ var1 + var2 + … + varK, data=df)
The data frame that contains the variables in the estimating equation
Formula to estimate, y is the LHS, the RHS is a linear function of the vars
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

114. 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

115. 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.