5
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
6
•
•
EVC
traced out
by
demand
curve
7
8
Profit-optimal Solution*
Choose prices such that:
L* = - E-1 1
12
• More of that model are sold
• At lower price
•
•
•
•
More peripherals – Surface Pen, Surface dock are sold
Fewer Surface Books are sold
Fewer MacBook Pros are sold
Some people planning to buy later are induced to buy
now
• Future sales at full margin are cannibalized
Office of the Chief Economist |
18
Log Sales
Office of the Chief Economist |
19
• Simple econometric model:
log 𝑠𝑎𝑙𝑒𝑠𝑖,𝑡 = 𝛼𝑖 + 𝜖𝑖 ⋅ log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 + 𝜖𝑖𝑡
• Implied counterfactual demand curves are
fixed from week to week.
• Simple econometric model implies that you
have assumed simple counterfactual.
• Is this counterfactual right? Maybe not:
• Seasonal trends.
• Products could wax/wane in popularity.
• If these factors are also related to pricing
policy, will cause omitted variable bias.
Log Sales
ignoring z
AND
log 𝑠𝑎𝑙𝑒𝑠𝑖,𝑡 = 𝛼𝑖 + 𝜖𝑖 ⋅ log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 + 𝛾 ⋅ 1{𝐶ℎ𝑟𝑖𝑠𝑡𝑎𝑚𝑠𝑡 } +𝜇𝑖𝑡
log 𝑠𝑎𝑙𝑒𝑠𝑖,𝑡 = 𝛼𝑖 + 𝜖𝑖 ⋅ log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 + 𝛾 ⋅ log 𝑠𝑎𝑙𝑒𝑠𝑖,𝑡−1 +𝜇𝑖𝑡
log 𝑠𝑎𝑙𝑒𝑠𝑖,𝑡 = 𝛼𝑖 + 𝜖𝑖 ⋅ log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 + 𝛾 ⋅ 𝑀𝑎𝑟𝑘𝑒𝑡𝑖𝑛𝑔𝑖,𝑡 +𝜇𝑖𝑡
and
or
Econometrics
Hand picked models that
exploit natural
experiments to mimic
A/B tests
The intersection is brand new
Harness the predictive power of
ML to assist in causal inference
Machine Learning
Automated model selection,
embrace high dimensional
data, focus on prediction
• Pure prediction steps
machine learning
• Measurement steps where elasticities are estimated in an unbiased way on left over variation.
Our Strategy: Estimate a “
outcome
treatment
treatment effect
Baseline features that predict prices or sales
Unknown predictive functions
Step 2: Compute residuals:
Step 3: Run a simple regression of tilde Q onto tilde P
Our Strategy: Estimate a “
outcome
treatment
treatment effect
Baseline features that predict prices or sales
Unknown predictive functions
Step 2: Compute residuals:
Step 3: Run a simple regression of tilde Q onto tilde P
𝜇
will not work.
they anticipate
become less popular
Predicting Sales
sales
t0+1.
This is just a prediction problem and can use any ML algorithm that maximizes
predictive power out of sample.
time t0.
time t0.
• Indicator variables for each site, product, and different months/weeks of the year (
• Arbitrary interactions and transformations of these variables.
• Important: Do NOT (yet) use any information on price offered in period t0+1.
𝑄𝑖,𝑡 = 𝑔 𝑋𝑖,𝑡 + 𝑄𝑖,𝑡
𝑄𝑖,𝑡
sales
“different from our expectation”
)
𝑄𝑖,𝑡 = 𝑔 𝑋𝑖,𝑡 + 𝑄𝑖,𝑡
Time Series:
Sales
t0-4
Time Series:
Prices
t0-3
t0-2
t0-1
t0
t0+1
Predicting Prices
prices
t0+1.
time t0
time t0
• Indicator variables for each site, product, and different months/weeks of the year (
• Arbitrary interactions and transformations of these variables.
• Important: Do NOT (yet) use any information on price offered in period t0+1.
𝑃𝑖,𝑡 = 𝑓 𝑋𝑖,𝑡 + 𝑃𝑖,𝑡
pricing
“different from our expectation”
)
𝑃𝑖,𝑡 = 𝑓 𝑋𝑖,𝑡 + 𝑃𝑖,𝑡
Time Series:
Sales
t0-4
Time Series:
Prices
t0-3
t0-2
t0-1
t0
t0+1
Measuring
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