UCSD MGT 100 Week 06
Discrete heterogeneity by segment
Continuous heterogeneity by customer attributes
Individual-level demand parameters
- We'll do 1 & 2
MNL can estimate quality; Het demand estimates quality & fit
Enables “policy experiments” for variables we {manage,can measure,predict sales}
- Pricing: price discrimination, two-part tariffs, fees, targeted coupons
- Customer relationships: Loyalty bonus, referral bonus, freebies
- Social media: Posts, likes, shares, comments, reviews
- Advertising: Ad frequency, content, media, channels
- Product attributes: Targeted attributes, line extensions, brand extensions
- Distribution: Partner selection, intensity/shelfspace, exclusion, in-store environment
Common individual- & market-level factors (\(\gamma_t\), \(\gamma_i\))
- E.g., customer income, usage intensity, category experience, etc.
- E.g., market size, history, population density,
- Changes over time could interact with product attributes to affect demand
Quantifies M&A results; oft used in antitrust
Let \(w_{it}\sim F(w_{it})\) be observed customer attributes that drive demand, e.g. usage
\(w_{it}\) is often a vector of customer attributes including an intercept
Assume \(\alpha=\gamma w_{it}\) and \(\beta=\delta w_{it}\)
Then \(u_{ijt}=x_{jt}\delta w_{it}- p_{jt}\gamma w_{it} +\epsilon_{ijt}\) and
\[s_{jt}=\int \frac{e^{x_{jt}\delta w_{it}- p_{jt}\gamma w_{it}}}{\sum_{k=1}^{J}e^{x_{jt}\delta w_{it}- p_{jt}\gamma w_{it}}} dF(w_{it}) \approx \frac{1}{N_t}\sum_i \frac{e^{x_{jt}\delta w_{it}- p_{jt}\gamma w_{it}}}{\sum_{k=1}^{J}e^{x_{jt}\delta w_{it}- p_{jt}\gamma w_{it}}}\]
- We usually approximate this integral with a Riemann sum
What goes into \(w_{it}\)?
What if \(dim(x)\) or \(dim(w)\) is large?
Assume \((\alpha_i,\beta_i)\sim F(\Theta)\)
- Includes the Hierarchical Bayesian Logit we talked about in weeks 3 & 4
Then \(s_{jt}=\int\frac{e^{x_{jt}\alpha_i-\beta_i p_{jt}}}{\sum_{k=1}^{J}e^{x_{jt}\alpha_i-\beta_i p_{jt}}}dF(\Theta)\)
Typically, we assume \(F(\Theta)\) is multivariate normal, for convenience, and estimate \(\Theta\)
We usually have to approximate the integral, often use Bayesian techniques (MSBA)
- Let's talk through how this works
Or, we can estimate \(F\) but that is very data intensive
In theory, we can estimate all \((\alpha_i,\beta_i)\) pairs without \(\sim F(\Theta)\) assumption, but requires numerous observations & sufficient variation for each \(i\)
Humans choose the model
How do you know if you specified the right model?
- Hints: No model is ever "correct." No assumption is ever "true" (why not?)
How do you choose among plausible specifications?
Pros and cons of model enrichments or simplifications?
Bias-variance tradeoff
- Adding predictors always increases model fit
- Yet parsimony often improves predictions
Many criteria drive model selection
- Modeling objectives
- Theoretical properties
- Model flexibility
- Precedents & prior beliefs
- In-sample fit
- Prediction quality
- Computational properties
Heterogeneous demand models enable personalized and segment-specific policy experiments
Demand models can incorporate discrete, continuous and/or individual-level heterogeneity structures
Heterogeneous models fit better, but may predict worse if over-specified