1. Carnegie Mellon University
Learning About New Products: An Empirical Study of Physicians’ Behavior
Maria Marta Ferreyra
Carnegie Mellon University
Grigory Kosenok
New Economic School

2. Motivation How do agents learn the quality of new products?
This paper:
Physicians learning about the quality (effectiveness) of a new pharmaceutical
Dynamic discrete choice model of physician Bayesian learning about the quality of a new drug
Solve the uncertainty through experimentation (prescription)
It is critical to understand physicians’ learning

3. Contributions Predict market demand for new drug
Model is behaviorally rich, yet parsimonious
Forward-looking physicians
Coscelli and Shum (2004): same data, myopic docs
Forward-looking docs fits data better
Quantify myopia effects and learning value
Crawford and Shum (2005): related patient-level data; patients learn their match w.r.t. drugs
We focus on predicting market demand
Physicians learn (not patients)  spillovers
Narayanan and Manchanda (2007): myopic docs

4. Contributions (cont.) Computational/methodological contribution
Forward-looking behavior + 500,000 prescriptions are challenging
Need to calculate value function for each prescription (and parameter point)
Exploit theoretical properties of model, and features of the data
Calculate threshold rules for optimal behavior
Reduce dimensionality of problem
Major reduction in computing time and accuracy gains
Approach may be applicable to other problems as well

5. Contributions (cont.) Counterfactuals:
Uncertainty affects prescription behavior and health outcomes
Myopia aggravates these effects
Price discount for new product can help

6. Plan Data Model Estimation Estimation results Counterfactuals
Concluding remarks

7. Data Data collected by the Italian National Institute of Health
All anti-ulcer prescriptions by random sample of docs in Rome b/w June 1990 and December 1992
256 physicians, 31 months
For each physician and month:
Total number of prescriptions
Number of omeprazole prescriptions
New drug v. “the incumbent”
Almost 8,000 doctor-month observations

8. Omeprazole Market Share

9. Model: Basic Story
Doctor sees a stream of patients; each one gets a prescription
Two anti-ulcer drugs:
incumbent drug  known quality
new drug  unknown quality  doctor has beliefs
Doctor sees patient’s condition writes prescription
Patient returns at the end of the treatment
If new drug:
Outcome is a signal of new drug’s quality
Update beliefs

10. Model Doctor i, patient k (who arrives at tk) Drugs:
Drug 0 (old drug)  known quality = 0
Drug 1 (new drug)  unknown quality = d
No agency problem between doc and patient

11. Model (cont.) Patient arrival process differs across doctors
Time elapsed between two consecutive patients follows Gamma distribution:

12. Utility and Outcomes Doctor i’s instantaneous utility:
= patient’s observed condition (match parameter)
= true (unknown) quality of the new drug
= outcome’s random term
and are i.i.d., independent of each other, and:

13. Utility and Outcomes (cont.)
Prices are also i.i.d.
New drug’s outcome:
When patient returns, doctor sees full outcome. In particular, he sees signal for new drug’s quality:

14. Beliefs Doctor’s beliefs at time 0:
Experimentation is the only source of learning
When seeing patient k, doctor’s beliefs are:
Doctor perceives the distribution of the signal as follows:

15. Beliefs (cont.)
Using the new drug’s signal, he updates his beliefs as follows:
No updating if he prescribes old drug

16. Doctor’s Objective Function
Doctor seeks to maximize expected discounted utility (payoff):

17. Analysis of Model
At time t, state variables are
Bellman Equation:

18. Value Function Rewrite value function as follows:
There is a threshold for that makes the doctor indifferent between drugs:

19. Threshold Rule, and Value Function

20. Threshold Function Write equation for threshold function as follows:
where
and

21. Estimation Parameter Vector: Steps:
Step 1: Calibrate discount factor (k = ; annual discounting of 0.997)
Step 2: Estimate mean of price difference from sample (1,106 liras per day)
Step 3: Estimate arrival process per doctor through MLE
Per doctor, match empirical distribution of patients per month to distribution implied by Gamma
Step 4: Estimate remaining parameters

22. Step 4: Simulated MLE Recall: data per month and doc:
Number of patients (=prescriptions)
Number of omeprazole prescriptions
We are missing some pieces of information:
Sequence of prescriptions (e.g., new, old, old, new, etc.)
Beliefs when writing each prescription
Signals
Thus, we pick S=1,000 prescription sequences consistent with the data
For each sequence (and parameter point):
Generate prescription signals
Calculate the implied beliefs

23. Step 4: Simulated MLE We maximize the following function:
with respect to five parameters

24. Computational Considerations
To evaluate likelihood for a parameter point:
Solve for threshold function for 40,000,000 combinations of beliefs and discount factor  15 seconds
Calculate probability for the S simulated sequences  15 seconds

25. Estimation Results

26. Goodness of Fit

27. Counterfactuals Use parameter estimates to gauge:
Cost of uncertainty
Cost of myopia
Effects of price
Value of learning
Alternative scenarios for:
Representative doc; 50 patients per month
10 years
Treatment lasts 14 days
Patient pays a 50% copay
Price difference is constant, equal to observed sample mean

28. Cases To Compare Forward-looking physician Myopic physician
Uncertain about new drug’s quality
Forward-looking
Myopic physician
Myopic (only maximizes current utility)
Fully-informed physician
Knows new drug’s quality
New drug’s outcome continues to be random

29. Prescription Behavior

30. Expected Health Outcomes (thousands of liras)

31. Summarizing (and Decomposing) the Losses (20 years following new drug’s entry)

32. Informational Failures: Other Implications
Revenue losses to the manufacturer
Over the first 10 years, revenues are 23% lower when physicians are forward-looking rather than fully-informed
Advertising and detailing make sense
Suboptimal health outcomes  central planner could choose price to maximize expected social welfare
Optimal price difference = -15 liras
Social welfare is 5% higher than with the observed price
What if optimal price is not feasible?
Implement price that yields same welfare as full information
Price difference is 1,031 liras (instead of 1,106 liras)

33. Concluding Remarks Experience goods  study learning process
Focus on new anti-ulcer drug in Italy
Bayesian learning process for forward-looking physicians
Parsimonious, rich model that fits data well
Very large computational savings
High learning value to prescribing new drug
Myopia is very costly
… but price subsidies can mitigate effects of informational failures
Approach may be applicable to other dynamic discrete choice models