Download Learning About New Products: An Empirical

Learning About New Products:
An Empirical Study of Physicians’
Behavior
Maria Marta Ferreyra
Carnegie Mellon University
Grigory Kosenok
New Economic School
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
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
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
Contributions (cont.)
• Counterfactuals:
• Uncertainty affects prescription behavior and health
outcomes
• Myopia aggravates these effects
• Price discount for new product can help
Plan
• Data
• Model
• Estimation
• Estimation results
• Counterfactuals
• Concluding remarks
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
Omeprazole Market Share
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
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
Model (cont.)
• Patient arrival process differs across doctors
• Time elapsed between two consecutive patients
follows Gamma distribution:
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:
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:
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:
Beliefs (cont.)
• Using the new drug’s signal, he updates his beliefs as
follows:
• No updating if he prescribes old drug
Doctor’s Objective Function
• Doctor seeks to maximize expected discounted utility
(payoff):
Analysis of Model
• At time t, state variables are
• Bellman Equation:
Value Function
• Rewrite value function as follows:
• There is a threshold for
doctor indifferent between drugs:
that makes the
Threshold Rule, and Value Function
Threshold Function
Write equation for threshold function as follows:
where
• and
Estimation
• Parameter Vector:
•
Steps:
• Step 1: Calibrate discount factor (k = 0.00025; 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
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
Step 4: Simulated MLE
• We maximize the following function:
with respect to five parameters
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
Estimation Results
Goodness of Fit
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
Cases To Compare
• Forward-looking physician
• Uncertain about new drug’s quality
• Forward-looking
• Myopic physician
• Uncertain about new drug’s quality
• Myopic (only maximizes current utility)
• Fully-informed physician
• Knows new drug’s quality
• New drug’s outcome continues to be random
Prescription Behavior
Expected Health Outcomes (thousands of liras)
Summarizing (and Decomposing) the Losses
(20 years following new drug’s entry)
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)
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