Download Estimating the Value of Improved Information

Estimating the Value of
Improved Information
Michael B. Ward
Jay P. Shimshack
Examples
• Value of Climate/Weather Forecasts to
Agriculture
• Value of Nutritional Information to
Consumers
• Value of Information on Toxics or
Pesticides in Food to Consumers
Standard Approach
• Revealed Preference
• How do Consumers or Producers change
behavior under different information sets?
• Assume that agents make optimal choices
given available information (as with all
revealed preference approaches).
• ??? Can we answer the question using
only cross-sectional or aggregate data ???
Welfare Loss
Standard Subsidy-Analysis Triangle
Price
Dead Weight Loss
P1
P0
Quantity
Value of Information, or
Cost of Ignorance
Information Loss Triangle
Price
Dead Weight Loss
P1
Wrong Information Demand
Right Information Demand
P0
Implicit Price
Quantity
Uninformed Quantity is as-if price were lower for informed demand
P1 *
Loss    Q (P0) Q ( p)dp
i
i P0 i
i
• Tax-Analysis … Aggregate demand gives right
results.
• Sum of Integrals equals Integral of Sums for
fixed integration limits (market prices: P0, P1).
• Information Analysis … Aggregate demand
gives wrong results.
• Implicit Price (P0) differs across consumers.
So, welfare limits of integration differ for each
consumer if there is any heterogeneity.
• We cannot move the summation inside integral.
Welfare Bound
• Preceding is a destructive result.
• Can we say anything useful about value of
information without full panel data?
• Yes, we have a constructive result.
• Value of information calculation on
Aggregate or Cross-Sectional data always
gives an under-estimate of the correct
measure.
Theoretical Approach
• Represent arbitrary demand curves nonparametrically, as infinite-dimensional
linear combinations of basis functions,
splines for example.
• Construct individual welfare measures as
a function of the basis function weights.
• Demonstrate curvature is convex in the
weights.
• Result follows by Jensen’s Inequality.
Simple Example
• Two consumers, linear demand, identical
demand under initial information.
• First consumer is indifferent to new
information
• Second consumer cuts consumption in
half at all prices.
• Measure based on average demand is ½
of the correct value, measure individually.
Bottom Line
• Correct information results cannot be obtained
from market or cross-sectional data given
heterogeneity.
• Optimal data is panel, to capture full range of
heterogeneity.
• However, we can still produce useful welfare
results given such limited data. The standard
analysis on aggregate demand produces a lower
bound.
• Empirical results, both future & past, based on
limited data can be rigorously defended from a
theoretical perspective.