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 Quantity Price P1 P0 Dead Weight Loss

Value of Information, or Cost of Ignorance Information Loss Triangle Quantity Price P1 P0 Dead Weight Loss Wrong Information Demand Right Information Demand Implicit Price Uninformed Quantity is as-if price were lower for informed demand

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 non- parametrically, 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.