The Optimal Level of Experimentation
20 Pages Posted: 28 Jun 1998
There are 2 versions of this paper
Date Written: January 2000
Abstract
We assume that an impatient decision maker (DM) runs variable-size experiments at an increasing, strictly convex cost before choosing an irreversible action. We introduce and solve a tractable continuous time version of this problem --- a control of variance of a diffusion with uncertain mean. Assuming two states and two actions, we prove: (a) the optimal experimentation level rises in the Bellman value; and deduce testable implications, like (b) experimentation costs drift up; and (c) a more impatient decision maker may experiment more, given lump-sum final payoffs. We show that (a) and (b) are robust to finitely many states and actions, and we also extend an R&D interpretation of the model, where experimentation is monotonic not only in the value, but also in beliefs.
Our intuition for our key monotonicity finding (a) is very economic. There are two decisions at each instant: stop or experiment, and then at what level n. The second choice equates the marginal costs and benefits of information: c'(n) = MB(n). In our diffusion setting, the marginal benefit of experimentation is constant, and so the total benefit TB is linear in the level: TB = n*MB = nc'(n). So the DM acts like a neoclassic competitive firm, producing information at an increasing marginal cost and selling it to himself at the fixed price c'(n). Since postponing the final decision entails a discounting cost, optimal stopping demands that the DM equate his producer surplus from experimentation nc'(n)-c(n) to the delay cost rV (given the interest rate r). Intuitively, the DM closes down his information firm (i.e. acts) when he cannot generate profits (producer surplus) to justify his capital rental (his deferred action). Since this surplus rises in quantity with convex costs, greater experimentation is needed to generate the higher surplus for a higher value V.
JEL Classification: C11, C12, C44, C61, D81, D83
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
The Optimal Level of Experimentation
By Giuseppe Moscarini and Lones Smith
-
The Demand for Information: More Heat than Light
By Jussi Keppo, Giuseppe Moscarini, ...
-
Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information
By Hector Chade and Edward E. Schlee
-
Investment Timing Under Incomplete Information
By J. P. Decamps, Thomas Mariotti, ...
-
Investment Timing Under Incomplete Information
By Jean-paul Decamps, Thomas Mariotti, ...
-
The Law of Large Demand for Information
By Lones Smith and Giuseppe Moscarini
-
The Law of Large Demand for Information
By Giuseppe Moscarini and Lones Smith
-
Expected Consumer's Surplus as an Approximate Welfare Measure
-
Optimal Electoral Timing: Exercise Wisely and You May Live Longer
By Jussi Keppo, Lones Smith, ...
-
Time-Consistent Optimal Stopping
By Lones Smith