About the VMP Method of Forecasting Incentives
- General Definition of VMP:
- The term "Value Marginal Product" (abbreviated as "VMP")
refers to a concept which has been used by economists for over 100 years.
The term "Product" refers to the output or production of a good or
The term "Marginal Product" refers to the additional or
incremental amount of Product which results from the use of an additional
input to the production process. The term "Value Marginal Product" (VMP)
refers to the monetary worth or value of the Marginal Product which is
- Definition of Forecaster VMP:
- In the context of forecasting and estimation, the Product is
the information contained in the forecast or estimate. The Marginal
Product of a forecaster is the change in the forecast or estimate which
results from the addition of that forecaster to the forecasting task.
The Value Marginal Product (VMP) of a forecaster is the value to the client
of the information which is added to the forecast or estimate by that
- Optimal Number of Forecasters:
- The more forecasters who are hired to a forecasting task, the
greater the expected accuracy of their combined forecast.
However, due to the law of diminishing marginal returns, as each new
forecaster is added, the expected VMP of each forecaster is reduced.
Ideally, the client (in order to maximize profit, social welfare, or other
objective) should hire additional forecasters until the VMP of each
forecaster equals the cost of hiring the additional forecaster.
In practice, this cannot be done unless the client has a measure of VMP.
By using the VMP method, the client can more
accurately gauge how many forecasters should be hired.
- Optimal Effort by Forecasters:
- The VMP method of incentives not only calculates VMP, but
pays forecasters in accordance with a measure of VMP.
By paying forecasters according to their VMP,
the VMP incentive method encourages forecasters
to set forth effort at optimal levels.
In other words, the forecaster is encouraged set forth additional
efforts until the expected VMP of an additional hour of effort
equals the time-cost (to the forecaster) of an additional hour of effort.
The VMP method of incentives automatically motivates forecasters
to set forth this optimal level of effort;
no supervision of the forecaster's independent work is required.
- Unbiased Incentives:
- The VMP of a forecaster can be measured, regardless of
whether there is only one forecaster or several forecasters.
However, if there are two or more forecasters,
the VMP forecasting incentives method has
the additional advantage of motivating risk-averse forecasters to
render (nearly) unbiased forecasts.
The VMP incentive method applied to only
one forecaster can give biased incentives.
The plural-forecaster system works better
because of the ability to compare the forecasts of different forecasters,
in addition to comparing the forecast with actual outcomes.
This comparison cannot be done if there is only one forecaster.
Because of this advantage in rendering unbiased forecasts,
Dr. Lundgren applied for a patent on the plural-forecaster method
of VMP forecasting incentives.
- Observable Variables:
- If the quantity to be estimated will be observed at a later
date, it is only necessary to use two or more forecasters to obtain
The quantity which is observed at the later date can
be used as a "criterion value" which is used to judge the accuracy
of forecasters' predictions.
An example of an observable variable
is the state of the ozone layer in the year 2009.
- Unobservable Variables:
- If the quantity to be estimated is unobservable,
or will not be observed for a very long time,
it is possible to use proxies for the criterion value.
These proxies are called "criterion estimates."
There are two types of criterion estimates:
"contemporaneous criterion estimates" and
"future criterion estimates."
The technique which uses a contemporaneous criterion estimate
requires three or more forecasters in the present.
The technique which uses a future criterion estimate
requires two or more forecasters in the present,
and two or more forecasters in the future.
An example of a variable which is not
observable for a very long time is the state of the ozone layer
in the year 2059.
An example of a variable which is never observable is
the change in the ozone layer in 2009 which is caused by man-made
pollution in 2005.
- Additional Details:
- Further details of a more technical nature can be found in
many of the papers listed under
Comments, questions, and suggestions can be sent to
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