San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
USA

 THE HAYAMI-PETERSON MEASURE OF THE SOCIAL LOSS DUE TO INACCURATE CROP FORECASTS

## Introduction

Hayami and Peterson in their innovative 1972 article (1) on the social returns to public crop forecasts developed a method for computing the economic value of increased accuracy of crop forecasts. Producers and users of crops may have to make decisions on inventories and plantings before the crop is harvested. To the extent that these decisions are made on erroneous expectations of output, prices will deviate from the correct values. If output expectations are too low prices will be too high, but once the error is realized when the crop is harvested then excess inventories will be sold off resulting in prices which are too low. The net result is a loss of consumer surplus equal to one half the product of the error in the quantity forecast and the deviation of price from the "correct" value. The same result would hold in the forecast is an overestimate rather then an underestimate.

Hayami and Peterson also developed a production adjustment model but the preponderance of their estimated benefits arise from the inventory adjustment model. For an improvement which reduces the typical sampling error from 3 percent to 2.5 percent, 97 percent of the benefits are from inventory adjustment and only 3 percent from production adjustment.

## Analysis of Welfare Loss Computation

The model utilized by Hayami and Peterson is simple but can be implemented using basic economic information and does give insights into the problem of quantifying the social losses of making decisions on inaccurate information. The specific equation developed by Hayami and Peterson for the social loss incurred from a forecast with a proportional error of e is:

#### social loss = ½e2(Value of Production/α)

where α is the price elasticity of demand. The derivation of this equation is summarized in Figures 1 and 1a.

The analysis for the case in which the forecast under estimates the crop harvest is shown below.

The corresponding analysis for an over estimate of the crop harvest is shown below.

## Using Changes in the Consumer Surplus as the Measure of Benefit or Loss Gives an Erroneous Result

In cost benefit analysis the change in consumer and producer surpluses is often used as the measure of benefits and costs. This procedure may or may not give the correct results. In some cases it is quantitatively in error because it does not take into account the effect of some program on all of the market participants involved. For more on this point see Resolving the Discrepancy Between the Two Approaches to Cost Benefit Analysis..

In the case of the social welfare impact of erroneous crop forecast the consumer surplus approach gives the opposite answer from the correct one; i.e., that there is a gain in benefits from having an erroneous crop forecast. This is shown below:

The analysis for the case in which the forecast under estimates the crop harvest is shown below.

This illustrates the danger of relying solely upon the change in surpluses approach to cost benefit analysis.

### References

• (1) Y. Hayami and W. Peterson, "Social returns to Public Information Services: Statistical Reporting of U.S. Farm Commodities," American Economic Review, Vol. LXII, No. 1, March, 1972, pp.119-130.
• (2) D.S. Lowe, R. P. Summers and E. J. Greenblat; An Econowic Evaluation of the Utility of ERTS Data for Developing Ccuntries, August, 1974.