pOTENTIAL BENEFITS TO AGRICULTURE OF AUGMENTING PRECIPITATION

This paper discusses ongoing research intended to develop a clearer understanding of the impact of weather modification on a portion of the agricultural sector of the U.So economy, the feed-livestock complex. The research framework models the interactive effects of changing weather, technology, government policies, and demand on market prices. Supply and demand relations may be estimated and solved within the context of a simultaneous equation econometric model~ Within the model, crop yield response relations must be estimated at an appropriate level of geographical aggregation to ensure uniform measurement of weather modification effects. An econometric technique, based on the use of binary variables, is proposed as means for selecting geographical aggregates. The transmission of the "weather effect" to the agricultural sector is accomplished in the supply-demand model. Benefits accruing to various market participants may then be identified under alternative scenarios of weather modification.


INTRODUCTION
Climatic and weather variability are important features of midwest agriculture°R ecent extremes in weather and concern over possible shifts in climatic patterns have led to an awareness that a more in.depthunderstanding of climatic and weather related impacts on society by sectors of the economy is essential.

This paper discusses
ongoing research intended to develop a clearer understanding of the impact of weather modification on a portion of the agricultural sector of the U.So econcmy, the feed-livestock complex.1983).
At the next level are regional aggregates, such as the Great Plains or Corn Belt, or subsets of states within those regions, (e.g., Thompson, 1969Thompson, , 1970))  attributable directly to the level of aggregation.
From the national perspective, yields may appear to have levelled off over the 1970s as acreage planted and harvested increased when more marginal lands were brought into production.Since yields on these parcels were lower than on the earlier base, the national average figure is reduced.
In  (1982) used CRD data for their study, but their method of aggregation may be improved.

To account
for inter-district differences arising out of agronomic and economic environmental variation, a systematic statistical framework for analysis may be based on the analysis of variance, implemented in regression analysis through the use of binary (dummy or zeroone) variables° This approach attempts to measure differences among regional aggregates without explicitly identifying the factors which lie at the root of the differences° In yield response studies the identification of the genesis of such underlying differences is less important than accounting for their existence° A "hierarchy" of model specifications can be constructed under varying degrees of similarity across regional units.The existence of these differences may then be tested to determine their significance in some statistical sense, and so should be allowed for in the modeling effort.At present, inter-regional differences are assumed constant across time, although the framework may be easily adapted te compensate for variation over years as well as across regions°4 .
MODEL FORMULATION To facilate empirical investigation, models of inter-regional or crosssectional (as opposed to time series) variation may be defined from the most restrictive hypothesis about response coefficients to the least.The general statistical model for this procedure may be written as: where i = l, ..,N refers to a cross-sectional unit and t = 1 .... ,T refers to a given time period.Thus, Yit is the value of the dependent variable (crop yield) for cross section unit (CRD) i at time t and Xki t is the value of the kth explanatory variable (technology~ weather, etc.) for unit i at time t.The stochastic error term eit is initially assumed to have mean zero and constant variance and be independent across units (i.e~., E(eieS') ~2~_.I, = 0 for i ~ j).The ~kit are unknown response coefficients; in the most general case, they may be different for different units i at different times t; here only differences over i are considered and so the t subscript may be dropped.Using this model, the hierarchy may be defined as below.I. Response coefficients do not differ over units: K Yi = ~0 + Z ~k Xki + el- (

2) k=l
IIo There are differences in the level of response (intercept) over units but not among the (slope) coefficients associated with the individual explanatory variables: K Yi = S0i + Z ~k Xki + el" (3) k=l III.Both intercept and slope coefficients differ over time, and the disturbances (e i) associated with different units are correlated at a given point in time but not over time : where the variance of the disturbance now reflects the correlation across units (E (eiej') = o2ij ~ 0 for i ~ j).
IV.Both slopes and intercepts differ across units, with no relations among contemporaneous errors: K Yi = ~0i + ~ ~ki Xki + el" (5) k=l These models may be applied to test hypotheses about the nature and extent of possible differences among units.

MODEL APPLICATION
In applying these models, the null hypothesis may be taken to be the model of no cross-sectional differences (model I) and the alternative may be formulated as any one of models II, III, or IV.In Thompson's studies, model II was taken as the maintained hypothesis, implying differences in overall yield levels across units (states in his formulation).However, the validity of that assumption may be tested statistically by comparing the explanatory power of model I to that of model II using a standard F test (involving the ratio of the sums of squared error from each model).
Model III suggests that certain random factors (perhaps events in the macroeconomy) may affect all units and that taking into account this similarity will improve the estimates of the individual response coefficients.
This model may be taken as the alternative hypothesis and compared to model I, again using an F test.Model IV implies differences in both level (intercept) and response (slope) coefficients across units, with no relation through the error terms.
If one of II, III, or IV represent the true model, then application of model I to the pooled data will result in biased estimates of the response coefficients.The direction and magnitude of the bias will often be difficult to determine a priori.
Models II, III, and IV account for the existence of various differences among response coefficients by region through the use of binary variables.In general, in each region a binary variable is defined to be one for observations on that region and zero for observations on all other regions.
A more ~etailed description of this technique is given in standard statistical and econometric texts (see, for example, Johnston (1984)).This procedure may be applied to sensible aggregates of data containing more than one CRD.yield; and an identity for production~ (i.eo, area harvested times yield; and an identity for production, (ioeo, area harvested times yield).These four equations are to be estimated for each years 1951-82, for each crop reporting district for the 9 major corn producing states; thereby adding 36 equations to the basic specification.Corn produced outside the major states will be modeled at the aggregated level.

Table I .
Selected Research on the Effects of Technology and Weather on U.S. Crop Yields.-lin.lin.N-lin.PP MP JP Jyp AP MT JT JyT AT pltd.price obsero