CANADIAN WHEAT ACREAGE RESPONSE*

ANDREW ECHMITZ* *

In spite of the criticisms which have been levied against statistical estimation of supply response, it is used in this study t o determine the factors causing yearly fluctuations in Canadian wheat acreage. The esti- mates are derived from 1947-1966 time series data. In formulating price expectations, both the tradirional and distributed lag models are used.

J r was found that wheat acreage response is not a random process. From a statistical standpoint, wheat and flax prices, wheat stocka on farms, and export sales did affect farmers’ wheat acreage decisions. Among the elasticities computed, those for wheat prices were the largest bur generally less than one. Barley prices, rainfall prior to seeding, and cattle prices were also considered but did not appear to have a serious influence on wheat acreage,

In Canada, wheat occupies more cultivated acreage than the total of all other cereal crops grown. Yet, little is known about the factors giving rise to yearly changes in aggregate wheat acreage.

Whether a meaningful Canadian wheat acreage response relationship can be estimated by statistical techniques is open to question. Schnittker [7, pp. 1087-881 points out that:

“Wheat is the most troublesome commodity in Canada and the United States. . . . For wheat, progress in clarifying the response of produc- tion to price changes is far short of the stage necessary to serve as an effective instrument for policy formulation. . . . I do not know the ideal method of studying the response of wheat production to price. But I would like to make it clear, with apologies to my colleagues who keep trying, that I consider statistical treatment of the time series of selected indicators of price and output a most unrewarding method.”

This study arises from a curiosity of whether or not the belief held by Schnittker is correct. I t attempts to measure the factors influencing Cana- dian wheat acreage response using single-equation, least-squares estimation applied to 1947-1966 time series data. Among the detailed studies which have used statistical techniques in estimating wheat acreage response are those by Candler [l] for New Zealand, Duloy and Watson [2] for Aus- tralia, and Oury [ 5 ] for France.

Wheat Acreage Response Relationships

Nonprice Variables A theoretical formulation of Canadian wheat acreage response must

include the following nonprice variables: Moisture prior t o and during

Helpful comments on an earlier draft of this paper were received from R. M. A. b y m and G. A.

* * Andrew Schmitr is Assistant Professor of Agricultural Economics u the University of California, MncEachern.

Berkeley.

79

seeding, wheat stocks stored at the farm level, wheat export sales, tech- nology, and capital availability. I t is hypothesized that: the more rainfall prior to and during seeding, the greater is the percentage of stubble land seeded to wheat; as wheat stocks accumulate on farms, there is a tendency for farmers to increase their plantings of such crops as barley and flax by reducing wheat acreage; wheat acreage increases as the volume of export sales increase; and as the level of technology improves and more capital becomes available, a greater percentage of uncultivated land is brought into production.

Since data prior to the termination of World War I1 are not used in estimation, no consideration is given to the effect of government immigra- tion and land settlement policies on acreage response. As is well known, the growth of wheat acreage in the early 1900’s was largely dependent on the influx of settlers.

Product and Input Prices On many of the wheat farms in Canada, among the commodities

produced are oats, barley, flax, and livestock. How aggregate wheat acreage responds to price changes of these commodities depends in part on the price expectation model formulated by the farmer at the time of seeding.

Several price expectation models have been used in statistical esti- mation of supply response [3]. Only two price expectation formulations are used in this study. These are the traditional and distributed lag models.’ To illustrate, suppose the model is 1 In estimating distributed lag models of the form discussed earlier. least-squares atimarion may be

inappropriate. This is because the estimated quatiom contain lagged acreage as an addirional var- iable; hence. they are no longer conditional expectation functions. To illustrate. suppose the popula. tion regression function for acreage response is:

YT

%I

E (-, . . ., XTK) where Y, (acreage) is conditional on the regressors X,, . . ., X,. The equation equals

et &, = & X, + . . . + BK XT, + E (-. . . ., XTK)

XT, where

XTI implying C (et , &,) = 0. Because of the lack of correlation bxwccn the error term and the regressors. a conditional expectation function exisa. and Insr-squares estimation is appropriate. How- ever, if the

e t E (-, ..., XTx) = 0. t h e C (e t , XTK) = 0. X,

This is the case with distributed 1% models since a conditional expectation function no longer exisa. Ideally. when a tha r ing distributed lag models, an estimation method devised by Liviatan (41 should be used. However. least-squares estimation is used since Duloy and Watson [2. p. 371 indiate that: “The bias of Ieastaqures estimates of disrributcd lag models compared with asymptorically unbiased estimamn can thus be considered in the same way as have similar problems arising with small sample estimates of rimulcaneour equations. There exists a tendency unongsr empirical worken in ecooo- metria to put forward the dpi that the asymptotic propenia of sirnuloneour a r h t o n axe noc sufficient grounds for their use where small samples .are involved. Funher. lepsr-squus a t imn ta have generally,~maller variances. and are. moreover. frquently very close to esdmPtn obtained by other methods.

8 1

At = a. + a, P*t + et (1) where At is wheat acreage seeded and P*, is expected product prices. The traditional model assumes that

The distributed lag structure takes the form

where P*, is the expected price for a commodity at time t and p is the coefficient of expectations. Equation (3) allows both short- and long-run price elasticities to be computed since the estimated acreage equation is of the following form:

where ut = e, - (1 - p) et-l. In equation (4), A, is acreage seeded and alp is the short-run price coefficient. The long-run price coefficient, al, can be calculated since (1 - p) is known.

In a theoretical formulation, acreage response (viewed as a compo- nent of output) is also a function of input prices. However, these are not considered in statistical estimation. Although input prices have been rising and capital has continually replaced labor as an input, aggregate wheat acreage response has likely been unaffected. The major effect of increasing input prices has been to expediate the rate of farm consolidation, causing an increase in land prices.

P*, = Pt-1. (2)

P*t = P*t-1 + p (Pt-1 - P*,_l) (3)

At = aoP + alp Pt-l + (1 - P I At-1 + Ut (4)

Statistical Estimation Variables and Units of Measurement

Trend is used as a proxy variable to measure the impact of capital availability and technology on wheat acreage response. Powell and Gruen [6, p. 1201 indicate for Australia, which is also true for Canada, that these factors are difficult, if not impossible, to measure.

“For an analysis of the long run it is clear that we would need indexes of the flow of capital services, for these essentially will deter- mine the schedule of production possibilities. Whether it is possible or not to construct such indicators independently of output measures is a moot point. In any event . . . Australian data on the amount o€ agricultural capital available - let alone the flow of services from such capital - is very inadequate.” The export sales and wheat farm stocks are measured as the amounts

existing on July 31 of each crop year. It is assumed that, at the time of seeding, farmers are able to calculate these levels. For wheat stocks, an alternative is also considered, based on a belief that farmers do not respond to changes in wheat stocks below a specified level. Therefore only stocks above 100 million bushels are considered in estimation.

.When measuring wheat and barley prices, any one of three price series for each one of the crops could be included in statistical estimation:

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the initial payment received from grain sales prior to seeding, the latest final price received prior to seeding and the final price actually received from the crop planted which assumes that farmers are able to calculate final receipts on the basis of initial payments.

In this study the latest final price (including the final payment) prior to seeding is used. For crops such as flax, not regulated by the Wheat Board, and for livestock, prices received at delivery include final payments. For these commodities, average prices received during the month of April are used.

An Interpretation and Discussion of Results

traditional and distributed log price expectation framework.

Interpretation The interpretation of the results is made with reference to the equa-

tions 9 and 25 in Table l which are based on the traditional and distri- buted lag price expectation models, respectively:

In Table 1 alternate equations estimated are presented using both the

A,= 10,416.73 + 9,440.89 P~,-1-801.06Pft-1 + 196.48T-0.013 S, (2,552.66) a (3 98.22)b (49.83). (0.004). ( 9 )

R? - - 0.855 D.W. = 2.09

A t = 11,937.36 + 7,028.51 P w , - ~ - 1,151.34 Pf t-1 + 0.272A,-1-O0.015 S, (3,588.82)C (425.89)c (0.214) (0.007)b (25)

R'= 0.795 D.W. = 1.58

In equation (9), seeded acreage, At, and stocks, St, are scaled by 1,000 bushels, therefore, a $1.00 change in wheat prices results in a 9,440,890 change in seeded acreage. A $1.00 change in flax prices changes acreage by 801,060 and for each 1 million bushel change in wheat stocks at the farm level, seeded acreage changes by 13,000 acres. A unit change in time, T, changes acreage by 196,480.

The four regressors are significant and explain 86 percent of the variation in acreage with autocorrelation absent.

For equation (25) a similar interpretation can be given. However, alB the short-run price coefficient for wheat response is 7,028,510. The long-run price coefficient is 9,654,547 since (1 - B) is 0.272.

Price Elasticities

Table 2 presents the range of price elasticities computed from the equations presented previously. The results indicate that the price elas- ticities of the commodities considered are less than one when using the traditional price expectation model. Among the elasticities, those for wheat are the highest, ranging from a low of .491 to a high of .877. The

84

Traditional

High

Low

wheat price elasticities, based on the distributed lag model, range from .420 to .754 for short-run response and from .622 to 1.30 for long-run response.

Coefficients and Their Startistical Significance In all the estimated equations, the signs of the rainfall and cattle

price coefficients are opposite to those expected. However, only cattle prices are statistically significant. Perhaps past changes in livestock prices have not greatly influenced acreage and, therefore, should not be included in estimation. It could be argued that variation in livestock numbers is more dependent on wheat export sales and the accumulation of wheat stocks on farms (resulting from quotas) than on changes in relative product prices. For example, the total number of cows and calves declined from

TABLE 2. THE RANGE OF PRICE ELASTICITIES BASED ON THE TRADITIONAL AND DISTRIBUTED LAG PRICE MODELS~.

PrIn EWeIties I

.811 .193 .oo 1 .132

.49 1 .080 b .058

Distributed Lag

High Low

Wheat Price ELactIcitiu I

.754 1.30

.420 .622

I I Short Run Long R m

11.9 million in 1964 to 11.5 million in 1966 in spite of an increase in relative cattle prices. This decrease in cattle numbers could have resulted from the buoyant wheat market associated with the Russian and Chinese wheat sales. One additional argument why wheat acreage response has unlikely been influenced by livestock price changes is that livestock are grown in conjunction with wheat as a means of utilizing winter labor and uncultivated land; this mitigates the competition between wheat and live- stock enterprises for the use of a given amount of resources.

Among the crops grown, barley prices are statistically insignificant while flax prices are at least significant at the 10 percent level of probabil-

85

ity. However, in no case does a $1.00 change in flax prices change acre- age by more than 1.5 million. In all cases, wheat prices are statistically significant. The results show that a $1.00 change in wheat prices causes an approximate 8 million change in wheat acreage, indicating that wheat prices have a greater influence on acreage decisions than do changes in flax prices.

In addition to the wheat price variable, export sales are statistically significant in all cases. This is also true, in many of the equations, for the wheat stock variable regardless of how it is measured. However, in spite of their statistical significance, the size of the coefficients for export sales and stocks is perhaps underestimated. For example, in no case does a 100 million bushel change in export sales cause more than a 15,000 change in wheat acreage. One explanation is that export sales and wheat prices are highly correlated, making it difficult to estimate their separate effects. Therefore, part of the effect of a change in export sales on wheat acreage could have been incorporated into the wheat price variable caus- ing the effect of the latter to be overstated. That is, the estimated price effect is likely to be smaller if only prices change and export sales are held constant than if both prices and export sales vary over the data used for estimation.

The variables referred to above are statistically significant even in those equations where autocorrelation is absent; this is critical when inter- preting the results. The presence of autocorrelation contributes to smaller standard errors than exist in the population, causing the student t values to be overstated. Therefore, in cases where autocorrelation exists, it is often incorrect to reject null hypotheses of no association on the basis of high student t values.

Economic Predictions

In spite of the limitations of testing the predictive accuracy of a model on data used in estimation, it is interesting to note the accuracy with which an equation containing only stocks, wheat and flax prices, and export sales can predict yearly wheat acreage response. This is indicated in Table 3. The results show that in each year the difference between the actual and predicted wheat plantings is less than 500,000 acres.

In conclusion this study indicates that Canadian wheat acreage re- sponse is not a random process; wheat acreage decisions have been influ- enced by changes in wheat and flax prices, wheat export sdes, and wheat farm stocks. Whether the statistical procedure used to derive these results is inappropriate, as asserted by Schnittker, is unanswerable at this time. To determine this, the previous equations have to be tested on forthcoming data.

86

Yepr Actual Acreas8 1 Prtdkted Amaec I Residual

1,OOO Acres

1962

1963

1964

1965

1966

428

305

311

273

79 I

~

26,237 25,809

26,996 26,691

29,080 28,769

27,790 27,517

29,780 29,70 1

References 1. Candler, W., “An Aggregate Supply Function for New Zealand Wheat,” 1. Farm

Econ., 39: 1732-1741, December 1957. 2. Duloy, J. H.. and A. S. Watson, “Supply Relationships in the Australian Wheat

Industry: New South Wales,” Australian 1. Agr. Econ.. 8:28-45, June 1964. 3. Griliches, Z., “Distributed Lags: A Survey,” Econoniefrico, 35: 16-49, January

1967. 4. Liviatan, N., “Consistent Estimation of Distributed Lags,” Internof. Econ. Rev.,

4:44-52, January 1963. 5. Oury, B.. “A Tentative Production Model for Wheat and Feedgrains in France.”

Unpublished Ph.D. dissertation, Department of Agricultural Economics. Univer- sity of Wisconsin, Madison, 1963.

6. Powell, A. A., and F. H. Gruen, “Problems in Aggregate Agricultural Supply Analysis: Preliminary Results for Cereals and Wool,” Rev. Markefing and Agr. Econ., Department of Agriculture, N. S. W., Australia, 34-186, December 1966.

7. Schnittket, J. A., “The Response of Wheat Production to Prices with Emphasis on Technological Change,” 1. Farm Econ., 30: 1087-1 100. December 1958.