Factors Affecting The Price And Supply Of ¡a®©

Factors Affecting The Price And Supply Of

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Technical Bulletin No. 1274

U.S. DEPARTMENT OF AGRICULTURE Washington, D.C.

Factors Affecting The Price And Supply Of

By: Arthur A. Harlow Agricultural Economic Statistician

Economic Research Service

Technical Bulletin No. 1274

Economic and Statistical Analysis Bivision U.S. Bepartment of Agriculture

Washington, B.C.

Preface

The major relationships that affect the supply and price of hogs are described in this bulletin. The formulation and statistical fitting of these relations assist in understanding and predicting the effects of economic factors upon hog production and prices. This bulletin is intended to aid Government officials, agricultural economists, extension workers, and members of the industry in imderstanding the forces that affect the hog economy. The chief benefits of the bulletin to farmers will come through its use by Federal and State personnel who work directly with farmers.

Hog production and prices have exhibited fairly regular recurrent cveles since 1949. An explanation for these cycles is developed, using the supply and demand functions for the industry and incorporating the time lags inherent in hog production. A system of six equations is fitted statistically to measure the relative effect of various factors upon variables in the hog economy.

This study deals primarily with the supply and price of hogs. An intensive analysis of the demand for pork, as well as that for beef and lamb, is presented in Technical Bulletin 1253, "Demand and Prices for Meat—Factors Influencing Their Historical Development,'' by Harold F. Breimyer.

In the preparation of this bulletin, extensive use was made of both published and impublished material in the files of the Economic Kesearch Service. Information and assistance were obtained from many specialists of the U.S. Department of Agriculture. Special acknowledgment is made to Anthony S. Rojko, Hyman Weingarten, and Martin E. Abel, of the Economic Research Service, who gave generously of their time and critical faculties during the study.

Issued December 1962. in

CONTENTS

Highlights 1 Introduction 3 Economic importance of hog pro-

duction 5 Efficiency of production 8 Regional variation 13

Major relationships in the hog economy 14

Price expectations of producers 17 The hog-corn ratio 19 Variable factors in pork and

lard production 24 Cycles in price and production 27

A model of the hog cycle 27 Comparison with actual data 29 The cobweb theorem 31

Elasticities of supply and demand- 38_ _ Supply elasticity estimates 39__ Demand elasticity estimates 41 __

IV

Page Elasticities—Continued

Relation between farm, wholesale, and retail demand elasticities 43

A statistical model of the hog economy 46

Statistical considerations in a recursive model 47

Equations in the model 49 Discussion of the variables 51 Evaluation of the model 55 Inclusion of additional variables 57 Evaluation of the revised model 60 Forecasting 62

Seasonal variation in hog production and prices 64

Literature cited 72 Appendix 77

A test for serial correlation 77 Data used in the recursive model 81

For sale by the Superintendent of Documents, U.S. Government Printing OíRce

Factors Affecting the Price and Supply of Hogs

HIGHLIGHTS

Hogs are an important product for U.S. farmers. Cash receipts to farmers from the sale of hogs in 1960 were $2.9 billion, a value exceeded only by poultry and eggs ($3.3 billion), dairy products ($4.7 biUion), and cattle and calves ($7.4 billion). Hogs are the major consumer of feed concentrates, particularly corn. They consistently consume nearly half the corn crop.

The correlation between corn and hog production has been quite close, both quantitatively and geographically. Although the quanti- tative relationship is not as precise in recent years, the regional tieup is still close. The 12 Corn Belt States produced 84 percent of the corn and 77 percent of the hogs raised in the United States in 1960. Government price-support and storage programs have made hog production less sensitive to changes in corn production because these programs provide an alternative market for corn at relatively stable prices.

The close relationship between hogs and corn has often been expressed analytically as the hog-corn price ratio. In the past, this ratio served as a reliable predictor of hog production. Production increased following a period when hog prices were high relative to corn prices and it decreased following a low hog-corn ratio. One short- coming of the ratio for analytical purposes is that it assigns equal importance to corn and hog prices as factors affecting hog production. Under present conditions, with ample corn supplies and prices supported under the price-support program, the ratio is no longer as reliable an indication as formerly. Hog prices have become more important than corn prices in determining future hog production.

The relative importance of com and hog prices is indicated by their effect upon the number of spring farrowings. For the period 1949- 60, a 1-percent increase in the October-December hog price was foUowed on the average by an 0.8-percent increase in the number of farrowings the following spring. In contrast, a 1-percent increase in the October-December corn price led to a decrease in farrowings of only —0.4 percent.

The hog price cycle was one of the earliest recognized economic cycles. Whether measm-ed by price or production, the cycle has become more regular in recent years since hog production is no longer affected as much by variation in the corn crop. Farmers have an alternative use for their corn since the advent of Commodity Credit Corporation loans and purchases under the price-support program. The time lags involved in the hog production process and the interrelationships among price, pig crop, and pig slaughter contribute to the development of a cycle.

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2 TECHNICAL BULLETIN 1274, U.S. DEPT. OF AGRICULTURE

The cobweb theorem provides a theoretical explanation for many economic cycles. This theorem explains a cycle in terms of the supply and demand curves for the industry that are based on a lag between production decisions and marketings. The hog production process has been described for many years as an example of a cobweb phenomenon. In a cobweb model, price in one period affects production in the succeeding period, which in turn affects price, and so on.

The price-quantity relation given in the cobweb is an extremely simplified model of hog production. There are many factors that cause variation in the quantity of pork produced and the price received for it. The number of sows farrowing, the pigs raised per sow, the number of hogs slaughtered and their average weight, all affect the quantity of pork produced. Storage holdings of pork and pork production affect the price of pork, which in turn affects the price of hogs, which affects the number of sows farrowing in following periods. All these variables within the hog industry are influenced by numerous factors outside the industry, such as the»,.prices and supplies of raw materials (feed grains) and competing goods (beef, poultry).

The effects'of these many factors upon variables in the hog economy are estimated in a statistical] model using quarterly data. The variables to be explained in the equations are: (1) the number of sows farrowing, (2) number of hogs slaughtered, (3) quantity of pork producedf, (4) cold storage holdings of pork, (5) retail price of pork, and (6) prices received by farmers for hogs.

The link-by-link procession of price-quantity-price-quantity described by the cobweb theorem marks the hog industry as suitable for analysis by a recursive system of equations. If there were considerable interaction between price and quantity within a given period, a simultaneous equation system would be preferable. To minimize this interaction, quarterly data are used in fitting a recursive system of six equations by least squares.

The residuals from the initial fitted equations were tested to determine whether they fulfilled the assumptions made about the disturbances in formulating the model. As a result, five of the equations were refitted, using additional independent variables. Accord- ing to the available tests, the residuals of the refitted equations meet most of the requirements necessary for maximum likelihood estimates of the parameters. There is little evidence of serial correlation in the residuals, and no evidence of correlation between residuals of different equations.

The final set of estimates of the coefficients in the equations furnish a creditable model of the hog economy, judging by the variation explained and the significance of coefficients. The explanatory variables in each equation explain more than 90 percent of the variation in the dependent variable. Only 7 of the 30 regression coeflâcients in the model are not significantly different from zero at accepted probability levels.

As estimated from this model, a 10-percent increase in the October- December hog price is associated, on the average, with a 4-percent increase in farrowings in each quarter of the following year. This assumes that other lactors that affect farrowings, such as corn and beef prices and grain production, remain constant. Corn and beef prices have a smaller opposite effect on farrowings. A 10-percent

FACTORS AFFECTING THE PRICE AND SUPPLY OF HOGS 3

increase in the October-December corn price results in a 2-percent decrease in farrowings each quarter of the succeeding year; a similar increase in beef prices decreases farrowings by 1 percent.

Cold storage holdings of pork are influenced primarily by pork production and the price of pork. As pork production increases, storage at the beginning of the following quarter is more than proportionately increased. On the average, a 1-percent increase in production is followed by a 1.7-percent increase in storage holdings. Pork storage also increases with a price rise, perhaps in anticipation of further price increases. A 1-percent increase in price is associated with a 1.1-percent increase in storage holdings for the beginning of the following quarter.

The model gave good results for predicting changes in direction of the dependent variables in the four quarters immediately following the period of fit in 1960, but it did poorly in the succeeding four quarters of 1961. In 1960, there were 13 changes in direction for the 6 dependent variables. Of these 13 changes, 11 were predicted correctly by the model. But in 1961, 2 years beyond the period of fit, only 6 of the 15 changes in direction were correctly predicted. The forecasts for the pork storage equation were very poor—2 being more than 50 percent in error. The forecasts of prices, retail and farm, were comparatively accurate. The largest error was less than 7 percent from the actual price for the quarter.

The study also made a special analysis of seasonal variations in the hog industry which stem largely from interrelated physiological and economic factors. Physiological factors limit farrowings to two per sow per year. Economic factors largely determine when these two farrowings occur. Sows are generally bred to farrow in the spring and fall when weather is favorable and, thus, there are two seasonal peaks in farrowings. The seasonal patterns of slaughter and prices are largely determined by the pattern of farrowing.

The amount of seasonal variation in the hog industry has gradually decreased during the last 10 years because of changes in breeding and production practices. In recent years, peak farrowings also occur earlier than previously. This change in the pattern of farrowings has also had a pronounced effect on the change in the seasonal pattern of slaughter and prices.

INTRODUCTION The study of hog prices and production has been long and fruitful.

The hog price cycle was one of the earliest recognized cycles, and the hog-corn ratio was one of the first product-feed price ratios that are now commonly used in analyzing variations in livestock production, e.g., milk-feed, egg-feed, beef steer-corn, and broiler-feed ratios.

Eighty-five years ago. Benner (Sy pointed out the regularly recur- ring cycles in hog prices. He also seemed to recognize some relationship between pig-iron production and hog prices. In 1914, 38 years later. Warren (53) pointed out the tendency toward a regularity in the hog production cycle and stressed the effect of an unusual corn crop in advancing or retarding the movement.

Wallace (52) was apparently the first to apply exact statistical methods to the analysis of hog prices. He pointed out the significance

1 Italic numbers in parentheses refer to Literature Cited, page 72.


of the relation of corn prices to future hog prices, and made multiple correlation studies of the relation of hog supplies and business activity to hog prices.

Warren and Pearson {5Jf) pointed out how hog production followed changes in the hog-corn ratio, and stated that it was probably the dominant element causing hog price changes. Wright {62) worked out mathematically the effect of this relation upon subsequent receipts and prices and gave what was apparently the first clear explanation of the causes of the fairly regular recurrence of the hog cycle.

Several investigations have pointed out the high degree of correspondence among wholesale and retail prices of hog products and prices of live hogs. Wallace {52), Wentworth and EUinger {56), and Wright {62) worked out mathematical statements of the nature and closeness of the relation.

Haas and Ezekiel {25), using multiple regression analysis, found that the dominant influences in the hog market were the supply of hogs, quantity of hog products in storage, the general price level, general business conditions, and the prices of alternative products. Graphic correlation methods were used by Wells {55) in 1933 for analyzing variations in hog production within individual market districts. States, and broad type-of-farming areas, as weU as the total United States.

This brief summary of some of the early studies of hog production and prices traces the gradually unfolding knowledge of the pricemaking forces for one product. More recent works mil be integrated into the present study at appropriate points. These successive studies have marked advances in the understanding of the subject, and a closer approach to a complete explanation of all factors involved. The present study is offered merely as another step toward the realiza- tion of Benner's prophecy in 1876 when he said {5, p. 131): ''The science of price cycles is yet in the cradle of its infancy, but waiting its time to mature full development, to unfold its principles, and declare its oracles to all mankind, and to demonstrate that the causes and the. laws of nature in production are not past finding out; and that man in his onward path of progress . . . will ultimately grasp the future.''

This bulletin discusses the principal economic forces that affect the hog economy and quantifies these forces in a statistical model. Quarterly data are used in the model in order to reduce aggregation over time and also to take into account the seasonal variation in demand pointed out by Stanton {4.3) and the well-known seasonal variations in supply. Recent studies of hogs and pork, using quarterly data, include those of Fuller and Ladd {23), Stanton {^3), and Maki {35). For the long-term historical developments in the demand for pork, see Breimyer {9).

The analyses in this bulletin are based on observations for the period since 1949. The disruption of normal economic relationships during World War II and the meat packing strike of 1948 eliminate most of that decade from consideration. And the different economic structure of the postwar period prevents the inclusion of prewar data in an analysis of present relationships.

FACTOES AFFECTING THE PEICE AND SUPPLY OF HOGS

ECONOMIC IMPORTANCE OF HOG PRODUCTION Hogs accounted for 7.6 percent of grossjfarm income in 1960. In

relative importance, their contribution was exceeded only by poultry and eggs, dairy products, and cattle and calves. Cash receipts to farmers from sale of hogs in 1960 were $2.9 billion. Poultry and egg sales amounted to $3.3 bülion; dairy products, $4.7 biUion; cattle and calves, $7.4 billion.

Hogs are the major consumer of feed concentrates, accounting for 34 percent of all concentrates consumed by livestock from 1956 through 1960. They consistently consume nearly half the corn crop, having eaten 42 percent of the corn consumed by livestock in 1956-60.

As the hog industry is not a primary enterprise but a converter of raw materials, the output capacity of the industry is determined in great measure by the supply of raw materials at its disposal. The major raw material for the hog industry is corn, which stiU furnishes over 60 percent of the feed consumed by hogs (table 1). The other feed grains and byproduct feeds have become increasingly important as the value of balanced rations has become known. A large proportion of the oats that are no longer fed to horses and mules ^ has gone to the omnivorous hog. The consumption of oats by hogs dropped sharply in 1959, but until that year, oats furnished over 10 percent of the average hog's diet in the postwar period. Barley is important in local areas, principally in the West. Small amounts of grain sorghums, wheat, and rye are also fed (table 2). Soybean meal is the major oilseed meal fed to hogs, accounting for over half the amount in this category. Substantial quantities of millfeeds and other byproduct feeds have also been fed in recent years.

TABLE 1.—Percentage oj total jeed consumed by hogs derived from different sources, 5-year averages, 1926-60 ^

High Millfeeds Seeds Period Corn Other protein and mis- and Pasture Total

grain 2 feeds 3 cellaneous byproducts*

milk«

Percent Percent Percent Percent Percent Percent Percent 1926-30-__ 67.8 14.3 5.1 2.4 6.7 3.7 100 1931-35.-_ 70.2 12.8 4.7 1.0 7.9 3.4 100 1936-40_-. 65.5 14.8 6.7 1.3 6.9 4.8 100 1941-45_-_ 62.2 20.3 7.3 1.0 4.4 4.8 100 1946-50--_ 66.2 14. 1 9.8 1.1 3.8 5.0 100 1951-55-_ 63. 1 15.5 11.5 2.5 2.9 4.5 100 1956-60--- 63.1 10.9 11.2 7.8 2. 1 4.9 100

1 Based on quantities expressed in feed units. 2 Oats, barley, sorghum grains, wheat, and rye. 3 Animal proteins and oilseed meals. * Alfalfa meal, molasses, etc. * Peanuts and soybeans fed as such or hogged off plus dry equivalent of skim

milk, buttermilk, and whey fed as liquids. Compiled from Consumption of Feed by Livestock, 1909-56 (30), and from records

of U.S. Economic Research Service.

2 The USD A stopped estimating horses and mules on farms in 1961 because the steadily dechning numbers became so small (3.1 milhon head in 1960).

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TABLE 2.—Hogs: Feeds Jed {except pasture) j 1926-60 ^

Year Grains Commercial byproducts

All concentrates

Seeds s beginning October Corn Oats Barley Sorghum

grains Wheat

and rye Oilseed meals ^

Animal protein 3

MiUfeeds Other < Milk»

1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937.. 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952

Thousand tons

29, 531 30, 929 28, 760 28, 753 24, 833 29, 777 33, 720 29, 807 16, 965 20, 984 20, 200 26, 121 27, 176 29, 981 28, 856 32, 770 40, 595 38, 413 33, 461 36, 742 34, 082 30, 697 31, 426 35, 674 36, 985 37, 039 28, 348

Thousand tons 2,907 3,000 3,920 2,011 4,000 2,855 2,540 1,975 2,546 3,057 3,515 4,083 3,739 3, 612 4,959 4,312 6,024 4,866 4,083 7,919 5,815 5,145 6,799 6,041 6,584 7,031 6,374

Thousand tons 1,308 1,691 2,629 2,546 2,042 1,655 1,810

503 741

1,173 853

1,015 1,381 1,707 2,305 2, 816 3,313 2,640 1,691 1,692 1,113 1,130 1,148 1,006 1,309 1,505 1,236

Thousand tons

788 947 721 455 250 410 550 424 137 440 221 493 493 357 578 769 660 591 927 590 540 316 469 384 460 413 275

Thousand tons

396 435 497 863

1,450 1,236

921 948

1,057 1,050

572 982 734 795 299

1,387 5,616 7,602 3,417 2,315

332 468 210 254 288 270 236

Thousand tons

510 433 440 372 312 269 270 204 355 316 498 566 481 641 830 895

1,660 1,345 1,190

935 1,423 1,331 1,528 1,673 2,090 1,830 1,741

Thousand tons

497 500 518 511 551 442 445 430 446 518 523 509 563 636 645 677 780 862 575 693 627 669 682 722 764 949 797

Thousand tons

900 800 700 720 703 310 345 300 251 439 365 400 490 516 378 370 449 440 400 401 635 480 395 367 370 370 340

Thousand tons

145 360 330 280 278

60 65 60 49 60 80 60 70

100 121 145 157 143 103 130 120 121 142 163 165 185 175

Thousand tons

36, 982 39, 095 38, 515 36,511 34, 419 37, 014 40, 666 34, 651 22, 547 28, 037 26, 827 34, 229 35, 127 38, 345 38, 971 44, 141 59, 254 56, 902 45, 847 51,417 44, 687 40, 357 42, 799 46, 284 49, 015 49, 592 39, 522

Thousand tons

766 633 613 684 687 828 725 851 663 748 715 883 716 687 783 668 898 922 696 540 390 419 335 262 231 274 228

Thousand tons 1,020

950 990 975

1,030 1,040 1,060

995 955 920 895 930 925 915 945 876 835 835 830 795 755 775 750 767 720 655 635

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1953. 1954. 1955. 1956. 1957 1958 1959 1960

30, 573 6,202 1,602 31, 463 7,044 1,870 31, 834 6,701 813 29, 252 4,535 855 29, 745 4,377 792 35, 227 6,203 305 37, 291 2,294 1,032 35, 815 3,332 1,426

265 415 407 325 520 955

1,736 1,111

210 100 239 205 202 790 418 351

1,671 1,601 952

1, 142 1,256 1,547 1,726 2,049

991 1,039 1,060 919 755 812

1,037 955

350 350

2,281 2,417 2,522 2,676 2,643 1,819

200 203

2,661 2,200 2,687 2,456 2,579 1,621

42, 064 236 44, 085 247 46, 948 175 41, 850 235 42, 586 245 50, 971 184 50, 756 188 48, 479 184

625 565 505 490 460 440 410 410

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1 Includes grains and other concentrates, fed as such, in mixed or formula feeds or hogged off.

2 Includes soybean, cottonseed, linseed, peanut, and cocoanut meals.

» Principally tankage, but also includes meat scraps, fishmeal, and dried milk products.

* Includes alfalfa meal, molasses, hominy feed and screenings, gluten feed and meal, and brewers' and distillers' dried grains.

5 Principally peanuts, grazed, and soybeans, but also includes cottonseed, cowpeas, and velvet beans fed as such.

^ Dry equivalent of skim milk, buttermilk, and whey fed as liquids.

Compiled from Consumption of Feed by Livestock, 1909-56 (30), and from records of U.S. Economic Research Service.


The dependence of a converter of raw materials on supplies of the primary product is not always a one-way relationship. Where there is no alternative use for the raw material, the relationship becomes interdependent. This has been the case for hogs and corn, each highly dependent upon the other. Hogs are the major consumer of feed concentrates and are the primary outlet for grain. Their importance in the consumption of various feeds is given in table 3. Over the years, hogs have consumed nearly half the corn fed to livestock, a third of the oats, about a fifth of the soybean meal, and over half of the animal protein meal.

Supplies of corn limited the volume of hog production in most years until Government storage began. Only recently, when stocks of corn began to accumiilate in Government hands, has hog production failed to keep pace with corn production. Prior to this time, the main outlet for corn was as feed for livestock. Little corn could be sold except by converting it to meat—primarily pork. Beef cattle and poultry, however, have become important converters of corn with the recent increases in cattle and poultry feeding.

Over 85 percent of the corn utilized is fed to livestock; food, industrial uses, seed, and exports account for the remainder of the crop (table 4). The proportion of total supply fed to hogs declined with the advent of large Government holdings, beginning in 1949. In- creased consumption by beef cattle and broilers has reduced the proportion of corn fed to hogs in recent years. In 1960 only 31 percent of the corn used was fed to hogs.

Efficiency of Production

Eflîciency of conversion of feed to hog products has been improving very slowly. Technological gains in hog production, and in the livestock industry generally, have been quicker to appear in the use of labor and capital than in the use of feed. A notable exception to this general statement is the broiler industry where remarkable improvement has been made in the feed conversion ratio.

Efficiency is defined as the ratio of output per unit of input. The various measures of technical efficiency presented here do not necessarily reflect economic efficiency which takes into account the whole inputs and outputs of a process. For instance, a particular hog may be a very efficient converter of feed into pork and yet be highly inefficient economically because he is unusually susceptible to disease, or requires an expensive type of feed, or an unusual amount of attention, or any other factor that increases the total inputs.

Ratios between total feed consumption and hog production have not changed much since the middle 1920's (table 5). They do not show any sustained improvement in feeding efficiency as measured by this aggregate comparison. As noted by Breimyer (Ö), there has been no great economic pressure to improve feed conversion ratios. Feed has been produced in such generous supply that there has been little incentive to economize in its use. Instead, as feed has become cheaper relative to the cost of labor and other factors of production, it has tended to be substituted for these factors.

The possibility of increased feeding efficiency, when necessary, is ^hown by the higher production per feed unit during the latter 1930's,

TABLE 3.—Percentage oj specified Jeed concentrates consumed by hogs, 6-year averagesj 1926-60

Soy- Cotton- Other Other Period Corni Oats Barley Sorghum Wheat bean seed oilmeals Animal Millfeeds commercial All con-

grains and rye meal meal and plant proteins ^

proteins ^ byproducts ^

centrates

Percent Percent Percent Percent Percent Percent Percent Percent Percent Percent Percent Percent 1926-30 47.2 19. 0 43.8 36. 4 25.6 9.4 18. 7 60.7 15.0 11.0 37.8 1931-35__ - _ 46. 7 20. 1 36. 1 27.8 26.8 16.5 8. 1 10.0 50.7 7. 3 2. 4 36. 8 1936-40-. -- 50. 3 25.9 35.5 26. 1 18. 9 15. 6 10. 5 15.7 53.3 9.0 3. 1 38. 4 1941-45--_ - 49.7 28.9 43.4 24. 0 41. 1 20. 6 9.6 16. 5 61.7 8. 1 4. 5 40. 6 1946-50 _ - - 49. 1 32.5 34.6 18.4 8.3 24. 1 8.8 15. 9 57.2 8.3 3. 9 38. 5 1951-55 45. 8 35.0 34.6 11.5 8. 5 24. 7 5. 6 13.2 53. 7 14. 9 11.4 36. 9 1956-60 41.7 24. 7 15.8 10. 7 20.6 21.5 6.8 20.6 43.0 48.8 34.5 33. 9

1 Excluding corn in silage. 2 Includes Unseed meal, peanut meal, copra, gluten feed and

meal, brewers' dried grains, and distillers' dried grains. 3 Includes tankage, meat scraps, fishmeal and dried milk

products. Does not include milk or skim milk fed as liquids.

* Includes alfalfa meal, molasses, hominy feed and screenings. Compiled from Consumption of Feed by Livestock^ 1909-56 (30),

and from records of U.S. Economic Research Service.

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TABLE 4 .- -Corn: Supply and disappearance, United States, 1926-60 ^

Year Carryover

Production Imports 8 Total supply

Livestock feed Food,

industrial uses, and

seed

Exports Total beginning

October Farm and commercial

Govern- ment 2 Hogs

Other livestock

disappearance

1926

Million bushels

280 217

94 147 140 168 270 386 256

65 176 66

316 326 217 242 294 376 225 306 172 274 123 320 195 252 181

Million bushels

Million bushels

2,547 2,616 2,666 2,516 2,080 2,576 2,930 2,398 1,449 2,299 1,506 2,643 2,549 2,581 2,457 2,652 3,069 2,966 3,088 2,869 3,217 2,355 3,605 3,237 3,075 9 Q9ß

Million bushels

3 3

(*) 1 1

w 1

37 21

104 1 1 1 1

(') 4 6

Million bushels

2,830 2,836 2,760 2,664 2,221 2,744 3,200 2,785 1,824 2,385 1,786 2,710 2,911 3,166 3,146 3,297 3,560 3,354 3,325 3,185 3,390 2,639 3,729 4,051 3,920 3,666 3,780

Million bushels

1,055 1,105 1,027 1,027

887 1,063 1,204 1,065

606 749 721 933 971

1,071 1,031 1,170 1,450 1,372 1,195 1,312 1,217 1,096 1,122 1,274 1,321 1,323 1,012

Million bushels

1,343 1,410 1,332 1,288

987 1,233 1,421 1,189

969 1,242

798 1,087 1,128 1,160 1,227 1,330 1,459 1,494 1,523 1,435 1,453 1,167 1,431 1,561 1,472 1,528 1,611

Million bushels

199 208 213 201 177 174 181 189 183 218 201 190 194 203 228 286 283 247 275 246 309 245 252 265 281 252 248

Million bushels

16 19 41

8 2 4 8 4 1

(') 139 34 44 15 20

5 10 17 20

127 7

111 107 107 76

140

Million bushels

2,613 2,742 2,613 2,524 2,053 2,474 2,814 2,447 1,759 2,209 1,720 2,349 2,327 2,478 2,501 2,806 3,197 3,123 3,010 3,013 3,106 2,515 2,916 3,207 3,181 3,179 3,011

1927 1928 1929 1930 1931 1932 1933 1934 .__ 82

0

<■' « 45

258 471 403 197

8 6 9

0) 9

w 493 649 487 306

1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950_ 1951 1952 3; 292 1 1 1

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1953. 1954. 1955 1956 1957 1958 1959 1960

189 580 3,210 1 184 736 3,058 1 151 884 3,220 1 106 1,060 3,445 1 125 1,295 3,400 2 115 1,355 3,725 1 130 1,400 4, 197 1 112 1,675 4,304 1

3,980 1,092 1,623 249 96 3,060 3,979 1,124 1,470 258 92 2,944 4,256 1,137 1,580 265 108 3,090 4,612 1,045 1,703 279 165 3,192 4,822 1,053 1,835 281 183 3,352 5, 196 1,258 1,892 302 214 3,666 5,728 1, 332 2,098 301 210 3,941 6,092 1,279 2,241 302 272 4,094

1 Includes corn harvested for grain and grain equivalent of corn utilized as silage, hogged, grazed, and in forage.

2 Stocks owned by Commodity Credit Corporation, and old

grain under loan. 3 Includes grain equivalent of corn meal and flour. * Less than 500,000 bushels.

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12 TECHNICAL BULLETESr 1274, U.S. DEPT. OF AGRICULTURE

TABLE 5.—Index numbers of meat animal production per man-hour and hog production per sow farrowing and per unit of feed fed, S-vear averages, 1926-60

Meat animal production

per man-hour * (1947-49 = 100)

Liveweight production of hogs

Year Per 1,000 feed

units fed Per sow farrowing during year

1926-30 91 90 91 99

100 107 112

Pounds 187 190 194 179 188 190 185

Pounds 1,170 1,188 1,247 1,342 1,385 1, 440 1, 489

1931-35 1936-40 1941-45 1946-50 1951-55 1956-60

1 Includes cattle and calves, sheep and lambs, and hogs.

ii>i-^°°ÏÇ^^®^ ^^^^ ^^^''^O^s in Farm Production and Efficiency (49), Livestock and Meat Situation, (48), and from records of U.S. Economic Research Service.

when feed was scarce because of drought. Then, during the war years, 1941-45, feeding efficiency decreased as plentiful feed was substituted for scarce labor. The sharp rise in production per man-hour in this period substantiates the hypothesis. After a gradual improvement, hog production per irnit of feed again declined in the latter 1950's when feed was plentiful and relatively cheap.

Technological progress has thus found its chief expression, not in improved feed input-hog production ratios, but in increasing efficiency in the use of labor and capital. Even so, hog production has not proven to be readily adaptable to mechanization. Indexes of labor efficiency are not compiled for hogs, but the index for all meat animals shows a 23-percent improvement since 1926-30. By contrast, production of crops per man-hour has nearly quadrupled since those years.

Productivity gains that have been made relative to capital investment are demonstrated by statistics of output per year in relation to the size of the breeding stock inventory. As shown in table 5, liveweight production per sow has risen from 1,170 pounds in 1926-30 to 1,489 pounds in 1956-60, an increase of 27 percent. This demon- strates not only an increased output relative to breeding animals but also in relation to housing and other capital investment that is provided in direct proportion to the size of the breeding herd. Higher productivity per breeding animal has also contributed to the higher productivity of labor in meat animals.

These gains in productivity are attributed to the whole complex of advances in hog production. They embrace genetic improvements in breeding, larger litters of pigs, protection from disease, and better feeds and rations "that shorten the time required for young pigs to reach slaughter'weight.


Regional Variation

Hogs have a conversion ratio of about 4 to 1, that is, four pounds of corn will produce one pound of live hog. Jennings (30) estimates that 100 pounds of corn equivalent in a balanced ration produces 23 pounds of live weight or 13.6 pounds of boneless pork and lard.

Economic theory predicts that an industry based on the conversion or processing of raw materials will be located near the source of the major raw material input. This location becomes especially important for efficient production when the processing results in a substantial reduction in bulk or weight. Simply put, this means that hogs are where the corn is.

The strong correspondence between areas of corn and hog production is shown by a comparison of figures 1 and 2. Production of both these commodities is heavily concentrated in the north-central part of the United States in an area commonly referred to as the Corn Belt. This area includes all of Iowa, Illinois, Indiana, and Ohio, and parts of North Dakota, South Dakota, Nebraska, Kansas, Minnesota, Mis- souri, Wisconsin, and Michigan. These 12 States produced 84 percent of the corn and 77 percent of the hogs raised in the United States m 1960.

The distributions of corn and hogs are very similar in most Corn Belt States. Iowa is the leading corn and hog producer, accounting for about 20 percent of U.S. production in each case. Second-ranked Illinois is a close competitor in corn production of 17 percent, but drops to only 14 percent of total hog production. The large number

FARM PRODUCTION OF CORN FOR GRAIN v^.y^ By States, as % of U. S. Total, 1960

U. S. TOTAL 3,891 MIL. BU

U.S. DEPARTMENT OF AGRICULTURE NEC. ERS 881-62(2) E CONOMIC R E SE ARCH SERVICE

FIGURE 1.—The 12 North Central States that make up the Corn Belt produce over 80 percent of the Nation's corn.

Ö45778—62 3


FARM PRODUCTION OF HOGS* By States, as % of US. Tofa/, ?9ó0

U.S. TOTAL 18,989 MIL. LB.

U.S. DEPARTMENT OF AGRICULTURE NEGERS 368-61(8) ECONOMIC RESEARCH SERVICE

FIGURE 2.—Nearly 80 percent of the country's hogs are produced in the same North Central States that are also the major corn-producing States.

of cash grain farms in Illinois contributes to the relatively higher production of corn. Nebraska also produces a much lower proportion of hogs than of corn but for a different reason. In most Corn Belt States, at least four times as much corn is fed to hogs as to beef cattle. The ratio is only 2 to 1 in Nebraska, indicating that a greater proportion of the corn crop is fed to beef cattle in this State.

Even outside the Corn Belt, the distributions of corn and hogs are remarkably similar. New England produces very little corn and few hogs. The Southern States have roughly similar percentages of corn and hogs produced in each State, except in Georgia, where considerable quantities of peanuts are hogged off, and in Texas, where grain sorghums are an important feed for hogs. The West also produces a slightly higher proportion of hogs than of corn; here, oats and barley are the principal feeds.

MAJOR RELATIONSHIPS IN THE HOG ECONOMY

The major economic relationships and variables that constitute the hog economy are shown in figure 3. Items that represent physical quantities are shown in boxes; factors representing price and value appear in circles. The many forces that enter into or affect the marketing system are included within a single dash-bordered box. The solid lines connecting the various items indicate the more important factors; broken lines indicate factors that are relatively minor or operate only occasionally. Arrows indicate the principal directions


THE DEMAND, SUPPLY AND PRICE STRUCTURE FOR HOGS

PORK

CONSUMPTION

/ -—

COLD

STORAGE

HOLDINGS

S

Jf

/

PORK i LARO

LARO

CONSUMPTION

P

A/?/fOWS SHOW DIRECTIOH OF INFLUBHCE. SOLID LIHES INDICATE HAJOR PATHS OF IHFLUEHCE.

SYUBOLS REFER TO NOTATION IN THE TEXT.

U.S.DEPARTMENT OF AGRICULTURE NEG. ERS 936-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 3.—The factors illustrated here—physical and economic—largely determine the basic economic relationships that exist in the hog economy.

of influence for each factor. Double pointed arrows indicate factors that are beheved to be simultaneously related.

The symbols in some of the boxes and circles refer to the variables listed on page 51 and to the equations on page 50. The statistical model and the diagrammatic representation of the relationships do not correspond exactly. Not all the factors that appear in the diagram are included in the equations because of data limitations and the requirement that the model be statistically manageable.

16 TECHNICAL BULLETIN 1274, U.S. DEiPT. OF AGRICULTURE

TABLE 6.—Supply and distribution of pork, by quarters, 1949-60

Year and quarter

1949, 1 2 3 4

1950, 1 2 3 4

1951, 1 2 3 4

1952, 1 2 3 4

1953, 1 2 3 4

1954, 1 2 3 4

1955, 1 2 3 4

1956, 1 2 3 4

1957, 1 2 3 4

1958, 1 2 3 4

1959, 1 2 3 4

1960, 1 2 3 4

Supply

Produc- tion 1

Million "pounds

,866 ,032 ,895 ,493 ,945 ,226 ,982 ,561 , 107 ,498 ,217 , 659 ,436 ,387

!, 070 ,634 ,966 ,050 ,895 ,095 ,570 ,992 i, 040 ,268 ,935 ;, 169 ,170 ,716 ,298 1,351 ,227 ,324 ,852 ,,281 , 188 , 103 ,690 ,299 ,306 , 159 ,078 ,617 ,616 ,682 ,300 1,712 1,463 , 155

Begin- ning

stocks 2

Million pounds

469 586 420 205 474 549 469 241 499 648 572 326 549 822 685 291 489 569 414 201 327 418 347 215 449 544 376 179 421 514 394 166 280 352 277 134 194 224 210 127 206 337 313 163 264 338 351 158

Imports

Million pounds

1 1 1 5 8

10 10 12 13 12 14 18 13 19 21 30 50 45 39 41 53 44 46 45 44 44 42 41 46 34 30 39 38 30 37 42 48 49 54 51 53 42 40 46 51 45 44

Distribution

Exports and ship- ments

Million pounds

20 35 31 24 29 27 23 31 37 25 30 44 40 41 37 36 42 31 30 31 24 25 28 28 33 32 26 35 40 32 29 37 44 41 28 31 31 29 27 31 36 32 37 38 35 34 30 38

Ending stocks 2

Million pounds

586 420 205 474 549 469 241 499 648 572 326 549 822 685 291 489 569 414 201 327 418 347 215 449 544 376 179 421 514 394 166 280 352 277 134 194 224 210 127 206 337 313 163 264 338 351 158 170

Mili- tary

Million pounds

59 45 26 53 40 29 64 89

127 159

89 114 131

89 72

100 77 76 58 87 78 64 58 78 57 66 48 63 56 59 52 62 56 47 58 52 49 46 49 48 46 48 46 41 46 56 41 40

Civilian consumption 3

Total

Million pounds

580 318 196 897 727 445 266 952 728 585 486 058 935 575 495 107 738 292 169 701 364 158 225 802 764 434 440 195 061 567 496 001 643 436 355 863 558 413 435 919 887 746 798 366 100 775 701 013

Per person

Million pounds

17.6 15.7 14.9 19. 5 18. 2 16.3 15. 1 19. 6 18. 1 17. 2 16.4 20. 2 19.3 16.8 16.2 20. 1 17.7 14.7 13.9 17.2 15.0 13.6 13.9 17.5 17.2 15.0 15.0 19.6 18.6 15.6 15. 1 18.0 15.8 14.5 13.9 16.9 15.0 14. 1 14. 2 16.9 16.7 15.7 16.0 19.2 17.5 15.7 15.2 16.9

1 Includes production from farm slaughter. 2 Commercial stocks only. Supply does not equal distribution on a quarterly

basis because changes in quarterly farm stocks are not accounted for. Yearly totals for supply and distribution are equal.

^ Includes consumption from farm slaughter. * Less than 500,000 pounds.


In the diagram a simultaneous relationship is indicated between pork price and consumption. In turn, consumption is closely tied to production; quarterly differences in storage, exports, and imports are of minor importance in the distribution of pork (table 6).

As pork is a perishable agricultural commodity produced continuously throughout the year, price must adjust so that current production continuously clears the market after allowing for storage, imports, and exports. Pork imports and exports have been approximately equal in recent years, so the major adjustment between production and consumption occurs through changes in storage. During the peak slaughter months in the fall and winter, pork moves into storage only to move out in the summer months when fewer hogs are slaughtered. Quarterly differences in storage stocks have been relatively small, however, averaging only 5.2 percent of production, disregarding sign, during the period 1949-60. In contrast, quarterly differences in production averaged 23 percent during the same period.

The close relationship between pork production and consumption means that production can be used as an indicator of consumption in a statistical model. Production in any given quarter is influenced to only a small degree by the retail price in the same period, so the simultaneity problem can be overcome by assuming that production is essentially predetermined as suggested by Fox (^0).

The consumption of competing meats is affected by pork consumption and price, but, as with pork, the production of other meats and poultry is essentially predetermined for a particular quarter.

The price of lard is only a minor factor affecting the price of hogs. Its coefficient was statistically insignificant in a regression equation used to determine factors affecting the price of hogs; thus, lard is ignored in the following analysis and discussion. The increased use of vegetable shortening and a surplus of lard has relegated lard to a byproduct of relatively minor importance to the hog-pork economy, although it is still of considerable importance in the fats and oils economy.

The decline in the importance of lard and fat cuts is shown in figure 4. In 1905-10, lean cuts and minor products contributed 53 percent of the total carcass value of hogs. Fat cuts and lard accounted for the other 47 percent—lard alone contributed 20 percent. During the 1950^s, lean and minor cuts furnished 73 percent of the total, as fat cuts and lard contributed only 27 percent. From 1950-60 lard contributed less than 10 percent of the carcass value. Its importance to the hog economy has been more than halved since the early years of this century.

Price Expectations of Producers

In deciding what action to take under changing profit situations, the individual producer is influenced not only by factors that influence costs and alternative profits, but also by the effect of psychological motivation. Various studies on uncertaint}^ and expectations indicate that there is a limit to how much certainty a farmer wants (6, lOj 57). As Boan (^, p. 95) states it: ''The degree of certainty de- sired probably depends upon the circumstances. If this is true, analysis that treats the farmer as a given factor, rather than part of the highly dynamic situation created bv the uncertaintv. is not likelv


PORK CUTS Value as Percentage of Carcass Value

%

80

60

1905 1915 1925 1935 1945 1955 1965 * COMPUTED FROM WHOLESALE PORK PRICES (FRESH BASIS), CHICAGO.

U- S. DEPARTMENT OF AGRICULTURE NEC. ERS24-61(4) ECONOMIC RESEARCH SERVICE

FIGURE 4.—The proportionate value of fat cuts and lard in a hog carcass has dechned steadily during the last 40 years, while the percentage value of lean cuts has increased.

to succeed in solving the mystery created by the very real but very difficult phenomenon of uncertainty.'' For this reason, the box labeled '^farmers' expectations'' has been included in the diagram (fig. 3). The prices of hogs, beef, and corn affect the number of farrowings through their influence on farmers' expectations of future hog prices and the relative profitability of hog production.

Individual producers do not formulate scientific hypotheses of their expectations concerning the future price of hogs, but they do weigh the factors that they believe influence the returns to be obtained from production. Schultz and Brownlee (40), in an attempt to formulate a price expectation model, found that in a sample of Iowa farmers, producers of corn based their actions on past relationships. While recent increases in corn yields were discounted about one-half, farmers appraised the other half as a real gain which they expected would continue. The relationship between past and expected yields was modified somewhat by location, age, tenure, and education of the operator. In the case of hog prices, however, which fluctuate more than corn yields, Iowa farmers showed a strong prefer- ence for using current prices in formulating their price expectations. The extension of current prices for future expectations is one of the prerequisites for the application of the cobweb theorem. The importance of this theorem in the theoretical development of the hog cycle wiU be explained later.

In formulating production plans, producers must decide how many sows to breed to produce future market hogs. Because the gestation


period for hogs is almost 4 months and an additional 6 to 8 months are required for feeding to market weight, present decisions are conditioned by the expected returns 10 to 12 months hence, as well as by producers' response to previous ret^urns. An indication of these decisions is given by farmers' intended farrowings as of June 1 and December 1, reported semiannually in the Pig Crop Report {50). Although farrowings may subsequently vary from farmers' stated intentions because of changing conditions during the months immediately Succeeding the intentions reports, year-to-year changes in the actual number of farrowings conform closely to year-to-year changes in early-season plans, as shown in figure 5. Production is essentially fixed, once sows are bred, at least on the upward side. Farmers can decrease production by marketing bred sows, but there is a considerable discount after the second month of pregnancy. This relative fixity on the upward side, with adjustments taking place by reducing production, is also shown in figure 5. If intentions were exactly fulfilled each year, except for some statistical error that might be present in the data, all points in the figure would He on the 45° diagonal line that passes through the intersection of the 100-percent lines. Most observations lie to the right of this diagonal line and indicate that intentions are often higher than actual farrowings.

The Hog-Corn Ratio

Hog supply has often been described as a direct function of the supply of corn. In a study of this relationship. Wells {55) observes that ^^this general statistical correspondence between the long-time trend and the cychc elements in corn production and hog slaughter or hog numbers, together with the general dependence of changes in hog production and seasonal marketing distribution and weight upon corn supplies, indicates that corn production and hog production are closely related." And Shepherd {41), in a 1942 bulletin, states that . . . *'changes in hog production closely follow the changes in corn production, whereas changes in beef cattle production follow a somewhat cychcal course of their own, largely independent of corn production."

In years prior to Government price-support and storage programs, nearly all the corn harvested each fall was fed during the ensuing year. Relatively Httle was carried over from one year to the next. Inasmuch as hogs were the largest and in many respects the most adjustable user of corn, their production felt the variabihty in corn supply most sharply.

Some farmers adjusted their hog enterprise directly according to their corn supply. More frequently, the close relationship between corn and hog production was brought about through the market mechanism. Changes in the price of corn relative to the price of hogs kept corn feeding and hog production in line with the available corn supply. With a large corn crop, the price of corn fell below the normal relationship to the price of hogs. Hog production then became attractive and was expanded. A small crop raised the price of corn and made hog production less attractive.

The price relationship between corn and hogs is called the hog- corn ratio—the ratio of the price of hogs per hundredweight to the


INTENDED FARROWINGS, DECEMBER 1 AND JUNE 1, RELATED TO SPRING AND FALL FARROWINGS, 1949-60

FARROWINGS / (% OF PREV. YR.)

1

/ / /

110 ' '54 X

/ x'58/ -

'55 /•''''

-

/ '55« «'54 /

/ '50 / ^/ / '50

/ • x'59

/ •'51

1 f\f\ / '51 ••58

100-

/ /

x'57

/ '^^^^ -56

'57 • Spring

90 y X = Fall /

/ /

/

• '52 X'53

80 8

— / • »'ÓO / '53

/ /

/ 1

.X'52

1 1 1

0 90 IC )0 110 12 0 INTENTIONS (% OF PREV. YR.)

U.S. DEPARTàaENT OF AGRICULTURE NEC. ERS 884-62(2) ECONOMIC RESEARCH SERVICE

FIGURE 5.—Farmers closely follow their early-season intentions for farrowings, rarely exceeding them by more than 1 or 2 percent. Reducing the number of farrowings below intentions is more readily accomplished.

price of corn per bushel. Another way of interpreting the ratio is that it is the number of bushels of corn that can be exchanged for 100 pounds of live hog at current prices. A high ratio indicates that hogs are relatively high in price and corn relatively cheap ; a low ratio has the opposite meaning.

Analytically, the hog-corn price ratio became a convenient tool for economists. The early works of Wallace {52), Wright {62), and Sarle {ß9) are examples of its initial application. A ratio that was above or below its normal level was followed by an increase or decrease in the number of sows farrowing in the forthcoming farrowing season. Furthermore, the relationship was roughly proportional; the wider the departure of the ratio from its average, the greater the change in farrowings.


Breimyer (8) notes that in a precise theoretical interpretation of the hog-corn ratio, it is to be compared with forthcoming changes in the number of farrowings, not with absolute numbers. The nu- merator of the ratio, which is the price of hogs, discounts the existing level of farrowings and hog production. If, for example, corn prices are at an average level, a high ratio imphes high prices for hogs and, therefore, below-average hog production, and it impels an increase in production toward average or normal levels. But a low ratio, indicating that hog production is above average, would stimulate a decrease toward the same average or normal production As figure 6 shows, the theory is substantiated by experience. A favorable

INFLUENCE OF HOG-CORN RATIO ON SPRING FARROWING

1924 1929 1934 1939 %

15

0

-15

-30

^

U

^i CHANGE IN SOWS FARROWING' II.

T3r rrrr ¥ ^^ mm

1925 1930 1935 1940 1945 1950 1955 1960 * Hog-corn price ratio Sept-Dec. U. S. farm basis (bushels of corn equal in value to 100 pounds of live hog)

o Change from previous year in sows farrowing spring pigs

U. S. DePARTMENT OF AGRICULTURE NEC. 1839-61 (3) AGRICULTURAL MARKETING SERVICE

FIGURE 6.—A favorable price relationship between hogs and corn during the principal breeding season usually leads to an increase m sows farrowing; a below-average ratio to a decrease.

price relationship between hogs and corn during the fall breeding season has usually led to an increase in sows farrowing the lollowmg spring. A below-average ratio has led to a decrease.

Changes in hog prices caused by variations m demand for Hog products, fluctuations in hog marketings, and changes m the corn supply are the principal factors that cause the hog-corn ratio to rise and fall The extreme variations in its movement between 1924 and I960 are a low of 6.8 and a high of 17.9 based on average prices received by farmers during the fall breeding season—beptember through December. In table 7, the averages of the monthly ratios for these 4 months, for the years 1924 to 1960, are arranged m de- scending order. The corresponding changes in the number ot sows farrowing the following spring are also given.

645778—62 4

22 TECHNICAL BULLETIN 12 74, U.S. DEPT. OF AGRICULTURE

TABLE 7.—Hog-corn price ratio during fall breeding season, United States, arrayed according to ratio, and number of sows farrowing following spring, 1924-60

Year Hog-corn price ratio

September- December 1

Number of sows

farrowing following

spring

Increase or decrease from preceding spring in sows farrowing

Number Percentage

1958 17.9 17.2 17.2 17.2 17. 1 16. 9 16.6 15.8 15.5 15.4 15.3 14. 8 14.7 14.2 13.5 13.5 12.8 12.7 12.4 12.3 12.3 12.2 12.0 12.0 n. 5 11.4 n. 3 U. 2 11.2 11.2 n. 2 10. 3 10.0 9.4 8.6 8.2 6.8

Thousand head

7,996 7,031 8,692

12, 174 8,820 7,281 9,754 7,669 9,684 9,179 6,795 8,548 6,954 9,123 9,484 9,048 8,347 8,077 9,246 8,302 7,194 6,777 8,247 8,811 8,311 7,655 7,045 7,833 9,301 8,854 8,971 8,278 7,760 6,177 6,825 8,334 5,467

Thousand head

715 254

1,897 2,490

987 87

706 624

1,924 359 618 471

1,487 312 305 714 678

-225 -2,928

-944 -461

-1,219 -445 -160

-1,173 -692

-1,266 -715 -453 -447

693 -576 -487 -777

-2,298 -1,465 -1,358

Percent 9. 8

1960 3. 7 1938- 27. 9 1942. _ 25. 7 1948-_- 12. 6 1957 1. 2 1926 7. 8 1953 8. 9 1941 24. 8 1949. 4. 1 1937 10. 0 1946 5. 8 1935 27. 2 1932 3. 5 1950._ 3. 3 1925 8. 6 1954 8. 8 1945 — 2. 7 1943 — 24. 1 1944. — 10 2 1956 — 6. 0 1959 — 15. 2 1939 — 5. 1 1931 — 1. 8 1951. — 12 4 1955. — 8 3 1952 — 15. 2 1947 — 8. 4 1927 — 4. 6 1928- — 4 8 1930-. _ _ - _ 8 4 1929 — 6. 5 1940-__ - - - — 5 9 1936 — IL 2 1933 — 25. 2 1924 —15 0 1934 — 19 9

1 Based on prices received by farmers.

The direction of change in farrowings as predicted by the ratio is extremely reliable. In every year since 1924, with the single exception of 1930, the number of sows farrowing has increased in the spring following a September-December average U.S. hog-corn ratio greater than 12.7. But the percentage changes in farrowings can be only roughly forecast from the ratio. The proportional relationship was fairly close during the prewar period, as shown by the scatter diagram, figure 7. The relationship during the postwar period is much less


consistent. For instance, a ratio of 12.8 in 1954 resulted in an 8.8- percent increase in farrowings, while a ratio of 17.9 in 1958 brought about the same percent increase, 9.8.

Price support and storage programs for corn have altered the tie between corn and hog production. Corn no longer needs to go exclusively into livestock production. Variations in the hog-com ratio now more often arise from changes in the price of hogs and less often from changes in the price of corn.

As pointed out by Breimyer (5), when hog production had to stay closely in line with the annual corn harvest and the hog-corn ratio was the intermediary, the ratio was necessarily efficient—at least superficially so. Now that hog production is loosened from this firm

RELATIONSHIP OF SPRING FARROWINGS TO FALL HOG-CORN RATIO PREVIOUS YEAR, 1925-61

CHANGE IN FARROWINGS '39

(

20 10

%) "Ï '42 1 • • • '43 -

- '31 •55 -26 ■38 .54 '49«

'59.

- '•

'51« .■33 •'"'•■50 • '27

0 -

-10 -20

-30 (

U. S. DEPA

- •41 < '37

'28. '29

»•'30 ;,-56 '48^

• '52 '53«

¡•40 •''«6 ' ••57

■35

1925 • • • '45

• •60

1 '34

• 1 1 _ • '44

1 1 1

b 8 10 12 14 16 1 HOG-CORN RATIO*

*RAT/0 OF PRICE OF HOGS PER HUNDREDWEICHT TO PRICE OF CORN PER BUSHEL.

SEPT-DEC. PREVIOUS YEAR, U. S. FARM BASIS.

RTMENT OF AGRICJLTURE NEC. ERS 883-62(2) ECONOMIC RESEARCH SERV

8

ICE

FIGURE 7.—The hog-corn ratio is a good indicator of the direction of change in farrowings. But the wide scatter shows that it is unreliable as a predictor for the amount of change, especially in recent years.

tie, it responds much less exactly to the ratio. The price outlook for hogs alone, independent of corn, has become more important.

Also, a higher hog-corn ratio is necessary to call forth a specified level of hog production than before World War II (Brandow [7]). As a long prewar average, a ratio of 12 to 12.5 was associated with stabihty in farrowings. Since the war, a ratio of about 13 has produced unchanged farrowings. Cause for a higher ratio now may lie partly in higher costs for labor and other nonfeed items. A major factor, however, is the difference in certainty of return between hogs and corn. When corn prices are supported but hogs are not, the corn producer weighs his assumed return for corn against the impredictable return if ho feeds it to hogs. He will doubtless choose

24 TECHNICAL BULLETIN 1274, u.s. DEIPT. OF AGRICULTURE

to sell corn at the support price unless the prospect for hogs appears more favorable than the long-term average.

The hog-corn ratio is often used as a single independent variable in regression analysis, instead of the price of hogs and the price of corn as separate variables. The use of the ratio implicitly removes the influence of variation in the general price level and, at the same time, conserves one degree of freedom. It also eliminates any problem of intercorrelation between corn and hog prices.

There are several significant questions which may be raised with respect to the use of the ratio. The interpretation of the regression coefficient for the price ratio forces one to accept that the price of corn has an almost equal effect on hog supply as does the price of hogs. Such is not always the case, as was found by Kohls and Paarlberg (3É). Further, the use of the ratio assumes the absolute level of hog and corn prices to be unimportant. This may be true within some range of prices, but it probably is not true over the observable range of prices for a given period of time. In any case, it is probably better to let the data determine the separate effects of the individual prices rather than force conclusions such as those indicated above.

Variable Factors in Pork and Lard Production

Farmers' expectations of the profitability of hogs are the major variable in the hog production process. Once sows are bred, pork production is essentially determined for the following year. There are a few areas where variation can occur between breeding and pork production. These areas and their relationships are shown dia- gramatically in figure 8. The major factors causing variation between breeding and pork output are in hexagonal boxes. For instance, varying numbers of bred sows may be slaughtered before farrowing; the number of pigs farrowed per sow varies with genetic selection and prenatal care; the number of pigs weaned per sow varies with the care given the sow, and with the weather at farrowing time; disease takes its toll at all ages; the slaughter weight of hogs can vary considerably; the dressing yield of pork and lard varies with the type and weight of the hog, and with trimming practices.

Most of these factors are fairly constant or can be estimated fairly closely by linear trends. The slaughter of piggy sows was more common in the prewar period than it is today. Burmeister (11) found a relation between an adverse January-February hog-corn ratio and a decrease in the nimiber of sows farrowing. Data for the postwar period show no such relation.

The number of pigs weaned per sow can be explained mainly by a linear trend that reflects the progress made through genetic selection for larger litters and through production practices, such as pig brood- ers, that decrease the death rate between birth and weaning. Almost 90 percent of the variation in pigs saved per sow between 1924 and 1960 can be explained by a linear trend. Fluctuations around this trend are due mainly to variations in weather at farrowing time. The effects of weather on litter size in a single Corn Belt State have been studied by Straszheim {44)- He found that the differences in average litter size from month to month have been largely eliminated, but that size still fluctuates considerably at various times. In Indiana,


data on weather conditions at time of farrowing explain much of this sporadic variation.

The number of deaths after weaning is a fau'ly constant proportion of the pigs weaned. It ranges from 10 to 14 percent of the pig crop with a sHght tendency to increase with large pig crops. The increase in the death rate with large pig crops seems reasonable because ot crowded facihties and the increased number of margmal producers raising hogs during these years. i i

Some gUts are saved for breeding each year. They may be replace- ments for older sows or additions to the breeding herd. If the number

FACTORS AFFECTING

PORK AND LARD

PRODUCTION NUMBER OF SOWS

FARROWING

NUMBER OF PIGS WEANED

NUMBER OF DEATHS AFTER

WEANING

NUMBER OF GILTS SAVED

FOR BREEDING

NUMBER OF HOGS

SLAUGHTERED

VARIABLE FACTORS (N HEXAGONAL BOXEJ.

DETERM/NED FACTORS IN RECTANGULAR BOXEJ.

LIVEWEIGHT OF HOGS

SLAUGHTERED

-(

NUMBER OF \ BREO SOWS )

SLAUGHTERED /

«(

\ NUMBEROF \

PIGS WEANED ) PER SOW /

*{ f \

NUMBEROF \ SOWS )

SLAUGHTERED /

V /

"{ ' AVERAGE \

SLAUGHTER ) . WEIGHT /

x( / DRESSING YIELD

y FOR

PORK\

LARD /

NUMBEROF SOWS

FARROWING

NUMBER OF HOGS

SLAUGHTERED

LIVEWEIGHT OF HOGS

SLAUGHTERED

PRODUC-

TION OF

U.S. DEPARTMENT OF AGRICULTLRE NEC. ERS 935-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 8—Pork and lard production is determined by a sequence of variable factors, beginning with the number of sows bred.

of farrowings remains unchanged, the number of gilts saved for breeding would equal the number of sows slaughtered and death losses. But change in the number of farrowmgs is the rule, bince 1924, the smallest change in sows farrowmg m the spring has been 87 thousand: the largest, 2.9 mUlion (table 7). Similar changes have occurred in fall farrowings, so that annual slaughter figures have been considerably affected by variations in sow replacenients.

According to a USDA survey (47), the usual marketing weight of hogs is determined by farmers' ideas of the "best weight or finish Some farmers take prices into account, but a larger number sunply market their hogs at these subjective "best" weights. Changes in

26 TECHNICAL BULLETIN 12 74, U.S. DEiPT. OF AGRICULTURE

the usual marketing weight were found to occur with variations in feed supply and hog prices.

A good predictor of yearly average slaughter weights is a ratio of the number of fall pigs to the number of spring pigs saved. Fall pigs are normally marketed at lighter weights than spring pigs because with two farrowings per year there is more incentive to sell pigs when they reach what are usually considered minimum marketable weights (200-225 pounds) after 6 to 8 months. Specialized hog producers have two (or more) farrowings per year, while the farmer who raises hogs as a sideline usually has only one farrowing period per year, in the spring. These hogs are, as a rule, fed longer and to heavier weights since there are no other pigs to replace them on feed after 6 months.

Therefore, an increasing proportion of fall pigs would decrease the average marketing weight during the year. Pigs farrowed in the fall would be marketed during the succeeding spring and summer, while a major portion of the spring pigs would be marketed in the fall of the same year. Thus, a change in the ratio of pigs saved in the fall of the preceding year to the number of pigs saved in the spring should be followed by a change in the average marketing weight. The average live weight of slaughter hogs has ranged from 223 to 251 pounds over the past 25 years. The ratio explains 78 percent of the variation in average slaughter weight during this period. The addition of hog prices and feed supplies did not increase this explanation to any appreciable extent.

The final source of variation between breeding sows]^and the production of pork is the dressing yields of pork (and lard. These yields are quite stable. Since 1935, lard yield has varied from 11.3 to 14.0 pounds per hundredweight of hogs slaughtered. Pork dressing yield ranged from 55.8 to 59.4 percent. Total pork and lard yield varied much less than its components, 69.7 to 71.0 percent of live weight, indicating that the amount of fat left on pork cuts, including intra- muscular fat, changes from year to year in response to relative pork and lard prices and consumer preferences.

A regression of changes in. lard yield per hog on average slaughter weight showed no correlation between the two. This result was unex- pected because analyses of hog carcasses have shown that the proportion of fat relative to lean increases as weight increases. The average slaughter weight varied from 223 to 251 pounds during this period, and the proportion of fat increases 2.5 percent over this weight range (Atkinson and Klein [2]). This slight increase could be obscured by trimming practices that vary among packers, regions, and years, as well as with the size of the hog. Also, the amount of trim may be affected more by changing price relationships between pork cuts and lard than by anatomical characteristics. Furthermore, the statistics of lard yield and slaughter weight may not be sufficiently accurate to detect such a small change.

Many of the factors discussed above are ignored in the statistical model that follows on page 46. Some simplification and aggregation were necessary to make the model statisticaUy manageable.


CYCLES IN PRICE AND PRODUCION

As was mentioned previously, the hog cycle was one of the earliest cycles to be recognized and has been the subject of numerous studies.^ The cycle may be described in terms of price or production. Pro- duction may be measured at the initial or final stage; that is, pig crop or slaughter. The interrelationships among these three manifestations of the hog cycle—price, pig crop, and slaughter—^give some insight into the way the cycle functions.*

For simpHcity, annual data are used to study the cycle in this section, although the use of annual data may tend to obscure some re- sponses of farmers to changing conditions because there are usually 2 farrowings per year. The typical practice is to breed sows in the fall to farrow in the spring about 4 months later. A large proportion of these sows farrow again the following fall. Most analysts have found that farmers make their basic decision as to the number of sows to farrow on a yearly basis, with some adjustment of fall farrowing in response to changed conditions (7, IS, 32). For this reason, annual figures are used in this presentation, although there is the possibility of a slight loss in precision due to over-aggregation.

A Model oí the Hog Cycle

In order to show clearly the interrelationships of the different aspects of the hog cycle, factors which affect hog production but are not mate- rially affected by it, i.e., independent or exogenous variables, such as the price of corn and the feed supply, are assumed to be constant. This assumption of other things equal is, of course, a distortion of reality, but it is necessary for a clear, simple explanation of the basic relationships.

The three measures of the hog cycle are related in the following manner. Price in one period affects the size of the pig crop the following period which, in turn, determines the niunber slaughtered. The number slaughtered affects the price which influences the next pig crop, and so on around a circular chain of reaction. The cyclical nature of the relationships is obvious. The lag between prices and pig crop, and between pig crop and slaughter, determines the length of the cycle.

A 4-year cycle, such as the one now observed for hogs, will result if each of the above lags is assumed to be 1 year. A model using these assumed lags will be developed, and then the validity of the assumptions will be examined.

Diagrams A, B, and C in figure 9 illustrate the assumed relationships of each of the three variables with each other. The relationships are shown in cyclical form, although the reason for the cyclicality is not evident imtil all three are examined simultaneously in diagram D. The 1-year lag between price and pig crop is shown in figure 9A. A high price in one year leads to a large pig crop the next year, and a low price is followed by a small crop. Pig crop precedes slaughter by a year, as indicated in figure 9B. The size of the pig crop determines the num-

3 In one of these, Bean (4) identified what he calls "major and minor" hog-price cycles.

* In an examination of livestock cycles, Lorie (34) stresses "the interrelationships among value, marketings, and numbers on farms (or production)."

28 TECHNICAL BULLETIN 1274, U.S. DEOPT. OP AGRICULTURE

HYPOTHETICAL RELATIONSHIPS BETWEEN MEASURES OF THE HOG CYCLE

HIGH -

NORMAL

LOW

HIGH

NORMAL

LOW

p

/ V \ > y \

^y N/ Slaughter v" \

1 1 1 1 1 1 1 1

HIGH

NORMAL

LOW

c

>i^"^ /

^ Price

/

_ / 1 1 1

A

\

Slaughter 1 1 1 1

\

HIGH D \ /

• x • X

„ . Pig crop

;Xx 7xr<X / ^ ^. VX ^ X/ "^ vX NORMAL

LOW _ / 1 1

Slaughter 1 1 1 1 ! 1

1 23456789 YEAR

U. S. DEPARTMENT OF AGRICULTURE NEC. ERS 929-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 9.—A continuous, theoretical hog cycle can be developed, assuming that the size of the pig crop is determined by price in the preceding period, that slaughter follows pig crop by one period, and that price varies inversely with slaughter.


ber slaughtered in the following year. The inverse relationship between slaughter and price is illustrated in figure 9C; when slaughter is high, price is low, and vice versa. With these relationships between each of the variables clearly in mind, it will be easier to understand the for- mation of the cycle which arises from their interaction.

The reason for the development of a cycle from the interrelationships is revealed by an examination of figure 9D, which combines the three series. Assuming the initial positions as shown for year 1, the cycle would proceed as follows. Initially, slaughter is low, price is high, and the pig crop is of normal size. The next year, slaughter will increase to the normal, or equilibrium level, reflecting the size of the previous year's pig crop, and price will correspondingly decrease to equilibrium. But now (year 2), the pig crop is larger than normal due to the high price in the previous year. Consequently, slaughter increases and price declines below equilibrium during year 3. Farmers breed fewer sows in year 2 because of the lower price, and hence the pig crop drops to the equilibrium level again the next year. The normal-sized pig crop in year 3 leads to lower slaughter and higher prices, which again reach equilibrium in year 4. However, the low price in year 3 led farmers to cut production further in year 4, and so the pig crop is now at a low point. The next year, slaughter declines due to the small pig crop the previous year and, consequently, price rises to a peak in year 5. The relatively higher price in year 4 led farmers to increase production to the equilibrium level in year 5, which results in the same relationships among the variables as occurred 4 years previously, and the cycle continues as before.

Different initial positions could result in different shapes for the curves. For example, the peaks would be less pointed if the pig crop and slaughter were both assumed to be at normal levels, initially, and a shift in demand caused a change in price. The cycle would stül be 4 years in length, however, as long as the lags were each 1 year.

Comparison With Actual Data

A comparison of this simple model with the actual data will determine whether the assumptions made in its formulation are appropriate. An exact likeness would not be expected because there are many exogenous variables which affect the hog industry and distort the smooth theoretical relationships. The price of hogs depends upon demand as well as supply and the demand for pork is affected by consumer income and the prices and supplies of competing meats.

On the supply side, there are many factors besides price that have an effect on the size of the pig crop. The price and supply of feed and the relative profitability of alternative uses of farmers^ labor and feed are important factors in determining the number of sows farrowing. The number of pigs saved is influenced by weather, genetics, and production practices, in addition to the number of sows farrowing. The number slaughtered differs from the size of the pig crop because of the number of gilts saved for breeding purposes and the number of deaths that occur between the counting of the pig crop and slaughter.^ Also

5 Ideally the pig crop should be the number of pigs weaned, but the "pigs saved" series compiled by the USD A consists of the number of spring or fall pigs on hand June 1 or December 1 or sold before those dates

645778—63 5

30 TECHNICAL BULLETIN 12 74, XJ.S. DElPT. OF AGRICULTURE

the supply of pork is determined by the average slaughter weight as well as the number slaughtered.

In order to obtain a 4-year cycle in the model, it was necessary to assume 1-year lags between price and pig crop, and between pig crop and slaughter. These lags are somewhat longer than those expected from the physiological processes involved in hog production. The gestation period is slightly less than 4 months, pigs are weaned in about 2 months, and an additional 4 to 6 months are usually required for feeding to market weights. Using these approximate 6-month lags between breeding and weaning, and between weaning and slaughter, the resultant cycle would be 2 years instead of 4 years in length.

There are two main reasons for the existence of yearly lags. The first is the previously cited evidence (p. 27) that, at least in the past, farmers have tended to plan hog production on an annual basis. Whether this practice will continue with the changing technology of hog production is open to question. In the last 2 years, the size of the fall pig crop has not varied with the spring crop as closely as it usually has in the past decade.

The second reason is the statistical limitation imposed by the use of annual data. Their use requires that measurements be made in terms of years although the actual figures may vary considerably from a precise 12 months. The use of a calendar year instead of a marketing year also introduces a predilection toward annual lags. The price of hogs when sows are bred in the fall affects the number of sows farrowing the following spring and the following fall. The actual lag, between the price that influences farmers to breed more sows and the increased pig crop resulting from this decision, may be as short as 6 months for the spring crop. However, the price occurs in one calendar year and the pig crop in the next, so the lag between them becomes a year by this imprecise measurement. The actual lag between pig crop and slaughter is also considerably less than a year. But since all the fall crop and part of the spring crop are slaughtered the following year, annual slaughter figures tend to lag the annual pig crop by a year.

When the actual data are graphed, their interrelationships are surprisingly close to the theoretical model, especially since 1950 (figure 10). There have been two complete 4-year cycles in the past 8 years, and the relationships among the variables were as predicted by the model. Price preceded pig crop by a year, and slaughter followed the pig crop by a year. Prices were high when slaughter was low, and vice versa. All three series rose for 2 years, fell 2 years, then rose again for 2 years and fell 2 years, as would be expected from the theoretical model.

Prior to 1950 the cycle was not as evident, although the interrelationships were similar. Pig crop led slaughter by a year except during the 1930^s when drought and depression obscured the relationship, and the inverse price-slaughter relation held except during some of the war years when price controls were in effect. Hog production was influenced much more by the supply of corn in the prewar than in the postwar period because smaller stocks were carried over from year to year. Fluctuations in the corn supply in the prewar period due primarily to the weather tended to create random disturbances in the cycle and prevented its regular appearance (8). In contrast,


MEASURES OF THE HOG CYCLE Pig Crop, Hog Slaughter, and Prices Received

by Farmers for Hogs

MIL. HEAD r

100

PRICE ($ PER CWT.)*

10.00

7.50

5.00

1925 1930 1935 1940 1945 1950 1955 1960 * AVERAGE ANNUAL FARM PRICE DEFLATED BY THE INDEX OF PRICES RECEIVED BY FARMERS.

[ U. S. DEPARTMENT OF AGRICULTURE NEC. ERS 928-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 10.—The actual measures of the hog cycle exhibit roughly the same relationships as hypothesized in the theoretical model—price varies inversely with slaughter, and the pig crop precedes slaughter by about a year.

the price-support program and favorable weather in the postwar years have contributed to the development of relatively stable corn prices and the accumulation of large stocks of feed grains.

In addition to discrepancies between the model and the actual figures that may arise because of the simplifying assumptions under- lying the model, discrepancies may also arise because of the limitations of the statistical data which, in many cases, are estimates based on sample surveys. The actual data fit the basic pattern surprisingly well, and this suggests that the above-mentioned limitations are not serious.

The Cobweb Theorem

The cobweb theorem is another theoretical tool that has been used as an explanation for cycles resulting from lags in production response. The length of time required for reproduction and growth results in an inevitable lag in the response of agricultural commodities to changes in the factors that infiuence their production. The relationship between price and supply, hypothesized by the cobweb theorem, can arise only if the time lag between a change in price and the resulting supply response is sufficient to create a relatively fixed supply for a given period.

According to the theorem, a large supply and low price in one period will be followed by a small supply and an accompanying high price in the next period, which in turn will be followed in the succeeding period by a large supply and a low price, and so on. Assuming


there are no external influences, these fluctuations will either increase or decrease in amphtude, or continue at the same level indefinitely, depending upon the slopes of the demand and supply curves.

The application of the theorem depends upon the fulfillment of three conditions: (1) Producers plan for output in the next period on the basis of present prices; (2) once production plans are made, they are unalterable until the following time period; and (3) price is determined by the available supply, i.e., price is set by the intersection of the demand curve with a vertical supply curve.

The production of hogs probably approximates these conditions as well as any agricultural commodity. Available evidence indicates that the extension of current prices is of major importance in future production plans. Production is essentially fixed once sows are bred, at least on the upward side. Farmers can decrease production by marketing bred sows, although there is a considerable discount after the second month of pregnancy. There is some variation in marketing weights in response to price and other factors, but supply is relatively fixed in any given year (IS),

The length of the cycle produced by the cobweb theorem depends upon the time required for a change in price to affect supply. The time required to produce an average pig, from breeding to slaughter, is approximately 12 months. Using this lag, the cobweb produces a 2-year cycle. The lag involved in the cobweb theorem, however, is the lag between price and its effect on market supply, which is not necessarily the lag between breeding and slaughter.

The lag between price and marketings has been longer than the one year between breeding and slaughter because of the lag between price and farmers' response to it. This latter lag is not determinate a priori because it depends largely upon producers' expectations. If farmers expect a price to continue in the future, they will respond to it, but if the price is thought to be only temporary, it will initiate little or no response. There is also a period of variable intensity of the effect of price. In other words, price during one year may have some effect on production decisions during the next 2 or 3 years, in addition to its more pronounced effect in the immediately succeeding year.

The imperfections of annual data with respect to hog production have been discussed previously. When annual data are used, there has been an approximate 2-year lag between price and its effect on marketings in recent years. Using this lag, the three conditions of the cobweb theorem are not approximated as closely, but the actual hog production process is perhaps better described.

The recent experience of a 2-year lag gives empirical evidence about the speed with which hog producers react to changes in price. The fastest possible reaction from price to marketing is the 1 year required to produce a pig. Thus, the 2-year lag indicates some lag between price and production response, in addition to the lag between breeding and slaughter.

With a 2-year lag in supply, Ezekiel's (16) extension of the cobweb theorem produces a 4-year cycle. The simplest case of the cobweb theorem is that of continuous fluctuations. This occurs when, assuming linear functions, the demand curve has the same absolute


THE COBWEB THEOREM WITH A TWO YEAR

PRICE 1

LAG IN RESPONSE

7 - D S

6 - P.4 X i\ / Qf2, Ot6

5 - \^ Pt3 X

^\ X^ Otl.OtS

4 - "X^ 3 -

// \^ . Pu

/^ °t3

2 - -< \^ . P.->

Ot4 s. ^

1 - s D

n 1 1 1 1 1 1 1 Kß

1 2 3 4 5 6 7 8 QUANTITY

U. $. DEPARTMENT OF AGRICULTURE N£G. ERS 930-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 11.—With a 2-year lag in response, the cobweb theorem exhibits two separate pathways—one for odd years, and one for even years.

slope as the supply curve. Figure 11 illustrates what happens in this case with a 2-year lag in supply; i.e., marketings.

Since it takes 2 years for the supply response to be completed, it is necessary to assume prices or quantities marketed for the first 2 years. The position of these assumed quantities will determine the shape of the cycle resulting from the cobweb within the limitations imposed by the supply and demand curves. The quantities Qtx and Qt2 are positioned so that the resultant cycle will roughly approximate the shape of the hog cycle observed during the past 8 years. These quantities result in prices P^ and Fti- The response to the low price Pa is reflected in marketings 2 years later by the quantity Qtz. This small quantity results in a high price P^a, which in turn is followed 2 years later by the large marketings Ç^g, and the process continues in alternate years around the same pathways. The price in the second year, Pí2, is followed in a similar manner 2 years later by the quantity Qt^ and by price Pí4, which is followed in another 2 years by quantity Çi6, and so on.

Theoretically, there are two separate pathways for odd and even years. In reality, however, conditions in the hog industry in one year affect conditions in the next. But, at least in the recent past,

34 TECHNICAL BULLETIN 12 74, U.S. DEÛPT. OF AGRICULTURE

the major impact has been delayed until 2 years later, so this separa- tion has been maintained to some degree. If the two pathways were completely independent of each other, an infinite number of possibilities in the cyclical pattern would exist, depending upon the location of Qt\ and Q^-

Since the Korean war there have been no major changes in outside factors affecting the hog industry. So, assuming that conditions have been favorable for the operation of the cobweb theorem since 1953, the high slaughter figures for 1951 and 1952 would determine the position of Q^ and Qa, and the pattern of 2 high years followed by 2 low years would be established.^

When the prices and quantities given in figure 11 are placed on a time series chart, the cychcal nature of the process is clearly evident. The 4-year cycle produced by this cobweb relationship is shown in figure 12. This cycle is similar to the one developed on page 28 by the examination of the interrelationships among price, pig crop, and slaughter. The only difference is that for ease of explanation, the

OBSERVATIONS FROM A THEORETICAL COBWEB PLOTTED AS A TIME SERIES

VALUE OR AMOUNT

Price

Quantity

YEAR

U.S. DEPARTMENT OF AGRICULTURE NEC. ERS 931-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 12.—The observations from figure 11, plotted as a time series, show a 4-year cycle similar to that occurring in hogs in recent years.

6 The two years prior to 1953 are used as initial points because, since then, outside inñuences are assumed to have been stable; and, theoretically, a period of instability is needed to create a movement away from an equilibrium position.

FACTORS AFî^ECTING THE PRICE AND SUPPLY OF HOGS 35

price and quantity series in figure 9 were assumed to be in equilibrium in alternate years, while no such assumption is made in figure 12. A cobweb relationship with a 2-year lag and the second year (e.g., Qt2 in figure 11) located at the intersection of the supply and demand curves, would result in a time series graph identical with figure 9C.

Various types of cycles can be produced by the cobweb theorem by using different supply and demand curves, initial positions, and lags. Supply and demand curves, plus the initial positions, determine the shape and amplitude of a cycle, while the lag between price and marketings determines the cycle length. The cobweb theorem thus has suflicient flexibility to serve as a theoretical basis for a variety of cycles. The Akerman {1) variant on the cobweb principle further increases its flexibility by introducing a series of different, successively arising and vanishing short-term supply curves which may be closer to reality than a single long-term supply curve.

The actual pattern of hog prices and slaughter, with a 2-year lag between them, is shown in figure 13. The price of hogs during the breeding season for spring farrowings, October through December, is plotted vertically; the number of hogs slaughtered 2 years later is plotted horizontally. Arrows indicate the direction of influence. As in figure 11, prices lie on the demand curve and quantities on the supply curve. The odd years are graphed separately from the even years so the cobweb pattern can be clearly seen. In each case, the pattern spirals downward and also to the right, in the case of odd-numbered years, suggesting shifts in the supply and demand curves; perhaps, therefore, the successive short-term supply curves suggested by Akerman {1) are appropriate in this case.

Shifts among a family of three paraUel-demand curves and three parallel-supply curves, drawn freehand to the data of figure 13, can adequately explain the cobweb pattern shown there. The form and slope of these curves were arbitrarily chosen for illustrative purposes. These curves and the shifting cobweb pattern are illustrated in the somewhat complex figure 14. The development of the cobweb pattern proceeds as follows. Starting with price P51 on demand curve D\ we have quantity Q53 on supply curve S^ 2 years later. This results in price P53 on D^ which leads to Ç55 on S\ It can be seen that this cobweb is converging and will reach equilibrium if other factors remain constant. But in 1955 demand shifted downward to 0''', so price P55 was on this new demand curve. The supply curve also shifted and ^57 is on the new curve S''\ Another shift in the demand curve and P57 is on D" which results in Ç59 on S'". Then in 1959, demand shifts back to P''' where we find P59. The quantity $61 may lie on yet another supply curve, but more observations are needed to determine it. A somewhat similar pattern of shifts can be traced out for the even years beginning with price P50.

Many factors that affect the demand and supply of hogs can cause shifts in the curves, but the reasons behind particular shifts will not be discussed here. Factors that could cause shifts in the curves include changes in population, consumer income, supply of competing meats and poultry, changes in production technology, and changes in tastes and preferences.

The discussion thus far has dealt with shifts in the curves, and no mention has been made of possible changes in the elasticities of supply

36 TECHNICAL BULLETIN 1274, U.S. DEFT. OF AGRICULTURE

RELATION BETWEEN HOG PRICES AND SLAUGHTER, TWO YEAR LAG, ODD AND EVEN YEARS, 1950-61

""'" '* "" ^^^ '* ODD YEARS

18 -

16

14

12

10

Pt= Price of hogs Oct.-Dec, year t.

Qt-No. of hogs slaughtered in year t.

70 75 80 SLAUGHTER (MIL. HEAD)

♦PR/CE RBCEIVBD BY FARMERS. OCT.-DEC. DEFLATED BY CPI


FIGURE 13.—The relation between hog prices and slaughter exhibits a shifting cobweb pattern when a 2-year lag in response is used.

and demand. Elasticities may change with changes in slope or with shifts in the curves. The analysis of figure 14 suggests that shifting curves of approximately equal slope are appropriate for this period, but this does not mean that there are no changes in elasticities. Other studies have found changes in elasticities over longer periods. Brei- myer (9) compared the decades of the 1920's, 1930's, and 1950's and found some differences in the elasticity of demand for pork. Both


RELATION BETWEEN HOG PRICES AND SLAUGHTER, TWO YEAR LAG, WITH SHIFTING DEMAND AND SUPPLY CURVES,1950-61

PRICE ($ PER CWT.)*

20

18

16

14

12

10 "Pt =Price of hogs Oct.-Dec.,year t

- Of = No. of hogs slaughtered ¡n yeor t

J ^ 65 70 75 80 85

SLAUGHTER (MIL HEAD)

*PRICe RECeiVED BY FARMERS, OCT.-OEC, DEFLATED BY CPI

90 95

U.S.DEPARTMENT OF AGRICULTURE NEC. ERS 900- 62(3) ECONOMIC RESEARCH SERVICE

FIGURE 14.—The addition of freehand supply and demand curves shows how the cobweb pattern is altered by shifts in the curves.

an increased elasticity of supply and a decreased demand elasticity in recent years were found by Dean and Heady (13)^ but here again the postwar years were compared with prewar. The changes in elasticities were relatively small in each case, so it is unlikely that changes of significant magnitude would occur within a shorter span of only 10 years. Some estimates of the elasticities of supply and demand for hogs will be given in the following section.


ELASTICITIES OF SUPPLY AND DEMAND

The concept of elasticity applies to any curve—not just demand and supply curves. For example, there could be an elasticity of the cost ot producing corn with respect to the amount of fertilizer used or more generally, an elasticity of x with respect to y where x and v are any related variables. ^

But in economic analysis, interest centers around elasticities of supply and demand. The elasticity of demand with respect to price is denned as the percentage change in consumption associated with a 1-percent change in price. Likewise, the elasticity of supply is defined as the percentage change in production associated with a 1-percent change in price.

In mathematical notation, price elasticities of supply and demand are given by—•

e='k.P dp 1

where ¿g/dp is the derivative (slope) of the curve at the point (¡o,«). Ihe magnitude of dq^ld-p can be measured empirically by finding the change m quantity associated with a small change in price at a particular point on the curve. » i- v

Any relation between empirical price and quantity data implies some set of elasticities, either constant or varying throughout the range of the supply or demand curve. The use of a particular form ot equation in a statistical analysis imposes a particular set of elasticities on the data. For example, in the case of most mathematical iunctions, including hnear ones, the imposed condition is that the elasticity differs at every point on the curve. But if a relation is given with both quantity and price expressed in logarithms, the elasticity is the same at everv point on the curve.'

Empirical estimates of price elasticities of supply and demand often vary depending upon the price and quantity series used in the analysis In addition, they are also influenced by the kind of shift variables included in the regression equation, or, in other words, the factors that are held constant. For example, Working ißl, p. 69) discusses what happens to demand price elasticities when quantities rather than prices are used as measures of substitutions in a regression analysis. He states that if prices of other meats are held constant, the elas- *rY.. ^t™^^^ If ^?"?ewhat greater than if supphes are held constant. ihe proof of Workmg's statement is given by Learn (55).

'The proof is as follows The equation for such a curve is log o=a+6 log v Applying standard principles of differentiation from calculus, we obtain—

or ^ f f

dp q

Th.r'Zr^'l^'Î.J'-^ the formula for elasticity given earlier, we see that «=&. P1„«HPíHÍ ,i considerable advantage in using logarithmic relations in measuring elasticities, provided, of course, that the data are amenable


In a strict sense, demand theory requires that prices of substitutes be held constant. But as a practical matter in fitting a demand equation, quantities are often used to reduce the high intercorrelation found among many price series.

Changes in demand are ultimately reflected at the farm, where adjustments in supply are made in response to them. Estimates of supply and demand elasticities, therefore, will be made at the farm level. A conversion of elasticities from retail and wholesale levels to the farm level will permit comparison of these estimates with those from other studies.

Supply Elasticity Estimates

During the hog production process, farmers make two principal decisions that influence the quantity of pork produced. These decisions are the number of sows to farrow and the weight at which hogs are marketed. As mentioned earlier, the major source of variation in pork production is in the number of sows farrowing, and variation in slaughter weight is of secondary importance. The most important supply elasticity is, thus, the response of farrowings to hog prices.

The primary decision as to the number of sows to farrow in a given year is made in the fall of the preceding year. Thus, the immediate price factors that affect this decision occur during the months October through December. Prices of hogs, corn, and beef cattle, during the fall, each affect the number of farrowings the following spring. The accumulation of various past factors that affect hog production can be accounted for by using the previous year's farrowings as an explanatory variable. And in addition to the supply of corn, which is reflected in the corn price, the previous year's production of oats, barley, and grain sorghum affects farrowings, especially in areas where little corn is grown.

An estimate of the supply elasticity for spring farrowings is derived froni the following regression equation, fitted to data for 1949-60. Variables are defined as follows:

i^5=Number of spring farrowings (1,000). P^=Price received by farmers for hogs, Oct.-Dec, deflated

by consumer price index ($ per cwt.). P(7=Price received by farmers for corn, Oct.-Dec, deflated

by consumer price index ($ per bu.). Pj5"Price received by farmers for beef cattle, Oct.-Dec,

deflated by consumer price index ($ per cwt.). ö^= Production of oats, barley, and sorghum grain (mil. tons).

Log P^=-3.20+0.82 log P^ -0.42 log P^, -0.37 log P. , (.15) '-' (.17) '-' (.12)

+1.81 log Po ^ +0.25 log Gt-i R'=M (.37) '-' (.11)

All coefficients have correct signs and all are significantly different from zero at the 5-percent level, except those for the price of corn and small-grain production. These two are both very close to significance.

This equation gives a supply elasticity of 0.82 which is higher than the estimates ranging from 0.60 to 0.65 obtained by Dean and


Heady (13) for the years 1938-41, 45-56. These authors found evidence of a more elastic supply response in the postwar period than during the prewar years. The continuance of this trend in the additional years included in this analysis plus the elimination of the earlier years may account for the higher elasticity.

Spring farrowings account for a little more than half of the total annual farrowings. An elasticity of supply for fall farrowings is also needed for a complete appraisal of supply response.

The best indicator of the number of fall farrowings is the number of farrowings in the spring of the same year. Feeder cattle and corn prices for the period, April through June, and small grain production for the year are included as additional explanatory variables in the estimating equation. The price of hogs during the spring breeding season was also used as an additional explanatory variable in the initial analysis and was found to be relatively unimportant.

Log 7^^=1.50+0.68 log ^^+0.12 log G+0.13 log P^ (.17) (.08) (.07)

-0.39 logPe ^2^.92 (.11)

P7r=Number of fall farrowings (1,000). Ps=Number of spring farrowings (1,000). G^= Production of oats, barley, and grain sorghum (mil. tons).

Pi^= Price of feeder cattle at Kansas City, April-June, deflated by consumer price index ($ per cwt.).

Pc= Price received by farmers for corn, April-June, deflated by consumer price index ($ per bu.).

All coefiicients are larger than their standard errors and have the expected signs. Coeflicients for small-grain production and feeder-cattle price are not significant at the 5-percent level, but they are left in the equation on logical grounds.

Since this equation contains no hog price variable, the supply price elasticity for fall farrowings can be computed by substituting the regression equation for spring farrowings on page 93 for the expression for log Fs in the above equation. This results in a coefficient of 0.68X0.82=0.56 for P^^^. The value, 0.56, is¡ the supply elasticity for fall farrowings with respect to the price of hogs for the previous Oct.-Dec. It is considerably higher than the value of 0.29 estimated by Dean and Heady. A more elastic response for fall farrowings is caused by the same reasons given for the higher spring farrowing elasticity, especially since the latter is included in the computation of the fall farrowing elasticity.

A short run elasticity of supply, i.e., the response to price of the marketing weights of hogs, is given by the quarterly equation—

log Tr=2.28+0.05 log P^+0.02 log S R^=.32 (.02) (.01)

T1^= Average quarterly slaughter weight of hogs (lbs.). Pfi^= Price received by farmers for hogs, by quarters, deflated

by consumer price index ($ per cwt.). S^Seasonal index based on mean quarterly temperatures.


The seasonal index is used to account for the variation in slaughter weights due to the seasonal variation in the number of sows slaughtered. It is computed by dividing estimates of quarterly average U.S. temperatures by the mean annual temperature.

The supply elasticity of 0.05 for the quarterly analysis is statistically significant and of approximately the same magnitude as Dean and Heady's estimates that ranged from 0.04 to 0.08 for varying time periods, using 6-month data. The result substantiates their con- clusion that the within-marketing-period supply response is positive but very inelastic.

Demand Elasticity Estimates

Since the pioneering paper by Working {60) on identification, price has commonly been used as the dependent variable when estimating demand functions for agricultural products by least squares. Justification, as shown by Fox {20), is that consumption of agricultural products can be treated as predetermined; whereas price cannot be so treated. With price dependent in a logarithmic relationship, the regression coefiicient for consumption is the price flexibility which is the reciprocal of price elasticity, providing other goods do not measurably affect consumption (see Meinken, Rojko, and King {36)). r. c c^r.

The farm level demand equation based on annual data for 1949-60 is— logP^=10.83-2.85 log Qp~1.33 log Qs-1.01 log Qc

(.59) (.36) (.37) -.19 log /+.09 log T i2ír=.92

(.71) (.07)

where—

P^=Deflated price of hogs ($ per cwt,). Çp=Per capita consumption of pork (lbs.). Ç^=iPer capita consumption of beef and veal (lbs.). Ç^=:Per capita consumption of poultry meat (lbs.). /=Deflated discretionary income per capita ($). r=Time.

The coefficients for income and time are not significantly different from zero, but the other coefliicients are significant with the expected signs. The reciprocal of the pork consumption coeflScient suggests a farm-level demand elasticity of —0.35. This estimate is only a rough approximation because pork consumption is affected by the consumption of beef and poultry meat. Meinken, Rojko, and King {36) show that in this case the reciprocal of price fiexibihty is not equal to the price elasticity. If the effects of other goods are taken into account, the price elasticity is greater than that obtained by taking the reciprocal of price fiexibihty. The estimate of —0.35 is somewhat lower than it should be for an accurate measurement of the farm-level demand elasticity.

Elasticity estimates at wholesale and retail levels can be derived from this farm-level estimate by the method given in the following section. This method yields corresponding estmiates of —0.44 for


the wholesale demand elasticity for pork and —0.61 for the retail elasticity.

These estimates are close to those obtained by Maki (35) using quarterly data for the period 1949-56. He obtained elasticities of —0.62 at retail, —0.44 to —0.67 at wholesale, and —0.37 at the farm level. Other estimates from published studies given in table 8 range from —0.49 to —1.83 at retail and from —0.55 to —0.66 at the farm level. In general, lower elasticities are obtained from analyses based on postwar data. Dean and Heady (IS) present some evidence of a more inelastic demand for pork in the postwar period.

TABLE 8 —Pork: Elasticities of demandj by

Study Period of analysis Type of dollars

Breimyer (9): Least squares:

Logarithms 1948-60 annual 1921-41, 48-60 annual.

1938-41, 47-56 Aug. 1- Feb. 1.

1938-41, 47-56 Feb. 1- Aug. 1.

1922-41 annual do do 1922-41 Oct.-Mar

1924-41, 47-54 annual.

1949-56 quarterly do do

Current ---do

Constant. __

---do

Current ---do ---do .--do

---do

Constant ---do .--do

Do Dean and Heady (13):

Just identified: Logarithms._ _ __ __ _

Do

Fox (^0): Least squares: * Alogarithms>_. _

Do Do Do _.

Learn (33): Least squares : Alogarithms

Maki (35): Least squares:

Actual data Do Do

Nordin, Judge, and Wahby (38) : Overidentified: Logarithms Just identified: Logarithms Least squares : Logarithms

Stanton (43): Least squares:

Logarithms _ _ _

1921-41 annual

1953-59 1st & 4th quarters.

1953-59 2d & 3d quarters.

' Î953-59Tst'& 4th quarters.

1922-41 annual do

---do ..-do ---do

---do

---do

.--do --.do

---do .--do

Do

Just identified: Logarithms

Do

Working (61): Least squares: Logarithms:

Long run Short run

FACTORS AFrECriNG THE PRICE AND SUPPLY OF HOGS 43

An exception to these general findings is the study by Stanton (^S) in which much higher elasticities were obtained for the first and fourth quarters when they were separated from the second and third quarters.

Relation Between Farm, Wholesale, and Retail Demand Elasticities

If retail, wholesale, and farm prices always have the same percentage relationship to each other, the elasticity of demand at all three levels will be identical. A 1-percent change in price will result in equal percentage quantity changes at all three levels. However, if margins

type oj analysis y for specified periods

Quantity measure

Dependent variable

Demand elasticity with respect to—

Farm price Wholesale price Retail price

Prod - -do, ___

Price -0. 82 ___do -.97

do -0.65

-.62 -do

Cons do Prod do

Cons

Prod do Cons _

Cons -.81 Price_ -. 86

---do ---do

_--do

---do _--do ___do

"""-."66"

-.55

-.37

-1.18

-0.44 to -0.67 -.62

do -. 81 do -.91

do

do

Cons _ -. 78

___do -. 84 to -. 96

_ do ___do -. 49 to -. 54

do -. 71 to -. 78 do -1. 27 to -1. 83

do _ do

Price -1.55 --do -.99


tend to be constant in dollar rather than percentage terms, then the elasticity at the retail level will be greater than at the wholesale level, and the latter will in turn be greater than at the farm level.^

A cursory inspection of the behavior of pork prices at the different marketing levels suggests that relationship seems to fall between these two extremes (see table 9). Margins have gradually widened in the postwar period, and the ratios of farm to wholesale and retail prices have declined. The increased marketing margin reflects increasing costs of providing marketing services, including labor, rent, transportation, e(]uipment, and supplies. It also reflects increased processing and customer services provided by retailers. For instance, bacon is now shced and wrapped instead of being in large slabs, pork chops are individually packaged, and ham is precooked, boned, and shced to size for sandwiches.

flnr\

An empirical estimate of the relation -^ can be made since this

derivative is equivalent to the regression coefficient of farm price when retail price is the dependent variable. The equation, using annual data for the years 1949 through 1960, is—

P/=21.84+0.95P/+0.69r. ^2^.95 (.07) (.10)

8 The proof of these statements can be combined with the derivation of a formula for achieving comparability between elasticities measured at the different levels. The elasticity of demand at the retail level is given by—

' dpr q

where p r is retail price and q is quantity consumed. Similarly, the elasticity at the farm level is—

ef = ^ ■ ^ dpf q

where Pf is the farm price. From calculus, we know that ^=^ * X^'* ^^^"

stituting the latter expression in the equation for farm level elasticity and multi-

plying by —> we have— Pr

dq Pr Pf dpr ^ dpr q Pr dpf

or Vf dpr

^ Vr dpf

The relation -^ between changes in retail prices and changes in farm prices dpf

depends upon the behavior of marketing firms. If retail and farm prices always

bear the same percentage relationship, Pr=cpf, and TT" c=~; Then ef—er- (xp f Pf

dxi 7) f But if margins are constant in dollar terms, pr=pj+k. Then -i~= 1 and 6/= er • —-

avf Pr Since farm prices are lower than retail prices, — is less than one, and the farm price

Pr elasticity is less than retail elasticity. The relationships between farm and wholesale elasticities and between wholesale and retail elasticities can be similarly derived.


TABLE 9.—Farm, wholesale, and retail prices and margins for pork, 1949-60

Farm- Ratio Farm- Ratio Price Whole- whole- of farm Retail Equiva- retail of

Year of sale sale to price lent mar- farm hogs 1 value 2 mar- whole- of farm gin to

gin sale prices

pork 3 value * retail prices

Dol- Dol- Dol- lars lars lars per per per

hun- hun- hun- Cents Cents Cents dred- dred- dred- per per per weight weight weight pound pound pound

1949 19.94 24.63 4.69 0.81 55.8 34.7 21. 1 0. 62 1950 19.60 23.98 4.38 .82 55. 1 34.0 21. 1 .62 1951 21.45 26. 04 4.59 .82 59.2 36.3 22.9 .61 1952 19.36 23. 99 4.63 .81 57.5 34. 1 23.4 .59 1953 22.99 27.58 4.59 .83 63.5 41.0 22.5 .65 1954 23.48 28.32 4.84 .83 64,8 41.0 23.8 .63 1955 16.41 22.08 5.67 .74 54.8 29.2 25.6 .53 1956 15.53 20.97 5. 44 .74 52. 1 27.2 24. 9 .52 1957 18.92 24.50 5.58 .77 60.2 33.2 27.0 .55 1958 21.02 26.70 5.68 .79 64.8 36.9 27.9 .57 1959 15.22 20.92 5.70 .73 57. 1 27.4 29.7 .48 1960 16.65 21.84 5. 19 .76 56.5 29.4 27. 1 .52

1 Average price of 200- to 220-pound barrows and gilts, Chicago. 2 Wholesale value at Chicago of 71 pounds of pork and lard obtained from 100

pounds of hve hog. 3 Estimated average composite price of pork sold as retail cuts (ham, bacon,

loin, picnic, butt, spareribs, bacrjn square). * Payment to farmer for 2.13 pounds of live hog, minus that portion of gross

farm value attributed to lard and to edible and inedible byproducts.

Prices are given in cents per pound for equivalent quantities of pork at farm and retail. Time is included as an explanatory variable to account for the gradually increasing cost of marketing services.

The coefficient of farm price, 0.95, is not significantly different from 1.0 at the 5-percent probability level. This regression coefficient indicates that when the increasing cost of marketing services is accounted for, the margin between farm and retail prices tends to be constant in dollar, not percentage, terms. The coefficient for time indicates that the margin has increased 0.7 cent per pound (retail equivalent) per year since 1949.

With a constant margin in dollar terms, the demand elasticities will differ at the farm and retail levels by the ratio of the two prices. This ratio has averaged 0.57 over the last 12 years. The elasticity of demand at the farm level, thus, would be 57 percent of the elasticity at the retail level.

In a similar analysis, the relation between farm and wholesale prices is given by the equation—

P,,'=5.34+0.95P;r+0.10r. (.04) (.04)

R'=M

Here, prices are in dollars per hundredweight for equivalent quantities at farm and wholesale. According to the coefficient for time, the


farm-wholesale margin has widened at the rate of $0.10 per live hundredweight per year, beginning in 1949.

The coefficient for farm price is again 0.95 and not significantly different from 1.0, indicating a constant dollar margin between farm and wholesale prices. The elasticities at these two levels thus will differ by the ratio of the two prices. The farm-wholesale price ratio averaged 0.79 for the period 1949-60.

These analyses show that the farm-wholesale and farm-retail margins tend to be constant when allowance is made for a constant rate of change over time. The inclusion of time in the farm-level demand equation allows for this change. Thus, the relation between elasticities at the various levels is given by the price ratios. Using these ratios, estimates of elasticities at wholesale and retail levels can be derived from the farm-level demand elasticity estimate of —0.35 given earfier. A wholesale demand elasticity for pork of —0.44 and a retail elasticity of —0.61 are obtained by this method. The computed wholesale and retail elasticities are appropriate for the midpoint of the period, 1949-60, as both the farm-wholesale price ratio and farm-retail price ratio were trending downward.

A STATISTICAL MODEL OF THE HOG ECONOMY

In formulating a statistical model, the nature of the economic system to be analyzed should determine the type of equations to be used and the method used in fitting them. The initial task in analysis is thus to determine the nature of the economic system under consideration.

An analysis of hog production, based on the cobweb theorem, was presented earlier. This theorem provides a simple description of hog production that is reasonably accurate. The general equations for a cobweb model are—

Pt=a2+b2Dt+Vt

where St is the quantity suppHed in period t, Pt-i is the price in the previous period, Pt the price in period t, Dt the quantity demanded, a and h are estimated parameters, and Ut and Vt are residual or error terms.

The technique of solving these equations is a matter of mathematics. It is simplified, in this and many other cases, because the model is of a type described by Wold {58) as recursive. With the above equation, given all variables up to period i—1, the model provides the variables in period ¿, and provides them one by one. Here, given Pt-u then Ä'i (=7>í) follows, and then P^ which, in turn, can be used to determine St+u and so on.

In more general terms, a recursive system consists of a set of equations, each containing a single, endogenous variable other than those that have been treated as dependent in prior equations. The endogenous variables, that is, the variables determined by the model, enter the system one by one, like links in a chain where each link is explained in terms of earlier links. The explanation of each variable


proceeds recursively, from one period to the next, and, within each period, in a specified order.

Equations in a recursive model are estimated by least squares, a relatively simple procedure. If there is interaction between demand and supply within a time period, the estimation of coefficients, such as the elasticity of demand, by a simple regression equation fitted by least squares may result in a statistical bias (Haavelmo [26]). To avoid this bias, a system of equations should be solved simultaneously. Simultaneous equation analysis usually involves much more complex mathematical manipulation.

The time divisions used in an analysis have considerable effect upon the simultaneity of the variables. With short time units, a recursive system might be more appropriate than a simultaneous equation system. But when substantial units of time, such as a year, are used, more variables have time to interact and, hence, a simultaneous system may be preferable.

Thus, in a recursive model, quarterly data are often preferred to annual observations. However, in quarterly models serial correlation in the residuals tends to become more of a problem. Nonindependence of residual terms from an equation fitted by least squares leads to loss of statistical efficiency, underestimation of the true variance by the usual formula, and invalid t- and 7^-tests (Foote [19]). Some statisticians have attempted to solve this difficulty by randomizing the disturbance terms through autoregressive schemes (3), (23), But the use of such schemes amounts to an admission that an economic explanation for a systematic part of the movement in the dependent variable has not been found.

The omission of relevant variables is an important, if not the main, reason for the existence of serial correlation in the residuals. Eco- nomic variables tend to be serially correlated. When relevant explanatory variables are omitted from a structural equation, their effects on the dependent variable are left with the unexplained residuals. As a result, the residuals are also serially correlated. An attempt to deal with this difficulty would thus require the inclusion of more explanatory variables in the structural relationships. These additional variables could be either current or lagged.

Nerlove and Addison (37) have found that the inclusion of the lagged quantity of a given commodity in its demand and supply functions is theoretically sound and often reduces serial correlation in the estimated residuals to insignificant levels. In the supply functions of agricultural products, lagged variables probably play a more important part than current variables. In the case of demand functions, however, a number of current variables, such as current prices of competitive and complementary products, may be at least as important as lagged quantity as explanatory variables. And they may also significantly reduce serial correlation in the residuals.

Statistical Considerations in a Recursive Model ^

The statistical properties of recursive models have been discussed for a number of years, a recent proponent being Wold (59). He has

» This section is somewhat technical and may be omitted by the general reader. Discussion of the hog economy resumes on page 49,

48 TECHNICAL BULLETIN 1274, U.S. DEIPT. OF AGRICULTURE

shown that under certain conditions recursive systems fitted by least squares produce maximum hkehhood estimates of the structural coefficients. This is in addition to the unbiased estimates of the dependent variable that the least squares method normally gives. Maximum likelihood estimates have certain optimum properties that recommend them to the statistician. The estimates are consistent— it is very unlikely that in large samples there would be any large difference between the estimate and the true value. They are also efficient in the sense that for large samples they have a smaller variance or standard error than any other estimate when the observations are from a normal population. In order to give some basis for evaluating the performance of the method, a simple econometric model will be described and the special characteristics of recursive systems will be briefly discussed.

A single-equation regression model that assumes no errors of measurement in the observed variables can be written as—

yt=biXu+b2X2t+ . . . +OAí+'í^í.

The dependent variable ^ and the independent variables a^i, X2 . . . Xk are observed; the disturbance u is an unobservable random variable. The index t runs from 1 to N, i.e., there are N observations in the sample. The 6's are constant but unobservable coefficients of the independent variables. The usual procedure is to estimate bi, 62, . . . h, and to make confidence statements about the estimates from the given sample.

Certain assumptions must be made about the disturbances Ut in order to simplify computation and to obtain estimates of the coefficients with desirable statistical properties, such as consistency and efficiency. The following assumptions are commonly made for most methods of estimation: i^« is a normally distributed random variable with a zero mean and a constant variance; Ut is distributed independently of the predetermined variables; and successive disturbances are distributed independently of one another, or, in other words, Ut is not serially correlated.

If the disturbances in the several equations in a recursive system are correlated with one another, they are also correlated with variables that were dependent in preceding equations of the system, since by definition a dependent variable in a particular equation is assumed to be correlated with the disturbances in that equation. This violates the assumption that the disturbances are independent of the predetermined variables in an equation.

One way to overcome this correlation is to use calculated values for endogenous variables serving as independent variables in succeeding equations. Calculated values for a dependent variable in an eauation are known to be uncorrelated with the disturbances in that equation because the residuals are ignored in the computation. Hence, calculated values for an endogenous variable obtained from one equation are uncorrelated with the disturbances in another equation within the same system.

Another way to meet this assumption in a recursive model is to assume that the covariance matrix E of the residuals Ut is diagonal. This means that the covariance matrix has zeros everywhere except


on the diagonal, that is, Ut has constant nonzero variance and zero covariance. Thus, the disturbance of one equation is not correlated with the disturbance in any other equation of the model in the same time period. This additional assumption permits the use of actual, rather than calculated, values in the estimating equations. It also leads to maximum likelihood estimates by the single equation least squares method in a recursive model.

The general mathematical condition for the use of the recursive method is that the Jacobian of the transformation connecting the disturbances with the endogenous variables be triangular and equal to one. The Jacobian of the transformation is the matrix of partial derivatives of Ut with respect to yt. This general condition may seem quite complicated, but there is a simple method of testing it. If the structural equations in a system are linear in the variables, the elements of the Jacobian are identical with the coefficients of the endogenous variables. So when these coefficients form a triangular matrix, the general condition is met.

With triangularity of the Jacobian but no restrictions on the E matrix, single equation least squares estimates are not necessarily also maximum likelihood estimates. Successive application of least squares methods to separate equations, using calculated values of previously dependent variables, leads to consistent but not efficient estimates in this case. This method is not recommended for large systems with a long chain of substitution of results from some equations into others. The accumulation of errors may eventually become prohibitive.

In many cases it does not appear justified to assume the diagonality of the covariance matrix. This assumption is clearly inapplicable in the following situations: (1) In a given year, all observations were subject to larger than usual errors, because less funds were available for the collection of statistics; (2) one variable, such as national income, is affected by errors of aggregation (perhaps due to shifts in distribution), and this variable enters several equations of the model; (3) omitted variables are known to affect two or more equations—^for instance, weather affects all crop production. On the other hand, if two crops are grown in widely separated areas, the inclusion of weather in the random disturbances is permissible because relatively independent drawings of weather affect the two crops.

But unless there is a specific reason for assuming that the E matrix is not diagonal, it is worthwhile to make this assumption, because, by doing so, the computations for maximum likelihood estimates can be reduced by a factor of 2 or 3 for a model of three equations and by a much greater factor for larger systems.

Equations in the Model

The following six equations, fitted by least squares to quarterly data for 1949 through 1959, form a recursive system based on an expansion of the simple cobweb model given earlier. Although there are now additional variables and more equations, production is still basically a function of lagged price, and price is a function of present production. But the addition of a storage variable has eliminated the identity of production and consumption. As intermediate steps, there

50 TECHNICAL BULLETIN 1274, XJ.S. DEiPT. OF AGRICULTURE

are now equations for the number of sows farrowing, hogs slaughtered, cold storage holdings of pork, and farm price of hogs.

(1) F--1163.260+.994i^,_4+28.716P^^_-714.202Pc(4),-i (.032) (20.100) (336.756)

-19.509PB(4)î,-I+15.2820,_I+84.350P^(4),-I (11.275) (7.678) (21.002)

i?2=:...965, ¿-1.840^

(2) ii=10583.172+3.10lP,_2-9010.958ö(3)+58.125r (.170) (477.373) (15.134)

^2=-.927,^=1.287*

(3) Qp=313.377 + .128ÍÍ-2.584P R'=.9M, ¿=1.278° (.002) (1.213)

(4) S=-750.755 + .218Qp^_^ + .890Ä,_i+6.448Pp^_^-1.358TF,_i (.028) (.058) (2.048) (.378)

J?2==.906, á=2.006^

(5) Pp=:103.127-1.249%-2.841 —.419 %-.678 % (.155)^ (.461)^ (.194)^ (.431)^

-.017 4-6.613 Ö(55)-.026W^ R'=,S73, d=1.29S'' (.017)^ (1.126) (.013)

* (6) P^=-8.933+ .602Pp-.044M-.009W. ^^^.945, á= 1.332 (.029) (.012) (.003)

^No serial correlation in residuals. ♦Inconclusive test for serial correlation in residuals. °Positive serial correlation in residuals.

The Durbin-Watson statistic (d) provides a test for the presence of serial correlation in the residuals, i.e., the degree of correlation of each residual with the residual for the previous year. The table for the Durbin-Watson test extends only to five independent variables. For equations with more independent variables, a linear extrapolation was used. The degree of serial correlation is indicated by the symbols given above.

In general, the mnemonic device of denoting each variable by its first letter is followed, although there are some exceptions to prevent duplication. All price variables are measured in constant prices by deflating them by the consumer price index. Unless otherwise specified, quarterly data are used. For lagged variables,^—!, t—2, etc., indicate the number of quarters lagged, and y—1 indicates a yearly lag. For instance, Pc(A)y-i refers to the price of corn in the fourth quarter of the previous year.


Variables are defined as follows:

i^=Sows farrowing (1,000 head). P^=Deflated price received by farmers for hogs (dol. per cwt.). P(7=Deflated price received by farmers for corn (dol. per bu.). Pß=Deflated price received by farmers for beef cattle (dol. per cwt.).

6^=Annual production of barley, oats, and grain sorghum (mil. tons).

£r=Hogs slaughtered (1,000 head). 0=Dummy variable (0 or 1 in different periods). 7= Time (1, 2, 3, . . . in successive quarters).

Qp=Quantity of pork produced (mil. lb.). S=Cold storage holdings of pork, beginning of quarter (mil. lb.).

Pp=Deflated retail price of pork (cents per lb.). TÍ^=Seasonal index, based on mean quarterly temperatures. öö=Quantity of beef produced (mil. lb.). Ä=Ratio of pigs saved, fall y—l to spring y.

Qfl^Quantity of broilers produced (mil. lb.). iV=U.S. population (mil.). /=Deflated discretionary income (bil. doL).

M= Index numbers of unit marketing charges (1947-49 = 100).

Discussion oí the Variables

The basic supply equation of the simple cobweb model has been expanded into three equations to reflect and measure some of the steps in the production process. There are no data on sows bred, but there are estimates of the number of sows farrowing, and most bred sows are held for farrowing. Factors that influence the number of sows farrowing include the facilities available on farfns for raising hogs, the expected price of hogs at marketing time, the price and supply of feed, and the relative profitability of alternative uses of farm resources used in hog production, mainly feed and labor. Since this analysis uses quarterly data, some provision for the seasonal pattern of farro wings is also needed.

One way of accounting for the equipment available for hog production, as well as the seasonal pattern, is to include the farrowings for the same quarter of the previous year as an explanatory variable. Various studies have indicated that farmers make their basic decisions in the fall concerning next year's hog production. Thus, the prices of hogs, corn, and beef cattle—-the latter being the main competitor of hogs for feed and labor—for the fourth quarter of the previous year are included. But, conditions may also change during the year Thus, prices of these three commodities lagged one quarter were also tried as explanatory variables. Since the gestation period for hogs from breeding to farrowing is about 4 months, a 3-month lag is not precise, but it is the closest approximation possible, using quarterly data. The previous year's production of small grains (oats, barley, and sorghum) affects farrowings during the first two quarters, while the present year's production influences third and fourth quarter farrowings.

Intercorrelation resulted in wrong signs and insigniflcant coefficients for corn and beef prices lagged one quarter; hence, these variables

52 TECHNICAL BULLETIN 1274, U.S. DEOPT. OF AGRICULTURE

were dropped from the equation. The effects of intercorrelation (that is, correlation between independent variables) upon correlation and regression coefficients are discussed by Fox and Cooney (^i). In general, high intercorrelation means lowered reliability for individual regression coefficients.

The regression coefficients in equation (1) all have the correct sign and all are larger than their standard errors, although they are not all significantly different from zero at the 5-percent level. This is the standard significance level used in this study and means that a coefficient has a 95-percent probabihty of being different from zero. Stated another way, the coefficient would be expected to differ significantly from zero in 19 times out of 20. The d statistic for the Durbin-Watson test shows no serial correlation in the residuals.

The coefficients for the lagged price variables indicate supply elasticities of 0.14 for hog prices lagged one quarter and 0.39 for prices in the fourth quarter of the preceding year evaluated at the means of the variables. These estimates seem to be reasonable, in view of the time periods used. Higher elasticities are expected when farmers have more time to adjust production.

A supply elasticity of 0.14 for quarterly farrowings, with respect to hog prices the previous quarter, shows little reaction to immediate prices. The estimate of 0.39 for quarterly farrowings, with respect to hog prices in the fourth quarter of the preceding year, is less elastic than the eariier estimates of 0.82 and 0.56 for spring and fall farrowings, respectively. These latter estimates use 6-month data on farrowings and, thus, are expected to be more elastic.

The number of hogs slaughtered depends upon the number of sows farrowing 6 to 8 months previously and the number of pigs raised pjer sow. The age of barrows and gilts at marketing varies from 5 to 10 months, so a precise determination of the lag between farrowing and marketing is difficult to achieve. But the majority of hogs are slaughtered at 6 to 8 months, so a two-quarter lag was used. As the number of pigs raised per sow has been increasing at a fairly steady rate in recent years, time was used as a variable to account for this trend. Examination of the data revealed that estimates of third- quarter slaughter based on lagged farrowings were considerably higher than actual slaughter. Many gilts are retained for breeding purposes early in the fall months, and, consequently, slaughter is reduced. Also the predominance of March farrowings in the first quarter, and the tendency to feed spring pigs longer before marketing, mean that many pigs farrowed in the first quarter are not marketed until the fourth. To account for this, a dummy variable was intro- duced having a value of 1 for the third quarter when there were fewer marketings and 0 for other quarters when conditions were normal.

All three regression coefficients are significant and have the expected signs. The d statistic is within the inconclusive range.

The quantity of pork produced depends upon the number of hogs slaughtered, their average slaughter weight, and their dressing yield. The latter is virtually stable, so it does not create changes in pork production. The average slaughter weight varies seasonally and from year to year.

The year-to-year variation in slaughter weights results from different quantities fed, and this may be caused by hog prices or grain supplies.


Also spring-faiTowed pigs are usually fed longer and to heavier weights than fall pigs. Thus, in a year when the number of spring pigs slaughtered is proportionately larger, the average slaughter weight would be expected to increase, and vice versa. Pigs farrowed in .^he fall are marketed during the following spring and summer while a major portion of spring pigs are marketed in the fall of thé same year. A ratio of pigs saved in the fall of the preceding year to the number of pigs saved m the spring is, therefore, included as a variable. The negative sign for this variable means that as the proportion of fall pigs marketed during the year increases, the quantity of pork produced decreases for any given number of hogs slaughtered.

No satisfactory method of accounting for the seasonal variation in slaughter weights was found. The absence of any measure for this variable m the equation is one likely reason for the positive serial correlation in the residuals.

Since it was found that cold storage holdings of pork at the beginning of a quarter have an effect on the retail price of pork during that quarter, a storage estimating equation was necessary. Because of curing processes and the normal delay between slaughter and consumer purchase, some pork is always in cold storage. Cold storage holdings, lagged one quarter, are used to account for these factors. The quantity of pork produced during the previous quarter also mfluences the amount in storage, as do price and the season of the year.

The seasonal variation may, perhaps, be accounted for by using a seasonal index of temperature variation. This is simply the average temperature for each quarter as a percentage of the '^normal" annual temperature. Estimates of average U.S. temperatures are used in computing the index, admittedly a rough approxmiation, yet one that gives some indication of variation due to the changing seasons.

All of these factors are significant, and the d statistic indicates no serial correlation in the residuals. The results show that cold storage holdings tend to increase following increases in quantity of pork produced. On the other hand, the sign of the price coefficient indicates that storage holdings increase as price increases. The storage equation, more than any of the others in the system, is antici- patory. The positive relation of storage with price in the previous quarter suggests that past prices may have been used as a basis for future price expectations. In addition, the production and price coefficients may also be affected, as these two variables can be intercorrelated. However, the correlation coefficient between these two variables, using quarterly data, is only 0.44.

On the demand side, price analysis for agricultural commodities is frequently centered at the retail level. In the short run, prices of the more basic commodity are regarded as derived primarily from the price determined for the retail product. As Thomsen {45, p. 52) states it: "The demand for products at the farm end of the marketing system consists of consumer demand (i.e., prices which consumers will pay for different quantities) minus a schedule of marketing charges . . .". But Breimyer {9, p. 13) adds a word of caution to this approach: "Even though the relatively close price relationship between prices of meat and meat animals lends much validity to this


point of view, it should not be overstressed ... Not in every respect is the farm price purely derived from and synchronized with the retail price . . Relationship of farm to retail prices in the very short run is especially influenced by the nature of the pricemaking process. Prices at retail are often 'sticky/ slow to be changed, especially lor processed meats. Prices at the farm are more variable and can even be volatile. The urgent position of the farmer whose cattle or hogs are at peak condition, and must be sold, proclaims the partial independence of farm-level pricing from that at a retad meat counter that may be thousands of miles distant.'' . . j

This study uses the approach that the retail price may be estimated first and the farm price derived from it. The retail price of pork is affected by the supply of pork available for consumption, the supply of competing meats, and consumer income. These variables are put on a per capita basis to allow for population increase. The supply of pork consists of the quantity in storage at the beginning of a quarter plus production during the quarter. The major competing meats are beef and broilers. Because the storage of these raeats is small, the available supply is approximately equal to production. Deflated discretionary income is used as a measure of consumer income because it is not so highly correlated with the other predetermined variables as is disposable income.^^ As was mentioned previously, high intercorrelation among the predetermined variables makes interpretation of their coefficients difficult because it increases standard errors and sometimes changes the signs of the coefficients. Graphic analysis of the data indicates a shift in demand for pork m 1955 To account for this, a dummy variable was used—0 from 1949 through 1954, and 1 from 1955 to 1959. Stanton (43) has shown that there is a seasonal difference in the demand for pork, so the previously described seasonal index is included as a variable.

All coefficients are larger than their standard errors, except that for discretionary income. The sign for the income coefficient indicates that as income rises, the price of pork falls. But, the coefficient is not significantly different from zero. The sign for the dumnay variable indicates a downward shift in the demand for pork. The seasonal factor shows a decrease in price during the warmer, spring and summer quarters, other things being constant. The coefficient for broiler production is not significant. The rest of the coefficients (except that for income) are more than twice their standard errors and are significant at accepted probability levels. The d statistic is in the inconclusive range.

10 Discretionary income is derived from disposable income by subtracting the essential expenses associated with the relatively high standard of liymg achieved in the postwar years. The items deducted from disposable mcome mclude niaior fixed commitments, such as rent, taxes, home mortgage, and installment debt repayments, and essential expenditures, including medical expenses, household utilities, local transportation, and the maintenance of a given level of food and clothing consumption. For a full explanation of the concept of discretionary income and the procedures for its calculation, see Franklin {22).

FACTORS AFFECTING THE PRICE AND SUPPLY OF H0<3.S 55

Estimates of demand elasticity normally cannot be obtained directly from regressions such as equation (5). The use of a storage variable precludes any assumption that production and consumption are equal. Even if they were identical, the reciprocal of the price flexi- bÛity coefficient is not equal to the demand elasticity unless other goods do not measurably affect the consumption of pork (36). This is not the case for pork. The production and consumption of other meats definitely affects pork consumption. However, equation (5) indicates that a 1-percent change in pork production, on the average, is followed by a 0.4-percent change in the retail price of pork in the opposite direction. This suggests that the quarterly demand for pork is elastic, and contrasts with results using annual data that imply an inelastic demand (see page 41).

There may be two reasons for the difference. First, consumers may be more sensitive to price changes in the very short run and are willing to substitute significant amounts of pork for the other meats if the price is right. However, over the longer pull, as indicated by Breimyer (9, p. 72), pork, in relation to beef, ranks low on the scale of preferences for meats. Secondly, the amount of intercorrelation between the independent variables—^pork production and the seasonal index based on mean quarterly temperatures—^may also have affected the regression coefficient associated with pork production. The correlation coefficient between these two variables was 0.78, and it is con- ceivable that some of the variation in price, due to pork production, may be reflected in the coefficient associated with the seasonal index. Thus, the true coefficient for pork production may be higher than that obtained from the quarterly analysis. Another factor that may also affect the size of the quarterly coefficient associated with pork production is that the storage variable may not be an adequate shifter for inventories at all levels of the marketing chain, particularly at the retail level. As a result, the quarterly regression equation (5) may not fully reflect the actual movement of pork to consumers. A further factor is that as the time period used in the analysis becomes shorter, variations in quantity (consumption) data tend to increase, while retail prices tend to become more sticky.

The farm price of hogs is derived from the retail price and a marketing margin. Index numbers of unit marketing charges are used as a measure of this margin. The margin varies seasonally, increasing during the summer. All three variables have the expected sign and are significantly different from zero at the 5-percent level. The test for serial correlation of the residuals is again inconclusive.

Evaluation o( the Model

This system of six equations is not linear in the variables because in equation (5) pork production and storage have been converted to per capita bases after being used as total figures in other equations. Therefore, the matrix of the coefficients of the endogenous variables does not equal the Jacobian, and the latter will have to be computed

56 TECHNICAL BULLETIN 1274, U.S. DEÍPT. OF AGEICULTUEE

in order to determine whether the general condition for recursive treatment is met. The Jacobian is—

. y,_ à(ui, «2, ih, ■«4, «6, «e)

1 0 0 0 0 0

0 1 0 0 0 0

0 .127 1 0 0 0

0 0 0 1 0 0

0 0 -1.249 N

-2.841 N

1 0

0 0 0 0 .602 1

=1,

so the general condition is fulfilled. . ,, AT i, ,. • The Jacobian contains unknown values of the variable N, but since

it is a triangular matrix, its determinantal value is the product ot the elements along the mam diagonal which equals unity. Ihus in this case, there is no need to develop Imear ai)proxunations of the nonlmear variables in order to evaluate the Jacobian. ,

Residuals are estimates of the unobservable disturbances u,. lue assumptions made earUer about the Ut do not necessarily apply to the residuals ut. If the equations have been properly formulated, however, the residuals should have the same properties as were assumed for the disturbances. .,1,1. t • \

Testing for serial correlation m the residuals has become iau-ly common in time series analysis, since it has been shown that serious errors and biases may result if residuals are autocorrelated. As mentioned on p. 49, nonindependence of residual terms ^om an equation fitted by least squares leads to loss of statistical eaciency, underestimation of the true variance by the usual formula, and m- valid t- and i'-tests; it does not lead to statistical bias or mconsistency. For equations utilizing lagged dependent variables as explanatory variables, Hurwicz (29) has demonstrated that least squares estunates of coeflacients are biased in small samples. But, provided the residuals are not autocorrelated, these estimates of the parameters are consistent. If the residuals for these equations are autocorrelated, least squares estimates of the parameters may be seriously biased, even in large samples (24-). , . , , .• • -j i i, „

A completely satisfactory test for serial correlation m residuals has not yet been devised A simple correlation between û, and û,-i accepts the mdependence hypothesis too frequently. In other words, the correlation coefficient will sometimes be nonsignificant when the sample has been drawn from a serially correlated population. Uurbm and Watson (U) derived some approximate tests for autocorrelation in successive residuals of least squares regression models. iñe tests do not apply to models that use lagged values of the dependent van- able as independent variables (14, p. 410). The d statistic computed

FACTORS ATIFECTING THE PRICE AND STJPPLY OF HOGS 57

from the residuals of such a regression often accepts the false hypothesis of nonautocorrelated errors. The test also has a considerable range of indeterminancy. In a later article, Durbin and Watson (15) present an approximate procedure for use when their boxmds test is inconclusive. This method involves transforming ()i)d to a Beta distribution and should be sufficiently accurate with a large number of degrees of freedom, say greater than 40. The transformation requires lengthy computations and gives only a rough approximation for small samples, so it is rarely used.

Although two of the six equations in the model use lagged values of the dependent variable for independent variables (equations (1) and (4)), the Durbin-Watson test is used to give some indication of the degree of serial correlation in the residuals for these analyses. The test indicates that the condition of serial independence of the residuals is relatively well met for a quarterly system. There is only one case of positive serial correlation; there are three cases where the test is inconclusive, and two cases of no autocorrelation. The two cas^ of nonautocorrelation are suspect, however, because these equations include lagged values of the dependent variable.

A common method of testing for independence between two^ distributions is to compute the correlation coefficient. Absence of linear correlation, however, is not proof of independence (17, p. 222). But for want of a more precise test for the independence of the residuals from different equations, a correlation matrix for the û^s was used to measure the degree of independence. The diagonality of the covariance matrix E can be determined from this matrix since—

covariance Xi X2 ri2 = V (variance Xi) (variance X2)

If there is no correlation between the tí's, the ri2=0, and the covari- ances are also zero, making the E matrix diagonal. The correlation matrix for the residuals of the six equations is:

A Û2 û. Ö4 us ût ûl 1.000 0.055 0.027 0.103 0.161 0.061 Û2 1.000 .124 .083 .013 .130

1.000 .141 .037 .194 1.000 .002 .019

ÛK 1.000 .183 **5 1.000

The residuals from different equations may be assumed to be mde- pendent because none of the correlation coefficients are significantly different from zero at the 5-percent level. The assumption of a diagonal covariance matrix, and the use of actual values of endogenous variables serving as predetermined variables in subsequent equations, appears justified.

Inclusion of Additional Variables

In an attempt to reduce the serial correlation in the residuals, the model was altered slightly by including more explanatory variables


in the equations. The method of determining the appropriate variables to include in the equations was to compute a correlation matrix of the residuals and the predetermined variables used in the system. An examination of this matrix showed that no predetermined variables are correlated significantly with ûi. The residuals of the other five equations, however, are correlated with at least one of the predetermined variables used in other equations of the system. After selecting the correlated variable that made the most economic sense in each case, equations (2) through (6) were refitted, using these additional variables.

Four predetermined variables are significantly correlated with Û2. As would be expected, they are highly intercorrelated, since they are each correlated with the same variable. Of the four, the price of hogs for the previous quarter was the most appropriate to include as an explanatory variable for the number of hogs slaughtered.

Since slaughter hogs can vary in age from 5 to 10 months, some response to price would be expected. A high price during the previous quarter would induce farmers to sell their hogs at that time. This would reduce the number of hogs sold in the present quarter. Con- versely, there would be an increase in hogs slaughtered in the present quarter following low prices during the preceding quarter. Thus a negative regression coefficient would be expected.

The inclusion of this variable in equation (2) increases the multiple coeflScient of determination to 0.94 and eliminates serial correlation in the residuals measured by the Durbin-Watson statistic. The sign of the regression coefficient is negative, as expected.

The residuals of equation (3) are significantly correlated with only one predetermined variable, the price of corn in the fourth quarter of the preceding year. It seems reasonable that the price of feed would influence the quantity of pork produced. A low corn price would lead to increased feeding and heavier hogs. When this variable IS mcluded in the equation, its coefiicient is significantly different from zero and has the expected negative sign. Serial correlation in the residuals is reduced so the d statistic now falls in the inconclusive range.

The residuals of equation (4), which estimates the storage of pork at the beginning of a quarter, are correlated with four predetermined variables. Of these, only the dummy variable (A) could be included on logical grounds. The estimates for third-quarter begmning storage were consistently low. The use of temperature as an indicator of seasonal changes in cold storage holdings implies a symmetric pattern m both storage holdings and temperature. The dummy variable for the third quarter was included in the analysis to introduce a necessary degree of assymmetry. Cold storage holdings for the beginning of the thu-d quarter probably tend to be higher than implied by the symmetric relation because packers and wholesalers may tend to increase storage holdings in anticipation of smaller supplies and higher pork prices during the summer. In any event, the addition of this variable increases the R^ to 0.94, and the d statistic stiU indicates that there is no serial correlation in the residuals.

Of the two variables correlated with Us, the price of hogs during the previous quarter seemed most appropriate. The introduction of this variable into the equation for the retail price of pork means that


pork prices are not completely determined by consimaer demand, as was previously hypothesized. Retail prices are somewhat ''sticky'' and for short periods may reflect the prices retailers paid for the pork now on their counters. Thus, if the price of hogs was high the previous quarter, the price of the pork also would tend to be high.

The addition of this variable changes the sign of the income coefficient to positive, but the coefficient is still not significantly different from zero. It also increases the R^ to 0.92 and reduces serial correlation in the residuals. The d statistic is now at the upper end of the inconclusive range. The coefficient of the variable, itself, is significant with a positive sign.

Five predetermined variables are correlated with u^. Of the five, per capita pork storage seems the most reasonable to affect the price of hogs. A large amount of pork in storage at the beginning of a quarter would be expected to decrease the price of hogs. But when this variable is included in the equation, its coefficient has a positive sign, and the marketing margin coefficient becomes insignificant.

There is a fairly strong negative correlation between marketing margins and per capita cold-storage holdings of pork. Thus, with other factors held constant, when storage increases, margins decrease, and when margins decrease, hog prices increase. By this indirect route, an increase in cold storage holdings of pork may raise the price of hogs.

The five equations that were refitted, using additional variables, are presented below. In each case, the additional variable is significantly different from zero, and serial correlation in the residuals is reduced.

(2a) ff=15,188.994+3.127F,_2-8905.125ö,3)+24.212r-243.264PH,_, (.154) (433.451) (17.486) (77.757)

/?2=:.941, ¿=1.792^

(3a) Qp=474.592+.128i/-3.657ß-81.884Pc(4),_, (.002) (1.254) (36.720)

222=::=.995, ¿^1.526*

(4a) Ä=-865.271 + .238Qp^_,+7.918Pp,_-1.456Ti^,_i (.023) (1.721) (.312)

+ .825S,_i+80.655í?(3) R'=-M7, ¿=1.718^ (.050) (18.318)

(5a) Pp=73.489-1.068 %-1.875 |-.332 %-.460 %+.003 ^ (.133)^ (.437)^ (.160) ^ (.355)^ (.015)^

-4.193Z?55--.025W^+.658P^^_^ R'=M8, ¿==1.831* (1.073) (.010) (.151)

(6a) P^=-14.826+.62lPp-.008M-.015l^+.512 -^ (.024) (.012) (.003) (.110)^

P2=: .965, ¿=1.498*

A No serial correlation in residuals. ♦Inconclusive test for serial correlation in residuals.


Of the six equations (including equation (1) which was not refitted), the Durbin-Watson test shows no serial correlation for three equations, and, for the other three, the d statistic is at the upper end of the inconclusive range. The fit for the system as a whole is quite good. The coefficient of multiple determination {R^) is above 0.90 for each equation.

Evaluation of the Revised Model

In an attempt to resolve the indeterminancy of the Durbin-Watson test, another test for serial correlation was tried. The von Neumann- Hart (5Í, 27) test is designed to test for autocorrelation in an observed sequence of random variables. When it is applied to residuals of fitted relations, it accepts the independence hypothesis too frequently. It does not take account of the added correlation of the estimated residuals resulting from the necessity of estimating the regression coefficients; this defect becomes worse as the number of independent variables increases. However, Hildreth and Lu {28) applied this test to the residuals of a number of least squares equations with good results.

The von Neumann-Hart test is based on the ratio of the mean square successive difference to the variance. The ratio is:

ô2 N-l

¿=1

The relation to the Durbin-Watson statistic, d, is readily apparent where—

a== Ñ

The mean of least squares residuals is zero so that—

S" N S^ N-1

d.

The two test statistics for each equation are given in table 10. The von Neumann-Hart test shows that in no equation is the inde-

pendence hypothesis rejected at the 5-percent level. The value of

02 for each equation is considerably above the critical value of 1.455

for a two-tailed test at this significance level. This test indicates that there is only a remote possibility of serial correlation in the residuals.

The inaccuracy of this test when applied to the residuals of a regression equation containing a large number of independent variables is shown by the results for equation (5a). Although this equation has


TABLE 10.—Tests jor autocorrelation in residuals

Durbin- von Equation Watson Neumann- number statistic Hart

statistic

(1) 1. 840A 1. 883A (2a) 1. 792A 1. 834A (3a) 1. 526* 1. 561A (4a) 1. 718A 1. 758A (5a) L 831* 1. 874A (6a) 1. 498* 1. 533A

AThe hypothesis of zero autocorrelation is not rejected at the 5-percent level.

*The test value falls within the indeterminate range.

a comparatively high d value, it contains eight independent variables, so the Durbin-Watson statistic falls within the indeterminate range. The von Neumann-Hart statistic, on the other hand, gives the same significance level for equation (5a) as for equation (1). The latter shows no serial correlation by the Durbin-Watson test. The residuals of equation (5a) may be serially independent but not to the same level of significance as those for equation (1).

The three equations in which the Durbin-Watson test is inconclusive do not contain lagged dependent variables, and each has at least 35 degrees of freedom. The procedure presented by Durbin and Watson {15), for use when their test is inconclusive, is, therefore, appropriate. The approximate critical values of Fisher's z for 5- and 1-percent tests against positive serial correlation were computed for each of the three equations. An example of the computations is given m the Appendix, page 77. These values and the observed value of z for each equation are presented in table 11. When the critical value is less than the observed value, there is significant serial correlation.

The observed value of z is greater than the 5-percent critical value for equations (3a) and (6a). Thus, the residuals of these two equations are serially correlated at accepted significance levels. The residuals for equation (5a) show no significant correlation by this test.

The correlation matrix of the residuals of the refitted equations was computed to give an approximation to the covariance matrix. The

TABLE 11.—Test for autocorrelation in residuals when d is inconclusive

Equation Critical value of z

Observed number

5% 1% value of z

3a 5a 6a

0. 2613 .4167 .2461

0. 3712 .5954 .3495

0. 2992 .3924 .3183


matrix for the residuals of the six equations still showed no significant correlation at the 5-percent level, hence the covariance matrix is still diagonal by this approximate test.

This recursive model adequately explains the variation in six major variables in the hog industry. The coefficient of multiple determination {R^) is above 0.90 for each equation. Of the 30 regression coefficients, only 7 are not significantly different from zero at the 5-percent level. The assumptions made about the disturbances are comparatively well met. An examination of the residuals shows only two cases of significant serial correlation as measured by the available tests. The residuals for each equation are uncorrelated with those from other equations.

Forecasting

It is one thing for a system of equations to adequately explain the variation in the data from which the coefficients are derived, but quite another for the model to accurately predict variables for years beyond the period of fit. Consequently, some idea of the model's predictive power, distinct from its explanatory ability, is needed for an appraisal of its overall worth.

In using this model to make forecasts, values of some of the independent variables must be known for the period to which the forecast applies. The practical forecaster may find it necessary to reformidate the equations or to estimate these independent variables before forecasting the dependent variable. Here, however, prediction is only a means of appraising the model, and actual values of these independent variables are used, although they were not determined until after the period to which the forecast applies had ended.

The procedure for testing the model is as follows. The sample period ends with 1959, so the model will be tested by making pre- dictions for 1960 and 1961. Values of the endogenous variables can be estimated for any quarter on the basis of observed values of all quantities for preceding quarters and data for exogenous variables for the current quarter. The estimates so obtained will be compared with the observed values of the endogenous variables for the current quarter.

The estimated and actual values of the six dependent variables for the eight quarters of 1960 and 1961 are given in table 12. As a further aid in assessing the merits of the model in estimating values in the hog economy, table 13 shows the variation between actual and estimated values of the relevant economic variables within the hog industry for the eight quarters of 1960 and 1961. These eight quarters were not included in the statistical fitting of the model, so the ratio of the variation in a variable not explained by the model to the total variation in a variable can exceed 1.0. The unexplained variation is the sum of the squared differences between the actual and estimated values of a variable. Total variation is the sum of the squared differences between the actual value and the mean value for 1960-61 for a variable.

As measured by this ratio, equation (1)—number of sows farrowing—produced the best forecasts. A ratio close to 1.0, such as those for equations (4) and (5), indicates a poor forecasting equation.

FACTORS AFFECTING THE PRICE AND SUPPLY OF HOOS 63

TABLE 12.—Economic factors in the hog economy: Actual and estimated values oj endogenous variables, 1Q60 and 1961

Year and Sows farrowing, F Hogs slaughtered, H Pork production, Qp

quarter Actual Estimated Actual Estimated Actual Estimated

1960,1 2 3 4

1961, 1 2 3 4

Thousand head 3,720 3,444 3,688 1,818 3,730 3,740 3,648 1,894

Thousand head 4,208 3,533 3,741 1,541 3,892 3,629 3, 742 1,909

Thousand head

24, 425 19, 526 17, 926 22, 498 22, 161 18, 829 17, 728 23, 815

Thousand head 26, 320 19, 092 16, 054 24, 020 24, 749 18,833 16, 102 24, 911

Million pounds

3,300 2,712 2,463 3,155 3,057 2,640 2,447 3,320

Million pounds

3,499 2, 560 2,165 3,200 3,333 2,564 2,209 3,354

Pork storage, S Deflated retail price of pork, Pp

Deflated farm price of hogs, PH

Actual Estimated Actual Estimated Actual Estimated

1960,1 2 3 4

1961,1 2 3 4

Million j:ounds

264 338 351 158 170 244 244 126

Million pounds

400 417 327 179 277 296 247

95

Cents per pound

41. 6 44.5 46.6 46.3 46. 7 45.7 46.9 45.9

Cents per pound

41.6 45.3 48.6 47. 1 45.9 47.9 49.5 47. 5

Dollars per hun-

dredweight 10.64 12.38 12. 79 13,03 13.39 12.71 13.33 12,53

Dollars per hundredweight

10.37 n. 90 13.42 12.74 12.47 13. 16 13.78 12.73

Estimates of pork storage and the retail price of pork would have been nearly as close if the mean for the period had been used as an estimate, but, of course, this mean is not known in advance.

The ratio of the unexplained variation to the total variation in a variable can be very large, due to the estimated value for one quarter being very poor, although for other quarters the estimated values may be quite close to the actual values. Based on percentage differences between actual and estimated values for 1960-61 given in table 14, equation (5) for the retail price of pork is a fairly good estimator. There was very little variation in retail price, which accounts for its high variance ratio. The large percentage differences in the first quarter of each year account for the poor ratio for the storage equation. As can be seen from table 12, the direction of change in the variables, as predicted by the model, is very good for the quarters in 1960, but it is mediocre for the quarters in 1961. Including 8 quarters for each of 6 variables, there are 48 quarters in which there were 28 changes of direction. Only 17 of these changes were predicted correctly. The model did much better in predicting


TABLE 13.—Analysis of variation between actual and estimated values in the hog economy for 1960 and 1961 ^

Variable Total

variation 2 Unexplained variation ^

Ratio of unexplained

variation to total

variation

Sows farrowing, F (1,000 head).___.. Hogs slaughtered, H (1,000 head) Pork production, QP (mil. lb.) Pork storage, S (mil. lb.)__

4, 956, 004 50,139, 096

923, 792 47, 075 2L66

5. 2850

373, 229 20,143,101

293, 286 40, 877 20.08

2. 0757

0. 0753 .4017 .3175 . 8683

Retail price of pork, Pp (ct./lb.) Farm price of hogs, PH (dol./cwt.)

.9271

.3928

1 Equations fitted to quarterly data for 1949 through 1959. See table 12 for values of variables.

8 _ 2 Total variation=X! (Xt-X)2

3 Unexplained variation=2 (Xt—Xt')^ ¿=i

TABLE 14.—Variables in the hog economy: Percentage di^erenees between actual and estimated values, 1960 and 1961 ^

Sows Hogs Pork Pork Deflated Deflated Quarter farrowing slaughtered production storage retail farm

F H Qp S price of pork Pp

price of hogs PH

Percent Percent Percent Percent Percent Percent 1960,1 13.1 7.8 6.0 5L5 0 -2.5

2 2.6 -2.2 -5.6 23.4 L8 -3.9 3 1.4 -10.4 -12.1 -6.8 4.3 4.9 4 -15.2 6.8 L4 13.3 L7 -2.2

1961,1 4.3 IL 7 9.0 62.9 -L7 -6.9 2..._ -3.0 .0 2.9 21.3 4.8 3.5 3 2.6 -9.2 9.7 1.2 5.5 3.4 4 0.8 4.6 1.0 -24.6 3.5 1.6

* Equations fitted to quarterly data for 1949 through 1959. values of variables.

See table 12 for

changes in direction for quarters close to the period of fit. In 1960, 11 of 13 changes were correctly predicted , but only 6 of 15, in 1961.

SEASONAL VARIATION IN HOG PRODUCTION AND PRICES

The use of quarterly data presents the additional problem of seasonal variation. Annual data ignore the variation caused by the tilt of the earth's axis as the earth orbits the sun, but a model using shorter time periods must account for this variation.


Seasonal variations in the hog industry stem largely from interrelated economic and physiological factors. The gestation period for hogs is about 4 months, and since sows normally are not bred before the pigs are weaned, the time between farrowings for the same sow IS about 6 months. Physiological factors thus limit farrowings to two per sow per year.

Economic and climatological factors largely determine when these two farrowings occur. To raise pigs which are farrowed in the cold of midwinter, considerable investment in speciaHzed farrowing equipment is needed, which increases costs. Therefore, sows are generally bred to farrow in the spring and fall when the weather is favorable, and there are two seasonal peaks in farrowings. As hogs are regularly slaughtered 6 to 9 months after farrowing, the seasonal patterns in slaughter and prices are largely determined by the pattern of farrowings.

While the basic seasonal patterns still hold, there has been a gradual decrease in the amount of seasonal variation in the hog industry during the last 10 years, as is shown by examining the monthly seasonal indexes. These seasonal indexes are ratios computed by dividing the original monthly data by a centered 12-month moving average, with adjustments for extreme or irregular values. The indexes show the value for each month as a percentage of the average monthly value for the year adjusted for trend, cyclical, and irregular components. An index of 129 for sows farrowing in May 1950, for example, means that the number of sows farrowing in that month is 29 percent greater than the average adjusted monthly farrowings for

HOGS: SEASONAL VARIATION IN PRICES, SLAUGHTER AND FARROWINGS

% OF ANN. AV

100

1950 1953 1956 1959 MONTHLY DA TA

U. S. DEPARTMENT OF AGRICULTURE NEC. ERS 898-62(2) ECONOMIC RESEARCH SERVICE

FIGURE 15.—Seasonal variation in farrowings and slaughter has moderated over the last 10 years.

66 TECHNICAL BULLETIN 1274, U.S. DEIPT. OF AGRICULTURE

TABLE 15.—Hogs: Indexes oj seasonal variation^ 1950,1965, and 1960 ^

Month

Price received by farmers

Commercial slaughter

Sows farrowing

1950 1955 1960 1950 1955 1960 1950 1955 1960

January February March April.

93 99 99 96

103 105 108 110 108 100 90 89

95 97 97 104 106 107 105 107 104 97 90 91

94 95

101 104 105 107 105 105 101 97 94 92

127 96

105 94 88 85 72 78 88

109 124 134

118 99

110 94 86 79 76 85 97 114 121 121

113 101 104 98 91 85 83 89 99 113 110 114

38 95

214 239 129 62 53

103 141 73 31 22

57 124 203 193 110 68 68 118 128 67 31 33

72 130 178 164

May 94 June» 78

7Q July_ -_- August September October November December

119 133 73 37 44

1 Percentage each month is of the average monthly value for the year adjusted for trend, cyclical, and irregular components.

that year. Table 15 gives the indexes for selected years, and figure 15 shows the seasonal patterns for the last 10 years.

The seasonal peaks and troughs in farrowings are now less pronounced because of changes in breeding and production practices. The number of spring farrowings still exceeds the number of fall farrowings, but monthly differences have been reduced as the fall crop has become larger relative to the spring crop. Fall farrowings have increased from 39 percent of the annual total in 1950 to 47 percent in 1960. The trend toward a greater proportion of fall farrowings has contributed to earlier spring farrowings. Until 1954, farrowings reached one maximum during April and another in September, 5 months later. ^ Since that year, March has been the peak month in spring farrowings, and the lag between the 2 peaks is now 6 months, the logical lag for the 2-crop system.

The increasing number of specialized hog producers who have the equipment necessary for year-round farrowing has reduced the con- centration of farrowings in the spring and fall. Some farmers also divide their sows into groups which farrow at different times and thus have litters at more than 2 periods each year. In 1950 the seasonal indexes of farrowings went from a spring high of 239 in April to a summer low of 53 in July. This was followed by a fall peak of 141 in September and a winter trough of 22 in December. By 1960, the variation had decreased to a spring high of 178 in March, a summer low of 78 in June, then a fall peak of 133 in September, and a winter trough of 37 in November.

Although the time that barrows and guts are slaughtered is closely tied to the time of farrowing, the seasonal variation in hog slaughter has a smaller amplitude than the variation in farrowings. Differences in the weights and ages of hogs marketed account for this reduced variation. For instance, some producers may feed for rapid gains or sell at light weights, as do those who market February pigs in


August when prices have usually been seasonally higher than in other months. Or they may feed pigs for slower gains or sell them at heavier weights, a common practice in preparing late fall pigs for sale in midsiunmer.

Until recently, the seasonal pattern for hog slaughter was similar to that for sows farrowing, although the variation was not as extreme. There were two peaks and two troughs per year. But the peaks were not so evenly spaced as they were for farro wings. The high point in slaughter was reached in December, 8 months after the spring peak in farro wings. A second peak was reached in March, just 6 months after the fall peak in farro wings. The reason for the longer time span between peak farrowing and peak slaughter for the spring pig crop is due partly to the withholding of gilts for breeding purposes.

The seasonal pattern of slaughter has changed considerably during the last 4 years. With earlier farro wings and increased feeding eíBciency, the late fall peak has leveled off and the 4 months from October through January now have fairly equal seasonal indexes. The February trough has all but disappeared as August farrowings have increased, but the summer low stÛl occurs in July.

The extremes of seasonal variation in slaughter are less pronounced than they were ten years ago—they follow the reduction in the variation in farrowings. The indexes for 1950 ranged from a low of 72 in July to a high of 134 in December. In 1960, the low was 83 in July, and the high was 114 in December.

Although there are seasonal changes in the demand for pork, as a general rule, the price received by farmers for hogs varies inversely with the number slaughtered. Prices are usually highest in any given year in midsummer, because slaughter is lowest at that time. Then, as slaughter increases, prices decline considerably during the fall, reaching a low in November or December. The secondary price peak late in winter has disappeared now that February marketings have increased—prices rise fairly steadily from December to the summer peak. This peak is now reached earlier m the summer; whereas August prices used to be the highest of the year, since 1955 June prices have typically been as high or higher than those in August.

There is less seasonal variation in prices than in slaughter or farrowings. But following the reduced variation in slaughter, there has been some decrease in the variation of seasonal indexes for prices during the last 10 years. In 1950, the indexes varied from a high of 110 in August to a low of 89 in December. The variation had decreased slightly by 1960, with a high of 107 in June and a low of 92 in December.

The seasonal distribution of farrowings varies regionally, as shown in figure 16. Here, the percentage of the total nimiber of sows farrowing in each month of 1960 is graphed for each of the six major regions of the United States. All regions have spring and fall peaks in farrowings, but the peaks are more pronounced in the North Cen- tral regions that include the Corn Belt. The warmer southern regions have a much evener distribution of farrowings.

The spring and fall peaks come earlier in the south—February having the highest percentage of farrowings in the South Atlantic and South Central States. March is the high month in all other regions, except the West North Central where the peak is in April.


SOWS FARROWING BY MONTHS, 1960 % OF REGION TOTAL"

10

0.

NORTH ATLANTIC

^ w 11 20

10

0. 20

10

0. 20

10

0. 20

10

0. 20

10

0_

SOUTH ATLANTIC

i til il i_m_l_ EAST NORTH CENTRAL

ri 1 m.

mmM%

WEST NORTH CENTRAL

1 I M- SOUTH CENTRAL

^ I á_i ■Jl

WESTERN

I ï_ï ̂ IJ DEC. FEB. APR. JUNE AUG. OCT.

U. S, DEPARTMENT OF AGRICULTURE NEC. ERS 882-62(2) ECONOMIC RESEARCH SERVICE

FIGURE 16.—The seasonal distribution of farro wings is slightly more pronounced in northern regions. More even temperatures in southern regions permit a more even distribution.

FACTORS AFFECTING THE PRICE AND SUPPLY OF HO<ÎS 69

The fall pattern is similar for all regions, September being the leading month everywhere except in the South Central region where August is slightly higher.

The coefficient of variation provides a measure for comparing the fluctuations in different regions. This measure is simply the standard deviation divided by the mean. These indexes confirm what can be seen visually from figure 16. The West North Central region has the greatest month-to-month variation; the South and West, the least. A decrease in seasonal variation over time is indicated by a comparison with the coefficients obtained by Kause {31) for 1954. Table 16 shows that there has been little change in the South, but large decreases have occurred in seasonal variation in farrowings in the North Central and Western regions, compared with 1954.

TABLE 16.—Coefficients of variation jor the number oj sows farrowing by region^ 1954 0,'^d 1960

Region 19541 1960

North Atlantic _ 0.45 .29 .63 .83 .30 .41

n 4-0 South Atlantic _ .^.^ East North Central _ _ _ 41 West North Central _ __ 51 South Central-_ _ __ 33 Western _ _ 31

1 Given by Kause (31, p. 17).

The changing seasonal pattern in hog production and prices affects the quarterly model. The factors responsible for the changing pattern are difficult to quantify, but an attempt to measure them must be made if the model is to be accurate. Ignoring these substantial changes would result in a poor fit in a quarterly model.

The basis for the changing pattern in slaughter and price is the change in the pattern for farrowings. The number of sows farrowing in a quarter lagged one year was used in equation (1) to account for the seasonal variation in farrowings. As long as the pattern was stable (1949-52), this equation estimated the quarterly changes in farrowings very well (fig. 17). But when the pattern changed each year, from 1953 to 1958, the estimated pattern lagged the actual pattern by a year. This result is expected, since the estimated pattern depends largely upon the lagged-farrowings variable in the equation.


SOWS FARROWING: ACTUAL AND COMPUTED NUMBERS BY QUARTERS, 1949-61

MIL HEAD

_L Q ''■' t ■'■''■■''■■'■'■''■''■'■'■■''■'''■'■'■'''■■■'■' '

1949 1951 1953 1955 1957 1959 1961 THE COMPUTED VALUES FOR 1960 » Í96I ARE FORECASTS BEYOND THE PERIOD OF FIT.


FIGURE 17.—Estimates of the number of sows farrowing, given by equation (1, p. 50) correspond closely to actual farro wings, but the quarterly pattern of estimated farrowings lags the actual pattern by a year, instead of coinciding with it.

The actual and estimated values for hog slaughter and prices are plotted in figures 18 and 19 to show how the changing seasonal pattern has affected the closeness of fit. For the number of hogs slaughtered, the actual and estimated seasonal patterns are very similar untü 1958. Since that year, slaughter estimates have been consistently too high for the first quarter and too low for the third quarter. The estimated change in direction is also incorrect for each of these quarters in 2 of the 3 years. Shorter feeding periods and earlier farrowings mean that, now, more hogs are slaughtered during the third quarter, and fewer spring pigs are held over until the first quarter. The estimates of the number of hogs slaughtered for the last 3 years suggest that the change in production practices may have been great enough to require a change in coefficients for accurate forecasting.

ï'ACrÔRS ÀiF^J^ECTING TSE PRICE ÀNÎ) SUPPLY OF HOGS 71

HOGS SLAUGHTERED: ACTUAL AND COMPUTED NUMBERS BY QUARTERS, 1949-61

MIL HEAD Actual

10 tu ij±kt mJjiibijdiJjijaiiui illUiiiXJJJ 1949 1951 1953 1955 1957 1959 1961

THE COHPUTED VALUES FOR 1940 * 19*J ARE FORECASTS BEYOND THE PERIOD OF FIT.

U. S. DEPARTMENT OF AGRICULTURE NEG. ERS 933-62(3) ECONOMIC RESEARCH SERVICE

FIGURE 18.—Estimates of the number of hogs slaughtered, given by equation (2a, p. 59) have been consistently high for the first quarter and low for the third quarter each year since 1958. These deviations suggest that recent changes in production practices have not been handled adequately in the equation.

In contrast to farrowings and slaughter where seasonal factors predominate, figure 19 shows that cyclical factors have greater influence on hog prices. The estimates of deflated prices received by- farmers for hogs conform closely to the actual values. There is no evidence of a changing seasonal pattern causing the estimates to diverge from the actual prices.


HOG PRICES*: ACTUAL AND COMPUTED VALUES, BY QUARTERS, 1949-61

$ PER CWT. ~

Actual

Computed

jjiiiiiLLiiLuji^aliiiWiiimijIuil^^ 1949 1951 1953 1955 1957 1959 1961

THE COMPUTED VALUES FOR I960 i 1961 ARE FORECASTS BEYOND THE PERIOD OF FIT.

♦ PRICE RECEIVED BY FARMERS DEFLATED BY CPI.

. S. DEPARTMENT OF AGRICULTURE NEC. ERS 934-62(3) ECONOMIC RESEARCH SERVICE I

FIGURE 19.—In contrast to farrowings and slaughter with their predominately seasonal patterns, hog prices tend to follow a longer cycHcal path. Estimates of hog prices given by equation (6a, p. 59) follow this path very well and correspond closely to actual prices.

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FACTORS AFFECTING THE PRICE AND SUPPLY OF HOOS 75

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APPENDIX

A Test for Serial Correlation

An approximate test for serial correlation in the residuals of least squares regression is presented in Durbin and Watson (15) for use when their bounds test is inconclusive. This test should be sufficiently accurate with a large number of degrees of freedom, say greater than 40. For smaller numbers, this test can only be regarded as giving a rough indication. The test does not apply to autoregressive schemes and distributed lag models where lagged values of the dependent variable occur as independent variables. The following description of the procedure used in applying the test is based on that given by Durbin and Watson (15, p. 163-166), using the data of equation 6a.

In general terms, the method used is to transform d so that its range of variation is approximately from 0 to 1 and to fit a Beta distribution with the same mean and variance. The mean and variance of d vary according to the values of the independent variables, so the first step is to calculate them for the particular case concerned.

The description of the computing procedure is greatly facihtated by the introduction of matrix notation. Thus, the set—

Xii

Xm

Xi\

X2n

Xki

Xjcn

of the observations of the independent variables is denoted by the matrix X. For the following calculations, all these observations are measured as deviations from the sample means. The corresponding set of first differences of the observations is denoted by AX A relation between the two is given by—

(AX)'(AX) = X'AX

where X' is the transpose of X and A is the real symmetric matrix—

1 — 1

-1 2

— 1

0 ... — 1 . .

0

0 2 ...

0 . . . 2 -1

0 . . . -1 1 77


The mean and variance of d are obtained by calculating the traces of certain matrices. The trace of a square matrix is simply the sima of the elements in the leading diagonal. For example, the trace of A^ denoted by tr -A, is 2(n— 1), where n is the number of rows or columns in A, The mean and variance of d are given by —

E{cD- n—k—1

var ((/) = {n-k-l)(rh-k+l) [Q-PE(d)]

where n is the number of observations, k is the number of independent variables,—

and

P^tr^-tr iX'AXiX'X)-'},

Q=trA'-2 tr {X'A'X{X'X)-'} +tv[{X'AX(X'X)-'}']

The elements of the inverse (X^X)'^ will have been obtained for the calculation of the regression coefiicients, and the elements of X^AX for the calculation of d, providing certain methods and formulas are used. In any event, they are readily obtainable. The elements of (X'X)~^ are obtained by inverting the matrix—

Z(xi—Xi){x2—X2)

^{Xjc—Xk)(Xi — Xiy

j:{xi-xi)(Xk-Xk) z(xjc-xj,y

The (Í, j)th element of X'AX is simply the sum of products XAXfAxj, since X'AX=(AX)' (AX), and the matrix is—

'z(Axiy 2(Aa;i)(Aa;2)

X(Ax,)(AxO'

j:(Axi)(Ax,) 2(Aa:,)2

The remaining matrix requiring calculation, X'A^Xy is very nearly equal to (A^X)'{A^X), where A^X represents the matrix of second differences of the independent variables. The {ij)th element of X^A^X is given exactly by—

i:(A%) {A%) + iXn-Xt2) {Xji-Xj2) + (Xin-i -Xin) {X^n-I-X^n) •

The latter two terms are comparatively small so the element will usually be given sufficiently closely by—

Z(A2xi)(A2:c,-)'

FACTORS AFFECTING THE PRICE AND SUPPLY OF HOGS

and the required matrix is—

2(A^x,)(A2x,)-

79

Using the data of equation 6a as an example, we have

X'AX=

{X'X)-'--

500.23 114.3

4702.4 40.602

114.3 172

1866 -.06

.00170 .00040

.00040 .00045 -.00009 —.00005 .00130 .00252

4702.4 1866

107918 961.38

-.00009 -.00005 .00002 -.00042

40.602 -.06

961.38 47.8126

.00130

.00252

.00042

.03574

52568 .11872 .02626 .41444 09509 .02967 .01841 -.20383 27765 -.25256 1.23806 -.15040 04463 .08863 -.00450 1.35767

Although tr X'AX {X'Xy^ is simply the sum of the diagonal elements of the product of these two matrices; the other elements will be needed for further calculations, so the whole matrix is computed, giving—

X'AX{X'X)-'

Thus,

trX'Air(X'X)-i = .52568+ .02967+ 1.23806+ 1.35767 =3.15108.

Remembering that tr .A=2(n—1)=86 in the present case, we have

P== 86-3.15108 = 82.84892,

82.84892 and

E{d)- 39

=2.12433.

The matrix of sums of squares and cross products of second differences is found to be—

X'A^X=

tr X'A^X{X'X)-^ is obtained by multiplying the matrices X'A^X and {X'X) ^ and then summing the diagonals of the product giving tr

1066.57 210.10 8811.70 114.387 210.10 257 3618 -7.11

8811.70 3618 207295 1765.27 114.387 -7.11 1765.27 99.9982

80 TECHNICAL BULLETIN 1274, U.S. DEPT. OF AGEICULTUBE

X'A'X (Z'X)-1=6.64757. tr [{X'AXiX'X)-'}'] is simply the sum of squares of the elements of the matrix X'AXiX'X)-\ so that—

tr [{X'AX(X'X)-'}']=4:Mél2.

Also, tr ^^=2(3n—4)=256. Substituting these values, we have—

Q=256-2(6.64757)+4.06412=246.76898,

and—-

var(a)=^gô)(4Ï)[246.76898-(82.84892)(2.12433)]

=0.08852.

We now assume that Id is distributed as a Beta distribution with density—

B(p,q)\4j V 47 ■

This distribution gives—

E{d)-^ P+2

from which we find p and q by the equations—

^^^ var id) '

P=l(p+q)E{d).

To test against positive serial correlation, we need the critical value of Id at the lower tail of the distribution. In equation 6a, d is less than 4—d, so a tendency toward positive serial correlation is indicated. If d were greater than 4—d, a test for negative serial correlation would be more appropriate. For testing against negative serial correlation, the same procedure is used, except that d is replaced throughout by 4—d.

Substituting the previously computed values for the mean and variance of d into the equations for p and q, we have ^=23.37447 and g=20.63840. The critical value of id may be obtained directly from Catherine Thompson's tables (46), or indirectly from tables of the variance ratio or Fisher's z, such as those in the Fisher-Yates tables (18), both with ni=2p, n2=2g[ degrees of freedom. Since 2p and 2q are rarely integers, a first approximation may be found by using the


nearest integral values. The transformation to the variance ratio is given by—

qd

and z=l loge Fi^ Fisher's z. For moderately large numbers of observations, a convenient way

of finding the significance point when 2p and 2ci are not integral is to use Carter's {12) approximation to Fisher's z. This states that the critical value of z is approximately—

E^/'h+\ h

where \2a'^2p){^+6-î)

s=-—\-—j h=-' 2p 2q s

The values of E and X to be used for 5- and 1-percent tests against positive serial correlation are as follows:

5% 1% E 1.6449 2.3263 X 0.4091 0.4020.

These same values are also used for the test against negative serial correlation.

Returning to the numerical value, we find that—

i^-=1.8908 and 2-0.3183.

Carter's approximation gives a critical 5-percent value for z of 0.2461, which is less than the observed value, thus indicating significant serial correlation. The critical 1-percent value is 0.3495, which is greater than the observed value and indicates no significant serial correlation at this higher significance level. An intimation of these results may be gained immediately by referring to a table of significant points of z or F around 7ii=40, 7^2=46, e.g., Snedecor (42j p. 186).

Data Used in the Recursive Model

Table 17 shows the data that were used in fitting the statistical model described on page 49. Some of the series used in fitting the model have since been revised. Data for 1948 are given because some lagged variables were used in the model. Figures for 1960 and 1961 were used to test the model's forecasting ability.

All of these variables are self-explanatory or have been discussed, except the index numbers of unit marketing charges. These index numbers are calculated from quarterly average spreads between retail cost of a constant market basket of farm food products and payments received by farmers for equivalent farm products. In other words, this series is simply the farm-retail price spread, or marketing margin, for the food market basket on a quarterly index basis, with 1947- 49=100.


TABLE 17.—Data used in the quarterly

Produc- Hogs Corn Beef tion Sea-

Sows prices prices prices oats, Hogs sonal Pork Year far- de- de- de- barley, slaugh- tem- produc- and rowing flated flated flated and tered perature tion

quarter F CPI CPI CPI grain H index Op PH Pc PB sor-

ghum G

W

Dollars Dollars per per

hun- Dollars hun- Thou- dred- per dred- Million Thou- Million

1948: sand weight bushel weight tons sand pounds 1_-- 3,218 23.07 2. 15 20.82 28.2 20, 283 49 2,837 2___ 5,088 20.56 2. 12 23.07 28.2 14, 944 122 2,165 3.__ 3,088 25.33 L81 23.01 34.5 11,072 145 1,630 4___ 1,546 2L69 1.23 20.08 34.5 24, 570 80 3,423

1949: 1___ 3,966 19.23 L16 19.52 34.5 20, 772 52 2,866 2.__ 5,302 17.97 1. 19 20.59 34.5 14, 620 125 2,032 3._. 3,550 18.94 L 18 19.37 29.4 13, 374 141 1,895 4___

1950: l_-_

1,536 15.78 L07 18.77 29.4 26, 231 85 3,493

4,312 15.81 1. 16 20.35 29.4 22, 109 48 2,945 2.__ 5,329 17.18 L30 22.61 29.4 16, 374 114 2,226 3__- 3,788 20.54 1,39 23,53 35.7 14, 150 134 1,982 4_._

1951: l-_-

1,709 17.27 L32 23.32 35.7 26, 630 73 3,561

4,419 19. 19 L44 26. 16 35.7 23, 151 46 3,107 2.._ 5,593 18.64 L47 26.95 35.7 18, 435 115 2,498 3_._ 3,795 18.41 L48 26.20 3L2 15, 935 135 2,217 4__- 1,610 16.53 L46 24.61 3L2 28, 019 69 3,659

1952: 1__- 3,959 15. 10 L48 24.33 3L2 25, 917 56 3,435 2_-- 4,878 16.21 L50 24.08 3L2 18, 062 123 2,387 3„- 3,300 17.31 L51 2L43 27.5 15, 221 140 2,070 4___ 1,195 14.94 L30 17.71 27.5 27, 372 75 3,635

1953: 1.-- 3,441 16.84 L29 16.22 27.5 22, 491 58 2,966 2__. 4,040 19.54 L29 14.84 27.5 14, 969 118 2,050 3___ 2,950 20.55 L29 14.15 27.6 13, 836 142 1,895 4___ 1,135 18.71 L 18 12.71 27.6 23, 072 85 3,095

1954: l.__ 4,081 2L74 L24 14.03 27.6 18, 810 59 2,570 2___ 4,102 2L06 L28 14.77 27.6 13, 669 121 1,992 3__. 3,297 17.74 L32 13.63 38.3 14, 948 144 2,040 4.__ 1,255 15.69 1.22 13.36 38.3 24, 068 81 3,268

1955: 1_.. 4,498 14. 17 1.21 14. 17 38.3 121,543 50 1 2, 934 2_.. 4,299 14.79 L21 14.41 38.3 115, 565 125 1 2, 175 3__. 3,689 13.89 1. 14 13.78 1 40.5 116, 052 149 1 2, 166 4._- 1,550 10.79 .98 12.38 1 40.5 1 27, 898 70 3,716

1956: 1--. 4,300 10.33 L03 12.39 1 40.5 1 25, 327 51 1 3, 306 2... 3,626 13. 13 1. 19 13. 19 1 40.5 117, 679 122 1 2, 353 3... 3,386 13. 45 1.22 13.53 1 33.5 116, 912 139 2,227 4... 1,511 13.02 L03 12.33 1 33.5 125, 275 83 1 3, 332

See footnotes at end of table.


recursive model of the hog economy, 1948-61

Index Pork Retail Broü- Discre- of unit Con-

Pig storage price U.S. Beef er pro- tionary market- sumer crop begin- of pork popula- produc- duc- income ing price ratio ning of deflated tion tion tion in charges index

R quarter CPI N QB QB 1947-49 1947-49 1947- S Pv dollars

/ = 100

M 49= 100

Cents Mil- Million per Million lion Billion pounds pound Million pounds pounds dollars

62 527 58.6 145. 7 2,372 162 65.6 98 100.7 62 661 58.7 146.3 2,133 206 70.9 103 102.3 62 582 63.8 146.9 2,195 227 72.2 103 104.6 62 235 58.8 147.6 2,375 178 72.4 106 103.6

59 469 54.4 148.3 2,392 256 69.4 105 102. 1 59 586 55.4 148.9 2,281 304 67.2 106 102.0 59 420 57.9 149.5 2,434 296 65.3 104 101.7 59 205 51.7 150.2 2,332 223 64.5 102 101.4

63 474 49.5 150.8 2,348 298 75.3 98 100.6 63 549 52.6 151.4 2,267 345 73.3 102 101.3 63 469 59. 1 152. 1 2,449 349 74.7 105 103.7 63 241 52.8 152.8 2,470 347 76.8 106 105.8

64 499 53.7 153.4 2,308 338 71, 1 109 109.6 64 648 53.4 154.0 2,011 453 73.9 111 110.7 64 572 54.5 154.7 2, 174 483 73.6 111 110.8 64 326 51.6 155.4 2,344 391 72.7 113 112.7

71 549 48.8 156. 1 2,347 425 71.7 114 112.6 71 822 49.5 156.7 2,193 539 72.5 117 113.1 71 685 53.7 157.4 2,457 468 73.8 117. 114.2 71 291 50.4 158. 1 2,653 380 76.9 118 114.2

70 489 50.4 158.7 2,854 480 79.6 117 113.6 70 569 56.3 159.3 3,005 536 80.0 118 114. 1 70 414 60.4 160.0 3,167 550 77. 8 118 115.0 70 201 54.8 160.8 3,381 441 76.2 118 115. 1

57 327 59. 1 161.4 3,215 559 75.5 118 115.0 57 418 59.9 162. 1 3,119 586 74.8 119 114.9 57 347 55.7 162.8 3,299 585 74.8 120 115.0 57 215 51.1 163.6 3,330 510 77.9 119 114.5

59 449 48.5 164.3 1 3, 225 448 79.0 118 114.3 59 544 48.6 164.9 1 3, 289 621 83.8 120 114.3 59 376 49.9 165.7 3,517 684 85.3 123 114.7 59 179 44. 6 166.5 1 3, 538 569 87.4 124 114. 9

72 421 41.4 167.2 1 3, 606 633 88.6 121 114.6 72 514 44.8 167.8 1 3, 545 790 1 90.3 121 115.5 72 394 47.2 168.6 1 3, 549 855 89.2 124 117.0 72 166 45.8 169.4 1 3, 762 722 1 90.6 124 117.8


TABLE 17,—Data used in the quarterly recursive

Produc- Hogs Corn Beef tion Sea-

Sows prices prices prices oats. Hogs sonal Pork Year far- de- de- de- barley, slaugh- tem- produc- and rowing flated flated flated and tered perature tion

quarter F CPI CPI CPI grain H index Op PH Pc PB sor-

ghum G

W

Dollars Dollars 'per per

hun- Dollars hun- Thou- dred- per dred- Million Thou- Million

1957: sand weight bushel weight tons sand pounds l-_. 3,991 14.33 L02 12.84 1 33.5 » 21, 789 53 1 2, 875 2.__ 3,556 14.81 1.02 14.56 1 33.5 116, 999 118 1 2, 284 3.._ 3,272 16. 14 LOO 14.96 47.1 116, 702 141 1 2, 191 4... 1,515 14. 11 .83 14.77 47. 1 123, 559 77 1 3, 132

l-_- 4,139 15.84 .78 16.87 47.1 1 20, 337 50 1 2, 716 2___ 3,561 16.96 .93 18.31 47.1 116, 598 119 1 2, 302 3._. 3,816 16.80 .94 17.85 1 5L3 117, 066 139 1 2,311 4.__ 1,781 14.51 .81 18. 15 1 5L3 123, 298 78 1 3, 199

1959: l-._ 4,562 12.75 .84 18.81 1 5L3 Í 22, 861 47 1 3, 119 2,.. 3,849 12.30 .92 19.44 1 5L3 118, 847 122 1 2, 625 3__. 3,951 10.80 .89 18.38 1 43.5 119, 439 142 1 2, 622 4._.

1960: 11, 717 9. 56 .78 16.33 143.5 127, 284 74 1 3, 744

l-__ 3,720 10.64 .79 16.78 42. 5 24, 425 40 3,300 2,._ 3,444 12.38 .84 16.97 42.5 19, 526 118 2,712 3,__ 3,688 12.79 .85 15. 60 46.2 17, 926 142 2,463 4___

1961- 1,818 13.03 .72 15.02 46.2 22, 498 77 3,155

12_. 3,730 13.39 .78 16.31 46.2 22, 161 57 3,057 2,640 2 2__ 3,740 12.71 .79 15.63 46.2 18, 829 114

3 2-. 3,648 13.33 .82 15.48 39. 1 17, 728 138 2,447 4 2_. 1,894 12. 53 .75 15.72 39.1 23, 815 79 3,320

1 Data have been revised from those used in analyses and given in this table. 2 Preliminary.


model of the hog economy, 1948—61 Continued

Index Pork Retail Broil- Discre- of unit Con-

Pig storage price U.S. Beef er pro- tionary market- sumer crop begin- of pork popula- produc- duc- income ing price ratio ning of deflated tion tion tion in charges index

R quarter CPI A^ QB QR 1947-49 1947-49 1947- S P. dollars

/ = 100

M 49 = 100

Cents Mil- Million per Million lion Billion pounds pound Million pounds pounds dollars

71 280 47. 9 170.2 ' 3, 654 727 1 90.6 126 118. 6 71 352 49.6 170.9 3,432 868 1 92. 1 128 119. 7 71 277 54. 1 171.6 1 3, 615 926 1 90.8 130 121. 0 71 134 48.8 ■ 172. 4 ' 3, 510 804 1 87.7 128 121.4

70 194 61. 4 173. 1 1 3, 297 833 1 86. 4 131 122. 7 70 224 63.6 173.7 1 3, 224 1,006 1 86.3 136 123.6 70 210 54.6 174. 6 1 3, 424 1, 152 1 89. 7 137 123.8 70 127 50.2 175. 3 1 3, 397 919 1 91.0 135 123. 8

74 206 47.8 176.9 1 3, 250 963 1 93.2 134 123.7 74 337 46.9 176. 6 1 3, 345 1, 153 ' 97. 7 135 124. 1 74 313 45.8 177.4 ' 3, 475 1, 128 1 94.0 137 125.0 74 163 42.9 1 178. 0 1 3, 638 891 ' 94. 3 137 126.5

91 264 41. 6 178. 9 3,630 1,009 97. 1 133 125.6 91 338 44. 5 179.5 3,574 1, 155 98. 1 136 126.3 91 351 46.6 180.2 3,817 1,218 96. 7 138 126. 7 91 158 46.3 181. 1 3,704 963 94. 4 136 127.4

82 170 46.7 181.8 3,704 1,052 93. 7 137 127.5 82 244 45.7 182.5 3,847 1,400 98.4 140 127. 5 82 244 46. 9 183.4 3,874 1,364 100.6 139 128. 1 82 126 45.9 184.0 3,837 1,039 102. 6 137 128.3

•U.S. GOVERNMENT PRINTING 0FFJCE:1963 O—645778

Factors Affecting The Price And Supply Of ¡a®©

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