, nsuv WWEIEM“ * L i l , n v , a VL win!" Mum. ‘ - W ., ..— .MJJ ‘ CHANGEE EH EBHE‘EEH EEAEEE :QEEOEH Haws? 119w. WM .. EHE EN TECEEEEEEQLGGV AME ECQEEWEC EACF®§§ “Emu E09 EEse Dogma of DE! D MIECHEEEAN SNAKE UNIVERSITY I . _ Kama! Ahmed E15. Ganzoury 1967 E ' Es 0F Wm“: ¥ f. 7“ Jainism This is to certify that the thesis entitled CHANGES IN UNITED STATES COTTON YIELDS, l939-l959--THE INFLUENCES OF WEATHER, TECHNOLOGY AND ECONOMIC FACTORS presented by Kamal Ahmed El—Ganzoury has been accepted towards fulfillment of the requirements for Ph.D. degree in Agricultural Economics Major professor Date May 3, 1967 0-169 ABSTRACT CHANGES IN UNITED STATES COTTON YIELDS, l939—l959——THE INFLUENCES OF WEATHER, TECHNOLOGY AND ECONOMIC FACTORS by Kamal Ahmed El—Ganzoury The main objective was to analyze the relative impor— tance of factors related to past changes (1939—1959) in cotton yields. The factors considered were: (1) pounds of fertilizer nutrients per acre of cotton, (2) man—hours of labor per acre of cotton, (3) number of tractors per 1000 acres of harvested cropland, (4) dollars Spent on gas and oil per acre of harvested cropland, (5) proportion of cotton acreage irrigated, (6) size of the cotton enterprise, (7) relative changes in cotton acreage, (8) percentage of total harvested crOpland in cotton, (9) value of land and buildings per acre, (10) price of cotton for previous sea— son, (11) monthly total rainfall, (12) monthly average tem- perature, (l3) squared monthly total rainfall, (l4) squared monthly average temperature, (15) monthly rainfall and tem- perature interaction, (16) successive month rainfall inter— action, (17) shifts in location of production among counties, and (18) shifts in location of production among states. Regression techniques employing a quadratic function Of time to represent monthly weather data were the tools Kamal Ahmed El-Ganzoury for the analyses. A combination of time series and cross— sectional data were used, with the basic unit of observation being the county in census years 1939, 1944, 1949, 1954 and 1959. A random sample of 258 counties represented the entire U. S. cotton area. Three levels of analyses were applied, i.e., state, regional and national levels. At the state level, fifteen analyses were made, one each for North Caro— lina, South Carolina, Georgia, Alabama, Missouri, Arkansas, Tennessee, Mississippi, Louisiana, Oklahoma, East Texas, West Texas, New Mexico, Arizona, and California. At the regional level, four analyses Were made, one each for the Southeastern, the Delta, the Southwestern, and Western Re- gions. Generally, the statistical analyses yielded coefficient signs which would be expected, from an economic and tech— nical point of view. The regional analyses were generally superior to those at the state and national levels from the standpoint of the size and the statistical significance of the estimated coefficients. Moreover, the regression results for technical and economic factors from the regional analyses were more consistent internally and more meaningful in terms of the technical and economic expectations than those obtained from either state or national analyses. The results for weather variables, particularly for rain— fall, from regional analyses were consistent region to re— gion. Kamal Ahmed El—Ganzoury In the state analysesl results, the main problem was the different signs and sizes of estimated coefficients for the same factor in different states. However, the var— iables used in the state regression models explained 46 to 84 percent of the variation in cotton yield increases. In the national analysis, the coefficient of multiple de— termination was smaller than that for regional or state analyses, indicating some heterogeneity in the relation— ships among the cross-sectionally combined states. The results indicate that the increase in cotton yields over the period 1939-59 was mainly imputed to three major factors. These factors are: (a) increased use of fer— tilizer, (b) shifts in location of production toward higher yielding areas, and (c) time-related factors, i.e., those factors which affected yields over time and were not expli— citly included in the analyses, such as improvement in seed varieties, production techniques and insect control. CHANGES IN UNITED STATES COTTON YIELDS, l939—l959-—THE INFLUENCES OF WEATHER, TECHNOLOGY AND ECONOMIC FACTORS BY Kamal Ahmed El—Ganzoury A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1967 ht ACKNOWLEDGMENTS I wish to thank my major professor, Dr. Lawrence W. Witt, for his patient guidance and assistance throughout my doctoral program and especially for his constructive guidance during this research. His constant encouragement and willingness to help on many problems, academic or other— wise, enabled me to pursue my study at Michigan State Univer— sity. Many thanks are extended to Dr. Richard G. Heifner, who served on my guidance committee, for making valuable comments and suggestions throughout the course of this study. Thanks are due to other members of my guidance com- mittee, Doctors James T. Bonnen, Victor E. Smith, and Robert D. Stevens, for reading a draft of the thesis and making helpful comments. I wish to thank Dr. Robert L. Gustafson for his help~ ful remarks and suggestions, especially during the early Stages of this work. Finally I wish to Specially thank my wife, Raafat, for her encouragement, interest, and assistance throughout all of my doctoral program. Of course, any errors of commission or omission are entirely my own. ii 93g TABLE OF CONTENTS Chapter I INTRODUCTION . . . The Problem . . Objectives. . . Cotton and Climate. Cotton Regions. Cotton Yields . II REVIEW OF LITERATURE III CONCEPTUAL FRAMEWORK Area of Study Data and Observation Unit Sampling Method 0 Parts of Analyses Selecting the Variables Technical and Economic 0 O 0 0 Weather Variables. Dummy Variables. Multicollinearity Problem IV STATE ANALYSES . . State Model I . Results for State Model I State Model II. D O O Q I, 6 Variables 10 21 21 21 22 23 25 25 31 34 36 38 38 43 6O Chaptel BIB] APPI Chapter Page Results for State Model II. . . . . . . 61 Concluding Points . . . . . . . . . . 66 V REGIONAL ANALYSES. . . . . . . . . . . . . 69 Regional Model. . . . . . . . . . . . 70 Results for Regional Model. . . . . . 72 Concluding Points . . . . . . . . . . 88 VI NATIONAL ANALYSES. . . . . . . . . . . 90 National Model. . . . . . . . . . . . . 91 Results for Technical and Economic Factors . . . . . . . . . . . . . 96 Results for Weather Factors . . . . . . 101 Results for Time Factors. . . . . . . . 106 Results for Location Factors. . . . . . 108 Summary . . . . . . . . . . 119 VII SUMMARY AND CONCLUSIONS. . . . . . . . . 126 BIBLIOGRAPHY . . . . . . . . . . . . . . . . 141 . . . . 147 APPENDICES . . . . . . . . . . . . . . LIST OF TABLES Table Page 1 The Number of Counties that Grew 1,000 Acres or More of Cotton in 1959, and the Number of Counties Selected in Each State . . . . . . . . . . . . . . . . . . . . 24 2 The Regression Results for State Analyses of Change in Cotton Yields, Nonnirrigated States. . . . . . . . . . . . . . . . . . . . 45 3 The Estimated Regression Coefficients for Monthly Total Rainfall, Marcthovember, Non—irrigated States. , . . . . . . . . . . . 53 4 The Estimated Regression Coefficients for Squared Monthly Total Rainfall, March— November, Non—irrigated States. . . . . . . . 54 5 The Estimated Regression Coefficients for Monthly Average Temperature, March—November, Non—irrigated States. . . . . . . . . . . . . 55 6 The F-Test Results Indicating the Signifi- cance of Weather Effects on Cotton Yields in Non—irrigated States . . . . . . . . . . . 59 7 The Regression Results for State Analyses of Changes in Cotton Yields, Irrigated States. . . . . . . . . . . . . . . . . . . . 62 8 The Regression Results for Regional Analyses of Changes in Cotton Yields. . . . . 73 9 The Estimated Regression Coefficients for Weather Variables, in Regional Analyses . . . 79 10 The F—Test Results Indicating the Signifi- cance of Weather Effects on Cotton Yields in Different Regions. . . . . . . . . . . . . 88 11 The Regression Results for National Analyses of Changes in Cotton Yields . . , , . . . . . 97 12 The Estimated Regression Coefficients for Monthly Weather Variables . . . . . . . . . . 103 @119. 13 16 I Table 13 14 lS—A 15—B 15—C 16 17 The Marginal Effects at the Mean for Monthly Total Rainfall and Monthly Average Temperature . . . . . . . . . . . . . . . . . 105 The Weighted Average Effect Upon Cotton Yields of Shifts in Production Among Coun- tries . . . . . . . . . . . . . . . . . . . . 112 The Calculated National Average Yield of Cotton Using Different Acreage Distributions for Weights, 1939-59. . . . . . . . . . . . . 115 The Estimated Effect of Shifts in Location of Production Among States on the National Average Yield of Cotton per Acre, 1939—59 . . 116 The Estimated Effects of Factors (Influ— encing Yields) on the National Average Yield of Cotton, Holding Acreage Constant, 1939- 59. . . . . . . . . . . . . . . . . . . . . . 118 The Calculated Average Effect of Factors on the National Average Yield of Cotton Per Acre, 1939—59 . . . . . . . . . . . . . . 121 The Calculated Average Effects on Cotton Yields of Changes in the Levels of Factors, for Indicated Periods 1939—59 . . . . . . . . 122 LIST OF FIGURES Page The United States Average Yield per Cotton Acre (1900-1933). . . . . . . . . . . . . . . 7 The United States Average Yield per Cotton Acre (1934- 1964). . . . . . . _ . . . . . 8 The Marginal Effects at the Mean for Monthly Total Rainfall on Cotton Yield per Acre . . . 83 The Marginal Effects at the Mean for Monthly Average Temperature on Cotton Yield per Acre. . . . . . . . . . . . . . . . . . . . . 84 vii Append: L121 Appendix A LIST OF APPENDICES The Data; Sources and Estimation Methods of Missing Data. . . . . . . The Selected Counties and Weather Stations in Each State Included in This Study . . . . . . .. . . . . . Simple Correlations of the Technical and Economic Variables, By States. . Simple Correlations of the Technical and Economic Variables, By Regions . Simple Correlations of the Technical and Economic Variables, the Entire Nation . . . . . . . . . . . . . . . viii a 148 165 184 192 194 In re crease in in the Un prdblemat aphenome agricultr tors rel; A large 1 and most Wheat, c tional t WEIe Stk 2 baSis. CHAPTER I INTRODUCTION In recent years, there has been a substantial in— crease in the yield per acre of many of the major crOps in the United States. This phenomenon has created some problematic situations for agricultural researchers. Such a phenomenal increase in major crop yields has prompted agricultural researchers to investigate the different fac— tors related to changes in yields of agricultural crops. A large number of studies of crop yields have been made, and most have been concerned with food crops. For instance, wheat, corn, oats, and barley were investigated on a na- tional basis by Johnson and Gustafson.l These same crops were studied by other researchers on a state or regional basis.2 Grain sorghums and soybeans were investigated by Thompson,3 and there is a further study being carried out 1D. G. Johnson and R. C. Gustafson, Grain Yields and American Food Supply (Chicago: University of Chicago Press, 1962). 2L. H. Shaw and D. D. Durost, The Effect of Weather and Technology on Corn Yields in the Corn Belt, 1929—62, U.S.D.A. Econ. Rpt. 80, July, 1964. 3L. M. Thompson, “Evaluation of Weather Factors in the Production of Grain Sorghum,“ Agronomy Journal, Vol. 55 (1963), 182—185. on the former concerned wit basis, even 1 crops in the of the most Therefore, i on a state, pointed out developed 11 yields in 0- AS mer in the cott interesting increase '1; HOW muCh t prices Whi Chem9es ir Questions Policy, 1 has been Wing b \ 4 SorghUm: ll Yet Comp] on the former crOp by Abel.4 But, few studies have been concerned with cotton yields, particularly on a national basis, even though cotton is one of the most important cash crOps in the United States, and cotton production is one of the most important enterprises found on American farms. Therefore, it was decided to investigate U. S. cotton yields on a state, regional, and national basis. It should be pointed out that the knowledge acquired and the methods developed in this study may be helpful in analyzing cotton yields in other countries. The Problem As mentioned, there has been a phenomenal increase in the cotton yield per acre, which has introduced many interesting questions, such as: How much of this dynamic increase in cotton yields can be attributed to weather? How much to technological advance? How much to favorable prices which may lie behind changes in technology and some changes in the areas of production? The answers to these questions have very important implications for agricultural policy. For instance, if the increase in cotton yields has been the result of improved technology. policies of cutting back cotton production are likely to require more 4F. Abel, ”A Study of Change in Yield per Acre in Grain Sorghum," (Ph.D. Thesis at Michigan State University, not Yet completed). acreage redu< Oder hand. result of ‘fa averaging wi cunemplate Objectives The ma relative in paSt change 9%: Cot1 gEDErall‘ Cessful temPerat of 180-2 acreage reduction than originally contemplated. On the other hand, if the increase in cotton yields has been the result of favorable weather, then the presumption is that averaging will essentially occur; so there is no need to contemplate other policies. Objectives The main objective of this study was to analyze the relative importance of the following factors related to past changes in yields per cotton acre; 1. Weather 2. Fertilizer 3. .Mechanization 4. Labor 5. Irrigation 6. Shifts in production 7. Value of land 8. Price of cotton Cotton and Climate Cotton is considered a warm climate crOp. It is generally agreed that the climatic requirements for suc— cessful commercial production of cotton are a mean annual temperature of not less than 600F., a frost—free season of 180—200 days, annual rainfall of not less than 20 and notnore that favorable cor with light 1)” warm both da uous growth autumn. Col seed in the orfavor se< ing season expense of shedding of in the sum W39, Cotto belt is be the northe and a near area dips tildes of 10W eleva West in I : more than 75 inches.5 "In the United States the most rorable conditions for cotton production are a mild Spring ;h light but frequent showers; a moderately moist summer, 7m both day and night so as to maintain even and contin— 1s growth and fruiting; and a dry, cool, and prolonged :umn. Cold weather with rain in the spring may rot the ad in the ground, retard the growth of the seedlings, favor seedling diseases. Too much rain during the grow— ; season causes the development of surface roots at the >ense of the deeper roots. This results in wilting and adding of leaves and bolls if the weather turns very dry the summer." Egon Regions Cotton is currently grown in twenty states. ”Cotton -t is bounded on the north by the frost line which marks a northern limit of 200 day frost—free growing season i a mean summer temperature of not less than 7OOF., the ea dips irregularly to the south around the higher alti— ies of the southern Appalachian to the north again in the J elevations of Mississippi and then tends to the south— st in response to both inadequate rainfall and low tem— 5U. S. Department of Agriculture, 1941 Yearbook of ZAQU1ture: Climate and Man, p. 34. 6Ibid., p. 353. perature. On by sub—tropiCE ';_gr.ring around However, into four reg through South to as the Soc river bottom taries in Tel known as the rest Region, Arizona, and Over t} COtton acre; regions. 0] PIOduction P‘SOduced 29 “Wages. Region Wit} as the Soul 47 perCent \ 7T. Y product-5101‘“ El]: A 1 MdSterrs r] 8 . Lbs On the east and south the cotton belt is fringed rOpical border, beginning at the Carolinas and fol— round the Gulf including practically all of Florida."7 ever, the United States Cotton Belt usually is divided ,r regions. An area extending from North Carolina South Carolina, Georgia, and Alabama is referred .e Southeast Region. Westward the broad delta or ~ttom areas along the Mississippi River and tribu— n Tennessee, Missouri, Arkansas, and Louisiana is the Delta Region.8 The third region is the South— ion, including Oklahoma and Texas. New Mexico, and California are known as the Western Region. ~r the last three decades, substantial shifts in .creages and production occurred among those four On the basis of the United States average cotton .on and acreages (1930—34), the Southeastern Region L 29 percent with 24 percent of the total cotton Another 29 percent was produced by the Delta 'ith 27 percent of the acreage. Oklahoma and Texas, Louthwestern Region, produced only 38 percent on ent of the acreage. And, 3 percent was produced Y. Patil, “A Study of Recent Changes in Cotton .on Pattern and Techniques in the United States and >plicabi1ity to Indian Conditions.” (unpublished : Thesis, Michigan State University, 1955), p. 21. >id. by the Wester the acreage. However, changed over age cotton p eastern Regi percent of t Region has I and Texas he in the West: production to be 19.8 States Cott this incree Was due to and SOUthWr Western Irrigated Region with only 1.3 percent of eage. wever, all these figures have been substantially over time. On the basis of the United States aver— ton production and acreages (1960-64), the South- Region has been producing only 14 percent from 16.5 of the total cotton acreage, whereas the Delta has produced 33 percent from 28 percent. Oklahoma as have produced 33.6 percent from 45.3 percent. Western Irrigated Region, the percentage of cotton ion and acreages has been substantially increased 9.8 and 9.3 percent, reSpectively, of the United cotton production and acreages. A large part of crease in the cotton production of the Western Region to expanded cotton production in Southern California thwest Arizona after 1950.9 Yields gures 1—A and l—B Show the trend for the United average yield per acre of cotton in the period . This trend for the whole period can be divided 0 distinct linear patterns. The first period is 00 to 1933. The trend during this period was down— .S.D.A., E.R.S., Agr. Econ. Rpt. No. 99, Costs and ng Upland Cotton in the U.S., 1964, September 1966. Figure 55v 500 ‘45:?» 1. a ,2 .00 n '0 C. 3 Q 35b— V ,1) i: , 300 )4 it no '21 H "J '1-4 ‘“ zoo L10 100 50 199 Figure l-A. United States Average Yield per Cotton Acre (19OO=1933) 550‘“ Y1 = 178.6 - o u5x 61 O +00" 300" 250” 3(DO—\vfiqfi/“VA //\\\V/«\ A ,/\ \// \\,/—_D/ ’ W / 50‘ 100" 50" a . .1 l i rill L. . . .l J L1 L1,. .. 11 a . I. 11 1900 1905 1910 1915 1920 1925 1930 Years Figure l .iu / ilillTlillll-TI‘I 0 AU AU 0 AU. Ni. my a x. A» O a ,/ At .t, . WU C, , 0 RI, . A V w , AU E El! ) ,1”; III? ON). pi UL f),— 1 1 A nwuu. Pulpafiwv .Jld HUAVV \Nflvflu Us. ,1); drum. Figure leB. United States Average Yield per Cotton Acre (193u»196A) /\ )e— Y2 = 17745 + 9.01X l-.. JltarilirtilIrritnr~isiiliirll 193M 19h0 1945 1950 1953 rage Years vard with a ‘ least square: at the rate about trend period, The to l964. Tl a relativelj squares lin per year.11 devoted to in cotton y 10: 11. with a very slight slope as shown in Figure lmA. The : squares line of the best fit decreases very slightly 1e rate of 0.45 pound per year.10 The fluctuations : trend were relatively small as compared with the later 3d. The second distinct period begins in 1934 and runs 364. Throughout this period the trend was upward with Latively sharp Slope as shown in Figure 1—B. The least res line of the best fit rises at the rate of 9.01 pounds gear.ll Hence, all emphasis in this present study is :ed to the second period in which a substantial increase )tton yields has occurred. 10 Y = 178.6 — 0.45X. 1"" [—4 > = 177.6 + 9.01X. A large Most have be principal c: can be revi 1. An ex Shillings , the; using USed earli \ 1J. on Agricu State Uni 2G. tucky Agr 3D. “\mm Bul- 250, l CHAPTER II REVIEW OF LITERATURE large number of crOp yield studies have been made. .ve been concerned with food crOps. However, the nal crOp yield studies related to the present study reviewed as the following two groups: 1. Studies employing the weather index approach. 2. Studies which attempt to establish direct relationships between weather variables, temperature, rainfall, etc., and yield. example of the first grOUp of studies is that by gs.l He developed indexes of the influence of wea— ing a plot data approach. The method, which was q rlier by Johnson‘ and Hathaway3 is essentially this: . L. Stallings, “Indexes of the Influence of Weather :ultural Output" (unpublished Ph.D. Thesis. Michigan riversity, 1958). L. Johnson, Burley Tobacco Control Program, Ken— ;r. Exp. Sta. Bul. 580, 1952. E. Hathaway. The Effects of the Price Support Pro— rthe Dry Bean Industry in Michigan, M S.U. Tech. ', 1955. —10— "From experin year—to—year weather. A field variat had constar ing practice in each yea: ofthe comp trend yield is 50 bushe Blother wc cause of f; would indi Yield are One g is “the s; Structiom in fact 1‘ plots for held Cons This Study of experiments where practices have been controlled, i~year variation in yield data is due primarily to '. A trend is fitted to the data to describe the 'ariation due to changes in factors which were not )nstant, such as soil conditions or changes in farm— Lcticesa The influence of weather is then measured L year as that year's actual yield as a percentage computed trend yield. For example, if for 1930 the 'ield is 40 bushels per acre and the actual yield >ushels, the weather effect would be measured as 125. 2r words. yields in 1930 were 25 percent higher be- )f favorable weather. A weather index value of 100 -ndicate a year where the trend yield and actual ire identical.” 1e question that might be raised about this method 2 sampling problem” common to many index number con— -ons. That is, are the locations and the data used . 5 , . _ representative? ALSO, in this method, control for yield eXperiments are used where technology is >nstant, 1is method was modified by Shaw and Durost in their >f the effects of weather and technology on corn I.S.D.A., ERS—72, Measuring the Effects of Weather LVOutput, October 1962, p. 2. 'ohnson and Gustafson. Op. ClE_. e...” - “29!.- __ yields in the yield test p'. Their statis [1929-62) . technology Vi prior to 191 has shown t] and improve has reduced ther.7 Anothe approach '1 ing with t' creases am wheat, oat tame hay. Series da by CIOps 1101093] We of crop E aSPECts ( \ 6Sh -12- in the corn belt.6 They used data from variety est plots where technology is not held constant. tatistical model was based on time series data 2). Their study led them to the conclusion that agy was introduced in two stages during a period 5 1942, and a period after 1954. Also their study wn that through the use of better varieties of corn roved cultivation and fertilization practices, man uced variation in yields in both good and bad wea— other example of studies employing weather index h is that by Heady and Auer.8 Their study was deal— h the imputation of crOp yield and production in— among several variables or technologies for corn, oats, barley, soybeans, cotton, grain sorghums, and y. Their statistical models were based on time data (1939—60). They estimated production functions 8 by states. The independent variables for tech— were: an index of variety. fertilizer rate, index acreage, and a time variable to represent other of technology. The weather variable was an index haw and Durost, op. cit, Lbid., p. iv. ' O. Heady and L. Auer, “Imputation of Production inologies," Journal of Farm Economics, Vol. 48, No. 1966). of weather ca plots. Conce them to the : improvements yields per a fertilizer a duction locz World War II eSpecially mfllion acr since only tion was ir 0f the Cotl 139 Variet. Southwest . not Compie The 5 direct re] rainfall, those res- studY can J.w \\ 9 He; 10 J of Corn, —13- ier calculated from data on eXperimental and test Concerning cotton yield analysis, their study led the following conclusions: fertilizer and variety nents had fairly large positive effects on cotton per acre. An increase of 42 pounds was imputed to zer and 35.5 pounds to variety improvement. Pro— location had a negative effect during part of the ar II and post—war periods when acreage expanded, Lly in the Southern Plains, where an additional 5.8 acres were planted between 1950 and 1951. But, 11y about half of the United States cotton produc— 3 included in their analysis of cotton yields, much :otton yield increase due to shifts from lower yield— ieties in the Southeast to irrigated cotton in the at was not considered, and the overall picture was plete. ..a a second group of studies attempts to establish relationships between weather variables, temperature, 1, etc., and yield. However, from the many studies, asponsible for shaping the ideas of this present an be very briefly reviewed as follows. W. Smith, in 1914, studied the effect of weather yields,lO By using simple correlation, he deter— eady and Auer, Op. cit;, p. 319. . W. Smith, "The Effect of Weather Upon the Yield " Monthly Weather Review, Vol. 42 {1914), 78-87. I mined the mos in Ohio, He in the great is rainfall be considere the corn yie Wallace better unde by employin oi the firs corn yields led him to rainfall, corn-belt method of liminary 6 gives fail 0f the co: nOrthern between c not Stric \ ll . l; 12 H Effect 0 States,“ 13 l ‘ -14- e most important weather factors in corn production He found that: "the controlling weather factor reat corn—growing districts of the United States all . . . . If the rainfall for calendar months dered that for July has a far greater effect upon yield than rainfall for any other month.“11 lace, in 1920, made an important contribution to inderstanding of corn production and weather factors Dying linear regression techniques.12 He was one first to use multiple regression methods to predict elds from selected weather variables. His study to the conclusion that: “Careful examination of , temperature, and corn yield data in the various 1t states leads to the belief that while that the of correlation coefficients is very useful for pre— [ examination of the data, and while this method airly good predicting formula in the southern part :orn belt, yet it is not at all well adapted to the 1 part of the corn belt, . . . . The relationship corn yield and July temperature, for instance, is .ctly linear . .“13 bid., p. 87. . A. Wallace, ”Mathematical Inquiring Into the f Weather on Corn Yield in the Eight Corn Belt Monthly Weather Review, Vol. 48 (1920), 439—56. bid., p. 445. Fisher, on wheat yie' nique.14 Th of time to a short time 1: objective oi notions tha' changes gra her of weat than in the multiple cc the result: smoothness In 19 ther condi no attempt due to be: StlldiES c, rolations' an intere \ l4 . R. W 15F bridge: M 16J my -15- her, in 1924, studied the influence of rainfall yield at Rothamsted, and introduced a new tech— This technique is to fit a polynomial function to a set of weather data representing successive me periods within the growing season.15 The main e of Fisher's technique is to incorporate a priori that the effect of each weather factor on yield gradually from month to month. Clearly, the num— eather variables used in this technique is less the conventional regression technique; thus the . . , 2 . correlation coefficient (R ) is reduced. However, lts are more consistent with a priori notions of ss over time in the weather effects on crOp yields. 1928, Kincer studied the relationship between wea— 1dition and the cotton boll weevil.l6 Yet he made ipt to measure the part of variation in cotton yields >oll weevil damage. B. B. Smith also made several concerning cotton production. In his study of the iship between cotton yields and weather, he made 'esting analysis to estimate that part of variation A. Fisher, "The Influence of Rainfall on the Wheat at Rothamsted,“ Philos0phica1 Transactions gyal Society of London, Vol. 213, pp. 89—142, 1924. . H. Sanderson, Methods of CrOp Forecasting (Cam— Harvard University Press, 1954). B. Kincer, “Weather and Cotton Boll Weevil," fleather Review, Vol. 56 (1928). 301—304. hicotton yf In 193‘ hat was ma data for 55 dimatic fa of the con In 191 of fitting the effect season on In If technique: the avera. the three States to In ] “iqUG to 17 and Yiel Rise: 18 we 19] and Dis- Gr0Wl 1‘19 20 York; _]_6- tton yields due to boll weevil damage.17 In 1936, a study of corn yield and climate in the corn as made by Rose.18 He used correlation methods on for 55 corn belt counties, and found that no Specific tic factor gave significant correlation for all parts e corn belt. In 1940, Davis and Pallesen used Fisher‘s technique tting polynomial function to weather data to study ffect of rainfall and evaporation during the growing on yields of corn and Spring wheat.l'9 In 1941, Ezekiel used multiple curvilinear regression iques to study weather and corn production.20 He used verage summer temperature, monthly total rainfall for hree summer months and combined production of eight 5 to capture the effect of weather on corn yields. In 1942, Houseman used curvilinear regression tech— to determine the period of the growing season when .— l . . . . 7B. B. Smith, "Relation Between Weather Conditions Leld of Cotton in Louisiana," Journal of Agricultural :ch, Vol. 30 (June, 1925), 1083—1086. L8J. K. Rose, “Corn Yield and Climate in the Corn Belt," gphical Review, Vol. 26 (January, 1938). 88—102. '9F. E. David and J. E. Pallesen, “Effect of Amount .stribution of Rainfall and Evaporation During the 19 Season on Yields of Corn and Spring Wheat,“ Jour— igAgricultural Research, Vol. 60 (1940), 1—23. O . M. Ezekiel, Methods of Correlation Analysis (New 1941). anincrease or most dama In 1943 regression t perature pre rnhfall, m< hue intera: of weather conclusion Men accomp iden rainfa Fulmei ending cot-.1 Nfidmont 0: Western Te: Um observ was used t omic factc Recer \ 21 02,- E. '~ leId W 22 0f Tem e;- Carolina 23 J Infernc: W rease in rainfall or temperature was most favorable t damaging.21 n 1943, Hendricks and Scholl used multiple linear sion techniques to study the joint effects of tem— re precipitation on corn yields.22 They used monthly 11, monthly temperature and monthly rainfall—tempera— nteractions as weather variables to measure the effects ther on corn yields. Their study led them to the sion that high temperatures are damaging to the crop ccompanied by low levels of rainfall, and beneficial rainfall is excessive. ‘ulmer and Botts, in 1951, studied the factors influ— l cotton yields and their variability in the upper >nt of South Carolina and Georgia and Rolly Plains of in Texas.23 In their study, the farm was taken as >servation unit, and the multiple correlation technique Led to measure the effect of some technical and econ— ?actors on the changes in cotton yields among farms. Lecently, Runge and Odell studied weather and crOp ._ 1E. E. Houseman, Methods of Computing A Regression 31d on Weather, Iowa Agr. EXp. Sta. Research Bul. 302, 2W. A. Hendricks and J. C. Scholl, The Joint Effects [perature and Precipitation on Corn Yields, North .na Agr. EXp. Sta. Tech. Bul. 74, 1943. 3J. L. Fulmer and R. R. Botts, Analysis of Factors gncing Cotton Yields and Their Variability, U.S.D.A., Bul. No. 1042, 1951. yield relatic corn yields.I yields.25 I tion of time soybean yiel Johnsor made an agg cross—secti They used t labor, mecl of land, t< only weath Their conc those draw and soybez are; the the early \ 24E. Precipit, Agronomy 50 (1958 2 5E Precipit Ag r011 Omy 52 (I96C 26. 27. tiOIl Qf‘ —18— relationships. In 1958, they studied weather and ’ields.24 In 1960 they studied weather and soybean .25 In both studies, they fitted a polynomial func— f time to capture the weather effects on corn and .n yields. 'ohnson and Gustafson in their study of grain yields, .n aggregate analysis.26 The analysis was essentially sectional with states being the unit of observation. ised the following technical variables: fertilizer, , mechanization, variety index, summer fallows, value .d, total crOpland harvested, and irrigation. The leather variable was the average annual precipitation. conclusions on the effect of the weather agree with drawn from a study of weather and technology in corn >ybeans production by Thompson.27 These conclusions that yields were adversely affected by weather in irly fifties and favorably affected by weather in the ‘ I 4E. C. A. Runge and R. T. Odell, "The Relation Between >itation, Temperature and the Yield of Corn on the imy South Farm, Urbana. I11.“ Agronomngournal, Vol. ’58), 448—454. 5E. C. A. Runge and R- T. Odell, “The Relation Between >itation, Temperature and the Yield of Soybeans on the imy South Farm, Urbana, Ill." Agronomy Journal, Vol. ’60), 245-247. Johnson and Gustafson, op. cit. .7 , L. M. Thompson, Weather and Technology in Produc— 3£_Corn and Soybeans, CAED, Rt. 17, Iowa State Univer- 1963. late fifties More re been conduct used to adjr the relatior grain sorgh‘ precipitati precipitati months of t to capture At th grain sorg a physical suring the 0f produc regressio hology ar dollars 5 \ 2 8L the Prod Lassa. 29 1 (.1963) - 9 30‘ 31 Grain S not Yet -19- ties. e recently, the most important studies which have ducted where direct weather variables have been adjust yields are those by Thompson. He studied tionship between weather and production of wheat28, rghumszg, and corn and soybeans30. Monthly total ation, monthly average temperature, and monthly ation—temperature interactions for the principal if the growing season were used as weather variables [re the weather effects on yield per acre. the present time, Abel is conducting a study on :rghum.31 His study is concerned with deve10ping Sal production function for grain sorghum, and mea— ;he influence of weather, technology and location iction on per acre yields of grain sorghum, by using .on analysis. The independent variables for tech— ire: acres of grain sorghum harvested per farm, Spent on gas and oil per acre of cropland harvested, .. M. Thompson, "Evaluation of Weather Factors in .uction of Wheat,“ Journal of Soil and Water Conser— Vol. 17, No. 4 (July and August, 1962). .. M. Thompson, "Evaluation of Weather Factors in on of Grain Sorghums,“ Agronomy Journal, Vol. 55 182—185. ee Reference No. 27. . Abel, ”A Study of Changes in Yield Per Acre in .rghum," (Ph.D. Thesis at Michigan State University, completed). number of ac tion of grai acre, pounds summer fall< variables, . to a set of periods (we The pi the direct and cotton lowing rea -20.. acres of crOpland harvested per tractor, prOpor- rain sorghum irrigated, man—hours of labor per ads of nutrients applied per acre, acres cultivated llow, and value of land per acre. For weather , Abel is fitting a polynomial function of time 3f weather data representing successive Short time weeks) within the growing season. present study represents an attempt to identify t relationships between certain weather variables 3 yields. This approach was chosen for the fol— asons: It is possible to determine which, if any, weather factor is limiting production. This technique can be used on any crOp and with any kind of observation units and does not depend upon the availability of a Spec— ially constructed weather index. Area of Stu The wI pOpulation. was divide: Carolina, namely, mi Louisiana; West, nanw Sinc greater h graphy, 5 States WE into time was cons Dat - we The ThlS ch (1939, for whi CHAPTER III CONCEPTUAL FRAMEWORK AND TECHNIQUES f Study ne whole United States cotton area was taken as the tion. For the purpose of analysis, this cotton area vided into four regions: Southeast, i.e., North na, South Carolina, Georgia, and Alabama; Delta, , Missouri, Arkansas, Tennessee, Mississippi, and ana; Southwest, including Oklahoma and Texas; and namely, New Mexico, Arizona, and California. ince a smaller area presumably has the advantage of r homogeneity of production techniques, weather, tOpo— I soil and climate, each state of the above fourteen was analyzed separately. Moreover, Texas was divided vo parts——eastern and western Texas——and each part asidered as a separate state. 1Q_Observation Unit 1e county was the basic geographical unit of this study. ioice limited data to the agricultural census years 1944, 1949, 1954, 1959), as they were the only years -ch there were reasonably complete and consistent data -21- for counties section data ing these ye 1. Alt pr: we 2. Ma oi Sampling Ml As me unit in th 1,000 acre collectiOI county wa ling meth l. the Proi 17, NO. -22- ities. A combination of time—series data and cross— data was used in this study. The reasons for select— se years can be summarized in the following points: Although data on cotton yields were available prior to 1939, the data on the other variables were not. Major changes in technology appear to come often Since 1939.1 g_Method mentioned, the county was taken as the observation this study. Since the number of counties growing cres or more of cotton_in 1959 was 676,2 and since ion of data on the variables associated with each was too arduous, it was decided to sample. The samp— thod was as follows: On the basis of the harvested cotton acreage in 1959, all counties harvesting 1,000 or more acres of cotton constituted the uni— verse. The total cotton acreage of these 676 counties represented 94 percent of the M. Thompson, "Evaluation of Weather Factors in iuction of Wheat," Journal of Soil and Water, Vol. 4 (July and August, 1962). e Table l. Uni 2. The sel ear mo: ea as wh ir m Threi Although the effec in COtton ferent 1E be discus the Seco will be 17.. 26-5 -23- United States cotton acreage in 1959.3 The sample was constructed by randomly selecting 40 percent of the counties in each state except that at least 8 and no more than 45 counties were selected for each state. The eight counties were used as minimum because the number of counties which grew 1,000 or more acres of cotton in 1959 was only 8 in some states. The total number of counties chosen by the above method to represent the whole cotton area was 258; the distribution of these counties is Shown in Table 1. .Analyses as different levels of analyses have been made. each was used for the same purpose of measuring cts of different factors related to past changes n yields per acre, each part was devoted to a dif— evel. The state analyses were made first, and will ssed in Chapter IV. On a more aggregate level, nd part was used for the regional analyses which introduced in Chapter V. S.D.A., 1959 Census of Agriculture, Vol. 1, Parts 8, 31—37, 42—43, and 48. Table l. NI oi State North Caro: South Caro Georgia Alabama Missouri Arkansas Tennessee Mississip Louisiana Oklahoma Texas New Mexi. AriZona Californ \ F \ \70 -24- 1. Number of Counties that Grew 1,000 Acres or More of Cotton in 1959, and the Number of Counties Selected in Each State Number of Counties Number of Counties e That Grew 1,000 or Selected in More of Cotton Each State b Acres in 1959 a Carolina 42 17 Carolina 44 18 a 75 30 a 65 26 ri 27 11 as 73 29 see 8 8 sippi 45 18 ana 32 13 ma 47 19 192 45 xico 8 8 a 8 8 rnia 10 8 Total 676 258 aSource: U.S.D.A. 1959 Census of Agriculture, 01. 1, Parts 17, 26—28, 31—37, 42-43, and 48. bSee Appendix B for names of counties selected. These : were the be used as a g national an Selectin i The d. built into are listed for select A» The dé The 8; this cotto B. The 1 Li _25_ hese first two parts of state and regional analyses he basis for the third and final part. They were S a guide for selecting an adequate procedure for al analyses which will be discussed in Chapter VI. ing the Variables he dependent and independent variables which were into the different regression models used in this study sted and described with some emphasis on the basis lecting these factors, as follows: e dependent variable: e single dependent variable which was considered in is study was the county average yield in pounds of tton lint per acre of cotton harvested. e independent variables: Technical and Economic Variables: (a) Pounds of fertilizer nutrients per acre of cot— ton:4 This variable was included, since it is well known that fertilizer is one major input in cotton production. Thus, it is eXpected that fertilizer has had a major effect on changes Available only on a state basis. —26— in yields per acre of cotton. (b) Man—hours of labor per acre of cotton:5 This variable was included to measure the effect of changes in labor used per acre on yields. It is believed that this factor has had some inverse relationship with yields. In other words, it is expected that as man-hours of labor per acre have decreased in the last three decades as the result of extensive mechanization, the yields per acre of cotton have increased. How~ ever, Johnson and Gustafson in their study of grain yields found that the decrease in the man-hours of labor were just offset by the in— creased mechanization and the net effect on yields per acre was negligible.6 Thus, it is eXpected that the net effect of the combined mechanization and man—hours of labor variables have had a minor effect on yield. (c) Number of tractors per 1,000 acres of harvested crOpland, and (d) Dollars Spent on gas and oil per acre of har— vested crOpland: These two variables were included as a possible ailable only on a state basis. inson and Gustafson, op. cit. (g) -27- approximate indicator of the extent of mechan— ization. Mechanization can affect yields by timeliness of Operations, and in other ways. Thus, one could eXpect that, as mechanization increases, the yields per acre increase. Since it is known that the mechanization of cotton has proceeded rapidly during the last three decades, it is eXpected that this has had some effect on increasing yields of cotton. PrOportion of cotton acreage irrigated: On the basis of the fact that irrigated land yields significantly more than non—irrigated land, it is expected that as the proportion of cotton acreage irrigated increases, the yields per acre increase. Size of the cotton enterprise: This variable was included to measure the effect the scale of Operations has on yields per acre. It is eXpected that more Specialized equipment is used as the size of cotton farms increases. Then, one could say that while the effect of increased mechanization is measured explicitly by the above two variables (c) and (d), the effect of a Shift to more Specialized equipment is measured by this variable. Relative changes in cotton acreage: -28.. This variable was included, since it appears reasonable that an increase in acreage should result either in land less well adapted to cot- ton production being added or in farmers with less management skill in cotton production entering production. In either case, increased acreage should result in a decrease in average yield per acre and vice versa. Hathaway in his study on the dry bean industry in Michigan intro— duced the same argument in selecting Similar factor in fitting a yield model.7 On this basis, one could say, since cotton production requires high quality land with high management skill, then as total cotton acreage decreases, one could expect that higher quality land will be kept and higher yields per acre will be obtained. (h) Percentage of total harvested cropland in cotton: It is believed that this figure can be taken as a possible indicator of the comparative ad— vantage for cotton in Specific areas. In other words, if this percentage is high in a certain county, it indicates that that county has a com— parative advantage for cotton relative to other harvested crOps. Thus, it is expected that E. Hathaway, Op. cit. (i) -29- this value has had some positive relationship with cotton yields per acre. Value of land and buildings per acre: This variable was included because it is believed that value of land reflects the basic produc— tivity of land. Thus, this variable is expected to estimate the relationship of land productivity and yields per acre. Moreover, Johnson and Gustafson used this variable as an independent factor in analyzing grain yields. In this re— Spect, they argue: “There has been fairly wide variation, among States, in the changes in land values which occurred between the two periods under study. One would expect, on economic grounds, that such changes would have some effect on yields, to the extent that yields are sub— ject to human influence. If, in an initial period, farms are being operated more or less optimally, or ”in economic equilibrium,“ and then the cost of land increases, everything else remaining the same, either yields must be in— creased to maintain the equilibrium, or the crOp will no longer be grown. Of course, we know that 'equilibrium' as used in economic theory never exists perfectly, but it is reasonable to hypothesize that there is a tendency to move _30_ toward it."8 At the same time, traditional economic theory and the concepts of land eco— nomics argue that an increase or decrease in yields and economic value will be capitalized into higher or lower land values. Thus, the statistical model used here Operates as if land values affected yields, while the economic model would argue that yields affect the value of land and buildings. Independence and dependence in the statistical model do not require formal cause-effect relationships, except in the Spe- cific mathematical balancing of data fitted to formulas. Johnson and Gustafson apparently are arguing that motivation may be influenced by a rise in land values. (j) Price of cotton for previous season: The inclusion of this variable can be eXplained in the following way: “Production economics assumes that if the expected price to be received for a commodity increases, an increase in the rate of variable inputs and higher yields should "9 ' ' ' ' result. It is believed that a major element of the eXpected price to which cotton producers nson and Gustafson, 9p. cit., p. 72. g haway, Op. cggp, p. 30. -31_ respond, is the price received in the previous season. Thus, it is eXpected that this variable had fairly large positive effects on cotton yields per acre. Weather Variables: (a) Monthly total rainfall. (b) Monthly average temperature. (c) Squared monthly total rainfall. (d) Squared monthly average temperature. (e) Monthly rainfall and temperature interaction. (f) Successive month rainfall interaction. By having the above six weather variables for each month of the growing season, then the weather var— iables for the whole growing season were 53. When all these weather variables were included in the initial regression models used in this study, the estimated regress;on coefficients for these variables were not consistent with a priori notions that the effect of each weather factor on crop yields changes gradually from month to month. Hence, it was decided to transform these monthly weather variables (53) to new variables (18), by employing a quadratic function of time to monthly weather data. This was accomplished by defining the new weather vari— ables as weighted sums of the old variables, e.g., 10 Sander -32- P z = E z 10 p=1 p P Z = Z pZ ll p=l p P Z = Z phZ 12 p=l p where 21’ 22, . . . Zp were the original obser— vations for one variable, say monthly total rainfall, monthly average temperature, or squared monthly 10, 211, and 212 were the new variables.10 The number of periods P, is 9 for all total rainfall, and Z but the successive month rainfall variables where it is 8. Clearly, the multiple correlation coeffi— cient (R2) was less than for the initial regression models, but the results were more consistent with a priori notions of smoothness over time in the weather effects on crop yields. However, the weather variables were included in the regression models to measure the effect of weather on yields per cotton acre. The data on yields of cotton harvested, Show great variation in both cross~section and time series. Then, it iis process is discussed in greater detail by Fred an in his book, Op. cit. iS beE of fa WE YtL -33- is expected that major parts of the variation have been caused by weather factors while a large part of trend has been caused by technical and economic factors. Rainfall and temperature were included as the weather variables because they are the dominant meteorological influences in yields, and because data on rainfall and temperature were readily avail- able. The Squares of weather variables (monthly tem— perature and rainfall) were used, Since many studies have Shown that crOp yields were curvilinear instead ' ' ' 11 u of linear functions of weather variables. In linear regression it is assumed. for example, that each additional inch of rain in July would have the same effect on yield as the first inch. This is not the case, however. because each additional inch has less effect until a point is reached where addi— ' ' 1 ' u 12 tional rain may actually reduce yields. Also, the interaction between monthly tempera- ture and rainfall and the interaction between rain— fall for successive months were included in this M. Thompson, Weather and Technology in Production and Soybeans, CAED, Rep. 17. Iowa State UniverSity, stu act pel ta: Du Tm -34- study, since Hendricks and Scholl used such inter- actions in their study of the joint effects of tem— perature and rainfall on corn yields, and they ob— tained valuable results.l3 Dummy variables: Two different sets of dummy variables were used for the national analyses. One set was concerned with time and the other was concerned with location. The set of dummy variables for time was used to measure the effect of factors that changed over time and were not considered in the national regres— sion analyses. Thus, factors such as improvement in varieties, improvement in production techniques, and improvement in insect control can be recognized. The dummy variables for time were five. one for each . year included in this study. To obtain non—singular 1 matrix and allow estimation of the parameters built in the models, the dummy variable for l939 was drOpped. The second set of dummy variables concerned with location were 31, one for each economic sub—region. The dummy variable for economic sub—region No. 16 was dropped to avoid singular matrix. The main A. Hendricks and J. C. Scholl, The Joint Effects rature and Rainfall on Corn Yields, N. Carolina Agr. ., Tech. Bull. 74. 1943. obj was EOE At th four of th included i all final chapters. ages irri vested er and cottc The region, 1 over the three st of Cott< Period l the fin estimat Tl age of droppe' betWee i35_ objective of this second set of dummy variables was to group the counties into relatively homogen- eous production areas so the basic production dif- ferences that persist over time might be measured. : this point, it seems necessary to point out that E the above technical and economic variables were only ed in the initial regression models, but dropped in nal models which will be discussed in the following rs. These variables were proportion of cotton acre- rrigated, number of tractors per 1,000 acres of har— cropland, percentage of cropland harvested in cotton, tton prices for previous season. 'he irrigated cotton land was used only in the western , namely, New Mexico, Arizona, and California, and he whole period of study, all cotton acreages in these states were irrigated. This means that proportion ton acreages irrigated was constant over the whole of study. Hence, this variable was drOpped from nal models to obtain non—singular matrix and allow tion of parameters. he other three variables, number of tractors, percent— crOpland harvested in cotton, and cotton prices, were d from the final models because of high correlation n each of these three variables and some other tech— HIM-ll nical and 6 these three iiy probler and econom some space Multicolli A prr oi the ex correlate their set estimate is preser Crease, always d Gustafso estimate (1) the negligil SO Smal \ l4 Variab] North ( priCeS applie< '93 an. —36— and economic factors.14 Thus, the reason of drOpping :hree variables was the existence of multicollinear- Dblem between these variables and some other technical >nomic factors. However, it seems useful to give pace for discussion of the multicollinearity problem. gllinearityjproblem problem of multicollinearity arises when some or all explanatory variables in a relation are so highly ated that it becomes very difficult to disentangle separate influences and obtain a reasonably precise te for their individual effects. When this problem 'sent the variances of the estimated coefficients in— 2. Of course, lack of statistical significance is not . due to the multicollinearity problem. Johnson and ison argue: “Lack of statistical significance in an .te might be due to one or more of several things: e true effect of the variable may really be zero or ible: (2) the true effect may not be zero but may be ll that it is submerged by the random or unexplain— ariations in the dependent variable: (3) the true Some examples of the high correlation between these les and other variables are the following, found in Carolina data. The simple correlation between cotton for previous season and either fertilizer nutrients d per cotton acre or man-hours per cotton acre were d -.92, respectively. See Appendix C. effect my model, (b) able data. variables.' Howev pair of va and these ity proble The 1 the exist iables, a variables drOpping ing how - OI abSen Was the Percent; for prex in the -37- may be obscured by (a) imprOper Specification of the (b) inadequacy, inaccuracy, or insufficiency of avail— ata, (c) high intercorrelations among the explanatory "15 -es. >wever, simple correlation coefficients among each E variables used in this study have been estimated, ase have indicated the existence of multicorrelinear— Dblems among some variables. ie method used in this study to examine the effect of istence of multicollinearity problem among some var— , and to improve the estimated coefficients of other les, was simply running regression models alternately ng (or adding) some independent variables and observ- iw the estimated coefficient was affected by the presence ence of any other variables. The result of this method e decision to drOp the variables, number of tractors, tage of crOpland harvested in cotton, and cotton prices evious season, from all the final models discussed following chapters. Johnson and Gustafson, op. cit., p. 67. For i fitted to to measur cotton yi twelve nc 0f the 01 first The has as j CHAPTER IV STATE ANALYSES the state analyses, two statistical models were :0 data on weather, technical and economic factors ire the effects of these factors on each state's fields. The first model was used for each of the ion—irrigated cotton states. and the second for each ather three states, with irrigated cotton. odel I e model used for each of the non—irrigated states follows: I th : bO + .23 biXict + Vct 121 c = l, 2, . . . , C (counties). t = l, 2, . . . , T (Years l939, 1944, 1949, 1954, 1959). i = l, 2, , 1 (Independent variables). b0 = The overall constant term. Vct = The error term associated with county c in year t. ~38— ing the the tot pounds, SPGHt < land h; by the SUppli units Countx Were l ahie . 1’1 Limb e mes -39_ Yet = Average pounds of cotton obtained per acre of harvested cotton for county c in year t. Xict = The value of the ith independent variable for county c in year t. The definition of each independent variable is as follows: X1 = Dollars Spent on gas and oil per acre of harvested cropland. X2 = Man—hours of labor used per cotton acre. X3 = Pounds of fertilizer nutrients applied per cotton acre. X4 = Average size of cotton enterprise in acres. he values for this variable were obtained by multiply— ratio of cotton production in bales for a county to al acres of cotton harvested in that county by 478 the usual net weight of the cotton bale. hese values were obtained as the ratio of total dollars n gas and oil in a county to the total acres of crOp- rvested in that county. These values were deflated index of average prices paid by farmers for motor 5. See Appendix A. he state averages of pre—harvest and harvest man work sed per cotton acre were used for this variable, since averages were not available. he state averages of fertilizer nutrients in pounds ed for this variable, since such data were not avail— a county basis. hese values were obtained by taking the ratio of total of cotton acres in a county to the total number of arvesting cotton in that county. \- 6Tb Year in county 5 7T} dOllars Agricul Smerp 8T mOnthly ther st States‘ The WEE ing Cr: ( _40- X5 = Ratio of cotton acreage in year t to that in base year (1939).6 X6 = Value of land and buildings per acre. 9 7 p=1 where R1, R2, . . . , R9 are monthly total rainfall,8 i.e., R1 is total rainfall for the first month of growing season (March), R2 is total rainfall for the second month (April), and so on . . ., R9 is total rainfall for the last month of growing season (November). 6 .The total acres of cotton harvested in a particular :ar in a county to that in the base year (1939) in that lunty supplied this variable. 7 . . . The values of land and buildings per acre (in current llars) were obtained, as reported in the U. S. Census of riculture. Then, these values were deflated by the con— mer price index. See Appendix A. 8The data for monthly total rainfall in inches and nthly average temperature in degrees F. for selected wea— er stations were obtained from "Climatological Data, by ates, by Months," Weather Bureau, Commerce Department. e weather stations were selected according to the follow— 9 criteria: (a) if there were more than one weather station in a county reporting rainfall and temperature, then the one at or near the center was selected for use in this study. (b) if there was only one weather station in a county, then it was selected. (c) if there was none in a county, then the nearest weather station to that county was selected. See Appendix B. 9 X 8 = LR = Z pR , where R are as defined P above, and p=l, 2, . , 9, i.e., p=l for the first month of growing season (March), p=2 for (April) and so on . . . , p=9 for (November). 9 2 X = QR = 2 p R , where R are as defined, 9 :1 p p P 2 and p are squares of p. 9 X = TR2 = 2 R2, where R2, R2, . . . , lO _ p l 2 p—l R: are squared monthly total rainfall. 9 Xll = LR2 = Z pR2. p=l p 9 2 2 X12 = QR2 = E p Rp. p=l 9 Xl3 = TT = Z T , where T1’ T2, . . . , p=l T9 are monthly average temperature. 9 X = LT = Z pT . l4 p=l P 9 2 X = QT = Z p T . 15 p=l P 9Refers to previous footnote, page 40. 1r. 1. . l r a. e S r II d . II\ at n R 3 Of this Stl 9 X19 = TRT = 421 Rpr, where RlTl' R2 2, are monthly rainfall and temperature interaction. 8 X22 = TRR = p51 Rp Rp+l' where RlRZ’ R2 3, , R R are successive month 8 9 rainfall interactions of growing sea— son, i.e., RlRZ is (March—April) rain— fall interaction, and so on . . . , R8R9 is (October—November) rainfall interaction. Of course, the above model and other models used in 10 q 3 study are based on the following standard assumptions: (a) The expected values of disturbance terms are zero, i.e., E(Vct) = O. (b) The disturbance terms have equal variances for all observations, i.e., E(V:t) = 6‘2. (c) The disturbance is independent, i.e., E(VCt VéE) = O. c % é or t # t. 10M. Ezekiel and K. Fox, Methods of Correlation and ression Analysis, 3rd edition, (New York: John Wiley Sons, 1959). At an regressior weather v; efficient from mont the main in utili: other mo: notions changes her of v than in a reduc But, on reqress each m< a prio than t ReSult -43- (d) The independent variables in each model are inde- pendent of the disturbance term. At an initial stage of this study, the conventional regression techniques were used to capture the effects of veather variables on cotton yields, but the resulting co— efficients for the weather variables varied irregularly from month to month. A new procedure was sought. Hence, the main objective of using a polynomial function of time in utilizing the weather data in the above model and in other models used in this study, was to incorporate a priori notions that the effect of each weather factor on yields, changes gradually from month to month.11 Clearly, the num— ber of weather variables used in the above model was less than in the conventional regression model and this led to a reduction in the multiple correlation coefficient (R2). But, on the basis of the above model, the estimation of regression coefficients for different weather factors in each month of the growing season were more consistent with a priori notions of smoothness over time in weather effects than those obtained from the conventional regression model. Results for State Model I The results from applying Model I for the twelve non— llSanderson, Op. cit. irrigated itis note many varie statistics (A their cients f0 duction t such mode Howe each var: Dollars 0f estin was posj i.e., N( and Lou Cients Coeffic ll indiCa per ac X in Unit 1 Was as per ac lira 13 th. Would the v Were _44_ irrigated states are summarized in Table 2. In such table, it is noted that the estimated regression coefficients for many variables are not statistically significant. But, the statistical non—significant variables were included because (a) their presence improved the estimated regression coeffi— cients for the other variables in the model, and (b) pro— duction theory suggests that they are a relevant part of such model. However, it seems useful to discuss the result for each variable separately. Dollars spent on gas and oil per acre of cropland: The Sign of estimated regression coefficient (b) for this variable was positive for seven states, but negative for five states, i.e., North Carolina, South Carolina, Missouri, Tennessee, and Louisiana.12 However, none of these negative coeffi~ cients was statistically significant.13 The size of positive coefficients ranged from 0.5 for Mississippi to 39.1 for 12(b) is the estimated regression coefficient which indicates the influence of the variable on average yield per acre. For example, the estimated coefficient 22.3 for X in the Georgia regression analysis indicates that a 1 unit increase (in dollars Spent on gas-oil) above average was associated with a 22.3 pound increase in cotton yield per acre, if other things remain the same. 13In this chapter, statistical Significant refers to 19 percent level of significance. 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Since this variable was used as an approximate indica— tor of the extent of mechanization, and if this relationship is valid, it appears that extent of mechanization has had significantly positive effects on cotton yields per acre in Seorgia, Oklahoma, East Texas and West Texas. flan-hours of labor usedyper cotton acre: The estimated co— efficients for this variable were negative and non-significant for only East and West Texas. They were positive for all other non—irrigated states and statistically significant for South Carolina, Georgia, Arkansas, Tennessee, and Okla— ioma. These positive coefficients were relatively large, ranging from 2.1 for Oklahoma to 14.2 for Tennessee. For the small magnitude and non—significance of either :his variable or the above variable (dollars spent on gas and oil per acre), in some states, there are two possible explanations: (a) Both variables were highly correlated Eor some states, so that it was difficult to disentangle :heir separate influences and obtain significant estimates 14 for one of them or both, (b) If it is true that mechaniza— 14A rather typical example of high correlation between :hese two variables is the following, found in the Missouri data. The simple correlation between dollars Spent on gas and oil per acre, and man-hours of labor per cotton acre vas ~.91, tion'has isnot cludes cancel this v relati of the gang; resul all s Caro: quit to 2 dice Effie the iab —48— on has been essentially a substitute for labor, then it not too surprising that in a regression model which in- udes variables representing both factors, they, in effect, ncel each other out, and one or both appear non-Significant.15 However, on the basis of the resulting coefficients for is variable, it appears that man—hours of labor has a latively positive effect on cotton yields per acre in most ’the non—irrigated states. iunds of fertilizer nutrients applied per cotton acre: The asulting coefficients for this variable were positive for .1 states, but statistically significant for only South irolina and Georgia. The size of these coefficients was lite small ranging from 0.3 for either East or West Texas > 2.1 for Missouri. These results do not necessarily in— .cate that more use of fertilizer nutrients has a minor ffect on yields, Since these unexpected results might be re result of: (a) the high correlation between this var— lble and another variable (cotton prices for previous 16 ear) and this might capture the effect of fertilizer, >) the aggregative nature of the values used for this 15Johnson and Gustafson, Op. cit., p. 72. 6An example of high correlation between these two iriables is the following found in the North Carolina data. re simple correlation between pounds of fertilizer nutri— LtS per cotton acre and cotton prices for previous season LS 0.93. -49_ riable, i.e., the values used for this variable were state erages rather than county averages (which were not avail— le), and this has reduced the number of observations for ch state analysis to only five (one for each year included this study). This substantial decrease in degrees of eedom might increase the standard error of coefficient r this variable and lead to a non—significant coefficient, ) in some states, particularly East Texas and West Texas, e pounds of fertilizer nutrients applied per cotton acre re too low to result in any reSponse on cotton yields.l7 Ferage size of cotton enterprise in acres: It was expected hat on farms with a larger average Size of cotton enter— rise in acres, more specialized equipment would be used, nd higher cotton yields per acre obtained. This variable as included to determine if there were any economies or iseconomies of scale in cotton production. However, the esulting coefficients were negative for three states, in~ luding North Carolina, South Carolina, and Missouri. None f these negative coefficients was statistically significant. n all other non-irrigated states, the coefficients were ositive, but only for four of these (Arkansas, Mississippi, 17The average pounds of fertilizer nutrients applied er cotton acre for the whole period of study in East Texas nd West Texas were 30 and 33 respectively, while in South arolina and Georgia they were 116 and lO9 respectively. _50- Louisiana, and Oklahoma) were statistically significant. The size of positive coefficients was relatively small, ranging from 0.1 for West Texas to 5.9 for Mississippi. Two things can be inferred from the non—significance of the coefficients for this variable in many states: there were no economies or diseconomies of scale, or, there were economies or diseconomies of scale but they were not mea— sured by this variable. This second case could be due to (a) this variable was not the appropriate one for measuring the scale effect, or (b) other variables captured its effects. Ratio of cotton acreage in a year to that in base year (1939): Since cotton production requires high quality land, it was expected that as total cotton acreages decreased, the higher quality land has been kept in cotton production, and higher average yields per acre were obtained. Thus, the relation between this ratio and cotton yields was expected to be nega— tive. But it seems unnecessary to expect that the relation— ship between this ratio and yields of cotton would be nega— tive over time for all states. In fact total cotton acre— ages decreased in some states and increased in others; deSpite this, cotton yields increased in all states—-thus some states had both increased yields and increased acreage. However, in most Southeastern States, namely North Carolina, South Carolina, and Alabama, where cotton acreages have substantially decreased over time, the resulting coef— _51_ ficientS for this variable were negative. One of these coefficients was statistically significant (for South Car— olina). In all Delta and Southwestern States, these regression coefficients were positive, and statistically Significant for Arkansas. The positive coefficients for all Delta and Southwestern States may at first seem somewhat surprising Since it is known that cotton acreages have substantially decreased over time in most of these states. However, this can be interpreted in this way: there have been shifts in cotton production within each of these states from low—yielding counties with very large cotton acreages to high—yielding counties with relatively small cotton acreages, so that the total cotton acreages have decreased within the state, but increased in high—yielding counties. Further, there is a possibility that many of the latter counties were included in this study to represent these states.18 Then, the ratio of cotton acreages to that in l939, has increased in these states and higher cotton yields per acre were obtained. However, on the basis of the result of this variable, it appears that the reduction in cotton acreages has had a major effect on average cotton yields per acre. 18There is a possibility that cotton acreages in those very low—yielding counties (with large cotton acres) have substantially decreased to be less than 1,000 acres in 1959. If so, these counties were not included in the population from which the counties were selected for this study. _52_ {glue of land and buildings per acre of cropland harvested: The estimated coefficients for this variable were positive for all non-irrigated states. Most of these coefficients Jere statistically significant, but their sizes were quite small, ranging from 0.2 for South Carolina to 1.3 for Ten— 1essee. Since it was assumed that the value of land reflected :he potential productivity of land, then, if this is true, it appears that the use of highly valuable land in cotton pro- iuction has some positive relation with cotton yields per acre. [gather variables: In State Model I, the weather variables were used in such a way as to be equivalent to forcing the regression coefficients for nine months on each set of ori— 19 to fit a quadratic function of time. The ginal variables individual coefficients for each month of these original veather variables were derived from the coefficients reported in Table 2, and are listed in Tables 3, 4, and 5. In Table 3, it is noted that the signs of estimated regression coefficients for monthly total rainfall were iegative in all Southeastern and Delta States except South Zarolina and Missouri. This means that the increase in rain— fall over the average——by itself—-has decreased cotton yields 19Monthly total rainfall, squared monthly total rainfall, nonthly average temperature. manna-WU m ”OHM-.dqwufi Dubai“ tncoz h Hwhflaflv§.oz 'FflUflHQZ a .H Hmmgufiwm Haynenwoufi \fluHFEUgdifluU: “om. m..uwflunw.uu “.unm‘umqe.c it .c. 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NET. To“. mafia ummm m.~ io fl? mg.“ 2‘5 Nan im. 9? Nu? maofifio was ¢.m N.ou o.mu o.mn «.on moon N.ou o.ma 00meQSQB H.mo o.o H.N ~.m m.m d.~ m.o ¢.mu moon mmwmmxu< .r m.mwu m.wc mama m.o m.m w.m mom mofl mofiu fiuaommfiz J4 m.o o.o m.ou m.ou m.On moon m.0n 0.0 m.o mammowu .3? «.mT 0:2... :3. ,3» {N 3w 3: fig mfififlafi m1“... m.mn mom» 5.? «.mu Q? 0:? mg.“ as 42823832 man 0.? fl? «:1 may i? 2,. «.0 fim mafia? m.¢ m.m H.o n.o H.h m.“ m.m H.h m.c mgwaoumo saaom 0.3.. 12» ms". 1?. 0.? n.0,. «.0 To «.0 3:33 afioz 3 3v 3: 3 3V :5 EV g «Q: mggm .w:< %pr mama mflz Hamm¢ swam: n these states. This negative effect of rainfall on cotton ields in Southeastern and Delta States may at first seem omewhat surprising. However, it is well known that in rela- ively humid areas, there may be too much rainfall, and this ight have a deleterious effect on cotton yields. This eleterious effect might occur, since too much rainfall uring the growing season causes the development of surface oots at the expense of the deeper roots. This results in ilting and shedding of leaves and bolls, particularly if e weather turns dry in the summer.20 The nature of nega— ive effect of rainfall in all these states, namely North arolina, Georgia, Alabama, Arkansas, Tennessee, Mississippi, nd Louisiana was relatively similar. The least damage from n increase in rainfall on cotton yields was during the lanting and harvesting periods, while the most damage was t the middle of the growing season. In other words, the egative effect of increase in rainfall over the average n cotton yields per acre was during March to April and Sep~ ember to November, while the most negative effect was dur— ng June to August. The most damage from rainfall on cotton ields occurred in summer months in these states; it is known hat a wet summer induces excessive vegetative growth, retards ruiting, and favors rapid increase of the boll weevil in otton crOp. 20 U.S.D.A., 1941 Yearbook of Agriculture: Man and limate. -57- In Tables 3 and 4, it is observed that the resulting fficients for rainfall in all Southwestern States, i.e., ahoma, East Texas, and West Texas, and also in South olina and Missouri were highly positive during the whole wing season. This means that the increase in rainfall r the average in these states has increased cotton yields. the case of Oklahoma, East Texas, and West Texas, the hly positive effect of rainfall does not seem surprising, ce it is known that rainfall in such a relatively arid la is generally lower than Optimum. More surprising is r highly positive effect of rainfall in the case of South “olina and Missouri, especially since the effect in all Ler relatively humid states was highly negative, as men~ .ned above. In Table 5, it is apparent that the temperature effect cotton yields per acre in the Southwestern area was ,ghtly negative (in Oklahoma and East Texas) or slightly itive (in West Texas) during the first few months of the wing season and relatively positive (in all three states) r the end of the growing season. The other type of tem— ature effect was in the humid area, particularly North olina, Alabama, Mississippi, and Louisiana, where the ect was positive at the beginning of the growing season, then reduced gradually to become highly negative near end of the season. However, the sizes of the regression coefficients for —58— her rainfall or temperature variables have only given e indication for the relative importance of these wea— r factors on cotton yields. To examine the joint effect rainfall or temperature variables on cotton yields, the .est has been used for all state analyses and the results a reported in Table 6.21 Table 6 shows that the joint effects of rainfall var— >les22 on cotton yields were statistically significant all non—irrigated states except Missouri, Louisiana, and at Texas. However, the joint effects of temperature var— >les23 were statistically significant in only six states, :ably, North Carolina, South Carolina, Missouri, Mississippi, lisiana and Oklahoma. 21To test the significance of a set of variables in a yression model, let the variables to be tested be repre— 1ted by Xp+l...X , and let the remaining variables in the iel be represented by X "'Xp° Obtain R2 from the regres— l P+l Then under the null hypotheses e., B = B = ... Bq = O) and the assumption that >n on X ...X , X ...X P HQ r4 P+l P+2 2 disturbances are normally distributed; F(q—p, N—q—l) = — R N— —1 p q - R q-p :erence: R. L. Gustafson, Procedure for Testing the Sig— m______ . _______. where N is the number of observations. gcance of a Subset of Regression Coefficients, mimeo, higan State University, October 27, 1960. 2 . . 2Monthly total rainfall, squared monthly total rainfall, thly rainfall—temperature interaction, and successive th rainfall interaction. 3Monthly average temperature, and monthly temperature— nfall interaction. .oflumnlm mo HOumcHEOGmU Mom Eoommuw -59- mo mmummo we NZ .OHumHIm mo Houmumasc How Eocmmnw mo mmummp we HZ m mm. m.o Anv.qc mo. n.m Ake.mv .e.3 on. m.o Amws.ao ma. ¢.H Amwa.mc .e.m Ho. H.0H Ans.wo so. m.m Ass.wv .maxo so. m.m xs¢.¢v mm. s.H As¢.mv .mq mo. m.m immg.wv Ho. m.m Asms.wv .mmflz ms. w.o Akm.ev so. m.m Asm.wv .came AH. o.m Ams.¢v mo. m.m Ams.mo .xue mo. v.m ANN.¢V mm. m.o Amm.wv .02 we. 0.0 Amss.vv so. ®.¢ Amga.wv .ms< mm. m.H Amma.ev Ho. o.m Amma.mc .mo Ho. m.m Ams.ev so. H.e Amn.mv .o.m mo. m.m Asm.¢v Ho. H.m Amm.mv .u.z mocmo OSHM> ANZ.HZV musmo mSHm> mANZ.HZv IHMHcmflm Im soommum lashqmgm um sowmmum mo Hm>mq we mmummo mo Hm>mq mo mmummo mumum OHSHMHmmEmB Hammcamm —60— On the basis of these results, it appears that rainfall s had more effect than temperature on cotton yields in n-irrigated states. :ate Model II By applying the previous State Model I, to the weather 1d non—weather data associated with each of the irrigated tates, i.e., New Mexico, Arizona, and California, it was ound that many weather variables were very highly correlated ith each other. This has led to non—significant coeffi— ients for many variables built into the model. Then, by unning the State Model I, alternately dropping (or adding) wome weather variables and observing how the estimated coef- Ticient was affected by the presence or absence of any other 'ariables, it was decided to drOp seven weather variables From State Model I to improve the estimates of coefficients For non—weather variables. This modified model — State [odel II — was as follows: th = bO + lel +...+ b7X7 + b13X13 + b19X19 + b22X22 + Vct. if course, the definition of all variables involved in the .bove model is as defined before as a part of State Model I.24 24The weather variables (X7, X13, X19, and X22) are the eason total for monthly total rainfall, monthly average tem— erature, monthly rainfall—temperature interaction, and suc— essive month rainfall interaction. —6l— glts for State Model II The results from applying State Model II for the three igated states are summarized in Table 7. It seems appro— ate to discuss the resulting coefficients for each var— le separately. _lars Spent on gas and oil per acre of cropland: The :ulting coefficients for this variable were positive in irrigated states. They were highly positive in New :ico, and Arizona (15.5 and 15.7, reSpectively) and slightly sitive (1.4) in California. All coefficients were statis— :ally significant. Thus, it appears that this variable has had more effect cotton yield increases in the irrigated states than in non—irrigated states. The heavy use of gas and oil ch was associated with an increase in cotton yields per e in the irrigated states is associated with the expansion irrigation in these states. —hours of labor used per cotton acre: While the estimated fficients for this variable were negative in only two ates of the non-irrigated states, they were negative in L irrigated states. Moreover, the sizes of these coeffi— ents were relatively large in most of the irrigated states compared with those in non—irrigated states. The coeffi- ants were fairly significant in California, but not at all ble 7. The Regression Results for State Analyses of Cotton Yields, Irrigated States {planatory States iriables New Mexico Arizona California (b) a (b) (b) 1: Gas—oil 15.5 15.7 1.4 (6.2)b (6.2) (0.4) 2: Man—hours —0.9 -3.8 —4.4 (5.3) (4.0) (1.2) 3: Nutrients 3.7 2.7 0.1 (2.4) (3.1) (0.6) 4: Size 0.1 0.8 0.1 (0.8) (0.2) (0.2) .5: Ratio —0.1 —0.4 0.02 (0.1) (0.3) (0.02) :6: Value —5.0 -0.1 0.2 (5.5) (0.4) (0.1) :7: TRC —7.4 47.5 0.1 (55.8) (85.0) (53.8) :13: TT 0.4 2.4 -0.7 (1.5) (1.4) (0.6) '19‘ TRT '0=3 -O.6 —o.5 (0.8) (1.0) (0.8) 22: TRR 5.8 2.0 7.1 (3.5) (3.3) (9.8) __ 2 d R 0.7160 0.7826 0.7552 a(b) is the estimated regression coefficient. Standard errors are given in parentheses. CTR, TT, TRT, and TRR are as defined in State Model II. dR2 is the multiple coefficient of determination. —63— nificant in New Mexico or Arizona. gds of fertilizer nutrients per cotton acre: The result— coefficients for this variable were positive in all igated states. And, the sizes of these coefficients in se states were relatively larger than in non—irrigated tes. Still, none of these coefficients was significant any irrigated state. The amount of fertilizer nutrients applied per cotton e is higher in irrigated states than in non—irrigated tes. Thus, it was expected that this variable was posi— e and significant in all irrigated states. This non— nificance could be the result of the high correlation ween this variable and the variable of man—hours of labor d per cotton acre in these states. The simple correlation ween these two variables, for instance, in New Mexico and zona was —0.95 and —0.96, respectively. rage size of cotton enterprise in acres: This variable included to determine if there were any economies or economies of scale in cotton production in the irrigated tes. The resulting coefficients for this variable in se irrigated states were more consistent with each other a in the case of non—irrigated states. They were posi— a in all irrigated states but significant only in Arizona. magnitude of these coefficients was very small, ranging —64— n 0.1 for New Mexico and California to 0.4 for Arizona. io of cotton acreage in a year to that in base year 32); None of the coefficients for this variable in all igated states was statistically significant. Moreover, absolute values of these coefficients were less than and these were small compared with those in non—irrigated tes.25 Thus, it appears that this variable has not had effect on cotton yields per acre in the irrigated states. 5 perhaps is because of (a) the true effect of this var— ‘le was zero or, (b) some other variables included in the .el may mask its effect. The latter possibility may be ‘e likely, since the coefficient of this variable was nificant in some non—irrigated states. Iue of land and buildings per acre: The results for this iable in irrigated states were very surprising. While coefficients for this variable were positive in all non— igated states and highly significant in most of them, y were negative and non—significant in two of the irri— ed states (New Mexico, Arizona). Only in California was s variable's coefficient positive and significant. Thus, value of land does not have a major relationship with 5For example, the regression coefficient for this var— le in Arkansas was 75.9. ~65— >tton yields per acre in most of the irrigated states, while : has had a significant and positive relationship with cot- 3n yields in the non—irrigated states. This conclusion as also valid based on the results for this variable in . 26 3e regional analyses. eather variables: The results from the F-test have shown hat the joint effects of either rainfall or temperature 28 ariables27 were not significant in New Mexico and Arizona. ut, these effects were significant in California.29 These esults could lead to the conclusion that the joint effect f rainfall or temperature has generally had a minor effect n cotton yields per acre in irrigated states, while they 26The regional analyses will be discussed in the next hapter. 7Rainfall variables are monthly total rainfall, monthly ainfall~temperature interaction, and successive month rain— all interaction. And, temperature variables are monthly verage temperature and monthly temperature—rainfall inter— ction. 28New Mexico: F—value for testing the joint effect of ainfall = 1.03 and significance level = 0.40. F-value for esting the joint effect of temperature = 0.09 and signifi— ance level = 0.91. rizona: F—value for testing the joint effect of rainfall 0.31 and significance level = 0.81. F-value for testing he joint effect of temperature = 2.10 and significance evel = 0.14. 29 . . . . . California: F—value for testing the jOint effect of ainfall = 2.31; and significance level = 0.10. F—value or testing the joint effect of temperature = 3.48; and ignificance level = 0.04. -66... 7e had a major effect in non-irrigated states. gcluding Points The selected variables used in either State Model I II generally eXplained a major part of the variation in :ton yield increases in different states. The results r state analyses have shown that there were considerable Eferences among states30 in the cotton yield increases :ributable to different variables. In case of the tech— :al and economic factors, for instance, mechanization 1ded to be more important in the Southwestern and Western :igated States than in the Southeastern and Delta States. 1, fertilizer tended to have a major effect in the Western :igated States, but a minor effect in the Southwestern ates, namely, Oklahoma, East Texas, and West Texas. In a case of the weather variables, e.g., the monthly total -nfall during the growing season has had a highly negative fect in most of the relatively humid states, but a highly sitive effect in most of the relatively arid states, i.e., _ahoma, East Texas and West Texas. And, the monthly aver— ‘ 3 temperature during growing season has had more effect _ther negative or positive) in the Southeastern and Delta an in the Southwestern area. 3OParticularly among those states within different gions. —67— However, the results for technical and economic fac— 5 used in the state analyses have shown that the signs all significant coefficients were generally consistent h the usual economic expectations. But, all coefficients h signs not consistent with a priori expectations were —significant. Generally, the basic problem in the results from state lyses was the different signs and sizes of estimated fficients for the same variable in different states. 5 problem perhaps was caused by the following factors: (a) The existence of multicollinearity problem among some variables used in the analyses. (b) The aggregative nature of the values used for some technical factors, e.g., the values used for fertilizer and labor variables were state averages rather than county averages (which were not available). (C) The variation among observations associated with a state perhaps was too small to provide reliable estimates. In other words, some states might have a great homogeneity which tends to result in insufficient variability among the observations for each variable to permit reliable estimates. 3]'Johnson and Gustafson, op. cit., p. 63. —68— However, some of these difficulties were generally reduced by making the analyses for regional level. These regional analyses will be discussed in the following chap- :er. CHAPTER V REGIONAL ANALYSES Grouping the counties, which presumably have a rela— ,ive homogeneity of production techniques, weather, soil, (opography and climate, into a region increases the observa— ions associated with each analysis substantially, and this ncrease in degrees of freedom might lead to more reliable stimates. Thus, this aggregative attribute of regional nalyses might result in sufficient variability among the bservations within a region to permit making reliable stimates. Four regional analyses were made, one each for the outheastern, the Delta, the Southwestern, and Western egions. The analysis for the Southeastern Region, i.e., orth Carolina, South Carolina, Georgia, and Alabama, in- luded ninety-one counties.1 For the Delta Region, namely, issouri, Arkansas, Tennessee, Mississippi, and Louisiana, eventy—nine counties were involved. In the Southwestern egion, including Oklahoma, East Texas, and West Texas, ixty—four counties were used. Only twenty—four counties 1The sampling method for selecting these counties was escribed in Chapter III. _69_ -70- were involved in the analysis of the Western Irrigated Re— gion, i.e., New Mexico, Arizona and California. Regional Model The model used for each regional analysis was as follows: 24 th : bo + iEl bi Xict + Vct' The definition of all variables in the above model is as defined earlier for the state models. But, in this re— gional model, there were seven new weather variables, i.e., K X and X The definition of 18’ X20' X21’ X23' 24' these new weather variables is as follows: 16' X17' 9 X 2 TT2 = 2 T2, where T 2 . T 2, ..., T 2 16 p l 2 9 p=l are squared monthly average temperature, i.e., T12 is squared average temperature for the first month of the growing season (March), 2 . . 2 . and T2 is for April, and so on..., T9 is for November. 2 In the analysis of the Western Irrigated Region, seven veather variables were dropped because they were highly cor— related with each other in this region. These variables were TTZ, LTZ, QT2, LRT, QRT, LRR, and QRR. With this, the model for this region was exactly like State Model I. 17 18 20 21 23 -71- 2 9 2 LT = Z pr, where p=l, 2, . . ., 9, i.e., p=l p21 is for the first month of growing season (March), p=2 is for April, and so on . . ., p=9 is for November. 9 2 2 2 OT = E p T . 19:1 p 9 LRT = p21 pRpr, where RlTl' R2T2, . . . , R9T9 are monthly rainfall—temperature inter- action, i.e., RlTl is March rainfall temperature interaction, and R2T2 is April interaction, and so on . . . , R9T9 is November interaction. 9 2 QRT= ZpRT p=l P P 8 LRR = Z pRpRp+l, where R1 2, R2R3, . . . , R8R9 are successive month rainfall interaction of growing season, i.e., R1R2 is March—April rainfall interaction, and R2R3 is April—May interaction, and so on . . . , R8R9 is October- November interaction. And p=l, 2, . . . , 8, where p=1 for March—April interaction, and p=8 for October—November interaction. Results for Regional Model The results from applying the regional model for each of the four cotton regions are presented in Table 8. These results show that the estimated coefficients for the tech- nical and economic factors Xl (dollars spent on gas and oil), X (fertilizer nutrients), X4 (size of cotton enter- 3 prise), and X6 (value of land) were positive in all regions. The coefficients estimated for the other two technical fac— tors X2 (man—hours of labor) and X5 (ratio of cotton acreages in a year to that in 1939) differed over different regions. For the man-hours variable, the coefficients were positive in the Southeastern and Delta Regions, and negative in the other two regions. Comparative cotton acreage ratio coeffi— cients were positive in the Southeastern and Western Regions, but negative in the Delta and Southwestern Regions. More Specifically, the fertilizer nutrients variable (X3) was statistically significant3 in all regions except in the Southwestern Region. Since, the levels of fertilizer nutrients applied per cotton acre during the whole period of study in the Southeastern, Delta, and Western Regions 3In this Chapter statistical significance refers to 10 percent level of significance. -73- Table 8. The Regression Results for Regional Analyses of Changes in Cotton Yields I II III IV Explanatory South— Delta South- Western Variables eastern Region western Irrigated Region Region Region X1: Gas—oil 1.593b 2.56 39.81 1.73 (2.91) (2.34) (4.51) (.48) X2: Man—hours 1.61 1.22 —0.75 —4.93 (0.37) (0.40) (0.97) (1.01) X3: Nutrients 1.06 0.81 0.04 0.84 (0.17) (0.14) (0.25) (0.49) X4: Size 0.84 0.27 0.41 0.33 (0.87) (0.29) (0.16) (0.14) X5: Ratio —0.29 —1.63 —0.02 0.01 (1.64) (1.64) (0.17) (0.01) X6: Value 0.44 1.41 0.49 0.06 (0.12) (0.14) (0.10) (0.09) x7: TRC 76.42 40.01 81.91 47.66 (21.41) (26.42) (32.46) (59.91) X8: LR —25.67 —32.58 —36.25 -24.11 (10.53) (13.56) (16.74) (18.41) X9: OR 1.84 3.43 3.35 1.95 (1.03) (1.36) (1.63) (1.64) K10: TR2 —0.73 -l.26 -2.61 —5.79 (0.45) (0.70) (1.32) (14.63) K11: LR2 0.20 0.69 0.90 2.06 (0.20) (0.33) (0.59) (4.86) (12: QR2 —0.02 -0.08 —0.07 ~0.15 (0.02) (0.03) (0.06) (0.40) (13: TT 3.55 —5.86 4.51 —4.73 (6.34) (21.67) (26.09) (5.18) (14: LT 0.27 —0.53 3.88 2.53 (3.34) (7.89) (14.71) (2.10) (15: QT —0.14 0.12 —0.49 —0.26 (0.42) (0.64) (1.37) (0.19) (16: TT2 —0.01 0.05 —0.02 d (0.05) (0.18) (0.18) continued -74- Table 8 continued. I II III IV Explanatory South- Delta South— Western Variables eastern Region western Irrigated Region Region Region x17: LT2 0.001 0.001 —0.03 _—_— (0.03) (0.06) (0.10) X18: 0T2 —0.0001 —0.001 0.003 ———— (0.01) (0.01) (0.01) X19: TRT —1.06 —0.38 -1.59 —0.08 (0.36) (0.45) (0.54) (0.45) X20: LRT 0.34 0.35 0.66 --—— (0.16) (0.21) (0.25) X21: QRT —0.02 —0.03 -0.06 -—-— (0.02) (0.02) (0.02) X22: TRR 0.83 1.38 0.12 3.99 (0.56) (0.96) (1.48) (2.26) X23: LRR -0.48 —l.0 —0.31 —-—- (0.31) (0.58) (0.82) X24: QRR 0.05 0.1 0.05 ____ (0.04) (0.09) (0.09) 2 0.5296 0.5846 0.5609 0.6776 aThis value is the estimated regression coefficient. CTR, LR, QR, TRZ, 0R2. TRT, LRT] QRTI QT in regional model. LR , 2 b . . Standard errors are given in parentheses. 2 2 TT, LT, QT, TT , LT I LRR, and QRR are as defined dIn the Western Irrigated Region, these weather var— iables (TT , 2 LT , QT2 LRT, QRT, dropped from the analysis. e R2 LRR, and QRR) were is the multiple coefficient of determination. -75- were very high compared with those in the Southwestern Region,4 it is not too surprising that fertilizer has had a minor effect on cotton yields in the latter region, but a major effect in the other regions. However, the sizes of the coefficients were smaller than expected. None was more than 1.1. This means that a one pound increase in fertilizer nutrients applied per cotton acre has increased the cotton yields per acre in different cotton regions by about one pound. Moreover, the estimated coefficients for the fertilizer variable were generally smaller than found in other studies, particularly those based on experimental plots.5 However, Johnson and Gustafson in their study of grain yields used technical variables in a way similar to the present study and concluded: To the extent that the regression coeffi— cient estimates are comparable with the results of other studies, particularly those based on experimental plot or field— trial results, the comparisons are generally consistent with what one would expect: the effects estimated here, based on actual average farm experience, are somewhat smaller than those obtained in experiments carried out under more or less ideal conditions. 6 4The average pounds of fertilizer nutrients applied per cotton acre for the whole period of study in the Southeastern, Delta, and Western Regions were 106, 70, and 76 reSpectively, While in the Southwestern were only 27. 5Fulmer and Botts, op. cit. 6Johnson and Gustafson, op. cit., p. 79. —76— The variable of dollars spent on gas and oil (X was 1) statistically significant in the Southwestern and Western Regions with positive coefficients in all regions. The size of the coefficients in the Southwestern Region was large (39.8) compared with those in the other regions (1.6 to 2.6). Man—hours of labor (X2) was significant in all regions except in the Western Region, with positive coeffi- cients in the Southeastern and Delta Regions, and negative coefficients in the other two regions. However, the results for these two variables (X and X2) indicate that mechaniza— 1 tion has been primarily a substitute for labor in cotton production, with positive net effects on yields per acre in most cotton regions. Average size of the cotton enterprise (X4) was statis— tically significant in the Southwestern and Western Regions, and not significant in the other regions. The results for this variable (X4) were quite similar to those obtained for the variable Xl (dollars Spent on gas and oil). Since (X4) was included to measure the effect of a Shift to more special— ized equipment, and (X1) to measure the effect of increased mechanization, and if these are valid, then it appears that the extent of mechanization in cotton production was associated with a shift to more Specialized equipment, and these have positively affected the cotton yields per acre. The coefficients for the ratio of cotton acreages in a year compared with 1939 (X5) were not significant in any -77_ ‘egion, with negative Signs in the Southeastern, Delta, and :outhwestern Regions, and positive in the Western Irrigated Legion. Furthermore, the coefficients of this variable in (11 regions were smaller than expected. None was more than -l.63. Value of land and buildings per acre (X6) was Signifi— :ant in all regions except the Western Region, with positive :oefficients in all regions. On the basis of the signifi- :ant results for this variable in most regional and state (nalyses, it appears that the changes in land values over :ime have had positive relationships with cotton yields in lOSt of the United States Cotton Belt. Weather variables, rainfall in particular, were con— ;istent over different regions. Each of the twelve rain— ?all variables has estimated regression coefficients with :he same Sign in the four different regions.7 The rainfall 'ariables X X X X and X have positive signs, 7' x9' 11' 20' 22' 24 nd the variables X , 8 X10' X12' X19' X 21, and X23 have nega— ive signs in the different regions. Moreover, the results for weather variables as reported n Table 8, have explicitly indicated the seasonal effects f the weather factors on cotton yields. To Show the distribu— ion of these weather effects over the growing season, and 7 . . All rainfall variables X7, . . . , X12, X19, . . . , 24 were defined before as a part of regional model. —78— determine which, if any, weather factor was limiting pro— duction, the individual coefficients for each month of the weather variables8 were derived from the coefficients for weather variables reported in Table 8, and are presented in Table 9. The estimated coefficients for monthly total rainfall variable in different cotton regions indicated that the effects of this variable were most beneficial to cotton yields in the early part of the season. But, these effects of monthly total rainfall were most injurious at the middle of the season, particularly June to September, then came to be slightly damaging or relatively beneficial in November. The Sizes of this variable's coefficients in all regions were larger than expected. For instance, in the South- eastern Region they ranged from —l3.l in September to 52.3 in March. The results of monthly rainfall—temperature interaction were generally similar for different regions. These rain— fall—temperature interactions were slightly injurious to cotton yields at the beginning of the season and changed gradually to be relatively beneficial at the end of the season. In the Delta Region, for example, the coefficient 8Monthly total rainfall, squared monthly total rain— fall, monthly average temperature, squared monthly average temperature, monthly rainfall—temperature interaction, and successive month rainfall interaction. v—‘4 IQ lrn -79- able 9. The Estimated Regression Coefficients for Weather Variables, in Regional Analyses I II III IV eather South- Delta South— Western ariables eastern Region western Irrigated Region Region Region Qtal Rainfall a March 52.3 10.9 49.0 25.5 April 32.4 —11.4 22.8 7.2 May 16.0 —26.9 3.3 —7.1 June 3.2 —35.4 —9.5 —l7.6 July —5.9 ~37.1 -15.6 —24.1 August -11.4 -32.0 —15.0 —26.8 September -13.1 —20.0 —7.7 —25.6 October —11.2 —l.l 6.3 —20.4 November —5.6 24.6 27.0 —11.4 guared Total Rainfall March —0.50 —0.65 —l.80 —3.88 April —0.40 —0.20 —1.10 —2.27 May -0.30 0.09 -0.50 -0.96 June —0.20 0.22 —0.10 0.05 July —0.20 0.19 0.15 0.76 August -0.20 0.00 0.28 1.17 September —0.30 —0.35 0.27 1.28 October —0.40 -0.86 0.12 1.09 ‘November —0.50 —1.53 —0.17 0.60 verage Temperature March 3.7 -6.3 7.9 —2.5 April 3.5 —6.4 10.3 ~-0.7 May 3.1 -6.4 11.7 0.5 June 2.4 —6.1 12.2 1.2 July 1.4 —5.5 11.7 1.4 August 0.1 —4.7 10.2 1.1 September -1.4 —3.7 7.7 0.2 October -3.3 -2.4 4.2 —1.1 November —5.4 —0.9 —0.3 —3.0 Average Temperature March —0.01 0.05 —0.05 b April -0.01 0.05 —0.07 ——— May ~0.01 0.04 -0.08 ——- continued ~80— 1b1e 9 continued I II III IV eather South- Delta South— Western iriables eastern Region western Irrigated Region Region Region 1, Average Temperature (cont.) June —0.01 0.04 —0.09 -—— July —0.01 0.03 —0.10 ——— August —0.01 0.02 —0.09 --- September —0.01 0.01 —0.08 —-— October —0.01 —0.01 —0.07 ——— November -0.0l ~0.02 0.05 -—- ain and Temperature Interaction March —0.74 —0.06 -0.96 —0.08 April -0.46 0.20 —0.44 -0.08 May —O.22 0.40 —0.04 —0.08 June —0.02 0.54 0.24 —0.08 July 0.14 0.62 0.40 —0.08 August 0.26 0.64 0.44 -0.08 September 0.34 0.60 0.36 —0.08 October 0.38 0.50 0.16 —0.08 November 0.38 0.34 -0.16 -0.08 ain Interaction March—April 0.40 0.48 —0.10 3.99 April-May 0.07 —0.22 -0.30 3.99 May-June -0.16 -0.72 —0.40 3.99 June—July -0.29 —1.02 —0.30 3.99 July—August —0.32 —l.12 —0.20 3.99 August—Sept. —0.25 —l.02 0.10 3.99 Sept.~Oct. —0.08 —O.72 0.50 3.99 0ct.—Nov. 0.19 —0.22 0.90 3.99 aThese are the estimated regression coeffi— cients and were obtained by the same procedure mentioned in the last chapter. bIn the Western Irrigated Region, these var— iables were dropped from analysis. -81- for March rainfall-temperature interaction was —0.06 and then changed upward to 0.34 at November. The results for successive month rainfall interaction indicated that these interactions have positively affected cotton yields during the beginning of the season in the Southeastern and Delta Regions, and become negative as the season advances. In the Southwestern Region, the pattern of these effects was the opposite, i.e., these effects were Slightly negative at the beginning of the season and became positive at the end of the season. In the West, the effects of these interactions were positive throughout the whole season. Thus, on the basis of the results for regional analyses, it appears that the results for rainfall variables were generally consistent in the different cotton regions. More— over, the results for temperature variables were relatively consistent from one region to the other, but were not as consistent as the results obtained for the rainfall variables. The coefficients for the monthly average temperature var— iable were negative throughout the whole season in the Delta Region, with large values for the planting period and smaller values at the end of the season. In the Southeast, these coefficients were highly positive at the early part of the season, and then reduced gradually to become negative for September to November. In the Southwestern Region, these effects of monthly average temperature were positive during -82— the whole season with the largest values in June. But, in the Western Region, these coefficients have a different pat- tern. They were relatively negative for March and April (—2.5 and —0.7 reSpectively), then slightly positive during five months, and became negative for October and November. However, the above results for weather variables show the effect of rainfall or temperature variables taken in— dividually, rather than the effect of either all rainfall or all temperature variables. Hence, to Show the effect of rainfall or temperature on cotton yields per acre, the marginal effects of rainfall or temperature in each month of the season were derived from the coefficients reported in Table 9, and are represented in Figures 2 and 3. The marginal effect at the mean for rainfall (or temperature) is the effect of a one—inch increase in rainfall (or a one degree F. increase in temperature) on the cotton yields in pounds per acre. The marginal effects for monthly total rainfall were estimated for each month by the following equation: _%%_ = bl + 2162 (R) +b5 (T) +66 (R“) where AY is the change in cotton yields in pounds per acre b b due to the change in rainfall in inches (11R). 1’ 2, b5 and b6 are the estimated coefficients for monthly rain— fall, squared monthly rainfall, monthly rainfall-temperature Inch Increase In Rainfall On COttOn Yields In Pounds Per Acre The Effect Of A One- -83- Figure 2: The Marginal Effect At The Mean For Monthly Total Rainfall 0n Cotton Yields Per Acre 40« Delta Region 30- Southwestern 20“ Region Southeastern Region 101 0 \\\\\ Western _10__ Irrigated Region -20-. -30 -uo. L l l 5 l ! March April May June July Aug. Sep. Oct. Nov. (Months) Increase In Temperature On The Effect Of A One Degree F. Cotton Yields In Pounds Per Acre -84- Figure 3: The Marginal Effect At The Mean For Monthly Average Temperature 0n Cotton Yields Per Acre Delta Region Western Region Southeastern Region Southwestern Region I L l I J LL 4 L 4 March April May June July Aug. Sep. Oct. Nov. (Months) —85- interaction, and successive month rainfall interaction respectively, as shown in Table 9. ”R is monthly mean rain- fall, T is monthly mean temperature, and R" is the mean rainfall for the preceding and following months10 for the whole period of study. The marginal effects for monthly average temperature were estimated for each month by the following equation: 23; = b3+2b4 (I) +b (R) where AY’iS the change in cotton yields in pounds per acre due to the change in temperature in degrees F. (ZXT). b3, b4, and b5 are the estimated coefficients for monthly tem— perature, squared monthly temperature, and monthly rainfall— temperature interaction respectively, as Shown in Table 9. T-is monthly mean temperature and R is monthly mean rainfall for the whole period of study. b6 for March is actually the estimated coefficient for March-April rainfall interaction, and for November is the estimated coefficient for October—November rainfall interaction as shown in Table 9. But for other months, b6 is the average value of estimated coefficients for that month and following month, i.e., b6 for April, for example, is the average value of estimated coefficients for March- April rainfall interaction and April-May rainfall inter- action. lovR' for March is actually the mean rainfall for March and April, and for November R' is the mean rainfall for October and November. But for other months, R‘ is the mean rainfall for preceding and following months, i.e.,‘R' for April, for example, is the mean rainfall for March and May. -86.. Figure 2 shows that the pattern of the marginal effects for rainfall was generally similar in all non-irrigated regions. These marginal effects for rainfall in March were positive in the Southeastern and Delta Regions and negative in the Southwestern Region, and became negative in all non- irrigated regions during the following two months. In July, these marginal effects for rainfall turned up to become positive in all non—irrigated regions, and increased as the season advanced to have largest values at the end of the season. The marginal effects for rainfall, for example, were 1.9, 11.0, and 11.9 in July in the Southeastern, Delta and Southwestern Regions respectively, and increased grad- ually to be 12.7, 33.2, and 20.3 at the end of the season (November) in the Southeastern, Delta, and Southwestern Regions reSpectively. This means that an increase of one inch in rainfall in the Southeastern Region in July increased the regional average yield per acre by 1.9, while such in- crease in rainfall in November increased the regional aver- age yield by 12.9 pounds. The pattern of the marginal effects for rainfall in the Western Irrigated Region was much different from that in the non—irrigated regions. In the Western Region, the marginal effects for rainfall were most beneficial at the beginning of the season, reduced gradually to become highly negative for July and August and turned up to become relatively negative in November. Figure 3 indicates that the marginal effects for tem— -87— perature on cotton yields were generally similar in the Southeastern, Delta and Western Regions. In these three regions, the marginal effects for temperature were unfavor- able during the planting and harvesting time, and were favorable in the middle of the season with largest values in June. In the Delta Region, for example, the marginal effects for temperature on cotton yields in pounds per acre were -l.2, 2.1, and —2.1 for March, June and November re— spectively. This means that a one degree F. increase in temperature in March or November decreased the regional average yield per cotton acre by 1.2 and 2.1 pounds reSpec- tively, while such an increase in temperature in June in— creased the regional average yield per acre by 2.1 pounds. In the Southwest, the marginal effects for temperature were Slightly positive for March, and reduced gradually to be highly negative at the end of the season. However, to test the significance of the joint effect of either rainfall or temperature variables, the F—test was applied to all regional analyses and the results are reported in Table 10. It should be noted that the set of rainfall variables X and the set 11 21' tested was X7, . . of temperature variables was X 19' ° ' ° ' X24' X ' X12' 13’ ’ ' ' ' 11See Table 8. ( f _88_ Table 10. The F-Test Results Indicating the Significance of Weather Effects on Cotton Yields in Differ— ent Regions Rainfall Temperature Degrees Level Degrees Level Regions of of of of Freedom F Signif— Freedom F Signif— (N1,N2)a Value icance (Nl,N2)a Value icance South— east (12,430) 9.4 .01 (9,43Q). 3.3 .01 Delta (12,370) 6.4 .01 (9,370) 2.1 .03 South— west (12,295) 1.2 .29 (9,295) 4.6 .01 West (8,102) 3.2 .01 (4,102) 0.5 .72 aN is degree of freedom for the numerator of the F—ratio, and N2 is degree of freedom for the denom— inator of the F—ratio. Table 10 shows that the joint effects of rainfall variables on cotton yields were statistically Significant in all regions except in the Southwestern Region, while the joint effects of temperature variables were significant in all regions except in the Western Region. Concluding Points The regression results for technical and economic fac- tors obtained from regional analyses were generally more internally consistent and statistically meaningful in terms of the technical and economic expectations than those ob— tained from state analyses. Moreover, the results for _89_ weather variables, particularly rainfall variables, obtained from regional analyses were consistent from region to region. But, one question concerning the results for technical and economic variables obtained from the regional analyses is that the estimated effects of these explanatory variables on the regional average yield were generally smaller in magnitude than was expected. This might generally be caused by the lack of appropriate data or the poor measure of some of the explanatory variables,12 and the existence of a multi— collinearity problem among some of these variables.13 In this reSpect, Johnson and Gustafson argued that: "It appears likely that much of this inadequacy will be remediable by the future accumulation of more complete and more accurate data. On the other hand, the problems caused by high intercorrelations among some of the explanatory variables are probably to some extent an unavoidable char- . . 14 acteristic of the procedure." 12Particularly the measure of technical variables X3 (fertilizer nutrients) and X2 (man—hours of labor). 13See Appendix D. 14Johnson and Gustafson, 0p. cit., p. 90. CHAPTER VI NATIONAL ANALYSES The prime motivation for the national analyses was the potential improvement of the estimates through taking into account a wider range of variation in the variables as well as the gain in degrees of freedom. At the same time, an economic and policy justification for doing these analyses was to understand better the relationships (between yields and related factors on the national level) so that an appropriate policy can be undertaken. In the national analyses two sets of dummy variables were added. One set was concerned with time and the other was concerned with location of production. Dummy variables for time were used to measure the effect of those factors that changed over time and were not expli- citly considered in the model such as: improvement in seed varieties, production techniques, and insect control. The second set of dummy variables for location was included to measure the effect of shifts in location of production among counties. The value of these dummy variables is either one or zero. A one is used if the observation belongs to the class represented by the variable; otherwise a zero is used. For _90_ _91- example, consider the first dummy variable for location. The value one is assigned to this variable for each county of sub—region 1, while the value zero is assigned to each county of all other sub-regions.l A detailed discussion for the national model is in the following section. National Model The model used for national analyses was as follows: 6 24 28 t = b + Z b.X. t + Z bixict + Z bixict c 0 i=1 1 1C 1:7 1:25 58 Z .X. + 1229 l ict ct C = 1, 2, ..., 258 (counties in each year with a total of 1290 counties for all 5 years of the study). t = 1939, 1944, 1949, 1954, 1959 (years). i = l, 2, ..., 58 (independent variables); and = 1, 2, ..., 6 (technical and economic variables), = 7, 8, ..., 24 (weather variables), = 25, ..., 28 (dummy variables for time), = 29, ..., 58 (dummy variables for location). Economic 1The definition of these sub—regions is in: 19, June sub-regions of the U. S., Series Census— BAE, No. 1953. -92_ b0 (constant term), V (error term), Yc (dependent ct t variable), ., X6ct (technical and economic var- cht’ iables), and X (weather variables) are 7ct’ "" X24ct as defined in the previous chapters. The definition of each of the other independent vari— ables is as follows: X25 2 l for all counties in 1944, and = 0 for all counties in all other years. X26 = l for all counties in 1949, and = 0 for all counties in all other years. X27 = 1 for all counties in 1954, and = O for all counties in all other years. X28 = 1 for all counties in 1959, and = 0 for all other counties. X29 = 1 for counties in subregion l (N.C., county no. 2, 4, 11)2 and = 0 for all other counties. X30 = 1 for counties in subregion 2 (N.C., 5, l3 and S.C., 7, 8, l4), and for all other counties. H O X = l for counties in subregion 3 (N.C., 6, 7, 10, 12, 31 14, 16, 17), and 2See Appendix B. 32 33 34 35 36 37 38 39 for for for for for for for for for for for for for for for for _93_ all other counties. counties in subregion 4 (N.C., 1, 3, 8, 15 and S.C., 5, 9, 17, 18), and all other counties. counties in subregion 5 (S.C., 2, 3, 6, 12, 13, 15, and Ga., 15, 30), and all other counties. 10, counties in subregion 6 (S.C., 4, 11, and Ga., 18), and all other counties. all counties in subregion 7 (S.C., 1, 16, and Ga., 8, 13, 21, 23, 24, 25, 26, 28, and Ala., 5, ll, 19, 24) and all other counties. all counties in subregion 8 (Ga., 1, 5, 10, 11, 12, 19, 29), and all other counties. all counties in subregion 9 (Ga., 2, 4, 14, 16, 17, 27, and Ala., 2, 4, 8, 9, 10, 15, 17), and all other counties. all counties in subregion 10 (Ga., 3, 9, 20, 22, and Ala., 18, 25), and all other counties. counties in subregion 11 (Ala., 1, 6, 14, 20, 23), and -94- = 0 for all other counties. X40 = l for counties in subregion 12 (Ala., 3, 12, 16, 22, 26, and Miss., 6, 20), and = 0 for all other counties. X41 = l for counties in subregion 13 (Ala., 13, 21, Miss., 15, and La., 10), and = 0 for all other counties. X42 = 1 for counties in subregion 14 (Ala., 7, and Miss., 2, 5, 7, 12, 13, 14, 19, 23, 24, 27, 28), and = 0 for all other counties. X43 = l for counties in subregion 15 (Miss., 1, 21, 26, and Tenn., 1, 2, 4, 7, 9, 11), and = 0 for all other counties. X44 : l for counties in subregion 173 (Ark., 9, 17, 18), and = 0 for all other counties. X45 2 1 for counties in subregion 18 (Ark., 1, 3, 7, 8, 10, 11, 13, 15), and = 0 for all other counties. X46 = 1 for counties in subregion 19 (Ark., 5, 6, 14, 16, Miss., 3, 11, 16, 22, 25, Mo., 1, 2, ..., 8, and La., 2, 3, 4, 6, 7, 9, 11, 12, 13), and 3Dummy variable for subregion 16 (Miss., 4, 8, 9, 10,. 17, 18, 29, and Tenn., 3, 5, 6, 8, 10) was dropped to obtain non—singular matrix and allow estimation of parameters built into the model. 47 48 49 50 52 53 54 for for for for for for for for for for for for for for for for -95- all other counties. counties in subregion 20 (La., 1, 11, 18, 29), and all other counties. and E. Tex., counties in subregion 21 (La., 5, 8, Okla., 17, Ark., 2, 4, 12, and E. Tex., l, 4, 6, 7, 8, 19, 22, 24, 27), and all other counties. counties in subregion 22 (Okla., 1, 10, 18), and all other counties. counties in subregion 23 (Okla., 4, 14, 16, 19, and E. Tex., 12, 14, 23, 25), and all other counties. counties in subregion 24 (E. Tex., 9, 13, l6, 17, 21, 28),and all other counties. counties in subregion 25 (E. Tex., 2, 3, 5, 15, 20, 26, 30, 31, 32), and all other counties. counties in subregion 26 (Okla., 2, 5, 7, 8, ll, 12, 13, 15, E. Tex., 10, and W. Tex., 1, 6, 10, 13), and all other counties. counties in subregion 27 (W. Tex., 4, 9, 12), and ~96- : 0 for all other counties. X55 = 1 for counties in subregion 28 (Okla., 3, 6, 9, and W. Tex., 2, 3, 5, 8, 11), and = 0 for all other counties. X56 = 1 for counties in subregion 29 (N. Mex., 1, 2, 11, 8, and W. Tex., 7), and = 0 for all other counties. X57 = l for counties in subregion 30 (Ariz., 1, 2, ..., 8, and Calif., 2), and = 0 for all other counties. X58 = 1 for counties in subregion 31 (Ca1if., 1, 3, 4, ..., 8), and = 0 for all other counties. The results from applying the above model for all 258 counties included in this study4 are reported in Table 11. The results for each group of technical and economic, weather, time, and location factors will be discussed respectively in the following four sections. Results for Technical and Economic Factors Table 11 indicates that the technical and economic factors Xl (dollars Spent on gas and oil per acre), X2 (man— 4The total number of observations for the whole period Of five census years was 1290. N213". N con-woos some” mmmmd SM..- nomx “MWM.WV xeam.amo Akae.6v Amee.sv was .osx .am . - . mmh.ofia H easemeog . N meoo H see .eHx emm.o me new Amee.ev, An . OHH-Ndv . . g a NW qu A $643 $3 .wux 38 o «so .mHN mean-s7 me new . Amue.ev Ace-.emv “www.mmV «mag “sax HmHe.eu was "New mma.mm as "Rx . Ammo.ov Aoao.eo Awmm.wmw Seas Nome meme.o Nee ”sax mam.o was”; "ex Amwe.eo name.oe Amwm.mwv .ma Nk~.o( ea ”max Hee.ea edema “he mwhomm -V.-N@H . um . . Aeea.o- Ameo.ev ea Awmw.mV ea Mess mmm.e wugm Mex NoH.e axe . x -/_ AHfiWowv AN-NMMaOV on e Ammm.eo .mam mme.mu ea .msx mmn.o meeeeeuaz . x . mas . see on Aaamuev Ammodv mo “3N $6.0 mun-031542 ”NM Amam.e- may ”New emoo.o N flee.H ense6.0o .Hx Semi a L:- 683 36.666 . ANNe.ev See “Ham muse.o- N meme.en mugmwfiowflmmmoo mquwflHmp . meme.“ eemmmoo mes assume. so..." 30%” shoe-waged 353.-“308 6.28.». sesame.“ 0m smegma-3%.."- seesaw floammwuwmm mean. . “scum-Enema seeeaeemm Rheeeeefiexm n M g m 0%“ figuwuouv NMH mmmgwno “We mgmkmmmfiC _mggfiwmz MO“ m9 ngmmm gOWmmwnHmm m m — m—flm.u.u @H a .mwmwguceyw .-wmusmwuwwmaoo scam A as awpww was muouuo mwhwwu fiwu- um thvfldum Ammo.wmv W mfiu 0H“ 0m0£B A d mHN.wHH: mu dowuqooq nomN Ammnnsev Aeamnwkv a sea. NH sausages .eex gas as. «N massages "sex Ammwnmev Aos~.ekv Amma.mev m 4H easeaoog .mnx ms¢.Nq~ Hm sowumeou “wmx Nam.wno Hm gownsooq “new Awww.oev 8.8.me 8363 .8. S 8333 “mmx 5.63 8 8383 he Sam... em 803...- RS. $363 0.3 mmu a defiuwuou ”hmx x-k.mn- em Aeno.mmv Ages. o eafl.ems an eoseeeoq . x Nem.ees as eageeoos .eex oae.wm- w Seausuoq “omx _ Amoe.meo xksm.mev flew . 8 o n. ”mm s n. o . N NMV 6., RR R a eon-82 a. 84 a 2 8033- .30- 33? R ...-0.8.- .3. Amee.mko Aaem.eev name.oeo omdod-Hu AN flowumuon ndmx omo.mon NH dowumooq ”...-1d” ammo-um... o dowwmooa ....dmN Amefl.amo sen.mmv . Anew.NeV n¢m.nmfin mm assessoq “mmN «mo.smn ma Sofiewuoa "Mex oow.wou m sowusoou “mmx . Anoe.ka New.neo nfimm.wwwu mu eoseaooa .me kee.mm- es messages ”Nee kmm.ema e aceugooe .me . 826$ m .amv Amww hmv . . a . ”Hm Awmw.mNH- em eoeueeoa Meme wae.m m- schemeos .Hex emm as m nouumooa x megeueemmuoe munwwuwmmuou mumwwwwwwwmm mmflamwum> scammwumwm mmHnmwum> sowmmmouwcm meanmwwmp H auoussmamxm pmumswunm hueewswfimxm emeesHemm sueummmHeRm emSSSAQmm Augmdwudouv .HH 0.3-NH. -99- hours of labor per cotton acre), X3 (pounds of fertilizer nutrients applied per cotton acre), X (average size of 4 cotton enterprise in acres), and X6 (value of land and buildings per acre) have positive relations with cotton yields per acre. Meanwhile, the effect of X5 (ratio of cotton acreage in a year to that in 1939) was virtually zero. National average cotton yield per acre has substan— tially increased over the period of study (1939-59). A word of caution should be added, particularly in the inter— pretation the positive relationship between the different technology factors and cotton yields. This positive rela— tionship does not necessarily mean that the increase in the levels of those factors over time has increased the cotton yields, but it might also mean that a decrease in the level of some factor of these has decreased——by itself-— the yields. The extent of mechanization, more use of fertilizer nutrients, larger size of cotton farm, and increase in values of land over the period of study are associated with increased cotton yields per acre. The factor X , man—hours of labor 2 per cotton acre, has decreased, while the effect of X a 6’ decrease in the ratio of cotton acreage in a year to that in year 1939, was virtually zero. More Specifically, the estimated regression coefficients, as shown in Table 11, indicate that an increase of one dollar —100— Spent on gas and oil per acre (over average) has increased the yields by about 1.6 pounds, while a decrease of each one man—hour of labor per acre has decreased such yields by about 0.7 pound. This implies that mechanization has been primarily just a substitute for labor in cotton pro— duction, with positive net effects on the yields. In other words, a substitution of mechanization (as measured by dol— lars spent on gas and oil) for labor has increased the yields. Also, the use of an additional pound of fertilizer nutri— ents per acre (above average) has increased the yields by 0.6 pound. A one acre increase in the average Size of a cotton farm increased the yields by 0.5 pound. And, an increase of one dollar in values of land per acre is asso— ciated with a positive yield increase of 0.3 pound. This increase in the yields related to the increase in values of land seems quite meaningful in terms of the economic expecta— tions. The traditional economic theory argues that an in— crease or decrease in yields and economic value will be capitalized into higher or lower land values. In general, the above results seem meaningful in terms of the economic and technical expectations. Even so, these results for different technical and economic factors and particularly for X1 (dollars spent on gas and oil), and X3 (pounds of fertilizer nutrients) provide estimated co- efficients smaller than expected. This may result from high correlation between each of these Xl (gas and oil), —101- X3 (fertilizer) and the time factors (X25, ..., X28). However, Table 11 indicates that the estimated regres— sion coefficients for most technical and economic factors were large relative to their standard errors. For Xl (gas and oil), X (fertilizer), X4 (farm size), and X6 (land 3 value) the estimated coefficients were Significantly dif— ferent from zero at less than the 10 percent level. But, (labor) or X (ratio) were not sta— the coefficients for X 5 2 tistically Significant. In the last section of this chapter, the relative im— portance of each of these factors in explaining national average yield will be discussed in detail. Results for Weather Factors In the national model, the weather factors (X7, ..., X24) were used in such a way as to be equivalent to forcing the regression coefficients over the whole growing season (nine months) for each set of original factors6 to fit a quadratic function of time. However, these regression co— efficients only indicate the effect of different weather 5The Significance levels for the coefficients for X2 (labor) and X5 (ratio) were .19 and .94, reSpectively. 6Monthly total rainfall, squared total rainfall, monthly average temperature, squared average temperature, monthly rainfall-temperature interaction, and successive month rain— fall interaction. —102— factors on the yields over the entire growing season; they do not explicitly Show the distribution of these weather factor effects within the season. Hence, the individual coefficients for each month of these original weather fac- tors were derived from the coefficients reported in Table 11, and are listed in Table 12. The estimated regression coefficients for monthly total rainfall variable, as shown in Table 12, indicate that the increase in rainfall above average was most beneficial to cotton yields in the early part of the season. Then, as the season advanced, the effects of an increase in rainfall above average became less and less to become relatively in— jurious late in the season. Concerning the monthly average temperature variable, their estimated coefficients indicate that an increase in temperature over the average in the early and late parts of the season have unfavorably affected yields. During the middle of the season, that is, May through August, a higher temperature favorably affected yields. Table 12 also shows that the effect of rainfall—tem- perature interaction was negative at the beginning of the season and changed gradually to be slightly positive in August and September, then turned down to become Slightly negative. The estimated coefficients for successive month rain— fall interactions, as listed in Table 12, indicate that —103— .ucmfloflmmmoo coflmmoumms Umpmfiflumm one mH wages 000.0 emQEm>oz 000.0- sesam>oz e00.0 quEm>oz|.noo 040.0 senoooo 000.0: “090000 000.0- hmnouoou.udmm 000.0 sesamummm mm0.0( senseodmm Hee.0u u0n50000010m000< N00.0 “memes 000.0- seemss 0me.0- emsmsausssn m00.0- ssee 000.0- whee 00k.0u xsseumeee m00.0| 00:0 mm0.0u 0000 000.0- 00:0-sm2 H00.0 s62 N00.0 s62 0km.0- smzaseema 000.0 sheds em0.0 Hesse 0km.0 Hahdaleoumz 0H0.0 roses 000.0 some: AQOHpomswch Aaamwsflmm Hammsflmmv -.QEmB .>< .qm- H0008 pmnmsvm- va.OI HmQEm>oZ own.MI quEmboz moo.ai HmQEm>OZ omo.01 nmnouoo mmn.al Honouoo mom.mu HmQODUO Nmo.o Mmflfiwbmwm ¢¢M.OI HmQEmummm hHN.NI uoflfimpmmm Hwo.o um5m5< Hom.o Dmsms< neo.o Dmsms< 000.0- sass NN0.0 >400 00m.e sage 000.0: wasp mmn.o mch Hov.oH mash 000.0: >02 NH0.0 >62 Hme.0s s62 mes.o| Hflum< mmm.-I Hands mnm.mm HHHQ< mom.ou zona: eno.ml some: smm.oe Scum: AQOHDUMHmDQH .mEmBIHHmeHmm- AmnsbmnmmEmB .> Hmfipmmz m-Qv mmaflmenm> Hmflumwz MAQ- mmHQMSMm> Hmcbmmz mmHQMHHm> Hmfipmwz SHLDCOZ How mucmeuammmoo coewmmhmmm pmumEflpmm 039 .ms msnee —104— these interactions negatively affected yields at the begin— ning of the season, became less important as the season advanced, and turned positive in November. The above results for weather variables show the effect of individual rainfall or temperature variables rather than the effect of rainfall or temperature as a whole on the national yields. To Show the effect of rainfall or tempera— ture in general on the national yields, the marginal effects for rainfall and temperature in each month of the season were derived from the coefficients listed in Table 12, and are reported in Table 13. These marginal effects for either rainfall or temperature were estimated as defined in the previous chapter. The marginal effects for rainfall were most beneficial for the first month of the season (March) and slightly beneficial throughout June to August. But these marginal effects for rainfall were injurious during April—May and October—November. The marginal effects for temperature unfavorably affected yields during the planting and harvesting time, and favorably affected yields in the middle, i.e., during the period of late vegetative growth and the early part of fruiting growth. To test the significance of the joint effect of rain— fall or temperature variables on the national average yield, the Futest was used. The results for the F—test indicated that the joint effect of rainfall variables was statisti— cally Significant, while the joint effect of temperature -105— Table 13. The Marginal Effects at the Mean for Monthly Total Rainfall and Monthly Average Temperature Marginal Effects Marginal Effects Months for Rainfall a for Temperatureb March 1.9 —4.2 April -0.2 -2.2 May -l.9 —l.3 June 0.4 0.1 July 1.0 0.7 August 0.9 1.1 September 0.6 1.0 October —3.6 0.4 November -7.3 —0.9 aThese are the effects of a one-inch increase in rain— fall on cotton yields in pounds per acre. These effects were estimated for each month by the following equation: (in) ..AX- : b +2b2(R)+b (T)+b 13R 1 6 5 where [KY is the change in cotton yields in pounds per acre due to the change in rainfall in inches (11R). b1 and b6 are the estimated coefficients for monthly lrainfall, squared monthly rainfall, monthly rainfall— —temperature inter- action, and successive month rainfall interaction reSpect— ively, as shown in Table 12. R’is _monthly mean rainfall, T is monthly mean temperature and R8 is the mean rainfall for the preceding and following months for the whole period of study. bThese are the effects of a one degree F. increase in temperature on cotton yields in pounds per acre. These effects were estimated for each month by the following equa- tion: AX- : b +2b (T)+b (R) AT 3 4 5 where (KY is the change in cotton yields in pounds per acre due to the changes in temperature in degrees F. (ZlT). b3, b4, and b5 are the estimated coefficients for monthly tem— perature, squared monthly temperature, and monthly rainfall- temperature interaction respectively, as shown in Table 12. T'is monthly mean temperature, and R is monthly mean rainfall for the whole period of study. -106— variables was not significant. However, it seems interesting to Show not only how each of the mentioned weather factors has affected yields, but also how much of the change in yields was attributable to changes in weather as a whole over the period of study. Therefore, the net effect of changes in weather conditions as a whole on the national average yield over time was cal— culated and will be discussed in detail in the last section of this chapter. Results for Time Factors As mentioned, the four dummy variables for time (X25, ... , X28) were used to measure the effect of changes in time—related factors. In other words, these dummy variables were included to measure the effect of those factors which presumably affected yields over time and were not explicitly included in the analyses. These factors include improvement in seed varieties, production techniques, and insect control. Moreover, these dummy variables for time may also pick up 7The set of rainfall variables tested was X , ..., X12, X19, ..., X24, and the set of temperature variab es was X13, ..., X21, as shown in Table 11. The degrees of freedom for numerator (N1) and denominator (N2) of the F—ratio for testing rainfall variables were 12 and 1231, reSpectively, and the F—value and Significance level (CK) obtained were 2.027 and 0.02, reSpectively, while for the testing tempera- ture variables, N1 = 9, N2 = 1231, the F—value = 1.193 and ( mo .mmmmuo¢ Dumm Ho “Comm w mo lumm msHm> .COHHUDUOHH Ugo msmcmo mbwbm .OZ HMDOB COHHOO .Ho> .m.D "How HmQESZ mHQMB WHQSOO .HHO was mmw Co ucmmm mHmHHOQ paw .mHODOMHB Ho HmHESZ .UCMH Ho wsHm> .mEHmm "H14 OHQME —150— I! "How Hmbfisz wHHMB hussoo ostHusoo . . . 0 o H H HH SH.H mmmH o m H H m 0H.H emmH m m H H m 0H.H memH m H H H m oH.H eemH HMSOm OH oH H H 0 m .H mmmH ImH2.m h o H H HH mm.H mmmH o m H H m HN.H emmH n o H H m HN.H mva m H H H m Hm.H eemH oH oH H H 0 v .H mmmH mEmbmH¢.¢ n o H H HH mm.H mmmH o m H H m BH.H emmH H.Hcoo- m m H H m RH.H memH mamnowo.m HHO paw muou mmuod UCMH mfinmm .OZ .moz .um< wow so IUMHB Umbmm> Ho .mmmmnod unmm Ho ucmmm w Ho (mom msHm> .GOHHUSUOHH Ugo mSmcmO mumum .OZ Hmuoe couuoo .Ho> .m.D HUCSCHHCOOV HI< GHHMB -151- TH UmSCHucoo . . . m m H H m mm.H mva m H H H m NN.H vemH Hmflflm OH OH H H n v .H mmmH ImHmmH2.m 0 O H H HH Hm.H mmmH O m H H m ON.H emmH m m H H m ON.H @00H m H H H N Om.H eemH mom OH OH H H 0 v .H mmmH Immacmfi.h n O H H HH em.H mmmH o m H H m mm.H emmH m m H H m mm.H memH m H H H m mm.H eva mmm OH OH H H 0 m .H mmmH ICMHH¢.O HHO one much mmnoé UCMH mfinmm .oZ .moz .umé wow so IUMHB Umumm> Ho .mmmmuod unmm Ho bsmmm w Ho (Hem msHm> .COHHUSUOHH paw mamcmo mumwm .OZ Hmuoa GOuHOO .Ho> .m.D "How umbfisz mHHma NHCSOO - HUOSCHHQOOV Hid OHHME —152- OOSCHHCOU . . . "How Hmbfisz mema Hussou n O H H HH Om.H mmmH O m H H m mm.H wmmH m m H H m mm.H mme m H H H m mm.H eemH 0803 OH OH H H n m .H mmmH IMHHO.OH B O H H HH mm.H mmmH O m H H O em.H emmH m m H H m em.H msmH m H H H m em.H eme mam OH OH H H 0 m .H mmmH (HmHSOH.O a 0 H H HH mm.H 000H -.Heoo- HQmHm O m H H m NN.H emmH ImHmmH2.m HHO paw mHOH mmnud OcmH mfinmm .oz .moz .um4 new so Josue Omumm> mo .mmmmuo< unmm Ho Hammm w Ho (Ham msHm> .COHHCSOOHH one mSmcmO mbmum .oZ Hmuos conuoo .Ho> .m.b HUOSCHHCOUV HI< meme ~153— UOSCHHCOU . . . m H H H m Hm.H eemH mcom OH OH H H 0 O .H mmmH (Hum.MH 0 O H H HH Om.H OmmH O m H H m Om.H emmH m m H H m Om.H memH m H H H N Om.H vemH OUwaz OH OH H H n O .H mmmH 3mZ.mH n O H H HH bm.H mmmH O m H H m ON.H emmH m m H H m ON.H mme w H H H m ON.H sva OH OH H H m m .H mmmH msXOEHH HHO was mHoH mmsod UCMH mfiumm .oz .moz .umd new so (COMB Umumm> Ho .mmmmuo< unmm Ho Dcmmm O HO lumm msHm> .COHHUSUOHH Ugo mSmcmO mpmum .oz Honoe COHHOO .Ho> .m.D “How HmbESz memB hassou HUOSCHHCOOV Hid mHHmB ~154— .memHHm>m DOC spams k 0 H H HH mw.H mmmH O m H H m mm.H emmH m m H H m mm.H meOH m H H H N mm.H vemH MHcHOH OH OH H H n O .H mmmH (HHmU.eH e O H H HH me.H mmmH O m H H m Hm.H vmmH -.Hcoo- mcom m m H H m Hm.H mva IHHQ.MH HHO mucm WHOU. mmHUHHN USN-H mEHmm oOZ owoz onag i mmw so (owns Omumm> Ho .mmmmno< bums Ho ucmmm O HO (Hem o5H6> .QOHHUSUOHH one mamcwo abmum .oz Hmuoe GOHDOO .Ho> .m.D "How HmHESZ mHHmB kbsdoo (Ill HOOSCHHCOUV H14 OHHMB -155— supplies were obtained from U.S.D.A. Stat. Bul— letin No. 319 (1962) and are listed in Table A—2. Table A-2: Index of Average Prices Paid by Farmers for Motor Supplies a Index of Average Prices Paid by Years Farmers for Motor Supplies, 1910—14 = 100 1939 102 1944 115 1949 146 1954 162 1959 173 aSource: U.S-D.A. Stat. Bul. No. 319, 1962. As shown in Table A—1, the data for this var— iable were not available on either county or state level in 1944. However, the data for this variable on the national level have indicated that of the total change in dollars (current) spent on gas and oil over 1939—49, 22.93 percent have occurred by 1944.1 By assuming that the change in dollars (current) Spent on gas and lU,s,D,A., ERS, Farm Income Situation, Table l7—H, p. 53, July, 1964. —156— oil in each county has changed in proportion to the change at the national level, then dollars (current) Spent on gas and oil in a county for 1944 were estimated as follows: the dollars (current) Spent on gas and oil in a county plus .2293 times the change in dollars (current) Spent on gas and oil over 1939—49 in that county. Man—Hours of Labor Used Per Cotton Acre: The state average of pre—harvest and harvest man work units used per cotton acre was the value used for this variable, Since the county average was not available. However, the data for this variable were obtained from the following sources: For 1939: M. R. Cooper, W. C. Holley, H. W. Hawthorne, and R. S. Washburn, Labor Reguirements for CrOpS and Livestock, U.S.D.A., Agrl. Econ., F.M. 40 (processed, 1943). For 1949: R. W. Hecht and K. R. Vice, Labor Used for Field CrOps, U.S.D.A., Stat. Bul. No. 144, 1954. For 1959: Labor Used to Produce Field CrOpS, Estimates by States, U.S.D.A. Stat. Bul. No. 346, May, 1964. Since the data for this variable for 1944 and -157— 1954 were not available, then the average of 1939—49 was used for 1944, and the average of 1949—59 was used for 1954. Pounds of Fertilizer Nutrients Applied per Cotton safe: 1 The state average of fertilizer nutrients in pounds was the values used for this variable, Since such data were not available on a county basis. However, the data for this variable were obtained from the following sources: For 1949: Fertilizer Use and Crgp Yields in the U. S., 1950 Estimates, U.S.D.A. Agrl. Handbook No. 68. For 1954: Fertilizer Used on Crops and Pastures in the U. S.: 1954 Estimates, U.S.DOA., Stat. Bul. No. 216, 1957. For 1959: Commercial Fertilizer Used on Crops and Pasture in the U.S.: 1959 Estimates, U.S.D.A., Stat. Bul. No. 348, 1964. Since the data for this variable in 1939 and 1944 were not available, then the estimation method for obtaining these data can be summarized as follows: -158- Let the pounds of nutrients per cotton acre in state s in year 1949 = Ns,49. And the pounds of fertilizer per cotton acre in state S in year 1949 = Fs,49. Then, the ratio of N 49 . F§4-. gives the pounds of nutrients per s,49 pound of fertilizer as used on cotton in 1949. Let the ratio of pounds of nutrients per pound of all fertilizer in state s in 1939 -N N “ XEIEEI' and in 1949 = Xgéég—a S,39 s,49 By assuming that in each state, the change in pounds of nutrients per pound of cotton fertilizer was proportional to the change in pounds of nutrients per pound of all fer- tilizer over the period of 1939—49, i.e., Ns,49 Ns,49 Fs,49 AFs,49 Ns,39 N5,39 Fs,39 AF5,39 N5,39 F N . AFs,39 F049 31:14.2. AFs,49 —159— 4. And by the same procedure in case of 1944, then Ns,44 AF 5,44 Ns,49 F 5149 NS,49 AFs,49 5,44 = Fs,44 - Average Size of Cotton Entepprise in Acres: These values were obtained by taking the ratio of total number of cotton acres in a county to the total number of farms harvesting cotton in that county. The sources of data for cotton acres and number of farms are as shown in Table A—l. Ratio of Cotton Acreage in a Year to that in 1939: The total acres of cotton harvested in a partic— ular year in a county to that in the base year (1939) in that county were the values used for this variable. Value of Land and Buildings per Acre: The values of land and buildings per acre (in current dollars) were obtained as reported in the U. S. Census of Agriculture. And then, these values were deflated by the consumer price index. The data for consumer price index were obtained from Business Statistics, 1961 Biennial Edition —l60- of the U.S.D. of Labor, Bureau of Labor Statis— tics, and are listed in Table A—3. Table A—3: Consumer Price Indexa Consumer Price Index years (1947-49 = 100) 1939 59.4 1944 75.2 1949 101.8 1954 114.8 1959 124.6 aSource: Business Statistics, 1961 Biennial Edition of U.S.D.L., Bureau of Labor Statistics. g. Number of Tractorsyper 1000 Acres of Harvested CrOpland: The values for this variable were obtained by taking the ratio of total number of tractors in a county to 1000 acres of harvested crOpland. The sources of data for total number of tractors and acres of harvested cropland are as shown in Table A—1. h. Proportion of Cotton Acreage Irrigated: The values for this variable were obtained by taking the ratio of cotton acreage irrigated in —l6l— a county to the total cotton acreage in that county. The sources of data on cotton acreage irrigated are reported in Table A—4. As Shown in Table A—4, the data for cotton acreage irrigated in 1944 by counties were not available. However, state totals of irrigated land were obtained from the 1949 U. S. Census of Agriculture, Vol. 1, Parts 30 for New Mexico, 31 for Arizona, and 33 for California. By assum— ing that the change in cotton acreage irrigated in each county had changed in the same propor— tion as the change in total acreage irrigated in the state, estimated cotton acreage irrigated in 1944 for a county was obtained as follows: 1. Let total acreage irrigated in 1939, 1944, and 1949 for the state = 5,39 , s,44 , and Is,49 reSpectively. And let cotton acre— age irrigated in 1939, 1944, and 1949 for the county = Ic,39 , Ic,44 , and Ic,49 re— spectively. 2. Let Is,49 — I5,39 = w and Is,44 — Is,39 = z. 3. Then, on the basis of the above assumption: I 0,44 = I0,39 + (z/w) - (10,49 — I0,39). -162— .memHHm>m Doc mummm mHH Ow mHH ma mHH Nd H mmmH mm mm 60 Hm 00 0.6. H 30H mm mm H mm Hm H mm Om H mva 6 mm H 6 H0 H ... 0m H 30H OH O H OH O H OH O H mmmH .OZ OHQMB .02 .02 .OZ OHQMB .02 .02 .OZ OHQME .02 .OZ MOM .Hm¢ Hucsoo Humm .Ho> Hucsoo Hnmm .Ho> bucsoo unmm .Ho> mo mam MHGHOHHHMO MCONHHm OUHXOS 302 (s00 .m D OOHOOHHHH mmmmnod Couuoo no spam mo mmuusom "elm 0Hbme ~163- i. Percentage of Cropland Harvested in Cotton: The values of this variable were obtained by taking the ratio of cotton acreage in a county to total cropland harvested in that county and multiplying this ratio by 100. The sources of data on cotton acreage and crOpland acres are Shown in Table A—1. j. Prices of Cotton for Previous Season: The values of this variable were obtained as reported in U.S.D.A., Agriculture Statistics, 1941, 1946, 1951, 1956, and 1961. Weather Variables: The data for monthly total rainfall in inches and monthly average temperature in degrees of F. for selected weather stations were obtained from: .913: matological Data, by States, by Months, Weather Bureau, U. S. Commerce Department, 1939, 1944, 1949, 1954, and 1959. The weather stations were selected according to the following criteria: 1. If there were more than one weather station in a county reporting rainfall and tempera— ture, then the one at or near the center was selected for use in this study. 2. If there was only one weather station in a -l64— county, then it was selected. If there was none in a county, then the nearest weather station to that county was selected. possHucoo.... I 1---; . i. . L L eoueHHo souaHHo souaHHo m N sousHHO m m eousHHo Seesaw .eH NOHHme MOMHHOH. 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