~ («vegan 537 OCT 0 199‘ M03 9‘49 ‘ '71 C 01‘ UUN172001 212-1 Opfffilq Q3135 ABSTRACT DEMAND ANALYSIS FOR COMMERCIAL FERTILIZER IN THE UNITED STATES, BY STATES by Eldon A. Reiling One of the major factors explaining productivity of American agriculture is the use of commercial fertilizer. Yet, the economic and noneconomic variables related to the level of fertilizer use are little understood. The purpose of this study was to relate and measure the effects of these variables on fertilizer use. Models were constructed for each of the principle fertilizer nutrients — nitrogen, phOSphate and potash. The annual quantity of each nutrient applied per acre of cropland in each of the MS continental states was the variable to be explained. Explanatory variables included the "real" price of the nutrient, "real" prices of the most important fertilizer consuming crops in the preceding year, average "real" farm income from the preceding year, a proxy vari- able for technological change and farmers' awareness of fertilizer reSponse, and a proxy variable for differences among states in fertilizer productivity and other factors. The basic data were both time-series and cross-section in nature. They represented the fifteen year period 1950 through 1964 with obser- vations on each state giving a total of 720 observations. The estimated model is a typical covariance model fitted with least squares procedures. A major effort was made to develop state indexes of nutrient Eldon A. Reiling price for nitrogen and phOSphate. Five alternative methods for con- structing the indexes were considered and the resulting indexes are included and evaluated in the study. The major conclusions of the study are: 1. The fertilizer nutrient price is an important factor in explaining the increased fertilizer consumption. Potash and nitrogen price - both lower over the period studied - explain more than 20 percent of the increase in nutrient consumption. 2. Net farm income as a variable representing the firm's expenditure restriction is a restrictive factor in all models. Easing of this restriction increases expenditures for all three nutrients. 3. Technological change and increased acceptance of fertilizer by farmers is the most important consideration in explaining increased consumption of nitrogen, phOSphate and potash. But the economic variables are relatively more important in explaining increased nitrogen consumption. U. To demonstrate the use of the models for state estimates, projections for Michigan were made. By 1980, it is estimated that Michigan will be consuming 187,000 tons of nitrogen, 172,000 tons of phOSphate and 167,000 tons of potash annually. 5. After considering five basic price index constructions for nitrogen and phOSphate on theoretical and empirical grounds, the chain indexes were selected for use in the nutrient models. The estimated state nutrient indexes warn against generalizations about fertilizer price from the aggregate index. For although the aggregate index is relatively stable. the aggregate is currently made up of two diverging elements and one stable element. 6. A variation of the usual coefficient of determination, R2, j Eldon A. Reiling is suggested as an improved measure of multicollinearity. Each major predetermined variable is regressed on the remaining predetermined variables. This measure identifies which variables are collinear and is independent of the matrix size. 7. The Durbin-Watson statistic and the VonNeumann—Hart ratio do not provide a sufficient test for serial correlation for models combining time-series and cross—section data. Depending upon the way the data are arranged for the problem, the test refers to either the successive differences over time or successive differences between elements of the cross—section. Both tests are necessary but may still not be sufficient. DEMAND ANALYSIS FOR COMMERCIAL FERTILIZER IN THE UNITED STATES, BY STATES By Eldon Alvin Reiling A THESIS Submitted to‘ Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1966 ACKNOWLEDGMENTS The author's progress and development during his graduate training at Michigan State University was influenced by numerous individuals. Professor Lester V. Manderscheid, chairman of the guidance committee, provided stimulating leadership at all stages of the program, eSpecially during the thesis research phase. The method of measuring the relative importance of variables in a regression equation was first suggested by Dr. Manderscheid. And many other concepts and interpretations found in the thesis result, no doubt, from ideas gained during discussions. The guidance committee included, in addition to Dr. Manderscheid, Drs. John Brake, Boris Pesek, Roland Robinson and James Stapleton. Dr. Brake read a preliminary draft of the thesis and his comments added substantially to the final product. The other committee members read the final draft of the thesis and provided useful comments and additions. The author is indebted to William Ruble and Laura Flanders for their conscientious assistance in computer programming and the efforts necessary to prepare problems for the computer. Appreciation is expressed to the Department of Agricultural Economics, Dr. Lawrence L. Boger, Chairman, and the United States Department of Agriculture for the financial assistance without which this study would have been impossible. Finally, the author would like to acknowledge the important ‘contribution of his wife, Charlene, and children whose patience, understanding and moral support helped the author over the many obstacles associated with graduate study. ‘ ii TABLE OF CONTENTS ACKNOWLEDGMENTS . . . . . . LIST OF TABLES C O O O O 0 LIST OF ILLUSTRATIONS . . . . LIST OF APPENDICES . . . . . Chapter I. INTRODUCTION . . . . The Problem Setting . Objectives . . . . Method . . . . . Review of Literature Organization of the Study II. THE ECONOMIC MODEL . . Introduction . . . Preliminary Structure Variables of the General Demand 'Specification Considerations . The General Model . Equation ‘0 O O O O O O O O C III. INDEXES OF PRICES PAID FOR FERTILIZER NUTRIENTS Introduction . . . Part I . . . . . Part II . . . . . Price Data . . . Quantity Data . . Estimated-Indexes Results of the Indexes . o o o _, o o Implicatibns for Fertilizer 1 Summary . . . . . iii 0 O O O O O O O O O O O C O O O O O O O O O O O 0 Price Indexes Page ii Vii viii H \O-F‘MJKDH 10 10 10 15 22 28 34 34 M M 42 “3 us ' 50 53 Chapter IV. V. VI. QUANTITATIVE RESULTS . . . . . . Introduction . . . . . . . . Selection of the Nutrient Models . Nitrogen Model . . . . . . . PhOSphate Model . . . . . . . Potash Model . . . . . . . . Some Problems Common to All utrient Mode A Comparison of the Three Models . Summary . . . . . . . . . . APPLICATION OF THE MODELS . . . . . Introduction . . . . . . . . Projections . . . . . . . . Summary . . . . . . . . . . SUMMARY, RECOMMENDATIONS AND CONCLUSIONS Summary . . Problem . . . . . . . . . Method . . . . . . . . . Results . . . . . . . . . Recommendations . . . . . . . Conclusions . BIBLIOGRAPHY O O C C C O 0 O 0 iv 0 O O O O O ooHoooo. S Page 10. 11. 12. 13. 14. 15. LIST OF TABLES Price index of available P O - United States . 2 5 Price index of nitrogen - United States . Annual changes in nitrogen indexes - United States Index of nitrogen and phosphate price in 1962, by region 0 O O O O O O I 0 Index of fertilizer price - United States, 1950-64 Estimated regression coefficients of nutrient price variables and net income variable - Model N-l Estimated regression coefficients of crop price variables - Model N-1 . . . . Estimated regression coefficients OD state constants for #8 states - Model N-l Estimated regression coefficients of time constants for the years 1951 through 1964 . Evaluation of the contribution attributable to sets of variables - Model N-1 and Model N-3 A method of measuring the importance of variables in the estimating equation . Percent of the change in nitrogen consumption between 1950 and 1964 explained by the economic variables and time - Model N-1 . Estimated regression coefficients of phOSphate price variables and the net income variable - MOdel P-l o o o o o o o 0 Estimated regression coefficients of crop price variables — Model P-1 . . . . Estimated regression coefficients of state constants for U8 states - Model P—l 9 O G Page W 48 “9 51 52 61 65 68 7O 73 75 79 81 82 Table 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. Page Estimated regression coefficients of time constants for the years 1951 through 1964 - Model P-1 . . . 84 Evaluation of the contribution attributable to sets of variables --Model P-1 and Model P-3 . . . . 85 Percent of the change in phOSphate consumption between 1950 and 1964 explained by the economic variables and time - Model P-1 . . . . . . . 86 Estimated regression coefficients of potash price variables and the net income variable - Model K-1 . 90 Estimated regression coefficients of crop price variables - Model K-l . . . . . . . . . . 91 Estimated regression coefficients of state constants for 48 states - Model K-l . . . . . . . . . 92 Estimated regression coefficients of time constants for the years 1951 through 1964 - Model K-1 . . . 94 Evaluation of the contribution attributable to sets of variables - Model K-l and Model K-3 . . . . 95 Percent of the change in potash consumption between 1950 and 1964 explained by the economic variables and time - Model K-1 . . . . . . . . . . 96 The coefficient of multiple correlation as a measure of multicollinearity . . . . . . . . . . 99 Price elasticities of primary plant nutrients by states, computed at the mean . . . . . . . . 104 Projection table: nitrogen . . . . . . . . . 112 Projection table: phosphate . . . . . . . . . 118 Projection table: potash . . . . . . . . . . 125 LIST OF ILLUSTRATIONS Figure Page 1. Estimated regression coefficients of time constants . 103 vii LIST OF APPENDICIES Appendix Page I. Estimated supply of fertilizer nutrients versus actual consumption . . . . . . . . . . 147 II. Price indexes used for deflation . . . . . . 148 III. Formulas for PhOSphate Price Indexes . . . . . 149 IV. Formulas for Nitrogen Price Indexes . . . . . 151 V. Indexes of prices paid by farmers for nitrogen, phOSphate and potash, by states and United States, 1950—196144 0 o o o o o o o o o 15L; VI. Models N-3, P-3 and K-3 and Their Parameter Estimates 0 O O O O O O O O O O I O 160 VII. Other Models Considered in the Study . . . . . 169 viii CHAPTER I INTRODUCTION The Problem Setting Commercial fertilizer, as one of the major inputs in the pro- duction of farm crops, has increased in importance both absolutely and relative to other inputs in recent years. In 1964 fertilizer expendi- tures constituted from 6 to 21 percent of the total cost of crop pro- duction1 depending on crops. As a percent of total inputs on commercial farms, fertilizer consumption doubled in the U.S. during the period 1947-49 to 1960—62. During the year ended June 30, 1964, fertilizers consumed in the continental United States contained 10,351,814 tons of primary plant nutrients (nitrogen, available phOSphate and potash). All three in- creased relative to 1963: nitrogen, 12.2 percent; available phOSphate, 9.5 percent; and potash, 9.0 percent. But these increases were not evenly distributed geographically. The East North Central Region, the West North Central Region and the West South Central Region increased the consumption of nitrogen (N) by 25.8 percent, 12.7 percent and 9.5 percent reSpectively, while the New England Region consumed only 5.5 percent more than in 1963. Likewise, the consumption of available phos— phate (referred to as P or phOSphoric acid) increased most in the 205 East and West North Central Regions (14.1 percent and 12.3 percent), but . 1U.S.D A., Economic Research Service, Farm Costs and Returns; Commercial Farms by Type, Size and Location, Agriculture Information Bulletin No. 230 (June 1964). Crop expense includes 1) fertilizer and lime, 2) other crop expenditures, 3) machinery, 4) one half or all the labor depending on the amount of livestock and 5) taxes. 1 2 increased only slightly in the South Atlantic and East South Central Regions (.4 percent and 1.3 percent). Changes in potash (K20) con- sumption ranged from a 2.3 percent decline in the Mountain Region to a 20.2 percent increase in the West North Central Region. During the 1950464 period the consumption of the three nutri- ents expanded at varying rates. While the 1964 consumption of nitrogen was 454 percent of the 1950 consumption, phosphate and potash were 173 and 250 percent of their 1950 levels. Regional expansion varies even more: primary nutrient consumption increased .8 percent in New England and 564 percent in the west North Central Region between 1950 and 1964. . Changes in consumption of this magnitude suggest changes in re- lated variables. Nitrogen price fell 10 percent; potash price fell 6 percent; and phOSphate price rose 20 percent. Comparison of these A fertilizer prices with the 12 percent increase in the Index of Prices Paid for Production Items (including fertilizer) suggests fertilizer prices, on the average, decreased relative to other production items. Part of this change is explained by use of_a more highly concentrated fertilizer. Between 1950 and 1964 the average nutrient content of fer— tilizer increased from 22.0 percent to 34.2 percent. The need to under- stand the reasons for these changes prompts this particular study. The factors effecting this rapid change in the consumption pate tern can be categorized as economic, technological and educational. These categories are not mutually exclusive and all will be considered.33 But economic variables will be emphasized in this study. The following types of questions are of prime interest: 1. What is the relationship between nutrient price changes and consumption of each fertilizer nutrient in each state and in the aggregate? 3 2. What is the relationship between crop or product price changes and each fertilizer nutrient consumption? 3. What conditional projections can be made of future con- sumption? Objectives It is within the framework of the above questions that this study is formulated. The primary objectives of this study are to identify, describe, quantify and analyze the factors affecting the demand for commercial fertilizer. More Specific objectives include: 1. To develop price indexes for nitrogen and available phos- phate necessary in the models of each nutrient. 2. To estimate parameters of economic models describing the market relationships for each nutrient. 3. To forecast consumption of fertilizer under Specified prices. 4. To compare the results of this study with those of earlier studies. Method This study begins by reviewing previous studies and by examining the economic relationships impinging on farmers' decisions regarding fertilizer use. This leads to the development of appropriate economic and statistical models. The lack of adequate data on nutrient prices by states led to the development of a series of indexes of nutrient prices. Separate economic models are estimated for each of the three primary nutrients; all regress the quantity of nutrient per acre on various Li. economic variables, dummy variables for each state, and various time variables. All models combine cross-section and time-series data: data from 48 states and the 15 year period 1950 through 1964 combine to give 720 observations. These covariance models, by considering the wide variation in resources, technology and environment among states, obtain estimates relevant to the individual states. ~The covariance models are estimated by ordinary least squares. Review of Literature Nonfarm agriculture inputs all have generally been neglected in economic research. But fertilizer is somewhat an exception. As early as 1927, E. E. Vail2 related U.S. fertilizer consumption to various factors and found that the lagged value of cotton per acre and tobacco . per acre contributed most to an explanation of the variations of fer- tilizer consumption. A. L. Mehring and B. T. Shaprublished a model in 1944 which implied that farmers Spend a constant proportion of their income on fertilizers. Their model, using the period 1911 through 1943, explained 93 percent of the total variation for that period.’4 But since 1950 the estimates fall considerably below the actual consumption. 2E. E. Vail, "Prices of Fertilizer Materials and Factors Affecting the Fertilizer Tonnage" (Unpublished Ph.D. thesis, Cornell University, Ithaca, N.Y., 1927). 3A. L. Mehring and B. T. Shaw, "Relationship Between Farm Income and Farmer's Expenditure for Fertilizer and a Forecast of the Commercial. Demand for Fertilizer in 1944 and 1945, by States”, American Fertilizer, (c. 1944). ' ‘ quuaEe explained variation with R2 where: R a SSR/SST 2 SSR = regression sum of squares = 2(Y - :)2 SST = total sum of squares = .Z(Y - Y) 5 , During the late 1950's Griliches undertook an extensive ferti- lizer research project testing the hypothesis that the decline in the "real" price of fertilizer largely expliins the great increase in con- sumption of fertilizer in the U.S. He developed several models: one cross-sectional and several time-series. In all, price of nutrient is hypothesized to be the most important variable. The first models, which is an equation linear in logarithms of the variables, argues that fertilizer use is a function of the "real" price of fertilizer, the price paid for fertilizer relative to the prices received for farm crops, and an adjustment factor proportional to the amount of "disequilibrium". The amount of disequilibrium is defined as the difference between the logarithm of actual and desired level of use. He fitted this model to national data for the years 1911-56. Then he divided this period into two sub-periods, 1911-33 and 1934—56, to test for changes in coefficients over time. Since the ex; planation fits both periods equally well Griliches concluded that the .tremendous increase in fertilizer consumption can be interpreted as a movement along a given production function in reSponse to changing relative prices. He argues that the technical change has occurred not in agriculture but in the fertilizer industry. As a further test of the hypothesis that fertilizer use can largely be explained by the decline in the "real" price of fertilizer 5Zvi Griliches, ”The Demand for Fertilizer: An Economic Inter- pretation of a Technical Change", Journal of Farm Economics, Vol. XL, No. 3, (Aug. 1958), pp. 591-606. 6 Griliches6 utilized the same variables but disaggregated to the nine census regions. Rather than simply summing the nitrogen, phOSphoric acid and potash content of the fertilizers as in the first model, the various nutrients were weighted by their relative prices before aggre; gating. He fitted this revised model to regional data for the years 1931-56 utilizing two sets of price data. Griliches found some regional differences: (1) the regions with historically more fertilizer experience adjust faster to changes in price than those with less, and (2) the de- mand for fertilizer is more price elastic, in the long run, in regions with low fertilizer use. 7 As a test of the time series models Griliches developed a cross-sectional model using data from the 1954 Census of Agriculture. Again fertilizer is viewed as a function of fertilizer price relative to. prices received. But in addition, the price of fertilizer relative to labor, fertilizer price relative to land and the average percent content of nitrogen in the soil contribute to the explanation. The form of the equation is the same as the one used in time series analysis: linear in the logarithms of the variables. The results show labor as a complement and land as a substitute for fertilizer. This model explained between 75 and 90 percent of the interstate variation. 6Zvi Griliches, "Distributed Lags Disaggregation, and Regional Demand Functions for Fertilizer", Journal of Farm Economics, Vol. XII, No. 1, (Feb. 1959), pp. 90-102. 7Zvi Griliches, ”The Demand for Fertilizer in 1954: An Inter- state Study", Journal of the American StatisticalgAssociation, Vol. 54, (June 1959), PP- 377-84- 7 Yeh and Heady8 (1958) employed numerous algebraic functional forms. But the main ones were linear in logarithms, and fitted to data from 1926-56, omitting 1944-50. Their logarithmic models for total commercial fertilizer consumption, and for consumption of each nutrient included the following independent variables: (1) ratio of current fer— tilizer price index to the general wholesale price index, (2) average of the crop price index lagged one year relative to the general whole- sale price index, (3) all cash receipts from farming lagged one year, (4) cash receipts from crops and government payments lagged one year, (5) total acreage of cropland, (6) time, (7) time squared, and (8) an income fraction, indicating trends in income over the previous three years. Results from the regional models, which explained more than 90 percent of the variation in fertilizer consumption, show an elasticity of demand with reSpect to fertilizer price greater in regions which have increased use the most in recent years. Contrast this with Griliches' conclusion that regions with historically more fertilizer experience adjust faster to changes in price than those with less. With the objective of improving predictive methods and explaining economic relationships, Brake9 (1959) disaggregated and concentrated his attention on two historically different regions: the East North Central 8E. O. Heady and M. H. Yeh, "National and Regional Demand Func- tions for Fertilizer", Journal of Farm Economics, Vol. 41, (May 1959), pp. 332-48. 9John R. Brake, "Prediction of Fertilizer Consumption in Two Regions of the United States", (Unpublished Ph.D. thesis, North Carolina State College, Raleigh, 1959). 8 and the South Atlantic. Both are heavy consumers of fertilizer, yet their historical consumption patterns differ considerably. Predictive variables used in the study can be grouped into five general classes: (1) product price, (2) fertilizer price, (3) price of associated inputs, (4) fertilizer acreage, and (5) capital restriction. Data for the years 1930-58 are used in models of three different forms: linear, first dif- ferences and distributed lag. To test predictive performance Brake tested the various models for the decade of the '50's. Some of the models demonstrate a high degree of stability with respect to the co- efficients over the time period and the recommended models all explained more than 95 percent of the total variation. Heady and Tweeten10 (1962) update and expand the study reported by Heady and Yeh. Total fertilizer tonnage and total nutrient quantity were estimated separately for the nutrients N, P205 and K20. Independent variables can be grouped into: (1) fertilizer price, (2) index of price for land, (3) cash receipts, (4) acres of cropland, (5) time, and (6) assets on the farm. Deflation, where used, was by crop prices. Both linear and logarithmic forms were experimented with but only the log- arithmic is reported and as in the earlier report by Heady and Yeh, the models yield high R2's. Most of the studies reviewed above utilized time series data. All of them encountered serious problems of multicollinearity. Because of this, avoidance of multicollinearity was emphasized in constructing 10E. O. Heady and L. G. Tweeten, Resource Demand and Structure of the Agricultural Industry (Ames, Ia., Iowa State University Press, 1963). 9 models for this study. More will be said on this in Chapter II. Organization of the Study Chapter II Specifies and rationalizes the models. Chapter III discusses and develops alternative nutrient price indexes for use in the models. Chapter IV presents and analyzes the results of the models. Chapter V demonstrates the applicability of the models in forecasting. And Chapter VI is a summary with recommendations and conclusions. CHAPTER II THE ECONOMIC MODEL Introduction Chapter I briefly surveyed the fertilizer market both as it varies from state to state and the changes occurring since 1950. In view of this as well as the earlier studies of fertilizer demand and some understanding of the economic framework within which the farmer makes decisions regarding fertilizer use, this chapter develops the general model used in this study. The formulation considers both economic theory and the charadteristics of the fertilizer market within the data restrictions. Preliminary Structure The demand for commercial fertilizer is derived from the de-. mand for farm crops. The quantity demanded of fartilizer, as any input, depends on the price of the input, the price of the product and the price of close complements or substitutes in production. Treating the supply of fertilizer equally crudely, we say the supply depends on the price of fertilizer, the prices of inputs (raw chemicals, machinery A and labor) and some concept of a production function. To consider pos- sible modifications it will be convenient to represent them symbol- ically. The following notation will be used: Q: = quantity of fertilizer demanded Q: = quantity of fertilizer supplied PF = price of fertilizer 10 11 (I) II a set of exogenous variables which affect the quantity of fertilizer demanded and the price of the fertilizer (D II 2 a set of exogenous variables affecting the supply of fertilizer and its price. The relations discussed above can now be summarized as: D QF ’ PF ’ 51 s QF ’ PF ’ S2 D _ s QF ‘ QF A colon may be read "depends on"; a semicolon may be read "appear in relation with”; and a comma may be read "and". Consider the variables to the left of the colon or semicolon as endogenous. Before further Specifying the model, variables presented as endogenous must be examined to see if, in fact, they are endogenous. Without question, the quantity of fertilizer demanded is determined within the system. But the price of fertilizer may be exogenously determined. And if this is true, then the structure outlined above is altered to: D ' QF ; S1 , where S H (D i- "U H U) + *U U 82 , where S D _ s QF ‘ QF 0 *ecn .0 N 0H 0 Whether the price of the fertilizer is considered endogenous or ex- ogenous depends on those relations which generate the data. The price of fertilizer paid by the farmer consists of charges for the fertilizer itself plus the costs of distribution. Since fer- tilizer haSSa low value per unit of weight, the tranSportation Share of the price is often quite large. This is eSpecially true of phOSphate ’ 12 and potash which, for the most part, must be shipped from Florida and New Mexico.11 Markam's12 estimate of production costs per ton of ordinary super phOSphate (20 percent aviilable P205) for the Midwest in 1950 attributed 63 percent of the farmer's final price to distri- bution costs, 17 percent to raw material costs and 20 percent to fabrication costs. This estimate of distribution costs is probably too high for the latter part of the period included in this study since the average nutrient content increased from 22 percent in 1950 to 34.2 percent in 1964. But the point remains, distribution costs constitute a large part of the total delivered price of fertilizer. And freight rates controlled by the Interstate Commerce Commission are very stable. Another characteristic of the phOSphate and potash sectors contributing to stable prices is a contracting arrangement between primary producers and their customers (processing and mixing plants). These contracts are Signed around the beginning of the fiacal year. They serve, not as rigid legal contracts, but as rough indicators to 11U.S. Dept. of Interior, Bureau of Mines, Minerals Yearbook 1263, p. 913: "Approximately 90 percent of the domestic (potash) pro- duction came from mines in the Carlsbad, New MSkico area with Cali- fornia and Utah furnishing the bulk of the remainder." Canadian shipments were also very important. p. 878: "Florida's production of marketable rock (phosphate) amounted to 74 percent of total domestic output: the Western States (wyoming, Idaho and Utah) accounted for 14 percent and Tennessee, for 12 percent.” 12Jesse‘W. Markham, The Fertilizer Industry, Study of an Imperfect Market (Nashville: Vanderbilt University Press, 1958), pp. 150-52. Markham, using a Specific example of Florida rock phOSphate (less than 3 percent available P O ), estimates the average cost of transportation to equal 75 percth5of the delivered price. 13 the primary producers of next year's consumption and as aids in scheduling production. Although the contracted quantity is not rigidly adhered to, the price normally is. This does not eliminate price variation at retail, but certainly restricts it. The productive capacity of an industry indirectly measures the pressure on price. Product prices of industries with insufficient capacity tend to rise, while those with excess capacitytend to fall or remain stable. Using the estimated supply of each nutrient avail- able for domestic consumption as an approximation of the industry's 13 capacity, the period since 1950 generally indicates excess capacity as shown in Appenditx I. Estimated nitrogen Supplyi‘tvfipacity) available for domestic use exceeded consumption in all but one year since 1950. During this same period the estimated domestic phOSphate supply (capacity) fell short of consumption three times. Estimated potash supplies generally deviate less from actual consumption than either nitrogen or phOSphate and estimated deficits occur more frequently. Five times in 15 years the actual consumption exceeded the estimated domestic supply (capacity) but, as in phOSphate, periods of excess capacity (estimated supply greater than consumption) preceded the periods of Shortage. Further evidence to suggest excess capacity in the fertilizer industry is suggested in a recent study by the Federal Reserve Bank of Chicago.1LL This study found that ”....Since the end of World war II.... 13U.S.D.A., Agricultural Stabilization and Conservation Service, The Fertilizer Situation (annual issues, 1950-64). 1“Federal Reserve Bank of Chicago, ”Commercial Fertilizer and Agricultural Production", Business Conditions (Sept. 1965), pp. 7-12. 14 the margin of unused capacity has increased substantially." Closely related to the estimated supply (capacity) is-the Size of inventory. Stocks held by producers on December 31, 1962, rep- resented 12 percent of the total K 0 sales for the year ended June 30, 2 1963; 47 percent of the available P total; and 31 percent, 6 percent 205 and 34 percent of anhydrous ammonia, ammonium nitrate and ammonium 15 sulfate totals reSpectively. Data available at both the producer and retail levels for these nitrogen commodities suggest fertilizer inven- tory estimates could easily double if both retail and producer inven- tories were included. Generalization from these limited nitrogen data edggests that stocks available January 1 of the fiscal year are in some cases greater than the sales in the remaining 6 months of the fertilizer year. This, of course, varies from year to year and for the different fertilizer materials, but does indicate a large inven- tory and limited pressure on prices. All the above arguments for stable prices neglect the effect of retail level margins. Observation of historical data reveals that fertilizer prices at retail vary only slightly within a fertilizer year (the fiscal year)16 thus confirming the arguments for stable prices within the year. No one of these arguments conclusively shows that prices of. the individual nutrients are exogenously determined. Nitrogen 150.8. Dept. of Interior, 0 . cit., p. 884, p. 917. U.S.D.A., o . cit., Fertilizer Situation (March 1964), pp. 10-11. 16U.S.D.A., Statistical Reporting Service, Agricultural Prices (April and Sept. issues). 15 capacity exceeded consumption requirements in the past, and current expansion rates suggest this pattern will continue. PhOSphate and potaSh prices include substantial transportation charges in addition to the contracted prices which contribute to stable prices; and all the reported nutrient prices are stable during the fertilizer year. For these reasons the nutrient prices originally regarded as endog- enous are now considered predetermined. This revision implies that the study can be focused on the demand equation of the form: A D . o QF ; S1 , where S1 = $1 + PF The variables in 81 are considered as eXogenous or predetermined and will be discussed in the next section. Variables of the General Demand Equation To find which variables belong in $1, the set of exogenous variables which affect the quantity of fertilizer demanded, we appeal to economic theory. The theory Specifies that the quantity of an input demanded depends upon the price of the factor, price of the' product, price of close substitutes and complements and the marginal physical product of the input. This set of variables divides into variables which refer to movements along the demand curve and those which Shift the demand. The variable related to movements along the demand curve is the nutrient price. .The U.S. Department.of Agriculture publishes17 a general U.S. index of fertilizer price and state level data of specific forms of N, P205 and K20 as well as mixtures of the three, 17Ibid. 16, but no price indexes for the individual nutrients. These state price data and state quantity data18 provide the raw materials for the construction of state price indexes for each nutrient._ Because of problems encountered in constructing the indexes and because it is really a major but subordinate study, the procedure and results are 1 presented in Chapter III. ; 3 Several factors cause Shifts in the demand curve of an input.‘ Chief among these shifters is the price of the product. As the price of the product changes the MVP of the nutrient changes proportion- ately and the quantity of input increases or deCreaseS depending on ~. the direction of the initial change. Selection of the most appropri- ate crop price is based on data published in the Census of Agricul- 19 ture. From the census it is possible to assess the relative importance of each crop (in every state) as a consumer of fertilizer. Prices of crops consuming the most fertilizer become "the“ product prices for the purpbses of analysis. -With few exceptions states' ' consume most of the fertilizer on one or two crops. In states where similar ambunts of fertilizer are consumed on two crops both crops. . are included in the models. The exceptions to this criterion are states applying a major share of the fertilizer on fruit and vegetable crops. Since neither fruit nor vegetable price indexes are available, a field crop price is used even though the crop is not the most 18W. Soholl, et.al., Consumption of Commercial Fertilizers and Primary Plant Nutrients in the U.S., UsS.D.A., Soil and water Conservation Research Division, Agricultural Research Service (Annual Issues). 19U.S. Dept. of Commerce, Bureau of Census, 1959 Census of Agriculture, Vol. IV. 17 important consumer of fertilizer. The question of which year's crop price is relevant to the model remains open. A study of farmers' attitudes toward the use of fertilizer by the National Plant Food Institute20 provides some insight into the farmer's decision-making process. In reSponse to the question "When did you first start thinking about using ( analysis ) on your 1956 ( selected crop, )?" slightly more than half of them named some month earlier than August 1, 1955.’ And of thoSe farmers generally using rates close to the recommended level, 64 percent reported thinking about their present analysis prior to August 1, 1955. This, along with the fact that over 70 percent of the total fertilizer purchases occur in the January-June period implies that the crop prices during the decision period are the most suitable price for the models. Therefore, the average annual price for the preceding crop is used in the models. A second shifter of the demand curve is changes in price of closely related substitutes and complements. If the related good is a substitute, then an increase in its price causes an increase in the consumption of fertilizer. Conversely, an increase in the price of a complement causes a decrease in the consumption of fertilizer. Exclusion of other inputs, viz., machinery, labor and land, does not imply independence between fertilizer and these inputs, but, rather, implies that the relationship is not close. Exclusion of these related inputs as independent variables assumes that farmers reSpond little to marginal price movements. Prices of the related inputs are not 20National Plant Food Institute, A Study of Farmers' Attitudes . Toward the Use of Fertilizer (washington, D. C., 1958), p. 53, p. 14 of Appendix A. The survey was taken in 1956. } Illll‘llilllll’lll’ll’lllll‘llllll l‘l‘(’lll 18 completely ignored in the models, however, because deflation, which is discussed later in the chapter, by the Index of Prices Paid for Production Items considers relative prices. A second reason for excluding the prices of other inputs is the lack of state data. Use of available national data would entail assuming that the same prices hold for all states. And the estimates of fertilizernutrient price indexes for states developed in Chapter III clearly suggest this assumption is questionable. For example, the 1964 index of nitrogen price in New Jersey and California equal 108.6 and 70.8 reSpectively (with 1950 = 100.0 in both cases). If prices of'relatedtinputs have changed in the same manner, then assuming equal prices for all states introduces a Specification error. But, at the same time, omitting the variables introduces a specification error. Therefore, a choice must be made between the Specification error of omitting the variables and thus attributing their effects to temporal variation; and the Specification error of including them I (all states equal), thus getting Spurious results across states. In all models the prices of related variables are excluded. The model, as it is Specified, ignores the complementarity between the three nutrients. The study referred to earlier by the National Plant Food Institute found that farmers who purchased fer- tilizer decide on the analysis and amount using trial and error Slightly more frequently than by accepting recommendations of soil tests. But farmers classified as those "using fertilizer close to the standards for most economical operation for his type of crop and Soil as compared to the best practice of agronomy” decide more fre- quently on the basis of Soil tests than trial and error.21 But in 19 either case, relative nutrient prices have not played an important role in the decision and for this reason are not included in the model. Andther shifter of the demand function for a factor of production is the expenditure restriction (cost constraint). This is analogous to the budget conStraint of consumer demand theory. It is assumed that for any given expenditure for factors of production farmers intend to maxi- mize profit. Those farmers who have no expenditure restriction purchase inputs until the last unit of factor purchased is worth in production just what it cost - and when each factor is purchased at this rate, then profit is maximized. Employing any more units of the factor will add less value to the output than it costs to produce. But there is another group of farmers - those with an expenditure restriction - who are unable or un- willing to purchase inputs to this point. In the National Plant Food In- stitute study22 28 percent of the farmers interviewed said they would not borrow money for fertilizer purchases (when available at a reasonable rate of interest). Twelve percent said they probably would not. This means that for about forty percent of the farmers their expenditure restric- tion (for fertilizer) is their income and other assets. Secondly, there is a group of farmers who are unable to utilize credit to buy fertilizer. For this group their fertilizer expenditure restriction is also conditioned by their income and asset position. A third group is made up of those farmers who do use credit to buy fertilizer (in the study referred to above 49 percent of the purchas- ers utilized credit). But, of course, the price and amount of the credit available is conditioned by their income and asset position. 22lbid., p. 117. 20 To bring the expenditure restriction into the model, experi- ments were conducted using alternately average gross farm income and average net farm income (both from the previous year) among the inde- pendent variables. The two variables contribute almost equally to explaining variation in fertilizer use, but the ratio of the estimated coefficient to its standard error was greater for the net income vari- able. Because of this, and the intuitive appeal of net income as the expenditure restriction, only net farm income is considered in the models presented in Chapter IV. The net farm income of the previous year serves as a proxy variable for measuring expenditure restrictions: as a rough measure of the ability to pay cash and the availability of credit. Inclusions of more than one year's income, weighted either arbitrarily or by the equation, would refine the measure but this added refinement is not considered in the study. The last variable to be considered as a demand shifter is technological change. We can ignore the technical progress in the production of fertilizer because it is reflected in the price of the nutrients. But Significant technological developments in the pro- duction of farm crops need consideration in the model. Since 1950 hybrid plants have improved; fertilizer placement is better; and machinery and other factors have improved. But for none of these are good measurements available. The use of time as representative of these changes may properly cause some concern. These specific factors mentioned are part of a set of influences whose net effect during the period of observation has fairly steadily increased the efficiency of converting inputs into cropso [Another factor, not included in the set of technological changes, which has been changing 21 steadily over the period is the knowledge or awareness farmers have about the effects of fertilizer. For example, the percentage of total corn acres fertilized in the U.S. increased from 60 percent in 1954 to 63.7 percent in 1959. If this five-year increase is assumed represent- ative of the period studied, then there were about 11 percent more corn acres fertilized in 1964 than in 1950. Extrapolating the percent of total crops and pasture fertilized from the same period results in an estimated 5.1 percent increase between 1950 and 1964 of the total crops and pastures fertilized. Concomitantly, awareness of the effects of higher rates of application increased the quantity used per acre. Because there is no way of Specifying this set of factors - both the technological changes and farmers' awareness - several alter- native forms of the time variable are explored. Various forms include the exclusion of time, time as a linear variable, two quadratic forms of time, and time as a set of 0,1 dummy variables. The linear form of time takes the values 1 through 15 with 1950 equal to 1. The first quadratic form is a set of 2 variables, one linear and the second, the Square of the linear. The second quadratic form of time is a Squared term and takes the values 1 through 225 with 1950 equal 1, 1951 equal 4, etc. And the set of dummy variables, a vari- able for each of the 14 years 1951 through 1964, take the value 0 or 1 depending on the year being observed. The mechanics of this set will be discussed later in the chapter with the actual model. The variables discussed above - the price of the nutrient, price of the product (crop price) and the average net farm income - tare the economic variables included in the models. Time, in several forms, is also included as a measure of technological changes and the 22 awareness of fertilizer reSponse by farmers. Just how these variables are included in the models is considered in the next section. Specification Considerations Fertilizer has been considered in a very general way until now. The commodity, fertilizer, consists of primary plant nutrients, sec- ondary plant nutrients, trace elements and a carrier which is often limestone or an inert material. For different fertilizer materials, the concentration of nutrients varies considerably: from less than 2 percent available phOSphate in rock phOSphate to over 80 percent elemental nitrogen in anhydrous ammonia. Simply considering fertilizer as a whole would mean treating a ton of fertilizer with a high concen- tration of nutrients equal to one with a low concentration. It also would mean ignoring the increase in concentration from 22 percent in 1950 to more than 34 percent in 1964: an increase in the real quantity of fertilizer. While the secondary elements (calcium, magnesium and sulfur) and the trace elements (copper, zinc, boron, manganese and iron) have increased in importance Since 1950, they accounted for less than 5 percent of the total fertilizer tonnage consumed in the fiscal year 1964. When considered on a nutrient basis this 5 percent reduces considerably since the concentration of secondary and trace elements is much less than of primary elements. While the secondary nutrients are becoming more important as the technical understanding of their function increases and as an increasing number of soils reSpond,they are not considered in this study. The primary nutrients (nitrogen, N; avail- able phOSphate, P205; and potash, K20) are the concern of this study. The description of the diverse consumption patterns of the 23 different nutrients in the introductory chapter suggests the esti- mation of the three~primary nutrients separately. Disaggregation of the three increases both the possibility of good explanation and the relevance of the individual estimates. The individual estimates can later be merged to yield a more aggregate description of the market. Because of the diversity of agriculture in the U.S. and the ways in which this diversity affects the consumption of fertilizer, the model developed in this chapter must be flexible enough to take this into consideration. One of the objectives is to estimate the parameters which describe the fertilizer consumption of each state. The covariance model, using both time-series and cross-section data 23 offers the most potential. This model, in addition to estimating the economic parameters mentioned earlier, is capable of estimating a parameter for each state: a constant term. These parameters are viewed as measuring the effect of unobservable characteristics that are peculiar to a state over time such as climate, soils and types of cropping. And statistical tests can be performed to determine the Significance of estimating a constant for each state. The cross- Section and time-series model also provides the opportunity to estimate parameters common to a set of states, but not the entire country. The characteristics of the data designate states as the meas- urement unit for the study. Consumption, price and income data are available or can be constructed for each state. But because states 23The models are a variation of those suggested by C. Hildreth, .Preliminary Considerations Regarding Time Series and/or Cross-Section Studies, Cowles Commission Discussion Paper: Statistics No. 333 (July 1949), and C. Hildreth, Combining Cross-Section Data and Time Series, Cowles Commission Paper: Statistics No. 347 (May 1950). I 24 vary markedly in size and rate of application the consumption (quan- tity) data are transformed to pounds of nutrient per harvested acre (harvested acreage of 59 major crops). Another argument for the co- variance model is larger sample size - in this study 48 states and 15 years giving 720 observations - which reduces sampling errors and makes tests of Significance more powerful. This study examines the period 1950 through 1964. Earlier periods were excluded because (1) generation of nutrient price data prior to 1950 presents serious difficulties, (2) the World War II and immediate post-war periods were adjustment periods, and (3) the combined time-series and cross-section model permits relatively shorter time periods than the time series alone. The combined time-series and cross-section model of this study utilizes more information and at the same time provides a means of avoiding multicollinearity. Earlier studies of the demand for fertili- zer, except Griliches' one cross-sectional study, all used time series and all confronted multicollinearity problems. Johnstonzu and The1125 point out that the solution to problems of multicollinearity lies in the acquisition of new data which will break the multicollinearity deadlock. Because time-series data are, in general, multicollinear, combined cross-section and time-series offers an alternative procedure. a 2 J. Johnston, Econometric Methods (New York: McGraw-Hill Book Co., 1963), p. 207. 25H. Theil, Economic Forecasts and Policy (Amsterdam: North Holland Publishing Co., 1962), p. 217. 25 Chipman26 argues that where the matrix of cross-section and the matrix of time-series data are complementary the combined cross-section and time-Series model iS the natural procedure to employ to avoid multi- collinearity. Even where multicollinearity exists, unbiased forecasts can be made. But successful forecasts with multicollinear variables require (1) perpetuation of a stable dependency relationship between the de- pendent and independent variables and (2) the perpetuation of a stable interdependency relationship within the set of explanatory variables. Where the intent of the model is explanation, the multicollin- earity reveals itself by increasing variance of the perameter eStimates. Arbitrary rules established as a criteria for defining unacceptable collinearity frequently break down in practice. The most common rules of thumb constrain Simple correlation (r) to less than .9 and often to leSS than .6. This is often qualified by arguing that intercorrelation is harmful only if the Simple correlation between explanatory variables exceeds the multiple correlation coefficient (rijZR)' Farrar and Glauber refute both these rules of thumb with, "complete multicollin- earity - i.e., perfect Singularity - with a set of explanatory varia- bles is quite consistent with very small Simple correlations between members of X (the set of eXplanatory variables). A set of dummy variables whose non-zero elements accidentally exhaust the sample Space 26John S. Chipman, ”On'Least Squares With Insufficient Obser- vations", Journal of the American Statistical Association, Vol. 59, No. 38, (December 1964), pp. 1078-1112, especially 1100-1102. 26 is an obvious and aggrevatingly common example."27 Combining time- series and cross-section data eliminates most of the pairwise inter- correlation between economic variables in the set of explanatory vari- ables of this study. To measure other than pairwise collinearity one can use the determinant of the X'X matrix. Where this determinant is based on a normalized matrix it takes a value between zero and one. Values approaching zero warn of a Singular matrix and a value of one would mean an orthogonal set of independent variables. But this is not a very good measure. True, it warns when multicollinearity exists, but it provides no meaningful measure of the problem. It ignores the fact that the determinant tends toward zero as the size of the matrix increases and it fails to recognize that collinearity between some variables is more serious than between others. And it cannot identify which variables are multicollinear. An alternative measure is the multiple correlation coefficient, R2, where each ”important" explanatory variable is regressed on the remaining variables of the X matrix. This is not a regression in the usual sense because it immediately violates the assumption of X being a fixed set, but is merely an exploitation of RZ'S property: percent of (the variance of one variable explained by a set of variables. This I measure of multicollinearity will be presented in Chapter IV with the results of the models.28 f 27 D. E. Farrar and R. R. Gauber, Multicollinearity in Regres- sion Analysis: The Problem Revisited (Sloan School of Management, Mass. Institute of Technology, Cambridge, 1964), Vol. 105-64, p. 23. 28I am indebted to William Ruble for discussions of the prob- lems of measuring multicollinearity. 27 Another consideration in Specifying the model is whether to use nominal or real prices and incomes. To use nominal prices and incomes implicitly assumes either (1) uniform price changes for the economic variables or (2) that farmers respond to nominal prices and not real prices. Tests of uniform price changes reveal that while the Index of Prices Paid for Production Items increased 31 index points from 1949 to 1964 the Index of Prices Paid by Farmers increased 58.6 index points, or nearly double. Because of this difference and the fact that economic theory suggests consumers and producers react to real prices, the economic variables in the models are deflated. The question of the appropriate deflator is confronted by asking the question - what deflator will transform the variable to real terms? The price of the nutrient is deflated by the Index of Prices Paid for Production Items. That is, "reel" is here considered to be how much does the fertilizer nutrient cost relative to the alternative inputs; or how much of the other inputs will a unit of fertilizer buy? The crop price was deflated by the same index because it is assumed that farmers consider the relative prices of the product and inputs when deciding the quantity of inputs to buy. Since both consumption and production have a claim on net farm income, the expenditure restrict- ion, the Index of Prices Paid by Farmers is used as the deflator. In all the deflation the actual deflator is the arithmetic average of the 29 February, March and April indexes. 29Actual deflators listed in Appendix II. 28 The General Model The nitrogen, phOSphate and potash models all follow the same general format. All consider the same economic variables, state con- stants and forms of time. The differences are in the way states are combined in the nutrient price variables and in the crop price varia- bles. Here, a general model is presented to aid discussion. To consider the variables and characteristics of Specification described above more fully and to consider possible modifications it will be convenient to expand the notation used early in the chapter and represent the relations symbolically. The set of exogenous variables (Si) affecting the quantity of fertilizer demanded includes: P: s = index price of the nutrient in t and S 9 where t refers to the years 1950-1964 S refers to the 48 continental states F indexes the nutrient in the model F is designated as: N, nitrogen; P, available P O ; 2 5 and K, potash P: S = price of crop (product) in t and S 9 where c indexes the particular crop and region: crops are either corn, cotton, wheat, hay or potatoes (Some crops, say corn, are the most important consumers of fertilizer in many states but be- cause of the environmental differences between states, the reSponse is not expected to be equal and therefore, the model is Specified with two or more corn price variables: each for a differ- ent set of states.) Yt s = average net farm income in t and s 9 Tt * = time variables for t 9 where * means constant for all states 8* s = dummy variables (0,1) for states 9 where * means constant for all years 29 The endogenous variable is: QF 8 = quantity of fertilizer nutrient consumed per harvested ’ acre in year t and state S The discussion can now be summarized in the following relations: k i g _ F c I a"? :8 Pt,s + 3. Yt-1,S + Zak Pt-1,s + 23.1 S*,S F t,s g Q j +-z@9 Tt,* + Ut,s where g = 6 different nutrient price variables k = 14 different crop price variables 1 = 1...47, state constant terms j = 1...14, time constant terms The variables of the equation can best be examined in sets Since all but the net income variable (Yt-l) are some form of synthetic variable. First consider the set of variablesfgag Pt,s’ the six nutrient price variables. Each of these Six variables is used over a region. For example, in the nitrogen model the first of the Six nitrogen price variable51383PE’s pertains to the states Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey and Pennsylvania. The estimated parameter,é53, is relevant only to these states. A description of the way the variable is in- cluded may help to clarify its meaning. Each observation of the dependent variable is associated with a fixed set of independent variables - Six of these independent variables are nutrient price variables. Let the observation on.Q be the 6th year, 1955, of the period and the state of Maine. Then the value of the first of the six N 1955, Maine in Maine. The value of the second of the Six nutrient price variables nutrient price variables (P ) will be the 1955 nitrogen price 30 will be zero (non-zero values will be entered in the second variable when the ON of each state in the second region of nitrogen price is being observed). The remaining four variables will also be zero. The second set of variables in the equation is lagged net farm income (RY ) and for each observed value of QN there is an t-1,s associated non-zero value of Yt 1. - k The third set of 14 (13 for K 0) variables (23 PC ) is 2 k t-1,S synthetic variables constructed much like the set of nutrient price variables. They have the value zero or the actual value of the vari- able. Let us extend the example used for the nutrient price variables. The 1959 census Shows that Maine applied 77 percent of the total nitrogen consumed on potatoes and 14 percent on hay. Using the cri- terion established earlier, potato price is "the" product price in Maine. Let variable 10 be the price of potatoes in Maine and Rhode Island. In the example, where the observation is 1955 of Maine, the first independent variable is the price of nitrogen in Maine 1955, variables 84 through 88 are zero, variable 67 is the 1954 net farm income in Maine (because income is a variable lagged one year), variables 8 potatoes 1954 Maine) is the 1954 price Of 9 and 9 are zero and variable 10 (810 P potatoes. 2 The fourth and fifth sets of variables are synthetic variables in the more common zero-one form. The fourth set (IQ.l 3*,8) consists of 47 zero-one dummy variables. These variables affect only the level of the line. To avoid a Singular matrix one state, Michigan, is in- cluded in the overall constant term (x) for the equation. To further extend the example considered above the variable for Maine (X18) will take the value one when the state's observations are read and zero for 31 all other observations. The other variables, X19 through X64’ will take the value zero when Maine's observations are read. The fifth set of variables C553 Tt,*) is zero-one variables for the years 1951 through 1964. Looking at the year 1955 (X72) again, this variable will take the value 1 when the observations for 1955 are read and zero for all other years. This example using the year 1955 and the state of Maine demon- strates the flexibility of the covariance model with time-series and cross-section data. Other models which differ from the model above only in the form of the time variable are presented in Appendix VI. Estimation by ordinary least squares of the above model pro- duces best linear unbiased estimates if the following assumptions are satisfied. 1. E(U = 0, where E means expected value _2 )—