Time series analysis of West Punjab district wheat production data (Lanhore District)

JThis paper is prep.ared for staff 7sv and is not for publication. Th= views expressed are those of t;he author and not necessarily those of^ the Bank. INTERNATIONAL BANK FOR RECONSTRUCTION AND DEVELOPMNT Economics Depart.ment Working Paper No. 19 TIME SERIES ANALYSIS OF WEST PUNJAB DISTRICT WHEAT PRODUCTION DATA (LAHORE DISTRICT) This paper reports on the analysis of time series data on wlheat product,ion in the Lahore District (lWest Punjab). It is restricted to the pre-Partition period. The study could not be carried through for the post-Partition period for lack of suitable price data. It is part of an exploration of the possibilities of deriv- ing agricultuiral supply models for developing countries. The data were processed by the Bank's Statistical Services Division. Interpretation of the results is only tentative due to the defi- ciencies in the data base and the author's lack of familiarity with the specifics of Wast Punjab agriculture. June 19, 1968 Tnvestment Plamning Division Prepared by: Bernard Oury Research Assistant: IHyung M. Kim  TABLE OF CONTENTS I. Introduction . . . . . . . . . . . . . . . . . . . . . . 1 II. The Data Base . ........... . ....... . . . ..... ... . . 3 III. Methodology. . . . . . . . . ........ . . . * * * 7 IV. Estimated Equations ....... ....... . . . . .... 10 V. Response to Individual Factors........ . . . . . . . 18 VI. Forecasting . ..... . . . . . 23 VII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 25 Appendix: Graphic Analysis of the Data ........ . ............. . 27 Tables No. 1. Lahore District Analysis of Trend in Acreage, Yield and Pro- duction of Wheat - Natural Exponential Model ............................. 5 2. Lahore Ditsrict: Acreage, Yield, and Production of Wheat prior to Partition ........................... 11 3. Lahore District: Data Pertaining to the Explanatory Variables Appearing in the pre-Partition Models. . . . . . . . 12 4. Lahore District: Wheat Production - Model I - Natlural Exponential Separate Equations for Acreage, Yield, and Production (1920/21-1945/46) . . . . . . . . . . . . . . . . . . 15 5. Lahore District: Wheat Production - Model II - Log-Linear - Separate Equations for Acreage, Yield, and Production (1920/21-1945/46) . . . . . . la . . . . . . . . a . . . . . 16 6, Lahore District: Wheat Production - Matrix of Intercorrelation Coefficients Among Explanatory Variables . . . . . . . . . . . 17 7. Lahore District: Wheat Production - Response of Acreage, Yield, and Production to Weather, Wheat/Sugarcane Price Ratio (t-2)) Irrigation, Time (l920/21-1945/46) . . . .. . . 20  Page Charts No. 1. Lahore District: Acreage of Wheat (1914/15 - 1964/65) . . . . 27 2. Lahore District: Average Yield of Wheat per Acre (1914/15 - 1964/65) . . . . . . . . . . . . . , . . . . . . 28 3. Lahore District: Production of Wheat (1914/15 - 1964/65) . 29 4. West Punjab: Calendar of Wheat Cultivation Practices . . a . . 30 5. Lahore District: Precipitation for the "Best" Year (1944/45) and the "WorsVIt Year (1927/28) for Wheat Production (Selected on the B4sis of the Average Yield per Acre) 1920/21 to Date. . 31 6. Lahore District: Average Precipitation of Three "Best" Years and Three "Worst" Years for Wheat Production (Selected on the Basis of the Average Yield per Acre) 1920/21 to Date . . * . 32 7. Lahore Dis:triet: ingstrom Humidity Index for the "Best" Year (1944/45) and the "Worst" Year (1927/28) for Wheat Production (Selected on the Basis of the Average Yield per Acre) 1920/21 to Date . . . . . . . . . . . t . 0 . . . . . 33 8. West Piuijab: Tlarvest Prices for Wheat and Major Substitutes per Naund, Deflated (1914/15 - 1950/51). . . . . . . . . . . . 34 9. Lalhore District: Wheat Acreage Irrigated, Actual and as Percentage of Total Wheat Acreage (1914/15 - 1964/65). . . . . 35  I. INTRODUCTION 1. The objective of this study is to explore the possibilities of deriving models based on time series data for developing countries which would help to explain and forecast changes in agri-cultural output, acre- age, and yield per acre. Then changes might be associated with weatlher variations, as well as with price movements and -'echnological changes, if any. It is concerned only withl non-perennial crops. Specific problems would arise in dealing with tree crops. 2. The methodology consists in specifying a model or alternative model(s) and estimating their parameters through regression analysis. -de then go on to use the model as a basis for predictioln, acting in this case as if it were a true structure. Predictions beyone the period of observation are valid only on the assumption that the same structural conditions continue to prevail beyond the sample period. When struc- tural changes are slow, as is typically the case in agriculture in developing countries, extrapolating -the parameter estimates derived from regression analysis of time series for one to five years beyond the period of fit would appear reasonable. Such extrapolations may be helpful in the preparation of development plans generally covering five years ahead. Al- ternatively, predictions may be made for two or three years ahead only and the models subsequently reformulated and. updated so as to derive corrected forecasts for future periods. 3. The probleiii of long-range forecasting is different. Since the purpose of agricultural development is to bring about changes in the traditional structure prevailing in the developing countries, it  seem inappropriate to use regression models derived from past observa- tions. GrowTth curves might offer a more satisfactory approach to this problem, though this also has its limitations. Is. An analysis of wheat production data in the Lahore District of West Pakistan, prior to Partition (l920/21-1945/l6), is presented as an illustration of the application of the methodology to a traditional agri- culture. A model for the post-Partition period (1948/h9-196 /65) also has been prepared. Unfortunately, it could not be carried through for lack of suitable price data.  -3- II. --E DATA D3SE 5. Located in West Pakistan on the 320 latitude North, the Lahore District is characterized by large canal irrigation systems built in the last century and using rivers as sources of water supplies. Additional water stupplies are pumped from high ground watertables by means of old Persian wheels and, increasingly, from modern tube wells. Climatic con- ditions make it possible to have two crops per year on irrigated land, tropical and subtropical CrlOps during the kharif (sumer) season and crops of the temperate zorne during the rabi (winter) season. Perenial crops such as sugar cane and fruits occupy the land throughout the year. The major kharif crops are rice, cotton, and kharif fodders, the major rabi crops wheat and rabi fodders. Though sugarcane is grown only on a relatively small area, it contributes significantly to farmers income and appears to be a major substitute for wheat. Agricultural produc- tivity is g-.nerally low. Yields per a.cre are among the lowest in the world. The shortage of water, the salinity and alkalinity of soils, high water table, the limited use of fertilizers and pesticides, poor seed quality, and outdated implements are usually regarded as the major limiting factors affecting agricultural production. 6. As about 80 percent of the wheat acreage grown to wheat in the Lahoi,e District is irrigated and only 20 percent grown on rainfed land, no distinction was made between irrigated and non-irrigated wheat. In the absence of modern in,)uts such as fertilizers, pesticides, im- plements the investigation of agricultural production requisites focused primarily on irrigation.  -h - 7. Estimation of ttle influence of the weather upon wheat produc- 0 1 tion has been carried out using the Angstrom humidity index as defined in IBRD Economics Department Working Paper No. 3. Related monthly weather data (namely precipitation and temperature) used for the calcu- lation of the index are those of the Lahore weather station, for which reasonably long historical series are available. 8. Major year-to-year changes in acreage, yield, and production of wheat were first identified through graphic analysis of the time series data. They are shown in Appendix, Charts 1, 2, and 3, for the period 1914/15 - 1964/65. The calendar of cultivation practices for wheat in West Punjab is shown in Chart 4. The monthly distribution of rainfall over the crop year is shown in Chart 5 for the "best" year (.i9944L45) and for the "worst" year (1927/28) of wheat production in terms of average yield per acre, and in Chart 6 for the three "best" and the three "'worst" years. The monthly distribution of the Rngstr&m humidity index is also shown along with the distribution of its two- month and three-month clhain combinations, for the "best" and the "worst" year for wheat in Chart 7. This information matched with t,he calendar of cultivation practices helped to delineate the critical periods of the growth of the wheat crop. Harvest prices deflated are shown in Chart 8. Irrigation acreage is shown in Chart 9. 1/ IBRD Economics Department Working Paper No. 3, Program Windex for the Systematic Calculation of a Weather Index To Be Used in Agricultural Production Analysis, AUgUSt 14 1967. 2/ Prices were first adjusted to the decimal system (Rupees and .Paisas). The deflator used is the weighted average of the prices of the major commodities grown in West Punjab. The weights are the quantities produced of each commodity,  Tab.le 1 Ldliore DIstrict: frialysis of Trernd in Acreage Yield and Production of' Wheat - Nlatural Exponential Trend Model Production: q = loge Q; Acreage: n = loge N; . loge Y; t= time Iquatuion 2 niurfoer Eqluations R -d Before Partition (1920/21 - 1945/46), N= 26 (1) q = 15.0359 - 0.0018 t 0.003 1.742 (271.562) (0.246) (0.000) (2) n-.= 12.8678 - 0.0o62 t 0.213 0.966 (699.930) (2.5)47) (0.180) (3) y = 2.1681 + 0.0044 t 0.019 1.946 ( 44.129) (o.676 (0.000) Vft After Partit.:on (1948/49 - 1964/65), N = .17 (4) q 14.4457 + 0.0367 t 0.443 1.961 (277.783) (3.454) (0.406) (5) n = 12.2162 + 0.0360 t 0.579 1.4-60 (314.128) (4.538) (0.551) (6) y 2.2295 + 0.0006 t 0.001 2.465 ( 74.635) (0.105) (0.000) Overall Trend (192C/21 - 1964/65), including crcp jear, 1946/47 and 1947/48, N = 45 (7) q 15.0519 0.0061 t 0.072 1.380 (348.893) (1.828) ((.G51) (8) n = 12.8452 - 0.0073 t 0.199 0.684 (441.634) (3.269) (0.180) (9) y = 2.2067 + 0.0012 t 0.007 1.973 ( 72.8c8) (0.536) (o.oon  -6- 9. The grapiiic analysis of the wheat time series data clearly indicates that agriculLure in the Lahore District is rather traditional: the average wheat yield per acre has been fairly constant ovbr the years. (a + bt) A trend analysis has been performed using the equation Y = e where Y is yield of wheat per acre, t the time in years, a the constant term and b the parameter estimate of the time variable. It confirms that there is no trend in yield. Results rf this equation for both before and after Partition are shown in Table l, which also gives the corresponding trends for wheat acreage, and production.  -7- III. METHODOIOGY 10. Two models have been used to perform the analysis and to ascertain the consistency of the findings. They are centered around the identity: (10) Q - N x Y wh e re Q is the total production of wheat, N is the area grovm to whleat and harvested, and Y is the average yiel(d per acre of wlheat. Ex{pressed in logarithmic form, equation (10) becomes (11) loge Q loge N + loge Y It is assumed that factors influencing yield potentially also affect acreage, and vice versa. The extent to which this assumption &ctually holds will be shown by the parameter estimates obtained from the re- gression equations. 11. The symbols used in the formulation of the models are as follows: X. are the i explanatory variables allowing for the various factors irvestigated (i = 1 k) ao, bo, co are the constant terms in the respective equations of Q, N, and Y. ai, bi, ci are the parameter estimates corresponding to vari- able X in the respective equat.ions of Q, N, and Y. 1 uO, ui?, uy are residual terms in the respective equations of Q, N, and Y.  12. The first -rodel used is exponential or semi-log in the dopendent variables. In reduced form, i5odel I may be formulated as follows: k (ao + a1 &.Xi + XiQ (12) Q-e