JThis paper is prep.ared for staff7sv and is not for publication.Th= views expressed are those oft;he author and not necessarilythose of^ the Bank.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 wlheatproduct,ion in the Lahore District (lWest Punjab). It is restrictedto the pre-Partition period. The study could not be carriedthrough for the post-Partition period for lack of suitable pricedata. It is part of an exploration of the possibilities of deriv-ing agricultuiral supply models for developing countries. The datawere 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 familiaritywith the specifics of Wast Punjab agriculture.

June 19, 1968

Tnvestment Plamning DivisionPrepared by: Bernard OuryResearch Assistant: IHyung M. Kim

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

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 Wheatprior to Partition ........................... 11

3. Lahore District: Data Pertaining to the ExplanatoryVariables Appearing in the pre-Partition Models. . . . . . . . 12

4. Lahore District: Wheat Production - Model I - Natlural ExponentialSeparate 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 IntercorrelationCoefficients 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 B4 sis 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 WheatProduction (Selected on the Basis of the Average Yieldper 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 1tion 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 forthe Systematic Calculation of a Weather Index To Be Used inAgricultural 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 majorcommodities grown in West Punjab. The weights are the quantitiesproduced of each commodity,

Tab.le 1 Ldliore DIstrict: frialysis of Trernd in Acreage Yieldand Production of' Wheat - Nlatural Exponential Trend Model

Production: q = loge Q; Acreage: n = loge N; . loge Y; t= time

Iquatuion 2niurfoer 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)

VftAfter 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 ° il ati Q

k(b + Z b. X. +ul

(13) N e ° i-l 1 1

k(c0 + e jX + Uy)

(14) Y-e iel

(i. 1 k explanatory variables investigated)

All equations may be estimated independently through the least squares

method. As relationship (11) is in terms of logarithms, and as the

variables on the right hand side of all equations are assumed to be

the samme, the following sets of constraints are met by the coeffi-

cient estimates and the residuals:

a =b + c0 0 0

a. = b. + c.1 1 1

13. The elasticity of production, ei(Q), the elasticity of acreage,

ei(N), and the elasticity of yield, ei(Y), with respect to any independ-

end variable, are defined as the ratios of the relative change in pro-

duction, acreage, or yield, to the relative change i.n the factor concerned

on the right hand side of the equations, all other factors being held

at their mean. In this model elasticities are equal to the corresponding

coefficients weighted by the level of the factor being considered, as:

ei(Q) aiXi; ei(N) - bixi; ei(Y) = eiXi

-9-

14. The se'ond model used is log-linear. In reduced form Model II

may be formulated as follows:

(lu) Q = kI nX.i uQi=l

(1) =o i i0 = 1

(17) Y= c it xi uyi=1

(i - 1 k explanatory variables investigated)

All equations may again be estimated independently through the least

squares method after trans2"ormation of all variables into logarithms.

As relationship (11) holds again the following constraints among co-

efficient estimates and residuals are met:

log, ao = loge bo +logec0

ai = b i + Ci

lo1ge uQ = loge + log u'Z

In this model. the esti-mated elasticities of response of output, acreage,

'and yield, as defined in paragraph 13 are equal to the coefficient

estimates proper.

IV. STISAMTED EQUATIONS

15. The dependent variables appearing in the equations are identi-

fied as follows:

Q, wheat production, in maunds(q - loge Q)

N, whLeat acreage lharvested in acres(n loge N)

Y, average yield of whleat per acre, in maunds per acre(y = log Y)

The correspondiUng dat,a are listed in Table 2.

16. The e:xplanatory variables entering the equations on the basis

of prior information (i.e., the Xi s of the theoretical equations

described in Section III) are identified as follows:

WYR is the ingstr8m -humidity chain index covering the whole

wiheat crop from preplanting to harvesting (July through

.ay),

WAU is the. %ngstrom huLiaidity indiex, August,

WJA is the igstr8m humidity index, January,

WAP is the 2ngstrom humidity index, April,

W? is thle tlgstrom humidity chain index covering preplanting

and planting (July-August-September),

WgG is the AngstrGm humidity chain index covering the period

of growth (December-January-February),

WH is the Rngstrm hiumidity chain index covering the

harvestinig period (March--Aoril-May),

Pt-2 is the wheat/sugarcane price ratio, lagged two years,

AI is the percentage of wheat acreage irrigated, and

Table 2: Lahore District: Acreaee Yield, and Production of lheat

-rior to ParTition 1920/21 - 19

1/Crop year- Acreage Yield Production

harvested per acre (1-1aunds)

(;aunds per acre)

1920/21 329,663 9.34 3,079,0431921/22 368,655 12.54 4,622,9341922/23 410,901 10.43 4,285,6971923/24 463,906 11.26 5,223,5821924/25 412,866 6.71 2,770,3311925/26 395,668 9.60 3,798,4131926/27 391,586 9.96 3,900,1971927/28 373,072 3.82 1,425,1351928/29 369,210 8.70 3,212,1271929/30 399,733 12.26 4,900,7271930/31 336,890 11.19 3,769,7991931/32 346,748 8.38 2,905,7481932/33 300,762 8.18 2,1460,2331933/34 340,213 8.16 2,776,1381934/35 324,023 9.67 3,133,3021935/36 303,000 7.46 2,260,3801936/37 319,388 9.48 3,027,7981937/38 346,971 8.80 3,053,3451938/39 349,911 7.01 2,452,8761939/40 325,685 10.65 3,1468,5451940/41 346,485 8.98 3411124351941/42 315,424 10.90 3,438,1221942/43 372,114 11.19 4,163,956

1943/44 344,426 9.93 3,420,1501944/45 350,599 12.95 4,540,2571945/46 374,635 10.06 3,768,828

1/ Crop year from July tlrough June.

Source: Agricultural Statistics of the Punjab (Pakistan), Board ofEconomic Inquiry, Punjab, Lahore, 1949; and Rab, Abdur, Acreage,Production and Prices of Major Agricultural Crops of WestPakistan-Punab,l_19311959, Statistical Paper No. I, TheInstitute of Development Economics, Karachi, 1961.

Table 3: Lahore District: Data Pertaining to the Explanatory Variables Appearing in the Models:Prior to Partition (1920/21 - i9h5/L46)-

Crop year l/T 'IXU WJA WAP Tz W WP d'i Pt-2 AI tt-2

1920/21 51 208 0 3 93 0 1 0.57 87.0 01921/22 129 201 61 9 201 49 13 0.67 81.9 11922/23 168 69 227 75 173 197 41 0.70 75.0 21 923/24 177 284 289 3 152 256 30 o.60 73.4 31924/25 114 62 64 2 156 77 20 0.68 68.9 41925/26 106 171 78 36 143 38 164 0.74 7P.6 51926/27 140 492 0 16 229 36 18 0.71 72.9 61927/28 90 141 34 35 120 64 25 0.57 77.5 71928/29 95 161 8 7 157 23 2 0.71 74.5 81929/30 167 507 85 71 240 95 13 0.74 79.7 91930/31 141 58 207 11 157 141 62 0.72 78.8 101931/32 179 343 156 12 272 74 46 0.52 67.8 111932/33 74 73 9 39 101 39 51 0.35 83.8 121933/34 146 393 78 ;2 229 42 65 0.52 73.8 131934/35 192 166 480 187 102 366 75 0.92 84.2 141935/36 72 125 13 30 73 75 61 0.59 83.5 151 93- /37 138 146 1 84 122 191 32 0.49 78.0 161937/38 140 10 230 17 124 173 10 0.57 83.6 171938/39 67 30 41 7 20 134 101 0.75 82.0 181939/4o 114 61 316 8 78 191 37 0.56 82.0 191940/41 75 122 183 3 75 92 21 0.35 78.2 201941/42 100 51 82 55 113 86 84 0.50 80.3 211942/43 126 283 170 17 162 101 10 0.08 80.3 221943/44 98 36 149 82 68 151 82 0.87 78.2 231944/45 180 194 548 134 147 265 55 0.80 80.3 241945/46 92 157 3 8 152 13 46 0.99 80.3 25

l/ Crop year from July t1hrough June.

Sourcee Raw data from Pakistan Meteorological Service, Karachi, and Board of Economic inquiry,Pxija'c, I akic;v.n, -)P. w(i r,

-13-

t is the time trend.

Corresponding data are listed in Table 3.

17. Estimates of the regression equations are shown in Table 4 for

the exponential (or semi-log) model' (Model I: equations 18. through 26),

and in Table 5 for the log-linear model (Model II: equations 27 through

35).

18. Separate regression equations have been fitted to the data for

tcreage, yield, and production, first involving an aggregate weather index

covering the whole crop year; second, involving separate weather indexes

for August (preplanting), January (growing), and April (harvesting) in

view of the critical importance of proper moisture at these periods of

the whieat cycle in the Lahore District; third,-involving separate three

months weather indexes covering every one of the major subperiods of the

crop cycle, in an effort to single out the weather effects during the

whole of each subperiod.

19. All equations have been estimated independently tlrough the

ordinary least squares method. A more consistent and slightly better fit

was obtained for Model I as compared to Model II. For all regression

equations the following statistics have been calculated:

(1) the constan t term of the equation,

(2) the coefficient of multiple determination R 2

(3) the coefficient of multiple determination adjusted for2degrees of freedom, shown between brackets belowT the R,

(4) the t-statistic, taken as the ratio of the coefficientestimate to its standard error, to test whether or not

. 2 2a7 t b, S il & .J@ # 4a d .5 f.1t a93:<D,S e S.tSa: U............... @s kt->r o -1..t. .1A a;A<. .....-fl .. X. res ... .s es a.( own:.~1 -- ~1ttz ..<. .. .:-.....

the parameter estimate of a partuicular independent varia-ble was significantly different from zero. For a sig-nificance level of 5 percent, we would accept assignificantly different from zero a parameter estimateyielding a t-statistic of 2.086 for 20 degrees of freedom,and 2.074 for 22 degrees of freedom -- and 1.325 and 1.321respectively, for a significance level of 10 percent,

(5) the Durbin-Wiatson d-statistic to test for the presence

of serial correlation among the residuals,

(6) the RHO:statistic. Whereas R2 showis the performance of

an equation compared to the naive hypothesis tnat thedependent variable always takes its mean value, the sta-tistic RHO (o2) measures the explanatory power of anequation compared to the somewhat less naive hypothesisthat the value of the dependent variable in period t

Will be.the same as its value in period t-l.

20. The matrix of intercorrelation among the explantory variables

involved in the models proposed is shown in Table 6 where it can be ver-

ified that variables significantly correlated at least at the standard

5 percent level (R = 0.38) do not appear together on the riglt hand side

of any equatiorns proposed subsequently, except for wveather and the

irri.gCte('I acreage ratio.

Taole 4j: Iaore District - -iheat Production - Model I - Natural Exonntial - Separate Equation3 for Acreage,Tield and Productim (192z0/z2 - 191615 ) I/

q - loge Q; n - log, N; y - log6 Y

Alternative Zquat i5ns a, d RHO

2rodiction

(OE) q = 13.690 + S.003h a + C._373r Pt-2 + '.&f28 A! O-.OC317 t 0.356 1.58) G.633(287.835) (2.503) (1 ) (0.707) (0.471) (C234)(19) = 14.180 + 0.00066**WAU + C;.00C91*WJA - 0.00^11 IWAP- 0.3530C + 0.00441 AI - 0.001448 t 0.380 1.751 0.644(289.057) (1.636) (2.121) (..1) (1.659) t2 (^37o) (;.618) . (0.184)(2C) q 13.200 + 0;.00261 W? + 3.300?5*k2 - 0.00008 -dP + .l3090 2 + -01353 AI - 0.00080 t 0.383 1.513 o.646(269.617) (2.221) (1.59';) (c.054) (1.333) (0.997) (0.109) (0.188)

Acreage harvested

(21) n= 13.460 + o.xoCo6 uR + 0.27L490 f .P - 0.01cr)6 AI - X.0057'. t 0.602 1.560 0.477(963.222) (0.136) (3.016) - (2.927) (2.928) (0.526)

(22) n 13.33C + 0.00005 W4AU + c.00C18*JA - ;.-0067nA?+ ,.29160CP*2 - 0.008614AT - C.o0582*t 0.664 1.647 0.567(988.398) (0.482) (1.5o5) (1.720) (3.285) (2.635) (2.922) (0.558)(23) n = 13.59C 2 .00016 ;i? + .X00,08 0 -r .X0037 4-i + C.28990 ?t- 2 - 0.01133 Al - 0.o0598 t 0.623 1.7- 3 0.508(949.630) (0.460) (C.43) (o.86o) (3.069) (2.855) (2.785) (0-503)

Yield

2b1) y = 0.22r + 0.003!3 .J,R T- 0.162L,i P C-018341 + .00262 t 0.336 1.851 0.659- t-2 .13 I+0.26t( 5.301) (2.712) (G.576) (1.725) (0-.428)

(0.210)(25) y = 0.846 + 0.00061 lWU + 0.OOG73 WJA - 0.00073 WA.P+ 0.24370 Pt-2 + 0.01305 AI * 0.00134 t 0.307 1.962 0.637(18.219) (1.589) (1.805) (3.548) (0.798) (1.157) (0.196) (0.088)(26) Y = - 0.388 + 0.00277 WP + O.C0088 i6 + 0.00029 dH + 0.14100 Pt2 + 0.02486 AI + 0.00517 t 0.379 1.821 o.68o8.829) (2.625) (1.638) (-0.220) (o.486) (2.041) (0.784) (0.183)

1/ The t-statistic is shown between brackets below the c3.3fficient estimates. indicates coefficient estitnates significant at least at the 5 percent level;indicates those significant at the 10 percent level.

Table 5: Iahore D!tr; t - Whet Production - Model II - Loe Linear - Separate Equations forAc;:^"V, Tield, and Prodictitx (!20/ZI - 1645/116) I/

In these equctims, all variable3 are in log, except for t (ti).

Equation 2Nunber Alternative Squations R dc RHO

Production

(27) q = 9.265 + 0.419ho + 0.23920 Pt-2 + 0.8951G ai - 0.00336 t 0.360 1.545 0.639( 2.083) (2.579) (1.234) (0.965) (0.507) (0.238)

(28) q = 12.830 + 0.o9407*1Iau + 0.04429 wja - 0.00667 wap + 0.33560cP + o.4to410 a- 0.00246 t 0.284 1.913 o.58B( 2.871) (1.439) (1.471) (0.195) (1.584) 2 (0o403) (0.315) (o.o58)

(29) q = 9.494 + 0.25040* p + 0.06380 wg - 0.02797 wh + 0.330106p + 0.98100 ao - 0.0oo57 t 0.357 1.637 0.634(1.953) (2.109) (1.199) (0.501) (1.694) 2 (o.952) (0.072) (0.154)

Acreage harvested

(30) n 16.040 + 0.012O04 vyr + 0 16360*P - 0.72800 ai - o.n/ 523 t 0.584 1.588 0.453(11.963) (0.246) (2:801) t- (2.604) (2.618) (o.5c4)(31) n = 15.630 + 0.00575 wau + 0.00989 wja - 0.01257 wap + 0.17080* Pt 2 - 0.62680 ai - 0.00523*t 0.628 1.556 0.514

(12.976) (0.326) (1.218) (1.047) (2.991) - (2.316) (2.491) (0.510)

(32) n = 16.190 - o.oo425 wp + 0.01610 wg - 0.01425 wh + 0.16580 Pt 2 - 0.74780 al O.00537*t o.60g 1.671 o.483(11.417) (0.123) (1.037) (0.875) (2.917) (2.489) (2.321) (0.485)

Yield

(33) y= -6776 + 0.40730* wyr + 0.07554 Pt-2 + 1.6230o>ai+ 0.00187 t 0.342 1.789 o.669(1.679) (2.763) (0.430) (1.930) (0.311) (0.216)

(34) -2.803 + 0.08832 waU + 0.03441 wja + 0.00391 yap + 0.16480 Pt 2 + 1.03100 ai 4 0.00277 t 0.224 2.121 0.595( 0.673) (1.451) (1.227) (0.094) (0.836) (1.103) (0.382)

(35) y -6.693 + 0.25470 wp + 0.04770 wg 0.01372 'wh + 0.16430 Pt-2 + 1.72900 ai + 0.00480 t 0.331 1.893 o.657(1l508) (2.349) (0.982) (0.269) (3.923) (1.838) (0.662) (0.119)

gm he t-Statistic is shown between brackets below the coefficint eatiutes. indicates coefficient estimates significant at least at the 5 percent level;irdicate those significant at the 10 percent level.

A

Table 6: Lahore Diistrict - Viheat Production - Hiatrix of Intercorrelation Coefficientsn lanatory Variables 120/21 - 194574-

W-TAU T-JA WAYfi-p ,Wp i-IG WH WYRP t t

WAU 1.00 -0.10 -005 075 -0.20 -0.25 0.4e 0.10 -0.334 -0.26

I.A 1.00 0.57* -0.06 O.8)4* 0.10 O.63* 0.24 0.09 0.27

4,,2 1.00 -0.11 0. 6 0 0.47* 0.32 0.25 0.24

1.00 -0.23 -0.27 0.62* 0. 08 -0. 60 -0.37

WG 1.00 0.12 0.62* 0.21 0. 2 0.23

WH 1.00 0.17 0.15 0.09 0.17

T;j) 1.00 0. .39* 0.1

pt2 1.00 0.07 0.20I 1.00 0.27

t 1.00

Signnficant at lea-.t at the 5 percent level. /

V. £EESPONSE TO INDIVIDUAL FACTORS ELASTICITIES AND THEIR INTERPRETATION

21. Elasticities of the responses of acreage, yield, and production

to the various factors involved in the models are sumarized in Table 7.

They are to be interpreted as the ratios of the relative change in acreage,

yield, or productiorn, to the elative change in any one of the factors

appoaring on the righat hand side of the equations, all other factors being

held at their average level for the time span covered by the sample.

22. Table 7 silows, (in the order of appearance of the explanatory

variables in the ecquations), that in the Lahore District, prior to Parti-

tion

- a 1 percent increase in the Angstrom humidity chain index for

the overall crop year (from July through May) would have been

associated withl a 0.4L2 percent increase in wheat production,

due entirely to a corresponding increase in the average

yield of wheat per acre;

- a 1 percent increase in the wheat/sugarcane price ratio

lagged two years would have been associated with a 0.24 to

0.29 percent increase in wqheat production, through a 0.16

to 0.18 percent increase in acreage and a 0.08 to 0.11

percent increase in yield per acre;

- a 1 percent increase in the percentage of irrigated acreage

of wheat would have been associated with a 0.65 to 0.90

percent increase in wheat production resulting from a 1.44

to 1.62 percent increase in the average yield of wheat per

acre combined with a 0.79 to 0.73 percent decrease in

acreage.

-19-

23. When attempting to single out the weather effects, at various

times of Lhe wheat crop cycle, the alternative models pioposed suggest

that0

- a 1 percent increase in the Angstrom chain humidity index at

pre-planting and planting would have been associated with a

0.25 to 0.37 percent increase in wheat production, again

entirely attributable to a yield increase of the same

magnitude;

- a 1 percent increase in moisture at growing time would have

been associated with a 0.06 to 0.11 percent increase in

wheat production, mostly through yield increase;

- a 1 percent increase in the w¢heat/sugarcane price ratio

lagged two years, would have been associated with a 0.28

to 0.33 percent increase in wheat production, half and half

attributable to acreage and yield increases according to the

log-linear model, against twio-thirst and one-third according

to the semi-log model;

- a 1 percent increase in the percentage of irrigated acreage

of wheat would have been associated with a 0.98 to 1.06

percent increase in whieat production, resulting apparently

from a 1.73 to 1.96 percent increase in the average yield

of wheat per acre combined with a 0.75 to 0.89 percent

decrease in acreage.

.24. These results provide some interesting measurements of the

influence of weather upon wheat productilon. Wheat yield per acre would

appear substantiilly affected by weather variations, even in an area

Table 7: anore Dist ict - Wheat Production - Response of Acreage, Yield, and Production to Wether, 'Wheat/Su.free Price Ratio (t-2). irrigation., ;nie (1923/21 - 19.5,6j 1/

c0 0 0

A.gstram Wheat/ Acreage Angstrom Angstrom Xngstr& Wheat/ A Angstrom AngstrAs Angstrom Wheat/ Acreage

t 19w-/ zi index Suzacane I Index Index index Sugarcane Index index Irnde Sugarcane ibiaiwa

h-o'le ?rct ?rice Ratio Ratic. Augst Janary April Price Rtio Ratio Planting Growing .a7rveating Price Ratio FRatio

fear Time .i Time Time

w 2 Al t WAU WJA NAP Pt.p Ai t Wn WG Pt-2 zI t

'eans 2;V 2.s7 J20 (78.635) (12.5) (174.769) (135.0773 (36.65Jl) (0.@;1) (78.635) (12.5) (140.73) (11I:.'9) (kL.t%0) (96,(e6;(12,5)

Model I - Natural Exponential or Si-Lo (Se Table k) N 26

Production i +a.24* +0.288Q +o.65l, -0.039 +0.116' +0.121* -0.052 +0.353' +o.317 -0.056 o.0367* +0. 109 -0.OOL +Q.28i+ +1.36u -0.010

Acrea,e + 1 307 +*.107l -Q.791* -0.072* +0.009 +0.024' -0.025" +0.192* .0.679* -0.073* -0.023* +0

.009

-. 0.17 +.1 91 -0.891' -0.375'f

Iiel' .-3 7 4107 +0.033 +0.107 +0.097 -0.027 40.161 +1.026 40.017 +0.390 0.100 00.313 +0.093 +1.955* 0.365

Model II - Log-Linear (See Table 5) S 26

?roduction +0.hl +0.2L0 +0.895 -0.003 +0.09h* +o.dU4 -0.009 +0.336w +o.14o -0.002 40.O251+ 40.o6J -0.028 +0.33(8 +''.981 --

-+0.3D2 3.loL -0.72B* -0. 005 0.006 *O.010 -3.013 +0.171 -0.627 -0.3 -0.OOL +0.01E -0.31Lk 40.166* -3.7h4

0.005*

field +0.407* +0.376 +1 .623s** +0.002 +0.088" +0.031L +3.03h +o.165 +1.031 +0.003 +0.255* +o.3138 -0.311 .. 16L .729* *.* .

lf indicates elasticities derived frm parameter estimates significant at least at the 5 percent level. indicate those which are derived from parameter estinates significant at the 10 p.rc.mu level.

.2/ Means: Production (3,'21,B88 Maunds); Acreage (358,174 Acres); Average yield (9.523 Haunds per Acre).

-21-

where most of the wheat acreage is irrigated. Wheat production appears

significantly responsive to changes in the wheat/sugarcane price ratio

with a two-year lag, on account of both acreage and yield. Regarding the

irrigation variable, in the form of the ratio of irrigated acreage of

wheat to all wheat acreage, it would appear logical that it should in-

fluence yield and acreage in opposite directions. We may expect that

the more wheat is grown on irrigated land, the higher the average yield

of wheat in the district; the less wheat is grown on non-irrigated land.

25. The reliability of these elasticities is, of course, no greater

than what of the coefficients from which they are derived. Also,there

have been suggestions that the responseS of acreage, yield, and total

output to changes in the explanatory variables (including the weather

indexes as well as prices), might not be of the same magnitudes in1/

either direction. To test such hypothesis, separate upward and downward

response models would have to be estimated. In addition, the constraints

of additivity between corresponding parameter estimates of a given vari-

able in the production, acreage, and yield equations of the models fitted

to the data would appear to evidence some shortcomings of the statistical

test of sigrnificance applied (t-statistic). For example, the parameter

estimates of, say, variable Pt-2 (wheat/sugarcane price ratio) in equa-

tionls 20, 23, and 26 (Table 4) do meet the constraint of additiivity:

Acreage Yield Production

Parameter estimates 0.191 0.093 0.284.

t-statistics (3.069) (O0h86) (1.333)

1/ Wold, Herman, TModel Building and Scientific Method"., lecture givenat the C.E.I.R. Symposium on Model Building, London, July 4- 6, 1967.

-22-

but the corresponding t-statistics indicate that the parameter estimates

of variable Pt - are significantly different fron zero at the 10 percent

level only in the acreage and production equa.tions. The parameter esti-

mate of P in the production equation would nevertheless embody thet-2parameter estimates of P in both the acreage and the yield equations.

t-2 zience, it would appear inconsistent to ignore the latter.

3 & WgM S2i - .i$ 2 ,,S . j , uE >,' t'S'f &-j '<:%/X. K.ik/' '5ht......................4.'..... :. S< 9fg- .....Ji6. .f: ... SM.!f ..t.M .-

-23-

VI. FORECASTIUTG

26. The equations of an agricultural supply model and the numerical

parameters appearing tiherein are in themselves of explanatory interest

in that they provide an insight into how domestic agricultural supply

is determined by various variables. But the ultimate "raison d'etre"

of a supply model lies in its usefulness to gauge the likely effects

of changes in the variables involved on future production, i.e., to

serve as a forecasting device.

27. Derived as tlhey are from actual observations, the equations of'

the regression models describe the pattern of wheat output responses in

the period of observation only. Nevertheless, in an environment where

structural changes are taking place but slowly, as is typically the case

in agriculture in developing countries, the parameter estimates of the

acreage., yield, and ouitput equations may be extrapolated a few years

beyond the period of observastion, hence providing short-run forecasts

of the likely responses of the dependent variables. Wle may, for example,

infer fromn models I and II proposed earlier that, all other things being

equal, the response of acreage, yield, and output attributable to the

weather are not likely to be substantially different a few years beyond

the period analyzed. Similarlyr, changes in acreage, yield, ,ad produc-

tion which are associated with changes in the wheat/sugarcane price

ratio, may be assaned to continue to be the same for some time a-head.

28. On tho other hand, making accurate forecasts of the dependent

variables, namely, acreage, yield, and output, beyond tlhe sample period

is a problem different from the one of explaining the prevailing

structure. Forecasts of the dependenit variable are usually generated

from equations offering high coefficients of multiple determination

(high R ). In this respect, a model can be a good forecasting model

even if it does not really explain the underlying structural relation-

ships.

29. The state-of-the-arts being constant in a traditional agriculture,

no trend is apparent in yield. Hence, expected yield is easily estimated.

An equation yielding reasonably good forecasts may then be obtained from

q3 i.e., log Q, uotal output, wJhich would include expected yield in logeform among the predetermined variables. A relatively simple forecasting

model for wheat output in a traditional agriculture such as in the Lahore

District may then be formulated as follows:

q = f (yield, wieather, prices, irrigation)

where expected yield embodies the level of technology for the equilib-

rium achi.eved (y = 9.523 maunds per acre). The insertion of the yield

variable in the acreage equation would considerably improve its fit and

help forecast acreage. Conditional forecasts may then be derived from

the forecasting eouations for a few years beyond the sample period by

inserting expected or conditional values of the explanatory variables,

including expected y-ield, illto -the predictive equations. Such short-

run forecasts are rneeded in short-run economic planning.

VII. CONCLTJSIONS

30. The study evidenices the importance of the weather effect upon

total wheat output, and upon yield per acre in particular. The analysis

also supports the view that traditional agriculture.is price responsive.

It appears to suggest that the response of wheat production to price

might consist of two components, a response in acreage and a response in

yield.

31. Since no significant trend in yield has developed from 1920/21

to 1964/65, it is possible to assume that some of the conclusions of the

pre-Partition model are likely to halve remained valid after Partition.

Wlhether this has really been so can,of course, only be determined by

comparing the pre-Partition estimates to the corresponding post-

Partition estimates. Such comparisons were, however, not possible with

the data available for this study.

APPENDIX

Graphic Analysis of the -Da La

LAHORE DISTRICT: ACREAGE OF WHEAT (1914/15 -1964/65)(THOUSANDS OF ACRES)

550 I TI-T I 550

5 0 0 i --- - - _ - - 500

450. 1450

400'i400

300 300

2501 250

200 200 ___

15 0 L 15O

1910/Il 1915/16 1920/21 1925/26 1930/31 1935/36 1940/41 1945/46 1950/51 1955/56 1960/61 1964/65

CROP YEARS

(R)Econ Dept., IBRD-3593

LAHORE DISTRICT: AVERAGE YIELD OF WHEAT PER ACRE(1914/15-1964/65)(MAUNDS /ACRE)

16 1 6

14 14

112

lo, I 0 11e I lI0I

8_ _ -- ~ -.--..-.---

2 --- --- -----tl . -�--t- 26

1910/li 1915/16 1920/21 1925/26 1930/31 1935/36 1940/41 1945/46 1950/51 1955/56 1960/61 1964/65

CROP YEARS >

(R)Econ. Dept., IBRD-3594

LAHORE DISTRICT: PRODUCTION OF WHEAT (1914/15-1964/65)(MILLIONS OF MAUNDS)

7 I X , X, , i, | -t-.T . - r-~---r. - - - --7

6 -- -T 6

.'"'';1'':,''.5' 15XAX,\* r] --- _l_____D

; - , B

4 -4

3j3

I _ _ _ _ _ _ _ _ _ _'

*1i III-. 1 ..

.. .oOK,1910/11 1915/16 .1920/21 1925/26 1930/31 1935/36 1940/41 1945/46 1950/51 1955/56 1960/61 1964/65

CROP YEARS

(R)Econ. Dept., !BRD-3595

WEST PUNJAB: CALENDAR OF WHEAT CULTIVATION PRACTICESI

OPERATION | JULY, AUG. SEPT. OCT NOV. D EC. JAN. FEB. MAR. APR. MAY J JU NE

PREPARE AND PLANT |--

FIELD PREPARATION---------------- - 3

PRE-CULTIVATiON IRRIGATION-- ------- i

-PLANT------------- o

FLOWERING

HARVEST ---- ---------- --------- ----- - - -m

- U@SUAL PERiOD VARIATION FROM USUAL PERIOD

SOURCE. IBRD-Progromme for the Development of Irrigation and Agriculture in West Pakistan,Comprehensive Report, Volume iO, Annexure 14, Watercourse Studies, May, 1966.

LAHORE DISTRICT: PRECIPITATION FOR THE "BEST" YEAR (1944/45) AND THE "WORST" iYEAR(1927/28) FOR WHEAT PRODUCTION (SELECTED ON THE BASIS OF THE AVERAGEYIELD PER ACRE) 1920/21 TO DATE(INCHES)

9g I - I ---j--------,-----gj

8 :8

t_ *- -PREPARE AND PLANT --

6 K - - . - - --. - - - . . - - -5__ _

5 - GROWING La-_|_,

4 i- -- \ \ -- -.--- -- -. -_ -_-_------__-__

BEST" YEAR (1944/45) ' A3 \HARVESTING - 3

"WORST" YEAR (192'7/28)

3a, / '4 --t -\

JU U . oJUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN0

(R)Econ Dept., IBRD-3591

LAHORE DISTRICT: AVERAGE PRECIPITATION OF THREE "BEST" YEARS AND THREE"WORST" YEARS FOR WHEAT PRODUCTION (SELECTED ON THE BASIS OF THEAVERAGE YIELD PER ACRE) 1920/21 TO DATE(INCHES)

9 1~~1~9

' <- PREPARE AND PLANT - _ :_._

7 / \ < GROWING ->7.

6 i \ .. -.. 6

5*-.HARVESTING -* |__

4 - ------ -- 14

AVERAGE OF "BEST" YEARS

2 I

0JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN C

I

(R)Econ. Dept., IBIRD-3592 0

LAHORE DISTRICT:ANGSTROM 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(ANGSTROM INDEX)

600 7-- - 00

"BEST" YEAR (1944/45)

00 HRVESTING 00

I WORST" YEAR (1927/28)

oL 'A

300r ROIN ' Vj- '-- --- - ---- i 10

s~~~ ; I

.1 MONHL I - /\ BY TWOST YERO197/T)HS\

Jul Aug Sep Oct Nov Dec Jon Feb Mar Apr Moy Jun JA AS SO ON ND DJ JF FM MA AM tAJ JAS ASO SON OND NDJ DJF JFM FMA MAM AMJMONTHLY ,1 B3Y Two MONTHS 31 BY THREE MfONTHS am-:

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37'- NUMBER OF THE VARIABLES IN THE MODEL

{(2REcon DepI,IBRD-3596 -

WEST PUNJAB: HARVEST PRICES FOR WHEAT AND MAJORSUBSTITUTES, PER MAUND., DEFLATED, (1914/15- i950/51)(DEFLATED PRICES) __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4- I 1 T I I IT T 4.0

3.5~ 1'-3.5

A-COTTON

3.0: ~- 3.0

I D-COTTONm...>..

2.5i t 2.5

SUGARCAN

1.5 11

5! 5

% /-4(REV.Dp.,IR-32

1.0 v

LAHORE DISTRICT: WHEAT ACREAGE IRRIGATED, ACTUAL, AND ASPERCENTAGE OF TOTAL WHEAT ACREAGE (1914/15-1964/65)

400 1 1 i 1 |

I ,350-

WHEAT ACREAGE IRRIGATED

F SLEFT SCALE)3000Xi v 0

AAcw250

LL0

V,, 2001z

O I501 90%

100 80%

50 7__% OF WHEAT ACREAGE IRRIGATED

(RIGHT SCALE )

1910/l1 1915/16 1920/21 1925/26 1930/31 1935/36 1940/41 1945/46 1950/51 1955/56 1960/61 1964/65

CROP YEARS

* Data not available from 1939/40 to 1946/47, therefore dashed lines are estimated.

(R)Econ Dept., IBRD- 3623