Panel Model for Wheat Prices

Transcription

1 ISSN Journal of Statstcs Vol: 1, No.1 (005) 59 Panel Model for Wheat Prces Tanveer Akhlaq* Muhammad Qaser Shahbaz** Abstract A forecast models for wheat prces for the country s developed by takng producton area and mports as ndependent varables for the data 1971 to 004.Panel model technque s used to develop the models. Introducton Pakstan has a rch and vast natural resource base, coverng varous ecologcal and clmatc zones; hence the country has great potental for producng all types of food commodtes. Agrculture s the hub of economc actvty n Pakstan. It lays down foundaton for economc development and growth of the economy. It drectly contrbutes 5 per cent to Gross Domestc Product (GDP) and provdes employment to 44 per cent of the total labour force of the country. Wheat s the man Rab crop t s the leadng food gran of Pakstan and beng the staple det of the people t occupes a central poston n agrcultural polces.it contrbutes 1.5% of the value added n agrculture and.9%to GDP. Wheat was cultvated at an area of 7983 thousand hectares.4%lower then last year.the sze of the wheat crop s provsonally estmated at thousand tones whch s.9%lower then last year.the long dry spell effected the crop both n baran and rrgated area The yeld per hectare also decreased by 0.5%. The ncrease n wheat producton was manly due to ncrease n area by % and yeld 15%. * Department of Statstcs, Garrson Degree College, Lahore Cantt. ** Department of Statstcs, Government College Unversty, Lahore.

2 60 Akhlaq and Shahbaz Table 1 AGRICULTURE GROWTH IN PAKISTAN ( ) YEAR AGRICULTURE MAJOR CROPS MINOR CROPS

3 61 Fgure 1 AGRICULTURE GROWTH IN PAKISTAN ( ) years Agrculture Major crops Mnor crops. PANAL DATA MODELS The basc frame work for ths dscusson s a regresson model of the form y = X β + z α + ε t t t.1 FIXED EFFECTS Ths formulaton of the model assumes that dfferences across unts can be captured n dfferences n the constant term. Each α s treated as an unknown parameter to be estmated. Let y and X be the T observatons for the th unt, I be a T I column of ones and let e be assocated T I vector of dsturbances, then y = X β + α + ε Cornwell and Schmdt (1984)

4 6 Akhlaq and Shahbaz β y = [ X d1 d dn] + α Where d s a dummy varable ndcatng the th unt. Let the nt n matrx d d d d. D = [ ] 1 3 n y = Xβ + Dα + ε The least squares estmators of β as 1 b= X M X X M y [ D ] [ D ] 1 a = [ DD ] D ( y Xb) Var(b) = s [ XM X] 1 The F rato used for ths test s Fn ( 1, nt n K) =. RANDOM EFFECTS y = x b+ ( a+ u ) + t t t D ( R LSDV R pooled )/( n 1) (1 R LSDV ) /( nt n K) Mundlak (1978) Where there are K regressor ncludng a constant and now the sngle constant term s the mean of the unobserved hetrogenty, [ z α ] E. The component s the random hetrogenty specfc to the th observaton and s constant through tme. And further more the assumpton nvolve n ths modelng are, E E E E [ ε / X ] = E[ μ / X ] t [ ε t / X ] = σ ε [ μ / X ] = σ μ [ ε ε ] = E[ μ μ ] = 0 f j and t s t js j = 0

5 63 The formulaton of the model n blocks of T observatons for group I, y, X, μ, andε. For these T observaton, let η = ε + μ t t η, The covarance matrx s gven below Σ = σ I + I I = η1, η ηt And [ ] ε T σ μ T T The generalzed least square estmate of β s, ˆβ = Ωˆ Ω ˆ 1 1 [ X X][ X y] Hsao (1986) Ω = I n Σ Breusch and pagan (1980) have devsed a Lagrange multpler test for the random effects model based on the OLS resduals for H o H 1 : σ : σ μ μ = 0 0 And the followng test statstcs s dstrbuted as Ch-Square wth one degree of freedom s nt T e e LM= 1 ( T 1) e e.3 RANDOM CO-EFFICIENTS MODELS y = X β + Hldreth and Houck (1968) We fnd that Ω s a block dagonal matrx wth

6 64 Akhlaq and Shahbaz Ω = E ( y Xβ)( y Xβ) X = σ IT + XΓX we can wrte the GLS estmator as where n X X X y Wb = 1 β = ( Ω ) Ω = n = ( σ ( ) ) ( σ ( Γ+ Γ+ ) ) = 1 W X X X X Swamy (1971) 3. ANLYSIS The data s used for ths purpose s form 1971 to 004. The data s taken from ffty years of Pakstan n statstcs and statstcal year book. The prces are taken to be dependent varable, and area and producton are taken to be ndependent varable. The descrptve results for all the varables are gven bellow TABLE Descrptve Statstcs N Mnmu m Maxmu m Mean Std. Devaton Prce Producton Area TABLE 3 RESULTS FOR POOLED MODEL Coeffcent St. error T-rato P value Area

7 Producton Constant TABLE 4 RESULTS FOR PANELE MODEL Coeffcent St. error Z P value Area Producton Import 3.86e e Constant Wthn Between Over all R σ u σ e CONCLUSION From the table of descrptve statstcs t can be seen that the average prce of Wheat s and the varaton s.9003, for producton the average s and varaton s From the above analyss the pooled model for prce of wheat s gven bellow w = w w pt pr And from the p value we t can be concluded that the area and producton has sgnfcant effect on the prce of wheat. Further more from the above analyss t can be conclude that the panel model for wheat prce s a w pt = a w pr w w Whch shows that producton has postve and area has negatve nfluence on prce of wheat, and from the p values t can be

8 66 Akhlaq and Shahbaz concluded that and from the value of σ U = 0 we can conclude that the over all varaton wth n panel s zero. But from the value of σ e = the concluson s that the varaton n the coeffcents of wheat producton and area are varable between the provnce.e. Punjab, Sndh, N.W.F.P., Balochstan s at the rate of.4190, and all coeffcent are hghly sgnfcant, and overall varaton controlled by ndependent varable s

9 67 REFERENCES Years of Pakstan n statstcs (1998), Federal Bureau of Statstcs-Statstcs Dvson Government of Pakstan.. Economc survey of Pakstan for the years 1998 to Anderson T.W. (1971), The statstcal Analyss of Tme Seres, John Wley, New York. 4. Irrgaton and fertlzng wnter Wheat n South Western Kansas, Kansas Agrc. Exp. Sta. Bull. 44. (Feld Crop Absts. 16(1): 6; (1963(. 5. Wllam H. Green Econometrcs Analyss ffth edton. 6. Anjum A. (1998). Wheat producton and forecastng model for Pakstan. Dept. of Agrculture Economcs. Un. Of Ard Agrculture, Rawalpnd, 7. Shamma El. (1973). Effect of ntrogen fertlzaton on yeld and yeld components of wheat varetes. (Trtcum aestrum L.) Iraq J. Agrc. Sc. 8(1): Hashm U.M. (1998). Import of support prce on wheat (trtum aestvum) producton n Pakstan. Dept of Agrculture Economcs and rural socology. Unversty of Ard, Agrculture, Rawalpnd. 9. Azz A.M (199). Analyss of wheat producton Data dstrcts Fasalabad (Punjab) by usng stepwse regresson procedure. M.Sc (Stats). Unversty of Agrculture Fasalabad. (Research report). 10. Saeed N., Saeed A., Zakra M., Bajwa M.T. (000). Forecastng of wheat producton n Pakstan usng ARIMA. Dept. of Maths and Stats and Plant Breedng, Gentcts (U.A.F) , Pakstan. College of veternary Scence, Lahore. Pakstan. Internatonal. Journal of Agrculture and Bology /000/