Dogan Shor e Communicaion al., J. Anim. Plan Sci. 4(4):014 The Journal of Animal & Plan Sciences, 4(5): 014, Page: 1573-1578 ISSN: 1018-7081 LONG YEARS APICULTURE DATA MODEL OF TURKEY: AN ECONOMETRIC TIME SERIES ANALYSIS Z. Dogan *, M. Karagoz ** and G. O. Ozbakir * * Harran Universiy, Faculy of Agriculure, Deparmen of Animal Science, Şanlıurfa, Turkey e-mail:zdogan@harran.edu.r ** Universiy of Yıldız Technical, Faculy of Ars and Science, Deparmen of Saisics, Isanbul, Turkey ABSTRACT The empirical sudies in he field of apiculure are rare boh in Turkey and abroad. Neverheless he imporance of apiculural producions for nuriion and indusry is growing. In his sudy we are modeling long years apiculure daa of Turkey. The employed mehodology is a compound of economeric srucural modeling combined wih ime series approach of ARMA. A he firs sep we have esimaed a Cobb-Douglas producion funcion for each of honey and wax producion series. Then he residuals are esed for uni roos and searched for ARMA srucures. Cobb-Douglas funcions of honey and wax producions are significan wih relevan ARMA modeling of residuals.we have found ha, he elasiciies of honey and wax producions agains he old ype hives are negaive while heir elasiciies agains new ypes are 0.45 and 0.35 respecively. Overall he resuls are indicaive of inelasiciy of producions for he number of colonies. This is a clear seback for he produciviy of apiculure indusry given he high rank Turkey s producion and colony numbers in he world ranking. More sophisicaed mehods should be searched in order o develop produciviy and compeiiveness of Turkish apiculure in he world markes. Key words and Phrases: Apiculure, Cobb-Douglas Funcions, ARMA Modeling. INTRODUCTION One of he earlies empirical sudy in he field of apiculure daes back o 1970s in Turkey. Isyar (1974) used a 10 years daa o esimae a preliminary economeric model of Turkey.Empirical sudies in he field of apiculure are relaively rare in he inernaional lieraure as well. One of he modelingsudies comes from Wille (1991). She has presened a naional beekeepingindusry model of USA, assuming raional expecaions. Wille and French (1991) presened a dynamic economeric model of he U.S. beekeeping indusry for policy analysis and economic projecions. Parlakay e al, (008) in heir sudycalculaed rends values by using colony numbers, honey producionand foreign rade so as o evaluae he beekeeping indusry in Turkey. Cviković e al, (009) deermined he basic economic parameers of honey producion expor and impor in Croaia and worldwide. They also esimaed he marke value of Croaian beekeeping as a whole for he year 007. Vural and Karaman (010) analyzed echnical and economic aspecs of apiculure indusry in Turkey. In his paper, he effec of old and new ype beehive use for he honey producion in Turkey was examined. Recenly, empirical economeric research has sared o ake ino accoun he poenial bias and loss of efficiency by employing he spaial economerics mehods which incorporae he spaial dependence ino model specificaion. Using classical linear and spaial economerics regression models Koshiyama e al, (011)sudied socio-economic, echnological, managemen and geographic facors ha have influenced he honey prices. The presen sudy has several moivaions. Firs of all, we aim o make a firs aemp for modeling he apiculure daa of Turkey. The elasiciy of honey and wax producions wih respec o various ypes of hive inpus can be evaluaed for policy purposes. The resuls of analysis can be used for economic analysis such as compeiiveness, susainabiliy and efficiency or produciviy of Turkish apiculure indusry. The consrucion of he paper is as follows: In he nex secion we presen a brief review of apiculure sudies in he modeling conex. In he hird secion, he main mehodological ideas employed in he sudy, namely Cobb-Douglas producion funcion, ARMA modeling, ADF uni roo es ec. are presened. In he fourh secion we presen he daa and main resuls of he sudy, combined wih imporan inference and implicaions. Las secion is devoed for overall conclusions. MATERIALS AND METHODS The source of our annual apiculure daa is Turkish Saisical Insiue (TURKSTAT). I spans from 1936 up o 01 and consiss from annual numbers of beehives (boh old and new ypes) and honey and wax producion as meric ons. In sum, he daa se of 77 annual observaions is a comforably sufficien sample 1573
Dogan e al., J. Anim. Plan Sci. 4(4):014 dimension for a ime series analysis. We have worked wih logarihmic series, which is a usual pracice o deal wih he heeroscedasiciy problem of ime series. 16 14 1 10 8 6 4 1940 1950 1960 1970 1980 1990 000 010 LOLD LNEW LHON LW AX Figure 1.Annual apiculure series of Turkey 1936-01. The producion of honey proceeds over he wax, and here is a clear slowdown in he speed of increase beginning wih 1980s.Several poins can be deduced from he visual inspecion of he above graph. The number of old ype hives are in a seady decrease saring wih 1970s while he number of new ype hives are on a seady increase wih he sar of 1950s. We employed a combinaion of economeric and ime series modeling approach, in he sense ha iniial model is an economeric model and residuals are modeled as an ARMA modeling. This wo-sep modeling approach specificaion is Y X u, A( L) u B ( L), 1,,,T (1) Y Here is he dependen variable, X is he vecor of independen variables, is a vecor of parameers, u is he random disurbance erm, p 1L al a p L A( L ) 1 a and B L b L b L b L q ( ) 1 q are lag polynomials 1 a appropriae p and q lenghs and is a whie noise. u For a saionary disurbance erm, any ARMA modeling can be represened in shor as u ~ ARMA( p, q ). This approach can be handled wih any economeric sofware such as Eview which is employed in he presen sudy. As a saring poin economeric model we use Cobb-Douglas producion funcion. Cobb-Douglas producion funcion posulaes Q a ime is a weighed Z ha any producion geomeric average of inpus Z1 and as follows: 1 u Q A Z1 Z e, 1,,, T () Where e u is he naural log base, is a disurbance erm wih zero mean and consan variance. In he conex of Q apiculure daa, sands for he level of annual honey Z or wax producion, 1 and Z sand for old and new ype beehives respecively.as he leas squares esimaion procedure possesses BLUE (bes, linear, unbiased esimaor) properies, we need o linearize he model (1). Themodel is linearized using log ransformaion as below ln Q ln A 1 ln Z1 ln Z u (3) Having changed name of variables as Y ln Q, X 1 ln Z1 X, ln Z and he inercep 0 ln A reparameerized as, he linear model will be given as Y 0 1 X 1 X u (4) This is a mulivariable linear regression model and i can now be esimaed using leas squares mehod. Afer his sage, ARMA (Auoregressive Moving Average) modeling ses in. Firs of all, he residuals should be saionary in ha, he mean, variance and auocovariances a any lag should be independen of ime poin, ha is, hey should be consan. To insure he saionariy condiion of residuals, an augmened Dickey- Fuller es can be handled using 1574
Dogan e al., J. Anim. Plan Sci. 4(4):014 e a 0 a e 1 k e i i 1 i (5) If he es value for he gamma parameer esimae is less han criical MacKinnon heoreical values in algebraic erms, hen we conclude ha, he residuals are saionary. If residuals are saionary we can go forward o check heir ACF and PACF values for some reasonable lag lenghs in order o deermine he AR and MA orders of residual ARMA modeling. As a rule of humb, he number of significan ACF values is an indicaive for number of MA erms, while he number of significan PACF values is considered o be an indicaor for he number of MA erms.the significance of ACF and PACF for any lag K is esed by Ljung-Box (1978) as Q K LB T(T ) rk /(T k ) k 1 K If Q LB hen he null hypohesis of H0 : 1 K 0 is rejeced. For a horough evaluaion of ARMA modeling we refer o Box and Jenkins (1976). (6) RESULTS and DISCUSSION The exisence of increasing or decreasing rend in he series is indicaive of non-saionariy in he series. Neverheless, he degree of inegraion in he series should be checked by uni roo ess. The able below summarizes he ADF es resuls. Table 1. ADF Uni Roo es resuls for he levels and firs differences of apiculure series. Series ADF Saisics MacKinnon one-sided prob. DW for ADF regression LOLD -1.14679 0.71.175495 LNEW 3.355743 0.9997.097388 LHON 3.880717 1.0000.101177 LWAX.75491 0.9984.058700 DLOLD -.511701 0.016.05868 DLNEW -.437890 0.0153 1.953484 DLHON -9.97671 0.0000 1.989393 DLWAX -10.0007 0.0000.001619 Noe: Tes Criical Values 1 % level -.596586, 5% level -1.94560 and 10 % level -1.61391 Durbin-Wason (1971) saisics in he las column being close o means ha here is no auocorrelaion srucure in he residuals of auxiliary ADF uni roo regressions. All he MacKinnon (1991) one sided probabiliy values are greaer han even 10 % significance level. We conclude ha all four series have uni roos on he levels or hey are non-saionary. We have performed same uni roo es for he firs differences and he resuls are presened in he second half of able above. MacKinnon one sided probabiliy values are indicaive of saionary. The resuling saionary series can be observed from he figure below. We conclude ha all four series are inegraed of order one, ha is I (1). These resuls have esablished he exisence of coinegraion relaions beween variables, which says ha if he residuals of any linear combinaion of variables are saionary hen he variables are co-inegraed. In fac, he Johansen (1991) coinegraion ess which were due o space limi no repored here show ha here are a mos wo linear combinaions wihin he variables involved. We are now in a comforable posiion o esimae he relevan producion funcions. We have wo producion funcions, one for honey and anoher for wax daa. As far as parameer esimaes are concerned all he coefficiens are significan even 1 % significance level. Boh models assume a very high level of deerminaion coefficien. Residuals are supposed o be whie noise in ha hey should no show any auocorrelaion behavior. To his end Durbin Wason (1971) saisics should be around. Honey producion residuals more or less can be said no o have auocorrelaions. However wax residuals being close o 1, seems o have posiive auocorrelaions. A his sage, we should check he saionariy of residuals by an ADF uni roo es. The resuls are presened in Table 6 below. Having significance level greaer han 5 %, we are no able o rejec he null hypohesis of no auocorrelaion srucure for he residuals of LHON equaion, bu we are able o rejec he same null hypohesis for he LWAX equaion. Tha means ha here is an auocorrelaion srucure and his should be exploied. Eview allows for differen ARMA specificaions of he error erm. Therefore we should look for alernaive specificaions. According o he rule of humb advised by Box and Jenkins (1976), jus one period lag AR or MA erms would suffice. The alernaive bu significan LWAX models combined wih ARMA specificaions are presened in Table 5 below, 1575
Dogan e al., J. Anim. Plan Sci. 4(4):014 where we have wo compeing models. Boh are of good qualiies in erms of coefficien significance and residual auocorrelaions. However, even slighly i migh be, he model wih one auoregressive coefficien presened in he firs panel seems o be ouperforming he second one in erms of AIC values..6.4..0 -. -.4 -.6 1940 1950 1960 1970 1980 1990 000 010 Table.Esimaion of producion funcions DLOLD DLHON DLNEW DLWAX Figure.Saionary apiculure series of Turkey wih firs differences. Dependen Independen Coefficien Sd. Er. -Sa. Prob. R-sq. DW LHON C 8.1070 0.379454 1.401 0.0000 0.99 1.81 LOLD -0.319333 0.00643-15.469 0.0000 LNEW 0.45509 0.009338 48.460 0.0000 LWAX C 4.94149 0.405688 1.18 0.0000 0.98 1.16 LOLD -0.159986 0.0070-7.488 0.0000 LNEW 0.340555 0.009983 34.11 0.0000 Table 3.Uni roo es for he residuals of producion funcions Model Variable Coefficien Sd. Error -Saisic Prob. DW LHON RES(-1) -1.154381 0.113704-10.1549 0.0000.06977 LWAX RES(-1) -0.595535 0.103947-5.7904 0.0000-1.958045 ADF es resuls confirm he saionariy of residuals for boh equaions, which implies ha residuals can be searched for ARMA modeling. To his end, we need he ACF and PACF of heresidual series. Table 4. Residuals ACF and PACF Residuals of Honey Funcion Residuals of Wax Funcion ACF PACF Q-Sa Prob ACF PACF Q-Sa Prob 1-0.155-0.155 1.8630 0.17 1 0.404 0.404 13.09 0.000-0.14-0.43 5.4793 0.065 0.53 0.107 18.300 0.000 3 0.77 0.16 11.69 0.009 3 0.09 0.089 1.879 0.000 4 0.114 0.163 1.69 0.013 4 0.081-0.057.43 0.000 5-0.057 0.101 1.960 0.04 5-0.070-0.148.85 0.000 6 0.055 0.059 13.15 0.040 6-0.17-0.094 4.45 0.000 7 0.11 0.086 14.451 0.044 7-0.14-0.138 8.33 0.000 8-0.04-0.03 14.603 0.067 8-0.55-0.10 33.961 0.000 9 0.139 0.158 16.90 0.061 9-0.33-0.049 38.813 0.000 10-0.116-0.167 17.481 0.064 10-0.305-0.167 47.37 0.000 Noe: sandard deviaion significance band for acf orpacf values is ( 1 / 77 ) 0.8. 1576
Dogan e al., J. Anim. Plan Sci. 4(4):014 Table 5.Alernaive wax models Independen Coefficien Sd. Er. -Sa. Prob. R-sq. DW AIC C 4.858945 0.61946 7.844 0.0000 0.985.034-1.89 LOLD -0.156456 0.033448-4.6775 0.0000 LNEW 0.343044 0.015499.133 0.0000 AR(1) 0.403468 0.10613 3.8015 0.0003 C 4.9953 0.510086 9.799 0.0000 0.984 1.896-1.84 LOLD -0.16113 0.07757-5.8404 0.0000 LNEW 0.338706 0.01548 6.99 0.0000 MA(1) 0.35180 0.108819 3.330 0.0018 In Table 5, we have wo compeing models. Boh are of good qualiies in erms of coefficien significance and residual auocorrelaions. However, even slighly i migh be, he model wih one auoregressive coefficien presened in he firs panel seems o be ouperforming he second one in erms of AIC values. Now we can ge ogeher wo final models, LHON and LWAX for inerpreaions. The explici represenaions of esimaed models are: LHON 8.10 0.3 LOLD 0.45 LNEW LWAX 4.86 0.16 LOLD 0.34 LNEW e 0.40 e 1 Technological produciviy in honey producion is almos wo imes ha of wax producion. In boh models he elasiciy of producion wih respec o old ype hives are negaive. This negaive effec is more pronounced in he case of honey producion. The elasiciy of honey producion wih respec o new ype producion is 0.45 which means ha, a 1% increase in he number of new ype hives will increase he honey producion less han 1%. Tha is, honey producion is less elasic agains he hive numbers. The imporan poin regarding he old ype hives is ha, he mainenance of such hives canno be acknowledged on commercial grounds. I is jus a coninuaion of radiion. The echnological produciviy in boh equaions accouns for he increases in producion more han hive inpus iself.tha could be explained by learning by doing, oherwise reurn o scales is under uniy, which means ha decreasing reurns o scale is prevailing. Conclusions: We have found ha echnological produciviy is greaer han 1 for boh producion funcions. We have aribued his o he phenomenon of learning by doing. The elasiciy of honey and wax producion o old ypes hives seen o be negaive meaning ha on commercial basis heir mainenance is no raional. The elasiciies of producion wih respec o new ype hives are posiive bu less hen uniy, means ha inelasic. This is a clear seback for he produciviy of apiculure indusry given he high rank Turkey s producion and colony numbers in he world ranking. More sophisicaed mehods should be searched in order o develop produciviy and compeiiveness of Turkish apiculure in he world markes. REFERENCES Box, G. E. P. and G. M. Jenkins (1976). Time Series Analysis: Forecasing and Conrol. Revised Ediion. Holden-Day; Oakland, CA. 575 p. Cviković, D., Z. Grgić, Ž. Maašin, M. Pavlak, J. Filipi, and I. T. Gajger (009). Economic aspecs of beekeeping producion in Croaia. Ve. Arhiv. 79: 397-408. Dickey, D.A. and W.A. Fuller (1979). Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo. J. Am. Sa. Assoc. 74: 47 431. Durbin, J. and G.S. Wason (1971). Tesing for Serial Correlaion in Leas Squares Regression. Biomerika. 58: 1 19. İşyar, Y. (197 4). A Research on he effecs of he New Type Beehives o he Honey Producion in Turkey. Aaürk Üniversiesi Ziraa Fakülesi Dergisi. 8 (1): 47-5. Johansen, S. (1991). Esimaion and Hypohesis Tesing of Coinegraion Vecors in Gaussian Vecor Auoregressive Models. Economerica. 59: 1551 1580. Koshiyama, A.S., M.C.A. Lorenzon and W.S. Tassinari (011) Spaial Economerics Applied o Sudy he Influencing Facors of Honey Prices in Brazil, Brazilian J. Operaions & Producion Managemen. 8 (1):11-13. Ljung, G. and G. E. P. Box. (1978). On a Measure of Lack of Fi in Time Series Models. Biomerika. 66: 67 7. MacKinnon, J. G. (1991). Criical values for Coinegraion Tes. Pp.66-76. In: Engle, R. F. and Granger, C.W.J. eds. 1991. Long-Run Economeric Relaionships: Readings in Coinegraion. Oxford Universiy Press; New York. 301 p 1577
Dogan e al., J. Anim. Plan Sci. 4(4):014 Parlakay, O., H. Yılmaz, B. Yaşar, A. Seçer, B. Bahadır, (008). The Siuaion of Beekeeping in Turkey and he Fuure Expecaions by he Trend Analysis Mehod. J. Agriculural Faculy of Uludag Universiy. (): 17-4. Vural, H. and S. Karaman (010). Socio-economic analysis of beekeeping and he effecs of beehive ypes on honey producion. African J. of Agr. Res. 5(): 3003-3008. Wille, L.S. (1991). An applicaion of he raional expecaions hypohesis in he US beekeeping indusry. Norheas J. Agriculural and Resource Economics. 0(): 189-01. Wille, L. S., and B. C. French (1991). An Economeric Model of he U.S. Beekeeping Indusry. Am J Agr Econ. 73:40 54. 1578