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ЕCONOMETRIC FORECAST OF AGRICULTURAL SECTOR INVESTING
IN LVOV REGION
Rostyslav Lytvyn, Research assistant Lvov national university of veterinary medicine and biotechnologies named after S.Z. Gzhytskyj, Lvov, Ukraine E-mail: lytvynr@ukr.net
ABSTRACT
Purpose of economic processes forecasting in agriculture is more relevant and urgent in recent years with application of applied econometric methods. In represented research paper, these methods are used to forecast investment and the main agricultural industry indicators of Lvov region of Ukraine. The linear trend model, the parabolic trend model and the exponential trend model were elaborated from the period from 2000 to 2009 in this scientific study using applied statistical tool STATGRAFICS and EXCEL spreadsheets. And with assistance of these models forecast for investment on the basis of data of essential indicators of agrarian sector of the region for 2010 and 2011 was made. All models with probability р=0,95 are adequate experimental data for 2000-2009 years, that allow to make the forecast of investments and main agricultural indicators of the researched region by these models for 2010 and 2011 years. Nevertheless, it should be pointed out that, because of small amount of input data analysis of regression equations coefficients have more qualitative than quantitative influence upon resulting variable y6.
^Y WORDS
Investment; Agrarian sector; Forecasting; Linear trend model; Parabolic trend model; Exponential trend model.
Accordingly to statistical data of agricultural sector of Lvov region and Ukraine provided by State Statistical Service of Ukraine for 2000-2009 years, presented in tables (1) in this applied research calculate main dynamics and trend models and calculate predicted values and their estimates for forthcoming two years with application of the applied statistical tool STATGRAFICS and EXCEL spreadsheets.
To vital issues of investing processes in agriculture of Ukraine's economy have dedicated one's researches many prominent scientists, among them: A. Carita, I. Luyt, N. Santos et al. [1], K. Crane, F.S. Larrabee [2], K. Vitale [3] and others. In this research one's attention is paid to study investment of agriculture of Ukraine and another developing economies with assistance of econometric methods, that are displayed in scientific works of: V. Yeleyko, O. Yeleyko, I. Kopych, R.. Bodnar, M. Demchyshyn, O. Synytskyy, A. Chemerys [4-7], M.I. Gómez, E.R. Gonzáles, L.F. Melo [8], F. Ruff [9], N. Carnot, V. Koen, B. Tissot [10], R.S. Mariano, Y.K. Tse [11] and R. Gupta, A. Kabundi [12].
Input data of the models:
Table 1 - Dynamics of agricultural sector main indicators of Lvov region
Year y6 bln. UAH y7 mln. UAH ys mln. USD ys mln. pers. y10 mln. UAH
2000 5,850 48,3 2,412 0,267 10,5
2001 7,305 -4,2 2,412 0,283 18,8
2002 8,578 -7,0 2,935 0,285 14,2
2003 10,547 45,0 0,041 0,228 30,7
2004 13,992 63,2 0,064 0,216 40,3
2005 17,192 70,8 0,438 0,213 75,1
2006 21,486 166,3 0,612 0,189 84,0
2007 27,987 231,9 1,653 0,188 211,0
2008 35,534 77,7 31,783 0,177 549,8
2009 39,893 17,9 91,482 0,175 321,9
Source: State Statistic Service of Lvov region and Ukraine [13,14].
Here comes:
y6 - gross regional product (Lvov region) in actual prices, in bln. UAH; y7 - financial result of general activity (agriculture) of Lvov region before taxation, in mln. UAH;
y8 - foreign direct investment in agriculture (Lvov region), in mln. USD; y9 - quantity of the employed persons in agriculture of Lvov region, in mln. pers.; y10 - investment in capital assets (agriculture) of Lvov region, in mln. UAH. Econometric forecast models. Thus linear (ylin), parabolic (ypar) and exponential (yexp) trend models will look like:
vin= -2,39867+3,86092 • t (1)
vr= 6,16267-0,41974 t+0,38915 t2 (2)
y:xp= exp {1,51972+0,22185 t} (3)
yf= 15,3333+10,5267 t (4)
yPar= -55,3167+45,8517 t-3,21136t2 (5)
ye7xp= exp {2,62598+0,20017 t} (6)
Vsin= -20,0469+6,07821 t (7)
vr= 31, 8863- 19,8884 t+2,3606 t2 (8)
VsXP= exp {-1,52552+0,35111 t} (9)
v!;n= 0,2946-0,01318 t (10)
vr= 0,3056-0,01868t+0,00050 • t2 (11)
vrp= exp {-1,19592-0,05906 t} (12)
ylin = -120,98+46,6564t (13)
ypar= ■'10 54,0783-40,8728 • t+7,9572 • t2 (14)
yexP= '10 exp {1,73874+0,43376 t} (15),
where yi (i=1,2,...,10) - regulatory or averaged values of the researched indicators; t - time.
Relevant predicted values and their estimates based on trends (1) - (15) were calculated, that are displayed in table (2). Here: ME - mean value of the error; MSE - mean square value of the error; MAE - mean absolute value of the error. It is necessary to notice that the closer the values of ME, MSE and MAE to zero, the better will be calculated forecasts value of the appropriate indicators.
Table 2 - Forecasting values and estimation indicators of Lvov region's agricultural sector
Indicator Indicator forecast ME MSE MAE
2010 2011
1 2 3 4 5 6
bln. UAH
v"n 40,071 43,932 0 8,4881 2,6473
vior |48,633| |57,163| 0 0,4921 0,5402
?rp 52,459 65,489 0,0132 0,9590 0,6575
mln. UAH
№ 131,127 141,653 0 3845,42 46,4147
yf7or |60,477| |32,467| 0 3300,90 48,9838
yexp 124,939 152,626 24,4689 4905,24 143,899
mln. USD
ylin 46,813 52,891 0 456,364 16,4355
yfor |98,747| |133,152| 0 162,139 10,8384
yexp 10,347 14,699 10,9969 782,519 12,4516
mln. Pers.
ylin 0,1501 0,136 0 0,00020 0,0116
1 2 3 4 5 6
9lor 10,1611 |0,153| 0 0,00019 0,0103
v:xp 0.158: 0.149 0,00039 0,00019 0,0104
mln. UAH
~lin 'm 392,240 438,896 0 10280,6 76,4327
-for '1» |567,298| |709,441| 0 6937,49 51,5211
Vexp 'in 671,917 1036,80 13,5174 8665,66 47,0208
Forecast with the least gross regional product error (Lvov region) receive on the basis of parabolic trend model (2):
y£"ir= 48>633 bln- UAH and yfi°7rmiSt= 57,163 bin. UAH
'6,2011
Forecast with the least financial result of general activity (agriculture) before taxation error (Lvov region) receive with the assistance of parabolic trend model (5):
ySiT= 60>477 mln- UAH and ySiiSt= 32,467 mln. UAH
Forecast with the least foreign direct investment in agriculture error (Lvov region) receive on the basis of parabolic trend model (8):
98>744 mln- USD and yR°7rmiSt= 133,152 mln. USD
8,2011
Forecast with the small error of persons quantity employed in agriculture (Lvov region) receive on the basis of parabolic trend model (11):
a0st= 0.161 mln. Pers. and y^™"8^ 0,153 mln. Pers.;
as well as on the basis of exponential trend model (12):
V9°2roioSt= °'158 mln- Pers- and V9°2roiiSt= °'149 mln-Pers. and linear (10) trend model:
'9,2010
= 0,150 mln. Pers. and y;
9,2011
- 0,136 mln. Pers.
Forecast with the least investments in capital assets error (agriculture) (Lvov region) receive with the assistance of parabolic trend model (14):
v5iot= 567>298 mln- UAH and yfnr,e"f= 709,441 mln. UAH
' 10,2011
Simple and multiple regression equations dependence of gross regional product (Lvov region) (y6) and financial result of general activity (agriculture) of Lvov region (y7) on influence of the studied indicators on the basis data tables (2) were elaborated.
y6= 14,64621+0,31309y8 , R2 = 0,56754; F = 10,4990; y6= 10,65241+0,06034y10 , R2 = 0,78208; F = 28,7107;
(16)
y6 = 10,74635+0,13442 y8+0,04638 yio , (18)
R2 = 0,84485; F = 19,0593;
y6 = 44,7041+0,12285 ^8-138,50257 ^9+0,02396 ^10 , (19)
R2 = 0,96301; F = 52,0693;
y6 = 26,43394+0,04147^7+0,19455 ^8-74,39491 ^9+0,02422 ^10 , (20)
R2 = 0,98242; F = 69,8539.
Value of the multiple determination coefficients R2 of the simple and multiple linear regression equations (16) - (19) give a reason to assert that all of them have a good probability or credibility, however, except equation (16), their value is greater than 0,7, and considerable part is rather close to one. Existence of the linear dependence between the resulting and factor variables also confirmed by obtained F - criteria, that with probability p = 0,95 is more greater than Ftable = 5,59, that was calculated with assistance of F - Fisher distribution.
Analysis of the simple linear regression equations (16) - (17) displays, that small positive influence on gross regional product of Lvov region y6 have foreign direct investment in agriculture of Lvov region y8 (3.46) (b8 = 0,313) and investments in capital assets (agriculture of Lvov region) y10 (3.47) (B10 = 0,06034).
Study of the regression model (18) shows slight positive influence on gross regional product of Lvov region y6 of foreign direct investment in agriculture of Lvov region y8 (b8 = 0,13442) and investments in capital assets (agriculture of Lvov region) y10 (b10 = 0,04638), in particular, while increase foreign direct investment inflow in agriculture of Lvov region at 1 mln. USD and some constant or mean investments in capital assets (agriculture of Lvov region) value y10 is expected to grow gross regional product of Lvov region y6 by an average of 0,13442 bln. UAH; moreover increase of investment in fixed assets (agriculture) of Lvov region y10 at 1 mln. UAH with an average or constant value of foreign direct investment in agriculture of Lvov region y8 will result in increment of gross regional product of Lvov region y6 in average at 0,04638 bln. UAH.
Analysis of the multiply linear regression equation (19) indicates moderate positive influence upon gross regional product of Lvov region y6 of foreign direct investment in agriculture of Lvov region y8 (b8 = 0,12285) and investments in capital assets (agriculture of Lvov region) y10 (b10 = 0,02396) and negative influence - employee quantity increase in agricultural industry of Lvov region y9 (b9 = -138,50257).
Regression coefficients' values of the multiply regression model (20) argue some slight positive impact on gross regional product of Lvov region y6 of foreign direct investment in agriculture of Lvov region y8 (b8 = 0,19455), financial results of general activity (agriculture) of Lvov region y7 (b7 = 0,04147) and investments in capital assets (agriculture) of Lvov region y10 (b10 = 0,02422), at the same time employees quantity grow in agriculture of Lvov region y9 will cause decrease of gross regional product of Lvov region (b9 = -74,3949).
Finally, one should notice, because of small amount of input sample table (2) analysis of regression equations coefficients (19) i (20) have more qualitative than quantitative influence upon resulting variable y6.
CONCLUSION
In this research linear, parabolic, and exponential trend models of investments and main agricultural indicators of Lvov region of Ukraine were presented. All the models with probability p=0,95 are adequate experimental data for 2000-2009, that permit to make the prediction of investments and main agricultural indicators of the researched region by these models for 2010 and 2011. However, it should be pointed out, because of small amount of input data analysis of regression equations coefficients have more qualitative than quantitative influence upon resulting variable y6.
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13. http://www.lv.ukrstat.gov.ua/
14. http://www.ukrstat.gov.ua/
