=Paper=
{{Paper
|id=Vol-1498/HAICTA_2015_paper74
|storemode=property
|title=The Evaluation of Meat Consumption Based on Different Models of the Matrix of Growth
|pdfUrl=https://ceur-ws.org/Vol-1498/HAICTA_2015_paper74.pdf
|volume=Vol-1498
|dblpUrl=https://dblp.org/rec/conf/haicta/LakicKA15
}}
==The Evaluation of Meat Consumption Based on Different Models of the Matrix of Growth==
https://ceur-ws.org/Vol-1498/HAICTA_2015_paper74.pdf
The Evaluation of Meat Consumption Based on Different
Models of the Matrix of Growth
Nada Lakić1, Mirjana Krivokapić2, Ana Anokić3
1
Faculty of agriculture, University of Belgrade, Serbia, e-mail nlakic@agrif.bg.ac.rs
2
Faculty of agriculture, University of Belgrade, Serbia, e-mail krivokapic.mirjana@gmail.com
3
Faculty of agriculture, University of Belgrade, Serbia, e-mail anokicana@agrif.bg.ac.rs
Abstract. The dynamics and the structure of agricultural activities can be
examined on the base of the matrix of growth. In this paper, the consumption
of different kinds of meat in Central Serbia, during the period from 2000. to
2011, is analyzed using the matrix of growth and curvilinear trend. First, the
growth of consumption of the i-th kind of meat was being observed as linear
function, using average indirect rates of growth. Subsequently, the evaluation
of meat consumption was performed using econometric linear model and non-
linear system of Cobb-Douglas type. The curvilinear trend is applied for the
same goal. The results obtained by these methods were compared with the data
of the realized average consumption of the observed types of meat for year
2012. It was concluded that the matrix of growth gives equally good results for
forecasting the average consumption of meat like trend method.
Keywords: the matrix of growth, linear and non-linear econometric system,
curvilinear trend, meat consumption.
1 Introduction
The meat production in the world has great economic and especially nutritional
significance. In human nutrition the meat is used in fresh and processed state. With
human population growth, respectively with the increase in consumer purchasing
power, the world meat production becomes increasingly important economic factor.
The meat, in human diet, satisfies most of the needs for proteins of animal origin,
whose biological value and structural quality are considerably higher compared to
plant proteins and are necessary for the construction and reconstruction of tissue.
Meat contains carbohydrates and fats, which are important for generation of heat and
energy of the human body. The meat is a source of essential minerals such as iron,
zinc and phosphorus which are significant for human organism being because they
participate in bone structure, as well as teeth, blood and other. Also meat contains
vitamins, especially B group (thiamin, riboflavin, niacin, pantothenic acid, vitamin
B6 and vitamin B12 which promote the growth and preservation of health. The effects
of meat on physical health and mental well-being are well known, and new
knowledge about human consciousness, considering healthy nutrition, yield to the
individual human need for control of meat consumption. In the study by Vinnari and
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Tapio (2009), five coherent images of different views of meat consumption in future
are constructed. The fact that meat represents agro-industrial materials for production
of numerous high-value and expensive meat products which are highly appreciated in
the market, confirms the importance of meat. Producers in markets all over the world
are making great efforts to satisfy the consumer expectations in terms of quality and
well-organized supply chains, and numerous studies are carried out in this direction
(Henchion et al., 2014).
Mutual relations in the field of the consumption of the material goods, especially
those intended for human diet as one of the most important consumption groups, can
be analyzed by setting the matrix of growth and the corresponding model where
direct and indirect relations are explicitly expressed. Analysis and evaluation of
consumption of certain types of meat can help to adequately adjust the structure of
production with demand structure in the next period. By predicting the consumption
of meat the necessary import can be ensured on time. The goal of this paper is to
present the prediction of meat consumption obtained using the matrix of growth and
compare it with the results obtained by widely used trend methods.
Forecasted values of different productions (Krivokapić and Anokić, 2012) can be
obtained using matrix of growth and also the movement of GDP by regions can be
analyzed (Anokić et al, 2013) using this method. More examples from literature of
using matrix of growth is for setting up a multimodal transport model in Croatia
(Nikolić, 2003) or for demographic analysis (Kovačić, 1976).
2 Method
The matrix of growth is a square scheme formed of direct and indirect rates of
growth. Direct rate of growth expresses the growth of one single activity
independently from the growth of other observed activities. The indirect rate of
growth denotes relative growth of the i-th activity in relation to the value of the j-th
activity in the previous (t-1) or the currently observed t time period. By simultaneous
covering of both direct and indirect rates of growth, the matrix of growth enables, in
addition to the intensity of growth, the identification of structural changes between
observed activities.
Activities at the beginning and the end of the observed period can be connected
with the average matrix of growth. Using the matrix of growth it is possible to
establish the dynamic system for projecting future structural relations. Different
types of meat can substitute one another in nutrition, which means that the levels of
their consumption are mutually dependent, that is, the increment of consumption of
the i-th kind is the function of the level of consumption of all other kinds of meat.
Depending on the relationship between the increments of consumption of the i-th
kind of meat and the level of consumption of all kinds of meat, different models of
growth can be defined. A model based on indirect rates of growth and econometric
linear and non-linear system of Cobb-Douglas type is used in this paper.
Subsequently, the method of curvilinear trend was applied. Selection of a line that is
best adapted to the actual data was estimated based on the index of correlation. The
equations of cubic and power trend, based on that indicator, are used in this paper.
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2.1 Models of Consumption Growth
The increment of the consumption of i-th kind of meat in period (t-1,t) is:
ΔYit = Yit − Yi ,t −1 i = 1,2,..., n (1)
There is a mutual dependence between consumptions of different kinds of meat, the
increment of consumption of the i-th kind of meat, ΔYit , is a function of levels of
consumption of all other kinds of meat
ΔYit = f i (Y1t ,..., Yi −1,t , Yi +1,t ,..., Ynt ), i = 1,2,..., n (2)
Therefore, it is possible to establish a following system of equations:
Yit − f i (Y1t ,..., Yi −1,t , Yi +1,t ,..., Ynt ) = Yi ,t −1, i = 1,2,..., n (3)
Depending on the kind of a relationship existing between the increment of the
consumption of the i-th kind of meat and the level of the consumption, different
models of growth are obtained.
A Model Based on Indirect Rates of Growth. Using indirect rates of growth in
order to express linear dependency of consumption increment of the i-th kind and the
level of consumption (Lakić and Krivokapić, 2008) there is a connection based on
the relation between the consumption in two successive periods, in the matrix form:
⎛ 1 ⎞
⎜ I − R ⎟Yt = Yt −1 , (4)
⎝ n − 1 ⎠
where I and R represent a unit matrix and a matrix of growth, respectively, and Yt-1
and Yt represent vectors of the consumption in period t-1 and t, respectively.
Assumed constancy of the matrix of growth means that changes between the
consumption of different kinds of meat are allowed in absolute values, but only with
condition that the relative relations remain unchanged.
In addition to its good sides, the observed system has weak points. Neglecting the
fact that indirect rates of growth are changing from period to period and that they can
be considered as constants only in the case when all direct rates of growth are equal,
can be overcome by introducing average (constant) matrix of growth for longer
period (0,T). Then it is possible to establish, for every moment of the interval (0,T),
t=1,2,3,…T, a following connection between the consumption vectors Yt and Yt-1 ,
based on the average matrix of the consumption growth:
−1
⎛ 1 ⎞ ⎛ 1 ⎞
⎜ I − R ⎟Yt = Yt −1 or Yt = ⎜ I − R ⎟ Yt −1 (5)
⎝ n − 1 ⎠ ⎝ n − 1 ⎠
On the basis of the last equation based on a known vector of consumption in
period (t-1) and average matrix of growth R , the vector of consumption in period t
can be evaluated.
An Econometric Model. An econometric model based on the matrix of growth
denotes structural changes of the consumption by connecting its trend into the
complete dynamic system. By this system, the structure of growth which is used to
connect two states of consumption is revealed.
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An econometric model can be formed on the basis of linear and nonlinear
dependence of coefficients of growth.
a) A linear econometric model
In the case of the linear dependence of coefficients of growth, the consumption of
observed kinds of products in period t and t-1 is expressed via the following system
of equations:
n
Yit - ∑ rijY jt = Yi ,t −1 (6)
j ≠ i =1
or in matrix form:
(I − R)Yt −1 = Yt , (7)
where I and R represent a unit matrix and a matrix of coefficients of growth,
respectively, and Yt-1 and Yt represent vectors of the consumption in period t-1 and t,
respectively.
In the case of the linear dependence upon parameters, the increment of
consumption in period t is equal to the following expression:
ΔYt = a1Y1t + a2Y2t + ... + anYnt + ε t , (8)
where ε t = ( ε 1,..., ε t ) is an error or a deviation from the linear dependence.
Considering that the sum of squared deviations is
T
2
∑ε = (ε ʹ′,ε ) = (ΔY − Ya)ʹ′(ΔY − Ya)
t =1
t (9)
the first derivative of a is
∂(ε ʹ′, ε )
= −2Y ʹ′(ΔY ) + 2Y ʹ′Ya ʹ′ (10)
∂a ʹ′
Equalizing this derivative with zero, the following is obtained:
a ʹ′ = (Y ʹ′Y )−1 Y ʹ′(ΔY ) (11)
If the label on the R̂ ' = (a1, a2 ,..., an )= aʹ′ , the transposed matrix of evaluated
coefficients of growth is obtained:
Rˆ ʹ′ = (Y ʹ′Y )−1 Y ʹ′(ΔY ) (12)
The evaluation of the consumption in period t, when the consumption in period t-1
is known, is being performed using the following relation:
( −1
)
Yt = I − Rˆ Yt −1 , (13)
in which matrix R̂ is the transposed matrix of evaluated coefficients of growth.
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b) An econometric model based on non-linear dependence of Cobb-Douglas
type
The change of phenomenon in period (t-1, t) can be followed also using
coefficients of dynamics of the consumption which expresses the relation between
the levels of the consumption of the i-th kind of meat in currently (t) and previously
observed (t-1) period, i.e.:
d it = Yit i = 1,2,..., n ; t = 1,2,..., T (14)
Yi ,t −1
The coefficient of the consumption can also be expressed as a function of the
consumption of Cob-Douglas type:
n
dit = Y1et
i1
. . . Ynte in
or log d it = ∑ eij log X jt (15)
j =1
In this process, the coefficients of elasticity of growth are marked as eij (i,j = 1,...,n).
Connections between different kinds of meat can be expressed using following
system of equations:
n
log Yit − ∑e logY = logYi,t −1
ij jt i = 1,2,..., n (16)
j =1
or in matrix form:
(I − E )log Yt = log Yt −1 (17)
The solution of this system gives the connection between vectors of the
consumption in period t and t-1 respectively:
−1
Yt = e(I − E ) log Yt −1 . (18)
Repeating the previous procedure the transposed matrix of the coefficients of
elasticity is determined by:
[ −1
]
Eˆ ʹ′ = (logY )ʹ′ (logY ) (logY )ʹ′ (Δ logY ) (19)
More theory about these issues can be found in Stojanović (1976 and 1990).
A Curvilinear Trend. With respect to the maximum value of the index of
correlations, the parabola of the third degree and the equation of a power trend are
used for extrapolation in this paper, respectively:
Yˆi = a + b1ti + b2ti2 + b3ti3 and Yˆi = a * tib , i = 1,2,..., n (20)
The software package IBM SPSS Statistics Version 20 was used for extrapolation
of the consumption in 2012 in this study.
3 Results and Discussion
The time series for the period from 2000 to 2011 for consumption of different
kind of meat: beef, baby beef, veal, pork, pork of suckling pig, mutton, goat meat,
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poultry meat, offal, fish and prepared fish in Central Serbia are used for the purpose
of analyzing the dynamics of structural changes of consumption of different types of
meat using methodology based on a matrix of growth (table 1).
Table 1: The average consumption of meat, fish and fish products in Central Serbia
Consumption of meat (kg/per household)
beef and baby
prepared fish
poultry meat
suckling pig
mutton and
goat meat
fish and
pork of
Year
pork
offal
beef
veal
2000 12.0 2.3 26.3 11.8 2.7 29.2 1.9 7.6
2001 13.1 2.2 25.6 10.5 3.1 30.6 1.9 11.2
2002 15.0 2.3 32.5 10.6 3.0 39.5 2.0 10.4
2003 15.5 2.6 33.8 10.7 2.3 39.2 2.5 14.5
2004 15.5 2.6 36.9 10.7 2.1 41.7 2.4 12.0
2005 14.3 2.5 35.6 9.2 2.0 42.3 2.4 15.5
2006 12.2 1.6 43.7 8.5 3.9 44.1 5.1 19.2
2007 12.7 0.5 50.7 8.9 4.2 45.3 7.6 18.6
2008 14.1 1.2 41.8 6.3 3.6 43.6 5.3 17.3
2009 11.7 0.4 41.8 6.3 4.2 52.1 3.9 17.2
2010 10.1 0.4 44.1 5.4 3.4 52.0 4.4 16.2
2011 11.8 0.8 43.8 5.5 2.7 49.6 4.0 19.5
Source: Bulletin, questionnaire of meat consumption, material-Office of Statistics of Republic
of Serbia
Assuming that the consumption of meat in 2012 shows the same tendency as in
the previous period, solution of the system defined on the basis of indirect rates of
growth is used for the estimation of the consumption levels in 2012.
666
−1
⎡ 1.0002 0.0017 0.0001 0.0003 0.0008 0.0001 0.0007 0.0002 ⎤ ⎡11.8 ⎤ ⎡11.8 ⎤
⎡ Y1,12 ⎤ ⎢ ⎥
⎢ ⎥ ⎢ 0.0015 1.0125 0.0005 0.0023 0.0062 0.0004 0.0052 0.0012 ⎥ ⎢ ⎥ ⎢ 0.7 ⎥
⎢Y2,12 ⎥ ⎢ ⎢ 0.8 ⎥ ⎢ ⎥
⎢Y3,12 ⎥ − 0.0171 − 0.1462 0.9942 − 0.0270 − 0.0725 − 0.0052 − 0.0602 − 0.0146⎥ ⎢ 43.8 ⎥ ⎢ 45.5 ⎥
⎢ ⎥ ⎢ 0.0062 0.0526 0.0021 1.0097 0.0261 0.0019 0.0217 0.0052 ⎥
⎥ ⎢ ⎥ ⎢ ⎥
⎢Y4,12 ⎥ = ⎢ ⎢ 5.5 ⎥ = ⎢ 4.9 ⎥
⎢Y ⎥ ⎢ 0.0004 0.0033 0.0001 0.0006 1.0017 0.0001 0.0014 0.0003 ⎥ ⎢ 2.7 ⎥ ⎢ 2.7 ⎥
⎢ 5,12 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢Y6,12 ⎥ ⎢− 0.0030 − 0.0259 − 0.0010 − 0.0048 − 0.0128 0.9991 − 0.0107 − 0.0026⎥ ⎢ 49.6 ⎥ ⎢ 49.9 ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢Y7,12 ⎥ ⎢− 0.0010 − 0.0083 − 0.0003 − 0.0015 − 0.0041 − 0.0003 0.9966 − 0.0008⎥ ⎢ 4.0 ⎥ ⎢ 4.1 ⎥
⎢Y8,12 ⎥ ⎢⎣− 0.0072 − 0.0618 − 0.0025 − 0.01142 − 0.0306 − 0.0022 − 0.0255 0.9938 ⎥⎦ ⎢⎣19.5 ⎥⎦ ⎢⎣ 20.2 ⎥⎦
⎣ ⎦
The consumption of beef and baby beef as well as the consumption of mutton and
goat meat will remain at the same level in 2012, the consumption of veal and pork of
suckling pig will decrease, and consumption of pork, poultry, offal and fish will
increase compared to the previous year.
Further, using the matrix of estimated coefficients of growth, the following
solution of the system of equations of the econometric model based on linear
dependence is obtained:
−1
⎡ 0.0766 2.4752 0.0374 0.0725 − 0.0526 0.0661 0.1617 0.1809 ⎤ ⎡11.8 ⎤ ⎡10.9 ⎤
⎡ Y1,12 ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎥ ⎢− 0.2927 0.9255 0.1701 0.2602 0.1290 − 0.1003 − 0.3973 0.0466 ⎥
⎢ 0.8 ⎥ ⎢ 0.5 ⎥
⎢
⎢Y2,12 ⎥ ⎢ 2.2120 1.9462 − 2.2406 − 1.7806 − 3.5574 1.7960 9.4835 0.3162 ⎥
⎢Y3,12 ⎥ ⎢ ⎢ 43.8⎥ ⎢ 43.7 ⎥
⎥ ⎢ ⎥ ⎢ ⎥
⎢ ⎥ 0.1472 2.2920 − 0.3712 0.3716 0.4685 0.1788 1.3734 0.0210 ⎥ ⎢ 5.5 ⎥ = ⎢ 5.0 ⎥
⎢Y4,12 ⎥ = ⎢
⎢Y ⎥ ⎢ 0.4657 − 1.1171 − 0.4052 0.0858 − 0.2123 0.2481 1.2068 − 0.0625⎥ ⎢ 2.7 ⎥ ⎢ 3.3 ⎥
⎢ 5,12 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢Y6,12 ⎥ ⎢− 0.0424 0.5229 − 2.1093 0.5049 − 3.9993 2.1955 6.6115 0.7779 ⎥ ⎢ 49.6 ⎥ ⎢ 47.8 ⎥
⎢ ⎥ ⎢ 0.8539 0.1738 − 0.3717 − 0.8271 − 0.1432 0.2134 1.9375 − 0.1808⎥
⎥ ⎢ ⎥ ⎢ ⎥
⎢Y7,12 ⎥ ⎢ ⎢ 4.0 ⎥ ⎢ 4.7 ⎥
⎢Y8,12 ⎥ ⎢⎣ 1.3521 − 3.0085 1.6075 − 1.3805 1.4544 − 0.8909 − 4.1750 0.0165 ⎥⎦ ⎢⎣19.5 ⎥⎦ ⎢⎣ 21.5 ⎥⎦
⎣ ⎦
Results of the system equations indicate that consumption of beef and baby beef,
veal, pork, pork of suckling pig and poultry meat will decrease in the forecasted 2012
year. The consumption of other kinds of meat increased compared to the previous
year. We noted, also that there is a tendency to replace one type of meat with another
which is characteristic for the countries affected by the economic crisis. For example,
poultry meat is a substitute for beef (Chamorro et al, 2012).
Econometric model based on the nonlinear dependence is based on the matrix of
estimated coefficients of elasticity of growth. After a sequence of operations using
natural logarithmic function and applying the procedure from the previous model,
transposed matrix of elasticity coefficients is obtained and used for consumption
evaluation in 2012.The system of equations gives the following results for 2012:
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−1
⎡ 0.1287 0.1402 −1.0942 0.4337 − 0.1821 1.1937 0.3783
0.1935 ⎤ ⎡11.8 ⎤
⎢ ⎥ ⎢ ⎥
⎢ − 2.3631 0.1307 16.4711 0.1669 0.8664 −14.3768 −5.5330 2.1467 ⎥ ⎢ 0.8 ⎥
⎢ 0.9111 − 0.0186 − 2.7616 0.0549 − 0.4040 2.7065 1.1890 0.0081 ⎥ ⎢ 43.8⎥
⎢ ⎥ ⎢ ⎥
⎢ 0.7780 0.1184 0.8679 0.2152 0.3383 −1.0737 − 0.3401 0.2166 ⎥ ⎢ 5.5 ⎥
⎡Y1,12 ⎤ ⎢ 2.4238 − 0.4697 −1.8712 − 0.3780 0.1408 0.7539 0.5999 − 0.4299⎥⎥
log⎢ ⎥ ⎡11.8 ⎤
⎢ ⎢ 2.7 ⎥ ⎢ ⎥
⎢ ⎥ ⎢ − 0.0135 0.0563 − 5.2009 0.8363 − 0.6360 5.2302 1.8504 − 0.1044⎥ ⎢ 49.6⎥ ⎢ 0.7 ⎥
⎢Y2,12 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 45.5⎥
⎢Y3,12 ⎥ ⎢ 2.8606 − 0.3047 0.1344 −1.5643 − 0.1442 − 0.6934 0.7356 − 0.5556⎥ ⎢ 4.0 ⎥ ⎢ ⎥
⎢ ⎥ ⎢ 0.4781 ⎢19.5 ⎥ ⎢ 5.3 ⎥
⎢Y4,12 ⎥ = e ⎣ − 0.0512 1.7717 − 0.6212 − 0.0720 − 0.7778 − 0.0376 − 0.2493⎥⎦ ⎣ ⎦ =
⎢Y ⎥ ⎢ 2.2 ⎥
⎢ 5,12 ⎥ ⎢ ⎥
⎢Y6,12 ⎥ ⎢57.6 ⎥
⎢ ⎥ ⎢ ⎥
⎢Y7,12 ⎥ ⎢ 3.0 ⎥
⎢Y8,12 ⎥ ⎢⎣17.3 ⎥⎦
⎣ ⎦
Obtained values show that consumption of following types of meat will decrease
in forecasted 2012 year compared to the previous year: veal meat by 0.7 kg per
household, suckling piglet meat by 5.3 kg, mutton and goat meat by 2.2 kg, offal by
3.0 kg and fish by 17.3 kg,. Consumption of pork meat will increase in 2012
compared to 2011 year by 45.5 kg and of poultry meat by 57.6 kg. It is forecasted
that the consumption of beef and baby beef meat will have the same value of 11.8 kg
per household. The prediction of the values of the average consumption of the
observed types of meat per household in 2012 are obtained using the adequate
equation of cubic and a power trend lines.
18
16
beef and baby beef meat (kg)
The average consumption of
14
12
10 real data
8 cubic
6
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13
ordinal number of the year
Fig. 1. Movement of the consumption of beef and baby beef per household in 2000 to 2011,
and the adequate trend line
When it comes to the average consumption of beef and baby beef, the largest
index of correlation in the amount of I2 = 0.731 corresponds to the mathematical
function Yˆi = 9.145455 + 3.221895t i − 0.524026t i2 + 0.022621t i3 . The projected
average consumption of beef per household in 2012, using rated function is 12.2 kg
(graph 1). For the average consumption of veal per household, the best adapted
function with I2 = 0.862 is obtained with forecasted consumption of 1.2 kg of veal
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per household in 2012. Using the cubic function that best corresponds to the average
consumption of pork with I2 = 0.845, the consumption of 39.3 kg of pork per
household in 2012 is forecasted. Cubic line with I2 = 0.940 gives the best description
for the average consumption of suckling pig meat per household and the forecasted
consumption per household in 2012 is 4.7 kg. The largest index of correlation I2 =
0.552 corresponds to the cubic line which projected the value of average
consumption of sheep and goat meat per household for 2012 in amount of 1.5 kg.
Levels of average consumption of poultry meat per household can be best modeled
using a mathematical function of a power form
Ŷi = 28.369443 * x 0 . 232894 2
with correlation index I =0.921. The obtained
forecasted value for 2012 amounts to 51.6 kg of poultry meat on average per
household (graph2). When it comes to offal, the best adapted line is cubic with the
correlation index I2 =0.671 and the average consumption is 1.3 kg in 2012. For the
assessment of the average consumption of fish and prepared fish a power function
with correlation index I2 =0.856 is used and the obtained forecasted value for 2012 is
19.9 kg.
The average consumption of poultry meat (kg)
60
50
40
real data
30
power
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13
ordinal number of the year
Fig. 2. Movement of the consumption of poultry meat per household in 2000 to 2011, and the
adequate trend line
The forecasted values of average consumption of the observed kinds of meat per
household in 2012, obtained by the model based on the matrix of growth, model
based on the indirect rate of growth, linear and non-linear econometric model, and
applying the curvilinear trend were compared with the actual average consumption
data for the year 2012. The real average consumptions per household of beef and
baby beef, pork, suckling pig meat in 2012 were 12.2 kg, 39.1 kg and 4.5 kg,
respectively, and the closest results to them are those predicted by cubic trend. The
best predicted values for average consumption of sheep and goat meat, offal and fish,
which had the real values of 2.3, 3.6 and 17.1 kg, respectively, were obtained by non-
669
linear econometric model. The linear econometric model gave the best prediction for
the average consumption of veal of 0.5 kg per household, which is equal to the real
consumption of this kind of meat. The closest result to the real average consumption
of poultry meat per household in 2012 equal of 49.1 kg was obtained by the method
based on indirect rates of growth.
4 Conclusion
Structural changes of meat consumption are established through direct and
indirect rates of growth, using the matrix of growth for period from 2000 to 2011.
Using appropriate models, prediction of consumption for the next year is performed.
The three models that had been used gave different estimates of meat consumption
by kinds of meat, as a result of their different approaches to the problem.
This paper confirmed the thesis that matrix of growth can be applied in the
analysis of meat consumption and forecasting for the next period of time. In addition
to many modern methods, of which the trend is commonly in use, the results
obtained by the presented computation using the matrix of growth, have shown the
way to determine the consumption trend and an appropriate assessment of meat
consumption in the future. Considering that the method of indirect rate of growth and
the linear econometric methods provided the value for one type of meat that was
closest to the real value, projecting the consumption for the next year, while the
econometric method based on nonlinear dependence and curvilinear trend values
obtained closest values to the real data for three kinds of meat, it can be concluded
that the matrix of growth gives equally good results in forecasting the average
consumption of meat as the widely used trend method. As meat production should
follow the same consumption, in order to maintain a balance in the market, the
importance of this study is in the fact that the forecasted consumption can be the
basis for planning the production volume of appropriate kinds of meat, which would
prevent any shortages and sudden price changes.
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