Theoretical framework
Theoretical framework of this study is mainly based on the market model (Sarmin, 1988).
Model Specification for Skin-Export
Goat-meat supply and price in short run and long run:
Goat-meat supply is related with the number of goat-population implies slaughtered goats as well as skin production. Goat can be increased by increasing the reproduction rate, kidding rate and reducing kid mortality rate. The increase and decrease of ‘price of goat-meat’ can affect the ‘decision of reproduction and slaughter of goat/goat-meat supply’. If price increases, supply of goat-meat increases in short run but higher price of goat-meat may or may not able to increase the supply of goat-meat due to lower number of goat-population in long run due to shortage of land. It is a function of the goat-meat price.
The model was specified as follows:
Goat -eat supply (GMS) and Goat-meat price (GMP) model
The supply of goat-meat would depend on its prices.
GMS=f(GMP)…………………......................................................................................... ..(1)
At present, the area of land is decreasing for crops as well as livestock also. On the other hand, rising supply of goat meat depends on the rising number of goat-population needs increasing rearing areas. In fact, in future there will remain a small land for livestock rearing. In short run, supply can increases for higher price. But in the long-run, supply of goat-meat may or may not be depended on the price of goat-meat and also the price may or may not be depended on supply of goat-meat. In this situation causality of goat-meat supply and price needs to be examined.
The model was specified as follows:
GMS=f(GMP)…………………...................................................................................... (2)
GMP=f(GMS)…………………...................................................................................... (3)
Goat population model:
The skin sub-sector traces the life cycle from goat-kid production to slaughter. The fresh goat-meat production is highly influenced by the number of slaughtered goat and skin production is the result of the number of slaughtered breeding stock and kids. On the other hand, for acute shortage of land, goat-population will need to be reduced by slaughtering to produce meat and skin. But higher slaughter rate can increase the amount of fresh goat-meat and skin production only for a few years but ultimately it will reduce the number of goat-population. So, the slaughter rate especially for female breeding stock shows a greater impact on fresh goat-meat and skin production. Interaction between goat-population and different rates (slaughter, kidding, mortality) may be useful way of estimating goat-meat and skin production in Bangladesh. On this background mathematical formulation of SIMM model developed by Yasmin, et al.,2001 used to calculate goat-skin in Bangladesh.
Analytical framework
Error Correction Mechanism
Short-run and long-run behavior:
It developed by Engle and Granger is a means of reconciling the short-run behavior of an economic variable with its long-run behavior. If two variables are co-integrated, that is there is a long-term equilibrium relationship between the two. Of course, in the short run there may be disequilibrium. Therefore one can treat the error term as the “Equilibrium Error”. Error term can be used to tie the short run behavior of variable to its long run value. In the regression, change in variable captures the adjustment towards the long run equilibrium.
Error Correction Model (ECM):
With the Error Correction Model (ECM), proportion of the disequilibrium in one period is corrected in the next period. It is related one variable to changes in another variable as well as to the past levels of the two variables.
Unit Root (Random Walk Model):
In econometrics, a time series that has a unit root is known as a Random Walk”. And a random walk is an example of a non stationary time series. For example asset prices, such as stock prices, follow a random walk that is they are non stationary. (Gujarati,1995).
Co integration:
The EG, AEG, co-integrated regression Durbin Watson CRDW tests can be used to find out if two or more time series are co-integrated of two (or more) time series suggested that there is a long–run or equilibrium relationship between them.
Granger Test for Causality:
In particular, the short-run adjustment term interacts significantly with several policy variables. ECM approach is powerful because its unique structure describes a relationship between two related variables and makes short-run and long-run behavior consistent. Incorporating short-run adjustments in a model is to use the error correction mechanism. It is possible to test the direction of causality by using Granger Causality Test (Ramu, 1995).
[SIMM model of goat skin production (Formulation of a Mathematical Model):
The total slaughtered (SLT) determines the slaughtered female breeding stock FBS, male breeding stock MBS, female kids FC, male kids MC of goat population combined (Yasmin et al. 2001). The equation:
SL(t+DT) = SFBS(t+DT) + SMBS(t+DT) + SFC(t+DT) + SMC(t+DT) ………………………….....(4)
Where,
SL(t+DT) = Current number of goat population come to slaughter
SFBS(t+DT) = Current number of slaughtered female breeding stock
SMBS(t+DT) = Current number of slaughtered male breeding stock
SFC(t+DT) = Current number of slaughtered female kids
SMC(t+DT) = Current number of slaughtered male kids
Estimation procedure
At the formal level, stationary can be checked by finding out if the time series contains a unit root. The Dickey-Fuller and Augmented Dickey-Fuller tests were used for this purpose.
Dickey-Fuller Test:
Yt=Yt-1+ut, Yt= b1+Yt-1+ut, Yt= b1+b2t+Yt-1+ut,where t is the time or trend variable. In each case the null hypothesis is that d=0, that is there is a unit root. If the error term ut is auto-correlated, then Yt= b1+b2t+Yt-1+ut+ a Yt-i+ t, where for example, Yt-1= (Yt-1-Yt-2), Yt-2= (Yt-2-Yt-3) etc. that is one uses lagged differences terms the null hypothesis is still that d=0 or p=1, that is a unit root exists in Y (i.e.Y is non-stationary) when the DF is applied to model then it is Augmentad Dickey-Fuller (ADF) test” (David et al, 1995).
The Granger Test for Causality:
Changes in explanatory variable induce changes in the dependent variable. This is the notion of causality in which information about X is expected to affect the conditional distribution of the future values of Y. Yt= Σ αYt-ip + Σ βjXt-jq + ut, where ut is white noise, p is the order of the lag for Y and q is the order of the lag for X. The null hypothesis that X does not Granger–cause Y is that bj =0 for j =1,2,. q. The restricted model is therefore Yt= ΣαYi-t + vt (Ramu, 1995).
Slaughter component of SIMM model:
The following equations define the structure of the system (Yasmin, 2001):
i.) SFBS(t+DT) = E1 * FBS(t+DT)
Where,
FBS(t+DT) = Number of female breeding stock
E1 = Slaughter rate
The number of slaughtered female breeding stock is generated by multiplying number of female breeding stock at annual slaughter rate (E1).
ii.) SMBS(t+DT) = E2 * MBS(t+DT)
Where,
MBS(t+DT) = Number of male breeding stock
E2 = Slaughter rate
The number of slaughtered male breeding stock is generated by multiplying number of male breeding stock at annual slaughter rate (E2).
iii.) SFC(t+DT) = E3 * FC(t+DT)
Where,
FC(t+DT) = Number of female kids
E3 = Slaughter rate
The number of slaughtered female kid is generated by multiplying number of female kids at annual slaughter rate (E3).
iv.) SFC(t+DT) = E4 * MC(t+DT)
Where,
MC(t+DT) = Number of male kids
E4 = Slaughter rate
The number of slaughtered male kids is generated by multiplying number of male kid at annual slaughter rate (E4).
Empirical framework
Data collection
Data on goat-meat production and price from 1980 to 2010 were collected from Bangladesh Bureau of Statistics (BBS, 1982-2012).
Data adjustment
Taka mound-1 for price data is converted into Taka ton-1. Base 1985 used as deflator for the real price data. The goat meat supply means production of goat-meat. The following variables are converted into log variables: LGMS=LOG (GMS), LGMP=LOG (GMP). Female goat, male goat and female kid, male kid have been categorized by using 35, 20, 23, 22 rate (Honhold, 2001) and assumed 50% of the current kid production is female kid and 50% is male kid. Assume slaughter rates are 5% for female goat breeding stock, 2% and 100 % for 2 and 3 years old male castrated goat respectively. One goat skin is equal to 3.5 sqft. Skin (Yasmin et al. 2004).
Goat meat supply model:
The goat-meat supply, price and their interrelationships in Bangladesh is explained by the following model:
LGMS=f (LGP)
The long-run co integrating equation for goat- meat can be written as:
LGMSt = α+ βi LGMPt+ ut the vector error correction model.
Where,
LGMSt is the goat-meat supply,
LGMPt is the deflated goat-meat price,
α is intercept,
βi is the long run static coefficient and
ut is the error term.
Evaluation procedure
Dickey-Fuller Test, Augmented Dickey-Fuller Test
If the null hypothesis that p=1 is rejected (i.e. time series is stationary) we can use the usual (student’s) t-test. If the computed absolute value of the tau statistic (i.e.) t exceeds the df or Mackinnon df absolute critical tau values, then we do not reject the hypothesis that the given time series is stationary. If, on the other hand, it is less than the critical value, the time series is non stationary. The estimated tau statistic usually has a negative sign. Therefore, a large negative tau value is generally an indication of stationary. Since in the absolute terms the estimated tau value exceeds any of these critical values, the conclusion would be that the estimated ut is stationary (i.e.) it does not have a unit root and therefore two variables despite being individually non stationary are co-integrated (Gujarati, 1995).
Granger test for causality
If X causes Y and Y causes X, then there is a feed back, which means that the two variables are jointly determined (the price of commodity and the quantity of good sold are examples of this feed back effect). If both tests (Standard Wald-F-statistic and Lagrange multiplier test) reject the null hypothesis, then we can conclude that there is a lagged feedback effect. (Ramu, 1995).
Export earning from SIMM model
SIMM model shows skin production under 3 scenarios from 2015 to 2020. From a goat 3.5 sft. skin is produced. Export earning calculated by multiplied per sft. of skin with 11 Tk.
E Views Software
Unit Root Test
The data were analyzed using the computer EViews software. To carry out the Augmented Dickey-Fulled test on a series, open the series window, push the view button, and select Unit Root Test. Need to specify Augmented Dickey-Fulled test and whether want to test for a unit root in the level, first differences, or second differences of the series. Need to specify whether the equation is to contain an intercept and a trend. Must specify the number of lagged difference terms to include in the test equation. Then the window will show the results of an Augmented Dickey-Fulled test for a unit root, with MacKinnon’s critical values. The bottom part of the window will show the regression results for the test. An alternative route is Quick/ Series Stats in the main EViews menu.
Johansen Co-integration Test
The selection View/Co-integration Test on the group or VAR toolbar will carry out a Johansen Co-integration Test. This view is only valid working with series that are known to be non-stationary. Need to supply information about the test in a dialog box: the first step is to choose one of the six buttons that describe the constant and trend terms in the vector auto-regressions that are estimated as part of the Johansen procedure. Next to specify the lag specification for the test VAR.
Vector Error Correction (VEC) Model
Estimation of a VEC model proceeds by first determining one or more co-integrating equations using the Johansen procedure. The first difference of each endogenous variable is then regressed on a one period lag of the co-integrating equation(s) and lagged first differences of all of the endogenous variables in the system. To calculate from Vector Error Correction model, click on Pocs/Make Model on the VAR toolbar (David et al.,1995)
Granger Test for Causality
EViews automatically runs regression. Y on lagged Ys, Y on lagged Ys and lagged Xs; X on lagged Xs, and X on lagged Xs and lagged Ys. Thus the null hypothesis being tested are that X does not granger-cause Y and that Y does not granger-cause X. Output from the test gives the relevant F-statistics for the hypothesis. (Gujarati, 1995).