RESULTS AND DISCUSSIONS
5.1 Estimation of Price Elasticity of Supply
As we have seen in chapter three, the degree of exploitation can be expressed as the reciprocal of price elasticity of supply. In this section we shall first estimate the price elasticity of supply. As has been mentioned earlier, in the supply function, price is an explanatory variable of the quantity supplied, but price itself gets affected by the amount of supply, thus there could be reverse causality here which leads to endogeneity problems. We want to resolve this problem by the use of instrumental variable (IV) and using two stage least square (2SLS) techniques.
Two stage least square (2SLS) technique is an extension of the OLS method. It is used when the dependent variable or endogenous variable’s error term is correlated with the independent variables. In the first stage, a new variable is created using the instrumental variable to compute
estimated values of the problematic variable. In the second stage, the model- estimated values from stage one are then used in place of the actual values of the problematic predictors to estimate a linear regression model of the dependent variable. Since the computed values are based on variables that are uncorrelated with the errors, the results of the two-stage model are optimal (Johnston and DiNardo, 1997).
The econometric model that we have in our mind is the following:
lnYi = β0 + β1lnPYi + β2lnPUi + β3lnPMi + β4lnPSi + β5lnPDi + β6lnPIi + β7lnPVi + β8lnPHi + β9lnwa_mi + β10lnwa_fi + β11lnfamsizei + β12d_lingi + εi …………. (5.1)
where
Y = Output (Tea Leaves);
PY = Price of the output;
PU = Price of Urea;
PM = Price of MOP;
PS = Price of SSP;
PD = Price of Cow-dung;
PI = Price of Irrigation;
PV = Price of Vitamin;
PH = Price of Herbicide;
wa_m = Wage rate of male workers;
wa_f = Wage rate of female workers;
farmsize = Farm Size;
d_ling = 1 if Assamese = 0 if non-Assamese.
i represents households. i = 1,2,…….., 210.
PY is the price of tea leaves produced by small tea growers. There could be reverse causality in equation (5.1). The theoretical concern is briefly explained in the appendix of the chapter (Appendix VII).
To get around the reverse causality we take the instrumental variable (IV) approach. In the first stage we instrument price of tea leaves with certain variables which are likely to directly affect
the price of tea leaves and through that channel only they affect the supply of tea leaves. In other words the instruments must satisfy the condition of (a) relevance, they should be related to the variable to be instrumented (price of leaves) and (b) exogeneity, they should be unrelated to the regressed (supply of leaves). The instruments we are considering are
1. Number of options which the tea growers have to sell their tea leaves.
2. Distance between the tea garden to the processing plant.
3. A dummy for tea gardens which are situated in the districts with greater concentration of STGs. These districts have had STGs for a longer time; they also have greater number of STGs. In our survey Golaghat and Dibrugarh are these districts. Nagaon, Sonitpur, Biswanath are relatively new entrants in small tea cultivation, they have fewer STGs.
4. A dummy for those tea growers who sell their tea leaves directly to the processing plant.
These four factors might affect the price of tea leaves which the tea growers get from various sources. First it is reasonable to expect that as the number of sales options rise the growers will get a better price for their leaves.
Secondly, as the distance of the grower to the processing unit rises that might affect the price in a negative direction.
Thirdly, nature of the district may play a part in affecting the price. Districts with high concentration of small tea growers may have better infrastructure which might improve the price for the grower. But on the other hand, a greater concentration of growers in the districts may also mean that the price that they get is not very high due to competition with other growers. In other words the direction of the sign cannot be predicted a priori. It would depend on which of the above conflicting factors is stronger.
And finally, if the grower is not selling through any middle man (i.e., agents) he/she may get a better price. The dummy for grower who self sell may be important.
So in our instrumental variable approach where we are adopting a two stage least square (2SLS) method, the first stage model is given by
lnPYi = α0 + α1optni + α2disni + α3d_doldi + α4d_selfsalei + α5lnPUi + α6lnPMi + α7lnPSi + α8lnPDi
+ α9lnPIi + α10lnPVi + α11lnPHi + α12lnwa_mi + α13lnwa_fi + α14lnfamsizei + α15d_lingi + νi
……….. (5.2)
optn = Number of sales options of a farmer;
disn = Distance from the farm to the point of sale;
d_dold = Dummy for districts with high concentration of STGs;
d_selfsale = Dummy for self sale of tea leaves;
PU = Price of Urea;
PM = Price of MOP;
PS = Price of SSP;
PD = Price of Cow-dung;
PI = Price of Irrigation;
PV = Price of Vitamin;
PH = Price of Herbicide;
wa_m = Wage rate of male workers;
wa_f = Wage rate of female workers;
famsize = Farm Size;
d_ling = 1 if Assamese = 0 if non-Assamese.
To remind ourselves, the second stage of the regression is given by equation 5.1. This is reproduced below,
lnYi = β0 + β1lnPYi + β2lnPUi + β3lnPMi + β4lnPSi + β5lnPDi + β6lnPIi + β7lnPVi + β8lnPHi + β9lnwa_mi + β10lnwa_fi + β11lnfamsizei + β12d_lingi + εi …………. (5.1)
We have estimated the models mentioned above through the two stage least square (2SLS) method. The results are reported in appendix of the chapter (Appendix VIII).
A series of tests pertaining to IV has been conducted that are reported below. These are related to the question whether the use of instrumental variable technique is feasible in our case. These are post-estimation tests. These tests have ascertained that the method that we have used is valid.
Post-Estimation Tests
To use the 2SLS technique we need to make sure the following three conditions are satisfied:
1. We need to make sure that the explanatory variables in (5.1) are indeed endogenous. That is, the price of Y is not an exogenous variable. If the test fails to verify that endogeneity is present, there is no need to estimate (5.1) using instruments. The results of the endogeneity tests are stated in the following table:
Tests of endogeneity Hₒ : variables are exogenous
Durbin (score) chi2(1) = 27.0961 (p = 0.0000) Wu-Hausman F(1,196) = 290362 (p = 0.0000)
As reported in the above table the Durbin chi square statistic is 27.09 with p ˗ value 0.0000 and the Wu-HausmanF statistic is 290362 with p – value 0.000. This implies we can reject the null hypothesis that the variables are exogenous. So the use of instruments is justified.
2. The second test we have conducted is the test for over ˗ identification. This test basically tries to verify if the instruments are sufficiently exogenous to the dependent variable lnY. Here the null hypothesis that our model is correct. The results of this over ˗ identification are given below:
Tests of over-identifying restrictions:
Sargan (score) chi2 (3) = 6.86242 (p = 0.0764) Basmann chi2 (3) = 6.55373 (p = 0.0876)
As we can see the p ˗ values are greater than 0.05. So we accept the null hypothesis at 5 percent level of significance. (However, if the level of significance is taken to be 10 percent then the null hypothesis is rejected.)
3. Finally the last test that we conduct is to ascertain that the instruments are sufficiently correlated to the variable we are instrumenting i.e., lnPy. For this we conduct the test for the null
First-stage regression summery statistics
Variable R-sq. Adjusted R-sq. Partial R-sq. F(4,194) Prob > F lnPY 0.3507 0.3005 0.2374 15.0977 0.0000
Critical Values
Ho : Instruments are weak
Of endogenous regressors: 1 Of excluded instruments: 4 2SLS relative bias 5% 10% 20% 30%
16.85 10.27 6.71 5.34
2SLS Size of nominal 5% Wald test LIML Size of nominal 5% Wald test
10% 15% 20% 25%
24.58 13.96 10.26 8.31 5.44 3.87 3.30 2.98
From the panel above we see that the F value is 15.10. At 10 percent relative bias the critical value is given in the second panel to be 10.27. Hence we can reject null hypothesis at 10 percent level. Clearly the null hypothesis of weak instruments gets rejected at a higher level of relative bias (20%, 30%), thus we continue to find that the instruments are strong. However, if we are ready to tolerate a lower level of bias (5%) the critical value is 16.85 exceeding 15.10. In conclusion, the strength of the instruments is established with a reasonable degree of relative bias.