Have smallholder tobacco prices improved?

In this sub-section the intention is to establish whether the absolute prices received by smallholders have registered statistically significant improvements as a result of the tobacco production and marketing reforms that started in 1990. To do this, an analysis for structural changes is conducted. This is achieved by employing the CUSUM-based24 and moving estimates-based (ME) empirical

23 _{The US$0.05 per kilogram estimate is the price that according to Jaffe (2003), farmers outside}

TAMA were paying to transport their tobacco and is reflective of the reality on the ground.

24 _{The idea of cumulative sums (CUSUM) process dates back to the work of Brown, Durbin, &}

Evans (1975). The process aims at determining the cumulative sums of recursive residuals as follows:

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fluctuation process (efp) tests. These tests are carried out by firstly determining an error correction model (ECM) for the tobacco price function as follows:

(3.4)

(3.5)

where, is price of tobacco in period ; while , which is later referred to as „diff.Smaprice‟, denotes changes in tobacco price received by smallholders. and are coefficients while is cointegration residual and is classical ordinary least squares (OLS) residual.

Secondly, from equation (3.5), cointegration analysis is conducted whose cointegration residuals, (later referred to as „coint.res‟), plus changes in the lagged (later referred to as „diff.Smapricel‟) are used as regressors in equation (3.4). Figure 3.4 below indicates the transformed data (1990 – 2008; April to September of each year) used to estimate equation (3.4). The original data was sourced from the Tobacco Control Commission in Blantyre, Malawi.

, “where, is the number of recursive residuals and ( ) is the integer part of ” (Zeileis et al., 2009, p. 4). However, the OLS-CUSUM type efp, as employed in this study, is given as:

The other important structural change tests include the moving sums of residuals (MOSUM), the Chow test and the F test (see, Zeileis et al., 2009).

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Figure 3.4: Transformed data: First difference and cointegration residuals

Sample size = 114

Based on the above transformed data, the cumulative sums of standardized residuals (CUSUM) and estimates-based approaches are employed to test for structural changes in the above described model. The null hypothesis is premised on the assumption that there are no structural changes hence:

(3.6)

(3.7)

According to Zeileis, Leisch, Hornik, & Kleiber (2009, p. 3), the efp test is principally designed: -2 0 20 60 d if f. S m a p ri ce -2 0 20 60 1990 1995 2000 2005 co in t. re s Time

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to fit a model to the given data and derive an empirical process, that captures the fluctuation either in residuals or in estimates. For these empirical processes the limiting processes are known, so that boundaries can be computed, whose crossing probability under the null hypothesis is . If the empirical process path crosses these boundaries, the fluctuation is probably large and hence the null hypothesis should be rejected.

In the case of this study, the derived empirical process is designed to capture changes in both residuals and estimates at 5 percent significance level. The OLS- based CUSUM test results are as indicated in Figure 3.5 below.

Figure ‎3.5: Results of the OLS-based CUSUM test

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Results indicate that the efp crosses the lower boundary firstly, in the year 1994 and secondly, in the year 2006. This implies that the fluctuations are unusually large and hence the null hypothesis is rejected at 5 percent significance level25. Since the residuals in this study‟s model are largely explained by differences between current and previous prices, a further interpretation of results from the CUSUM-based test may be appropriate. In terms of absolute prices, results indicate a general slide in price changes for the majority of smallholders starting from the year 1990. The downward trajectory reaches the bottom and starts to continuously increase starting from 2002.

Next, the study looks at the moving estimate-based (ME) test of structural changes. The test is basically similar to the CUSUM-based one except for the fact that instead of explaining fluctuation processes based on residuals, estimates of the excluded regression coefficients represented by the constant are used. Its ability to provide more information regarding the kind of the structural change in the model gives it an advantage over the CUSUM-based approach. Figure 3.6 below indicates results of the ME test.

25 _{The structural change test (sctest) provides the following results: S0 = 4.6347, p-value = 2.2e-}

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Figure ‎3.6: Results from the moving estimate (ME) test

Sample size = 114

The above indicated ME test has three components which are related to regression coefficient estimates of the intercept, error term and the explanatory variable. The major shift in movements of the intercept takes place after 1999 while in the case of „smallpricel‟ and „coint.res‟, the major shifts take place after 2002. Results indicate that, starting from 2002, the shift in the intercept is statistically significant at 5 percent level. On the other hand, shifts in „smallpricel‟ and „coint.res‟ are not statistically significant at 5 percent level. One important point immerging from these tests is that results from the ME-based test are similar to the ones obtained from the CUSUM-based test. Both tests indicate that

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there has been a significant change in absolute prices of tobacco that smallholders get.

However, changes in absolute prices that smallholders receive do not necessarily divulge a complete picture with regard to how such price improvements (or decreases) compare with what their counterparts (estate owners) get. In order to gain this insight, the study carries out two econometrics tests, namely the Poe (convolutions) test and the Kolmogorov-Smirnov (KS) test. The Poe test is conducted to establish whether there are significant differences between the distributions of the prices received by smallholders (smaprice) and estate owners (estprice). The KS test augments the Poe test by examining whether the means of these two price distributions are significantly different. These tests are addressed in the following sub-section.